[amp] 01/18: New upstream version 0.6~git20170729
Muammar El Khatib
muammar at moszumanska.debian.org
Mon Jul 31 19:59:39 UTC 2017
This is an automated email from the git hooks/post-receive script.
muammar pushed a commit to branch master
in repository amp.
commit e2854ab10ddb084bfc8a3aa6953653ca4a182048
Author: Muammar El Khatib <muammarelkhatib at gmail.com>
Date: Sat Jul 29 14:42:05 2017 -0400
New upstream version 0.6~git20170729
---
.gitignore | 6 +
README.md | 51 +
amp/Makefile | 21 +
amp/__init__.py | 470 +
amp/analysis.py | 741 +
amp/descriptor/Makefile | 3 +
amp/descriptor/__init__.py | 5 +
amp/descriptor/analysis.py | 100 +
amp/descriptor/bispectrum.py | 683 +
amp/descriptor/cutoffs.f90 | 60 +
amp/descriptor/cutoffs.py | 150 +
amp/descriptor/example.py | 336 +
amp/descriptor/gaussian.f90 | 525 +
amp/descriptor/gaussian.py | 1320 +
amp/descriptor/zernike.f90 | 320 +
amp/descriptor/zernike.py | 1005 +
amp/model.f90 | 922 +
amp/model/Makefile | 3 +
amp/model/__init__.py | 1144 +
amp/model/__main__.py | 119 +
amp/model/neuralnetwork.f90 | 1883 ++
amp/model/neuralnetwork.py | 1208 +
amp/model/tflow.py | 1766 ++
amp/regression/__init__.py | 100 +
amp/stats/__init__.py | 0
amp/stats/bootstrap.py | 400 +
amp/utilities.py | 1195 +
docs/README | 2 +
docs/_static/amp-logo.svg | 1059 +
docs/_static/animation.gif | Bin 0 -> 210154 bytes
docs/_static/branches.svg | 337 +
docs/_static/completeexample.py | 70 +
docs/_static/convergence.svg | 19896 +++++++++++++
docs/_static/fpranges.svg | 9974 +++++++
docs/_static/gaussian.svg | 2893 ++
docs/_static/nn.svg | 986 +
docs/_static/nodeplot-Pt.svg | 8338 ++++++
docs/_static/parity_error_sensitivity.svg | 28915 +++++++++++++++++++
docs/_static/zernike.svg | 5768 ++++
docs/analysis.rst | 31 +
docs/building.rst | 187 +
docs/community.rst | 33 +
docs/conf.py | 345 +
docs/credits.rst | 41 +
docs/databases.rst | 49 +
docs/develop.rst | 91 +
docs/examplescripts.rst | 185 +
docs/gaussian.rst | 34 +
docs/index.rst | 70 +
docs/installation.rst | 142 +
docs/introduction.rst | 18 +
docs/modules/analysis.rst | 13 +
docs/modules/descriptor.rst | 37 +
docs/modules/main.rst | 13 +
docs/modules/model.rst | 34 +
docs/modules/regression.rst | 13 +
docs/modules/utilities.rst | 14 +
docs/moredescriptor.rst | 34 +
docs/moremodel.rst | 41 +
docs/releasenotes.rst | 65 +
docs/tensorflow.rst | 106 +
docs/theory.rst | 181 +
docs/useamp.rst | 208 +
setup.py | 21 +
.../gaussian_neural_test/force_call_test.py | 340 +
.../gaussian_neural_test/force_call_test_tflow.py | 373 +
.../CuOPd_test/gaussian_neural_test/train_test.py | 556 +
.../gaussian_neural_test/force_call_test.py | 560 +
.../gaussian_neural_test/train_test.py | 603 +
tests/consistency_test/gaussian_test.py | 114 +
tests/consistency_test/zernike_test.py | 80 +
tests/misc_test/displaced_atom_test.py | 116 +
tests/misc_test/fpplot_test.py | 63 +
tests/misc_test/numeric_analytic_test.py | 133 +
tests/misc_test/rotated_atoms_test.py | 78 +
tests/test_NN_nodeplot.py | 82 +
tests/test_gaussian_neural.py | 69 +
tests/test_gaussian_tflow.py | 83 +
tools/amp-compress | 46 +
tools/amp-plotconvergence | 27 +
80 files changed, 98103 insertions(+)
diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..e7dda0d
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,6 @@
+*.pyc
+*.so
+*.mod
+*.o
+*.py~
+*.py.swp
diff --git a/README.md b/README.md
new file mode 100644
index 0000000..2bd8e8e
--- /dev/null
+++ b/README.md
@@ -0,0 +1,51 @@
+# Amp: Atomistic Machine-learning Package #
+
+
+*Amp* is an open-source package designed to easily bring machine-learning to atomistic calculations. This project is being developed at Brown University in the School of Engineering, primarily by Andrew Peterson and Alireza Khorshidi, and is released under the GNU General Public License. *Amp* allows for the modular representation of the potential energy surface, enabling the user to specify or create descriptor and regression methods.
+
+This project lives at:
+https://bitbucket.org/andrewpeterson/amp
+
+Documentation lives at:
+http://amp.readthedocs.org
+
+Users' mailing list lives at:
+https://listserv.brown.edu/?A0=AMP-USERS
+
+If you would like to compile a local version of the documentation, see the README file in the docs directory.
+
+(This project was formerly known as "Neural". The last stable version of Neural can be found at https://bitbucket.org/andrewpeterson/neural)
+
+
+License
+=======
+
+ This program is free software: you can redistribute it and/or modify
+ it under the terms of the GNU General Public License as published by
+ the Free Software Foundation, either version 3 of the License, or
+ (at your option) any later version.
+
+ This program is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ GNU General Public License for more details.
+
+ You should have received a copy of the GNU General Public License
+ along with this program. If not, see <http://www.gnu.org/licenses/>.
+
+
+Installation
+============
+
+You can find the installation instructions for this version of Amp in the
+documentation file `docs/installation.rst`.
+
+Documentation
+=============
+
+We currently host multiple versions of the documentation, which includes
+installation instructions, at http://amp.readthedocs.io.
+
+You can build a local copy of the documentation for this version of Amp.
+You will find instructions to do this in the "Documentation" section of the
+file `docs/develop.rst`.
diff --git a/amp/Makefile b/amp/Makefile
new file mode 100644
index 0000000..e319b34
--- /dev/null
+++ b/amp/Makefile
@@ -0,0 +1,21 @@
+python2:
+ +$(MAKE) -C model
+ +$(MAKE) -C descriptor
+ f2py -c -m fmodules model.f90 descriptor/cutoffs.f90 descriptor/gaussian.f90 descriptor/zernike.f90 model/neuralnetwork.f90
+
+python3:
+ +$(MAKE) -C model
+ +$(MAKE) -C descriptor
+ f2py3 -c -m fmodules model.f90 descriptor/cutoffs.f90 descriptor/gaussian.f90 descriptor/zernike.f90 model/neuralnetwork.f90
+
+AMPDIR:=$(shell pwd)
+
+py2tests:
+ rm -fr /tmp/py2_amptests
+ mkdir -p /tmp/py2_amptests
+ cd /tmp/py2_amptests && nosetests $(AMPDIR)/..
+
+py3tests:
+ rm -fr /tmp/py3_amptests
+ mkdir -p /tmp/py3_amptests
+ cd /tmp/py3_amptests && nosetests3 $(AMPDIR)/..
diff --git a/amp/__init__.py b/amp/__init__.py
new file mode 100644
index 0000000..96306c4
--- /dev/null
+++ b/amp/__init__.py
@@ -0,0 +1,470 @@
+import os
+import sys
+import shutil
+import numpy as np
+import tempfile
+import platform
+from getpass import getuser
+from socket import gethostname
+import subprocess
+import warnings
+
+import ase
+from ase.calculators.calculator import Calculator, Parameters
+try:
+ from ase import __version__ as aseversion
+except ImportError:
+ # We're on ASE 3.9 or older
+ from ase.version import version as aseversion
+
+from .utilities import (make_filename, hash_images, Logger, string2dict,
+ logo, now, assign_cores, TrainingConvergenceError,
+ check_images)
+
+try:
+ from amp import fmodules
+except ImportError:
+ warnings.warn('Did not find fortran modules.')
+else:
+ fmodules_version = 9
+ wrong_version = fmodules.check_version(version=fmodules_version)
+ if wrong_version:
+ raise RuntimeError('fortran modules are not updated. Recompile '
+ 'with f2py as described in the README. '
+ 'Correct version is %i.' % fmodules_version)
+
+_ampversion = '(development)'
+
+
+class Amp(Calculator, object):
+
+ """Atomistic Machine-Learning Potential (Amp) ASE calculator
+
+ Parameters
+ ----------
+ descriptor : object
+ Class representing local atomic environment.
+ model : object
+ Class representing the regression model. Can be only NeuralNetwork for
+ now. Input arguments for NeuralNetwork are hiddenlayers, activation,
+ weights, and scalings; for more information see docstring for the class
+ NeuralNetwork.
+ label : str
+ Default prefix/location used for all files.
+ dblabel : str
+ Optional separate prefix/location for database files, including
+ fingerprints, fingerprint derivatives, and neighborlists. This file
+ location can be shared between calculator instances to avoid
+ re-calculating redundant information. If not supplied, just uses the
+ value from label.
+ cores : int
+ Can specify cores to use for parallel training; if None, will determine
+ from environment
+ envcommand : string
+ For parallel processing across nodes, a command can be supplied
+ here to load the appropriate environment before starting workers.
+ logging : boolean
+ Option to turn off logging; e.g., to speed up force calls.
+ atoms : object
+ ASE atoms objects with positions, symbols, energy, and forces in ASE
+ format.
+ """
+ implemented_properties = ['energy', 'forces']
+
+ def __init__(self, descriptor, model, label='amp', dblabel=None,
+ cores=None, envcommand=None, logging=True, atoms=None):
+
+ self.logging = logging
+ Calculator.__init__(self, label=label, atoms=atoms)
+ # Note self._log is set and self._printheader is called by above
+ # call when it runs self.set_label.
+
+ self._parallel = {'envcommand': envcommand}
+
+ # Note the following are properties: these are setter functions.
+ self.descriptor = descriptor
+ self.model = model
+ self.cores = cores # Note this calls 'assign_cores'.
+
+ self.dblabel = label if dblabel is None else dblabel
+
+ @property
+ def cores(self):
+ """
+ Get or set the cores for the parallel environment.
+
+ Parameters
+ ----------
+ cores : int or dictionary
+ Parallel configuration. If cores is an integer, parallelizes over
+ this many processes on machine localhost. cores can also be
+ a dictionary of the type {'node324': 16, 'node325': 16}. If not
+ specified, tries to determine from environment, using
+ amp.utilities.assign_cores.
+ """
+ return self._parallel['cores']
+
+ @cores.setter
+ def cores(self, cores):
+ self._parallel['cores'] = assign_cores(cores, log=self._log)
+
+ @property
+ def descriptor(self):
+ """
+ Get or set the atomic descriptor.
+
+ Parameters
+ ----------
+ descriptor : object
+ Class instance representing the local atomic environment.
+ """
+ return self._descriptor
+
+ @descriptor.setter
+ def descriptor(self, descriptor):
+ descriptor.parent = self # gives the descriptor object a reference to
+ # the main Amp instance. Then descriptor can pull parameters directly
+ # from Amp without needing them to be passed in each method call.
+ self._descriptor = descriptor
+ self.reset() # Clears any old calculations.
+
+ @property
+ def model(self):
+ """
+ Get or set the machine-learning model.
+
+ Parameters
+ ----------
+ model : object
+ Class instance representing the regression model.
+ """
+ return self._model
+
+ @model.setter
+ def model(self, model):
+ model.parent = self # gives the model object a reference to the main
+ # Amp instance. Then model can pull parameters directly from Amp
+ # without needing them to be passed in each method call.
+ self._model = model
+ self.reset() # Clears any old calculations.
+
+ @classmethod
+ def load(Cls, file, Descriptor=None, Model=None, **kwargs):
+ """Attempts to load calculators and return a new instance of Amp.
+
+ Only a filename or file-like object is required, in typical cases.
+
+ If using a home-rolled descriptor or model, also supply uninstantiated
+ classes to those models, as in Model=MyModel. (Not as
+ Model=MyModel()!)
+
+ Any additional keyword arguments (such as label or dblabel) can be
+ fed through to Amp.
+
+ Parameters
+ ----------
+ file : str
+ Name of the file to load data from.
+ Descriptor : object
+ Class representing local atomic environment.
+ Model : object
+ Class representing the regression model.
+ """
+ if hasattr(file, 'read'):
+ text = file.read()
+ else:
+ with open(file) as f:
+ text = f.read()
+
+ # Unpack parameter dictionaries.
+ p = string2dict(text)
+ for key in ['descriptor', 'model']:
+ p[key] = string2dict(p[key])
+
+ # If modules are not specified, find them.
+ if Descriptor is None:
+ Descriptor = importhelper(p['descriptor'].pop('importname'))
+ if Model is None:
+ Model = importhelper(p['model'].pop('importname'))
+ # Key 'importname' and the value removed so that it is not splatted
+ # into the keyword arguments used to instantiate in the next line.
+
+ # Instantiate the descriptor and model.
+ descriptor = Descriptor(**p['descriptor'])
+ # ** sends all the key-value pairs at once.
+ model = Model(**p['model'])
+
+ # Instantiate Amp.
+ calc = Cls(descriptor=descriptor, model=model, **kwargs)
+ calc._log('Loaded file: %s' % file)
+ return calc
+
+ def set(self, **kwargs):
+ """Function to set parameters.
+
+ For now, this doesn't do anything as all parameters are within the
+ model and descriptor.
+ """
+ changed_parameters = Calculator.set(self, **kwargs)
+ if len(changed_parameters) > 0:
+ self.reset()
+
+ def set_label(self, label):
+ """Sets label, ensuring that any needed directories are made.
+
+ Parameters
+ ----------
+ label : str
+ Default prefix/location used for all files.
+ """
+ Calculator.set_label(self, label)
+
+ # Create directories for output structure if needed.
+ # Note ASE doesn't do this for us.
+ if self.label:
+ if (self.directory != os.curdir and
+ not os.path.isdir(self.directory)):
+ os.makedirs(self.directory)
+
+ if self.logging is True:
+ self._log = Logger(make_filename(self.label, '-log.txt'))
+ else:
+ self._log = Logger(None)
+
+ self._printheader(self._log)
+
+ def calculate(self, atoms, properties, system_changes):
+ """Calculation of the energy of system and forces of all atoms.
+
+ """
+ # The inherited method below just sets the atoms object,
+ # if specified, to self.atoms.
+ Calculator.calculate(self, atoms, properties, system_changes)
+
+ log = self._log
+ log('Calculation requested.')
+
+ images = hash_images([self.atoms])
+ key = list(images.keys())[0]
+
+ if properties == ['energy']:
+ log('Calculating potential energy...', tic='pot-energy')
+ self.descriptor.calculate_fingerprints(images=images,
+ log=log,
+ calculate_derivatives=False)
+ energy = self.model.calculate_energy(
+ self.descriptor.fingerprints[key])
+ self.results['energy'] = energy
+ log('...potential energy calculated.', toc='pot-energy')
+
+ if properties == ['forces']:
+ log('Calculating forces...', tic='forces')
+ self.descriptor.calculate_fingerprints(images=images,
+ log=log,
+ calculate_derivatives=True)
+ forces = \
+ self.model.calculate_forces(
+ self.descriptor.fingerprints[key],
+ self.descriptor.fingerprintprimes[key])
+ self.results['forces'] = forces
+ log('...forces calculated.', toc='forces')
+
+ def train(self,
+ images,
+ overwrite=False,
+ ):
+ """Fits the model to the training images.
+
+ Parameters
+ ----------
+ images : list or str
+ List of ASE atoms objects with positions, symbols, energies, and
+ forces in ASE format. This is the training set of data. This can
+ also be the path to an ASE trajectory (.traj) or database (.db)
+ file. Energies can be obtained from any reference, e.g. DFT
+ calculations.
+ overwrite : bool
+ If an output file with the same name exists, overwrite it.
+ """
+
+ log = self._log
+ log('\nAmp training started. ' + now() + '\n')
+ log('Descriptor: %s\n (%s)' % (self.descriptor.__class__.__name__,
+ self.descriptor))
+ log('Model: %s\n (%s)' % (self.model.__class__.__name__, self.model))
+
+ images = hash_images(images, log=log)
+
+ log('\nDescriptor\n==========')
+ train_forces = self.model.forcetraining # True / False
+ check_images(images, forces=train_forces)
+ self.descriptor.calculate_fingerprints(
+ images=images,
+ parallel=self._parallel,
+ log=log,
+ calculate_derivatives=train_forces)
+
+ log('\nModel fitting\n=============')
+ result = self.model.fit(trainingimages=images,
+ descriptor=self.descriptor,
+ log=log,
+ parallel=self._parallel)
+
+ if result is True:
+ log('Amp successfully trained. Saving current parameters.')
+ filename = self.label + '.amp'
+ else:
+ log('Amp not trained successfully. Saving current parameters.')
+ filename = make_filename(self.label, '-untrained-parameters.amp')
+ filename = self.save(filename, overwrite)
+ log('Parameters saved in file "%s".' % filename)
+ log("This file can be opened with `calc = Amp.load('%s')`" %
+ filename)
+ if result is False:
+ raise TrainingConvergenceError('Amp did not converge upon '
+ 'training. See log file for'
+ ' more information.')
+
+ def save(self, filename, overwrite=False):
+ """Saves the calculator in a way that it can be re-opened with
+ load.
+
+ Parameters
+ ----------
+ filename : str
+ File object or path to the file to write to.
+ overwrite : bool
+ If an output file with the same name exists, overwrite it.
+ """
+ if os.path.exists(filename):
+ if overwrite is False:
+ oldfilename = filename
+ filename = tempfile.NamedTemporaryFile(mode='w', delete=False,
+ suffix='.amp').name
+ self._log('File "%s" exists. Instead saving to "%s".' %
+ (oldfilename, filename))
+ else:
+ oldfilename = tempfile.NamedTemporaryFile(mode='w',
+ delete=False,
+ suffix='.amp').name
+
+ self._log('Overwriting file: "%s". Moving original to "%s".'
+ % (filename, oldfilename))
+ shutil.move(filename, oldfilename)
+ descriptor = self.descriptor.tostring()
+ model = self.model.tostring()
+ p = Parameters({'descriptor': descriptor,
+ 'model': model})
+ p.write(filename)
+ return filename
+
+ def _printheader(self, log):
+ """Prints header to log file; inspired by that in GPAW.
+ """
+ log(logo)
+ log('Amp: Atomistic Machine-learning Package')
+ log('Developed by Andrew Peterson, Alireza Khorshidi, and others,')
+ log('Brown University.')
+ log('PI Website: http://brown.edu/go/catalyst')
+ log('Official repository: http://bitbucket.org/andrewpeterson/amp')
+ log('Official documentation: http://amp.readthedocs.org/')
+ log('Citation:')
+ log(' Alireza Khorshidi & Andrew A. Peterson,')
+ log(' Computer Physics Communications 207: 310-324 (2016).')
+ log(' http://doi.org/10.1016/j.cpc.2016.05.010')
+ log('=' * 70)
+ log('User: %s' % getuser())
+ log('Hostname: %s' % gethostname())
+ log('Date: %s' % now(with_utc=True))
+ uname = platform.uname()
+ log('Architecture: %s' % uname[4])
+ log('PID: %s' % os.getpid())
+ log('Amp version: %s' % _ampversion)
+ ampdirectory = os.path.dirname(os.path.abspath(__file__))
+ log('Amp directory: %s' % ampdirectory)
+ commithash, commitdate = get_git_commit(ampdirectory)
+ log(' Last commit: %s' % commithash)
+ log(' Last commit date: %s' % commitdate)
+ log('Python: v{0}.{1}.{2}: %s'.format(*sys.version_info[:3]) %
+ sys.executable)
+ log('ASE v%s: %s' % (aseversion, os.path.dirname(ase.__file__)))
+ log('NumPy v%s: %s' %
+ (np.version.version, os.path.dirname(np.__file__)))
+ # SciPy is not a strict dependency.
+ try:
+ import scipy
+ log('SciPy v%s: %s' %
+ (scipy.version.version, os.path.dirname(scipy.__file__)))
+ except ImportError:
+ log('SciPy: not available')
+ # ZMQ an pxssh are only necessary for parallel calculations.
+ try:
+ import zmq
+ log('ZMQ/PyZMQ v%s/v%s: %s' %
+ (zmq.zmq_version(), zmq.pyzmq_version(),
+ os.path.dirname(zmq.__file__)))
+ except ImportError:
+ log('ZMQ: not available')
+ try:
+ import pxssh
+ log('pxssh: %s' % os.path.dirname(pxssh.__file__))
+ except ImportError:
+ log('pxssh: Not available from pxssh.')
+ try:
+ from pexpect import pxssh
+ except ImportError:
+ log('pxssh: Not available from pexpect.')
+ else:
+ import pexpect
+ log('pxssh (via pexpect v%s): %s' %
+ (pexpect.__version__, pxssh.__file__))
+ log('=' * 70)
+
+
+def importhelper(importname):
+ """Manually compiled list of available modules.
+
+ This is to prevent the execution of arbitrary (potentially malicious) code.
+
+ However, since there is an `eval` statement in string2dict maybe this
+ is silly.
+ """
+ if importname == '.descriptor.gaussian.Gaussian':
+ from .descriptor.gaussian import Gaussian as Module
+ elif importname == '.descriptor.zernike.Zernike':
+ from .descriptor.zernike import Zernike as Module
+ elif importname == '.descriptor.bispectrum.Bispectrum':
+ from .descriptor.bispectrum import Bispectrum as Module
+ elif importname == '.model.neuralnetwork.NeuralNetwork':
+ from .model.neuralnetwork import NeuralNetwork as Module
+ elif importname == '.model.neuralnetwork.tflow':
+ from .model.tflow import NeuralNetwork as Module
+ elif importname == '.model.LossFunction':
+ from .model import LossFunction as Module
+ else:
+ raise NotImplementedError(
+ 'Attempt to import the module %s. Was this intended? '
+ 'If so, trying manually importing this module and '
+ 'feeding it to Amp.load. To avoid this error, this '
+ 'module can be added to amp.importhelper.' %
+ importname)
+
+ return Module
+
+
+def get_git_commit(ampdirectory):
+ """Attempts to get the last git commit from the amp directory.
+ """
+ pwd = os.getcwd()
+ os.chdir(ampdirectory)
+ try:
+ with open(os.devnull, 'w') as devnull:
+ output = subprocess.check_output(['git', 'log', '-1',
+ '--pretty=%H\t%ci'],
+ stderr=devnull)
+ except:
+ output = 'unknown hash\tunknown date'
+ output = output.strip()
+ commithash, commitdate = output.split(b'\t')
+ os.chdir(pwd)
+ return commithash, commitdate
diff --git a/amp/analysis.py b/amp/analysis.py
new file mode 100644
index 0000000..6bcace4
--- /dev/null
+++ b/amp/analysis.py
@@ -0,0 +1,741 @@
+#!/usr/bin/env python
+
+from . import Amp
+from .utilities import now, hash_images, make_filename
+import os
+import numpy as np
+from matplotlib import pyplot
+from matplotlib.backends.backend_pdf import PdfPages
+from matplotlib import rcParams
+rcParams.update({'figure.autolayout': True})
+
+
+def plot_sensitivity(load,
+ images,
+ d=0.0001,
+ label='sensitivity',
+ dblabel=None,
+ plotfile=None,
+ overwrite=False,
+ energy_coefficient=1.0,
+ force_coefficient=0.04):
+ """Returns the plot of loss function in terms of perturbed parameters.
+
+ Takes the load file and images. Any other keyword taken by the Amp
+ calculator can be fed to this class also.
+
+ Parameters
+ ----------
+ load : str
+ Path for loading an existing ".amp" file. Should be fed like
+ 'load="filename.amp"'.
+ images : list or str
+ List of ASE atoms objects with positions, symbols, energies, and forces
+ in ASE format. This can also be the path to an ASE trajectory (.traj)
+ or database (.db) file. Energies can be obtained from any reference,
+ e.g. DFT calculations.
+ d : float
+ The amount of perturbation in each parameter.
+ label : str
+ Default prefix/location used for all files.
+ dblabel : str
+ Optional separate prefix/location of database files, including
+ fingerprints, fingerprint primes, and neighborlists, to avoid
+ calculating them. If not supplied, just uses the value from label.
+ plotfile : Object
+ File for the plot.
+ overwrite : bool
+ If a plot or an script containing values found overwrite it.
+ energy_coefficient : float
+ Coefficient of energy loss in the total loss function.
+ force_coefficient : float
+ Coefficient of force loss in the total loss function.
+ """
+
+ from amp.model import LossFunction
+
+ calc = Amp.load(file=load)
+
+ if plotfile is None:
+ plotfile = make_filename(label, '-plot.pdf')
+
+ if (not overwrite) and os.path.exists(plotfile):
+ raise IOError('File exists: %s.\nIf you want to overwrite,'
+ ' set overwrite=True or manually delete.' % plotfile)
+
+ calc.dblabel = label if dblabel is None else dblabel
+
+ if force_coefficient == 0.:
+ calculate_derivatives = False
+ else:
+ calculate_derivatives = True
+
+ calc._log('\nAmp sensitivity analysis started. ' + now() + '\n')
+ calc._log('Descriptor: %s' % calc.descriptor.__class__.__name__)
+ calc._log('Model: %s' % calc.model.__class__.__name__)
+
+ images = hash_images(images)
+
+ calc._log('\nDescriptor\n==========')
+ calc.descriptor.calculate_fingerprints(
+ images=images,
+ parallel=calc._parallel,
+ log=calc._log,
+ calculate_derivatives=calculate_derivatives)
+
+ vector = calc.model.vector.copy()
+
+ lossfunction = LossFunction(energy_coefficient=energy_coefficient,
+ force_coefficient=force_coefficient,
+ parallel=calc._parallel,
+ )
+ calc.model.lossfunction = lossfunction
+
+ # Set up local loss function.
+ calc.model.lossfunction.attach_model(
+ calc.model,
+ fingerprints=calc.descriptor.fingerprints,
+ fingerprintprimes=calc.descriptor.fingerprintprimes,
+ images=images)
+
+ originalloss = calc.model.lossfunction.get_loss(
+ vector, lossprime=False)['loss']
+
+ calc._log('\n Perturbing parameters...', tic='perturb')
+
+ allparameters = []
+ alllosses = []
+ num_parameters = len(vector)
+
+ for count in range(num_parameters):
+ calc._log('parameter %i out of %i' % (count + 1, num_parameters))
+ parameters = []
+ losses = []
+ # parameter is perturbed -d and loss function calculated.
+ vector[count] -= d
+ parameters.append(vector[count])
+ perturbedloss = calc.model.lossfunction.get_loss(
+ vector, lossprime=False)['loss']
+ losses.append(perturbedloss)
+
+ vector[count] += d
+ parameters.append(vector[count])
+ losses.append(originalloss)
+ # parameter is perturbed +d and loss function calculated.
+ vector[count] += d
+ parameters.append(vector[count])
+ perturbedloss = calc.model.lossfunction.get_loss(
+ vector, lossprime=False)['loss']
+ losses.append(perturbedloss)
+
+ allparameters.append(parameters)
+ alllosses.append(losses)
+ # returning back to the original value.
+ vector[count] -= d
+
+ calc._log('...parameters perturbed and loss functions calculated',
+ toc='perturb')
+
+ calc._log('Plotting loss function vs perturbed parameters...',
+ tic='plot')
+
+ with PdfPages(plotfile) as pdf:
+ count = 0
+ for parameter in vector:
+ fig = pyplot.figure()
+ ax = fig.add_subplot(111)
+ ax.plot(allparameters[count],
+ alllosses[count],
+ marker='o', linestyle='--', color='b',)
+
+ xmin = allparameters[count][0] - \
+ 0.1 * (allparameters[count][-1] - allparameters[count][0])
+ xmax = allparameters[count][-1] + \
+ 0.1 * (allparameters[count][-1] - allparameters[count][0])
+ ymin = min(alllosses[count]) - \
+ 0.1 * (max(alllosses[count]) - min(alllosses[count]))
+ ymax = max(alllosses[count]) + \
+ 0.1 * (max(alllosses[count]) - min(alllosses[count]))
+ ax.set_xlim([xmin, xmax])
+ ax.set_ylim([ymin, ymax])
+
+ ax.set_xlabel('parameter no %i' % count)
+ ax.set_ylabel('loss function')
+ pdf.savefig(fig)
+ pyplot.close(fig)
+ count += 1
+
+ calc._log(' ...loss functions plotted.', toc='plot')
+
+
+def plot_parity(load,
+ images,
+ label='parity',
+ dblabel=None,
+ plot_forces=True,
+ plotfile=None,
+ color='b.',
+ overwrite=False,
+ returndata=False,
+ energy_coefficient=1.0,
+ force_coefficient=0.04):
+ """Makes a parity plot of Amp energies and forces versus real energies and
+ forces.
+
+ Parameters
+ ----------
+ load : str
+ Path for loading an existing ".amp" file. Should be fed like
+ 'load="filename.amp"'.
+ images : list or str
+ List of ASE atoms objects with positions, symbols, energies, and forces
+ in ASE format. This can also be the path to an ASE trajectory (.traj)
+ or database (.db) file. Energies can be obtained from any reference,
+ e.g. DFT calculations.
+ label : str
+ Default prefix/location used for all files.
+ dblabel : str
+ Optional separate prefix/location of database files, including
+ fingerprints, fingerprint primes, and neighborlists, to avoid
+ calculating them. If not supplied, just uses the value from label.
+ plot_forces : bool
+ Determines whether or not forces should be plotted as well.
+ plotfile : Object
+ File for the plot.
+ color : str
+ Plot color.
+ overwrite : bool
+ If a plot or an script containing values found overwrite it.
+ returndata : bool
+ Whether to return a reference to the figures and their data or not.
+ energy_coefficient : float
+ Coefficient of energy loss in the total loss function.
+ force_coefficient : float
+ Coefficient of force loss in the total loss function.
+ """
+
+ calc = Amp.load(file=load, label=label, dblabel=dblabel)
+
+ if plotfile is None:
+ plotfile = make_filename(label, '-plot.pdf')
+
+ if (not overwrite) and os.path.exists(plotfile):
+ raise IOError('File exists: %s.\nIf you want to overwrite,'
+ ' set overwrite=True or manually delete.'
+ % plotfile)
+
+ if (force_coefficient != 0.) or (plot_forces is True):
+ calculate_derivatives = True
+ else:
+ calculate_derivatives = False
+
+ calc._log('\nAmp parity plot started. ' + now() + '\n')
+ calc._log('Descriptor: %s' % calc.descriptor.__class__.__name__)
+ calc._log('Model: %s' % calc.model.__class__.__name__)
+
+ images = hash_images(images, log=calc._log)
+
+ calc._log('\nDescriptor\n==========')
+ calc.descriptor.calculate_fingerprints(
+ images=images,
+ parallel=calc._parallel,
+ log=calc._log,
+ calculate_derivatives=calculate_derivatives)
+
+ calc._log('Calculating potential energies...', tic='pot-energy')
+ energy_data = {}
+ for hash, image in images.iteritems():
+ amp_energy = calc.model.calculate_energy(
+ calc.descriptor.fingerprints[hash])
+ actual_energy = image.get_potential_energy(apply_constraint=False)
+ energy_data[hash] = [actual_energy, amp_energy]
+ calc._log('...potential energies calculated.', toc='pot-energy')
+
+ min_act_energy = min([energy_data[hash][0]
+ for hash, image in images.iteritems()])
+ max_act_energy = max([energy_data[hash][0]
+ for hash, image in images.iteritems()])
+
+ if plot_forces is False:
+ fig = pyplot.figure(figsize=(5., 5.))
+ ax = fig.add_subplot(111)
+ else:
+ fig = pyplot.figure(figsize=(5., 10.))
+ ax = fig.add_subplot(211)
+
+ calc._log('Plotting energies...', tic='energy-plot')
+ for hash, image in images.iteritems():
+ ax.plot(energy_data[hash][0], energy_data[hash][1], color)
+ # draw line
+ ax.plot([min_act_energy, max_act_energy],
+ [min_act_energy, max_act_energy],
+ 'r-',
+ lw=0.3,)
+ ax.set_xlabel("ab initio energy, eV")
+ ax.set_ylabel("Amp energy, eV")
+ ax.set_title("Energies")
+ calc._log('...energies plotted.', toc='energy-plot')
+
+ if plot_forces is True:
+ ax = fig.add_subplot(212)
+
+ calc._log('Calculating forces...', tic='forces')
+ force_data = {}
+ for hash, image in images.iteritems():
+ amp_forces = \
+ calc.model.calculate_forces(
+ calc.descriptor.fingerprints[hash],
+ calc.descriptor.fingerprintprimes[hash])
+ actual_forces = image.get_forces(apply_constraint=False)
+ force_data[hash] = [actual_forces, amp_forces]
+ calc._log('...forces calculated.', toc='forces')
+
+ min_act_force = min([force_data[hash][0][index][k]
+ for hash, image in images.iteritems()
+ for index in range(len(image))
+ for k in range(3)])
+
+ max_act_force = max([force_data[hash][0][index][k]
+ for hash, image in images.iteritems()
+ for index in range(len(image))
+ for k in range(3)])
+
+ calc._log('Plotting forces...', tic='force-plot')
+ for hash, image in images.iteritems():
+ for index in range(len(image)):
+ for k in range(3):
+ ax.plot(force_data[hash][0][index][k],
+ force_data[hash][1][index][k], color)
+ # draw line
+ ax.plot([min_act_force, max_act_force],
+ [min_act_force, max_act_force],
+ 'r-',
+ lw=0.3,)
+ ax.set_xlabel("ab initio force, eV/Ang")
+ ax.set_ylabel("Amp force, eV/Ang")
+ ax.set_title("Forces")
+ calc._log('...forces plotted.', toc='force-plot')
+
+ fig.savefig(plotfile)
+
+ if returndata:
+ if plot_forces is False:
+ return fig, energy_data
+ else:
+ return fig, energy_data, force_data
+
+
+def plot_error(load,
+ images,
+ label='error',
+ dblabel=None,
+ plot_forces=True,
+ plotfile=None,
+ color='b.',
+ overwrite=False,
+ returndata=False,
+ energy_coefficient=1.0,
+ force_coefficient=0.04):
+ """Makes an error plot of Amp energies and forces versus real energies and
+ forces.
+
+ Parameters
+ ----------
+ load : str
+ Path for loading an existing ".amp" file. Should be fed like
+ 'load="filename.amp"'.
+ images : list or str
+ List of ASE atoms objects with positions, symbols, energies, and forces
+ in ASE format. This can also be the path to an ASE trajectory (.traj)
+ or database (.db) file. Energies can be obtained from any reference,
+ e.g. DFT calculations.
+ label : str
+ Default prefix/location used for all files.
+ dblabel : str
+ Optional separate prefix/location of database files, including
+ fingerprints, fingerprint primes, and neighborlists, to avoid
+ calculating them. If not supplied, just uses the value from label.
+ plot_forces : bool
+ Determines whether or not forces should be plotted as well.
+ plotfile : Object
+ File for the plot.
+ color : str
+ Plot color.
+ overwrite : bool
+ If a plot or an script containing values found overwrite it.
+ returndata : bool
+ Whether to return a reference to the figures and their data or not.
+ energy_coefficient : float
+ Coefficient of energy loss in the total loss function.
+ force_coefficient : float
+ Coefficient of force loss in the total loss function.
+ """
+
+ calc = Amp.load(file=load)
+
+ if plotfile is None:
+ plotfile = make_filename(label, '-plot.pdf')
+
+ if (not overwrite) and os.path.exists(plotfile):
+ raise IOError('File exists: %s.\nIf you want to overwrite,'
+ ' set overwrite=True or manually delete.'
+ % plotfile)
+
+ calc.dblabel = label if dblabel is None else dblabel
+
+ if (force_coefficient != 0.) or (plot_forces is True):
+ calculate_derivatives = True
+ else:
+ calculate_derivatives = False
+
+ calc._log('\nAmp error plot started. ' + now() + '\n')
+ calc._log('Descriptor: %s' % calc.descriptor.__class__.__name__)
+ calc._log('Model: %s' % calc.model.__class__.__name__)
+
+ images = hash_images(images, log=calc._log)
+
+ calc._log('\nDescriptor\n==========')
+ calc.descriptor.calculate_fingerprints(
+ images=images,
+ parallel=calc._parallel,
+ log=calc._log,
+ calculate_derivatives=calculate_derivatives)
+
+ calc._log('Calculating potential energy errors...', tic='pot-energy')
+ energy_data = {}
+ for hash, image in images.iteritems():
+ no_of_atoms = len(image)
+ amp_energy = calc.model.calculate_energy(
+ calc.descriptor.fingerprints[hash])
+ actual_energy = image.get_potential_energy(apply_constraint=False)
+ act_energy_per_atom = actual_energy / no_of_atoms
+ energy_error = abs(amp_energy - actual_energy) / no_of_atoms
+ energy_data[hash] = [act_energy_per_atom, energy_error]
+ calc._log('...potential energy errors calculated.', toc='pot-energy')
+
+ # calculating energy per atom rmse
+ energy_square_error = 0.
+ for hash, image in images.iteritems():
+ energy_square_error += energy_data[hash][1] ** 2.
+ energy_per_atom_rmse = np.sqrt(energy_square_error / len(images))
+
+ min_act_energy_per_atom = min([energy_data[hash][0]
+ for hash, image in images.iteritems()])
+ max_act_energy_per_atom = max([energy_data[hash][0]
+ for hash, image in images.iteritems()])
+
+ if plot_forces is False:
+ fig = pyplot.figure(figsize=(5., 5.))
+ ax = fig.add_subplot(111)
+ else:
+ fig = pyplot.figure(figsize=(5., 10.))
+ ax = fig.add_subplot(211)
+
+ calc._log('Plotting energy errors...', tic='energy-plot')
+ for hash, image in images.iteritems():
+ ax.plot(energy_data[hash][0], energy_data[hash][1], color)
+ # draw horizontal line for rmse
+ ax.plot([min_act_energy_per_atom, max_act_energy_per_atom],
+ [energy_per_atom_rmse, energy_per_atom_rmse],
+ color='black', linestyle='dashed', lw=1,)
+ ax.text(max_act_energy_per_atom,
+ energy_per_atom_rmse,
+ 'energy rmse = %6.5f' % energy_per_atom_rmse,
+ ha='right',
+ va='bottom',
+ color='black')
+ ax.set_xlabel("ab initio energy (eV) per atom")
+ ax.set_ylabel("$|$ab initio energy - Amp energy$|$ / number of atoms")
+ ax.set_title("Energies")
+ calc._log('...energy errors plotted.', toc='energy-plot')
+
+ if plot_forces is True:
+ ax = fig.add_subplot(212)
+
+ calc._log('Calculating force errors...', tic='forces')
+ force_data = {}
+ for hash, image in images.iteritems():
+ amp_forces = \
+ calc.model.calculate_forces(
+ calc.descriptor.fingerprints[hash],
+ calc.descriptor.fingerprintprimes[hash])
+ actual_forces = image.get_forces(apply_constraint=False)
+ force_data[hash] = [
+ actual_forces,
+ abs(np.array(amp_forces) - np.array(actual_forces))]
+ calc._log('...force errors calculated.', toc='forces')
+
+ # calculating force rmse
+ force_square_error = 0.
+ for hash, image in images.iteritems():
+ no_of_atoms = len(image)
+ for index in range(no_of_atoms):
+ for k in range(3):
+ force_square_error += \
+ ((1.0 / 3.0) * force_data[hash][1][index][k] ** 2.) / \
+ no_of_atoms
+ force_rmse = np.sqrt(force_square_error / len(images))
+
+ min_act_force = min([force_data[hash][0][index][k]
+ for hash, image in images.iteritems()
+ for index in range(len(image))
+ for k in range(3)])
+
+ max_act_force = max([force_data[hash][0][index][k]
+ for hash, image in images.iteritems()
+ for index in range(len(image))
+ for k in range(3)])
+
+ calc._log('Plotting force errors...', tic='force-plot')
+ for hash, image in images.iteritems():
+ for index in range(len(image)):
+ for k in range(3):
+ ax.plot(force_data[hash][0][index][k],
+ force_data[hash][1][index][k], color)
+ # draw horizontal line for rmse
+ ax.plot([min_act_force, max_act_force],
+ [force_rmse, force_rmse],
+ color='black',
+ linestyle='dashed',
+ lw=1,)
+ ax.text(max_act_force,
+ force_rmse,
+ 'force rmse = %5.4f' % force_rmse,
+ ha='right',
+ va='bottom',
+ color='black',)
+ ax.set_xlabel("ab initio force, eV/Ang")
+ ax.set_ylabel("$|$ab initio force - Amp force$|$")
+ ax.set_title("Forces")
+ calc._log('...force errors plotted.', toc='force-plot')
+
+ fig.savefig(plotfile)
+
+ if returndata:
+ if plot_forces is False:
+ return fig, energy_data
+ else:
+ return fig, energy_data, force_data
+
+
+def read_trainlog(logfile, verbose=True):
+ """Reads the log file from the training process, returning the relevant
+ parameters.
+
+ Parameters
+ ----------
+ logfile : str
+ Name or path to the log file.
+
+ verbose : bool
+ Write out logfile during analysis.
+ """
+ data = {}
+
+ with open(logfile, 'r') as f:
+ lines = f.read().splitlines()
+
+ def print_(text):
+ if verbose:
+ print(text)
+
+ # Get number of images.
+ for line in lines:
+ if 'unique images after hashing.' in line:
+ no_images = int(line.split()[0])
+ break
+ data['no_images'] = no_images
+
+ # Find where convergence data starts.
+ startline = None
+ for index, line in enumerate(lines):
+ if 'Loss function convergence criteria:' in line:
+ startline = index
+ data['convergence'] = {}
+ d = data['convergence']
+ break
+ else:
+ return data
+
+ # Get convergence parameters.
+ ready = [False] * 7
+ for index, line in enumerate(lines[startline:]):
+ if 'energy_rmse:' in line:
+ ready[0] = True
+ d['energy_rmse'] = float(line.split(':')[-1])
+ elif 'force_rmse:' in line:
+ ready[1] = True
+ _ = line.split(':')[-1].strip()
+ if _ == 'None':
+ d['force_rmse'] = None
+ trainforces = False
+ else:
+ d['force_rmse'] = float(line.split(':')[-1])
+ trainforces = True
+ print_('train forces: %s' % trainforces)
+ elif 'force_coefficient:' in line:
+ ready[2] = True
+ _ = line.split(':')[-1].strip()
+ if _ == 'None':
+ d['force_coefficient'] = 0.
+ else:
+ d['force_coefficient'] = float(_)
+ elif 'energy_coefficient:' in line:
+ ready[3] = True
+ d['energy_coefficient'] = float(line.split(':')[-1])
+ elif 'energy_maxresid:' in line:
+ ready[5] = True
+ _ = line.split(':')[-1].strip()
+ if _ == 'None':
+ d['energy_maxresid'] = None
+ else:
+ d['energy_maxresid'] = float(_)
+ elif 'force_maxresid:' in line:
+ ready[6] = True
+ _ = line.split(':')[-1].strip()
+ if _ == 'None':
+ d['force_maxresid'] = None
+ else:
+ d['force_maxresid'] = float(_)
+ elif 'Step' in line and 'Time' in line:
+ ready[4] = True
+ startline += index + 2
+ if ready == [True] * 7:
+ break
+
+ for _ in d.iteritems():
+ print_('{}: {}'.format(_[0], _[1]))
+ E = d['energy_rmse']**2 * no_images
+ if trainforces:
+ F = d['force_rmse']**2 * no_images
+ else:
+ F = 0.
+ costfxngoal = d['energy_coefficient'] * E + d['force_coefficient'] * F
+ d['costfxngoal'] = costfxngoal
+
+ # Extract data (emrs and fmrs are max residuals).
+ steps, es, fs, emrs, fmrs, costfxns = [], [], [], [], [], []
+ costfxnEs, costfxnFs = [], []
+ index = startline
+ d['converged'] = None
+ while index < len(lines):
+ line = lines[index]
+ if 'Saving checkpoint data.' in line:
+ index += 1
+ continue
+ elif 'Overwriting file' in line:
+ index += 1
+ continue
+ elif 'optimization completed successfully.' in line: # old version
+ d['converged'] = True
+ break
+ elif '...optimization successful.' in line:
+ d['converged'] = True
+ break
+ elif 'could not find parameters for the' in line:
+ break
+ elif '...optimization unsuccessful.' in line:
+ d['converged'] = False
+ break
+ print_(line)
+ if trainforces:
+ step, time, costfxn, e, _, emr, _, f, _, fmr, _ = line.split()
+ fs.append(float(f))
+ fmrs.append(float(fmr))
+ F = float(f)**2 * no_images
+ costfxnFs.append(d['force_coefficient'] * F / float(costfxn))
+ else:
+ step, time, costfxn, e, _, emr, _ = line.split()
+ steps.append(int(step))
+ es.append(float(e))
+ emrs.append(float(emr))
+ costfxns.append(costfxn)
+ E = float(e)**2 * no_images
+ costfxnEs.append(d['energy_coefficient'] * E / float(costfxn))
+ index += 1
+ d['steps'] = steps
+ d['es'] = es
+ d['fs'] = fs
+ d['emrs'] = emrs
+ d['fmrs'] = fmrs
+ d['costfxns'] = costfxns
+ d['costfxnEs'] = costfxnEs
+ d['costfxnFs'] = costfxnFs
+
+ return data
+
+
+def plot_convergence(logfile, plotfile='convergence.pdf'):
+ """Makes a plot of the convergence of the cost function and its energy
+ and force components.
+
+ Parameters
+ ----------
+ logfile : str
+ Name or path to the log file.
+ plotfile : str
+ Name or path to the plot file.
+ """
+
+ data = read_trainlog(logfile)
+
+ # Find if multiple runs contained in data set.
+ d = data['convergence']
+ steps = range(len(d['steps']))
+ breaks = []
+ for index, step in enumerate(d['steps'][1:]):
+ if step < d['steps'][index]:
+ breaks.append(index)
+
+ # Make plots.
+ fig = pyplot.figure(figsize=(6., 8.))
+ # Margins, vertical gap, and top-to-bottom ratio of figure.
+ lm, rm, bm, tm, vg, tb = 0.12, 0.05, 0.08, 0.03, 0.08, 4.
+ bottomaxheight = (1. - bm - tm - vg) / (tb + 1.)
+
+ ax = fig.add_axes((lm, bm + bottomaxheight + vg,
+ 1. - lm - rm, tb * bottomaxheight))
+ ax.semilogy(steps, d['es'], 'b', lw=2, label='energy rmse')
+ ax.semilogy(steps, d['emrs'], 'b:', lw=2, label='energy maxresid')
+ if d['force_rmse']:
+ ax.semilogy(steps, d['fs'], 'g', lw=2, label='force rmse')
+ ax.semilogy(steps, d['fmrs'], 'g:', lw=2, label='force maxresid')
+ ax.semilogy(steps, d['costfxns'], color='0.5', lw=2,
+ label='loss function')
+ # Targets.
+ if d['energy_rmse']:
+ ax.semilogy([steps[0], steps[-1]], [d['energy_rmse']] * 2,
+ color='b', linestyle='-', alpha=0.5)
+ if d['energy_maxresid']:
+ ax.semilogy([steps[0], steps[-1]], [d['energy_maxresid']] * 2,
+ color='b', linestyle=':', alpha=0.5)
+ if d['force_rmse']:
+ ax.semilogy([steps[0], steps[-1]], [d['force_rmse']] * 2,
+ color='g', linestyle='-', alpha=0.5)
+ if d['force_maxresid']:
+ ax.semilogy([steps[0], steps[-1]], [d['force_maxresid']] * 2,
+ color='g', linestyle=':', alpha=0.5)
+ ax.set_ylabel('error')
+ ax.legend(loc='best', fontsize=9.)
+ if len(breaks) > 0:
+ ylim = ax.get_ylim()
+ for b in breaks:
+ ax.plot([b] * 2, ylim, '--k')
+
+ if d['force_rmse']:
+ # Loss function component plot.
+ axf = fig.add_axes((lm, bm, 1. - lm - rm, bottomaxheight))
+ axf.fill_between(x=np.array(steps), y1=d['costfxnEs'],
+ color='blue')
+ axf.fill_between(x=np.array(steps), y1=d['costfxnEs'],
+ y2=np.array(d['costfxnEs']) +
+ np.array(d['costfxnFs']),
+ color='green')
+ axf.set_ylabel('loss function component')
+ axf.set_xlabel('loss function call')
+ axf.set_ylim(0, 1)
+ else:
+ ax.set_xlabel('loss function call')
+
+ fig.savefig(plotfile)
+ pyplot.close(fig)
diff --git a/amp/descriptor/Makefile b/amp/descriptor/Makefile
new file mode 100644
index 0000000..bf3d8e4
--- /dev/null
+++ b/amp/descriptor/Makefile
@@ -0,0 +1,3 @@
+cutoffs.mod:
+ gfortran -c cutoffs.f90
+ cp cutoffs.mod ..
diff --git a/amp/descriptor/__init__.py b/amp/descriptor/__init__.py
new file mode 100644
index 0000000..8eb85af
--- /dev/null
+++ b/amp/descriptor/__init__.py
@@ -0,0 +1,5 @@
+#!/usr/bin/env python
+"""
+Folder that contains different local environment descriptors.
+
+"""
diff --git a/amp/descriptor/analysis.py b/amp/descriptor/analysis.py
new file mode 100644
index 0000000..ed5f246
--- /dev/null
+++ b/amp/descriptor/analysis.py
@@ -0,0 +1,100 @@
+import numpy as np
+from ..utilities import hash_images, get_hash
+
+
+class FingerprintPlot:
+ """Create plots of fingerprint ranges.
+
+ Initialize with an Amp calculator object.
+ """
+
+ def __init__(self, calc):
+ self._calc = calc
+
+ def __call__(self, images, name='fingerprints.pdf', overlay=None):
+ """Creates a violin plot of fingerprints for each element type in the
+ fed images; saves to specified filename.
+
+ Optionally, the user can supply either an ase.Atoms or a list of
+ ase.Atom objects with the overlay keyword; this will result in
+ points being added to the fingerprints indicating the values for
+ that atom or atoms object.
+ """
+
+ from matplotlib import pyplot
+ from matplotlib.backends.backend_pdf import PdfPages
+
+ self.compile_fingerprints(images)
+
+ self.figures = {}
+ for element in self.data.keys():
+ self.figures[element] = pyplot.figure(figsize=(11., 8.5))
+ fig = self.figures[element]
+ ax = fig.add_subplot(211)
+ ax.violinplot(self.data[element])
+ ax.set_ylabel('raw value')
+ ax.set_xlim([0, self.data[element].shape[1] + 1])
+ if hasattr(self._calc.model.parameters, 'fprange'):
+ ax2 = fig.add_subplot(212)
+ fprange = self._calc.model.parameters.fprange[element]
+ fprange = np.array(fprange)
+ fprange.transpose()
+ d = self.data[element]
+ scaled = ((d - fprange[:, 0]) /
+ (fprange[:, 1] - fprange[:, 0]) * 2.0 - 1.0)
+ ax2.violinplot(scaled)
+ ax2.set_ylabel('scaled value')
+ ax2.set_xlim([0, self.data[element].shape[1] + 1])
+ ax2.set_ylim([-1.05, 1.05])
+ ax2.set_xlabel('fingerprint')
+ else:
+ ax.set_xlabel('fingerprint')
+ fig.text(0.5, 0.25,
+ '(No fprange in model; therefore no scaled '
+ 'fingerprints shown.)',
+ ha='center')
+ fig.text(0.5, 0.95, element, ha='center')
+
+ if overlay:
+ # Find all atoms.
+ images = [atom.atoms for atom in overlay]
+ images = hash_images(images)
+ self._calc.descriptor.calculate_fingerprints(images)
+ for atom in overlay:
+ key = get_hash(atom.atoms)
+ fingerprints = self._calc.descriptor.fingerprints[key]
+ fingerprint = fingerprints[atom.index]
+ fig = self.figures[fingerprint[0]]
+ ax = fig.axes[0]
+ ax.plot(range(1, len(fingerprint[1]) + 1),
+ fingerprint[1], '.b')
+ fprange = self._calc.model.parameters.fprange[atom.symbol]
+ fprange = np.array(fprange)
+ fprange.transpose()
+ scaled = ((np.array(fingerprint[1]) - fprange[:, 0]) /
+ (fprange[:, 1] - fprange[:, 0]) * 2.0 - 1.0)
+ ax = fig.axes[1]
+ ax.plot(range(1, len(fingerprint[1]) + 1),
+ scaled, '.b')
+
+ with PdfPages(name) as pdf:
+ for fig in self.figures.values():
+ pdf.savefig(fig)
+ pyplot.close(fig)
+
+ def compile_fingerprints(self, images):
+ """Calculates or looks up fingerprints and compiles them, per
+ element, for the images.
+ """
+ data = self.data = {}
+ images = hash_images(images)
+ self._calc.descriptor.calculate_fingerprints(images)
+ for hash in images.keys():
+ fingerprints = self._calc.descriptor.fingerprints[hash]
+ for element, fingerprint in fingerprints:
+ if element not in data:
+ data[element] = []
+ data[element].append(fingerprint)
+ print(element, len(fingerprint))
+ for element in data.keys():
+ data[element] = np.array(data[element])
diff --git a/amp/descriptor/bispectrum.py b/amp/descriptor/bispectrum.py
new file mode 100644
index 0000000..2c34672
--- /dev/null
+++ b/amp/descriptor/bispectrum.py
@@ -0,0 +1,683 @@
+import numpy as np
+from numpy import cos, sqrt, exp
+from ase.data import atomic_numbers
+from ase.calculators.calculator import Parameters
+from ..utilities import Data, Logger, importer
+from .cutoffs import Cosine, dict2cutoff
+NeighborList = importer('NeighborList')
+
+
+class Bispectrum(object):
+ """Class that calculates spherical harmonic bispectrum fingerprints.
+
+ Parameters
+ ----------
+ cutoff : object or float
+ Cutoff function, typically from amp.descriptor.cutoffs. Can be also
+ fed as a float representing the radius above which neighbor
+ interactions are ignored; in this case a cosine cutoff function will be
+ employed. Default is a 6.5-Angstrom cosine cutoff.
+ Gs : dict
+ Dictionary of symbols and dictionaries for making fingerprints. Either
+ auto-genetrated, or given in the following form, for example:
+
+ >>> Gs = {"Au": {"Au": 3., "O": 2.}, "O": {"Au": 5., "O": 10.}}
+
+ jmax : integer or half-integer or dict
+ Maximum degree of spherical harmonics that will be included in the
+ fingerprint vector. Can be also fed as a dictionary with chemical
+ species as keys.
+ dblabel : str
+ Optional separate prefix/location for database files, including
+ fingerprints, fingerprint derivatives, and neighborlists. This file
+ location can be shared between calculator instances to avoid
+ re-calculating redundant information. If not supplied, just uses the
+ value from label.
+ elements : list
+ List of allowed elements present in the system. If not provided, will
+ be found automatically.
+ version : str
+ Version of fingerprints.
+
+ Raises:
+ -------
+ RuntimeError, TypeError
+ """
+
+ def __init__(self, cutoff=Cosine(6.5), Gs=None, jmax=5, dblabel=None,
+ elements=None, version='2016.02', mode='atom-centered'):
+
+ # Check of the version of descriptor, particularly if restarting.
+ compatibleversions = ['2016.02', ]
+ if (version is not None) and version not in compatibleversions:
+ raise RuntimeError('Error: Trying to use bispectrum fingerprints'
+ ' version %s, but this module only supports'
+ ' versions %s. You may need an older or '
+ ' newer version of Amp.' %
+ (version, compatibleversions))
+ else:
+ version = compatibleversions[-1]
+
+ # Check that the mode is atom-centered.
+ if mode != 'atom-centered':
+ raise RuntimeError('Bispectrum scheme only works '
+ 'in atom-centered mode. %s '
+ 'specified.' % mode)
+
+ # If the cutoff is provided as a number, Cosine function will be used
+ # by default.
+ if isinstance(cutoff, int) or isinstance(cutoff, float):
+ cutoff = Cosine(cutoff)
+ # If the cutoff is provided as a dictionary, assume we need to load it
+ # with dict2cutoff.
+ if type(cutoff) is dict:
+ cutoff = dict2cutoff(cutoff)
+
+ # The parameters dictionary contains the minimum information
+ # to produce a compatible descriptor; that is, one that gives
+ # an identical fingerprint when fed an ASE image.
+ p = self.parameters = Parameters(
+ {'importname': '.descriptor.bispectrum.Bispectrum',
+ 'mode': 'atom-centered'})
+ p.version = version
+ p.cutoff = cutoff.todict()
+ p.Gs = Gs
+ p.jmax = jmax
+ p.elements = elements
+
+ self.dblabel = dblabel
+ self.parent = None # Can hold a reference to main Amp instance.
+
+ def tostring(self):
+ """Returns an evaluatable representation of the calculator that can
+ be used to restart the calculator."""
+ return self.parameters.tostring()
+
+ def calculate_fingerprints(self, images, parallel=None, log=None,
+ calculate_derivatives=False):
+ """Calculates the fingerpints of the images, for the ones not already
+ done.
+
+ Parameters
+ ----------
+ images : list or str
+ List of ASE atoms objects with positions, symbols, energies, and
+ forces in ASE format. This is the training set of data. This can
+ also be the path to an ASE trajectory (.traj) or database (.db)
+ file. Energies can be obtained from any reference, e.g. DFT
+ calculations.
+ parallel : dict
+ Configuration for parallelization. Should be in same form as in
+ amp.Amp.
+ log : Logger object
+ Write function at which to log data. Note this must be a callable
+ function.
+ calculate_derivatives : bool
+ Decides whether or not fingerprintprimes should also be calculated.
+ """
+ if parallel is None:
+ parallel = {'cores': 1}
+ if calculate_derivatives is True:
+ import warnings
+ warnings.warn('Zernike descriptor cannot train forces yet. '
+ 'Force training automatically turnned off. ')
+ calculate_derivatives = False
+
+ log = Logger(file=None) if log is None else log
+
+ if (self.dblabel is None) and hasattr(self.parent, 'dblabel'):
+ self.dblabel = self.parent.dblabel
+ self.dblabel = 'amp-data' if self.dblabel is None else self.dblabel
+
+ p = self.parameters
+
+ log('Cutoff function: %s' % repr(dict2cutoff(p.cutoff)))
+
+ if p.elements is None:
+ log('Finding unique set of elements in training data.')
+ p.elements = set([atom.symbol for atoms in images.values()
+ for atom in atoms])
+ p.elements = sorted(p.elements)
+ log('%i unique elements included: ' % len(p.elements) +
+ ', '.join(p.elements))
+
+ log('Maximum degree of spherical harmonic bispectrum:')
+ if isinstance(p.jmax, dict):
+ for _ in p.jmax.keys():
+ log(' %2s: %d' % (_, p.jmax[_]))
+ else:
+ log('jmax: %d' % p.jmax)
+
+ if p.Gs is None:
+ log('No coefficient for atomic density function supplied; '
+ 'creating defaults.')
+ p.Gs = generate_coefficients(p.elements)
+ log('Coefficients of atomic density function for each element:')
+ for _ in p.Gs.keys():
+ log(' %2s: %s' % (_, str(p.Gs[_])))
+
+ # Counts the number of descriptors for each element.
+ no_of_descriptors = {}
+ for element in p.elements:
+ count = 0
+ if isinstance(p.jmax, dict):
+ for _2j1 in range(int(2 * p.jmax[element]) + 1):
+ for j in range(int(min(_2j1, p.jmax[element])) + 1):
+ count += 1
+ else:
+ for _2j1 in range(int(2 * p.jmax) + 1):
+ for j in range(int(min(_2j1, p.jmax)) + 1):
+ count += 1
+ no_of_descriptors[element] = count
+
+ log('Number of descriptors for each element:')
+ for element in p.elements:
+ log(' %2s: %d' % (element, no_of_descriptors.pop(element)))
+
+ log('Calculating neighborlists...', tic='nl')
+ if not hasattr(self, 'neighborlist'):
+ calc = NeighborlistCalculator(cutoff=p.cutoff['kwargs']['Rc'])
+ self.neighborlist = Data(filename='%s-neighborlists'
+ % self.dblabel,
+ calculator=calc)
+ self.neighborlist.calculate_items(images, parallel=parallel, log=log)
+ log('...neighborlists calculated.', toc='nl')
+
+ log('Fingerprinting images...', tic='fp')
+ if not hasattr(self, 'fingerprints'):
+ calc = FingerprintCalculator(neighborlist=self.neighborlist,
+ Gs=p.Gs,
+ jmax=p.jmax,
+ cutoff=p.cutoff,)
+ self.fingerprints = Data(filename='%s-fingerprints'
+ % self.dblabel,
+ calculator=calc)
+ self.fingerprints.calculate_items(images, parallel=parallel, log=log)
+ log('...fingerprints calculated.', toc='fp')
+
+
+# Calculators #################################################################
+
+
+# Neighborlist Calculator
+class NeighborlistCalculator:
+ """For integration with .utilities.Data
+
+ For each image fed to calculate, a list of neighbors with offset
+ distances is returned.
+ """
+
+ def __init__(self, cutoff):
+ self.globals = Parameters({'cutoff': cutoff})
+ self.keyed = Parameters()
+ self.parallel_command = 'calculate_neighborlists'
+
+ def calculate(self, image, key):
+ cutoff = self.globals.cutoff
+ n = NeighborList(cutoffs=[cutoff / 2.] * len(image),
+ self_interaction=False,
+ bothways=True,
+ skin=0.)
+ n.update(image)
+ return [n.get_neighbors(index) for index in range(len(image))]
+
+
+class FingerprintCalculator:
+ """For integration with .utilities.Data
+ """
+
+ def __init__(self, neighborlist, Gs, jmax, cutoff,):
+ self.globals = Parameters({'cutoff': cutoff,
+ 'Gs': Gs,
+ 'jmax': jmax})
+ self.keyed = Parameters({'neighborlist': neighborlist})
+ self.parallel_command = 'calculate_fingerprints'
+
+ self.factorial = [1]
+ for _ in range(int(3. * jmax) + 2):
+ if _ > 0:
+ self.factorial += [_ * self.factorial[_ - 1]]
+
+ def calculate(self, image, key):
+ """Makes a list of fingerprints, one per atom, for the fed image.
+
+ Parameters
+ ----------
+ image : object
+ ASE atoms object.
+ key : str
+ key of the image after being hashed.
+ """
+ nl = self.keyed.neighborlist[key]
+ fingerprints = []
+ for atom in image:
+ symbol = atom.symbol
+ index = atom.index
+ neighbors, offsets = nl[index]
+ neighborsymbols = [image[_].symbol for _ in neighbors]
+ Rs = [image.positions[neighbor] + np.dot(offset, image.cell)
+ for (neighbor, offset) in zip(neighbors, offsets)]
+ self.atoms = image
+ indexfp = self.get_fingerprint(index, symbol, neighborsymbols, Rs)
+ fingerprints.append(indexfp)
+
+ return fingerprints
+
+ def get_fingerprint(self, index, symbol, n_symbols, Rs):
+ """Returns the fingerprint of symmetry function values for atom
+ specified by its index and symbol.
+
+ n_symbols and Rs are lists of
+ neighbors' symbols and Cartesian positions, respectively.
+
+ Parameters
+ ----------
+ index : int
+ Index of the center atom.
+ symbol : str
+ Symbol of the center atom.
+ n_symbols : list of str
+ List of neighbors' symbols.
+ Rs : list of list of float
+ List of Cartesian atomic positions of neighbors.
+
+ Returns
+ -------
+ symbols, fingerprints : list of float
+ fingerprints for atom specified by its index and symbol.
+ """
+
+ home = self.atoms[index].position
+ cutoff = self.globals.cutoff
+ Rc = cutoff['kwargs']['Rc']
+ jmax = self.globals.jmax
+
+ if cutoff['name'] == 'Cosine':
+ cutoff_fxn = Cosine(Rc)
+ elif cutoff['name'] == 'Polynomial':
+# cutoff_fxn = Polynomial(cutoff)
+ raise NotImplementedError()
+
+ rs = []
+ psis = []
+ thetas = []
+ phis = []
+ for neighbor in Rs:
+ x = neighbor[0] - home[0]
+ y = neighbor[1] - home[1]
+ z = neighbor[2] - home[2]
+ r = np.linalg.norm(neighbor - home)
+ if r > 10.**(-10.):
+
+ psi = np.arcsin(r / Rc)
+
+ theta = np.arccos(z / r)
+ if abs((z / r) - 1.0) < 10.**(-8.):
+ theta = 0.0
+ elif abs((z / r) + 1.0) < 10.**(-8.):
+ theta = np.pi
+
+ if x < 0.:
+ phi = np.pi + np.arctan(y / x)
+ elif 0. < x and y < 0.:
+ phi = 2 * np.pi + np.arctan(y / x)
+ elif 0. < x and 0. <= y:
+ phi = np.arctan(y / x)
+ elif x == 0. and 0. < y:
+ phi = 0.5 * np.pi
+ elif x == 0. and y < 0.:
+ phi = 1.5 * np.pi
+ else:
+ phi = 0.
+
+ rs += [r]
+ psis += [psi]
+ thetas += [theta]
+ phis += [phi]
+
+ fingerprint = []
+ for _2j1 in range(int(2 * jmax) + 1):
+ j1 = 0.5 * _2j1
+ j2 = 0.5 * _2j1
+ for j in range(int(min(_2j1, jmax)) + 1):
+ value = calculate_B(j1, j2, 1.0 * j, self.globals.Gs[symbol],
+ Rc, cutoff['name'],
+ self.factorial, n_symbols,
+ rs, psis, thetas, phis)
+ value = value.real
+ fingerprint.append(value)
+
+ return symbol, fingerprint
+
+# Auxiliary functions #########################################################
+
+
+def calculate_B(j1, j2, j, G_element, cutoff, cutofffn, factorial, n_symbols,
+ rs, psis, thetas, phis):
+ """Calculates bi-spectrum B_{j1, j2, j} according to Eq. (5) of "Gaussian
+ Approximation Potentials: The Accuracy of Quantum Mechanics, without the
+ Electrons", Phys. Rev. Lett. 104, 136403.
+ """
+
+ mvals = m_values(j)
+ B = 0.
+ for m in mvals:
+ for mp in mvals:
+ c = calculate_c(j, mp, m, G_element, cutoff, cutofffn, factorial,
+ n_symbols, rs, psis, thetas, phis)
+ m1bound = min(j1, m + j2)
+ mp1bound = min(j1, mp + j2)
+ m1 = max(-j1, m - j2)
+ while m1 < (m1bound + 0.5):
+ mp1 = max(-j1, mp - j2)
+ while mp1 < (mp1bound + 0.5):
+ c1 = calculate_c(j1, mp1, m1, G_element, cutoff, cutofffn,
+ factorial, n_symbols, rs, psis, thetas,
+ phis)
+ c2 = calculate_c(j2, mp - mp1, m - m1, G_element, cutoff,
+ cutofffn, factorial, n_symbols, rs, psis,
+ thetas, phis)
+ B += CG(j1, m1, j2, m - m1, j, m, factorial) * \
+ CG(j1, mp1, j2, mp - mp1, j, mp, factorial) * \
+ np.conjugate(c) * c1 * c2
+ mp1 += 1.
+ m1 += 1.
+
+ return B
+
+###############################################################################
+
+
+def calculate_c(j, mp, m, G_element, cutoff, cutofffn, factorial, n_symbols,
+ rs, psis, thetas, phis):
+ """Calculates c^{j}_{m'm} according to Eq. (4) of "Gaussian Approximation
+ Potentials: The Accuracy of Quantum Mechanics, without the Electrons",
+ Phys. Rev. Lett. 104, 136403
+ """
+
+ if cutofffn is 'Cosine':
+ cutoff_fxn = Cosine(cutoff)
+ elif cutofffn is 'Polynomial':
+# cutoff_fxn = Polynomial(cutoff)
+ raise NotImplementedError
+
+ value = 0.
+ for n_symbol, r, psi, theta, phi in zip(n_symbols, rs, psis, thetas, phis):
+
+ value += G_element[n_symbol] * \
+ np.conjugate(U(j, m, mp, psi, theta, phi, factorial)) * \
+ cutoff_fxn(r)
+
+ return value
+
+###############################################################################
+
+
+def m_values(j):
+ """Returns a list of m values for a given j."""
+
+ assert j >= 0, '2*j should be a non-negative integer.'
+
+ return [j - i for i in range(int(2 * j + 1))]
+
+###############################################################################
+
+
+def binomial(n, k, factorial):
+ """Returns C(n,k) = n!/(k!(n-k)!)."""
+
+ assert n >= 0 and k >= 0 and n >= k, \
+ 'n and k should be non-negative integers with n >= k.'
+ c = factorial[int(n)] / (factorial[int(k)] * factorial[int(n - k)])
+ return c
+
+###############################################################################
+
+
+def WignerD(j, m, mp, alpha, beta, gamma, factorial):
+ """Returns the Wigner-D matrix. alpha, beta, and gamma are the Euler
+ angles."""
+
+ result = 0
+ if abs(beta - np.pi / 2.) < 10.**(-10.):
+ # Varshalovich Eq. (5), Section 4.16, Page 113.
+ # j, m, and mp here are J, M, and M', respectively, in Eq. (5).
+ for k in range(int(2 * j + 1)):
+ if k > j + mp or k > j - m:
+ break
+ elif k < mp - m:
+ continue
+ result += (-1)**k * binomial(j + mp, k, factorial) * \
+ binomial(j - mp, k + m - mp, factorial)
+
+ result *= (-1)**(m - mp) * \
+ sqrt(float(factorial[int(j + m)] * factorial[int(j - m)]) /
+ float((factorial[int(j + mp)] * factorial[int(j - mp)]))) / \
+ 2.**j
+ result *= exp(-1j * m * alpha) * exp(-1j * mp * gamma)
+
+ else:
+ # Varshalovich Eq. (10), Section 4.16, Page 113.
+ # m, mpp, and mp here are M, m, and M', respectively, in Eq. (10).
+ mvals = m_values(j)
+ for mpp in mvals:
+ # temp1 = WignerD(j, m, mpp, 0, np.pi/2, 0) = d(j, m, mpp, np.pi/2)
+ temp1 = 0.
+ for k in range(int(2 * j + 1)):
+ if k > j + mpp or k > j - m:
+ break
+ elif k < mpp - m:
+ continue
+ temp1 += (-1)**k * binomial(j + mpp, k, factorial) * \
+ binomial(j - mpp, k + m - mpp, factorial)
+ temp1 *= (-1)**(m - mpp) * \
+ sqrt(float(factorial[int(j + m)] * factorial[int(j - m)]) /
+ float((factorial[int(j + mpp)] *
+ factorial[int(j - mpp)]))) / 2.**j
+
+ # temp2 = WignerD(j, mpp, mp, 0, np.pi/2, 0) = d(j, mpp, mp,
+ # np.pi/2)
+ temp2 = 0.
+ for k in range(int(2 * j + 1)):
+ if k > j - mp or k > j - mpp:
+ break
+ elif k < - mp - mpp:
+ continue
+ temp2 += (-1)**k * binomial(j - mp, k, factorial) * \
+ binomial(j + mp, k + mpp + mp, factorial)
+ temp2 *= (-1)**(mpp + mp) * \
+ sqrt(float(factorial[int(j + mpp)] * factorial[int(j - mpp)]) /
+ float((factorial[int(j - mp)] *
+ factorial[int(j + mp)]))) / 2.**j
+
+ result += temp1 * exp(-1j * mpp * beta) * temp2
+
+ # Empirical normalization factor so results match Varshalovich
+ # Tables 4.3-4.12
+ # Note that this exact normalization does not follow from the
+ # above equations
+ result *= (1j**(2 * j - m - mp)) * ((-1)**(2 * m))
+ result *= exp(-1j * m * alpha) * exp(-1j * mp * gamma)
+
+ return result
+
+###############################################################################
+
+
+def U(j, m, mp, omega, theta, phi, factorial):
+ """Calculates rotation matrix U_{MM'}^{J} in terms of rotation angle omega as
+ well as rotation axis angles theta and phi, according to Varshalovich,
+ Eq. (3), Section 4.5, Page 81. j, m, mp, and mpp here are J, M, M', and M''
+ in Eq. (3).
+ """
+
+ result = 0.
+ mvals = m_values(j)
+ for mpp in mvals:
+ result += WignerD(j, m, mpp, phi, theta, -phi, factorial) * \
+ exp(- 1j * mpp * omega) * \
+ WignerD(j, mpp, mp, phi, -theta, -phi, factorial)
+ return result
+
+
+###############################################################################
+
+
+def CG(a, alpha, b, beta, c, gamma, factorial):
+ """Clebsch-Gordan coefficient C_{a alpha b beta}^{c gamma} is calculated
+ acoording to the expression given in Varshalovich Eq. (3), Section 8.2,
+ Page 238."""
+
+ if int(2. * a) != 2. * a or int(2. * b) != 2. * b or int(2. * c) != 2. * c:
+ raise ValueError("j values must be integer or half integer")
+ if int(2. * alpha) != 2. * alpha or int(2. * beta) != 2. * beta or \
+ int(2. * gamma) != 2. * gamma:
+ raise ValueError("m values must be integer or half integer")
+
+ if alpha + beta - gamma != 0.:
+ return 0.
+ else:
+ minimum = min(a + b - c, a - b + c, -a + b + c, a + b + c + 1.,
+ a - abs(alpha), b - abs(beta), c - abs(gamma))
+ if minimum < 0.:
+ return 0.
+ else:
+ sqrtarg = \
+ factorial[int(a + alpha)] * \
+ factorial[int(a - alpha)] * \
+ factorial[int(b + beta)] * \
+ factorial[int(b - beta)] * \
+ factorial[int(c + gamma)] * \
+ factorial[int(c - gamma)] * \
+ (2. * c + 1.) * \
+ factorial[int(a + b - c)] * \
+ factorial[int(a - b + c)] * \
+ factorial[int(-a + b + c)] / \
+ factorial[int(a + b + c + 1.)]
+
+ sqrtres = sqrt(sqrtarg)
+
+ zmin = max(a + beta - c, b - alpha - c, 0.)
+ zmax = min(b + beta, a - alpha, a + b - c)
+ sumres = 0.
+ for z in range(int(zmin), int(zmax) + 1):
+ value = \
+ factorial[int(z)] * \
+ factorial[int(a + b - c - z)] * \
+ factorial[int(a - alpha - z)] * \
+ factorial[int(b + beta - z)] * \
+ factorial[int(c - b + alpha + z)] * \
+ factorial[int(c - a - beta + z)]
+ sumres += (-1.)**z / value
+
+ result = sqrtres * sumres
+
+ return result
+
+###############################################################################
+
+
+def generate_coefficients(elements):
+ """Automatically generates coefficients if not given by the user.
+
+ Parameters
+ ---------
+ elements : list of str
+ List of symbols of all atoms.
+
+ Returns
+ -------
+ G : dict of dicts
+ """
+ _G = {}
+ for element in elements:
+ _G[element] = atomic_numbers[element]
+ G = {}
+ for element in elements:
+ G[element] = _G
+ return G
+
+###############################################################################
+
+
+if __name__ == "__main__":
+ """Directly calling this module; apparently from another node.
+ Calls should come as
+
+ python -m amp.descriptor.example id hostname:port
+
+ This session will then start a zmq session with that socket, labeling
+ itself with id. Instructions on what to do will come from the socket.
+ """
+ import sys
+ import tempfile
+ import zmq
+ from ..utilities import MessageDictionary
+
+ hostsocket = sys.argv[-1]
+ proc_id = sys.argv[-2]
+ msg = MessageDictionary(proc_id)
+
+ # Send standard lines to stdout signaling process started and where
+ # error is directed. This should be caught by pxssh. (This could
+ # alternatively be done by zmq, but this works.)
+ print('<amp-connect>') # Signal that program started.
+ sys.stderr = tempfile.NamedTemporaryFile(mode='w', delete=False,
+ suffix='.stderr')
+ print('Log and error written to %s<stderr>' % sys.stderr.name)
+
+ # Establish client session via zmq; find purpose.
+ context = zmq.Context()
+ socket = context.socket(zmq.REQ)
+ socket.connect('tcp://%s' % hostsocket)
+ socket.send_pyobj(msg('<purpose>'))
+ purpose = socket.recv_pyobj()
+
+ if purpose == 'calculate_neighborlists':
+ # Request variables.
+ socket.send_pyobj(msg('<request>', 'cutoff'))
+ cutoff = socket.recv_pyobj()
+ socket.send_pyobj(msg('<request>', 'images'))
+ images = socket.recv_pyobj()
+ # sys.stderr.write(str(images)) # Just to see if they are there.
+
+ # Perform the calculations.
+ calc = NeighborlistCalculator(cutoff=cutoff)
+ neighborlist = {}
+ # for key in images.iterkeys():
+ while len(images) > 0:
+ key, image = images.popitem() # Reduce memory.
+ neighborlist[key] = calc.calculate(image, key)
+
+ # Send the results.
+ socket.send_pyobj(msg('<result>', neighborlist))
+ socket.recv_string() # Needed to complete REQ/REP.
+
+ elif purpose == 'calculate_fingerprints':
+ # Request variables.
+ socket.send_pyobj(msg('<request>', 'cutoff'))
+ cutoff = socket.recv_pyobj()
+ socket.send_pyobj(msg('<request>', 'Gs'))
+ Gs = socket.recv_pyobj()
+ socket.send_pyobj(msg('<request>', 'jmax'))
+ jmax = socket.recv_pyobj()
+ socket.send_pyobj(msg('<request>', 'neighborlist'))
+ neighborlist = socket.recv_pyobj()
+ socket.send_pyobj(msg('<request>', 'images'))
+ images = socket.recv_pyobj()
+
+ calc = FingerprintCalculator(neighborlist, Gs, jmax, cutoff,)
+ result = {}
+ while len(images) > 0:
+ key, image = images.popitem() # Reduce memory.
+ result[key] = calc.calculate(image, key)
+ if len(images) % 100 == 0:
+ socket.send_pyobj(msg('<info>', len(images)))
+ socket.recv_string() # Needed to complete REQ/REP.
+
+ # Send the results.
+ socket.send_pyobj(msg('<result>', result))
+ socket.recv_string() # Needed to complete REQ/REP.
+
+ else:
+ raise NotImplementedError('purpose %s unknown.' % purpose)
diff --git a/amp/descriptor/cutoffs.f90 b/amp/descriptor/cutoffs.f90
new file mode 100644
index 0000000..d0376c4
--- /dev/null
+++ b/amp/descriptor/cutoffs.f90
@@ -0,0 +1,60 @@
+ module cutoffs
+ implicit none
+
+ contains
+ function cutoff_fxn(r, rc, cutofffn, p_gamma)
+ double precision:: r, rc, pi, cutoff_fxn
+ ! gamma parameter for the polynomial cutoff
+ double precision, optional:: p_gamma
+ character(len=20):: cutofffn
+
+! To avoid noise, for each call of this function, it is better to
+! set returned variables to 0.0d0.
+ cutoff_fxn = 0.0d0
+
+ if (cutofffn == 'Cosine') then
+ if (r > rc) then
+ cutoff_fxn = 0.0d0
+ else
+ pi = 4.0d0 * datan(1.0d0)
+ cutoff_fxn = 0.5d0 * (cos(pi*r/rc) + 1.0d0)
+ end if
+ elseif (cutofffn == 'Polynomial') then
+ if (r > rc) then
+ cutoff_fxn = 0.0d0
+ else
+ cutoff_fxn = 1. + p_gamma &
+ * (r / rc) ** (p_gamma + 1) &
+ - (p_gamma + 1) * (r / rc) ** p_gamma
+ end if
+ endif
+ end function cutoff_fxn
+
+ function cutoff_fxn_prime(r, rc, cutofffn, p_gamma)
+ double precision:: r, rc, cutoff_fxn_prime, pi
+ ! gamma parameter for the polynomial cutoff
+ double precision, optional:: p_gamma
+ character(len=20):: cutofffn
+
+! To avoid noise, for each call of this function, it is better to
+! set returned variables to 0.0d0.
+ cutoff_fxn_prime = 0.0d0
+
+ if (cutofffn == 'Cosine') then
+ if (r > rc) then
+ cutoff_fxn_prime = 0.0d0
+ else
+ pi = 4.0d0 * datan(1.0d0)
+ cutoff_fxn_prime = -0.5d0 * pi * sin(pi*r/rc) / rc
+ end if
+ elseif (cutofffn == 'Polynomial') then
+ if (r > rc) then
+ cutoff_fxn_prime = 0.0d0
+ else
+ cutoff_fxn_prime = (p_gamma * (p_gamma + 1) / rc) &
+ * ((r / rc) ** p_gamma - (r / rc) ** (p_gamma - 1))
+ end if
+ end if
+ end function cutoff_fxn_prime
+
+ end module cutoffs
diff --git a/amp/descriptor/cutoffs.py b/amp/descriptor/cutoffs.py
new file mode 100644
index 0000000..d0613b7
--- /dev/null
+++ b/amp/descriptor/cutoffs.py
@@ -0,0 +1,150 @@
+#!/usr/bin/env python
+"""
+This script contains different cutoff function forms.
+
+Note all cutoff functions need to have a "todict" method
+to support saving/loading as an Amp object.
+
+All cutoff functions also need to have an `Rc` attribute which
+is the maximum distance at which properties are calculated; this
+will be used in calculating neighborlists.
+
+"""
+
+import numpy as np
+
+
+def dict2cutoff(dct):
+ """This function converts a dictionary (which was created with the
+ to_dict method of one of the cutoff classes) into an instantiated
+ version of the class. Modeled after ASE's dict2constraint function.
+ """
+ if len(dct) != 2:
+ raise RuntimeError('Cutoff dictionary must have only two values,'
+ ' "name" and "kwargs".')
+ return globals()[dct['name']](**dct['kwargs'])
+
+
+class Cosine(object):
+ """Cosine functional form suggested by Behler.
+
+ Parameters
+ ---------
+ Rc : float
+ Radius above which neighbor interactions are ignored.
+ """
+
+ def __init__(self, Rc):
+
+ self.Rc = Rc
+
+ def __call__(self, Rij):
+ """
+ Parameters
+ ----------
+ Rij : float
+ Distance between pair atoms.
+
+ Returns
+ -------
+ float
+ The value of the cutoff function.
+ """
+ if Rij > self.Rc:
+ return 0.
+ else:
+ return 0.5 * (np.cos(np.pi * Rij / self.Rc) + 1.)
+
+ def prime(self, Rij):
+ """Derivative of the Cosine cutoff function.
+
+ Parameters
+ ----------
+ Rij : float
+ Distance between pair atoms.
+
+ Returns
+ -------
+ float
+ The value of derivative of the cutoff function.
+ """
+ if Rij > self.Rc:
+ return 0.
+ else:
+ return -0.5 * np.pi / self.Rc * np.sin(np.pi * Rij / self.Rc)
+
+ def todict(self):
+ return {'name': 'Cosine',
+ 'kwargs': {'Rc': self.Rc}}
+
+ def __repr__(self):
+ return ('<Cosine cutoff with Rc=%.3f from amp.descriptor.cutoffs>'
+ % self.Rc)
+
+
+class Polynomial(object):
+ """Polynomial functional form suggested by Khorshidi and Peterson.
+
+ Parameters
+ ----------
+ gamma : float
+ The power of polynomial.
+ Rc : float
+ Radius above which neighbor interactions are ignored.
+ """
+
+ def __init__(self, Rc, gamma=4):
+ self.gamma = gamma
+ self.Rc = Rc
+
+ def __call__(self, Rij):
+ """
+ Parameters
+ ----------
+ Rij : float
+ Distance between pair atoms.
+
+ Returns
+ -------
+ value : float
+ The value of the cutoff function.
+ """
+ if Rij > self.Rc:
+ return 0.
+ else:
+ value = 1. + self.gamma * (Rij / self.Rc) ** (self.gamma + 1) - \
+ (self.gamma + 1) * (Rij / self.Rc) ** self.gamma
+ return value
+
+ def prime(self, Rij):
+ """Derivative of the Polynomial cutoff function.
+
+ Parameters
+ ----------
+ Rij : float
+ Distance between pair atoms.
+
+ Returns
+ -------
+ float
+ The value of derivative of the cutoff function.
+ """
+ if Rij > self.Rc:
+ return 0.
+ else:
+ value = (self.gamma * (self.gamma + 1) / self.Rc) * \
+ ((Rij / self.Rc) ** self.gamma -
+ (Rij / self.Rc) ** (self.gamma - 1))
+ return value
+
+ def todict(self):
+ return {'name': 'Polynomial',
+ 'kwargs': {'Rc': self.Rc,
+ 'gamma': self.gamma
+ }
+ }
+
+ def __repr__(self):
+ return ('<Polynomial cutoff with Rc=%.3f and gamma=%i '
+ 'from amp.descriptor.cutoffs>'
+ % (self.Rc, self.gamma))
diff --git a/amp/descriptor/example.py b/amp/descriptor/example.py
new file mode 100644
index 0000000..5246095
--- /dev/null
+++ b/amp/descriptor/example.py
@@ -0,0 +1,336 @@
+import time
+import numpy as np
+
+from ase.calculators.calculator import Parameters
+from ..utilities import Data, Logger, importer
+from .cutoffs import Cosine
+NeighborList = importer('NeighborList')
+
+
+class AtomCenteredExample(object):
+
+ """Class that calculates fingerprints.
+
+ This is an example class that doesn't do much; it just shows the code
+ structure. If making your own module, you can copy and modify this one.
+
+ Parameters
+ ----------
+ cutoff : object or float
+ Cutoff function. Can be also fed as a float representing the radius
+ above which neighbor interactions are ignored. Default is 6.5
+ Angstroms.
+ anotherparameter : float
+ Just an example.
+ dblabel : str
+ Optional separate prefix/location for database files, including
+ fingerprints, fingerprint derivatives, and neighborlists. This file
+ location can be shared between calculator instances to avoid
+ re-calculating redundant information. If not supplied, just uses the
+ value from label.
+ elements : list
+ List of allowed elements present in the system. If not provided, will
+ be found automatically.
+ version : str
+ Version of fingerprints.
+
+ Raises
+ ------
+ RuntimeError, TypeError
+ """
+
+ def __init__(self, cutoff=Cosine(6.5), anotherparameter=12.2, dblabel=None,
+ elements=None, version=None, mode='atom-centered'):
+
+ # Check of the version of descriptor, particularly if restarting.
+ compatibleversions = ['2016.02', ]
+ if (version is not None) and version not in compatibleversions:
+ raise RuntimeError('Error: Trying to use Example fingerprints'
+ ' version %s, but this module only supports'
+ ' versions %s. You may need an older or '
+ ' newer version of Amp.' %
+ (version, compatibleversions))
+ else:
+ version = compatibleversions[-1]
+
+ # Check that the mode is atom-centered.
+ if mode != 'atom-centered':
+ raise RuntimeError('This scheme only works '
+ 'in atom-centered mode. %s '
+ 'specified.' % mode)
+
+ # If the cutoff is provided as a number, Cosine function will be used
+ # by default.
+ if isinstance(cutoff, int) or isinstance(cutoff, float):
+ cutoff = Cosine(cutoff)
+
+ # The parameters dictionary contains the minimum information
+ # to produce a compatible descriptor; that is, one that gives
+ # an identical fingerprint when fed an ASE image.
+ p = self.parameters = Parameters(
+ {'importname': '.descriptor.example.AtomCenteredExample',
+ 'mode': 'atom-centered'})
+ p.version = version
+ p.cutoff = cutoff.Rc
+ p.cutofffn = cutoff.__class__.__name__
+ p.anotherparameter = anotherparameter
+ p.elements = elements
+
+ self.dblabel = dblabel
+ self.parent = None # Can hold a reference to main Amp instance.
+
+ def tostring(self):
+ """Returns an evaluatable representation of the calculator that can
+ be used to restart the calculator."""
+ return self.parameters.tostring()
+
+ def calculate_fingerprints(self, images, parallel=None, log=None,
+ calculate_derivatives=False):
+ """Calculates the fingerpints of the images, for the ones not already
+ done.
+
+ Parameters
+ ----------
+ images : list or str
+ List of ASE atoms objects with positions, symbols, energies, and
+ forces in ASE format. This is the training set of data. This can
+ also be the path to an ASE trajectory (.traj) or database (.db)
+ file. Energies can be obtained from any reference, e.g. DFT
+ calculations.
+ parallel : dict
+ Configuration for parallelization. Should be in same form as in
+ amp.Amp.
+ log : Logger object
+ Write function at which to log data. Note this must be a callable
+ function.
+ calculate_derivatives : bool
+ Decides whether or not fingerprintprimes should also be calculated.
+ """
+ if parallel is None:
+ parallel = {'cores': 1}
+ log = Logger(file=None) if log is None else log
+
+ if (self.dblabel is None) and hasattr(self.parent, 'dblabel'):
+ self.dblabel = self.parent.dblabel
+ self.dblabel = 'amp-data' if self.dblabel is None else self.dblabel
+
+ p = self.parameters
+
+ log('Cutoff radius: %.2f' % p.cutoff)
+ log('Cutoff function: %s' % p.cutofffn)
+
+ if p.elements is None:
+ log('Finding unique set of elements in training data.')
+ p.elements = set([atom.symbol for atoms in images.values()
+ for atom in atoms])
+ p.elements = sorted(p.elements)
+ log('%i unique elements included: ' % len(p.elements) +
+ ', '.join(p.elements))
+
+ log('anotherparameter: %.3f' % p.anotherparameter)
+
+ log('Calculating neighborlists...', tic='nl')
+ if not hasattr(self, 'neighborlist'):
+ calc = NeighborlistCalculator(cutoff=p.cutoff)
+ self.neighborlist = Data(filename='%s-neighborlists'
+ % self.dblabel,
+ calculator=calc)
+ self.neighborlist.calculate_items(images, parallel=parallel, log=log)
+ log('...neighborlists calculated.', toc='nl')
+
+ log('Fingerprinting images...', tic='fp')
+ if not hasattr(self, 'fingerprints'):
+ calc = FingerprintCalculator(neighborlist=self.neighborlist,
+ anotherparamter=p.anotherparameter,
+ cutoff=p.cutoff,
+ cutofffn=p.cutofffn)
+ self.fingerprints = Data(filename='%s-fingerprints'
+ % self.dblabel,
+ calculator=calc)
+ self.fingerprints.calculate_items(images, parallel=parallel, log=log)
+ log('...fingerprints calculated.', toc='fp')
+
+
+# Calculators #################################################################
+
+
+# Neighborlist Calculator
+class NeighborlistCalculator:
+ """For integration with .utilities.Data
+
+ For each image fed to calculate, a list of neighbors with offset distances
+ is returned.
+
+ Parameters
+ ----------
+ cutoff : float
+ Radius above which neighbor interactions are ignored.
+ """
+ def __init__(self, cutoff):
+ self.globals = Parameters({'cutoff': cutoff})
+ self.keyed = Parameters()
+ self.parallel_command = 'calculate_neighborlists'
+
+ def calculate(self, image, key):
+ """For integration with .utilities.Data
+
+ For each image fed to calculate, a list of neighbors with offset
+ distances is returned.
+
+ Parameters
+ ----------
+ image : object
+ ASE atoms object.
+ key : str
+ key of the image after being hashed.
+ """
+ cutoff = self.globals.cutoff
+ n = NeighborList(cutoffs=[cutoff / 2.] * len(image),
+ self_interaction=False,
+ bothways=True,
+ skin=0.)
+ n.update(image)
+ return [n.get_neighbors(index) for index in range(len(image))]
+
+
+class FingerprintCalculator:
+ """For integration with .utilities.Data"""
+
+ def __init__(self, neighborlist, anotherparamter, cutoff, cutofffn):
+ self.globals = Parameters({'cutoff': cutoff,
+ 'cutofffn': cutofffn,
+ 'anotherparameter': anotherparamter})
+ self.keyed = Parameters({'neighborlist': neighborlist})
+ self.parallel_command = 'calculate_fingerprints'
+
+ def calculate(self, image, key):
+ """Makes a list of fingerprints, one per atom, for the fed image.
+ """
+ nl = self.keyed.neighborlist[key]
+ fingerprints = []
+ for atom in image:
+ symbol = atom.symbol
+ index = atom.index
+ neighbors, offsets = nl[index]
+ neighborsymbols = [image[_].symbol for _ in neighbors]
+ Rs = [image.positions[neighbor] + np.dot(offset, image.cell)
+ for (neighbor, offset) in zip(neighbors, offsets)]
+ self.atoms = image
+ indexfp = self.get_fingerprint(index, symbol, neighborsymbols, Rs)
+ fingerprints.append(indexfp)
+
+ return fingerprints
+
+ def get_fingerprint(self, index, symbol, n_symbols, Rs):
+ """ Returns the fingerprint of symmetry function values for atom
+ specified by its index and symbol.
+
+ n_symbols and Rs are lists of neighbors' symbols and Cartesian
+ positions, respectively.
+
+ This function doesn't actually do anything but sleep and return
+ a vector of ones.
+
+ Parameters
+ ----------
+ index : int
+ index: Index of the center atom.
+ symbol: str
+ Symbol of the center atom.
+ n_symbols: list of str
+ List of neighbors' symbols.
+ Rs: list of list of float
+ List of Cartesian atomic positions.
+
+ Returns
+ -------
+ symbols, fingerprints : list of float
+ Fingerprints for atom specified by its index and symbol.
+ """
+ time.sleep(1.0) # Pretend to do some work.
+ fingerprint = [1., 1., 1., 1.]
+ return symbol, fingerprint
+
+
+if __name__ == "__main__":
+ """Directly calling this module; apparently from another node.
+ Calls should come as
+
+ python -m amp.descriptor.example id hostname:port
+
+ This session will then start a zmq session with that socket, labeling
+ itself with id. Instructions on what to do will come from the socket.
+ """
+ import sys
+ import tempfile
+ import zmq
+ from ..utilities import MessageDictionary
+
+ hostsocket = sys.argv[-1]
+ proc_id = sys.argv[-2]
+ msg = MessageDictionary(proc_id)
+
+ # Send standard lines to stdout signaling process started and where
+ # error is directed. This should be caught by pxssh. (This could
+ # alternatively be done by zmq, but this works.)
+ print('<amp-connect>') # Signal that program started.
+ sys.stderr = tempfile.NamedTemporaryFile(mode='w', delete=False,
+ suffix='.stderr')
+ print('Log and error written to %s<stderr>' % sys.stderr.name)
+
+ # Establish client session via zmq; find purpose.
+ context = zmq.Context()
+ socket = context.socket(zmq.REQ)
+ socket.connect('tcp://%s' % hostsocket)
+ socket.send_pyobj(msg('<purpose>'))
+ purpose = socket.recv_pyobj()
+
+ if purpose == 'calculate_neighborlists':
+ # Request variables.
+ socket.send_pyobj(msg('<request>', 'cutoff'))
+ cutoff = socket.recv_pyobj()
+ socket.send_pyobj(msg('<request>', 'images'))
+ images = socket.recv_pyobj()
+ # sys.stderr.write(str(images)) # Just to see if they are there.
+
+ # Perform the calculations.
+ calc = NeighborlistCalculator(cutoff=cutoff)
+ neighborlist = {}
+ # for key in images.iterkeys():
+ while len(images) > 0:
+ key, image = images.popitem() # Reduce memory.
+ neighborlist[key] = calc.calculate(image, key)
+
+ # Send the results.
+ socket.send_pyobj(msg('<result>', neighborlist))
+ socket.recv_string() # Needed to complete REQ/REP.
+
+ elif purpose == 'calculate_fingerprints':
+ # Request variables.
+ socket.send_pyobj(msg('<request>', 'cutoff'))
+ cutoff = socket.recv_pyobj()
+ socket.send_pyobj(msg('<request>', 'cutofffn'))
+ cutofffn = socket.recv_pyobj()
+ socket.send_pyobj(msg('<request>', 'anotherparameter'))
+ anotherparameter = socket.recv_pyobj()
+ socket.send_pyobj(msg('<request>', 'neighborlist'))
+ neighborlist = socket.recv_pyobj()
+ socket.send_pyobj(msg('<request>', 'images'))
+ images = socket.recv_pyobj()
+
+ calc = FingerprintCalculator(neighborlist, anotherparameter, cutoff,
+ cutofffn)
+ result = {}
+ while len(images) > 0:
+ key, image = images.popitem() # Reduce memory.
+ result[key] = calc.calculate(image, key)
+ if len(images) % 100 == 0:
+ socket.send_pyobj(msg('<info>', len(images)))
+ socket.recv_string() # Needed to complete REQ/REP.
+
+ # Send the results.
+ socket.send_pyobj(msg('<result>', result))
+ socket.recv_string() # Needed to complete REQ/REP.
+
+ else:
+ raise NotImplementedError('purpose %s unknown.' % purpose)
diff --git a/amp/descriptor/gaussian.f90 b/amp/descriptor/gaussian.f90
new file mode 100644
index 0000000..cbcf1e7
--- /dev/null
+++ b/amp/descriptor/gaussian.f90
@@ -0,0 +1,525 @@
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+
+ subroutine calculate_g2(neighbornumbers, neighborpositions, &
+ g_number, g_eta, p_gamma, rc, cutofffn, ri, num_neighbors, ridge)
+
+ use cutoffs
+ implicit none
+ integer, dimension(num_neighbors):: neighbornumbers
+ integer, dimension(1):: g_number
+ double precision, dimension(num_neighbors, 3):: &
+ neighborpositions
+ double precision, dimension(3):: ri
+ integer:: num_neighbors
+ double precision:: g_eta, rc
+ ! gamma parameter for the polynomial cutoff
+ double precision, optional:: p_gamma
+ character(len=20):: cutofffn
+ double precision:: ridge
+!f2py intent(in):: neighbornumbers, neighborpositions, g_number
+!f2py intent(in):: g_eta, rc, ri, p_gamma
+!f2py intent(hide):: num_neighbors
+!f2py intent(out):: ridge
+ integer:: j, match, xyz
+ double precision, dimension(3):: Rij_vector
+ double precision:: Rij, term
+
+
+ ridge = 0.0d0
+ do j = 1, num_neighbors
+ match = compare(neighbornumbers(j), g_number(1))
+ if (match == 1) then
+ do xyz = 1, 3
+ Rij_vector(xyz) = &
+ neighborpositions(j, xyz) - ri(xyz)
+ end do
+ Rij = sqrt(dot_product(Rij_vector, Rij_vector))
+ term = exp(-g_eta*(Rij**2.0d0) / (rc ** 2.0d0))
+ if (present(p_gamma)) then
+ term = term * cutoff_fxn(Rij, rc, &
+ cutofffn, p_gamma)
+ else
+ term = term * cutoff_fxn(Rij, rc, cutofffn)
+ endif
+ ridge = ridge + term
+ end if
+ end do
+
+ CONTAINS
+
+ function compare(try, val) result(match)
+! Returns 1 if try is the same set as val, 0 if not.
+ implicit none
+ integer, intent(in):: try, val
+ integer:: match
+ if (try == val) then
+ match = 1
+ else
+ match = 0
+ end if
+ end function compare
+
+ end subroutine calculate_g2
+
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+
+ subroutine calculate_g4(neighbornumbers, neighborpositions, &
+ g_numbers, g_gamma, g_zeta, g_eta, rc, cutofffn, ri, &
+ num_neighbors, ridge, p_gamma)
+
+ use cutoffs
+ implicit none
+ integer, dimension(num_neighbors):: neighbornumbers
+ integer, dimension(2):: g_numbers
+ double precision, dimension(num_neighbors, 3):: &
+ neighborpositions
+ double precision, dimension(3):: ri
+ integer:: num_neighbors
+ double precision:: g_gamma, g_zeta, g_eta, rc
+ ! gamma parameter for the polynomial cutoff
+ double precision, optional:: p_gamma
+ character(len=20):: cutofffn
+ double precision:: ridge
+!f2py intent(in):: neighbornumbers, neighborpositions
+!f2py intent(in):: g_numbers, g_gamma, g_zeta
+!f2py intent(in):: g_eta, rc, ri, p_gamma
+!f2py intent(hide):: num_neighbors
+!f2py intent(out):: ridge
+ integer:: j, k, match, xyz
+ double precision, dimension(3):: Rij_vector, Rik_vector
+ double precision, dimension(3):: Rjk_vector
+ double precision:: Rij, Rik, Rjk, costheta, term
+
+ ridge = 0.0d0
+ do j = 1, num_neighbors
+ do k = (j + 1), num_neighbors
+ match = compare(neighbornumbers(j), &
+ neighbornumbers(k), g_numbers(1), g_numbers(2))
+ if (match == 1) then
+ do xyz = 1, 3
+ Rij_vector(xyz) = &
+ neighborpositions(j, xyz) - ri(xyz)
+ Rik_vector(xyz) = &
+ neighborpositions(k, xyz) - ri(xyz)
+ Rjk_vector(xyz) = &
+ neighborpositions(k, xyz) - &
+ neighborpositions(j, xyz)
+ end do
+ Rij = sqrt(dot_product(Rij_vector, Rij_vector))
+ Rik = sqrt(dot_product(Rik_vector, Rik_vector))
+ Rjk = sqrt(dot_product(Rjk_vector, Rjk_vector))
+ costheta = &
+ dot_product(Rij_vector, Rik_vector) / Rij / Rik
+ term = (1.0d0 + g_gamma * costheta)**g_zeta
+ term = term*&
+ exp(-g_eta*(Rij**2 + Rik**2 + Rjk**2)&
+ /(rc ** 2.0d0))
+ if (present(p_gamma)) then
+ term = term*cutoff_fxn(Rij, rc, cutofffn, &
+ p_gamma)
+ term = term*cutoff_fxn(Rik, rc, cutofffn, &
+ p_gamma)
+ term = term*cutoff_fxn(Rjk, rc, cutofffn, &
+ p_gamma)
+ else
+ term = term*cutoff_fxn(Rij, rc, cutofffn)
+ term = term*cutoff_fxn(Rik, rc, cutofffn)
+ term = term*cutoff_fxn(Rjk, rc, cutofffn)
+ endif
+ ridge = ridge + term
+ end if
+ end do
+ end do
+ ridge = ridge * 2.0d0**(1.0d0 - g_zeta)
+
+
+ CONTAINS
+
+ function compare(try1, try2, val1, val2) result(match)
+! Returns 1 if (try1, try2) is the same set as (val1, val2), 0 if not.
+ implicit none
+ integer, intent(in):: try1, try2, val1, val2
+ integer:: match
+ integer:: ntry1, ntry2, nval1, nval2
+ ! First sort to avoid endless logical loops.
+ if (try1 < try2) then
+ ntry1 = try1
+ ntry2 = try2
+ else
+ ntry1 = try2
+ ntry2 = try1
+ end if
+ if (val1 < val2) then
+ nval1 = val1
+ nval2 = val2
+ else
+ nval1 = val2
+ nval2 = val1
+ end if
+ if (ntry1 == nval1 .AND. ntry2 == nval2) then
+ match = 1
+ else
+ match = 0
+ end if
+ end function compare
+
+ end subroutine calculate_g4
+
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+
+ subroutine calculate_g2_prime(neighborindices, neighbornumbers, &
+ neighborpositions, g_number, g_eta, rc, cutofffn, i, ri, m, l, &
+ num_neighbors, ridge, p_gamma)
+
+ use cutoffs
+ implicit none
+ integer, dimension(num_neighbors):: neighborindices
+ integer, dimension(num_neighbors):: neighbornumbers
+ integer, dimension(1):: g_number
+ double precision, dimension(num_neighbors, 3):: &
+ neighborpositions
+ double precision, dimension(3):: ri, Rj
+ integer:: num_neighbors, m, l, i
+ double precision:: g_eta, rc
+ ! gamma parameter for the polynomial cutoff
+ double precision, optional:: p_gamma
+ character(len=20):: cutofffn
+ double precision:: ridge
+!f2py intent(in):: neighborindices, neighbornumbers
+!f2py intent(in):: neighborpositions, g_number
+!f2py intent(in):: g_eta, rc, i, ri, m, l, p_gamma
+!f2py intent(hide):: num_neighbors
+!f2py intent(out):: ridge
+ integer:: j, match, xyz
+ double precision, dimension(3):: Rij_vector
+ double precision:: Rij, term1, dRijdRml
+
+ ridge = 0.0d0
+ do j = 1, num_neighbors
+ match = compare(neighbornumbers(j), g_number(1))
+ if (match == 1) then
+ do xyz = 1, 3
+ Rj(xyz) = neighborpositions(j, xyz)
+ Rij_vector(xyz) = Rj(xyz) - ri(xyz)
+ end do
+ dRijdRml = &
+ dRij_dRml(i, neighborindices(j), ri, Rj, m, l)
+ if (dRijdRml /= 0.0d0) then
+ Rij = sqrt(dot_product(Rij_vector, Rij_vector))
+
+ if (present(p_gamma)) then
+ term1 = - 2.0d0 * g_eta * Rij * &
+ cutoff_fxn(Rij, rc, cutofffn, p_gamma) / &
+ (rc ** 2.0d0) + cutoff_fxn_prime(Rij, rc, &
+ cutofffn, p_gamma)
+ else
+ term1 = - 2.0d0 * g_eta * Rij * &
+ cutoff_fxn(Rij, rc, cutofffn) / &
+ (rc ** 2.0d0) + cutoff_fxn_prime(Rij, rc, &
+ cutofffn)
+ endif
+
+ ridge = ridge + exp(- g_eta * (Rij**2.0d0) / &
+ (rc ** 2.0d0)) * term1 * dRijdRml
+ end if
+ end if
+ end do
+
+ CONTAINS
+
+ function compare(try, val) result(match)
+! Returns 1 if try is the same set as val, 0 if not.
+ implicit none
+ integer, intent(in):: try, val
+ integer:: match
+ if (try == val) then
+ match = 1
+ else
+ match = 0
+ end if
+ end function compare
+
+
+ function dRij_dRml(i, j, Ri, Rj, m, l)
+ integer i, j, m, l
+ double precision, dimension(3):: Ri, Rj, Rij_vector
+ double precision:: dRij_dRml, Rij
+ do xyz = 1, 3
+ Rij_vector(xyz) = Rj(xyz) - Ri(xyz)
+ end do
+ Rij = sqrt(dot_product(Rij_vector, Rij_vector))
+ if ((m == i) .AND. (i /= j)) then
+ dRij_dRml = - (Rj(l + 1) - Ri(l + 1)) / Rij
+ else if ((m == j) .AND. (i /= j)) then
+ dRij_dRml = (Rj(l + 1) - Ri(l + 1)) / Rij
+ else
+ dRij_dRml = 0.0d0
+ end if
+ end function
+
+ end subroutine calculate_g2_prime
+
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+
+ subroutine calculate_g4_prime(neighborindices, neighbornumbers, &
+ neighborpositions, g_numbers, g_gamma, g_zeta, g_eta, rc, &
+ cutofffn, i, ri, m, l, num_neighbors, ridge, p_gamma)
+
+ use cutoffs
+ implicit none
+ integer, dimension(num_neighbors):: neighborindices
+ integer, dimension(num_neighbors):: neighbornumbers
+ integer, dimension(2):: g_numbers
+ double precision, dimension(num_neighbors, 3):: &
+ neighborpositions
+ double precision, dimension(3):: ri, Rj, Rk
+ integer:: num_neighbors, i, m, l
+ double precision:: g_gamma, g_zeta, g_eta, rc
+ ! gamma parameter for the polynomial cutoff
+ double precision, optional:: p_gamma
+ character(len=20):: cutofffn
+ double precision:: ridge
+!f2py intent(in):: neighbornumbers, neighborpositions
+!f2py intent(in):: g_numbers, g_gamma, g_zeta, p_gamma
+!f2py intent(in):: g_eta, rc, ri, neighborindices , i, m, l
+!f2py intent(hide):: num_neighbors
+!f2py intent(out):: ridge
+ integer:: j, k, match, xyz
+ double precision, dimension(3):: Rij_vector, Rik_vector
+ double precision, dimension(3):: Rjk_vector
+ double precision:: Rij, Rik, Rjk, costheta
+ double precision:: c1, fcRij, fcRik, fcRjk
+ double precision:: fcRijfcRikfcRjk, dCosthetadRml
+ double precision:: dRijdRml, dRikdRml, dRjkdRml
+ double precision:: term1, term2, term3, term4, term5
+ double precision:: term6
+
+ ridge = 0.0d0
+ do j = 1, num_neighbors
+ do k = (j + 1), num_neighbors
+ match = compare(neighbornumbers(j), &
+ neighbornumbers(k), g_numbers(1), g_numbers(2))
+ if (match == 1) then
+ do xyz = 1, 3
+ Rj(xyz) = neighborpositions(j, xyz)
+ Rk(xyz) = neighborpositions(k, xyz)
+ Rij_vector(xyz) = Rj(xyz) - ri(xyz)
+ Rik_vector(xyz) = Rk(xyz) - ri(xyz)
+ Rjk_vector(xyz) = Rk(xyz) - Rj(xyz)
+ end do
+ Rij = sqrt(dot_product(Rij_vector, Rij_vector))
+ Rik = sqrt(dot_product(Rik_vector, Rik_vector))
+ Rjk = sqrt(dot_product(Rjk_vector, Rjk_vector))
+ costheta = &
+ dot_product(Rij_vector, Rik_vector) / Rij / Rik
+ c1 = (1.0d0 + g_gamma * costheta)
+ if (present(p_gamma)) then
+ fcRij = cutoff_fxn(Rij, rc, cutofffn, p_gamma)
+ fcRik = cutoff_fxn(Rik, rc, cutofffn, p_gamma)
+ fcRjk = cutoff_fxn(Rjk, rc, cutofffn, p_gamma)
+ else
+ fcRij = cutoff_fxn(Rij, rc, cutofffn)
+ fcRik = cutoff_fxn(Rik, rc, cutofffn)
+ fcRjk = cutoff_fxn(Rjk, rc, cutofffn)
+ endif
+
+
+ if (g_zeta == 1.0d0) then
+ term1 = exp(-g_eta*(Rij**2 + Rik**2 + Rjk**2)&
+ / (rc ** 2.0d0))
+ else
+ term1 = (c1**(g_zeta - 1.0d0)) &
+ * exp(-g_eta*(Rij**2 + Rik**2 + Rjk**2)&
+ / (rc ** 2.0d0))
+ end if
+ term2 = 0.d0
+ fcRijfcRikfcRjk = fcRij * fcRik * fcRjk
+ dCosthetadRml = &
+ dCos_ijk_dR_ml(i, neighborindices(j), &
+ neighborindices(k), ri, Rj, Rk, m, l)
+ if (dCosthetadRml /= 0.d0) then
+ term2 = term2 + g_gamma * g_zeta * dCosthetadRml
+ end if
+ dRijdRml = &
+ dRij_dRml(i, neighborindices(j), ri, Rj, m, l)
+ if (dRijdRml /= 0.0d0) then
+ term2 = &
+ term2 - 2.0d0 * c1 * g_eta * Rij * dRijdRml &
+ / (rc ** 2.0d0)
+ end if
+ dRikdRml = &
+ dRij_dRml(i, neighborindices(k), ri, Rk, m, l)
+ if (dRikdRml /= 0.0d0) then
+ term2 = &
+ term2 - 2.0d0 * c1 * g_eta * Rik * dRikdRml &
+ / (rc ** 2.0d0)
+ end if
+ dRjkdRml = &
+ dRij_dRml(neighborindices(j), neighborindices(k), &
+ Rj, Rk, m, l)
+ if (dRjkdRml /= 0.0d0) then
+ term2 = &
+ term2 - 2.0d0 * c1 * g_eta * Rjk * dRjkdRml &
+ / (rc ** 2.0d0)
+ end if
+ term3 = fcRijfcRikfcRjk * term2
+
+ if (present(p_gamma)) then
+ term4 = &
+ cutoff_fxn_prime(Rij, rc, cutofffn, p_gamma) &
+ * dRijdRml * fcRik * fcRjk
+ term5 = &
+ fcRij * cutoff_fxn_prime(Rik, rc, cutofffn, &
+ p_gamma) * dRikdRml * fcRjk
+ term6 = &
+ fcRij * fcRik * cutoff_fxn_prime(Rjk, rc, &
+ cutofffn, p_gamma) * dRjkdRml
+ else
+ term4 = &
+ cutoff_fxn_prime(Rij, rc, cutofffn) &
+ * dRijdRml * fcRik * fcRjk
+ term5 = &
+ fcRij * cutoff_fxn_prime(Rik, rc, cutofffn) &
+ * dRikdRml * fcRjk
+ term6 = &
+ fcRij * fcRik * cutoff_fxn_prime(Rjk, rc, &
+ cutofffn) * dRjkdRml
+ endif
+ ridge = ridge + &
+ term1 * (term3 + c1 * (term4 + term5 + term6))
+ end if
+ end do
+ end do
+ ridge = ridge * (2.0d0**(1.0d0 - g_zeta))
+
+ CONTAINS
+
+
+ function compare(try1, try2, val1, val2) result(match)
+! Returns 1 if (try1, try2) is the same set as (val1, val2), 0 if not.
+ implicit none
+ integer, intent(in):: try1, try2, val1, val2
+ integer:: match
+ integer:: ntry1, ntry2, nval1, nval2
+ ! First sort to avoid endless logical loops.
+ if (try1 < try2) then
+ ntry1 = try1
+ ntry2 = try2
+ else
+ ntry1 = try2
+ ntry2 = try1
+ end if
+ if (val1 < val2) then
+ nval1 = val1
+ nval2 = val2
+ else
+ nval1 = val2
+ nval2 = val1
+ end if
+ if (ntry1 == nval1 .AND. ntry2 == nval2) then
+ match = 1
+ else
+ match = 0
+ end if
+ end function compare
+
+ function dRij_dRml(i, j, Ri, Rj, m, l)
+ integer i, j, m, l
+ double precision, dimension(3):: Ri, Rj, Rij_vector
+ double precision:: dRij_dRml, Rij
+ do xyz = 1, 3
+ Rij_vector(xyz) = Rj(xyz) - Ri(xyz)
+ end do
+ Rij = sqrt(dot_product(Rij_vector, Rij_vector))
+ if ((m == i) .AND. (i /= j)) then
+ dRij_dRml = - (Rj(l + 1) - Ri(l + 1)) / Rij
+ else if ((m == j) .AND. (i /= j)) then
+ dRij_dRml = (Rj(l + 1) - Ri(l + 1)) / Rij
+ else
+ dRij_dRml = 0.0d0
+ end if
+ end function
+
+ function dCos_ijk_dR_ml(i, j, k, ri, Rj, Rk, m, l)
+ implicit none
+ integer:: i, j, k, m, l
+ double precision:: dCos_ijk_dR_ml
+ double precision, dimension(3):: ri, Rj, Rk
+ integer, dimension(3):: dRijdRml, dRikdRml
+ double precision:: dRijdRml_, dRikdRml_
+
+ do xyz = 1, 3
+ Rij_vector(xyz) = Rj(xyz) - ri(xyz)
+ Rik_vector(xyz) = Rk(xyz) - ri(xyz)
+ end do
+ Rij = sqrt(dot_product(Rij_vector, Rij_vector))
+ Rik = sqrt(dot_product(Rik_vector, Rik_vector))
+ dCos_ijk_dR_ml = 0.0d0
+
+ dRijdRml = dRij_dRml_vector(i, j, m, l)
+ if ((dRijdRml(1) /= 0) .OR. (dRijdRml(2) /= 0) .OR. &
+ (dRijdRml(3) /= 0)) then
+ dCos_ijk_dR_ml = dCos_ijk_dR_ml + 1.0d0 / (Rij * Rik) * &
+ dot_product(dRijdRml, Rik_vector)
+ end if
+
+ dRikdRml = dRij_dRml_vector(i, k, m, l)
+ if ((dRikdRml(1) /= 0) .OR. (dRikdRml(2) /= 0) .OR. &
+ (dRikdRml(3) /= 0)) then
+ dCos_ijk_dR_ml = dCos_ijk_dR_ml + 1.0d0 / (Rij * Rik) * &
+ dot_product(dRikdRml, Rij_vector)
+ end if
+
+ dRijdRml_ = dRij_dRml(i, j, ri, Rj, m, l)
+ if (dRijdRml_ /= 0.0d0) then
+ dCos_ijk_dR_ml = dCos_ijk_dR_ml - 1.0d0 / (Rij * Rij * Rik) * &
+ dot_product(Rij_vector, Rik_vector) * dRijdRml_
+ end if
+
+ dRikdRml_ = dRij_dRml(i, k, ri, Rk, m, l)
+ if (dRikdRml_ /= 0.0d0) then
+ dCos_ijk_dR_ml = dCos_ijk_dR_ml - 1.0d0 / (Rij * Rik * Rik) * &
+ dot_product(Rij_vector, Rik_vector) * dRikdRml_
+ end if
+
+ end function
+
+ function dRij_dRml_vector(i, j, m, l)
+ implicit none
+ integer:: i, j, m, l, c1
+ integer, dimension(3):: dRij_dRml_vector
+
+ if ((m /= i) .AND. (m /= j)) then
+ dRij_dRml_vector(1) = 0
+ dRij_dRml_vector(2) = 0
+ dRij_dRml_vector(3) = 0
+ else
+ c1 = Kronecker(m, j) - Kronecker(m, i)
+ dRij_dRml_vector(1) = c1 * Kronecker(0, l)
+ dRij_dRml_vector(2) = c1 * Kronecker(1, l)
+ dRij_dRml_vector(3) = c1 * Kronecker(2, l)
+ end if
+
+ end function
+
+ function Kronecker(i, j)
+ implicit none
+ integer:: i, j
+ integer:: Kronecker
+
+ if (i == j) then
+ Kronecker = 1
+ else
+ Kronecker = 0
+ end if
+
+ end function
+
+ end subroutine calculate_g4_prime
+
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
diff --git a/amp/descriptor/gaussian.py b/amp/descriptor/gaussian.py
new file mode 100644
index 0000000..278d557
--- /dev/null
+++ b/amp/descriptor/gaussian.py
@@ -0,0 +1,1320 @@
+import numpy as np
+
+from ase.data import atomic_numbers
+from ase.calculators.calculator import Parameters
+from ..utilities import Data, Logger, importer
+from .cutoffs import Cosine, dict2cutoff
+NeighborList = importer('NeighborList')
+try:
+ from .. import fmodules
+except ImportError:
+ fmodules = None
+
+
+class Gaussian(object):
+ """Class that calculates Gaussian fingerprints (i.e., Behler-style).
+
+ Parameters
+ ----------
+ cutoff : object or float
+ Cutoff function, typically from amp.descriptor.cutoffs. Can be also
+ fed as a float representing the radius above which neighbor
+ interactions are ignored; in this case a cosine cutoff function will be
+ employed. Default is a 6.5-Angstrom cosine cutoff.
+ Gs : dict
+ Dictionary of symbols and lists of dictionaries for making symmetry
+ functions. Either auto-genetrated, or given in the following form, for
+ example:
+
+ >>> Gs = {"O": [{"type":"G2", "element":"O", "eta":10.},
+ ... {"type":"G4", "elements":["O", "Au"],
+ ... "eta":5., "gamma":1., "zeta":1.0}],
+ ... "Au": [{"type":"G2", "element":"O", "eta":2.},
+ ... {"type":"G4", "elements":["O", "Au"],
+ ... "eta":2., "gamma":1., "zeta":5.0}]}
+
+ dblabel : str
+ Optional separate prefix/location for database files, including
+ fingerprints, fingerprint derivatives, and neighborlists. This file
+ location can be shared between calculator instances to avoid
+ re-calculating redundant information. If not supplied, just uses the
+ value from label.
+ elements : list
+ List of allowed elements present in the system. If not provided, will
+ be found automatically.
+ version : str
+ Version of fingerprints.
+ fortran : bool
+ If True, will use fortran modules, if False, will not.
+ mode : str
+ Can be either 'atom-centered' or 'image-centered'.
+
+ Raises
+ ------
+ RuntimeError
+ """
+
+ def __init__(self, cutoff=Cosine(6.5), Gs=None, dblabel=None,
+ elements=None, version=None, fortran=True,
+ mode='atom-centered'):
+
+ # Check of the version of descriptor, particularly if restarting.
+ compatibleversions = ['2015.12', ]
+ if (version is not None) and version not in compatibleversions:
+ raise RuntimeError('Error: Trying to use Gaussian fingerprints'
+ ' version %s, but this module only supports'
+ ' versions %s. You may need an older or '
+ ' newer version of Amp.' %
+ (version, compatibleversions))
+ else:
+ version = compatibleversions[-1]
+
+ # Check that the mode is atom-centered.
+ if mode != 'atom-centered':
+ raise RuntimeError('Gaussian scheme only works '
+ 'in atom-centered mode. %s '
+ 'specified.' % mode)
+
+ # If the cutoff is provided as a number, Cosine function will be used
+ # by default.
+ if isinstance(cutoff, int) or isinstance(cutoff, float):
+ cutoff = Cosine(cutoff)
+ # If the cutoff is provided as a dictionary, assume we need to load it
+ # with dict2cutoff.
+ if type(cutoff) is dict:
+ cutoff = dict2cutoff(cutoff)
+
+ # The parameters dictionary contains the minimum information
+ # to produce a compatible descriptor; that is, one that gives
+ # an identical fingerprint when fed an ASE image.
+ p = self.parameters = Parameters(
+ {'importname': '.descriptor.gaussian.Gaussian',
+ 'mode': 'atom-centered'})
+ p.version = version
+ p.cutoff = cutoff.todict()
+ p.Gs = Gs
+ p.elements = elements
+
+ self.dblabel = dblabel
+ self.fortran = fortran
+ self.parent = None # Can hold a reference to main Amp instance.
+
+ def tostring(self):
+ """Returns an evaluatable representation of the calculator that can
+ be used to restart the calculator.
+ """
+ return self.parameters.tostring()
+
+ def calculate_fingerprints(self, images, parallel=None, log=None,
+ calculate_derivatives=False):
+ """Calculates the fingerpints of the images, for the ones not already
+ done.
+
+ Parameters
+ ----------
+ images : dict
+ Dictionary of images; the key is a unique ID assigned to each
+ image and each value is an ASE atoms object. Typically created
+ from amp.utilities.hash_images.
+ parallel : dict
+ Configuration for parallelization. Should be in same form as in
+ amp.Amp.
+ log : Logger object
+ Write function at which to log data. Note this must be a callable
+ function.
+ calculate_derivatives : bool
+ Decides whether or not fingerprintprimes should also be calculated.
+ """
+ if parallel is None:
+ parallel = {'cores': 1}
+ log = Logger(file=None) if log is None else log
+
+ if (self.dblabel is None) and hasattr(self.parent, 'dblabel'):
+ self.dblabel = self.parent.dblabel
+ self.dblabel = 'amp-data' if self.dblabel is None else self.dblabel
+
+ p = self.parameters
+
+ log('Cutoff function: %s' % repr(dict2cutoff(p.cutoff)))
+
+ if p.elements is None:
+ log('Finding unique set of elements in training data.')
+ p.elements = set([atom.symbol for atoms in images.values()
+ for atom in atoms])
+ p.elements = sorted(p.elements)
+ log('%i unique elements included: ' % len(p.elements) +
+ ', '.join(p.elements))
+
+ if p.Gs is None:
+ log('No symmetry functions supplied; creating defaults.')
+ p.Gs = make_default_symmetry_functions(p.elements)
+ log('Number of symmetry functions for each element:')
+ for _ in p.Gs.keys():
+ log(' %2s: %i' % (_, len(p.Gs[_])))
+ for element, fingerprints in p.Gs.items():
+ log('{} feature vector functions:'.format(element))
+ for index, fp in enumerate(fingerprints):
+ if fp['type'] == 'G2':
+ log(' {}: {}, {}, eta = {}'
+ .format(index, fp['type'], fp['element'], fp['eta']))
+ elif fp['type'] == 'G4':
+ log(' {}: {}, ({}, {}), eta={}, gamma={}, zeta={}'
+ .format(index, fp['type'], fp['elements'][0],
+ fp['elements'][1], fp['eta'], fp['gamma'],
+ fp['zeta']))
+ else:
+ log(str(fp))
+
+ log('Calculating neighborlists...', tic='nl')
+ if not hasattr(self, 'neighborlist'):
+ calc = NeighborlistCalculator(cutoff=p.cutoff['kwargs']['Rc'])
+ self.neighborlist = \
+ Data(filename='%s-neighborlists' % self.dblabel,
+ calculator=calc)
+ self.neighborlist.calculate_items(images, parallel=parallel, log=log)
+ log('...neighborlists calculated.', toc='nl')
+
+ log('Fingerprinting images...', tic='fp')
+ if not hasattr(self, 'fingerprints'):
+ calc = FingerprintCalculator(neighborlist=self.neighborlist,
+ Gs=p.Gs,
+ cutoff=p.cutoff,
+ fortran=self.fortran)
+ self.fingerprints = Data(filename='%s-fingerprints'
+ % self.dblabel,
+ calculator=calc)
+ self.fingerprints.calculate_items(images, parallel=parallel, log=log)
+ log('...fingerprints calculated.', toc='fp')
+
+ if calculate_derivatives:
+ log('Calculating fingerprint derivatives...',
+ tic='derfp')
+ if not hasattr(self, 'fingerprintprimes'):
+ calc = \
+ FingerprintPrimeCalculator(neighborlist=self.neighborlist,
+ Gs=p.Gs,
+ cutoff=p.cutoff,
+ fortran=self.fortran)
+ self.fingerprintprimes = \
+ Data(filename='%s-fingerprint-primes'
+ % self.dblabel,
+ calculator=calc)
+ self.fingerprintprimes.calculate_items(
+ images, parallel=parallel, log=log)
+ log('...fingerprint derivatives calculated.', toc='derfp')
+
+
+# Calculators #################################################################
+
+
+# Neighborlist Calculator
+class NeighborlistCalculator:
+ """For integration with .utilities.Data
+
+ For each image fed to calculate, a list of neighbors with offset distances
+ is returned.
+
+ Parameters
+ ----------
+ cutoff : float
+ Radius above which neighbor interactions are ignored.
+ """
+ def __init__(self, cutoff):
+ self.globals = Parameters({'cutoff': cutoff})
+ self.keyed = Parameters()
+ self.parallel_command = 'calculate_neighborlists'
+
+ def calculate(self, image, key):
+ """For integration with .utilities.Data
+
+ For each image fed to calculate, a list of neighbors with offset
+ distances is returned.
+
+ Parameters
+ ----------
+ image : object
+ ASE atoms object.
+ key : str
+ key of the image after being hashed.
+ """
+ cutoff = self.globals.cutoff
+ n = NeighborList(cutoffs=[cutoff / 2.] * len(image),
+ self_interaction=False,
+ bothways=True,
+ skin=0.)
+ n.update(image)
+ return [n.get_neighbors(index) for index in range(len(image))]
+
+
+class FingerprintCalculator:
+ """For integration with .utilities.Data
+
+ Parameters
+ ----------
+ neighborlist : list of str
+ List of neighbors.
+ Gs : dict
+ Dictionary of symbols and lists of dictionaries for making symmetry
+ functions. Either auto-genetrated, or given in the following form, for
+ example:
+
+ >>> Gs = {"O": [{"type":"G2", "element":"O", "eta":10.},
+ ... {"type":"G4", "elements":["O", "Au"],
+ ... "eta":5., "gamma":1., "zeta":1.0}],
+ ... "Au": [{"type":"G2", "element":"O", "eta":2.},
+ ... {"type":"G4", "elements":["O", "Au"],
+ ... "eta":2., "gamma":1., "zeta":5.0}]}
+
+ cutoff : float
+ Radius above which neighbor interactions are ignored.
+ fortran : bool
+ If True, will use fortran modules, if False, will not.
+ """
+ def __init__(self, neighborlist, Gs, cutoff, fortran):
+ self.globals = Parameters({'cutoff': cutoff,
+ 'Gs': Gs})
+ self.keyed = Parameters({'neighborlist': neighborlist})
+ self.parallel_command = 'calculate_fingerprints'
+ self.fortran = fortran
+
+ def calculate(self, image, key):
+ """Makes a list of fingerprints, one per atom, for the fed image.
+
+ Parameters
+ ----------
+ image : object
+ ASE atoms object.
+ key : str
+ key of the image after being hashed.
+ """
+ self.atoms = image
+ nl = self.keyed.neighborlist[key]
+ fingerprints = []
+ for atom in image:
+ symbol = atom.symbol
+ index = atom.index
+ neighborindices, neighboroffsets = nl[index]
+ neighborsymbols = [image[_].symbol for _ in neighborindices]
+ neighborpositions = \
+ [image.positions[neighbor] + np.dot(offset, image.cell)
+ for (neighbor, offset) in zip(neighborindices,
+ neighboroffsets)]
+ indexfp = self.get_fingerprint(
+ index, symbol, neighborsymbols, neighborpositions)
+ fingerprints.append(indexfp)
+
+ return fingerprints
+
+ def get_fingerprint(self, index, symbol,
+ neighborsymbols, neighborpositions):
+ """Returns the fingerprint of symmetry function values for atom
+ specified by its index and symbol.
+
+ neighborsymbols and neighborpositions are lists of neighbors' symbols
+ and Cartesian positions, respectively.
+
+ Parameters
+ ----------
+ index : int
+ Index of the center atom.
+ symbol : str
+ Symbol of the center atom.
+ neighborsymbols : list of str
+ List of neighbors' symbols.
+ neighborpositions : list of list of float
+ List of Cartesian atomic positions.
+
+ Returns
+ -------
+ symbol, fingerprint : list of float
+ fingerprints for atom specified by its index and symbol.
+ """
+ Ri = self.atoms[index].position
+
+ num_symmetries = len(self.globals.Gs[symbol])
+ fingerprint = [None] * num_symmetries
+
+ for count in range(num_symmetries):
+ G = self.globals.Gs[symbol][count]
+
+ if G['type'] == 'G2':
+ ridge = calculate_G2(neighborsymbols, neighborpositions,
+ G['element'], G['eta'],
+ self.globals.cutoff, Ri, self.fortran)
+ elif G['type'] == 'G4':
+ ridge = calculate_G4(neighborsymbols, neighborpositions,
+ G['elements'], G['gamma'],
+ G['zeta'], G['eta'], self.globals.cutoff,
+ Ri, self.fortran)
+ else:
+ raise NotImplementedError('Unknown G type: %s' % G['type'])
+ fingerprint[count] = ridge
+
+ return symbol, fingerprint
+
+
+class FingerprintPrimeCalculator:
+ """For integration with .utilities.Data
+
+ Parameters
+ ----------
+ neighborlist : list of str
+ List of neighbors.
+ Gs : dict
+ Dictionary of symbols and lists of dictionaries for making symmetry
+ functions. Either auto-genetrated, or given in the following form, for
+ example:
+
+ >>> Gs = {"O": [{"type":"G2", "element":"O", "eta":10.},
+ ... {"type":"G4", "elements":["O", "Au"],
+ ... "eta":5., "gamma":1., "zeta":1.0}],
+ ... "Au": [{"type":"G2", "element":"O", "eta":2.},
+ ... {"type":"G4", "elements":["O", "Au"],
+ ... "eta":2., "gamma":1., "zeta":5.0}]}
+
+ cutoff : float
+ Radius above which neighbor interactions are ignored.
+ fortran : bool
+ If True, will use fortran modules, if False, will not.
+ """
+
+ def __init__(self, neighborlist, Gs, cutoff, fortran):
+ self.globals = Parameters({'cutoff': cutoff,
+ 'Gs': Gs})
+ self.keyed = Parameters({'neighborlist': neighborlist})
+ self.parallel_command = 'calculate_fingerprint_primes'
+ self.fortran = fortran
+
+ def calculate(self, image, key):
+ """Makes a list of fingerprint derivatives, one per atom,
+ for the fed image.
+
+ Parameters
+ ----------
+ image : object
+ ASE atoms object.
+ key : str
+ key of the image after being hashed.
+ """
+ self.atoms = image
+ nl = self.keyed.neighborlist[key]
+ fingerprintprimes = {}
+ for atom in image:
+ selfsymbol = atom.symbol
+ selfindex = atom.index
+ selfneighborindices, selfneighboroffsets = nl[selfindex]
+ selfneighborsymbols = [
+ image[_].symbol for _ in selfneighborindices]
+
+ selfneighborpositions = [image.positions[_index] +
+ np.dot(_offset, image.get_cell())
+ for _index, _offset
+ in zip(selfneighborindices,
+ selfneighboroffsets)]
+
+ for i in range(3):
+ # Calculating derivative of fingerprints of self atom w.r.t.
+ # coordinates of itself.
+ fpprime = self.get_fingerprintprime(
+ selfindex, selfsymbol,
+ selfneighborindices,
+ selfneighborsymbols,
+ selfneighborpositions, selfindex, i)
+
+ fingerprintprimes[
+ (selfindex, selfsymbol, selfindex, selfsymbol, i)] = \
+ fpprime
+ # Calculating derivative of fingerprints of neighbor atom
+ # w.r.t. coordinates of self atom.
+ for nindex, nsymbol, noffset in \
+ zip(selfneighborindices,
+ selfneighborsymbols,
+ selfneighboroffsets):
+ # for calculating forces, summation runs over neighbor
+ # atoms of type II (within the main cell only)
+ if noffset.all() == 0:
+ nneighborindices, nneighboroffsets = nl[nindex]
+ nneighborsymbols = \
+ [image[_].symbol for _ in nneighborindices]
+
+ neighborpositions = [image.positions[_index] +
+ np.dot(_offset, image.get_cell())
+ for _index, _offset
+ in zip(nneighborindices,
+ nneighboroffsets)]
+
+ # for calculating derivatives of fingerprints,
+ # summation runs over neighboring atoms of type
+ # I (either inside or outside the main cell)
+ fpprime = self.get_fingerprintprime(
+ nindex, nsymbol,
+ nneighborindices,
+ nneighborsymbols,
+ neighborpositions, selfindex, i)
+
+ fingerprintprimes[
+ (selfindex, selfsymbol, nindex, nsymbol, i)] = \
+ fpprime
+
+ return fingerprintprimes
+
+ def get_fingerprintprime(self, index, symbol,
+ neighborindices,
+ neighborsymbols,
+ neighborpositions,
+ m, l):
+ """ Returns the value of the derivative of G for atom with index and
+ symbol with respect to coordinate x_{l} of atom index m.
+
+ neighborindices, neighborsymbols and neighborpositions are lists of
+ neighbors' indices, symbols and Cartesian positions, respectively.
+
+ Parameters
+ ----------
+ index : int
+ Index of the center atom.
+ symbol : str
+ Symbol of the center atom.
+ neighborindices : list of int
+ List of neighbors' indices.
+ neighborsymbols : list of str
+ List of neighbors' symbols.
+ neighborpositions : list of list of float
+ List of Cartesian atomic positions.
+ m : int
+ Index of the pair atom.
+ l : int
+ Direction of the derivative; is an integer from 0 to 2.
+
+ Returns
+ -------
+ fingerprintprime : list of float
+ The value of the derivative of the fingerprints for atom with index
+ and symbol with respect to coordinate x_{l} of atom index m.
+ """
+
+ num_symmetries = len(self.globals.Gs[symbol])
+ Rindex = self.atoms.positions[index]
+ fingerprintprime = [None] * num_symmetries
+
+ for count in range(num_symmetries):
+ G = self.globals.Gs[symbol][count]
+ if G['type'] == 'G2':
+ ridge = calculate_G2_prime(
+ neighborindices,
+ neighborsymbols,
+ neighborpositions,
+ G['element'],
+ G['eta'],
+ self.globals.cutoff,
+ index,
+ Rindex,
+ m,
+ l,
+ self.fortran)
+ elif G['type'] == 'G4':
+ ridge = calculate_G4_prime(
+ neighborindices,
+ neighborsymbols,
+ neighborpositions,
+ G['elements'],
+ G['gamma'],
+ G['zeta'],
+ G['eta'],
+ self.globals.cutoff,
+ index,
+ Rindex,
+ m,
+ l,
+ self.fortran)
+ else:
+ raise NotImplementedError('Unknown G type: %s' % G['type'])
+
+ fingerprintprime[count] = ridge
+
+ return fingerprintprime
+
+# Auxiliary functions #########################################################
+
+
+def calculate_G2(neighborsymbols,
+ neighborpositions, G_element, eta, cutoff, Ri, fortran):
+ """Calculate G2 symmetry function.
+
+ Ideally this will not be used but will be a template for how to build the
+ fortran version (and serves as a slow backup if the fortran one goes
+ uncompiled). See Eq. 13a of the supplementary information of Khorshidi,
+ Peterson, CPC(2016).
+
+ Parameters
+ ----------
+ neighborsymbols : list of str
+ List of symbols of all neighbor atoms.
+ neighborpositions : list of list of floats
+ List of Cartesian atomic positions.
+ G_element : str
+ Chemical symbol of the center atom.
+ eta : float
+ Parameter of Gaussian symmetry functions.
+ cutoff : dict
+ Cutoff function, typically from amp.descriptor.cutoffs. Should be also
+ formatted as a dictionary by todict method, e.g.
+ cutoff=Cosine(6.5).todict()
+ Ri : list
+ Position of the center atom. Should be fed as a list of three floats.
+ fortran : bool
+ If True, will use the fortran subroutines, else will not.
+
+ Returns
+ -------
+ ridge : float
+ G2 fingerprint.
+ """
+ if fortran: # fortran version; faster
+ G_number = [atomic_numbers[G_element]]
+ neighbornumbers = \
+ [atomic_numbers[symbol] for symbol in neighborsymbols]
+ if len(neighbornumbers) == 0:
+ ridge = 0.
+ else:
+
+ cutofffn = cutoff['name']
+ Rc = cutoff['kwargs']['Rc']
+
+ args_calculate_g2 = dict(
+ neighbornumbers=neighbornumbers,
+ neighborpositions=neighborpositions,
+ g_number=G_number,
+ g_eta=eta,
+ rc=Rc,
+ cutofffn=cutofffn,
+ ri=Ri
+ )
+ if cutofffn == 'Polynomial':
+ args_calculate_g2['p_gamma'] = cutoff['kwargs']['gamma']
+
+ ridge = fmodules.calculate_g2(**args_calculate_g2)
+
+ else:
+ Rc = cutoff['kwargs']['Rc']
+ cutoff_fxn = dict2cutoff(cutoff)
+ ridge = 0. # One aspect of a fingerprint :)
+ num_neighbors = len(neighborpositions) # number of neighboring atoms
+ for count in range(num_neighbors):
+ symbol = neighborsymbols[count]
+ Rj = neighborpositions[count]
+ if symbol == G_element:
+ Rij = np.linalg.norm(Rj - Ri)
+ args_cutoff_fxn = dict(Rij=Rij)
+ if cutoff['name'] == 'Polynomial':
+ args_cutoff_fxn['gamma'] = cutoff['kwargs']['gamma']
+ ridge += (np.exp(-eta * (Rij ** 2.) / (Rc ** 2.)) *
+ cutoff_fxn(**args_cutoff_fxn))
+ return ridge
+
+
+def calculate_G4(neighborsymbols, neighborpositions,
+ G_elements, gamma, zeta, eta, cutoff,
+ Ri, fortran):
+ """Calculate G4 symmetry function.
+
+ Ideally this will not be used but will be a template for how to build the
+ fortran version (and serves as a slow backup if the fortran one goes
+ uncompiled). See Eq. 13c of the supplementary information of Khorshidi,
+ Peterson, CPC(2016).
+
+ Parameters
+ ----------
+ neighborsymbols : list of str
+ List of symbols of neighboring atoms.
+ neighborpositions : list of list of floats
+ List of Cartesian atomic positions of neighboring atoms.
+ G_elements : list of str
+ A list of two members, each member is the chemical species of one of
+ the neighboring atoms forming the triangle with the center atom.
+ gamma : float
+ Parameter of Gaussian symmetry functions.
+ zeta : float
+ Parameter of Gaussian symmetry functions.
+ eta : float
+ Parameter of Gaussian symmetry functions.
+ cutoff : dict
+ Cutoff function, typically from amp.descriptor.cutoffs. Should be also
+ formatted as a dictionary by todict method, e.g.
+ cutoff=Cosine(6.5).todict()
+ Ri : list
+ Position of the center atom. Should be fed as a list of three floats.
+ fortran : bool
+ If True, will use the fortran subroutines, else will not.
+
+ Returns
+ -------
+ ridge : float
+ G4 fingerprint.
+ """
+ if fortran: # fortran version; faster
+ G_numbers = sorted([atomic_numbers[el] for el in G_elements])
+ neighbornumbers = \
+ [atomic_numbers[symbol] for symbol in neighborsymbols]
+ if len(neighborpositions) == 0:
+ return 0.
+ else:
+ cutofffn = cutoff['name']
+ Rc = cutoff['kwargs']['Rc']
+
+ args_calculate_g4 = dict(
+ neighbornumbers=neighbornumbers,
+ neighborpositions=neighborpositions,
+ g_numbers=G_numbers,
+ g_gamma=gamma,
+ g_zeta=zeta,
+ g_eta=eta,
+ rc=Rc,
+ cutofffn=cutofffn,
+ ri=Ri
+ )
+ if cutofffn == 'Polynomial':
+ args_calculate_g4['p_gamma'] = cutoff['kwargs']['gamma']
+
+ ridge = fmodules.calculate_g4(**args_calculate_g4)
+ return ridge
+ else:
+ Rc = cutoff['kwargs']['Rc']
+ cutoff_fxn = dict2cutoff(cutoff)
+ ridge = 0.
+ counts = range(len(neighborpositions))
+ for j in counts:
+ for k in counts[(j + 1):]:
+ els = sorted([neighborsymbols[j], neighborsymbols[k]])
+ if els != G_elements:
+ continue
+ Rij_vector = neighborpositions[j] - Ri
+ Rij = np.linalg.norm(Rij_vector)
+ Rik_vector = neighborpositions[k] - Ri
+ Rik = np.linalg.norm(Rik_vector)
+ Rjk_vector = neighborpositions[k] - neighborpositions[j]
+ Rjk = np.linalg.norm(Rjk_vector)
+ cos_theta_ijk = np.dot(Rij_vector, Rik_vector) / Rij / Rik
+ term = (1. + gamma * cos_theta_ijk) ** zeta
+ term *= np.exp(-eta * (Rij ** 2. + Rik ** 2. + Rjk ** 2.) /
+ (Rc ** 2.))
+ _Rij = dict(Rij=Rij)
+ _Rik = dict(Rij=Rik)
+ _Rjk = dict(Rij=Rjk)
+ if cutoff['name'] == 'Polynomial':
+ _Rij['gamma'] = cutoff['kwargs']['gamma']
+ _Rik['gamma'] = cutoff['kwargs']['gamma']
+ _Rjk['gamma'] = cutoff['kwargs']['gamma']
+ term *= cutoff_fxn(**_Rij)
+ term *= cutoff_fxn(**_Rik)
+ term *= cutoff_fxn(**_Rjk)
+ ridge += term
+ ridge *= 2. ** (1. - zeta)
+ return ridge
+
+
+def make_symmetry_functions(elements, type, etas, zetas=None, gammas=None):
+ """Helper function to create Gaussian symmetry functions.
+ Returns a list of dictionaries with symmetry function parameters
+ in the format expected by the Gaussian class.
+
+ Parameters
+ ----------
+ elements : list of str
+ List of element types. The first in the list is considered the
+ central element for this fingerprint. #FIXME: Does that matter?
+ type : str
+ Either G2 or G4.
+ etas : list of floats
+ eta values to use in G2 or G4 fingerprints
+ zetas : list of floats
+ zeta values to use in G4 fingerprints
+ gammas : list of floats
+ gamma values to use in G4 fingerprints
+
+ Returns
+ -------
+ G : list of dicts
+ A list, each item in the list contains a dictionary of fingerprint
+ parameters.
+ """
+ if type == 'G2':
+ G = [{'type': 'G2', 'element': element, 'eta': eta}
+ for eta in etas
+ for element in elements]
+ return G
+ elif type == 'G4':
+ G = []
+ for eta in etas:
+ for zeta in zetas:
+ for gamma in gammas:
+ for i1, el1 in enumerate(elements):
+ for el2 in elements[i1:]:
+ els = sorted([el1, el2])
+ G.append({'type': 'G4',
+ 'elements': els,
+ 'eta': eta,
+ 'gamma': gamma,
+ 'zeta': zeta})
+ return G
+ raise NotImplementedError('Unknown type: {}.'.format(type))
+
+
+def make_default_symmetry_functions(elements):
+ """Makes symmetry functions as in Nano Letters 14:2670, 2014.
+
+
+ Parameters
+ ----------
+ elements : list of str
+ List of the elements, as in: ["C", "O", "H", "Cu"].
+
+ Returns
+ -------
+ G : dict of lists
+ The generated symmetry function parameters.
+ """
+ G = {}
+ for element0 in elements:
+
+ # Radial symmetry functions.
+ etas = [0.05, 4., 20., 80.]
+ _G = [{'type': 'G2', 'element': element, 'eta': eta}
+ for eta in etas
+ for element in elements]
+
+ # Angular symmetry functions.
+ etas = [0.005]
+ zetas = [1., 4.]
+ gammas = [+1., -1.]
+ for eta in etas:
+ for zeta in zetas:
+ for gamma in gammas:
+ for i1, el1 in enumerate(elements):
+ for el2 in elements[i1:]:
+ els = sorted([el1, el2])
+ _G.append({'type': 'G4',
+ 'elements': els,
+ 'eta': eta,
+ 'gamma': gamma,
+ 'zeta': zeta})
+
+ G[element0] = _G
+ return G
+
+
+def Kronecker(i, j):
+ """Kronecker delta function.
+
+ Parameters
+ ----------
+ i : int
+ First index of Kronecker delta.
+ j : int
+ Second index of Kronecker delta.
+
+ Returns
+ -------
+ int
+ The value of the Kronecker delta.
+ """
+ if i == j:
+ return 1
+ else:
+ return 0
+
+
+def dRij_dRml_vector(i, j, m, l):
+ """Returns the derivative of the position vector R_{ij} with respect to
+ x_{l} of itomic index m.
+
+ See Eq. 14d of the supplementary information of Khorshidi, Peterson,
+ CPC(2016).
+
+ Parameters
+ ----------
+ i : int
+ Index of the first atom.
+ j : int
+ Index of the second atom.
+ m : int
+ Index of the atom force is acting on.
+ l : int
+ Direction of force.
+
+ Returns
+ -------
+ list of float
+ The derivative of the position vector R_{ij} with respect to x_{l} of
+ atomic index m.
+ """
+ if (m != i) and (m != j):
+ return [0, 0, 0]
+ else:
+ dRij_dRml_vector = [None, None, None]
+ c1 = Kronecker(m, j) - Kronecker(m, i)
+ dRij_dRml_vector[0] = c1 * Kronecker(0, l)
+ dRij_dRml_vector[1] = c1 * Kronecker(1, l)
+ dRij_dRml_vector[2] = c1 * Kronecker(2, l)
+ return dRij_dRml_vector
+
+
+def dRij_dRml(i, j, Ri, Rj, m, l):
+ """Returns the derivative of the norm of position vector R_{ij} with
+ respect to coordinate x_{l} of atomic index m.
+
+ See Eq. 14c of the supplementary information of Khorshidi, Peterson,
+ CPC(2016).
+
+ Parameters
+ ----------
+ i : int
+ Index of the first atom.
+ j : int
+ Index of the second atom.
+ Ri : float
+ Position of the first atom.
+ Rj : float
+ Position of the second atom.
+ m : int
+ Index of the atom force is acting on.
+ l : int
+ Direction of force.
+
+ Returns
+ -------
+ dRij_dRml : list of float
+ The derivative of the noRi of position vector R_{ij} with respect to
+ x_{l} of atomic index m.
+ """
+ Rij = np.linalg.norm(Rj - Ri)
+ if m == i and i != j: # i != j is necessary for periodic systems
+ dRij_dRml = -(Rj[l] - Ri[l]) / Rij
+ elif m == j and i != j: # i != j is necessary for periodic systems
+ dRij_dRml = (Rj[l] - Ri[l]) / Rij
+ else:
+ dRij_dRml = 0
+ return dRij_dRml
+
+
+def dCos_theta_ijk_dR_ml(i, j, k, Ri, Rj, Rk, m, l):
+ """Returns the derivative of Cos(theta_{ijk}) with respect to
+ x_{l} of atomic index m.
+
+ See Eq. 14f of the supplementary information of Khorshidi, Peterson,
+ CPC(2016).
+
+ Parameters
+ ----------
+ i : int
+ Index of the center atom.
+ j : int
+ Index of the first atom.
+ k : int
+ Index of the second atom.
+ Ri : float
+ Position of the center atom.
+ Rj : float
+ Position of the first atom.
+ Rk : float
+ Position of the second atom.
+ m : int
+ Index of the atom force is acting on.
+ l : int
+ Direction of force.
+
+ Returns
+ -------
+ dCos_theta_ijk_dR_ml : float
+ Derivative of Cos(theta_{ijk}) with respect to x_{l} of atomic index m.
+ """
+ Rij_vector = Rj - Ri
+ Rij = np.linalg.norm(Rij_vector)
+ Rik_vector = Rk - Ri
+ Rik = np.linalg.norm(Rik_vector)
+ dCos_theta_ijk_dR_ml = 0
+
+ dRijdRml = dRij_dRml_vector(i, j, m, l)
+ if np.array(dRijdRml).any() != 0:
+ dCos_theta_ijk_dR_ml += np.dot(dRijdRml, Rik_vector) / (Rij * Rik)
+
+ dRikdRml = dRij_dRml_vector(i, k, m, l)
+ if np.array(dRikdRml).any() != 0:
+ dCos_theta_ijk_dR_ml += np.dot(Rij_vector, dRikdRml) / (Rij * Rik)
+
+ dRijdRml = dRij_dRml(i, j, Ri, Rj, m, l)
+ if dRijdRml != 0:
+ dCos_theta_ijk_dR_ml += - np.dot(Rij_vector, Rik_vector) * dRijdRml / \
+ ((Rij ** 2.) * Rik)
+
+ dRikdRml = dRij_dRml(i, k, Ri, Rk, m, l)
+ if dRikdRml != 0:
+ dCos_theta_ijk_dR_ml += - np.dot(Rij_vector, Rik_vector) * dRikdRml / \
+ (Rij * (Rik ** 2.))
+ return dCos_theta_ijk_dR_ml
+
+
+def calculate_G2_prime(neighborindices, neighborsymbols, neighborpositions,
+ G_element, eta, cutoff,
+ i, Ri, m, l, fortran):
+ """Calculates coordinate derivative of G2 symmetry function for atom at
+ index i and position Ri with respect to coordinate x_{l} of atom index
+ m.
+
+ See Eq. 13b of the supplementary information of Khorshidi, Peterson,
+ CPC(2016).
+
+ Parameters
+ ---------
+ neighborindices : list of int
+ List of int of neighboring atoms.
+ neighborsymbols : list of str
+ List of symbols of neighboring atoms.
+ neighborpositions : list of list of float
+ List of Cartesian atomic positions of neighboring atoms.
+ G_element : dict
+ Symmetry functions of the center atom.
+ eta : float
+ Parameter of Behler symmetry functions.
+ cutoff : dict
+ Cutoff function, typically from amp.descriptor.cutoffs. Should be also
+ formatted as a dictionary by todict method, e.g.
+ cutoff=Cosine(6.5).todict()
+ i : int
+ Index of the center atom.
+ Ri : list
+ Position of the center atom. Should be fed as a list of three floats.
+ m : int
+ Index of the atom force is acting on.
+ l : int
+ Direction of force.
+ fortran : bool
+ If True, will use the fortran subroutines, else will not.
+
+ Returns
+ -------
+ ridge : float
+ Coordinate derivative of G2 symmetry function for atom at index a and
+ position Ri with respect to coordinate x_{l} of atom index m.
+ """
+ if fortran: # fortran version; faster
+ G_number = [atomic_numbers[G_element]]
+ neighbornumbers = \
+ [atomic_numbers[symbol] for symbol in neighborsymbols]
+ if len(neighborpositions) == 0:
+ ridge = 0.
+ else:
+ cutofffn = cutoff['name']
+ Rc = cutoff['kwargs']['Rc']
+
+ args_calculate_g2_prime = dict(
+ neighborindices=list(neighborindices),
+ neighbornumbers=neighbornumbers,
+ neighborpositions=neighborpositions,
+ g_number=G_number,
+ g_eta=eta,
+ rc=Rc,
+ cutofffn=cutofffn,
+ i=i,
+ ri=Ri,
+ m=m,
+ l=l
+ )
+ if cutofffn == 'Polynomial':
+ args_calculate_g2_prime['p_gamma'] = cutoff['kwargs']['gamma']
+
+ ridge = fmodules.calculate_g2_prime(**args_calculate_g2_prime)
+ else:
+ Rc = cutoff['kwargs']['Rc']
+ cutoff_fxn = dict2cutoff(cutoff)
+ ridge = 0. # One aspect of a fingerprint :)
+ num_neighbors = len(neighborpositions) # number of neighboring atoms
+ for count in range(num_neighbors):
+ symbol = neighborsymbols[count]
+ Rj = neighborpositions[count]
+ j = neighborindices[count]
+ if symbol == G_element:
+ dRijdRml = dRij_dRml(i, j, Ri, Rj, m, l)
+ if dRijdRml != 0:
+ Rij = np.linalg.norm(Rj - Ri)
+ args_cutoff_fxn = dict(Rij=Rij)
+ if cutoff['name'] == 'Polynomial':
+ args_cutoff_fxn['gamma'] = cutoff['kwargs']['gamma']
+ term1 = (-2. * eta * Rij * cutoff_fxn(**args_cutoff_fxn) /
+ (Rc ** 2.) +
+ cutoff_fxn.prime(**args_cutoff_fxn))
+ ridge += np.exp(- eta * (Rij ** 2.) / (Rc ** 2.)) * \
+ term1 * dRijdRml
+
+ return ridge
+
+
+def calculate_G4_prime(neighborindices, neighborsymbols, neighborpositions,
+ G_elements, gamma, zeta, eta,
+ cutoff, i, Ri, m, l, fortran):
+ """Calculates coordinate derivative of G4 symmetry function for atom at
+ index i and position Ri with respect to coordinate x_{l} of atom index m.
+
+ See Eq. 13d of the supplementary information of Khorshidi, Peterson,
+ CPC(2016).
+
+ Parameters
+ ----------
+ neighborindices : list of int
+ List of int of neighboring atoms.
+ neighborsymbols : list of str
+ List of symbols of neighboring atoms.
+ neighborpositions : list of list of float
+ List of Cartesian atomic positions of neighboring atoms.
+ G_elements : list of str
+ A list of two members, each member is the chemical species of one of
+ the neighboring atoms forming the triangle with the center atom.
+ gamma : float
+ Parameter of Behler symmetry functions.
+ zeta : float
+ Parameter of Behler symmetry functions.
+ eta : float
+ Parameter of Behler symmetry functions.
+ cutoff : dict
+ Cutoff function, typically from amp.descriptor.cutoffs. Should be also
+ formatted as a dictionary by todict method, e.g.
+ cutoff=Cosine(6.5).todict()
+ i : int
+ Index of the center atom.
+ Ri : list
+ Position of the center atom. Should be fed as a list of three floats.
+ m : int
+ Index of the atom force is acting on.
+ l : int
+ Direction of force.
+ fortran : bool
+ If True, will use the fortran subroutines, else will not.
+
+ Returns
+ -------
+ ridge : float
+ Coordinate derivative of G4 symmetry function for atom at index i and
+ position Ri with respect to coordinate x_{l} of atom index m.
+ """
+ if fortran: # fortran version; faster
+ G_numbers = sorted([atomic_numbers[el] for el in G_elements])
+ neighbornumbers = [atomic_numbers[symbol]
+ for symbol in neighborsymbols]
+ if len(neighborpositions) == 0:
+ ridge = 0.
+ else:
+ cutofffn = cutoff['name']
+ Rc = cutoff['kwargs']['Rc']
+
+ args_calculate_g4_prime = dict(
+ neighborindices=list(neighborindices),
+ neighbornumbers=neighbornumbers,
+ neighborpositions=neighborpositions,
+ g_numbers=G_numbers,
+ g_gamma=gamma,
+ g_zeta=zeta,
+ g_eta=eta,
+ rc=Rc,
+ cutofffn=cutofffn,
+ i=i,
+ ri=Ri,
+ m=m,
+ l=l
+ )
+ if cutofffn == 'Polynomial':
+ args_calculate_g4_prime['p_gamma'] = cutoff['kwargs']['gamma']
+
+ ridge = fmodules.calculate_g4_prime(**args_calculate_g4_prime)
+ else:
+ Rc = cutoff['kwargs']['Rc']
+ cutoff_fxn = dict2cutoff(cutoff)
+ ridge = 0.
+ # number of neighboring atoms
+ counts = range(len(neighborpositions))
+ for j in counts:
+ for k in counts[(j + 1):]:
+ els = sorted([neighborsymbols[j], neighborsymbols[k]])
+ if els != G_elements:
+ continue
+ Rj = neighborpositions[j]
+ Rk = neighborpositions[k]
+ Rij_vector = neighborpositions[j] - Ri
+ Rij = np.linalg.norm(Rij_vector)
+ Rik_vector = neighborpositions[k] - Ri
+ Rik = np.linalg.norm(Rik_vector)
+ Rjk_vector = neighborpositions[k] - neighborpositions[j]
+ Rjk = np.linalg.norm(Rjk_vector)
+ cos_theta_ijk = np.dot(Rij_vector, Rik_vector) / Rij / Rik
+ c1 = (1. + gamma * cos_theta_ijk)
+
+ _Rij = dict(Rij=Rij)
+ _Rik = dict(Rij=Rik)
+ _Rjk = dict(Rij=Rjk)
+ if cutoff['name'] == 'Polynomial':
+ _Rij['gamma'] = cutoff['kwargs']['gamma']
+ _Rik['gamma'] = cutoff['kwargs']['gamma']
+ _Rjk['gamma'] = cutoff['kwargs']['gamma']
+
+ fcRij = cutoff_fxn(**_Rij)
+ fcRik = cutoff_fxn(**_Rik)
+ fcRjk = cutoff_fxn(**_Rjk)
+ if zeta == 1:
+ term1 = \
+ np.exp(- eta * (Rij ** 2. + Rik ** 2. + Rjk ** 2.) /
+ (Rc ** 2.))
+ else:
+ term1 = c1 ** (zeta - 1.) * \
+ np.exp(- eta * (Rij ** 2. + Rik ** 2. + Rjk ** 2.) /
+ (Rc ** 2.))
+ term2 = 0.
+ fcRijfcRikfcRjk = fcRij * fcRik * fcRjk
+ dCosthetadRml = dCos_theta_ijk_dR_ml(i,
+ neighborindices[j],
+ neighborindices[k],
+ Ri, Rj,
+ Rk, m, l)
+ if dCosthetadRml != 0:
+ term2 += gamma * zeta * dCosthetadRml
+ dRijdRml = dRij_dRml(i, neighborindices[j], Ri, Rj, m, l)
+ if dRijdRml != 0:
+ term2 += -2. * c1 * eta * Rij * dRijdRml / (Rc ** 2.)
+ dRikdRml = dRij_dRml(i, neighborindices[k], Ri, Rk, m, l)
+ if dRikdRml != 0:
+ term2 += -2. * c1 * eta * Rik * dRikdRml / (Rc ** 2.)
+ dRjkdRml = dRij_dRml(neighborindices[j],
+ neighborindices[k],
+ Rj, Rk, m, l)
+ if dRjkdRml != 0:
+ term2 += -2. * c1 * eta * Rjk * dRjkdRml / (Rc ** 2.)
+ term3 = fcRijfcRikfcRjk * term2
+ term4 = cutoff_fxn.prime(**_Rij) * dRijdRml * fcRik * fcRjk
+ term5 = fcRij * cutoff_fxn.prime(**_Rik) * dRikdRml * fcRjk
+ term6 = fcRij * fcRik * cutoff_fxn.prime(**_Rjk) * dRjkdRml
+
+ ridge += term1 * (term3 + c1 * (term4 + term5 + term6))
+
+ ridge *= 2. ** (1. - zeta)
+
+ return ridge
+
+if __name__ == "__main__":
+ """Directly calling this module; apparently from another node.
+
+ Calls should come as
+
+ python -m amp.descriptor.gaussian id hostname:port
+
+ This session will then start a zmq session with that socket, labeling
+ itself with id. Instructions on what to do will come from the socket.
+ """
+ import sys
+ import tempfile
+ import zmq
+ from ..utilities import MessageDictionary
+
+ fortran = False if fmodules is None else True
+ hostsocket = sys.argv[-1]
+ proc_id = sys.argv[-2]
+ msg = MessageDictionary(proc_id)
+
+ # Send standard lines to stdout signaling process started and where
+ # error is directed. This should be caught by pxssh. (This could
+ # alternatively be done by zmq, but this works.)
+ print('<amp-connect>') # Signal that program started.
+ sys.stderr = tempfile.NamedTemporaryFile(mode='w', delete=False,
+ suffix='.stderr')
+ print('Log and error written to %s<stderr>' % sys.stderr.name)
+ sys.stderr.write('initiated\n')
+ sys.stderr.flush()
+
+ # Establish client session via zmq; find purpose.
+ context = zmq.Context()
+ sys.stderr.write('context started\n')
+ sys.stderr.flush()
+ socket = context.socket(zmq.REQ)
+ sys.stderr.write('socket started\n')
+ sys.stderr.flush()
+ socket.connect('tcp://%s' % hostsocket)
+ sys.stderr.write('connection made\n')
+ sys.stderr.flush()
+ socket.send_pyobj(msg('<purpose>'))
+ sys.stderr.write('message sent\n')
+ sys.stderr.flush()
+ purpose = socket.recv_pyobj()
+ sys.stderr.write('purpose received\n')
+ sys.stderr.flush()
+ sys.stderr.write('purpose: %s \n' % purpose)
+ sys.stderr.flush()
+
+ if purpose == 'calculate_neighborlists':
+ # Request variables.
+ socket.send_pyobj(msg('<request>', 'cutoff'))
+ cutoff = socket.recv_pyobj()
+ socket.send_pyobj(msg('<request>', 'images'))
+ images = socket.recv_pyobj()
+ # sys.stderr.write(str(images)) # Just to see if they are there.
+
+ # Perform the calculations.
+ calc = NeighborlistCalculator(cutoff=cutoff)
+ neighborlist = {}
+ # for key in images.iterkeys():
+ while len(images) > 0:
+ key, image = images.popitem() # Reduce memory.
+ neighborlist[key] = calc.calculate(image, key)
+
+ # Send the results.
+ socket.send_pyobj(msg('<result>', neighborlist))
+ socket.recv_string() # Needed to complete REQ/REP.
+
+ elif purpose == 'calculate_fingerprints':
+ # Request variables.
+ socket.send_pyobj(msg('<request>', 'cutoff'))
+ cutoff = socket.recv_pyobj()
+ socket.send_pyobj(msg('<request>', 'Gs'))
+ Gs = socket.recv_pyobj()
+ socket.send_pyobj(msg('<request>', 'neighborlist'))
+ neighborlist = socket.recv_pyobj()
+ socket.send_pyobj(msg('<request>', 'images'))
+ images = socket.recv_pyobj()
+
+ calc = FingerprintCalculator(neighborlist, Gs, cutoff,
+ fortran)
+ result = {}
+ while len(images) > 0:
+ key, image = images.popitem() # Reduce memory.
+ result[key] = calc.calculate(image, key)
+ if len(images) % 100 == 0:
+ socket.send_pyobj(msg('<info>', len(images)))
+ socket.recv_string() # Needed to complete REQ/REP.
+
+ # Send the results.
+ socket.send_pyobj(msg('<result>', result))
+ socket.recv_string() # Needed to complete REQ/REP.
+
+ elif purpose == 'calculate_fingerprint_primes':
+ # Request variables.
+ socket.send_pyobj(msg('<request>', 'cutoff'))
+ cutoff = socket.recv_pyobj()
+ socket.send_pyobj(msg('<request>', 'Gs'))
+ Gs = socket.recv_pyobj()
+ socket.send_pyobj(msg('<request>', 'neighborlist'))
+ neighborlist = socket.recv_pyobj()
+ socket.send_pyobj(msg('<request>', 'images'))
+ images = socket.recv_pyobj()
+
+ calc = FingerprintPrimeCalculator(neighborlist, Gs, cutoff,
+ fortran)
+ result = {}
+ while len(images) > 0:
+ key, image = images.popitem() # Reduce memory.
+ result[key] = calc.calculate(image, key)
+ if len(images) % 100 == 0:
+ socket.send_pyobj(msg('<info>', len(images)))
+ socket.recv_string() # Needed to complete REQ/REP.
+
+ # Send the results.
+ socket.send_pyobj(msg('<result>', result))
+ socket.recv_string() # Needed to complete REQ/REP.
+
+ else:
+ raise NotImplementedError('purpose %s unknown.' % purpose)
diff --git a/amp/descriptor/zernike.f90 b/amp/descriptor/zernike.f90
new file mode 100644
index 0000000..22cbfdb
--- /dev/null
+++ b/amp/descriptor/zernike.f90
@@ -0,0 +1,320 @@
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+
+ subroutine calculate_zernike_prime(n, l, n_length, n_indices, &
+ numbers, rs, g_numbers, cutoff, indexx, home, p, q, &
+ fac_length, factorial, norm_prime, cutofffn, p_gamma)
+ use cutoffs
+ implicit none
+ integer:: n, l
+ integer:: indexx, p, q, n_length, fac_length
+ integer, dimension(n_length):: n_indices, numbers, g_numbers
+ double precision, dimension(n_length, 3):: rs
+ double precision, dimension(3):: home
+ double precision, dimension(fac_length):: factorial
+ double precision:: cutoff
+ ! gamma parameter for the polynomial cutoff
+ double precision, optional:: p_gamma
+ character(len=20):: cutofffn
+ complex*16:: norm_prime
+!f2py intent(in):: n, l, n_indices, numbers, g_numbers, rs, p_gamma
+!f2py intent(in):: home, indexx, p, q, cutoff, n_length, fac_length
+!f2py intent(out):: norm_prime
+ integer:: m
+ complex*16:: c_nlm, c_nlm_prime, z_nlm_, z_nlm, &
+ z_nlm_prime, z_nlm_prime_
+ integer:: n_index, n_symbol, iter
+ double precision, dimension(3):: neighbor
+ double precision:: x, y, z, rho
+
+ norm_prime = (0.0d0, 0.0d0)
+
+ do m = 0, l
+ c_nlm = (0.0d0, 0.0d0)
+ c_nlm_prime = (0.0d0, 0.0d0)
+ do iter = 1, n_length
+ n_index = n_indices(iter)
+ n_symbol = numbers(iter)
+ neighbor(1) = rs(iter, 1)
+ neighbor(2) = rs(iter, 2)
+ neighbor(3) = rs(iter, 3)
+ x = (neighbor(1) - home(1)) / cutoff
+ y = (neighbor(2) - home(2)) / cutoff
+ z = (neighbor(3) - home(3)) / cutoff
+ rho = (x ** 2.0d0 + y ** 2.0d0 + z ** 2.0d0) ** 0.5d0
+
+ call calculate_z(n, l, m, x, y, z, factorial, &
+ fac_length, z_nlm_)
+
+ ! Calculate z_nlm
+ if (present(p_gamma)) then
+ z_nlm = z_nlm_ * cutoff_fxn(rho * cutoff, &
+ cutoff, cutofffn, p_gamma)
+ ! Calculates z_nlm_prime
+ z_nlm_prime = z_nlm_ * &
+ cutoff_fxn_prime(rho * cutoff, cutoff, &
+ cutofffn, p_gamma) * &
+ der_position(indexx, n_index, home, neighbor, p, q)
+ else
+ z_nlm = z_nlm_ * cutoff_fxn(rho * cutoff, &
+ cutoff, cutofffn)
+ ! Calculates z_nlm_prime
+ z_nlm_prime = z_nlm_ * &
+ cutoff_fxn_prime(rho * cutoff, cutoff, &
+ cutofffn) * &
+ der_position(indexx, n_index, home, neighbor, p, q)
+ endif
+
+ call calculate_z_prime(n, l, m, x, y, z, q, factorial, &
+ fac_length, z_nlm_prime_)
+
+ if (kronecker(n_index, p) - &
+ kronecker(indexx, p) == 1) then
+ if (present(p_gamma)) then
+ z_nlm_prime = z_nlm_prime + &
+ cutoff_fxn(rho * cutoff, cutoff, &
+ cutofffn, p_gamma) * z_nlm_prime_ / &
+ cutoff
+ else
+ z_nlm_prime = z_nlm_prime + &
+ cutoff_fxn(rho * cutoff, cutoff, &
+ cutofffn) * z_nlm_prime_ / cutoff
+ end if
+ else if (kronecker(n_index, p) - kronecker(indexx, p) &
+ == -1) then
+ if (present(p_gamma)) then
+ z_nlm_prime = z_nlm_prime - &
+ cutoff_fxn(rho * cutoff, cutoff, &
+ cutofffn, p_gamma) * z_nlm_prime_ / &
+ cutoff
+ else
+ z_nlm_prime = z_nlm_prime - &
+ cutoff_fxn(rho * cutoff, cutoff, &
+ cutofffn) * z_nlm_prime_ / cutoff
+ end if
+ end if
+
+ ! sum over neighbors
+ c_nlm = c_nlm + g_numbers(iter) * conjg(z_nlm)
+ c_nlm_prime = c_nlm_prime + &
+ g_numbers(iter) * conjg(z_nlm_prime)
+ end do
+ ! sum over m values
+ if (m == 0) then
+ norm_prime = norm_prime + &
+ 2.0d0 * c_nlm * conjg(c_nlm_prime)
+ else
+ norm_prime = norm_prime + &
+ 4.0d0 * c_nlm * conjg(c_nlm_prime)
+ end if
+ enddo
+
+ CONTAINS
+
+ function der_position(mm, nn, Rm, Rn, ll, ii)
+ implicit none
+ integer:: mm, nn, ll, ii, xyz
+ double precision, dimension(3):: Rm, Rn, Rmn_
+ double precision:: der_position, Rmn
+ do xyz = 1, 3
+ Rmn_(xyz) = Rm(xyz) - Rn(xyz)
+ end do
+ Rmn = sqrt(dot_product(Rmn_, Rmn_))
+
+ if ((ll == mm) .AND. (mm /= nn)) then
+ der_position = (Rm(ii + 1) - Rn(ii + 1)) / Rmn
+ else if ((ll == nn) .AND. (mm /= nn)) then
+ der_position = - (Rm(ii + 1) - Rn(ii + 1)) / Rmn
+ else
+ der_position = 0.0d0
+ end if
+ end function
+
+ function kronecker(i, j)
+ implicit none
+ integer:: i, j
+ integer:: kronecker
+
+ if (i == j) then
+ kronecker = 1
+ else
+ kronecker = 0
+ end if
+ end function
+
+ end subroutine calculate_zernike_prime
+
+ subroutine calculate_z(n, l, m, x, y, z, factorial, length, &
+ output)
+ implicit none
+ integer:: n, l, m, length
+ double precision:: x, y, z
+ double precision, dimension(length):: factorial
+ complex*16:: output, ii, term4, term6
+!f2py intent(in):: n, l, m, x, y, z, factorial, length
+!f2py intent(out):: output
+ integer:: k, nu, alpha, beta, eta, u, mu, r, s, t
+ double precision:: term1, term2, q, b1, b2, term3
+ double precision:: term5, b5, b6, b7, b8, pi
+
+ pi = 4.0d0 * datan(1.0d0)
+
+ output = (0.0d0, 0.0d0)
+ term1 = sqrt((2.0d0 * l + 1.0d0) * &
+ factorial(int(2 * (l + m)) + 1) * &
+ factorial(int(2 * (l - m)) + 1)) / factorial(int(2 * l) + 1)
+ term2 = 2.0d0 ** (-m)
+ ii = (0.0d0, 1.0d0)
+ k = int((n - l) / 2.0d0)
+ do nu = 0, k
+ call calculate_q(nu, k, l, factorial, length, q)
+ do alpha = 0, nu
+ call binomial(float(nu), float(alpha), &
+ factorial, length, b1)
+ do beta = 0, nu - alpha
+ call binomial(float(nu - alpha), float(beta), &
+ factorial, length, b2)
+ term3 = q * b1 * b2
+ do u = 0, m
+ call binomial(float(m), float(u), factorial, &
+ length, b5)
+ term4 = ((-1.0d0)**(m - u)) * b5 * (ii**u)
+ do mu = 0, int((l - m) / 2.0d0)
+ call binomial(float(l), float(mu), &
+ factorial, length, b6)
+ call binomial(float(l - mu), float(m + mu),&
+ factorial, length, b7)
+ term5 = ((-1.0d0) ** mu) * (2.0d0 ** &
+ (-2.0d0 * mu)) * b6 * b7
+ do eta = 0, mu
+ call binomial(float(mu), float(eta), &
+ factorial, length, b8)
+ r = 2 * (eta + alpha) + u
+ s = 2 * (mu - eta + beta) + m - u
+ t = 2 * (nu - alpha - beta - mu) + l - m
+ output = output + term3 * term4 &
+ * term5 * b8 * (x ** r) &
+ * (y ** s) * (z ** t)
+ end do
+ end do
+ end do
+ end do
+ end do
+ end do
+ term6 = (ii) ** m
+ output = term1 * term2 * term6 * output
+ output = output / sqrt(4.0d0 * pi / 3.0d0)
+ end subroutine calculate_z
+
+ subroutine calculate_z_prime(n, l, m, x, y, z, p, factorial, &
+ length, output)
+ implicit none
+ integer:: n, l, m, length, p
+ double precision:: x, y, z
+ double precision, dimension(length):: factorial
+ complex*16:: output, ii, coefficient, term4, term6
+!f2py intent(in):: n, l, m, x, y, z, factorial, p, length
+!f2py intent(out):: output
+ integer:: k, nu, alpha, beta, eta, u, mu, r, s, t
+ double precision:: term1, term2, q, b1, b2, term3
+ double precision:: term5, b3, b4, b5, b6, pi
+
+ pi = 4.0d0 * datan(1.0d0)
+
+ output = (0.0d0, 0.0d0)
+ term1 = sqrt((2.0d0 * l + 1.0d0) * &
+ factorial(int(2 * (l + m)) + 1) * &
+ factorial(int(2 * (l - m)) + 1)) / &
+ factorial(int(2 * l) + 1)
+ term2 = 2.0d0 ** (-m)
+ ii = (0.0d0, 1.0d0)
+
+ k = int((n - l) / 2.)
+ do nu = 0, k
+ call calculate_q(nu, k, l, factorial, length, q)
+ do alpha = 0, nu
+ call binomial(float(nu), float(alpha), factorial, &
+ length, b1)
+ do beta = 0, nu - alpha
+ call binomial(float(nu - alpha), float(beta), &
+ factorial, length, b2)
+ term3 = q * b1 * b2
+ do u = 0, m
+ call binomial(float(m), float(u), factorial, length, &
+ b3)
+ term4 = ((-1.0d0)**(m - u)) * b3 * (ii**u)
+ do mu = 0, int((l - m) / 2.)
+ call binomial(float(l), float(mu), factorial, &
+ length, b4)
+ call binomial(float(l - mu), float(m + mu), &
+ factorial, length, b5)
+ term5 = &
+ ((-1.0d0)**mu) * (2.0d0**(-2.0d0 * mu)) * b4 * b5
+ do eta = 0, mu
+ call binomial(float(mu), float(eta), factorial, &
+ length, b6)
+ r = 2 * (eta + alpha) + u
+ s = 2 * (mu - eta + beta) + m - u
+ t = 2 * (nu - alpha - beta - mu) + l - m
+ coefficient = term3 * term4 * term5 * b6
+ if (p == 0) then
+ if (r .NE. 0) then
+ output = output + coefficient * r * &
+ (x ** (r - 1)) * (y ** s) * (z ** t)
+ end if
+ else if (p == 1) then
+ if (s .NE. 0) then
+ output = output + coefficient * s * &
+ (x ** r) * (y ** (s - 1)) * (z ** t)
+ end if
+ else if (p == 2) then
+ if (t .NE. 0) then
+ output = output + coefficient * t * &
+ (x ** r) * (y ** s) * (z ** (t - 1))
+ end if
+ end if
+ end do
+ end do
+ end do
+ end do
+ end do
+ end do
+ term6 = (ii) ** m
+ output = term1 * term2 * term6 * output
+ output = output / sqrt(4.0d0 * pi / 3.0d0)
+ end subroutine calculate_z_prime
+
+ subroutine calculate_q(nu, k, l, factorial, length, output)
+ implicit none
+ integer:: nu, k, l, length
+ double precision, dimension(length):: factorial
+ double precision:: output, b1, b2, b3, b4
+!f2py intent(in):: nu, k, l, factorial
+!f2py intent(out):: output
+
+ call binomial(float(k), float(nu), factorial, length, b1)
+ call binomial(float(2 * k), float(k), factorial, length, b2)
+ call binomial(float(2 * (k + l + nu) + 1), float(2 * k), &
+ factorial, length, b3)
+ call binomial(float(k + l + nu), float(k), factorial, &
+ length, b4)
+ output = ((-1.0d0) ** (k + nu)) * &
+ sqrt((2.0d0 * l + 4.0d0 * k + 3.0d0) / 3.0d0) * b1 * b2 * &
+ b3 / b4 / (2.0d0 ** (2.0d0 * k))
+ end subroutine calculate_q
+
+ subroutine binomial(n, k, factorial, length, output)
+ implicit none
+ real(4):: n, k
+ integer:: length
+ double precision, dimension(length):: factorial
+ double precision:: output
+!f2py intent(in):: n, k, factorial, length
+!f2py intent(out):: output
+ output = factorial(INT(2 * n) + 1) / &
+ factorial(INT(2 * k) + 1) / &
+ factorial(INT(2 * (n - k)) + 1)
+ end subroutine binomial
+
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
diff --git a/amp/descriptor/zernike.py b/amp/descriptor/zernike.py
new file mode 100644
index 0000000..18120fb
--- /dev/null
+++ b/amp/descriptor/zernike.py
@@ -0,0 +1,1005 @@
+import numpy as np
+from numpy import sqrt
+
+from ase.data import atomic_numbers
+from ase.calculators.calculator import Parameters
+from scipy.special import sph_harm
+
+from ..utilities import Data, Logger, importer
+from .cutoffs import Cosine, Polynomial, dict2cutoff
+NeighborList = importer('NeighborList')
+try:
+ from .. import fmodules
+except ImportError:
+ fmodules = None
+
+
+class Zernike(object):
+
+ """Class that calculates Zernike fingerprints.
+
+ Parameters
+ ----------
+ cutoff : object or float
+ Cutoff function, typically from amp.descriptor.cutoffs. Can be also
+ fed as a float representing the radius above which neighbor
+ interactions are ignored; in this case a cosine cutoff function will be
+ employed. Default is a 6.5-Angstrom cosine cutoff.
+ Gs : dict
+ Dictionary of symbols and dictionaries for making symmetry functions.
+ Either auto-genetrated, or given in the following form, for example:
+
+ >>> Gs = {"Au": {"Au": 3., "O": 2.}, "O": {"Au": 5., "O": 10.}}
+ This is basically the same as \eta in Eq. (16) of
+ https://doi.org/10.1016/j.cpc.2016.05.010.
+
+ nmax : integer or dict
+ Maximum degree of Zernike polynomials that will be included in the
+ fingerprint vector. Can be different values for different species fed
+ as a dictionary with chemical elements as keys.
+ dblabel : str
+ Optional separate prefix/location for database files, including
+ fingerprints, fingerprint derivatives, and neighborlists. This file
+ location can be shared between calculator instances to avoid
+ re-calculating redundant information. If not supplied, just uses the
+ value from label.
+ elements : list
+ List of allowed elements present in the system. If not provided, will
+ be found automatically.
+ version : str
+ Version of fingerprints.
+ mode : str
+ Can be either 'atom-centered' or 'image-centered'.
+ fortran : bool
+ If True, will use fortran modules, if False, will not.
+
+ Raises
+ ------
+ RuntimeError, TypeError
+ """
+
+ def __init__(self, cutoff=Cosine(6.5), Gs=None, nmax=5, dblabel=None,
+ elements=None, version='2016.02', mode='atom-centered',
+ fortran=True):
+
+ # Check of the version of descriptor, particularly if restarting.
+ compatibleversions = ['2016.02', ]
+ if (version is not None) and version not in compatibleversions:
+ raise RuntimeError('Error: Trying to use Zernike fingerprints'
+ ' version %s, but this module only supports'
+ ' versions %s. You may need an older or '
+ ' newer version of Amp.' %
+ (version, compatibleversions))
+ else:
+ version = compatibleversions[-1]
+
+ # Check that the mode is atom-centered.
+ if mode != 'atom-centered':
+ raise RuntimeError('Zernike scheme only works '
+ 'in atom-centered mode. %s '
+ 'specified.' % mode)
+
+ # If the cutoff is provided as a number, Cosine function will be used
+ # by default.
+ if isinstance(cutoff, int) or isinstance(cutoff, float):
+ cutoff = Cosine(cutoff)
+ # If the cutoff is provided as a dictionary, assume we need to load it
+ # with dict2cutoff.
+ if type(cutoff) is dict:
+ cutoff = dict2cutoff(cutoff)
+
+ # The parameters dictionary contains the minimum information
+ # to produce a compatible descriptor; that is, one that gives
+ # an identical fingerprint when fed an ASE image.
+ p = self.parameters = Parameters(
+ {'importname': '.descriptor.zernike.Zernike',
+ 'mode': 'atom-centered'})
+ p.version = version
+ p.cutoff = cutoff.todict()
+ if p.cutoff['name'] == 'Polynomial':
+ self.gamma = cutoff.gamma
+ p.Gs = Gs
+ p.nmax = nmax
+ p.elements = elements
+
+ self.dblabel = dblabel
+ self.fortran = fortran
+ self.parent = None # Can hold a reference to main Amp instance.
+
+ def tostring(self):
+ """Returns an evaluatable representation of the calculator that can
+ be used to restart the calculator."""
+ return self.parameters.tostring()
+
+ def calculate_fingerprints(self, images, parallel=None, log=None,
+ calculate_derivatives=False):
+ """Calculates the fingerpints of the images, for the ones not already
+ done.
+
+ Parameters
+ ----------
+ images : list or str
+ List of ASE atoms objects with positions, symbols, energies, and
+ forces in ASE format. This is the training set of data. This can
+ also be the path to an ASE trajectory (.traj) or database (.db)
+ file. Energies can be obtained from any reference, e.g. DFT
+ calculations.
+ parallel : dict
+ Configuration for parallelization. Should be in same form as in
+ amp.Amp.
+ log : Logger object
+ Write function at which to log data. Note this must be a callable
+ function.
+ calculate_derivatives : bool
+ Decides whether or not fingerprintprimes should also be calculated.
+ """
+ if parallel is None:
+ parallel = {'cores': 1}
+ log = Logger(file=None) if log is None else log
+
+ if (self.dblabel is None) and hasattr(self.parent, 'dblabel'):
+ self.dblabel = self.parent.dblabel
+ self.dblabel = 'amp-data' if self.dblabel is None else self.dblabel
+
+ p = self.parameters
+
+ if p.cutoff['name'] == 'Cosine':
+ log('Cutoff radius: %.2f ' % p.cutoff['kwargs']['Rc'])
+ else:
+ log('Cutoff radius: %.2f and gamma=%i '
+ % (p.cutoff['kwargs']['Rc'], self.gamma))
+ log('Cutoff function: %s' % repr(dict2cutoff(p.cutoff)))
+
+ if p.elements is None:
+ log('Finding unique set of elements in training data.')
+ p.elements = set([atom.symbol for atoms in images.values()
+ for atom in atoms])
+ p.elements = sorted(p.elements)
+ log('%i unique elements included: ' % len(p.elements) +
+ ', '.join(p.elements))
+
+ log('Maximum degree of Zernike polynomials:')
+ if isinstance(p.nmax, dict):
+ for _ in p.nmax.keys():
+ log(' %2s: %d' % (_, p.nmax[_]))
+ else:
+ log('nmax: %d' % p.nmax)
+
+ if p.Gs is None:
+ log('No coefficient for atomic density function supplied; '
+ 'creating defaults.')
+ p.Gs = generate_coefficients(p.elements)
+ log('Coefficients of atomic density function for each element:')
+ for _ in p.Gs.keys():
+ log(' %2s: %s' % (_, str(p.Gs[_])))
+
+ # Counts the number of descriptors for each element.
+ no_of_descriptors = {}
+ for element in p.elements:
+ count = 0
+ if isinstance(p.nmax, dict):
+ for n in range(p.nmax[element] + 1):
+ for l in range(n + 1):
+ if (n - l) % 2 == 0:
+ count += 1
+ else:
+ for n in range(p.nmax + 1):
+ for l in range(n + 1):
+ if (n - l) % 2 == 0:
+ count += 1
+ no_of_descriptors[element] = count
+
+ log('Number of descriptors for each element:')
+ for element in p.elements:
+ log(' %2s: %d' % (element, no_of_descriptors.pop(element)))
+
+ log('Calculating neighborlists...', tic='nl')
+ if not hasattr(self, 'neighborlist'):
+ calc = NeighborlistCalculator(cutoff=p.cutoff['kwargs']['Rc'])
+ self.neighborlist = Data(filename='%s-neighborlists'
+ % self.dblabel,
+ calculator=calc)
+ self.neighborlist.calculate_items(images, parallel=parallel, log=log)
+ log('...neighborlists calculated.', toc='nl')
+
+ log('Fingerprinting images...', tic='fp')
+ if not hasattr(self, 'fingerprints'):
+ calc = FingerprintCalculator(neighborlist=self.neighborlist,
+ Gs=p.Gs,
+ nmax=p.nmax,
+ cutoff=p.cutoff,
+ fortran=self.fortran)
+ self.fingerprints = Data(filename='%s-fingerprints'
+ % self.dblabel,
+ calculator=calc)
+ self.fingerprints.calculate_items(images, parallel=parallel, log=log)
+ log('...fingerprints calculated.', toc='fp')
+
+ if calculate_derivatives:
+ log('Calculating fingerprint derivatives of images...',
+ tic='derfp')
+ if not hasattr(self, 'fingerprintprimes'):
+ calc = \
+ FingerprintPrimeCalculator(neighborlist=self.neighborlist,
+ Gs=p.Gs,
+ nmax=p.nmax,
+ cutoff=p.cutoff,
+ fortran=self.fortran)
+ self.fingerprintprimes = \
+ Data(filename='%s-fingerprint-primes'
+ % self.dblabel,
+ calculator=calc)
+ self.fingerprintprimes.calculate_items(
+ images, parallel=parallel, log=log)
+ log('...fingerprint derivatives calculated.', toc='derfp')
+
+
+# Calculators #################################################################
+
+
+# Neighborlist Calculator
+class NeighborlistCalculator:
+
+ """For integration with .utilities.Data
+
+ For each image fed to calculate, a list of neighbors with offset
+ distances is returned.
+
+ Parameters
+ ----------
+ cutoff : object or float
+ Cutoff function, typically from amp.descriptor.cutoffs. Can be also
+ fed as a float representing the radius above which neighbor
+ interactions are ignored; in this case a cosine cutoff function will be
+ employed. Default is a 6.5-Angstrom cosine cutoff.
+ """
+
+ def __init__(self, cutoff):
+ self.globals = Parameters({'cutoff': cutoff})
+ self.keyed = Parameters()
+ self.parallel_command = 'calculate_neighborlists'
+
+ def calculate(self, image, key):
+ """For integration with .utilities.Data
+ For each image fed to calculate, a list of neighbors with offset
+ distances is returned.
+
+ Parameters
+ ----------
+ image : object
+ ASE atoms object.
+ key : str
+ Key of the image after being hashed.
+ """
+ cutoff = self.globals.cutoff
+ n = NeighborList(cutoffs=[cutoff / 2.] * len(image),
+ self_interaction=False,
+ bothways=True,
+ skin=0.)
+ n.update(image)
+ return [n.get_neighbors(index) for index in range(len(image))]
+
+
+class FingerprintCalculator:
+ """For integration with .utilities.Data"""
+
+ def __init__(self, neighborlist, Gs, nmax, cutoff, fortran):
+ self.globals = Parameters({'cutoff': cutoff,
+ 'Gs': Gs,
+ 'nmax': nmax})
+ self.keyed = Parameters({'neighborlist': neighborlist})
+ self.parallel_command = 'calculate_fingerprints'
+ self.fortran = fortran
+ self.cutoff = cutoff
+
+ try: # for scipy v <= 0.90
+ from scipy import factorial as fac
+ except ImportError:
+ try: # for scipy v >= 0.10
+ from scipy.misc import factorial as fac
+ except ImportError: # for newer version of scipy
+ from scipy.special import factorial as fac
+
+ self.factorial = [fac(0.5 * _) for _ in range(4 * nmax + 3)]
+
+ def calculate(self, image, key):
+ """Makes a list of fingerprints, one per atom, for the fed image.
+
+ Parameters
+ ----------
+ image : object
+ ASE atoms object.
+ key : str
+ Key of the image after being hashed.
+ """
+ nl = self.keyed.neighborlist[key]
+ fingerprints = []
+ for atom in image:
+ symbol = atom.symbol
+ index = atom.index
+ neighbors, offsets = nl[index]
+ neighborsymbols = [image[_].symbol for _ in neighbors]
+ Rs = [image.positions[neighbor] + np.dot(offset, image.cell)
+ for (neighbor, offset) in zip(neighbors, offsets)]
+ self.atoms = image
+ indexfp = self.get_fingerprint(index, symbol, neighborsymbols, Rs)
+ fingerprints.append(indexfp)
+
+ return fingerprints
+
+ def get_fingerprint(self, index, symbol, n_symbols, Rs):
+ """Returns the fingerprint of symmetry function values for atom
+ specified by its index and symbol.
+
+ n_symbols and Rs are lists of neighbors' symbols and Cartesian
+ positions, respectively.
+
+ Parameters
+ ----------
+ index : int
+ Index of the center atom.
+ symbol : str
+ Symbol of the center atom.
+ n_symbols : list of str
+ List of neighbors' symbols.
+ Rs : list of list of float
+ List of Cartesian atomic positions of neighbors.
+
+ Returns
+ -------
+ symbols, fingerprints : list of float
+ Fingerprints for atom specified by its index and symbol.
+ """
+
+ home = self.atoms[index].position
+ cutoff = self.cutoff
+ Rc = cutoff['kwargs']['Rc']
+
+ if cutoff['name'] == 'Cosine':
+ cutoff_fxn = Cosine(Rc)
+ elif cutoff['name'] == 'Polynomial':
+ p_gamma = cutoff['kwargs']['gamma']
+ cutoff_fxn = Polynomial(Rc, gamma=p_gamma)
+
+ fingerprint = []
+ for n in range(self.globals.nmax + 1):
+ for l in range(n + 1):
+ if (n - l) % 2 == 0:
+ norm = 0.
+ for m in range(l + 1):
+ c_nlm = 0.
+ for n_symbol, neighbor in zip(n_symbols, Rs):
+ x = (neighbor[0] - home[0]) / Rc
+ y = (neighbor[1] - home[1]) / Rc
+ z = (neighbor[2] - home[2]) / Rc
+ rho = np.linalg.norm([x, y, z])
+
+ if self.fortran:
+ c_args = [Rc * rho]
+ if cutoff['name'] == 'Polynomial':
+ c_args.append(p_gamma)
+ Z_nlm = fmodules.calculate_z(
+ n=n, l=l, m=m,
+ x=x, y=y, z=z,
+ factorial=self.factorial,
+ length=len(self.factorial))
+ Z_nlm = self.globals.Gs[symbol][n_symbol] * \
+ Z_nlm * cutoff_fxn(*c_args)
+
+ else:
+ # Alternative ways to calculate Z_nlm
+# Z_nlm = self.globals.Gs[symbol][n_symbol] * \
+# calculate_Z(n, l, m, x, y, z,
+# self.factorial) * \
+# cutoff_fxn(rho * Rc)
+# Z_nlm = self.globals.Gs[symbol][n_symbol] * \
+# calculate_Z2(n, l, m, x, y, z) * \
+# cutoff_fxn(rho * Rc)
+
+ if rho > 0.:
+ theta = np.arccos(z / rho)
+ else:
+ theta = 0.
+
+ if x < 0.:
+ phi = np.pi + np.arctan(y / x)
+ elif 0. < x and y < 0.:
+ phi = 2 * np.pi + np.arctan(y / x)
+ elif 0. < x and 0. <= y:
+ phi = np.arctan(y / x)
+ elif x == 0. and 0. < y:
+ phi = 0.5 * np.pi
+ elif x == 0. and y < 0.:
+ phi = 1.5 * np.pi
+ else:
+ phi = 0.
+
+ c_args = [Rc * rho]
+ if cutoff['name'] == 'Polynomial':
+ c_args.append(p_gamma)
+
+ Z_nlm = self.globals.Gs[symbol][n_symbol] * \
+ calculate_R(n, l, rho, self.factorial) * \
+ sph_harm(m, l, phi, theta) * \
+ cutoff_fxn(*c_args)
+
+ # sum over neighbors
+ c_nlm += np.conjugate(Z_nlm)
+ # sum over m values
+ if m == 0:
+ norm += c_nlm * np.conjugate(c_nlm)
+ else:
+ norm += 2. * c_nlm * np.conjugate(c_nlm)
+
+ fingerprint.append(norm.real)
+
+ return symbol, fingerprint
+
+
+class FingerprintPrimeCalculator:
+ """For integration with .utilities.Data"""
+
+ def __init__(self, neighborlist, Gs, nmax, cutoff, fortran):
+ self.globals = Parameters({'cutoff': cutoff,
+ 'Gs': Gs,
+ 'nmax': nmax})
+ self.keyed = Parameters({'neighborlist': neighborlist})
+ self.parallel_command = 'calculate_fingerprint_primes'
+ self.fortran = fortran
+
+ try: # for scipy v <= 0.90
+ from scipy import factorial as fac
+ except ImportError:
+ try: # for scipy v >= 0.10
+ from scipy.misc import factorial as fac
+ except ImportError: # for newer version of scipy
+ from scipy.special import factorial as fac
+
+ self.factorial = [fac(0.5 * _) for _ in range(4 * nmax + 3)]
+
+ def calculate(self, image, key):
+ """Makes a list of fingerprint derivatives, one per atom, for the fed
+ image.
+
+ Parameters
+ ---------
+ image : object
+ ASE atoms object.
+ key : str
+ Key of the image after being hashed.
+ """
+ self.atoms = image
+ nl = self.keyed.neighborlist[key]
+ fingerprintprimes = {}
+ for atom in image:
+ selfsymbol = atom.symbol
+ selfindex = atom.index
+ selfneighborindices, selfneighboroffsets = nl[selfindex]
+ selfneighborsymbols = [
+ image[_].symbol for _ in selfneighborindices]
+ for i in range(3):
+ # Calculating derivative of self atom fingerprints w.r.t.
+ # coordinates of itself.
+ nneighborindices, nneighboroffsets = nl[selfindex]
+ nneighborsymbols = [image[_].symbol for _ in nneighborindices]
+
+ Rs = [image.positions[_index] +
+ np.dot(_offset, image.get_cell())
+ for _index, _offset
+ in zip(nneighborindices,
+ nneighboroffsets)]
+
+ der_indexfp = self.get_fingerprintprime(
+ selfindex, selfsymbol,
+ nneighborindices,
+ nneighborsymbols,
+ Rs, selfindex, i)
+
+ fingerprintprimes[
+ (selfindex, selfsymbol, selfindex, selfsymbol, i)] = \
+ der_indexfp
+ # Calculating derivative of neighbor atom fingerprints w.r.t.
+ # coordinates of self atom.
+ for nindex, nsymbol, noffset in \
+ zip(selfneighborindices,
+ selfneighborsymbols,
+ selfneighboroffsets):
+ # for calculating forces, summation runs over neighbor
+ # atoms of type II (within the main cell only)
+ if noffset.all() == 0:
+ nneighborindices, nneighboroffsets = nl[nindex]
+ nneighborsymbols = \
+ [image[_].symbol for _ in nneighborindices]
+
+ Rs = [image.positions[_index] +
+ np.dot(_offset, image.get_cell())
+ for _index, _offset
+ in zip(nneighborindices,
+ nneighboroffsets)]
+
+ # for calculating derivatives of fingerprints,
+ # summation runs over neighboring atoms of type
+ # I (either inside or outside the main cell)
+ der_indexfp = self.get_fingerprintprime(
+ nindex, nsymbol,
+ nneighborindices,
+ nneighborsymbols,
+ Rs, selfindex, i)
+
+ fingerprintprimes[
+ (selfindex, selfsymbol, nindex, nsymbol, i)] = \
+ der_indexfp
+
+ return fingerprintprimes
+
+ def get_fingerprintprime(self, index, symbol, n_indices, n_symbols, Rs,
+ p, q):
+ """Returns the value of the derivative of G for atom with index and
+ symbol with respect to coordinate x_{i} of atom index m. n_indices,
+ n_symbols and Rs are lists of neighbors' indices, symbols and Cartesian
+ positions, respectively.
+
+ Parameters
+ ----------
+ index : int
+ Index of the center atom.
+ symbol : str
+ Symbol of the center atom.
+ n_indices : list of int
+ List of neighbors' indices.
+ n_symbols : list of str
+ List of neighbors' symbols.
+ Rs : list of list of float
+ List of Cartesian atomic positions.
+ p : int
+ Index of the pair atom.
+ q : int
+ Direction of the derivative; is an integer from 0 to 2.
+
+ Returns
+ -------
+ fingerprint_prime : list of float
+ The value of the derivative of the fingerprints for atom with index
+ and symbol with respect to coordinate x_{i} of atom index m.
+ """
+ home = self.atoms[index].position
+ cutoff = self.globals.cutoff
+ Rc = cutoff['kwargs']['Rc']
+
+ if cutoff['name'] is 'Cosine':
+ cutoff_fxn = Cosine(Rc)
+ elif cutoff['name'] is 'Polynomial':
+ p_gamma = cutoff['kwargs']['gamma']
+ cutoff_fxn = Polynomial(Rc, gamma=p_gamma)
+
+ fingerprint_prime = []
+ for n in range(self.globals.nmax + 1):
+ for l in range(n + 1):
+ if (n - l) % 2 == 0:
+ if self.fortran: # fortran version; faster
+ G_numbers = [self.globals.Gs[symbol][elm]
+ for elm in n_symbols]
+ numbers = [atomic_numbers[elm] for elm in n_symbols]
+ if len(Rs) == 0:
+ norm_prime = 0.
+ else:
+ args_calculate_zernike_prime = dict(
+ n=n,
+ l=l,
+ n_length=len(n_indices),
+ n_indices=list(n_indices),
+ numbers=numbers,
+ rs=Rs,
+ g_numbers=G_numbers,
+ cutoff=Rc,
+ cutofffn=cutoff['name'],
+ indexx=index,
+ home=home,
+ p=p,
+ q=q,
+ fac_length=len(self.factorial),
+ factorial=self.factorial)
+
+ if cutoff['name'] == 'Polynomial':
+ args_calculate_zernike_prime['p_gamma'] =\
+ cutoff['kwargs']['gamma']
+
+ norm_prime = \
+ fmodules.calculate_zernike_prime(
+ **args_calculate_zernike_prime)
+ else:
+ norm_prime = 0.
+ for m in range(l + 1):
+ c_nlm = 0.
+ c_nlm_prime = 0.
+ for n_index, n_symbol, neighbor in zip(n_indices,
+ n_symbols,
+ Rs):
+ x = (neighbor[0] - home[0]) / Rc
+ y = (neighbor[1] - home[1]) / Rc
+ z = (neighbor[2] - home[2]) / Rc
+ rho = np.linalg.norm([x, y, z])
+ c_args = [rho * Rc]
+ if cutoff['name'] == 'Polynomial':
+ c_args.append(p_gamma)
+
+ _Z_nlm = calculate_Z(n, l, m,
+ x, y, z,
+ self.factorial)
+ # Calculates Z_nlm
+ Z_nlm = _Z_nlm * \
+ cutoff_fxn(*c_args)
+
+ # Calculates Z_nlm_prime
+ Z_nlm_prime = _Z_nlm * \
+ cutoff_fxn.prime(*c_args) * \
+ der_position(
+ index, n_index, home, neighbor, p, q)
+
+ _Z_nlm_prime = calculate_Z_prime(
+ n, l, m, x, y, z, q, self.factorial)
+
+ if (Kronecker(n_index, p) -
+ Kronecker(index, p)) == 1:
+ Z_nlm_prime += \
+ cutoff_fxn(*c_args) * \
+ _Z_nlm_prime / Rc
+ elif (Kronecker(n_index, p) -
+ Kronecker(index, p)) == -1:
+ Z_nlm_prime -= \
+ cutoff_fxn(*c_args) * \
+ _Z_nlm_prime / Rc
+
+ # sum over neighbors
+ c_nlm += self.globals.Gs[symbol][
+ n_symbol] * np.conjugate(Z_nlm)
+ c_nlm_prime += self.globals.Gs[symbol][
+ n_symbol] * np.conjugate(Z_nlm_prime)
+
+ # sum over m values
+ if m == 0:
+ norm_prime += 2. * c_nlm * \
+ np.conjugate(c_nlm_prime)
+ else:
+ norm_prime += 4. * c_nlm * \
+ np.conjugate(c_nlm_prime)
+
+ fingerprint_prime.append(norm_prime.real)
+
+ return fingerprint_prime
+
+
+# Auxiliary functions #########################################################
+
+
+def binomial(n, k, factorial):
+ """ Returns C(n,k) = n!/(k!(n-k)!).
+ """
+ assert n >= 0 and k >= 0 and n >= k, \
+ 'n and k should be non-negative integers with n >= k.'
+
+ c = factorial[int(2 * n)] / \
+ (factorial[int(2 * k)] * factorial[int(2 * (n - k))])
+ return c
+
+
+def calculate_R(n, l, rho, factorial):
+ """Calculates R_{n}^{l}(rho) according to the last equation of wikipedia.
+ """
+ if (n - l) % 2 != 0:
+ return 0
+ else:
+ value = 0.
+ k = (n - l) / 2
+ term1 = np.sqrt(2. * n + 3.)
+
+ for s in range(int(k) + 1):
+ b1 = binomial(k, s, factorial)
+ b2 = binomial(n - s - 1 + 1.5, k, factorial)
+ value += ((-1) ** s) * b1 * b2 * (rho ** (n - 2. * s))
+
+ value *= term1
+ return value
+
+
+def generate_coefficients(elements):
+ """Automatically generates coefficients if not given by the user.
+
+ Parameters
+ ----------
+ elements : list of str
+ List of symbols of all atoms.
+
+ Returns
+ -------
+ G : dict of dicts
+ """
+ _G = {}
+ for element in elements:
+ _G[element] = atomic_numbers[element]
+ G = {}
+ for element in elements:
+ G[element] = _G
+ return G
+
+
+def Kronecker(i, j):
+ """Kronecker delta function.
+
+ i : int
+ First index of Kronecker delta.
+ j : int
+ Second index of Kronecker delta.
+
+ Returns
+ -------
+ Kronecker delta : int
+ """
+ if i == j:
+ return 1
+ else:
+ return 0
+
+
+def der_position(m, n, Rm, Rn, l, i):
+ """Returns the derivative of the norm of position vector R_{mn} with
+ respect to x_{i} of atomic index l.
+
+ Parameters
+ ----------
+ m : int
+ Index of the first atom.
+ n : int
+ Index of the second atom.
+ Rm : float
+ Position of the first atom.
+ Rn : float
+ Position of the second atom.
+ l : int
+ Index of the atom force is acting on.
+ i : int
+ Direction of force.
+
+ Returns
+ -------
+ der_position : list of float
+ The derivative of the norm of position vector R_{mn} with respect to
+ x_{i} of atomic index l.
+ """
+ Rmn = np.linalg.norm(Rm - Rn)
+ # mm != nn is necessary for periodic systems
+ if l == m and m != n:
+ der_position = (Rm[i] - Rn[i]) / Rmn
+ elif l == n and m != n:
+ der_position = -(Rm[i] - Rn[i]) / Rmn
+ else:
+ der_position = 0.
+ return der_position
+
+
+def calculate_q(nu, k, l, factorial):
+ """Calculates q_{kl}^{nu} according to the unnumbered equation afer Eq. (7)
+ of "3D Zernike Descriptors for Content Based Shape Retrieval",
+ Computer-Aided Design 36 (2004) 1047-1062.
+ """
+ result = ((-1) ** (k + nu)) * sqrt((2. * l + 4. * k + 3.) / 3.) * \
+ binomial(k, nu, factorial) * \
+ binomial(2. * k, k, factorial) * \
+ binomial(2. * (k + l + nu) + 1., 2. * k, factorial) / \
+ binomial(k + l + nu, k, factorial) / (2. ** (2. * k))
+
+ return result
+
+
+def calculate_Z(n, l, m, x, y, z, factorial):
+ """Calculates Z_{nl}^{m}(x, y, z) according to the unnumbered equation afer
+ Eq. (11) of "3D Zernike Descriptors for Content Based Shape Retrieval",
+ Computer-Aided Design 36 (2004) 1047-1062.
+ """
+ value = 0.
+ term1 = sqrt((2. * l + 1.) * factorial[int(2 * (l + m))] *
+ factorial[int(2 * (l - m))]) / factorial[int(2 * l)]
+ term2 = 2. ** (-m)
+
+ k = int((n - l) / 2.)
+ for nu in range(k + 1):
+ q = calculate_q(nu, k, l, factorial)
+ for alpha in range(nu + 1):
+ b1 = binomial(nu, alpha, factorial)
+ for beta in range(nu - alpha + 1):
+ b2 = binomial(nu - alpha, beta, factorial)
+ term3 = q * b1 * b2
+ for u in range(m + 1):
+ b5 = binomial(m, u, factorial)
+ term4 = ((-1.)**(m - u)) * b5 * (1j**u)
+ for mu in range(int((l - m) / 2.) + 1):
+ b6 = binomial(l, mu, factorial)
+ b7 = binomial(l - mu, m + mu, factorial)
+ term5 = ((-1.)**mu) * (2.**(-2. * mu)) * b6 * b7
+ for eta in range(mu + 1):
+ r = 2. * (eta + alpha) + u
+ s = 2. * (mu - eta + beta) + m - u
+ t = 2. * (nu - alpha - beta - mu) + l - m
+ value += term3 * term4 * term5 * \
+ binomial(mu, eta, factorial) * \
+ (x ** r) * (y ** s) * (z ** t)
+ term6 = (1j) ** m
+ value = term1 * term2 * term6 * value
+ value = value / sqrt(4. * np.pi / 3.)
+
+ return value
+
+
+def calculate_Z_prime(n, l, m, x, y, z, p, factorial):
+ """Calculates dZ_{nl}^{m}(x, y, z)/dR_{p} according to the unnumbered
+ equation afer Eq. (11) of "3D Zernike Descriptors for Content Based Shape
+ Retrieval", Computer-Aided Design 36 (2004) 1047-1062.
+ """
+ value = 0.
+ term1 = sqrt((2. * l + 1.) * factorial[int(2 * (l + m))] *
+ factorial[int(2 * (l - m))]) / factorial[int(2 * l)]
+ term2 = 2. ** (-m)
+
+ k = int((n - l) / 2.)
+ for nu in range(k + 1):
+ q = calculate_q(nu, k, l, factorial)
+ for alpha in range(nu + 1):
+ b1 = binomial(nu, alpha, factorial)
+ for beta in range(nu - alpha + 1):
+ b2 = binomial(nu - alpha, beta, factorial)
+ term3 = q * b1 * b2
+ for u in range(m + 1):
+ term4 = ((-1.)**(m - u)) * binomial(
+ m, u, factorial) * (1j**u)
+ for mu in range(int((l - m) / 2.) + 1):
+ term5 = ((-1.)**mu) * (2.**(-2. * mu)) * \
+ binomial(l, mu, factorial) * \
+ binomial(l - mu, m + mu, factorial)
+ for eta in range(mu + 1):
+ r = 2 * (eta + alpha) + u
+ s = 2 * (mu - eta + beta) + m - u
+ t = 2 * (nu - alpha - beta - mu) + l - m
+ coefficient = term3 * term4 * \
+ term5 * binomial(mu, eta, factorial)
+ if p == 0:
+ if r != 0:
+ value += coefficient * r * \
+ (x ** (r - 1)) * (y ** s) * (z ** t)
+ elif p == 1:
+ if s != 0:
+ value += coefficient * s * \
+ (x ** r) * (y ** (s - 1)) * (z ** t)
+ elif p == 2:
+ if t != 0:
+ value += coefficient * t * \
+ (x ** r) * (y ** s) * (z ** (t - 1))
+ term6 = (1j) ** m
+ value = term1 * term2 * term6 * value
+ value = value / sqrt(4. * np.pi / 3.)
+
+ return value
+
+
+if __name__ == "__main__":
+ """Directly calling this module; apparently from another node.
+ Calls should come as
+
+ python -m amp.descriptor.example id hostname:port
+
+ This session will then start a zmq session with that socket, labeling
+ itself with id. Instructions on what to do will come from the socket.
+ """
+ import sys
+ import tempfile
+ import zmq
+ from ..utilities import MessageDictionary
+
+ fortran = False if fmodules is None else True
+ hostsocket = sys.argv[-1]
+ proc_id = sys.argv[-2]
+ msg = MessageDictionary(proc_id)
+
+ # Send standard lines to stdout signaling process started and where
+ # error is directed. This should be caught by pxssh. (This could
+ # alternatively be done by zmq, but this works.)
+ print('<amp-connect>') # Signal that program started.
+ sys.stderr = tempfile.NamedTemporaryFile(mode='w', delete=False,
+ suffix='.stderr')
+ print('Log and error written to %s<stderr>' % sys.stderr.name)
+
+ def w(text):
+ """Writes to stderr and flushes."""
+ sys.stderr.write(text + '\n')
+ sys.stderr.flush()
+
+ # Establish client session via zmq; find purpose.
+ context = zmq.Context()
+ w('Context started.')
+ socket = context.socket(zmq.REQ)
+ w('Socket started.')
+ socket.connect('tcp://%s' % hostsocket)
+ w('Connection made.')
+ socket.send_pyobj(msg('<purpose>'))
+ w('Message sent.')
+ purpose = socket.recv_pyobj()
+ w('Purpose received: {}.'.format(purpose))
+
+ if purpose == 'calculate_neighborlists':
+ # Request variables.
+ socket.send_pyobj(msg('<request>', 'cutoff'))
+ cutoff = socket.recv_pyobj()
+ socket.send_pyobj(msg('<request>', 'images'))
+ images = socket.recv_pyobj()
+ # sys.stderr.write(str(images)) # Just to see if they are there.
+
+ # Perform the calculations.
+ calc = NeighborlistCalculator(cutoff=cutoff)
+ neighborlist = {}
+ # for key in images.iterkeys():
+ while len(images) > 0:
+ key, image = images.popitem() # Reduce memory.
+ neighborlist[key] = calc.calculate(image, key)
+
+ # Send the results.
+ socket.send_pyobj(msg('<result>', neighborlist))
+ socket.recv_string() # Needed to complete REQ/REP.
+
+ elif purpose == 'calculate_fingerprints':
+ # Request variables.
+ socket.send_pyobj(msg('<request>', 'cutoff'))
+ cutoff = socket.recv_pyobj()
+ socket.send_pyobj(msg('<request>', 'Gs'))
+ Gs = socket.recv_pyobj()
+ socket.send_pyobj(msg('<request>', 'nmax'))
+ nmax = socket.recv_pyobj()
+ socket.send_pyobj(msg('<request>', 'neighborlist'))
+ neighborlist = socket.recv_pyobj()
+ socket.send_pyobj(msg('<request>', 'images'))
+ images = socket.recv_pyobj()
+ w('Received images and parameters.')
+
+ calc = FingerprintCalculator(neighborlist, Gs, nmax,
+ cutoff, fortran)
+ w('Established calculator. Calculating.')
+ result = {}
+ while len(images) > 0:
+ key, image = images.popitem() # Reduce memory.
+ result[key] = calc.calculate(image, key)
+ if len(images) % 100 == 0:
+ socket.send_pyobj(msg('<info>', len(images)))
+ socket.recv_string() # Needed to complete REQ/REP.
+
+ # Send the results.
+ w('Sending results.')
+ socket.send_pyobj(msg('<result>', result))
+ socket.recv_string() # Needed to complete REQ/REP.
+
+ elif purpose == 'calculate_fingerprint_primes':
+ # Request variables.
+ socket.send_pyobj(msg('<request>', 'cutoff'))
+ cutoff = socket.recv_pyobj()
+ socket.send_pyobj(msg('<request>', 'Gs'))
+ Gs = socket.recv_pyobj()
+ socket.send_pyobj(msg('<request>', 'nmax'))
+ nmax = socket.recv_pyobj()
+ socket.send_pyobj(msg('<request>', 'neighborlist'))
+ neighborlist = socket.recv_pyobj()
+ socket.send_pyobj(msg('<request>', 'images'))
+ images = socket.recv_pyobj()
+
+ calc = FingerprintPrimeCalculator(neighborlist, Gs, nmax,
+ cutoff, fortran)
+ result = {}
+ while len(images) > 0:
+ key, image = images.popitem() # Reduce memory.
+ result[key] = calc.calculate(image, key)
+ if len(images) % 100 == 0:
+ socket.send_pyobj(msg('<info>', len(images)))
+ socket.recv_string() # Needed to complete REQ/REP.
+
+ # Send the results.
+ socket.send_pyobj(msg('<result>', result))
+ socket.recv_string() # Needed to complete REQ/REP.
+
+ else:
+ raise NotImplementedError('purpose %s unknown.' % purpose)
diff --git a/amp/model.f90 b/amp/model.f90
new file mode 100644
index 0000000..935320d
--- /dev/null
+++ b/amp/model.f90
@@ -0,0 +1,922 @@
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+
+! Fortran Version = 9
+ subroutine check_version(version, warning)
+ implicit none
+
+ integer:: version, warning
+!f2py intent(in):: version
+!f2py intent(out):: warning
+ if (version .NE. 9) then
+ warning = 1
+ else
+ warning = 0
+ end if
+ end subroutine
+
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+! module containing all the data of fingerprints (should be fed in
+! by python)
+ module fingerprint_props
+ implicit none
+
+ integer, allocatable:: num_fingerprints_of_elements(:)
+ double precision, allocatable:: raveled_fingerprints(:, :)
+ double precision, allocatable:: raveled_fingerprintprimes(:, :)
+
+ end module fingerprint_props
+
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+! module containing model data (should be fed in by python)
+ module model_props
+ implicit none
+ ! mode_signal is 1 for image-centered mode, and 2 for
+ ! atom-centered mode
+ integer:: mode_signal
+ logical:: train_forces
+ double precision:: energy_coefficient
+ double precision:: force_coefficient
+ double precision:: overfit
+ logical:: numericprime
+ double precision:: d
+
+ end module model_props
+
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+! module containing all the data of images (should be fed in by
+! python)
+ module images_props
+ implicit none
+
+ integer:: num_images
+! atom-centered variables
+ integer:: num_elements
+ integer, allocatable:: elements_numbers(:)
+ integer, allocatable:: num_images_atoms(:)
+ integer, allocatable:: atomic_numbers(:)
+ integer, allocatable:: num_neighbors(:)
+ integer, allocatable:: raveled_neighborlists(:)
+ double precision, allocatable:: actual_energies(:)
+ double precision, allocatable:: actual_forces(:, :)
+! image-centered variables
+ integer:: num_atoms
+ double precision, allocatable:: atomic_positions(:, :)
+
+ end module images_props
+
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+! subroutine that calculates the loss function and its prime
+ subroutine calculate_loss(parameters, num_parameters, &
+ lossprime, loss, dloss_dparameters, energyloss, forceloss, &
+ energy_maxresid, force_maxresid)
+
+ use images_props
+ use fingerprint_props
+ use model_props
+ use neuralnetwork
+
+!!!!!!!!!!!!!!!!!!!!!!!! input/output variables !!!!!!!!!!!!!!!!!!!!!!!!
+
+ integer:: num_parameters
+ double precision:: parameters(num_parameters)
+ logical:: lossprime
+ double precision:: loss, energyloss, forceloss
+ double precision:: energy_maxresid, force_maxresid
+ double precision:: dloss_dparameters(num_parameters)
+!f2py intent(in):: parameters, num_parameters
+!f2py intent(in):: lossprime
+!f2py intent(out):: loss, energyloss, forceloss
+!f2py intent(out):: energy_maxresid, force_maxresid
+!f2py intent(out):: dloss_dparameters
+
+!!!!!!!!!!!!!!!!!!!!!!!!!!! type definition !!!!!!!!!!!!!!!!!!!!!!!!!!!!
+
+ type:: image_forces
+ sequence
+ double precision, allocatable:: atom_forces(:, :)
+ end type image_forces
+
+ type:: integer_one_d_array
+ sequence
+ integer, allocatable:: onedarray(:)
+ end type integer_one_d_array
+
+ type:: embedded_real_one_one_d_array
+ sequence
+ type(real_one_d_array), allocatable:: onedarray(:)
+ end type embedded_real_one_one_d_array
+
+ type:: embedded_real_one_two_d_array
+ sequence
+ type(real_two_d_array), allocatable:: onedarray(:)
+ end type embedded_real_one_two_d_array
+
+ type:: embedded_integer_one_one_d_array
+ sequence
+ type(integer_one_d_array), allocatable:: onedarray(:)
+ end type embedded_integer_one_one_d_array
+
+ type:: embedded_one_one_two_d_array
+ sequence
+ type(embedded_real_one_two_d_array), allocatable:: onedarray(:)
+ end type embedded_one_one_two_d_array
+
+!!!!!!!!!!!!!!!!!!!!!!!!!! dummy variables !!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+
+ double precision, allocatable:: fingerprint(:)
+ type(embedded_real_one_one_d_array), allocatable:: &
+ unraveled_fingerprints(:)
+ type(integer_one_d_array), allocatable:: &
+ unraveled_atomic_numbers(:)
+ double precision:: amp_energy, actual_energy, atom_energy
+ double precision:: residual_per_atom, dforce, force_resid
+ double precision:: overfitloss
+ integer:: i, index, j, p, k, q, l, m, &
+ len_of_fingerprint, symbol, element, image_no, num_inputs
+ double precision:: denergy_dparameters(num_parameters)
+ double precision:: daenergy_dparameters(num_parameters)
+ double precision:: dforce_dparameters(num_parameters)
+ double precision:: doverfitloss_dparameters(num_parameters)
+ type(real_two_d_array), allocatable:: dforces_dparameters(:)
+ type(image_forces), allocatable:: unraveled_actual_forces(:)
+ type(embedded_integer_one_one_d_array), allocatable:: &
+ unraveled_neighborlists(:)
+ type(embedded_one_one_two_d_array), allocatable:: &
+ unraveled_fingerprintprimes(:)
+ double precision, allocatable:: fingerprintprime(:)
+ integer:: nindex, nsymbol, selfindex
+ double precision, allocatable:: &
+ actual_forces_(:, :), amp_forces(:, :)
+ integer, allocatable:: neighborindices(:)
+! image-centered mode
+ type(real_one_d_array), allocatable:: &
+ unraveled_atomic_positions(:)
+ double precision, allocatable:: inputs(:), inputs_(:)
+
+!!!!!!!!!!!!!!!!!!!!!!!!!!!! calculations !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+
+ if (mode_signal == 1) then
+ allocate(inputs(3 * num_atoms))
+ allocate(inputs_(3 * num_atoms))
+ allocate(unraveled_atomic_positions(num_images))
+ call unravel_atomic_positions()
+ else
+ allocate(unraveled_fingerprints(num_images))
+ allocate(unraveled_atomic_numbers(num_images))
+ allocate(unraveled_neighborlists(num_images))
+ allocate(unraveled_fingerprintprimes(num_images))
+ call unravel_atomic_numbers()
+ call unravel_fingerprints()
+ end if
+ if (train_forces .EQV. .TRUE.) then
+ allocate(unraveled_actual_forces(num_images))
+ call unravel_actual_forces()
+ if (mode_signal == 2) then
+ call unravel_neighborlists()
+ call unravel_fingerprintprimes()
+ end if
+ end if
+
+ energyloss = 0.0d0
+ forceloss = 0.0d0
+ energy_maxresid = 0.0d0
+ force_maxresid = 0.0d0
+ do j = 1, num_parameters
+ dloss_dparameters(j) = 0.0d0
+ end do
+
+! summation over images
+ do image_no = 1, num_images
+
+ if (mode_signal == 1) then
+ num_inputs = 3 * num_atoms
+ inputs = unraveled_atomic_positions(image_no)%onedarray
+ else
+ num_atoms = num_images_atoms(image_no)
+ end if
+ actual_energy = actual_energies(image_no)
+ ! calculates amp_energy
+ call calculate_energy(image_no)
+ ! calculates energy_maxresid
+ residual_per_atom = ABS(amp_energy - actual_energy) / num_atoms
+ if (residual_per_atom .GT. energy_maxresid) then
+ energy_maxresid = residual_per_atom
+ end if
+ ! calculates energyloss
+ energyloss = energyloss + residual_per_atom ** 2.0d0
+ if (lossprime .EQV. .TRUE.) then
+ ! calculates denergy_dparameters
+ if (mode_signal == 1) then ! image-centered mode
+ denergy_dparameters = &
+ calculate_denergy_dparameters_(num_inputs, inputs, &
+ num_parameters, parameters)
+ else ! atom-centered mode
+ do j = 1, num_parameters
+ denergy_dparameters(j) = 0.0d0
+ end do
+ if (numericprime .EQV. .FALSE.) then
+ call calculate_denergy_dparameters(image_no)
+ else
+ call calculate_numerical_denergy_dparameters(image_no)
+ end if
+ end if
+ ! calculates contribution of energyloss to dloss_dparameters
+ do j = 1, num_parameters
+ dloss_dparameters(j) = dloss_dparameters(j) + &
+ energy_coefficient * 2.0d0 * &
+ (amp_energy - actual_energy) * &
+ denergy_dparameters(j) / (num_atoms ** 2.0d0)
+ end do
+ end if
+ if (train_forces .EQV. .TRUE.) then
+ allocate(actual_forces_(num_atoms, 3))
+ do selfindex = 1, num_atoms
+ do i = 1, 3
+ actual_forces_(selfindex, i) = &
+ unraveled_actual_forces(&
+ image_no)%atom_forces(selfindex, i)
+ end do
+ end do
+ ! calculates amp_forces
+ call calculate_forces(image_no)
+ ! calculates forceloss
+ do selfindex = 1, num_atoms
+ do i = 1, 3
+ forceloss = forceloss + &
+ (1.0d0 / 3.0d0) * (amp_forces(selfindex, i) - &
+ actual_forces_(selfindex, i)) ** 2.0d0 / num_atoms
+ end do
+ end do
+
+ ! calculates force_maxresid
+ do selfindex = 1, num_atoms
+ do i = 1, 3
+ force_resid = &
+ ABS(amp_forces(selfindex, i) - &
+ actual_forces_(selfindex, i))
+ if (force_resid .GT. force_maxresid) then
+ force_maxresid = force_resid
+ end if
+ end do
+ end do
+ if (lossprime .EQV. .TRUE.) then
+ allocate(dforces_dparameters(num_atoms))
+ do selfindex = 1, num_atoms
+ allocate(dforces_dparameters(&
+ selfindex)%twodarray(3, num_parameters))
+ do i = 1, 3
+ do j = 1, num_parameters
+ dforces_dparameters(&
+ selfindex)%twodarray(i, j) = 0.0d0
+ end do
+ end do
+ end do
+ ! calculates dforces_dparameters
+ if (numericprime .EQV. .FALSE.) then
+ call calculate_dforces_dparameters(image_no)
+ else
+ call calculate_numerical_dforces_dparameters(image_no)
+ end if
+ ! calculates contribution of forceloss to
+ ! dloss_dparameters
+ do selfindex = 1, num_atoms
+ do i = 1, 3
+ do j = 1, num_parameters
+ dloss_dparameters(j) = &
+ dloss_dparameters(j) + &
+ force_coefficient * (2.0d0 / 3.0d0) * &
+ (amp_forces(selfindex, i) - &
+ actual_forces_(selfindex, i)) * &
+ dforces_dparameters(&
+ selfindex)%twodarray(i, j) / num_atoms
+ end do
+ end do
+ end do
+ do p = 1, size(dforces_dparameters)
+ deallocate(dforces_dparameters(p)%twodarray)
+ end do
+ deallocate(dforces_dparameters)
+ end if
+ deallocate(actual_forces_)
+ deallocate(amp_forces)
+ end if
+ end do
+ loss = energy_coefficient * energyloss + &
+ force_coefficient * forceloss
+
+ ! if overfit coefficient is more than zero, overfit
+ ! contribution to loss and dloss_dparameters is also added.
+ if (overfit .GT. 0.0d0) then
+ overfitloss = 0.0d0
+ do j = 1, num_parameters
+ overfitloss = overfitloss + &
+ parameters(j) ** 2.0d0
+ end do
+ overfitloss = overfit * overfitloss
+ loss = loss + overfitloss
+ do j = 1, num_parameters
+ doverfitloss_dparameters(j) = &
+ 2.0d0 * overfit * parameters(j)
+ dloss_dparameters(j) = dloss_dparameters(j) + &
+ doverfitloss_dparameters(j)
+ end do
+ end if
+
+! deallocations for all images
+ if (mode_signal == 1) then
+ do image_no = 1, num_images
+ deallocate(unraveled_atomic_positions(image_no)%onedarray)
+ end do
+ deallocate(unraveled_atomic_positions)
+ deallocate(inputs)
+ deallocate(inputs_)
+ else
+ do image_no = 1, num_images
+ deallocate(unraveled_atomic_numbers(image_no)%onedarray)
+ end do
+ deallocate(unraveled_atomic_numbers)
+ do image_no = 1, num_images
+ num_atoms = num_images_atoms(image_no)
+ do index = 1, num_atoms
+ deallocate(unraveled_fingerprints(&
+ image_no)%onedarray(index)%onedarray)
+ end do
+ deallocate(unraveled_fingerprints(image_no)%onedarray)
+ end do
+ deallocate(unraveled_fingerprints)
+ end if
+
+ if (train_forces .EQV. .TRUE.) then
+ do image_no = 1, num_images
+ deallocate(unraveled_actual_forces(image_no)%atom_forces)
+ end do
+ deallocate(unraveled_actual_forces)
+ if (mode_signal == 2) then
+ do image_no = 1, num_images
+ num_atoms = num_images_atoms(image_no)
+ do selfindex = 1, num_atoms
+ do nindex = 1, &
+ size(unraveled_fingerprintprimes(&
+ image_no)%onedarray(selfindex)%onedarray)
+ deallocate(&
+ unraveled_fingerprintprimes(&
+ image_no)%onedarray(selfindex)%onedarray(&
+ nindex)%twodarray)
+ end do
+ deallocate(unraveled_fingerprintprimes(&
+ image_no)%onedarray(selfindex)%onedarray)
+ end do
+ deallocate(unraveled_fingerprintprimes(&
+ image_no)%onedarray)
+ end do
+ deallocate(unraveled_fingerprintprimes)
+ do image_no = 1, num_images
+ num_atoms = num_images_atoms(image_no)
+ do index = 1, num_atoms
+ deallocate(unraveled_neighborlists(&
+ image_no)%onedarray(index)%onedarray)
+ end do
+ deallocate(unraveled_neighborlists(image_no)%onedarray)
+ end do
+ deallocate(unraveled_neighborlists)
+ end if
+ end if
+
+
+ contains
+
+ !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+
+ ! calculates amp_energy
+ subroutine calculate_energy(image_no)
+
+ if (mode_signal == 1) then
+ amp_energy = &
+ calculate_image_energy(num_inputs, inputs, num_parameters, &
+ parameters)
+ else
+ amp_energy = 0.0d0
+ do index = 1, num_atoms
+ symbol = unraveled_atomic_numbers(&
+ image_no)%onedarray(index)
+ do element = 1, num_elements
+ if (symbol == elements_numbers(element)) then
+ exit
+ end if
+ end do
+ len_of_fingerprint = num_fingerprints_of_elements(element)
+ allocate(fingerprint(len_of_fingerprint))
+ do p = 1, len_of_fingerprint
+ fingerprint(p) = &
+ unraveled_fingerprints(&
+ image_no)%onedarray(index)%onedarray(p)
+ end do
+
+ atom_energy = calculate_atomic_energy(symbol, &
+ len_of_fingerprint, fingerprint, num_elements, &
+ elements_numbers, num_parameters, parameters)
+ deallocate(fingerprint)
+ amp_energy = amp_energy + atom_energy
+ end do
+ end if
+
+ end subroutine calculate_energy
+
+ !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+
+ ! calculates amp_forces
+ subroutine calculate_forces(image_no)
+
+ allocate(amp_forces(num_atoms, 3))
+ do selfindex = 1, num_atoms
+ do i = 1, 3
+ amp_forces(selfindex, i) = 0.0d0
+ end do
+ end do
+
+ do selfindex = 1, num_atoms
+ if (mode_signal == 1) then
+ do i = 1, 3
+ do p = 1, 3 * num_atoms
+ inputs_(p) = 0.0d0
+ end do
+ inputs_(3 * (selfindex - 1) + i) = 1.0d0
+ amp_forces(selfindex, i) = calculate_force_(num_inputs, &
+ inputs, inputs_, num_parameters, parameters)
+ end do
+ else
+ ! neighborindices list is generated.
+ allocate(neighborindices(size(&
+ unraveled_neighborlists(image_no)%onedarray(&
+ selfindex)%onedarray)))
+ do p = 1, size(unraveled_neighborlists(&
+ image_no)%onedarray(selfindex)%onedarray)
+ neighborindices(p) = unraveled_neighborlists(&
+ image_no)%onedarray(selfindex)%onedarray(p)
+ end do
+
+ do l = 1, size(neighborindices)
+ nindex = neighborindices(l)
+ nsymbol = unraveled_atomic_numbers(&
+ image_no)%onedarray(nindex)
+ do element = 1, num_elements
+ if (nsymbol == elements_numbers(element)) then
+ exit
+ end if
+ end do
+ len_of_fingerprint = &
+ num_fingerprints_of_elements(element)
+ allocate(fingerprint(len_of_fingerprint))
+ do p = 1, len_of_fingerprint
+ fingerprint(p) = unraveled_fingerprints(&
+ image_no)%onedarray(nindex)%onedarray(p)
+ end do
+
+ do i = 1, 3
+ allocate(fingerprintprime(len_of_fingerprint))
+ do p = 1, len_of_fingerprint
+ fingerprintprime(p) = &
+ unraveled_fingerprintprimes(&
+ image_no)%onedarray(&
+ selfindex)%onedarray(l)%twodarray(i, p)
+ end do
+ dforce = calculate_force(nsymbol, len_of_fingerprint, &
+ fingerprint, fingerprintprime, &
+ num_elements, elements_numbers, &
+ num_parameters, parameters)
+ amp_forces(selfindex, i) = &
+ amp_forces(selfindex, i) + dforce
+ deallocate(fingerprintprime)
+ end do
+ deallocate(fingerprint)
+ end do
+ deallocate(neighborindices)
+ end if
+ end do
+
+ end subroutine calculate_forces
+
+ !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+
+ ! calculates analytical denergy_dparameters in
+ ! the atom-centered mode.
+ subroutine calculate_denergy_dparameters(image_no)
+
+ do index = 1, num_atoms
+ symbol = unraveled_atomic_numbers(image_no)%onedarray(index)
+ do element = 1, num_elements
+ if (symbol == elements_numbers(element)) then
+ exit
+ end if
+ end do
+ len_of_fingerprint = num_fingerprints_of_elements(element)
+ allocate(fingerprint(len_of_fingerprint))
+ do p = 1, len_of_fingerprint
+ fingerprint(p) = unraveled_fingerprints(&
+ image_no)%onedarray(index)%onedarray(p)
+ end do
+ daenergy_dparameters = calculate_datomicenergy_dparameters(&
+ symbol, len_of_fingerprint, fingerprint, &
+ num_elements, elements_numbers, num_parameters, parameters)
+ deallocate(fingerprint)
+ do j = 1, num_parameters
+ denergy_dparameters(j) = denergy_dparameters(j) + &
+ daenergy_dparameters(j)
+ end do
+ end do
+
+ end subroutine calculate_denergy_dparameters
+
+ !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+
+ ! calculates numerical denergy_dparameters in the
+ ! atom-centered mode.
+ subroutine calculate_numerical_denergy_dparameters(image_no)
+
+ double precision:: eplus, eminus
+
+ do j = 1, num_parameters
+ parameters(j) = parameters(j) + d
+ call calculate_energy(image_no)
+ eplus = amp_energy
+ parameters(j) = parameters(j) - 2.0d0 * d
+ call calculate_energy(image_no)
+ eminus = amp_energy
+ denergy_dparameters(j) = (eplus - eminus) / (2.0d0 * d)
+ parameters(j) = parameters(j) + d
+ end do
+ call calculate_energy(image_no)
+
+ end subroutine calculate_numerical_denergy_dparameters
+
+ !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+
+ ! calculates dforces_dparameters.
+ subroutine calculate_dforces_dparameters(image_no)
+
+ if (mode_signal == 1) then ! image-centered mode
+ do selfindex = 1, num_atoms
+ do i = 1, 3
+ do p = 1, 3 * num_atoms
+ inputs_(p) = 0.0d0
+ end do
+ inputs_(3 * (selfindex - 1) + i) = 1.0d0
+ dforce_dparameters = calculate_dforce_dparameters_(&
+ num_inputs, inputs, inputs_, num_parameters, parameters)
+ do j = 1, num_parameters
+ dforces_dparameters(selfindex)%twodarray(i, j) = &
+ dforce_dparameters(j)
+ end do
+ end do
+ end do
+
+ else ! atom-centered mode
+ do selfindex = 1, num_atoms
+ ! neighborindices list is generated.
+ allocate(neighborindices(size(&
+ unraveled_neighborlists(image_no)%onedarray(&
+ selfindex)%onedarray)))
+ do p = 1, size(unraveled_neighborlists(&
+ image_no)%onedarray(selfindex)%onedarray)
+ neighborindices(p) = unraveled_neighborlists(&
+ image_no)%onedarray(selfindex)%onedarray(p)
+ end do
+ do l = 1, size(neighborindices)
+ nindex = neighborindices(l)
+ nsymbol = unraveled_atomic_numbers(&
+ image_no)%onedarray(nindex)
+ do element = 1, num_elements
+ if (nsymbol == elements_numbers(element)) then
+ exit
+ end if
+ end do
+ len_of_fingerprint = &
+ num_fingerprints_of_elements(element)
+ allocate(fingerprint(len_of_fingerprint))
+ do p = 1, len_of_fingerprint
+ fingerprint(p) = unraveled_fingerprints(&
+ image_no)%onedarray(nindex)%onedarray(p)
+ end do
+ do i = 1, 3
+ allocate(fingerprintprime(len_of_fingerprint))
+ do p = 1, len_of_fingerprint
+ fingerprintprime(p) = &
+ unraveled_fingerprintprimes(&
+ image_no)%onedarray(selfindex)%onedarray(&
+ l)%twodarray(i, p)
+ end do
+ dforce_dparameters = calculate_dforce_dparameters(&
+ nsymbol, len_of_fingerprint, fingerprint, &
+ fingerprintprime, num_elements, &
+ elements_numbers, num_parameters, parameters)
+ deallocate(fingerprintprime)
+ do j = 1, num_parameters
+ dforces_dparameters(&
+ selfindex)%twodarray(i, j) = &
+ dforces_dparameters(&
+ selfindex)%twodarray(i, j) + &
+ dforce_dparameters(j)
+ end do
+ end do
+ deallocate(fingerprint)
+ end do
+ deallocate(neighborindices)
+ end do
+ end if
+
+ end subroutine calculate_dforces_dparameters
+
+ !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+
+ ! calculates numerical dforces_dparameters in the
+ ! atom-centered mode.
+ subroutine calculate_numerical_dforces_dparameters(image_no)
+
+ double precision, allocatable:: fplus(:, :), fminus(:, :)
+
+ do j = 1, num_parameters
+ parameters(j) = parameters(j) + d
+ deallocate(amp_forces)
+ call calculate_forces(image_no)
+ allocate(fplus(num_atoms, 3))
+ do selfindex = 1, num_atoms
+ do i = 1, 3
+ fplus(selfindex, i) = amp_forces(selfindex, i)
+ end do
+ end do
+ parameters(j) = parameters(j) - 2.0d0 * d
+ deallocate(amp_forces)
+ call calculate_forces(image_no)
+ allocate(fminus(num_atoms, 3))
+ do selfindex = 1, num_atoms
+ do i = 1, 3
+ fminus(selfindex, i) = amp_forces(selfindex, i)
+ end do
+ end do
+ do selfindex = 1, num_atoms
+ do i = 1, 3
+ dforces_dparameters(selfindex)%twodarray(i, j) = &
+ (fplus(selfindex, i) - fminus(selfindex, i)) / &
+ (2.0d0 * d)
+ end do
+ end do
+ parameters(j) = parameters(j) + d
+ deallocate(fplus)
+ deallocate(fminus)
+ end do
+ deallocate(amp_forces)
+ call calculate_forces(image_no)
+
+ end subroutine calculate_numerical_dforces_dparameters
+
+ !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+
+! used only in the image-centered mode.
+ subroutine unravel_atomic_positions()
+
+ do image_no = 1, num_images
+ allocate(unraveled_atomic_positions(image_no)%onedarray(&
+ 3 * num_atoms))
+ do index = 1, num_atoms
+ do i = 1, 3
+ unraveled_atomic_positions(image_no)%onedarray(&
+ 3 * (index - 1) + i) = atomic_positions(&
+ image_no, 3 * (index - 1) + i)
+ end do
+ end do
+ end do
+
+ end subroutine unravel_atomic_positions
+
+ !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+
+ subroutine unravel_atomic_numbers()
+
+ k = 0
+ do image_no = 1, num_images
+ num_atoms = num_images_atoms(image_no)
+ allocate(unraveled_atomic_numbers(&
+ image_no)%onedarray(num_atoms))
+ do l = 1, num_atoms
+ unraveled_atomic_numbers(image_no)%onedarray(l) &
+ = atomic_numbers(k + l)
+ end do
+ k = k + num_atoms
+ end do
+
+ end subroutine unravel_atomic_numbers
+
+ !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+
+ subroutine unravel_neighborlists()
+
+ k = 0
+ q = 0
+ do image_no = 1, num_images
+ num_atoms = num_images_atoms(image_no)
+ allocate(unraveled_neighborlists(image_no)%onedarray(&
+ num_atoms))
+ do index = 1, num_atoms
+ allocate(unraveled_neighborlists(image_no)%onedarray(&
+ index)%onedarray(num_neighbors(k + index)))
+ do p = 1, num_neighbors(k + index)
+ unraveled_neighborlists(image_no)%onedarray(&
+ index)%onedarray(p) = raveled_neighborlists(q + p)+1
+ end do
+ q = q + num_neighbors(k + index)
+ end do
+ k = k + num_atoms
+ end do
+
+ end subroutine unravel_neighborlists
+
+ !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+
+ subroutine unravel_actual_forces()
+
+ k = 0
+ do image_no = 1, num_images
+ if (mode_signal == 1) then
+ num_atoms = num_atoms
+ else
+ num_atoms = num_images_atoms(image_no)
+ end if
+ allocate(unraveled_actual_forces(image_no)%atom_forces(&
+ num_atoms, 3))
+ do index = 1, num_atoms
+ do i = 1, 3
+ unraveled_actual_forces(image_no)%atom_forces(&
+ index, i) = actual_forces(k + index, i)
+ end do
+ end do
+ k = k + num_atoms
+ end do
+
+ end subroutine unravel_actual_forces
+
+ !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+
+ subroutine unravel_fingerprints()
+
+ k = 0
+ do image_no = 1, num_images
+ num_atoms = &
+ num_images_atoms(image_no)
+ allocate(unraveled_fingerprints(&
+ image_no)%onedarray(num_atoms))
+ do index = 1, num_atoms
+ do element = 1, num_elements
+ if (unraveled_atomic_numbers(&
+ image_no)%onedarray(index)== &
+ elements_numbers(element)) then
+ allocate(unraveled_fingerprints(&
+ image_no)%onedarray(index)%onedarray(&
+ num_fingerprints_of_elements(element)))
+ exit
+ end if
+ end do
+ do l = 1, num_fingerprints_of_elements(element)
+ unraveled_fingerprints(&
+ image_no)%onedarray(index)%onedarray(l) = &
+ raveled_fingerprints(k + index, l)
+ end do
+ end do
+ k = k + num_atoms
+ end do
+
+ end subroutine unravel_fingerprints
+
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+
+ subroutine unravel_fingerprintprimes()
+
+ integer:: no_of_neighbors
+
+ k = 0
+ m = 0
+ do image_no = 1, num_images
+ num_atoms = &
+ num_images_atoms(image_no)
+ allocate(unraveled_fingerprintprimes(&
+ image_no)%onedarray(num_atoms))
+ do selfindex = 1, num_atoms
+ ! neighborindices list is generated.
+ allocate(neighborindices(size(unraveled_neighborlists(&
+ image_no)%onedarray(selfindex)%onedarray)))
+ do p = 1, size(unraveled_neighborlists(&
+ image_no)%onedarray(selfindex)%onedarray)
+ neighborindices(p) = unraveled_neighborlists(&
+ image_no)%onedarray(selfindex)%onedarray(p)
+ end do
+ no_of_neighbors = num_neighbors(k + selfindex)
+ allocate(unraveled_fingerprintprimes(&
+ image_no)%onedarray(selfindex)%onedarray(no_of_neighbors))
+ do nindex = 1, no_of_neighbors
+ do nsymbol = 1, num_elements
+ if (unraveled_atomic_numbers(&
+ image_no)%onedarray(neighborindices(nindex)) == &
+ elements_numbers(nsymbol)) then
+ exit
+ end if
+ end do
+ allocate(unraveled_fingerprintprimes(&
+ image_no)%onedarray(selfindex)%onedarray(&
+ nindex)%twodarray(3, num_fingerprints_of_elements(&
+ nsymbol)))
+ do p = 1, 3
+ do q = 1, num_fingerprints_of_elements(nsymbol)
+ unraveled_fingerprintprimes(&
+ image_no)%onedarray(selfindex)%onedarray(&
+ nindex)%twodarray(p, q) = &
+ raveled_fingerprintprimes(&
+ 3 * m + 3 * nindex + p - 3, q)
+ end do
+ end do
+ end do
+ deallocate(neighborindices)
+ m = m + no_of_neighbors
+ end do
+ k = k + num_atoms
+ end do
+
+ end subroutine unravel_fingerprintprimes
+
+ !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+
+ end subroutine calculate_loss
+
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+
+! subroutine that deallocates variables
+ subroutine deallocate_variables()
+
+ use images_props
+ use fingerprint_props
+ use model_props
+ use neuralnetwork
+
+ !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+
+! deallocating fingerprint_props
+ if (allocated(num_fingerprints_of_elements) .EQV. .TRUE.) then
+ deallocate(num_fingerprints_of_elements)
+ end if
+ if (allocated(raveled_fingerprints) .EQV. .TRUE.) then
+ deallocate(raveled_fingerprints)
+ end if
+ if (allocated(raveled_fingerprintprimes) .EQV. .TRUE.) then
+ deallocate(raveled_fingerprintprimes)
+ end if
+
+! deallocating images_props
+ if (allocated(elements_numbers) .EQV. .TRUE.) then
+ deallocate(elements_numbers)
+ end if
+ if (allocated(num_images_atoms) .EQV. .TRUE.) then
+ deallocate(num_images_atoms)
+ end if
+ if (allocated(atomic_numbers) .EQV. .TRUE.) then
+ deallocate(atomic_numbers)
+ end if
+ if (allocated(num_neighbors) .EQV. .TRUE.) then
+ deallocate(num_neighbors)
+ end if
+ if (allocated(raveled_neighborlists) .EQV. .TRUE.) then
+ deallocate(raveled_neighborlists)
+ end if
+ if (allocated(actual_energies) .EQV. .TRUE.) then
+ deallocate(actual_energies)
+ end if
+ if (allocated(actual_forces) .EQV. .TRUE.) then
+ deallocate(actual_forces)
+ end if
+ if (allocated(atomic_positions) .EQV. .TRUE.) then
+ deallocate(atomic_positions)
+ end if
+
+! deallocating neuralnetwork
+ if (allocated(min_fingerprints) .EQV. .TRUE.) then
+ deallocate(min_fingerprints)
+ end if
+ if (allocated(max_fingerprints) .EQV. .TRUE.) then
+ deallocate(max_fingerprints)
+ end if
+ if (allocated(no_layers_of_elements) .EQV. .TRUE.) then
+ deallocate(no_layers_of_elements)
+ end if
+ if (allocated(no_nodes_of_elements) .EQV. .TRUE.) then
+ deallocate(no_nodes_of_elements)
+ end if
+
+ !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+
+ end subroutine deallocate_variables
+
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
diff --git a/amp/model/Makefile b/amp/model/Makefile
new file mode 100644
index 0000000..e409cbb
--- /dev/null
+++ b/amp/model/Makefile
@@ -0,0 +1,3 @@
+neuralnetwork.mod:
+ gfortran -c neuralnetwork.f90
+ cp neuralnetwork.mod ..
diff --git a/amp/model/__init__.py b/amp/model/__init__.py
new file mode 100755
index 0000000..4b62144
--- /dev/null
+++ b/amp/model/__init__.py
@@ -0,0 +1,1144 @@
+import sys
+import numpy as np
+from ase.calculators.calculator import Parameters
+from ..utilities import (Logger, ConvergenceOccurred, make_sublists, now,
+ setup_parallel)
+try:
+ from .. import fmodules
+except ImportError:
+ fmodules = None
+
+
+class Model(object):
+ """Class that includes common methods between different models."""
+
+ @property
+ def log(self):
+ """Method to set or get a logger. Should be an instance of
+ amp.utilities.Logger.
+
+ Parameters
+ ----------
+ log : Logger object
+ Write function at which to log data. Note this must be a callable
+ function.
+ """
+ if hasattr(self, '_log'):
+ return self._log
+ if hasattr(self.parent, 'log'):
+ return self.parent.log
+ return Logger(None)
+
+ @log.setter
+ def log(self, log):
+ self._log = log
+
+ def tostring(self):
+ """Returns an evaluatable representation of the calculator that can
+ be used to re-establish the calculator."""
+ # Make sure numpy prints out enough data.
+ np.set_printoptions(precision=30, threshold=999999999)
+ return self.parameters.tostring()
+
+ def calculate_energy(self, fingerprints):
+ """Calculates the model-predicted energy for an image, based on its
+ fingerprint.
+
+ Parameters
+ ----------
+ fingerprints : dict
+ Dictionary with images hashs as keys and the corresponding
+ fingerprints as values.
+ """
+
+ if self.parameters.mode == 'image-centered':
+ raise NotImplementedError('This needs to be coded.')
+ elif self.parameters.mode == 'atom-centered':
+ self.atomic_energies = []
+ energy = 0.0
+ for index, (symbol, afp) in enumerate(fingerprints):
+ atom_energy = self.calculate_atomic_energy(afp=afp,
+ index=index,
+ symbol=symbol)
+ self.atomic_energies.append(atom_energy)
+ energy += atom_energy
+ return energy
+
+ def calculate_forces(self, fingerprints, fingerprintprimes):
+ """Calculates the model-predicted forces for an image, based on
+ derivatives of fingerprints.
+
+ Parameters
+ ----------
+ fingerprints : dict
+ Dictionary with images hashs as keys and the corresponding
+ fingerprints as values.
+ fingerprintprimes : dict
+ Dictionary with images hashs as keys and the corresponding
+ fingerprint derivatives as values.
+ """
+
+ if self.parameters.mode == 'image-centered':
+ raise NotImplementedError('This needs to be coded.')
+ elif self.parameters.mode == 'atom-centered':
+ selfindices = set([key[0] for key in fingerprintprimes.keys()])
+ forces = np.zeros((len(selfindices), 3))
+ for key in fingerprintprimes.keys():
+ selfindex, selfsymbol, nindex, nsymbol, i = key
+ derafp = fingerprintprimes[key]
+ afp = fingerprints[nindex][1]
+ dforce = self.calculate_force(afp=afp,
+ derafp=derafp,
+ nindex=nindex,
+ nsymbol=nsymbol,
+ direction=i,)
+ forces[selfindex][i] += dforce
+ return forces
+
+ def calculate_dEnergy_dParameters(self, fingerprints):
+ """Calculates a list of floats corresponding to the derivative of
+ model-predicted energy of an image with respect to model parameters.
+
+ Parameters
+ ----------
+ fingerprints : dict
+ Dictionary with images hashs as keys and the corresponding
+ fingerprints as values.
+ """
+
+ if self.parameters.mode == 'image-centered':
+ raise NotImplementedError('This needs to be coded.')
+ elif self.parameters.mode == 'atom-centered':
+ denergy_dparameters = None
+ for index, (symbol, afp) in enumerate(fingerprints):
+ temp = self.calculate_dAtomicEnergy_dParameters(afp=afp,
+ index=index,
+ symbol=symbol)
+ if denergy_dparameters is None:
+ denergy_dparameters = temp
+ else:
+ denergy_dparameters += temp
+ return denergy_dparameters
+
+ def calculate_numerical_dEnergy_dParameters(self, fingerprints, d=0.00001):
+ """Evaluates dEnergy_dParameters using finite difference.
+
+ This will trigger two calls to calculate_energy(), with each parameter
+ perturbed plus/minus d.
+
+ Parameters
+ ----------
+ fingerprints : dict
+ Dictionary with images hashs as keys and the corresponding
+ fingerprints as values.
+ d : float
+ The amount of perturbation in each parameter.
+ """
+
+ if self.parameters.mode == 'image-centered':
+ raise NotImplementedError('This needs to be coded.')
+ elif self.parameters.mode == 'atom-centered':
+ vector = self.vector
+ denergy_dparameters = []
+ for _ in range(len(vector)):
+ vector[_] += d
+ self.vector = vector
+ eplus = self.calculate_energy(fingerprints)
+ vector[_] -= 2 * d
+ self.vector = vector
+ eminus = self.calculate_energy(fingerprints)
+ denergy_dparameters += [(eplus - eminus) / (2 * d)]
+ vector[_] += d
+ self.vector = vector
+ denergy_dparameters = np.array(denergy_dparameters)
+ return denergy_dparameters
+
+ def calculate_dForces_dParameters(self, fingerprints, fingerprintprimes):
+ """Calculates an array of floats corresponding to the derivative of
+ model-predicted atomic forces of an image with respect to model
+ parameters.
+
+ Parameters
+ ----------
+ fingerprints : dict
+ Dictionary with images hashs as keys and the corresponding
+ fingerprints as values.
+ fingerprintprimes : dict
+ Dictionary with images hashs as keys and the corresponding
+ fingerprint derivatives as values.
+ """
+
+ if self.parameters.mode == 'image-centered':
+ raise NotImplementedError('This needs to be coded.')
+ elif self.parameters.mode == 'atom-centered':
+ selfindices = set([key[0] for key in fingerprintprimes.keys()])
+ dforces_dparameters = {(selfindex, i): None
+ for selfindex in selfindices
+ for i in range(3)}
+ for key in fingerprintprimes.keys():
+ selfindex, selfsymbol, nindex, nsymbol, i = key
+ derafp = fingerprintprimes[key]
+ afp = fingerprints[nindex][1]
+ temp = self.calculate_dForce_dParameters(afp=afp,
+ derafp=derafp,
+ direction=i,
+ nindex=nindex,
+ nsymbol=nsymbol,)
+ if dforces_dparameters[(selfindex, i)] is None:
+ dforces_dparameters[(selfindex, i)] = temp
+ else:
+ dforces_dparameters[(selfindex, i)] += temp
+ return dforces_dparameters
+
+ def calculate_numerical_dForces_dParameters(self, fingerprints,
+ fingerprintprimes, d=0.00001):
+ """Evaluates dForces_dParameters using finite difference. This will
+ trigger two calls to calculate_forces(), with each parameter perturbed
+ plus/minus d.
+
+ Parameters
+ ---------
+ fingerprints : dict
+ Dictionary with images hashs as keys and the corresponding
+ fingerprints as values.
+ fingerprintprimes : dict
+ Dictionary with images hashs as keys and the corresponding
+ fingerprint derivatives as values.
+ d : float
+ The amount of perturbation in each parameter.
+ """
+
+ if self.parameters.mode == 'image-centered':
+ raise NotImplementedError('This needs to be coded.')
+ elif self.parameters.mode == 'atom-centered':
+ selfindices = set([key[0] for key in fingerprintprimes.keys()])
+ dforces_dparameters = {(selfindex, i): []
+ for selfindex in selfindices
+ for i in range(3)}
+ vector = self.vector
+ for _ in range(len(vector)):
+ vector[_] += d
+ self.vector = vector
+ fplus = self.calculate_forces(fingerprints, fingerprintprimes)
+ vector[_] -= 2 * d
+ self.vector = vector
+ fminus = self.calculate_forces(fingerprints, fingerprintprimes)
+ for selfindex in selfindices:
+ for i in range(3):
+ dforces_dparameters[(selfindex, i)] += \
+ [(fplus[selfindex][i] - fminus[selfindex][i]) / (
+ 2 * d)]
+ vector[_] += d
+ self.vector = vector
+ for selfindex in selfindices:
+ for i in range(3):
+ dforces_dparameters[(selfindex, i)] = \
+ np.array(dforces_dparameters[(selfindex, i)])
+ return dforces_dparameters
+
+
+class LossFunction:
+
+ """Basic loss function, which can be used by the model.get_loss
+ method which is required in standard model classes.
+
+ This version is pure python and thus will be slow compared to a
+ fortran/parallel implementation.
+
+ If parallel is None, it will pull it from the model itself. Only use
+ this keyword to override the model's specification.
+
+ Also has parallelization methods built in.
+
+ See self.default_parameters for the default values of parameters
+ specified as None.
+
+ Parameters
+ ----------
+ energy_coefficient : float
+ Coefficient of the energy contribution in the loss function.
+ force_coefficient : float
+ Coefficient of the force contribution in the loss function.
+ Can set to None as shortcut to turn off force training.
+ convergence : dict
+ Dictionary of keys and values defining convergence. Keys are
+ 'energy_rmse', 'energy_maxresid', 'force_rmse', and 'force_maxresid'.
+ If 'force_rmse' and 'force_maxresid' are both set to None, force
+ training is turned off and force_coefficient is set to None.
+ parallel : dict
+ Parallel configuration dictionary. Will pull from model itself if
+ not specified.
+ overfit : float
+ Multiplier of the weights norm penalty term in the loss function.
+ raise_ConvergenceOccurred : bool
+ If True will raise convergence notice.
+ log_losses : bool
+ If True will log the loss function value in the log file else will not.
+ d : None or float
+ If d is None, both loss function and its gradient are calculated
+ analytically. If d is a float, then gradient of the loss function is
+ calculated by perturbing each parameter plus/minus d.
+ """
+
+ default_parameters = {'convergence': {'energy_rmse': 0.001,
+ 'energy_maxresid': None,
+ 'force_rmse': None,
+ 'force_maxresid': None, }
+ }
+
+ def __init__(self, energy_coefficient=1.0, force_coefficient=0.04,
+ convergence=None, parallel=None, overfit=0.,
+ raise_ConvergenceOccurred=True, log_losses=True, d=None):
+ p = self.parameters = Parameters(
+ {'importname': '.model.LossFunction'})
+ # 'dict' creates a copy; otherwise mutable in class.
+ c = p['convergence'] = dict(self.default_parameters['convergence'])
+ if convergence is not None:
+ for key, value in convergence.items():
+ p['convergence'][key] = value
+ p['energy_coefficient'] = energy_coefficient
+ p['force_coefficient'] = force_coefficient
+ p['overfit'] = overfit
+ self.raise_ConvergenceOccurred = raise_ConvergenceOccurred
+ self.log_losses = log_losses
+ self.d = d
+ self._step = 0
+ self._initialized = False
+ self._data_sent = False
+ self._parallel = parallel
+ if (c['force_rmse'] is None) and (c['force_maxresid'] is None):
+ p['force_coefficient'] = None
+ if p['force_coefficient'] is None:
+ c['force_rmse'] = None
+ c['force_maxresid'] = None
+
+ def attach_model(self, model, fingerprints=None,
+ fingerprintprimes=None, images=None):
+ """Attach the model to be used to the loss function.
+
+ fingerprints and training images need not be supplied if they are
+ already attached to the model via model.trainingparameters.
+
+ Parameters
+ ----------
+ model : object
+ Class representing the regression model.
+ fingerprints : dict
+ Dictionary with images hashs as keys and the corresponding
+ fingerprints as values.
+ fingerprintprimes : dict
+ Dictionary with images hashs as keys and the corresponding
+ fingerprint derivatives as values.
+ images : list or str
+ List of ASE atoms objects with positions, symbols, energies, and
+ forces in ASE format. This is the training set of data. This can
+ also be the path to an ASE trajectory (.traj) or database (.db)
+ file. Energies can be obtained from any reference, e.g. DFT
+ calculations.
+ """
+ self._model = model
+ self.fingerprints = fingerprints
+ self.fingerprintprimes = fingerprintprimes
+ self.images = images
+
+ def _initialize(self):
+ """Procedures to be run on the first call only, such as establishing
+ SSH sessions, etc."""
+ if self._initialized is True:
+ return
+
+ if self._parallel is None:
+ self._parallel = self._model._parallel
+ log = self._model.log
+
+ if self.fingerprints is None:
+ self.fingerprints = \
+ self._model.trainingparameters.descriptor.fingerprints
+
+ # May also make sense to decide whether or not to calculate
+ # fingerprintprimes based on the value of train_forces.
+ if ((self.parameters.force_coefficient is not None) and
+ (self.fingerprintprimes is None)):
+ self.fingerprintprimes = \
+ self._model.trainingparameters.descriptor.fingerprintprimes
+ if self.images is None:
+ self.images = self._model.trainingparameters.trainingimages
+
+ if self._parallel['cores'] != 1: # Initialize workers.
+ python = sys.executable
+ workercommand = '%s -m %s' % (python, self.__module__)
+ server, connections, n_pids = setup_parallel(self._parallel,
+ workercommand, log)
+ self._sessions = {'master': server,
+ 'connections': connections, # SSH's/nodes
+ 'n_pids': n_pids} # total no. of workers
+
+ if self.log_losses:
+ p = self.parameters
+ convergence = p['convergence']
+ log(' Loss function convergence criteria:')
+ log(' energy_rmse: ' + str(convergence['energy_rmse']))
+ log(' energy_maxresid: ' + str(convergence['energy_maxresid']))
+ log(' force_rmse: ' + str(convergence['force_rmse']))
+ log(' force_maxresid: ' + str(convergence['force_maxresid']))
+ log(' Loss function set-up:')
+ log(' energy_coefficient: ' + str(p.energy_coefficient))
+ log(' force_coefficient: ' + str(p.force_coefficient))
+ log(' overfit: ' + str(p.overfit))
+ log('\n')
+ if p.force_coefficient is None:
+ header = '%5s %19s %12s %12s %12s'
+ log(header %
+ ('', '', '', '', 'Energy'))
+ log(header %
+ ('Step', 'Time', 'Loss (SSD)', 'EnergyRMSE', 'MaxResid'))
+ log(header %
+ ('=' * 5, '=' * 19, '=' * 12, '=' * 12, '=' * 12))
+ else:
+ header = '%5s %19s %12s %12s %12s %12s %12s'
+ log(header %
+ ('', '', '', '', 'Energy',
+ '', 'Force'))
+ log(header %
+ ('Step', 'Time', 'Loss (SSD)', 'EnergyRMSE', 'MaxResid',
+ 'ForceRMSE', 'MaxResid'))
+ log(header %
+ ('=' * 5, '=' * 19, '=' * 12, '=' * 12, '=' * 12,
+ '=' * 12, '=' * 12))
+
+ self._initialized = True
+
+ def _send_data_to_fortran(self,):
+ """Procedures to be run in fortran mode for a single requested core
+ only. Also just on the first call for sending data to fortran modules.
+ """
+ if self._data_sent is True:
+ return
+
+ num_images = len(self.images)
+ p = self.parameters
+ energy_coefficient = p.energy_coefficient
+ overfit = p.overfit
+ if p.force_coefficient is None:
+ train_forces = False
+ force_coefficient = 0.
+ else:
+ train_forces = True
+ force_coefficient = p.force_coefficient
+ mode = self._model.parameters.mode
+ if mode == 'atom-centered':
+ num_atoms = None
+ elif mode == 'image-centered':
+ raise NotImplementedError('Image-centered mode is not coded yet.')
+
+ (actual_energies, actual_forces, elements, atomic_positions,
+ num_images_atoms, atomic_numbers, raveled_fingerprints, num_neighbors,
+ raveled_neighborlists, raveled_fingerprintprimes) = (None,) * 10
+
+ value = ravel_data(train_forces,
+ mode,
+ self.images,
+ self.fingerprints,
+ self.fingerprintprimes,)
+
+ if mode == 'image-centered':
+ if not train_forces:
+ (actual_energies, atomic_positions) = value
+ else:
+ (actual_energies, actual_forces, atomic_positions) = value
+ else:
+ if not train_forces:
+ (actual_energies, elements, num_images_atoms,
+ atomic_numbers, raveled_fingerprints) = value
+ else:
+ (actual_energies, actual_forces, elements, num_images_atoms,
+ atomic_numbers, raveled_fingerprints, num_neighbors,
+ raveled_neighborlists, raveled_fingerprintprimes) = value
+
+ send_data_to_fortran(fmodules,
+ energy_coefficient,
+ force_coefficient,
+ overfit,
+ train_forces,
+ num_atoms,
+ num_images,
+ actual_energies,
+ actual_forces,
+ atomic_positions,
+ num_images_atoms,
+ atomic_numbers,
+ raveled_fingerprints,
+ num_neighbors,
+ raveled_neighborlists,
+ raveled_fingerprintprimes,
+ self._model,
+ self.d)
+ self._data_sent = True
+
+ def _cleanup(self):
+ """Closes SSH sessions."""
+ self._initialized = False
+ if not hasattr(self, '_sessions'):
+ return
+ server = self._sessions['master']
+
+ finished = np.array([False] * self._sessions['n_pids'])
+ while not finished.all():
+ message = server.recv_pyobj()
+ if (message['subject'] == '<request>' and
+ message['data'] == 'parameters'):
+ server.send_pyobj('<stop>')
+ finished[int(message['id'])] = True
+
+ for _ in self._sessions['connections']:
+ if hasattr(_, 'logout'):
+ _.logout()
+ del self._sessions['connections']
+
+ def get_loss(self, parametervector, lossprime):
+ """Returns the current value of the loss function for a given set of
+ parameters, or, if the energy is less than the energy_tol raises a
+ ConvergenceException.
+
+ Parameters
+ ----------
+ parametervector : list
+ Parameters of the regression model in the form of a list.
+ lossprime : bool
+ If True, will calculate and return dloss_dparameters, else will
+ only return zero for dloss_dparameters.
+ """
+
+ self._initialize()
+
+ if self._parallel['cores'] == 1:
+ if self._model.fortran:
+ self._model.vector = parametervector
+ self._send_data_to_fortran()
+ (loss, dloss_dparameters, energy_loss, force_loss,
+ energy_maxresid, force_maxresid) = \
+ fmodules.calculate_loss(parameters=parametervector,
+ num_parameters=len(
+ parametervector),
+ lossprime=lossprime)
+ else:
+ loss, dloss_dparameters, energy_loss, force_loss, \
+ energy_maxresid, force_maxresid = \
+ self.calculate_loss(parametervector,
+ lossprime=lossprime)
+ else:
+ server = self._sessions['master']
+ n_pids = self._sessions['n_pids']
+
+ # Subdivide tasks.
+ keys = make_sublists(self.images.keys(), n_pids)
+
+ args = {'lossprime': lossprime,
+ 'd': self.d}
+
+ results = self.process_parallels(parametervector,
+ server,
+ n_pids,
+ keys,
+ args=args)
+ loss = results['loss']
+ dloss_dparameters = results['dloss_dparameters']
+ energy_loss = results['energy_loss']
+ force_loss = results['force_loss']
+ energy_maxresid = results['energy_maxresid']
+ force_maxresid = results['force_maxresid']
+
+ self.loss, self.energy_loss, self.force_loss, \
+ self.energy_maxresid, self.force_maxresid = \
+ loss, energy_loss, force_loss, energy_maxresid, force_maxresid
+
+ if lossprime:
+ self.dloss_dparameters = dloss_dparameters
+
+ if self.raise_ConvergenceOccurred:
+ # Only during calculation of loss function (and not lossprime)
+ # convergence is checked and values are printed out in the log
+ # file.
+ if lossprime is False:
+ self._model.vector = parametervector
+ converged = self.check_convergence(loss,
+ energy_loss,
+ force_loss,
+ energy_maxresid,
+ force_maxresid)
+ if converged:
+ self._cleanup()
+ if self._parallel['cores'] != 1:
+ # Needed to properly close socket connection
+ # (python3).
+ server.close()
+ raise ConvergenceOccurred()
+
+ return {'loss': self.loss,
+ 'dloss_dparameters': (self.dloss_dparameters
+ if lossprime is True
+ else dloss_dparameters),
+ 'energy_loss': self.energy_loss,
+ 'force_loss': self.force_loss,
+ 'energy_maxresid': self.energy_maxresid,
+ 'force_maxresid': self.force_maxresid, }
+
+ def calculate_loss(self, parametervector, lossprime):
+ """Method that calculates the loss, derivative of the loss with respect
+ to parameters (if requested), and max_residual.
+
+ Parameters
+ ----------
+ parametervector : list
+ Parameters of the regression model in the form of a list.
+
+ lossprime : bool
+ If True, will calculate and return dloss_dparameters, else will
+ only return zero for dloss_dparameters.
+ """
+ self._model.vector = parametervector
+ p = self.parameters
+ energyloss = 0.
+ forceloss = 0.
+ energy_maxresid = 0.
+ force_maxresid = 0.
+ dloss_dparameters = np.array([0.] * len(parametervector))
+ model = self._model
+ for hash in self.images.keys():
+ image = self.images[hash]
+ no_of_atoms = len(image)
+ amp_energy = model.calculate_energy(self.fingerprints[hash])
+ actual_energy = image.get_potential_energy(apply_constraint=False)
+ residual_per_atom = abs(amp_energy - actual_energy) / \
+ len(image)
+ if residual_per_atom > energy_maxresid:
+ energy_maxresid = residual_per_atom
+ energyloss += residual_per_atom**2
+
+ # Calculates derivative of the loss function with respect to
+ # parameters if lossprime is true
+ if lossprime:
+ if model.parameters.mode == 'image-centered':
+ raise NotImplementedError('This needs to be coded.')
+ elif model.parameters.mode == 'atom-centered':
+ if self.d is None:
+ denergy_dparameters = \
+ model.calculate_dEnergy_dParameters(
+ self.fingerprints[hash])
+ else:
+ denergy_dparameters = \
+ model.calculate_numerical_dEnergy_dParameters(
+ self.fingerprints[hash], d=self.d)
+ temp = p.energy_coefficient * 2. * \
+ (amp_energy - actual_energy) * \
+ denergy_dparameters / \
+ (no_of_atoms ** 2.)
+ dloss_dparameters += temp
+
+ if p.force_coefficient is not None:
+ amp_forces = \
+ model.calculate_forces(self.fingerprints[hash],
+ self.fingerprintprimes[hash])
+ actual_forces = image.get_forces(apply_constraint=False)
+ for index in range(no_of_atoms):
+ for i in range(3):
+ force_resid = abs(amp_forces[index][i] -
+ actual_forces[index][i])
+ if force_resid > force_maxresid:
+ force_maxresid = force_resid
+ temp = (1. / 3.) * (amp_forces[index][i] -
+ actual_forces[index][i]) ** 2. / \
+ no_of_atoms
+ forceloss += temp
+ # Calculates derivative of the loss function with respect to
+ # parameters if lossprime is true
+ if lossprime:
+ if model.parameters.mode == 'image-centered':
+ raise NotImplementedError('This needs to be coded.')
+ elif model.parameters.mode == 'atom-centered':
+ if self.d is None:
+ dforces_dparameters = \
+ model.calculate_dForces_dParameters(
+ self.fingerprints[hash],
+ self.fingerprintprimes[hash])
+ else:
+ dforces_dparameters = \
+ model.calculate_numerical_dForces_dParameters(
+ self.fingerprints[hash],
+ self.fingerprintprimes[hash],
+ d=self.d)
+ for selfindex in range(no_of_atoms):
+ for i in range(3):
+ temp = p.force_coefficient * (2.0 / 3.0) * \
+ (amp_forces[selfindex][i] -
+ actual_forces[selfindex][i]) * \
+ dforces_dparameters[(selfindex, i)] \
+ / no_of_atoms
+ dloss_dparameters += temp
+
+ loss = p.energy_coefficient * energyloss
+ if p.force_coefficient is not None:
+ loss += p.force_coefficient * forceloss
+ dloss_dparameters = np.array(dloss_dparameters)
+
+ # if overfit coefficient is more than zero, overfit contribution to
+ # loss and dloss_dparameters is also added.
+ if p.overfit > 0.:
+ overfitloss = 0.
+ for component in parametervector:
+ overfitloss += component ** 2.
+ overfitloss *= p.overfit
+ loss += overfitloss
+ doverfitloss_dparameters = \
+ 2 * p.overfit * np.array(parametervector)
+ dloss_dparameters += doverfitloss_dparameters
+
+ return loss, dloss_dparameters, energyloss, forceloss, \
+ energy_maxresid, force_maxresid
+
+ # All incoming requests will be dictionaries with three keys.
+ # d['id']: process id number, assigned when process created above.
+ # d['subject']: what the message is asking for / telling you.
+ # d['data']: optional data passed from worker.
+
+ def process_parallels(self, vector, server, n_pids, keys, args):
+ """
+
+ Parameters
+ ----------
+ vector : list
+ Parameters of the regression model in the form of a list.
+ server : object
+ Master session of parallel processing.
+ processes: list of objects
+ Worker sessions for parallel processing.
+ keys : list
+ List of images keys for worker processes.
+ args : dict
+ Dictionary containing arguments of the method to be called on each
+ worker process.
+ """
+ # For each process
+ finished = np.array([False] * n_pids)
+ results = {'loss': 0.,
+ 'dloss_dparameters': [0.] * len(vector),
+ 'energy_loss': 0.,
+ 'force_loss': 0.,
+ 'energy_maxresid': 0.,
+ 'force_maxresid': 0.}
+ while not finished.all():
+ message = server.recv_pyobj()
+ if message['subject'] == '<purpose>':
+ server.send_string('calculate_loss_function')
+ elif message['subject'] == '<request>':
+ request = message['data'] # Variable name.
+ if request == 'images':
+ subimages = {k: self.images[k] for k in
+ keys[int(message['id'])]}
+ server.send_pyobj(subimages)
+ elif request == 'fortran':
+ server.send_pyobj(self._model.fortran)
+ elif request == 'modelstring':
+ server.send_pyobj(self._model.tostring())
+ elif request == 'lossfunctionstring':
+ server.send_pyobj(self.parameters.tostring())
+ elif request == 'fingerprints':
+ server.send_pyobj({k: self.fingerprints[k] for k in
+ keys[int(message['id'])]})
+ elif request == 'fingerprintprimes':
+ if self.fingerprintprimes is not None:
+ server.send_pyobj({k: self.fingerprintprimes[k] for k
+ in keys[int(message['id'])]})
+ else:
+ server.send_pyobj(None)
+ elif request == 'args':
+ server.send_pyobj(args)
+ elif request == 'parameters':
+ if finished[int(message['id'])]:
+ server.send_pyobj('<continue>')
+ else:
+ server.send_pyobj(vector)
+ else:
+ raise NotImplementedError()
+ elif message['subject'] == '<result>':
+ result = message['data']
+ server.send_string('meaningless reply')
+
+ results['loss'] += result['loss']
+ results['dloss_dparameters'] += result['dloss_dparameters']
+ results['energy_loss'] += result['energy_loss']
+ results['force_loss'] += result['force_loss']
+ if result['energy_maxresid'] > results['energy_maxresid']:
+ results['energy_maxresid'] = result['energy_maxresid']
+ if result['force_maxresid'] > results['force_maxresid']:
+ results['force_maxresid'] = result['force_maxresid']
+ finished[int(message['id'])] = True
+
+ return results
+
+ def check_convergence(self, loss, energy_loss, force_loss,
+ energy_maxresid, force_maxresid):
+ """Check convergence
+
+ Checks to see whether convergence is met; if it is, raises
+ ConvergenceException to stop the optimizer.
+
+ Parameters
+ ----------
+ loss : float
+ Value of the loss function.
+ energy_loss : float
+ Value of the energy contribution of the loss function.
+ force_loss : float
+ Value of the force contribution of the loss function.
+ energy_maxresid : float
+ Maximum energy residual.
+ force_maxresid : float
+ Maximum force residual.
+ """
+ p = self.parameters
+ energy_rmse_converged = True
+ log = self._model.log
+ if p.convergence['energy_rmse'] is not None:
+ energy_rmse = np.sqrt(energy_loss / len(self.images))
+ if energy_rmse > p.convergence['energy_rmse']:
+ energy_rmse_converged = False
+ energy_maxresid_converged = True
+ if p.convergence['energy_maxresid'] is not None:
+ if energy_maxresid > p.convergence['energy_maxresid']:
+ energy_maxresid_converged = False
+ if p.force_coefficient is not None:
+ force_rmse_converged = True
+ if p.convergence['force_rmse'] is not None:
+ force_rmse = np.sqrt(force_loss / len(self.images))
+ if force_rmse > p.convergence['force_rmse']:
+ force_rmse_converged = False
+ force_maxresid_converged = True
+ if p.convergence['force_maxresid'] is not None:
+ if force_maxresid > p.convergence['force_maxresid']:
+ force_maxresid_converged = False
+
+ if self.log_losses:
+ log('%5i %19s %12.4e %10.4e %1s'
+ ' %10.4e %1s %10.4e %1s %10.4e %1s' %
+ (self._step, now(), loss, energy_rmse,
+ 'C' if energy_rmse_converged else '-',
+ energy_maxresid,
+ 'C' if energy_maxresid_converged else '-',
+ force_rmse,
+ 'C' if force_rmse_converged else '-',
+ force_maxresid,
+ 'C' if force_maxresid_converged else '-'))
+
+ self._step += 1
+ return energy_rmse_converged and energy_maxresid_converged and \
+ force_rmse_converged and force_maxresid_converged
+ else:
+ if self.log_losses:
+ log('%5i %19s %12.4e %10.4e %1s %10.4e %1s' %
+ (self._step, now(), loss, energy_rmse,
+ 'C' if energy_rmse_converged else '-',
+ energy_maxresid,
+ 'C' if energy_maxresid_converged else '-'))
+ self._step += 1
+ return energy_rmse_converged and energy_maxresid_converged
+
+
+def calculate_fingerprints_range(fp, images):
+ """Calculates the range for the fingerprints corresponding to images,
+ stored in fp. fp is a fingerprints object with the fingerprints data
+ stored in a dictionary-like object at fp.fingerprints. (Typically this
+ is a .utilties.Data structure.) images is a hashed dictionary of atoms
+ for which to consider the range.
+
+ In image-centered mode, returns an array of (min, max) values for each
+ fingerprint. In atom-centered mode, returns a dictionary of such
+ arrays, one per element.
+ """
+ if fp.parameters.mode == 'image-centered':
+ raise NotImplementedError()
+ elif fp.parameters.mode == 'atom-centered':
+ fprange = {}
+ for hash in images.keys():
+ imagefingerprints = fp.fingerprints[hash]
+ for element, fingerprint in imagefingerprints:
+ if element not in fprange:
+ fprange[element] = [[_, _] for _ in fingerprint]
+ else:
+ assert len(fprange[element]) == len(fingerprint)
+ for i, ridge in enumerate(fingerprint):
+ if ridge < fprange[element][i][0]:
+ fprange[element][i][0] = ridge
+ elif ridge > fprange[element][i][1]:
+ fprange[element][i][1] = ridge
+ for key, value in fprange.items():
+ fprange[key] = value
+ return fprange
+
+
+def ravel_data(train_forces,
+ mode,
+ images,
+ fingerprints,
+ fingerprintprimes,):
+ """
+ Reshapes data of images into lists.
+
+ Parameters
+ ---------
+ train_forces : bool
+ Determining whether forces are also trained or not.
+ mode : str
+ Can be either 'atom-centered' or 'image-centered'.
+ images : list or str
+ List of ASE atoms objects with positions, symbols, energies, and forces
+ in ASE format. This is the training set of data. This can also be the
+ path to an ASE trajectory (.traj) or database (.db) file. Energies can
+ be obtained from any reference, e.g. DFT calculations.
+
+ fingerprints : dict
+ Dictionary with images hashs as keys and the corresponding fingerprints
+ as values.
+ fingerprintprimes : dict
+ Dictionary with images hashs as keys and the corresponding fingerprint
+ derivatives as values.
+ """
+ from ase.data import atomic_numbers
+
+ actual_energies = [image.get_potential_energy(apply_constraint=False)
+ for image in images.values()]
+
+ if mode == 'atom-centered':
+ num_images_atoms = [len(image) for image in images.values()]
+ atomic_numbers = [atomic_numbers[atom.symbol]
+ for image in images.values() for atom in image]
+
+ def ravel_fingerprints(images,
+ fingerprints):
+ """
+ Reshape fingerprints of images into a list.
+ """
+ raveled_fingerprints = []
+ elements = []
+ for hash, image in images.items():
+ for index in range(len(image)):
+ elements += [fingerprints[hash][index][0]]
+ raveled_fingerprints += [fingerprints[hash][index][1]]
+ elements = sorted(set(elements))
+ # Could also work without images:
+# raveled_fingerprints = [afp
+# for hash, value in fingerprints.iteritems()
+# for (element, afp) in value]
+ return elements, raveled_fingerprints
+
+ elements, raveled_fingerprints = ravel_fingerprints(images,
+ fingerprints)
+ else:
+ atomic_positions = [image.positions.ravel()
+ for image in images.values()]
+
+ if train_forces is True:
+
+ actual_forces = \
+ [image.get_forces(apply_constraint=False)[index]
+ for image in images.values() for index in range(len(image))]
+
+ if mode == 'atom-centered':
+
+ def ravel_neighborlists_and_fingerprintprimes(images,
+ fingerprintprimes):
+ """
+ Reshape neighborlists and fingerprintprimes of images into a
+ list and a matrix, respectively.
+ """
+ # Only neighboring atoms of type II (within the main cell)
+ # need to be sent to fortran for force training.
+ # All keys in fingerprintprimes are for type II neighborhoods.
+ # Also note that each atom is considered as neighbor of
+ # itself in fingerprintprimes.
+ num_neighbors = []
+ raveled_neighborlists = []
+ raveled_fingerprintprimes = []
+ for hash, image in images.items():
+ for atom in image:
+ selfindex = atom.index
+ selfsymbol = atom.symbol
+ selfneighborindices = []
+ selfneighborsymbols = []
+ for key, derafp in fingerprintprimes[hash].items():
+ # key = (selfindex, selfsymbol, nindex, nsymbol, i)
+ # i runs from 0 to 2. neighbor indices and symbols
+ # should be added just once.
+ if key[0] == selfindex and key[4] == 0:
+ selfneighborindices += [key[2]]
+ selfneighborsymbols += [key[3]]
+
+ neighborcount = 0
+ for nindex, nsymbol in zip(selfneighborindices,
+ selfneighborsymbols):
+ raveled_neighborlists += [nindex]
+ neighborcount += 1
+ for i in range(3):
+ fpprime = fingerprintprimes[hash][(selfindex,
+ selfsymbol,
+ nindex,
+ nsymbol,
+ i)]
+ raveled_fingerprintprimes += [fpprime]
+ num_neighbors += [neighborcount]
+
+ return (num_neighbors,
+ raveled_neighborlists,
+ raveled_fingerprintprimes)
+
+ (num_neighbors,
+ raveled_neighborlists,
+ raveled_fingerprintprimes) = \
+ ravel_neighborlists_and_fingerprintprimes(images,
+ fingerprintprimes)
+ if mode == 'image-centered':
+ if not train_forces:
+ return (actual_energies, atomic_positions)
+ else:
+ return (actual_energies, actual_forces, atomic_positions)
+ else:
+ if not train_forces:
+ return (actual_energies, elements, num_images_atoms,
+ atomic_numbers, raveled_fingerprints)
+ else:
+ return (actual_energies, actual_forces, elements, num_images_atoms,
+ atomic_numbers, raveled_fingerprints, num_neighbors,
+ raveled_neighborlists, raveled_fingerprintprimes)
+
+
+def send_data_to_fortran(_fmodules,
+ energy_coefficient,
+ force_coefficient,
+ overfit,
+ train_forces,
+ num_atoms,
+ num_images,
+ actual_energies,
+ actual_forces,
+ atomic_positions,
+ num_images_atoms,
+ atomic_numbers,
+ raveled_fingerprints,
+ num_neighbors,
+ raveled_neighborlists,
+ raveled_fingerprintprimes,
+ model,
+ d):
+ """
+ Function that sends images data to fortran code. Is used just once on each
+ core.
+ """
+ from ase.data import atomic_numbers as an
+
+ if model.parameters.mode == 'image-centered':
+ mode_signal = 1
+ elif model.parameters.mode == 'atom-centered':
+ mode_signal = 2
+
+ _fmodules.images_props.num_images = num_images
+ _fmodules.images_props.actual_energies = actual_energies
+ if train_forces:
+ _fmodules.images_props.actual_forces = actual_forces
+
+ _fmodules.model_props.energy_coefficient = energy_coefficient
+ _fmodules.model_props.force_coefficient = force_coefficient
+ _fmodules.model_props.overfit = overfit
+ _fmodules.model_props.train_forces = train_forces
+ _fmodules.model_props.mode_signal = mode_signal
+ if d is None:
+ _fmodules.model_props.numericprime = False
+ else:
+ _fmodules.model_props.numericprime = True
+ _fmodules.model_props.d = d
+
+ if model.parameters.mode == 'atom-centered':
+ fprange = model.parameters.fprange
+ elements = sorted(fprange.keys())
+ num_elements = len(elements)
+ elements_numbers = [an[elm] for elm in elements]
+ min_fingerprints = \
+ [[fprange[elm][_][0] for _ in range(len(fprange[elm]))]
+ for elm in elements]
+ max_fingerprints = [[fprange[elm][_][1]
+ for _
+ in range(len(fprange[elm]))]
+ for elm in elements]
+ num_fingerprints_of_elements = \
+ [len(fprange[elm]) for elm in elements]
+
+ _fmodules.images_props.num_elements = num_elements
+ _fmodules.images_props.elements_numbers = elements_numbers
+ _fmodules.images_props.num_images_atoms = num_images_atoms
+ _fmodules.images_props.atomic_numbers = atomic_numbers
+ if train_forces:
+ _fmodules.images_props.num_neighbors = num_neighbors
+ _fmodules.images_props.raveled_neighborlists = \
+ raveled_neighborlists
+
+ _fmodules.fingerprint_props.num_fingerprints_of_elements = \
+ num_fingerprints_of_elements
+ _fmodules.fingerprint_props.raveled_fingerprints = raveled_fingerprints
+ _fmodules.neuralnetwork.min_fingerprints = min_fingerprints
+ _fmodules.neuralnetwork.max_fingerprints = max_fingerprints
+ if train_forces:
+ _fmodules.fingerprint_props.raveled_fingerprintprimes = \
+ raveled_fingerprintprimes
+ else:
+ _fmodules.images_props.num_atoms = num_atoms
+ _fmodules.images_props.atomic_positions = atomic_positions
+
+ # for neural neyworks only
+ if model.parameters['importname'] == '.model.neuralnetwork.NeuralNetwork':
+
+ hiddenlayers = model.parameters.hiddenlayers
+ activation = model.parameters.activation
+
+ if model.parameters.mode == 'atom-centered':
+ from collections import OrderedDict
+ no_layers_of_elements = \
+ [3 if isinstance(hiddenlayers[elm], int)
+ else (len(hiddenlayers[elm]) + 2)
+ for elm in elements]
+ nn_structure = OrderedDict()
+ for elm in elements:
+ len_of_fps = len(fprange[elm])
+ if isinstance(hiddenlayers[elm], int):
+ nn_structure[elm] = \
+ ([len_of_fps] + [hiddenlayers[elm]] + [1])
+ else:
+ nn_structure[elm] = \
+ ([len_of_fps] +
+ [layer for layer in hiddenlayers[elm]] + [1])
+
+ no_nodes_of_elements = [nn_structure[elm][_]
+ for elm in elements
+ for _ in range(len(nn_structure[elm]))]
+
+ else:
+ num_atoms = model.parameters.num_atoms
+ if isinstance(hiddenlayers, int):
+ no_layers_of_elements = [3]
+ else:
+ no_layers_of_elements = [len(hiddenlayers) + 2]
+ if isinstance(hiddenlayers, int):
+ nn_structure = ([3 * num_atoms] + [hiddenlayers] + [1])
+ else:
+ nn_structure = ([3 * num_atoms] +
+ [layer for layer in hiddenlayers] + [1])
+ no_nodes_of_elements = [nn_structure[_]
+ for _ in range(len(nn_structure))]
+
+ _fmodules.neuralnetwork.no_layers_of_elements = no_layers_of_elements
+ _fmodules.neuralnetwork.no_nodes_of_elements = no_nodes_of_elements
+ if activation == 'tanh':
+ activation_signal = 1
+ elif activation == 'sigmoid':
+ activation_signal = 2
+ elif activation == 'linear':
+ activation_signal = 3
+ _fmodules.neuralnetwork.activation_signal = activation_signal
diff --git a/amp/model/__main__.py b/amp/model/__main__.py
new file mode 100644
index 0000000..557d31b
--- /dev/null
+++ b/amp/model/__main__.py
@@ -0,0 +1,119 @@
+"""Directly calling this module; apparently from another node.
+Calls should come as
+
+python -m amp.model id hostname:port
+
+This session will then start a zmq session with that socket, labeling
+itself with id. Instructions on what to do will come from the socket.
+"""
+import sys
+import tempfile
+import zmq
+
+from ..utilities import MessageDictionary, string2dict, Logger
+from .. import importhelper
+
+
+hostsocket = sys.argv[-1]
+proc_id = sys.argv[-2]
+msg = MessageDictionary(proc_id)
+
+# Send standard lines to stdout signaling process started and where
+# error is directed.
+print('<amp-connect>') # Signal that program started.
+sys.stderr = tempfile.NamedTemporaryFile(mode='w', delete=False,
+ suffix='.stderr')
+print('Log and stderr written to %s<stderr>' % sys.stderr.name)
+
+# Also send logger output to stderr to aid in debugging.
+log = Logger(file=sys.stderr)
+
+# Establish client session via zmq; find purpose.
+context = zmq.Context()
+socket = context.socket(zmq.REQ)
+socket.connect('tcp://%s' % hostsocket)
+socket.send_pyobj(msg('<purpose>'))
+purpose = socket.recv_string()
+
+if purpose == 'calculate_loss_function':
+ # Request variables.
+ socket.send_pyobj(msg('<request>', 'fortran'))
+ fortran = socket.recv_pyobj()
+ socket.send_pyobj(msg('<request>', 'modelstring'))
+ modelstring = socket.recv_pyobj()
+ dictionary = string2dict(modelstring)
+ Model = importhelper(dictionary.pop('importname'))
+ log('Model received:')
+ log(str(dictionary))
+ model = Model(fortran=fortran, **dictionary)
+ model.log = log
+ log('Model set up.')
+
+ socket.send_pyobj(msg('<request>', 'args'))
+ args = socket.recv_pyobj()
+ d = args['d']
+ socket.send_pyobj(msg('<request>', 'lossfunctionstring'))
+ lossfunctionstring = socket.recv_pyobj()
+ dictionary = string2dict(lossfunctionstring)
+ log(str(dictionary))
+ LossFunction = importhelper(dictionary.pop('importname'))
+ lossfunction = LossFunction(parallel={'cores': 1},
+ raise_ConvergenceOccurred=False,
+ d=d, **dictionary)
+ log('Loss function set up.')
+
+ images = None
+ socket.send_pyobj(msg('<request>', 'images'))
+ images = socket.recv_pyobj()
+ log('Images received.')
+
+ fingerprints = None
+ socket.send_pyobj(msg('<request>', 'fingerprints'))
+ fingerprints = socket.recv_pyobj()
+ log('Fingerprints received.')
+
+ fingerprintprimes = None
+ socket.send_pyobj(msg('<request>', 'fingerprintprimes'))
+ fingerprintprimes = socket.recv_pyobj()
+ log('Fingerprintprimes received.')
+
+ # Set up local loss function.
+ lossfunction.attach_model(model,
+ fingerprints=fingerprints,
+ fingerprintprimes=fingerprintprimes,
+ images=images)
+ log('Images, fingerprints, and fingerprintprimes '
+ 'attached to the loss function.')
+
+ if model.fortran:
+ log('fmodules will be used to evaluate loss function.')
+ else:
+ log('Fortran will not be used to evaluate loss function.')
+ # Now wait for parameters, and send the component of the loss function.
+ while True:
+ socket.send_pyobj(msg('<request>', 'parameters'))
+ parameters = socket.recv_pyobj()
+ if parameters == '<stop>':
+ # FIXME/ap: I removed an fmodules.deallocate_variables() call
+ # here. Do we need to add this to LossFunction?
+ break
+ elif parameters == '<continue>':
+ # Master is waiting for other workers to finish.
+ # Any more elegant way
+ # to do this without opening another comm channel?
+ # or having a thread for each process?
+ pass
+ else:
+ # FIXME/ap: Why do we need to request this every time?
+ # Couldn't it be part of earlier request?
+ socket.send_pyobj(msg('<request>', 'args'))
+ args = socket.recv_pyobj()
+ lossprime = args['lossprime']
+ output = lossfunction.get_loss(parameters,
+ lossprime=lossprime)
+
+ socket.send_pyobj(msg('<result>', output))
+ socket.recv_string()
+
+else:
+ raise NotImplementedError('Purpose "%s" unknown.' % purpose)
diff --git a/amp/model/neuralnetwork.f90 b/amp/model/neuralnetwork.f90
new file mode 100644
index 0000000..498eaf7
--- /dev/null
+++ b/amp/model/neuralnetwork.f90
@@ -0,0 +1,1883 @@
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+! module that utilizes the regression model to calculate energies
+! and forces as well as their derivatives. Function names ending
+! with an underscore correspond to image-centered mode.
+
+ module neuralnetwork
+ implicit none
+
+! the data of neuralnetwork (should be fed in by python)
+ double precision, allocatable::min_fingerprints(:, :)
+ double precision, allocatable::max_fingerprints(:, :)
+ integer, allocatable:: no_layers_of_elements(:)
+ integer, allocatable:: no_nodes_of_elements(:)
+ integer:: activation_signal
+
+ type:: real_two_d_array
+ sequence
+ double precision, allocatable:: twodarray(:,:)
+ end type real_two_d_array
+
+ type:: element_parameters
+ sequence
+ double precision:: intercept
+ double precision:: slope
+ type(real_two_d_array), allocatable:: weights(:)
+ end type element_parameters
+
+ type:: real_one_d_array
+ sequence
+ double precision, allocatable:: onedarray(:)
+ end type real_one_d_array
+
+ contains
+
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+! Returns energy value in the image-centered mode.
+ function calculate_image_energy(num_inputs, inputs, num_parameters, &
+ parameters)
+ implicit none
+
+ integer:: num_inputs, num_parameters
+ double precision:: inputs(num_inputs)
+ double precision:: parameters(num_parameters)
+ double precision:: calculate_image_energy
+
+ integer:: p, m, n, layer
+ integer:: l, j, num_rows, num_cols, q
+ integer, allocatable:: hiddensizes(:)
+ double precision, allocatable:: net(:)
+ type(real_one_d_array), allocatable:: o(:), ohat(:)
+ type(real_two_d_array), allocatable:: weights(:)
+ double precision:: intercept
+ double precision:: slope
+
+! changing the form of parameters from vector into derived-types
+ l = 0
+ allocate(weights(no_layers_of_elements(1)-1))
+ do j = 1, no_layers_of_elements(1) - 1
+ num_rows = no_nodes_of_elements(j) + 1
+ num_cols = no_nodes_of_elements(j + 1)
+ allocate(weights(j)%twodarray(num_rows, num_cols))
+ do p = 1, num_rows
+ do q = 1, num_cols
+ weights(j)%twodarray(p, q) = &
+ parameters(l + (p - 1) * num_cols + q)
+ end do
+ end do
+ l = l + num_rows * num_cols
+ end do
+ intercept = parameters(l + 1)
+ slope = parameters(l + 2)
+
+ allocate(hiddensizes(no_layers_of_elements(1) - 2))
+ do m = 1, no_layers_of_elements(1) - 2
+ hiddensizes(m) = no_nodes_of_elements(m + 1)
+ end do
+
+ allocate(o(no_layers_of_elements(1)))
+ allocate(ohat(no_layers_of_elements(1)))
+ layer = 1
+ allocate(o(1)%onedarray(num_inputs))
+ allocate(ohat(1)%onedarray(num_inputs + 1))
+ do m = 1, num_inputs
+ o(1)%onedarray(m) = inputs(m)
+ end do
+ do layer = 1, size(hiddensizes) + 1
+ do m = 1, size(weights(layer)%twodarray, dim=1) - 1
+ ohat(layer)%onedarray(m) = o(layer)%onedarray(m)
+ end do
+ ohat(layer)%onedarray(&
+ size(weights(layer)%twodarray, dim=1)) = 1.0d0
+ allocate(net(size(weights(layer)%twodarray, dim=2)))
+ allocate(o(layer + 1)%onedarray(&
+ size(weights(layer)%twodarray, dim=2)))
+ allocate(ohat(layer + 1)%onedarray(&
+ size(weights(layer)%twodarray, dim=2) + 1))
+ do m = 1, size(weights(layer)%twodarray, dim=2)
+ net(m) = 0.0d0
+ do n = 1, size(weights(layer)%twodarray, dim=1)
+ net(m) = net(m) + &
+ ohat(layer)%onedarray(n) &
+ * weights(layer)%twodarray(n, m)
+ end do
+ if (activation_signal == 1) then
+ o(layer + 1)%onedarray(m) = &
+ tanh(net(m))
+ else if (activation_signal == 2) then
+ o(layer + 1)%onedarray(m) = &
+ 1.0d0 / (1.0d0 + exp(- net(m)))
+ else if (activation_signal == 3) then
+ o(layer + 1)%onedarray(m) = net(m)
+ end if
+ ohat(layer + 1)%onedarray(m) = o(layer + 1)%onedarray(m)
+ end do
+ ohat(layer + 1)%onedarray(&
+ size(weights(layer)%twodarray, dim=2) + 1) = 1.0d0
+ deallocate(net)
+ end do
+
+ calculate_image_energy = slope * o(layer)%onedarray(1) + intercept
+
+! deallocating neural network
+ deallocate(hiddensizes)
+ do p = 1, size(o)
+ deallocate(o(p)%onedarray)
+ end do
+ deallocate(o)
+ do p = 1, size(ohat)
+ deallocate(ohat(p)%onedarray)
+ end do
+ deallocate(ohat)
+
+! deallocating derived type parameters
+ do p = 1, size(weights)
+ deallocate(weights(p)%twodarray)
+ end do
+ deallocate(weights)
+
+ end function calculate_image_energy
+
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+! Returns energy value in the atom-centered mode.
+ function calculate_atomic_energy(symbol, &
+ len_of_fingerprint, fingerprint, &
+ num_elements, elements_numbers, &
+ num_parameters, parameters)
+ implicit none
+
+ integer:: symbol, num_parameters, &
+ len_of_fingerprint, num_elements
+ double precision:: fingerprint(len_of_fingerprint)
+ integer:: elements_numbers(num_elements)
+ double precision:: parameters(num_parameters)
+ double precision:: calculate_atomic_energy
+
+ integer:: p, element, m, n, layer
+ integer:: k, l, j, num_rows, num_cols, q
+ integer, allocatable:: hiddensizes(:)
+ double precision, allocatable:: net(:)
+ type(real_one_d_array), allocatable:: o(:), ohat(:)
+ type(element_parameters):: unraveled_parameters(num_elements)
+ double precision:: fingerprint_(len_of_fingerprint)
+
+ ! scaling fingerprints
+ do element = 1, num_elements
+ if (symbol == &
+ elements_numbers(element)) then
+ exit
+ end if
+ end do
+ do l = 1, len_of_fingerprint
+ if ((max_fingerprints(element, l) - &
+ min_fingerprints(element, l)) .GT. &
+ (10.0d0 ** (-8.0d0))) then
+ fingerprint_(l) = -1.0d0 + 2.0d0 * &
+ (fingerprint(l) - min_fingerprints(element, l)) / &
+ (max_fingerprints(element, l) - &
+ min_fingerprints(element, l))
+ else
+ fingerprint_(l) = fingerprint(l)
+ endif
+ end do
+
+! changing the form of parameters from vector into derived-types
+ k = 0
+ l = 0
+ do element = 1, num_elements
+ allocate(unraveled_parameters(element)%weights(&
+ no_layers_of_elements(element)-1))
+ if (element .GT. 1) then
+ k = k + no_layers_of_elements(element - 1)
+ end if
+ do j = 1, no_layers_of_elements(element) - 1
+ num_rows = no_nodes_of_elements(k + j) + 1
+ num_cols = no_nodes_of_elements(k + j + 1)
+ allocate(unraveled_parameters(&
+ element)%weights(j)%twodarray(num_rows, num_cols))
+ do p = 1, num_rows
+ do q = 1, num_cols
+ unraveled_parameters(element)%weights(j)%twodarray(&
+ p, q) = parameters(l + (p - 1) * num_cols + q)
+ end do
+ end do
+ l = l + num_rows * num_cols
+ end do
+ end do
+ do element = 1, num_elements
+ unraveled_parameters(element)%intercept = &
+ parameters(l + 2 * element - 1)
+ unraveled_parameters(element)%slope = &
+ parameters(l + 2 * element)
+ end do
+
+ p = 0
+ do element = 1, num_elements
+ if (symbol == elements_numbers(element)) then
+ exit
+ else
+ p = p + no_layers_of_elements(element)
+ end if
+ end do
+ allocate(hiddensizes(no_layers_of_elements(element) - 2))
+ do m = 1, no_layers_of_elements(element) - 2
+ hiddensizes(m) = no_nodes_of_elements(p + m + 1)
+ end do
+
+ allocate(o(no_layers_of_elements(element)))
+ allocate(ohat(no_layers_of_elements(element)))
+ layer = 1
+ allocate(o(1)%onedarray(len_of_fingerprint))
+ allocate(ohat(1)%onedarray(len_of_fingerprint + 1))
+ do m = 1, len_of_fingerprint
+ o(1)%onedarray(m) = fingerprint_(m)
+ end do
+ do layer = 1, size(hiddensizes) + 1
+ do m = 1, size(unraveled_parameters(element)%weights(&
+ layer)%twodarray, dim=1) - 1
+ ohat(layer)%onedarray(m) = o(layer)%onedarray(m)
+ end do
+ ohat(layer)%onedarray(size(unraveled_parameters(&
+ element)%weights(layer)%twodarray, dim=1)) = 1.0d0
+ allocate(net(size(unraveled_parameters(&
+ element)%weights(layer)%twodarray, dim=2)))
+ allocate(o(layer + 1)%onedarray(size(unraveled_parameters(&
+ element)%weights(layer)%twodarray, dim=2)))
+ allocate(ohat(layer + 1)%onedarray(size(unraveled_parameters(&
+ element)%weights(layer)%twodarray, dim=2) + 1))
+ do m = 1, size(unraveled_parameters(element)%weights(&
+ layer)%twodarray, dim=2)
+ net(m) = 0.0d0
+ do n = 1, size(unraveled_parameters(element)%weights(&
+ layer)%twodarray, dim=1)
+ net(m) = net(m) + &
+ ohat(layer)%onedarray(n) * unraveled_parameters(&
+ element)%weights(layer)%twodarray(n, m)
+ end do
+ if (activation_signal == 1) then
+ o(layer + 1)%onedarray(m) = tanh(net(m))
+ else if (activation_signal == 2) then
+ o(layer + 1)%onedarray(m) = &
+ 1.0d0 / (1.0d0 + exp(- net(m)))
+ else if (activation_signal == 3) then
+ o(layer + 1)%onedarray(m) = net(m)
+ end if
+ ohat(layer + 1)%onedarray(m) = o(layer + 1)%onedarray(m)
+ end do
+ ohat(layer + 1)%onedarray(size(unraveled_parameters(&
+ element)%weights(layer)%twodarray, dim=2) + 1) = 1.0d0
+ deallocate(net)
+ end do
+
+ calculate_atomic_energy = unraveled_parameters(element)%slope * &
+ o(layer)%onedarray(1) + unraveled_parameters(element)%intercept
+
+! deallocating neural network
+ deallocate(hiddensizes)
+ do p = 1, size(o)
+ deallocate(o(p)%onedarray)
+ end do
+ deallocate(o)
+ do p = 1, size(ohat)
+ deallocate(ohat(p)%onedarray)
+ end do
+ deallocate(ohat)
+
+! deallocating derived type parameters
+ do element = 1, num_elements
+ deallocate(unraveled_parameters(element)%weights)
+ end do
+
+ end function calculate_atomic_energy
+
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+! Returns force value in the image-centered mode.
+ function calculate_force_(num_inputs, inputs, inputs_, &
+ num_parameters, parameters)
+ implicit none
+
+ integer:: num_inputs, num_parameters
+ double precision:: inputs(num_inputs)
+ double precision:: inputs_(num_inputs)
+ double precision:: parameters(num_parameters)
+ double precision:: calculate_force_
+
+ double precision, allocatable:: temp(:)
+ integer:: p, q, m, n, nn, layer
+ integer:: l, j, num_rows, num_cols
+ integer, allocatable:: hiddensizes(:)
+ double precision, allocatable:: net(:)
+ type(real_one_d_array), allocatable:: o(:), ohat(:)
+ type(real_one_d_array), allocatable:: doutputs_dinputs(:)
+ type(real_two_d_array), allocatable:: weights(:)
+ double precision:: intercept
+ double precision:: slope
+
+! changing the form of parameters to derived-types
+ l = 0
+ allocate(weights(no_layers_of_elements(1)-1))
+ do j = 1, no_layers_of_elements(1) - 1
+ num_rows = no_nodes_of_elements(j) + 1
+ num_cols = no_nodes_of_elements(j + 1)
+ allocate(weights(j)%twodarray(num_rows, num_cols))
+ do p = 1, num_rows
+ do q = 1, num_cols
+ weights(j)%twodarray(p, q) = &
+ parameters(l + (p - 1) * num_cols + q)
+ end do
+ end do
+ l = l + num_rows * num_cols
+ end do
+
+ intercept = parameters(l + 1)
+ slope = parameters(l + 2)
+
+ allocate(hiddensizes(no_layers_of_elements(1) - 2))
+ do m = 1, no_layers_of_elements(1) - 2
+ hiddensizes(m) = no_nodes_of_elements(m + 1)
+ end do
+ allocate(o(no_layers_of_elements(1)))
+ allocate(ohat(no_layers_of_elements(1)))
+ layer = 1
+ allocate(o(1)%onedarray(num_inputs))
+ allocate(ohat(1)%onedarray(num_inputs + 1))
+ do m = 1, num_inputs
+ o(1)%onedarray(m) = inputs(m)
+ end do
+ do layer = 1, size(hiddensizes) + 1
+ do m = 1, size(weights(layer)%twodarray, dim=1) - 1
+ ohat(layer)%onedarray(m) = o(layer)%onedarray(m)
+ end do
+ ohat(layer)%onedarray(&
+ size(weights(layer)%twodarray, dim=1)) = 1.0d0
+ allocate(net(size(weights(layer)%twodarray, dim=2)))
+ allocate(o(layer + 1)%onedarray(&
+ size(weights(layer)%twodarray, dim=2)))
+ allocate(ohat(layer + 1)%onedarray(&
+ size(weights(layer)%twodarray, dim=2) + 1))
+ do m = 1, size(weights(layer)%twodarray, dim=2)
+ net(m) = 0.0d0
+ do n = 1, size(weights(layer)%twodarray, dim=1)
+ net(m) = net(m) + &
+ ohat(layer)%onedarray(n) * &
+ weights(layer)%twodarray(n, m)
+ end do
+ if (activation_signal == 1) then
+ o(layer + 1)%onedarray(m) = tanh(net(m))
+ else if (activation_signal == 2) then
+ o(layer + 1)%onedarray(m) = &
+ 1.0d0 / (1.0d0 + exp(- net(m)))
+ else if (activation_signal == 3) then
+ o(layer + 1)%onedarray(m) = net(m)
+ end if
+ ohat(layer + 1)%onedarray(m) = o(layer + 1)%onedarray(m)
+ end do
+ deallocate(net)
+ end do
+ nn = size(o) - 2
+ allocate(doutputs_dinputs(nn + 2))
+ allocate(doutputs_dinputs(1)%onedarray(num_inputs))
+ do m = 1, num_inputs
+ doutputs_dinputs(1)%onedarray(m) = inputs_(m)
+ end do
+ do layer = 1, nn + 1
+ allocate(temp(size(weights(layer)%twodarray, dim = 2)))
+ do p = 1, size(weights(layer)%twodarray, dim = 2)
+ temp(p) = 0.0d0
+ do q = 1, size(weights(layer)%twodarray, dim = 1) - 1
+ temp(p) = temp(p) + doutputs_dinputs(&
+ layer)%onedarray(q) * weights(layer)%twodarray(q, p)
+ end do
+ end do
+ q = size(o(layer + 1)%onedarray)
+ allocate(doutputs_dinputs(layer + 1)%onedarray(q))
+ do p = 1, size(o(layer + 1)%onedarray)
+ if (activation_signal == 1) then
+ doutputs_dinputs(layer + 1)%onedarray(p) = &
+ temp(p) * (1.0d0 - o(layer + 1)%onedarray(p) * &
+ o(layer + 1)%onedarray(p))
+ else if (activation_signal == 2) then
+ doutputs_dinputs(layer + 1)%onedarray(p) = &
+ temp(p) * (1.0d0 - o(layer + 1)%onedarray(p)) * &
+ o(layer + 1)%onedarray(p)
+ else if (activation_signal == 3) then
+ doutputs_dinputs(layer+ 1)%onedarray(p) = temp(p)
+ end if
+ end do
+ deallocate(temp)
+ end do
+
+ calculate_force_ = slope * doutputs_dinputs(nn + 2)%onedarray(1)
+ ! force is multiplied by -1, because it is -dE/dx and not dE/dx.
+ calculate_force_ = -1.0d0 * calculate_force_
+! deallocating neural network
+ deallocate(hiddensizes)
+ do p = 1, size(o)
+ deallocate(o(p)%onedarray)
+ end do
+ deallocate(o)
+ do p = 1, size(ohat)
+ deallocate(ohat(p)%onedarray)
+ end do
+ deallocate(ohat)
+ do p = 1, size(doutputs_dinputs)
+ deallocate(doutputs_dinputs(p)%onedarray)
+ end do
+ deallocate(doutputs_dinputs)
+
+! deallocating derived type parameters
+ do p = 1, size(weights)
+ deallocate(weights(p)%twodarray)
+ end do
+ deallocate(weights)
+
+ end function calculate_force_
+
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+! Returns force value in the atom-centered mode.
+ function calculate_force(symbol, len_of_fingerprint, fingerprint, &
+ fingerprintprime, num_elements, elements_numbers, &
+ num_parameters, parameters)
+ implicit none
+
+ integer:: symbol, len_of_fingerprint, num_parameters
+ integer:: num_elements
+ double precision:: fingerprint(len_of_fingerprint)
+ double precision:: fingerprintprime(len_of_fingerprint)
+ integer:: elements_numbers(num_elements)
+ double precision:: parameters(num_parameters)
+ double precision:: calculate_force
+
+ double precision, allocatable:: temp(:)
+ integer:: p, q, element, m, n, nn, layer
+ integer:: k, l, j, num_rows, num_cols
+ integer, allocatable:: hiddensizes(:)
+ double precision, allocatable:: net(:)
+ type(real_one_d_array), allocatable:: o(:), ohat(:)
+ type(real_one_d_array), allocatable:: doutputs_dinputs(:)
+ type(element_parameters):: unraveled_parameters(num_elements)
+ double precision:: fingerprint_(len_of_fingerprint)
+ double precision:: fingerprintprime_(len_of_fingerprint)
+
+ ! scaling fingerprints
+ do element = 1, num_elements
+ if (symbol == &
+ elements_numbers(element)) then
+ exit
+ end if
+ end do
+ do l = 1, len_of_fingerprint
+ if ((max_fingerprints(element, l) - &
+ min_fingerprints(element, l)) .GT. &
+ (10.0d0 ** (-8.0d0))) then
+ fingerprint_(l) = -1.0d0 + 2.0d0 * &
+ (fingerprint(l) - min_fingerprints(element, l)) / &
+ (max_fingerprints(element, l) - &
+ min_fingerprints(element, l))
+ else
+ fingerprint_(l) = fingerprint(l)
+ endif
+ end do
+ ! scaling fingerprintprimes
+ do l = 1, len_of_fingerprint
+ if ((max_fingerprints(element, l) - &
+ min_fingerprints(element, l)) .GT. &
+ (10.0d0 ** (-8.0d0))) then
+ fingerprintprime_(l) = &
+ 2.0d0 * fingerprintprime(l) / &
+ (max_fingerprints(element, l) - &
+ min_fingerprints(element, l))
+ else
+ fingerprintprime_(l) = fingerprintprime(l)
+ endif
+ end do
+
+! changing the form of parameters to derived-types
+ k = 0
+ l = 0
+ do element = 1, num_elements
+ allocate(unraveled_parameters(element)%weights(&
+ no_layers_of_elements(element)-1))
+ if (element .GT. 1) then
+ k = k + no_layers_of_elements(element - 1)
+ end if
+ do j = 1, no_layers_of_elements(element) - 1
+ num_rows = no_nodes_of_elements(k + j) + 1
+ num_cols = no_nodes_of_elements(k + j + 1)
+ allocate(unraveled_parameters(&
+ element)%weights(j)%twodarray(num_rows, num_cols))
+ do p = 1, num_rows
+ do q = 1, num_cols
+ unraveled_parameters(element)%weights(j)%twodarray(&
+ p, q) = parameters(l + (p - 1) * num_cols + q)
+ end do
+ end do
+ l = l + num_rows * num_cols
+ end do
+ end do
+ do element = 1, num_elements
+ unraveled_parameters(element)%intercept = &
+ parameters(l + 2 * element - 1)
+ unraveled_parameters(element)%slope = &
+ parameters(l + 2 * element)
+ end do
+
+ p = 0
+ do element = 1, num_elements
+ if (symbol == elements_numbers(element)) then
+ exit
+ else
+ p = p + no_layers_of_elements(element)
+ end if
+ end do
+
+ allocate(hiddensizes(no_layers_of_elements(element) - 2))
+ do m = 1, no_layers_of_elements(element) - 2
+ hiddensizes(m) = no_nodes_of_elements(p + m + 1)
+ end do
+ allocate(o(no_layers_of_elements(element)))
+ allocate(ohat(no_layers_of_elements(element)))
+ layer = 1
+ allocate(o(1)%onedarray(len_of_fingerprint))
+ allocate(ohat(1)%onedarray(len_of_fingerprint + 1))
+ do m = 1, len_of_fingerprint
+ o(1)%onedarray(m) = fingerprint_(m)
+ end do
+ do layer = 1, size(hiddensizes) + 1
+ do m = 1, size(unraveled_parameters(element)%weights(&
+ layer)%twodarray, dim=1) - 1
+ ohat(layer)%onedarray(m) = o(layer)%onedarray(m)
+ end do
+ ohat(layer)%onedarray(size(unraveled_parameters(&
+ element)%weights(layer)%twodarray, dim=1)) = 1.0d0
+ allocate(net(size(unraveled_parameters(&
+ element)%weights(layer)%twodarray, dim=2)))
+ allocate(o(layer + 1)%onedarray(size(unraveled_parameters(&
+ element)%weights(layer)%twodarray, dim=2)))
+ allocate(ohat(layer + 1)%onedarray(size(unraveled_parameters(&
+ element)%weights(layer)%twodarray, dim=2) + 1))
+ do m = 1, size(unraveled_parameters(element)%weights(&
+ layer)%twodarray, dim=2)
+ net(m) = 0.0d0
+ do n = 1, size(unraveled_parameters(element)%weights(&
+ layer)%twodarray, dim=1)
+ net(m) = net(m) + &
+ ohat(layer)%onedarray(n) * unraveled_parameters(&
+ element)%weights(layer)%twodarray(n, m)
+ end do
+ if (activation_signal == 1) then
+ o(layer + 1)%onedarray(m) = tanh(net(m))
+ else if (activation_signal == 2) then
+ o(layer + 1)%onedarray(m) = &
+ 1.0d0 / (1.0d0 + exp(- net(m)))
+ else if (activation_signal == 3) then
+ o(layer + 1)%onedarray(m) = net(m)
+ end if
+ ohat(layer + 1)%onedarray(m) = o(layer + 1)%onedarray(m)
+ end do
+ deallocate(net)
+ end do
+ nn = size(o) - 2
+ allocate(doutputs_dinputs(nn + 2))
+ allocate(doutputs_dinputs(1)%onedarray(&
+ len_of_fingerprint))
+ do m = 1, len_of_fingerprint
+ doutputs_dinputs(1)%onedarray(m) = fingerprintprime_(m)
+ end do
+ do layer = 1, nn + 1
+ allocate(temp(size(unraveled_parameters(element)%weights(&
+ layer)%twodarray, dim = 2)))
+ do p = 1, size(unraveled_parameters(element)%weights(&
+ layer)%twodarray, dim = 2)
+ temp(p) = 0.0d0
+ do q = 1, size(unraveled_parameters(element)%weights(&
+ layer)%twodarray, dim = 1) - 1
+ temp(p) = temp(p) + doutputs_dinputs(&
+ layer)%onedarray(q) * unraveled_parameters(&
+ element)%weights(layer)%twodarray(q, p)
+ end do
+ end do
+ q = size(o(layer + 1)%onedarray)
+ allocate(doutputs_dinputs(layer + 1)%onedarray(q))
+ do p = 1, size(o(layer + 1)%onedarray)
+ if (activation_signal == 1) then
+ doutputs_dinputs(layer + 1)%onedarray(p) = temp(p) * &
+ (1.0d0 - o(layer + 1)%onedarray(p) * &
+ o(layer + 1)%onedarray(p))
+ else if (activation_signal == 2) then
+ doutputs_dinputs(layer + 1)%onedarray(p) = &
+ temp(p) * (1.0d0 - o(layer + 1)%onedarray(p)) * &
+ o(layer + 1)%onedarray(p)
+ else if (activation_signal == 3) then
+ doutputs_dinputs(layer+ 1)%onedarray(p) = temp(p)
+ end if
+ end do
+ deallocate(temp)
+ end do
+
+ calculate_force = unraveled_parameters(element)%slope * &
+ doutputs_dinputs(nn + 2)%onedarray(1)
+ ! force is multiplied by -1, because it is -dE/dx and not dE/dx.
+ calculate_force = -1.0d0 * calculate_force
+! deallocating neural network
+ deallocate(hiddensizes)
+ do p = 1, size(o)
+ deallocate(o(p)%onedarray)
+ end do
+ deallocate(o)
+ do p = 1, size(ohat)
+ deallocate(ohat(p)%onedarray)
+ end do
+ deallocate(ohat)
+ do p = 1, size(doutputs_dinputs)
+ deallocate(doutputs_dinputs(p)%onedarray)
+ end do
+ deallocate(doutputs_dinputs)
+
+! deallocating derived type parameters
+ do element = 1, num_elements
+ deallocate(unraveled_parameters(element)%weights)
+ end do
+
+ end function calculate_force
+
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+! Returns derivative of energy w.r.t. parameters in the
+! image-centered mode.
+ function calculate_denergy_dparameters_(num_inputs, inputs, &
+ num_parameters, parameters)
+ implicit none
+
+ integer:: num_inputs, num_parameters
+ double precision:: calculate_denergy_dparameters_(num_parameters)
+ double precision:: parameters(num_parameters)
+ double precision:: inputs(num_inputs)
+
+ integer:: m, n, j, l, layer, p, q, nn, num_cols, num_rows
+ double precision:: temp1, temp2
+ integer, allocatable:: hiddensizes(:)
+ double precision, allocatable:: net(:)
+ type(real_one_d_array), allocatable:: o(:), ohat(:)
+ type(real_one_d_array), allocatable:: delta(:), D(:)
+ type(real_two_d_array), allocatable:: weights(:)
+ double precision:: intercept
+ double precision:: slope
+ type(real_two_d_array), allocatable:: &
+ unraveled_denergy_dweights(:)
+ double precision:: denergy_dintercept
+ double precision:: denergy_dslope
+
+! changing the form of parameters from vector into derived-types
+ l = 0
+ allocate(weights(no_layers_of_elements(1)-1))
+ do j = 1, no_layers_of_elements(1) - 1
+ num_rows = no_nodes_of_elements(j) + 1
+ num_cols = no_nodes_of_elements(j + 1)
+ allocate(weights(j)%twodarray(num_rows, num_cols))
+ do p = 1, num_rows
+ do q = 1, num_cols
+ weights(j)%twodarray(p, q) = &
+ parameters(l + (p - 1) * num_cols + q)
+ end do
+ end do
+ l = l + num_rows * num_cols
+ end do
+ intercept = parameters(l + 1)
+ slope = parameters(l + 2)
+
+ denergy_dintercept = 0.d0
+ denergy_dslope = 0.d0
+ l = 0
+ allocate(unraveled_denergy_dweights(no_layers_of_elements(1)-1))
+ do j = 1, no_layers_of_elements(1) - 1
+ num_rows = no_nodes_of_elements(j) + 1
+ num_cols = no_nodes_of_elements(j + 1)
+ allocate(unraveled_denergy_dweights(j)%twodarray(num_rows, &
+ num_cols))
+ do p = 1, num_rows
+ do q = 1, num_cols
+ unraveled_denergy_dweights(j)%twodarray(p, q) = 0.0d0
+ end do
+ end do
+ l = l + num_rows * num_cols
+ end do
+
+ allocate(hiddensizes(no_layers_of_elements(1) - 2))
+ do m = 1, no_layers_of_elements(1) - 2
+ hiddensizes(m) = no_nodes_of_elements(m + 1)
+ end do
+ allocate(o(no_layers_of_elements(1)))
+ allocate(ohat(no_layers_of_elements(1)))
+ layer = 1
+ allocate(o(1)%onedarray(num_inputs))
+ allocate(ohat(1)%onedarray(num_inputs + 1))
+ do m = 1, num_inputs
+ o(1)%onedarray(m) = inputs(m)
+ end do
+ do layer = 1, size(hiddensizes) + 1
+ do m = 1, size(weights(layer)%twodarray, dim=1) - 1
+ ohat(layer)%onedarray(m) = o(layer)%onedarray(m)
+ end do
+ ohat(layer)%onedarray(&
+ size(weights(layer)%twodarray, dim=1)) = 1.0d0
+ allocate(net(size(weights(layer)%twodarray, dim=2)))
+ allocate(o(layer + 1)%onedarray(&
+ size(weights(layer)%twodarray, dim=2)))
+ allocate(ohat(layer + 1)%onedarray(&
+ size(weights(layer)%twodarray, dim=2) + 1))
+ do m = 1, size(weights(layer)%twodarray, dim=2)
+ net(m) = 0.0d0
+ do n = 1, size(weights(layer)%twodarray, dim=1)
+ net(m) = net(m) + &
+ ohat(layer)%onedarray(n) * weights(&
+ layer)%twodarray(n, m)
+ end do
+ if (activation_signal == 1) then
+ o(layer + 1)%onedarray(m) = tanh(net(m))
+ else if (activation_signal == 2) then
+ o(layer + 1)%onedarray(m) = &
+ 1.0d0 / (1.0d0 + exp(- net(m)))
+ else if (activation_signal == 3) then
+ o(layer + 1)%onedarray(m) = net(m)
+ end if
+ ohat(layer + 1)%onedarray(m) = o(layer + 1)%onedarray(m)
+ end do
+ ohat(layer + 1)%onedarray(&
+ size(weights(layer)%twodarray, dim=2) + 1) = 1.0d0
+ deallocate(net)
+ end do
+
+ nn = size(o) - 2
+ allocate(D(nn + 1))
+ do layer = 1, nn + 1
+ allocate(D(layer)%onedarray(size(o(layer + 1)%onedarray)))
+ do j = 1, size(o(layer + 1)%onedarray)
+ if (activation_signal == 1) then
+ D(layer)%onedarray(j) = &
+ (1.0d0 - o(layer + 1)%onedarray(j)* &
+ o(layer + 1)%onedarray(j))
+ elseif (activation_signal == 2) then
+ D(layer)%onedarray(j) = o(layer + 1)%onedarray(j) * &
+ (1.0d0 - o(layer + 1)%onedarray(j))
+ elseif (activation_signal == 3) then
+ D(layer)%onedarray(j) = 1.0d0
+ end if
+ end do
+ end do
+ allocate(delta(nn + 1))
+ allocate(delta(nn + 1)%onedarray(1))
+ delta(nn + 1)%onedarray(1) = D(nn + 1)%onedarray(1)
+ do layer = nn, 1, -1
+ allocate(delta(layer)%onedarray(size(D(layer)%onedarray)))
+ do p = 1, size(D(layer)%onedarray)
+ delta(layer)%onedarray(p) = 0.0d0
+ do q = 1, size(delta(layer + 1)%onedarray)
+ temp1 = D(layer)%onedarray(p) * &
+ weights(layer + 1)%twodarray(p, q)
+ temp2 = temp1 * delta(layer + 1)%onedarray(q)
+ delta(layer)%onedarray(p) = &
+ delta(layer)%onedarray(p) + temp2
+ end do
+ end do
+ end do
+
+ denergy_dintercept = 1.0d0
+ denergy_dslope = o(nn + 2)%onedarray(1)
+ do layer = 1, nn + 1
+ do p = 1, size(ohat(layer)%onedarray)
+ do q = 1, size(delta(layer)%onedarray)
+ unraveled_denergy_dweights(layer)%twodarray(p, q) = &
+ slope * &
+ ohat(layer)%onedarray(p) * delta(layer)%onedarray(q)
+ end do
+ end do
+ end do
+
+ deallocate(hiddensizes)
+ do p = 1, size(o)
+ deallocate(o(p)%onedarray)
+ end do
+ deallocate(o)
+ do p = 1, size(ohat)
+ deallocate(ohat(p)%onedarray)
+ end do
+ deallocate(ohat)
+ do p = 1, size(delta)
+ deallocate(delta(p)%onedarray)
+ end do
+ deallocate(delta)
+ do p = 1, size(D)
+ deallocate(D(p)%onedarray)
+ end do
+ deallocate(D)
+
+! changing the derivatives of the energy from derived-type
+! form into vector
+ l = 0
+ do j = 1, no_layers_of_elements(1) - 1
+ num_rows = no_nodes_of_elements(j) + 1
+ num_cols = no_nodes_of_elements(j + 1)
+ do p = 1, num_rows
+ do q = 1, num_cols
+ calculate_denergy_dparameters_(&
+ l + (p - 1) * num_cols + q) = &
+ unraveled_denergy_dweights(j)%twodarray(p, q)
+ end do
+ end do
+ l = l + num_rows * num_cols
+ end do
+
+ calculate_denergy_dparameters_(l + 1) = denergy_dintercept
+ calculate_denergy_dparameters_(l + 2) = denergy_dslope
+
+! deallocating derived-type parameters
+ do p = 1, size(weights)
+ deallocate(weights(p)%twodarray)
+ end do
+ deallocate(weights)
+ do p = 1, size(unraveled_denergy_dweights)
+ deallocate(unraveled_denergy_dweights(p)%twodarray)
+ end do
+ deallocate(unraveled_denergy_dweights)
+
+ end function calculate_denergy_dparameters_
+
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+! Returns derivative of energy w.r.t. parameters in the
+! atom-centered mode.
+ function calculate_datomicenergy_dparameters(symbol, &
+ len_of_fingerprint, fingerprint, num_elements, &
+ elements_numbers, num_parameters, parameters)
+ implicit none
+
+ integer:: num_parameters, num_elements
+ integer:: symbol, len_of_fingerprint
+ double precision:: calculate_datomicenergy_dparameters(num_parameters)
+ double precision:: parameters(num_parameters)
+ double precision:: fingerprint(len_of_fingerprint)
+ integer:: elements_numbers(num_elements)
+
+ integer:: element, m, n, j, k, l, layer, p, q, nn, num_cols
+ integer:: num_rows
+ double precision:: temp1, temp2
+ integer, allocatable:: hiddensizes(:)
+ double precision, allocatable:: net(:)
+ type(real_one_d_array), allocatable:: o(:), ohat(:)
+ type(real_one_d_array), allocatable:: delta(:), D(:)
+ type(element_parameters):: unraveled_parameters(num_elements)
+ type(element_parameters):: &
+ unraveled_daenergy_dparameters(num_elements)
+ double precision:: fingerprint_(len_of_fingerprint)
+
+ ! scaling fingerprints
+ do element = 1, num_elements
+ if (symbol == &
+ elements_numbers(element)) then
+ exit
+ end if
+ end do
+ do l = 1, len_of_fingerprint
+ if ((max_fingerprints(element, l) - &
+ min_fingerprints(element, l)) .GT. &
+ (10.0d0 ** (-8.0d0))) then
+ fingerprint_(l) = -1.0d0 + 2.0d0 * &
+ (fingerprint(l) - min_fingerprints(element, l)) / &
+ (max_fingerprints(element, l) - &
+ min_fingerprints(element, l))
+ else
+ fingerprint_(l) = fingerprint(l)
+ endif
+ end do
+
+! changing the form of parameters to derived types
+ k = 0
+ l = 0
+ do element = 1, num_elements
+ allocate(unraveled_parameters(element)%weights(&
+ no_layers_of_elements(element)-1))
+ if (element .GT. 1) then
+ k = k + no_layers_of_elements(element - 1)
+ end if
+ do j = 1, no_layers_of_elements(element) - 1
+ num_rows = no_nodes_of_elements(k + j) + 1
+ num_cols = no_nodes_of_elements(k + j + 1)
+ allocate(unraveled_parameters(element)%weights(&
+ j)%twodarray(num_rows, num_cols))
+ do p = 1, num_rows
+ do q = 1, num_cols
+ unraveled_parameters(element)%weights(j)%twodarray(&
+ p, q) = parameters(l + (p - 1) * num_cols + q)
+ end do
+ end do
+ l = l + num_rows * num_cols
+ end do
+ end do
+ do element = 1, num_elements
+ unraveled_parameters(element)%intercept = &
+ parameters(l + 2 * element - 1)
+ unraveled_parameters(element)%slope = &
+ parameters(l + 2 * element)
+ end do
+
+ do element = 1, num_elements
+ unraveled_daenergy_dparameters(element)%intercept = 0.d0
+ unraveled_daenergy_dparameters(element)%slope = 0.d0
+ end do
+ k = 0
+ l = 0
+ do element = 1, num_elements
+ allocate(unraveled_daenergy_dparameters(element)%weights(&
+ no_layers_of_elements(element)-1))
+ if (element > 1) then
+ k = k + no_layers_of_elements(element - 1)
+ end if
+ do j = 1, no_layers_of_elements(element) - 1
+ num_rows = no_nodes_of_elements(k + j) + 1
+ num_cols = no_nodes_of_elements(k + j + 1)
+ allocate(unraveled_daenergy_dparameters(&
+ element)%weights(j)%twodarray(num_rows, num_cols))
+ do p = 1, num_rows
+ do q = 1, num_cols
+ unraveled_daenergy_dparameters(&
+ element)%weights(j)%twodarray(p, q) = 0.0d0
+ end do
+ end do
+ l = l + num_rows * num_cols
+ end do
+ end do
+
+ p = 0
+ do element = 1, num_elements
+ if (symbol == elements_numbers(element)) then
+ exit
+ else
+ p = p + no_layers_of_elements(element)
+ end if
+ end do
+ allocate(hiddensizes(no_layers_of_elements(element) - 2))
+ do m = 1, no_layers_of_elements(element) - 2
+ hiddensizes(m) = no_nodes_of_elements(p + m + 1)
+ end do
+ allocate(o(no_layers_of_elements(element)))
+ allocate(ohat(no_layers_of_elements(element)))
+ layer = 1
+ allocate(o(1)%onedarray(len_of_fingerprint))
+ allocate(ohat(1)%onedarray(len_of_fingerprint + 1))
+ do m = 1, len_of_fingerprint
+ o(1)%onedarray(m) = fingerprint_(m)
+ end do
+ do layer = 1, size(hiddensizes) + 1
+ do m = 1, size(unraveled_parameters(element)%weights(&
+ layer)%twodarray, dim=1) - 1
+ ohat(layer)%onedarray(m) = o(layer)%onedarray(m)
+ end do
+ ohat(layer)%onedarray(size(unraveled_parameters(&
+ element)%weights(layer)%twodarray, dim=1)) = 1.0d0
+ allocate(net(size(unraveled_parameters(&
+ element)%weights(layer)%twodarray, dim=2)))
+ allocate(o(layer + 1)%onedarray(size(unraveled_parameters(&
+ element)%weights(layer)%twodarray, dim=2)))
+ allocate(ohat(layer + 1)%onedarray(size(unraveled_parameters(&
+ element)%weights(layer)%twodarray, dim=2) + 1))
+ do m = 1, size(unraveled_parameters(element)%weights(&
+ layer)%twodarray, dim=2)
+ net(m) = 0.0d0
+ do n = 1, size(unraveled_parameters(element)%weights(&
+ layer)%twodarray, dim=1)
+ net(m) = net(m) + &
+ ohat(layer)%onedarray(n) * unraveled_parameters(&
+ element)%weights(layer)%twodarray(n, m)
+ end do
+ if (activation_signal == 1) then
+ o(layer + 1)%onedarray(m) = tanh(net(m))
+ else if (activation_signal == 2) then
+ o(layer + 1)%onedarray(m) = &
+ 1.0d0 / (1.0d0 + exp(- net(m)))
+ else if (activation_signal == 3) then
+ o(layer + 1)%onedarray(m) = net(m)
+ end if
+ ohat(layer + 1)%onedarray(m) = o(layer + 1)%onedarray(m)
+ end do
+ ohat(layer + 1)%onedarray(size(unraveled_parameters(&
+ element)%weights(layer)%twodarray, dim=2) + 1) = 1.0d0
+ deallocate(net)
+ end do
+
+ nn = size(o) - 2
+ allocate(D(nn + 1))
+ do layer = 1, nn + 1
+ allocate(D(layer)%onedarray(size(o(layer + 1)%onedarray)))
+ do j = 1, size(o(layer + 1)%onedarray)
+ if (activation_signal == 1) then
+ D(layer)%onedarray(j) = (1.0d0 - &
+ o(layer + 1)%onedarray(j)* o(layer + 1)%onedarray(j))
+ elseif (activation_signal == 2) then
+ D(layer)%onedarray(j) = o(layer + 1)%onedarray(j) * &
+ (1.0d0 - o(layer + 1)%onedarray(j))
+ elseif (activation_signal == 3) then
+ D(layer)%onedarray(j) = 1.0d0
+ end if
+ end do
+ end do
+ allocate(delta(nn + 1))
+ allocate(delta(nn + 1)%onedarray(1))
+ delta(nn + 1)%onedarray(1) = D(nn + 1)%onedarray(1)
+ do layer = nn, 1, -1
+ allocate(delta(layer)%onedarray(size(D(layer)%onedarray)))
+ do p = 1, size(D(layer)%onedarray)
+ delta(layer)%onedarray(p) = 0.0d0
+ do q = 1, size(delta(layer + 1)%onedarray)
+ temp1 = D(layer)%onedarray(p) * unraveled_parameters(&
+ element)%weights(layer + 1)%twodarray(p, q)
+ temp2 = temp1 * delta(layer + 1)%onedarray(q)
+ delta(layer)%onedarray(p) = &
+ delta(layer)%onedarray(p) + temp2
+ end do
+ end do
+ end do
+
+ unraveled_daenergy_dparameters(element)%intercept = 1.0d0
+ unraveled_daenergy_dparameters(element)%slope = &
+ o(nn + 2)%onedarray(1)
+ do layer = 1, nn + 1
+ do p = 1, size(ohat(layer)%onedarray)
+ do q = 1, size(delta(layer)%onedarray)
+ unraveled_daenergy_dparameters(element)%weights(&
+ layer)%twodarray(p, q) = &
+ unraveled_parameters(element)%slope * &
+ ohat(layer)%onedarray(p) * delta(layer)%onedarray(q)
+ end do
+ end do
+ end do
+
+ deallocate(hiddensizes)
+ do p = 1, size(o)
+ deallocate(o(p)%onedarray)
+ end do
+ deallocate(o)
+ do p = 1, size(ohat)
+ deallocate(ohat(p)%onedarray)
+ end do
+ deallocate(ohat)
+ do p = 1, size(delta)
+ deallocate(delta(p)%onedarray)
+ end do
+ deallocate(delta)
+ do p = 1, size(D)
+ deallocate(D(p)%onedarray)
+ end do
+ deallocate(D)
+
+! changing the derivatives of the energy from derived-type
+! form into vector
+ k = 0
+ l = 0
+ do element = 1, num_elements
+ if (element > 1) then
+ k = k + no_layers_of_elements(element - 1)
+ end if
+ do j = 1, no_layers_of_elements(element) - 1
+ num_rows = no_nodes_of_elements(k + j) + 1
+ num_cols = no_nodes_of_elements(k + j + 1)
+ do p = 1, num_rows
+ do q = 1, num_cols
+ calculate_datomicenergy_dparameters(&
+ l + (p - 1) * num_cols + q) = &
+ unraveled_daenergy_dparameters(&
+ element)%weights(j)%twodarray(p, q)
+ end do
+ end do
+ l = l + num_rows * num_cols
+ end do
+ end do
+ do element = 1, num_elements
+ calculate_datomicenergy_dparameters(l + 2 * element - 1) = &
+ unraveled_daenergy_dparameters(element)%intercept
+ calculate_datomicenergy_dparameters(l + 2 * element) = &
+ unraveled_daenergy_dparameters(element)%slope
+ end do
+
+! deallocating derived-type parameters
+ do element = 1, num_elements
+ deallocate(unraveled_parameters(element)%weights)
+ deallocate(unraveled_daenergy_dparameters(element)%weights)
+ end do
+
+ end function calculate_datomicenergy_dparameters
+
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+! Returns derivative of force w.r.t. parameters in the
+! image-centered mode.
+ function calculate_dforce_dparameters_(num_inputs, inputs, &
+ inputs_, num_parameters, parameters)
+ implicit none
+
+ integer:: num_inputs, num_parameters
+ double precision:: calculate_dforce_dparameters_(num_parameters)
+ double precision:: parameters(num_parameters)
+ double precision:: inputs(num_inputs)
+ double precision:: inputs_(num_inputs)
+
+ integer:: m, n, j, l, layer, p, q, nn, num_cols
+ integer:: num_rows
+ double precision:: temp1, temp2
+ integer, allocatable:: hiddensizes(:)
+ double precision, allocatable:: net(:)
+ type(real_one_d_array), allocatable:: o(:), ohat(:)
+ type(real_one_d_array), allocatable:: delta(:), D(:)
+ type(real_one_d_array), allocatable:: doutputs_dinputs(:)
+ double precision, allocatable:: dohat_dinputs(:)
+ type(real_one_d_array), allocatable:: dD_dinputs(:)
+ type (real_one_d_array), allocatable:: ddelta_dinputs(:)
+ double precision, allocatable:: &
+ doutput_dinputsdweights(:, :)
+ double precision, allocatable:: temp(:), temp3(:), temp4(:)
+ double precision, allocatable:: temp5(:), temp6(:)
+ type(real_two_d_array), allocatable:: weights(:)
+ double precision:: intercept
+ double precision:: slope
+ type(real_two_d_array), allocatable:: unraveled_dforce_dweights(:)
+ double precision:: dforce_dintercept
+ double precision:: dforce_dslope
+
+! changing the form of parameters from vector into derived-types
+ l = 0
+ allocate(weights(no_layers_of_elements(1)-1))
+ do j = 1, no_layers_of_elements(1) - 1
+ num_rows = no_nodes_of_elements(j) + 1
+ num_cols = no_nodes_of_elements(j + 1)
+ allocate(weights(j)%twodarray(num_rows, num_cols))
+ do p = 1, num_rows
+ do q = 1, num_cols
+ weights(j)%twodarray(p, q) = &
+ parameters(l + (p - 1) * num_cols + q)
+ end do
+ end do
+ l = l + num_rows * num_cols
+ end do
+ intercept = parameters(l + 1)
+ slope = parameters(l + 2)
+
+ dforce_dintercept = 0.d0
+ dforce_dslope = 0.d0
+ l = 0
+ allocate(unraveled_dforce_dweights(no_layers_of_elements(1)-1))
+ do j = 1, no_layers_of_elements(1) - 1
+ num_rows = no_nodes_of_elements(j) + 1
+ num_cols = no_nodes_of_elements(j + 1)
+ allocate(unraveled_dforce_dweights(j)%twodarray(num_rows, &
+ num_cols))
+ do p = 1, num_rows
+ do q = 1, num_cols
+ unraveled_dforce_dweights(j)%twodarray(p, q) = 0.0d0
+ end do
+ end do
+ l = l + num_rows * num_cols
+ end do
+
+ allocate(hiddensizes(no_layers_of_elements(1) - 2))
+ do m = 1, no_layers_of_elements(1) - 2
+ hiddensizes(m) = no_nodes_of_elements(m + 1)
+ end do
+ allocate(o(no_layers_of_elements(1)))
+ allocate(ohat(no_layers_of_elements(1)))
+ layer = 1
+ allocate(o(1)%onedarray(num_inputs))
+ allocate(ohat(1)%onedarray(num_inputs + 1))
+ do m = 1, num_inputs
+ o(1)%onedarray(m) = inputs(m)
+ end do
+ do layer = 1, size(hiddensizes) + 1
+ do m = 1, size(weights(layer)%twodarray, dim=1) - 1
+ ohat(layer)%onedarray(m) = o(layer)%onedarray(m)
+ end do
+ ohat(layer)%onedarray(&
+ size(weights(layer)%twodarray, dim=1)) = 1.0d0
+ allocate(net(size(weights(layer)%twodarray, dim=2)))
+ allocate(o(layer + 1)%onedarray(&
+ size(weights(layer)%twodarray, dim=2)))
+ allocate(ohat(layer + 1)%onedarray(&
+ size(weights(layer)%twodarray, dim=2) + 1))
+ do m = 1, size(weights(layer)%twodarray, dim=2)
+ net(m) = 0.0d0
+ do n = 1, size(weights(layer)%twodarray, dim=1)
+ net(m) = net(m) + &
+ ohat(layer)%onedarray(n) * &
+ weights(layer)%twodarray(n, m)
+ end do
+ if (activation_signal == 1) then
+ o(layer + 1)%onedarray(m) = tanh(net(m))
+ else if (activation_signal == 2) then
+ o(layer + 1)%onedarray(m) = &
+ 1.0d0 / (1.0d0 + exp(- net(m)))
+ else if (activation_signal == 3) then
+ o(layer + 1)%onedarray(m) = net(m)
+ end if
+ ohat(layer + 1)%onedarray(m) = o(layer + 1)%onedarray(m)
+ end do
+ ohat(layer + 1)%onedarray(&
+ size(weights(layer)%twodarray, dim=2) + 1) = 1.0d0
+ deallocate(net)
+ end do
+
+ nn = size(o) - 2
+ allocate(D(nn + 1))
+ do layer = 1, nn + 1
+ allocate(D(layer)%onedarray(size(o(layer + 1)%onedarray)))
+ do j = 1, size(o(layer + 1)%onedarray)
+ if (activation_signal == 1) then
+ D(layer)%onedarray(j) = (1.0d0 - &
+ o(layer + 1)%onedarray(j)* o(layer + 1)%onedarray(j))
+ elseif (activation_signal == 2) then
+ D(layer)%onedarray(j) = o(layer + 1)%onedarray(j) * &
+ (1.0d0 - o(layer + 1)%onedarray(j))
+ elseif (activation_signal == 3) then
+ D(layer)%onedarray(j) = 1.0d0
+ end if
+ end do
+ end do
+ allocate(delta(nn + 1))
+ allocate(delta(nn + 1)%onedarray(1))
+ delta(nn + 1)%onedarray(1) = D(nn + 1)%onedarray(1)
+ do layer = nn, 1, -1
+ allocate(delta(layer)%onedarray(size(D(layer)%onedarray)))
+ do p = 1, size(D(layer)%onedarray)
+ delta(layer)%onedarray(p) = 0.0d0
+ do q = 1, size(delta(layer + 1)%onedarray)
+ temp1 = D(layer)%onedarray(p) * weights(&
+ layer + 1)%twodarray(p, q)
+ temp2 = temp1 * delta(layer + 1)%onedarray(q)
+ delta(layer)%onedarray(p) = &
+ delta(layer)%onedarray(p) + temp2
+ end do
+ end do
+ end do
+
+ allocate(doutputs_dinputs(nn + 2))
+ allocate(doutputs_dinputs(1)%onedarray(num_inputs))
+ do m = 1, num_inputs
+ doutputs_dinputs(1)%onedarray(m) = inputs_(m)
+ end do
+ do layer = 1, nn + 1
+ allocate(temp(size(weights(layer)%twodarray, dim = 2)))
+ do p = 1, size(weights(layer)%twodarray, dim = 2)
+ temp(p) = 0.0d0
+ do q = 1, size(weights(layer)%twodarray, dim = 1) - 1
+ temp(p) = temp(p) + doutputs_dinputs(&
+ layer)%onedarray(q) * weights(layer)%twodarray(q, p)
+ end do
+ end do
+ q = size(o(layer + 1)%onedarray)
+ allocate(doutputs_dinputs(layer + 1)%onedarray(q))
+ do p = 1, size(o(layer + 1)%onedarray)
+ if (activation_signal == 1) then
+ doutputs_dinputs(layer + 1)%onedarray(p) = temp(p) * &
+ (1.0d0 - o(layer + 1)%onedarray(p) * &
+ o(layer + 1)%onedarray(p))
+ else if (activation_signal == 2) then
+ doutputs_dinputs(layer + 1)%onedarray(p) = &
+ temp(p) * (1.0d0 - o(layer + 1)%onedarray(p)) * &
+ o(layer + 1)%onedarray(p)
+ else if (activation_signal == 3) then
+ doutputs_dinputs(layer+ 1)%onedarray(p) = temp(p)
+ end if
+ end do
+ deallocate(temp)
+ end do
+
+ allocate(dD_dinputs(nn + 1))
+ do layer = 1, nn + 1
+ allocate(dD_dinputs(layer)%onedarray(&
+ size(o(layer + 1)%onedarray)))
+ do p = 1, size(o(layer + 1)%onedarray)
+ if (activation_signal == 1) then
+ dD_dinputs(layer)%onedarray(p) = &
+ - 2.0d0 * o(layer + 1)%onedarray(p) * &
+ doutputs_dinputs(layer + 1)%onedarray(p)
+ elseif (activation_signal == 2) then
+ dD_dinputs(layer)%onedarray(p) = &
+ doutputs_dinputs(layer + 1)%onedarray(p) * &
+ (1.0d0 - 2.0d0 * o(layer + 1)%onedarray(p))
+ elseif (activation_signal == 3) then
+ dD_dinputs(layer)%onedarray(p) =0.0d0
+ end if
+ end do
+ end do
+
+ allocate(ddelta_dinputs(nn + 1))
+ allocate(ddelta_dinputs(nn + 1)%onedarray(1))
+ ddelta_dinputs(nn + 1)%onedarray(1) = &
+ dD_dinputs(nn + 1)%onedarray(1)
+
+ do layer = nn, 1, -1
+ allocate(temp3(&
+ size(weights(layer + 1)%twodarray, dim = 1) - 1))
+ allocate(temp4(&
+ size(weights(layer + 1)%twodarray, dim = 1) - 1))
+ do p = 1, size(weights(layer + 1)%twodarray, dim = 1) - 1
+ temp3(p) = 0.0d0
+ temp4(p) = 0.0d0
+ do q = 1, size(delta(layer + 1)%onedarray)
+ temp3(p) = temp3(p) + weights(layer + 1)%twodarray(&
+ p, q) * delta(layer + 1)%onedarray(q)
+ temp4(p) = temp4(p) + weights(layer + 1)%twodarray(&
+ p, q) * ddelta_dinputs(layer + 1)%onedarray(q)
+ end do
+ end do
+ allocate(temp5(size(dD_dinputs(layer)%onedarray)))
+ allocate(temp6(size(dD_dinputs(layer)%onedarray)))
+ allocate(ddelta_dinputs(layer)%onedarray(&
+ size(dD_dinputs(layer)%onedarray)))
+ do p = 1, size(dD_dinputs(layer)%onedarray)
+ temp5(p) = &
+ dD_dinputs(layer)%onedarray(p) * temp3(p)
+ temp6(p) = D(layer)%onedarray(p) * temp4(p)
+ ddelta_dinputs(layer)%onedarray(p)= &
+ temp5(p) + temp6(p)
+ end do
+ deallocate(temp3)
+ deallocate(temp4)
+ deallocate(temp5)
+ deallocate(temp6)
+ end do
+
+ dforce_dslope = doutputs_dinputs(nn + 2)%onedarray(1)
+ ! force is multiplied by -1, because it is -dE/dx and not dE/dx.
+ dforce_dslope = -1.0d0 * dforce_dslope
+ do layer = 1, nn + 1
+ allocate(dohat_dinputs(&
+ size(doutputs_dinputs(layer)%onedarray) + 1))
+ do p = 1, size(doutputs_dinputs(layer)%onedarray)
+ dohat_dinputs(p) = &
+ doutputs_dinputs(layer)%onedarray(p)
+ end do
+ dohat_dinputs(&
+ size(doutputs_dinputs(layer)%onedarray) + 1) = 0.0d0
+ allocate(doutput_dinputsdweights(&
+ size(dohat_dinputs), size(delta(layer)%onedarray)))
+ do p = 1, size(dohat_dinputs)
+ do q = 1, size(delta(layer)%onedarray)
+ doutput_dinputsdweights(p, q)= 0.0d0
+ end do
+ end do
+ do p = 1, size(dohat_dinputs)
+ do q = 1, size(delta(layer)%onedarray)
+ doutput_dinputsdweights(p, q) = &
+ doutput_dinputsdweights(p, q) + &
+ dohat_dinputs(p) * delta(layer)%onedarray(q) + &
+ ohat(layer)%onedarray(p)* &
+ ddelta_dinputs(layer)%onedarray(q)
+ end do
+ end do
+ do p = 1, size(ohat(layer)%onedarray)
+ do q = 1, size(delta(layer)%onedarray)
+ unraveled_dforce_dweights(layer)%twodarray(p, q) = &
+ slope * doutput_dinputsdweights(p, q)
+ ! force is multiplied by -1, because it is -dE/dx and
+ ! not dE/dx.
+ unraveled_dforce_dweights(layer)%twodarray(p, q) = &
+ -1.0d0 * unraveled_dforce_dweights(layer)%twodarray(p, q)
+ end do
+ end do
+ deallocate(dohat_dinputs)
+ deallocate(doutput_dinputsdweights)
+ end do
+
+! deallocating neural network
+ deallocate(hiddensizes)
+ do p = 1, size(o)
+ deallocate(o(p)%onedarray)
+ end do
+ deallocate(o)
+ do p = 1, size(ohat)
+ deallocate(ohat(p)%onedarray)
+ end do
+ deallocate(ohat)
+ do p = 1, size(delta)
+ deallocate(delta(p)%onedarray)
+ end do
+ deallocate(delta)
+ do p = 1, size(D)
+ deallocate(D(p)%onedarray)
+ end do
+ deallocate(D)
+ do p = 1, size(doutputs_dinputs)
+ deallocate(doutputs_dinputs(p)%onedarray)
+ end do
+ deallocate(doutputs_dinputs)
+ do p = 1, size(ddelta_dinputs)
+ deallocate(ddelta_dinputs(p)%onedarray)
+ end do
+ deallocate(ddelta_dinputs)
+ do p = 1, size(dD_dinputs)
+ deallocate(dD_dinputs(p)%onedarray)
+ end do
+ deallocate(dD_dinputs)
+
+ l = 0
+ do j = 1, no_layers_of_elements(1) - 1
+ num_rows = no_nodes_of_elements(j) + 1
+ num_cols = no_nodes_of_elements(j + 1)
+ do p = 1, num_rows
+ do q = 1, num_cols
+ calculate_dforce_dparameters_(&
+ l + (p - 1) * num_cols + q) = &
+ unraveled_dforce_dweights(j)%twodarray(p, q)
+ end do
+ end do
+ l = l + num_rows * num_cols
+ end do
+ calculate_dforce_dparameters_(l + 1) = dforce_dintercept
+ calculate_dforce_dparameters_(l + 2) = dforce_dslope
+
+! deallocating derived-type parameters
+ do p = 1, size(weights)
+ deallocate(weights(p)%twodarray)
+ end do
+ deallocate(weights)
+ do p = 1, size(unraveled_dforce_dweights)
+ deallocate(unraveled_dforce_dweights(p)%twodarray)
+ end do
+ deallocate(unraveled_dforce_dweights)
+
+ end function calculate_dforce_dparameters_
+
+ !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+! Returns derivative of force w.r.t. parameters in the
+! atom-centered mode
+ function calculate_dforce_dparameters(symbol, len_of_fingerprint, &
+ fingerprint, fingerprintprime, num_elements, elements_numbers, &
+ num_parameters, parameters)
+ implicit none
+
+ integer:: symbol, len_of_fingerprint
+ integer:: num_parameters, num_elements
+ double precision:: fingerprint(len_of_fingerprint)
+ double precision:: fingerprintprime(len_of_fingerprint)
+ integer:: elements_numbers(num_elements)
+ double precision:: parameters(num_parameters)
+ double precision:: calculate_dforce_dparameters(num_parameters)
+
+ integer:: element, m, n, j, k, l, layer, p, q, nn, num_cols
+ integer:: num_rows
+ double precision:: temp1, temp2
+ integer, allocatable:: hiddensizes(:)
+ double precision, allocatable:: net(:)
+ type(real_one_d_array), allocatable:: o(:), ohat(:)
+ type(real_one_d_array), allocatable:: delta(:), D(:)
+ type(real_one_d_array), allocatable:: doutputs_dinputs(:)
+ double precision, allocatable:: dohat_dinputs(:)
+ type(real_one_d_array), allocatable:: dD_dinputs(:)
+ type (real_one_d_array), allocatable:: ddelta_dinputs(:)
+ double precision, allocatable:: &
+ doutput_dinputsdweights(:, :)
+ double precision, allocatable:: temp(:), temp3(:), temp4(:)
+ double precision, allocatable:: temp5(:), temp6(:)
+ type(element_parameters):: unraveled_parameters(num_elements)
+ type(element_parameters):: &
+ unraveled_dforce_dparameters(num_elements)
+ double precision:: fingerprint_(len_of_fingerprint)
+ double precision:: fingerprintprime_(len_of_fingerprint)
+
+ ! scaling fingerprints
+ do element = 1, num_elements
+ if (symbol == &
+ elements_numbers(element)) then
+ exit
+ end if
+ end do
+ do l = 1, len_of_fingerprint
+ if ((max_fingerprints(element, l) - &
+ min_fingerprints(element, l)) .GT. &
+ (10.0d0 ** (-8.0d0))) then
+ fingerprint_(l) = -1.0d0 + 2.0d0 * &
+ (fingerprint(l) - min_fingerprints(element, l)) / &
+ (max_fingerprints(element, l) - &
+ min_fingerprints(element, l))
+ else
+ fingerprint_(l) = fingerprint(l)
+ endif
+ end do
+ ! scaling fingerprintprimes
+ do l = 1, len_of_fingerprint
+ if ((max_fingerprints(element, l) - &
+ min_fingerprints(element, l)) .GT. &
+ (10.0d0 ** (-8.0d0))) then
+ fingerprintprime_(l) = &
+ 2.0d0 * fingerprintprime(l) / &
+ (max_fingerprints(element, l) - &
+ min_fingerprints(element, l))
+ else
+ fingerprintprime_(l) = fingerprintprime(l)
+ endif
+ end do
+
+! changing the form of parameters from vector into derived-types
+ k = 0
+ l = 0
+ do element = 1, num_elements
+ allocate(unraveled_parameters(element)%weights(&
+ no_layers_of_elements(element)-1))
+ if (element .GT. 1) then
+ k = k + no_layers_of_elements(element - 1)
+ end if
+ do j = 1, no_layers_of_elements(element) - 1
+ num_rows = no_nodes_of_elements(k + j) + 1
+ num_cols = no_nodes_of_elements(k + j + 1)
+ allocate(unraveled_parameters(&
+ element)%weights(j)%twodarray(num_rows, num_cols))
+ do p = 1, num_rows
+ do q = 1, num_cols
+ unraveled_parameters(element)%weights(j)%twodarray(&
+ p, q) = parameters(l + (p - 1) * num_cols + q)
+ end do
+ end do
+ l = l + num_rows * num_cols
+ end do
+ end do
+ do element = 1, num_elements
+ unraveled_parameters(element)%intercept = &
+ parameters(l + 2 * element - 1)
+ unraveled_parameters(element)%slope = &
+ parameters(l + 2 * element)
+ end do
+
+ do element = 1, num_elements
+ unraveled_dforce_dparameters(element)%intercept = 0.d0
+ unraveled_dforce_dparameters(element)%slope = 0.d0
+ end do
+ k = 0
+ l = 0
+ do element = 1, num_elements
+ allocate(unraveled_dforce_dparameters(element)%weights(&
+ no_layers_of_elements(element)-1))
+ if (element > 1) then
+ k = k + no_layers_of_elements(element - 1)
+ end if
+ do j = 1, no_layers_of_elements(element) - 1
+ num_rows = no_nodes_of_elements(k + j) + 1
+ num_cols = no_nodes_of_elements(k + j + 1)
+ allocate(unraveled_dforce_dparameters(&
+ element)%weights(j)%twodarray(num_rows, num_cols))
+ do p = 1, num_rows
+ do q = 1, num_cols
+ unraveled_dforce_dparameters(&
+ element)%weights(j)%twodarray(p, q) = 0.0d0
+ end do
+ end do
+ l = l + num_rows * num_cols
+ end do
+ end do
+
+ p = 0
+ do element = 1, num_elements
+ if (symbol == elements_numbers(element)) then
+ exit
+ else
+ p = p + no_layers_of_elements(element)
+ end if
+ end do
+
+ allocate(hiddensizes(no_layers_of_elements(element) - 2))
+ do m = 1, no_layers_of_elements(element) - 2
+ hiddensizes(m) = no_nodes_of_elements(p + m + 1)
+ end do
+ allocate(o(no_layers_of_elements(element)))
+ allocate(ohat(no_layers_of_elements(element)))
+ layer = 1
+ allocate(o(1)%onedarray(len_of_fingerprint))
+ allocate(ohat(1)%onedarray(len_of_fingerprint + 1))
+ do m = 1, len_of_fingerprint
+ o(1)%onedarray(m) = fingerprint_(m)
+ end do
+ do layer = 1, size(hiddensizes) + 1
+ do m = 1, size(unraveled_parameters(&
+ element)%weights(layer)%twodarray, dim=1) - 1
+ ohat(layer)%onedarray(m) = o(layer)%onedarray(m)
+ end do
+ ohat(layer)%onedarray(size(unraveled_parameters(&
+ element)%weights(layer)%twodarray, dim=1)) = 1.0d0
+ allocate(net(size(unraveled_parameters(&
+ element)%weights(layer)%twodarray, dim=2)))
+ allocate(o(layer + 1)%onedarray(size(unraveled_parameters(&
+ element)%weights(layer)%twodarray, dim=2)))
+ allocate(ohat(layer + 1)%onedarray(size(unraveled_parameters(&
+ element)%weights(layer)%twodarray, dim=2) + 1))
+ do m = 1, size(unraveled_parameters(element)%weights(&
+ layer)%twodarray, dim=2)
+ net(m) = 0.0d0
+ do n = 1, size(unraveled_parameters(element)%weights(&
+ layer)%twodarray, dim=1)
+ net(m) = net(m) + &
+ ohat(layer)%onedarray(n) * &
+ unraveled_parameters(element)%weights(&
+ layer)%twodarray(n, m)
+ end do
+ if (activation_signal == 1) then
+ o(layer + 1)%onedarray(m) = tanh(net(m))
+ else if (activation_signal == 2) then
+ o(layer + 1)%onedarray(m) = &
+ 1.0d0 / (1.0d0 + exp(- net(m)))
+ else if (activation_signal == 3) then
+ o(layer + 1)%onedarray(m) = net(m)
+ end if
+ ohat(layer + 1)%onedarray(m) = o(layer + 1)%onedarray(m)
+ end do
+ ohat(layer + 1)%onedarray(size(unraveled_parameters(&
+ element)%weights(layer)%twodarray, dim=2) + 1) = 1.0d0
+ deallocate(net)
+ end do
+
+ nn = size(o) - 2
+
+ allocate(D(nn + 1))
+ do layer = 1, nn + 1
+ allocate(D(layer)%onedarray(size(o(layer + 1)%onedarray)))
+ do j = 1, size(o(layer + 1)%onedarray)
+ if (activation_signal == 1) then
+ D(layer)%onedarray(j) = &
+ (1.0d0 - o(layer + 1)%onedarray(j)* &
+ o(layer + 1)%onedarray(j))
+ elseif (activation_signal == 2) then
+ D(layer)%onedarray(j) = o(layer + 1)%onedarray(j) * &
+ (1.0d0 - o(layer + 1)%onedarray(j))
+ elseif (activation_signal == 3) then
+ D(layer)%onedarray(j) = 1.0d0
+ end if
+ end do
+ end do
+ allocate(delta(nn + 1))
+ allocate(delta(nn + 1)%onedarray(1))
+ delta(nn + 1)%onedarray(1) = D(nn + 1)%onedarray(1)
+ do layer = nn, 1, -1
+ allocate(delta(layer)%onedarray(size(D(layer)%onedarray)))
+ do p = 1, size(D(layer)%onedarray)
+ delta(layer)%onedarray(p) = 0.0d0
+ do q = 1, size(delta(layer + 1)%onedarray)
+ temp1 = D(layer)%onedarray(p) * &
+ unraveled_parameters(element)%weights(&
+ layer + 1)%twodarray(p, q)
+ temp2 = temp1 * delta(layer + 1)%onedarray(q)
+ delta(layer)%onedarray(p) = &
+ delta(layer)%onedarray(p) + temp2
+ end do
+ end do
+ end do
+
+ allocate(doutputs_dinputs(nn + 2))
+ allocate(doutputs_dinputs(1)%onedarray(&
+ len_of_fingerprint))
+ do m = 1, len_of_fingerprint
+ doutputs_dinputs(1)%onedarray(m) = fingerprintprime_(m)
+ end do
+ do layer = 1, nn + 1
+ allocate(temp(size(unraveled_parameters(&
+ element)%weights(layer)%twodarray, dim = 2)))
+ do p = 1, size(unraveled_parameters(&
+ element)%weights(layer)%twodarray, dim = 2)
+ temp(p) = 0.0d0
+ do q = 1, size(unraveled_parameters(&
+ element)%weights(layer)%twodarray, dim = 1) - 1
+ temp(p) = temp(p) + doutputs_dinputs(&
+ layer)%onedarray(q) * unraveled_parameters(&
+ element)%weights(layer)%twodarray(q, p)
+ end do
+ end do
+ q = size(o(layer + 1)%onedarray)
+ allocate(doutputs_dinputs(layer + 1)%onedarray(q))
+ do p = 1, size(o(layer + 1)%onedarray)
+ if (activation_signal == 1) then
+ doutputs_dinputs(layer + 1)%onedarray(p) = temp(p) * &
+ (1.0d0 - o(layer + 1)%onedarray(p) * &
+ o(layer + 1)%onedarray(p))
+ else if (activation_signal == 2) then
+ doutputs_dinputs(layer + 1)%onedarray(p) = temp(p) * &
+ (1.0d0 - o(layer + 1)%onedarray(p)) * &
+ o(layer + 1)%onedarray(p)
+ else if (activation_signal == 3) then
+ doutputs_dinputs(layer+ 1)%onedarray(p) = temp(p)
+ end if
+ end do
+ deallocate(temp)
+ end do
+
+ allocate(dD_dinputs(nn + 1))
+ do layer = 1, nn + 1
+ allocate(dD_dinputs(layer)%onedarray(&
+ size(o(layer + 1)%onedarray)))
+ do p = 1, size(o(layer + 1)%onedarray)
+ if (activation_signal == 1) then
+ dD_dinputs(layer)%onedarray(p) =- 2.0d0 * &
+ o(layer + 1)%onedarray(p) * &
+ doutputs_dinputs(layer + 1)%onedarray(p)
+ elseif (activation_signal == 2) then
+ dD_dinputs(layer)%onedarray(p) = &
+ doutputs_dinputs(layer + 1)%onedarray(p) * &
+ (1.0d0 - 2.0d0 * o(layer + 1)%onedarray(p))
+ elseif (activation_signal == 3) then
+ dD_dinputs(layer)%onedarray(p) =0.0d0
+ end if
+ end do
+ end do
+
+ allocate(ddelta_dinputs(nn + 1))
+ allocate(ddelta_dinputs(nn + 1)%onedarray(1))
+ ddelta_dinputs(nn + 1)%onedarray(1) = &
+ dD_dinputs(nn + 1)%onedarray(1)
+
+ do layer = nn, 1, -1
+ allocate(temp3(size(unraveled_parameters(element)%weights(&
+ layer + 1)%twodarray, dim = 1) - 1))
+ allocate(temp4(size(unraveled_parameters(element)%weights(&
+ layer + 1)%twodarray, dim = 1) - 1))
+ do p = 1, size(unraveled_parameters(element)%weights(&
+ layer + 1)%twodarray, dim = 1) - 1
+ temp3(p) = 0.0d0
+ temp4(p) = 0.0d0
+ do q = 1, size(delta(layer + 1)%onedarray)
+ temp3(p) = temp3(p) + unraveled_parameters(&
+ element)%weights(layer + 1)%twodarray(p, q) * &
+ delta(layer + 1)%onedarray(q)
+ temp4(p) = temp4(p) + unraveled_parameters(&
+ element)%weights(layer + 1)%twodarray(p, q) * &
+ ddelta_dinputs(layer + 1)%onedarray(q)
+ end do
+ end do
+ allocate(temp5(size(dD_dinputs(layer)%onedarray)))
+ allocate(temp6(size(dD_dinputs(layer)%onedarray)))
+ allocate(ddelta_dinputs(layer)%onedarray(&
+ size(dD_dinputs(layer)%onedarray)))
+ do p = 1, size(dD_dinputs(layer)%onedarray)
+ temp5(p) = &
+ dD_dinputs(layer)%onedarray(p) * temp3(p)
+ temp6(p) = D(layer)%onedarray(p) * temp4(p)
+ ddelta_dinputs(layer)%onedarray(p)= &
+ temp5(p) + temp6(p)
+ end do
+ deallocate(temp3)
+ deallocate(temp4)
+ deallocate(temp5)
+ deallocate(temp6)
+ end do
+
+ unraveled_dforce_dparameters(element)%slope = &
+ doutputs_dinputs(nn + 2)%onedarray(1)
+ ! force is multiplied by -1, because it is -dE/dx and not dE/dx.
+ unraveled_dforce_dparameters(element)%slope = &
+ -1.0d0 * unraveled_dforce_dparameters(element)%slope
+ do layer = 1, nn + 1
+ allocate(dohat_dinputs(&
+ size(doutputs_dinputs(layer)%onedarray) + 1))
+ do p = 1, size(doutputs_dinputs(layer)%onedarray)
+ dohat_dinputs(p) = &
+ doutputs_dinputs(layer)%onedarray(p)
+ end do
+ dohat_dinputs(&
+ size(doutputs_dinputs(layer)%onedarray) + 1) = 0.0d0
+ allocate(doutput_dinputsdweights(&
+ size(dohat_dinputs), size(delta(layer)%onedarray)))
+ do p = 1, size(dohat_dinputs)
+ do q = 1, size(delta(layer)%onedarray)
+ doutput_dinputsdweights(p, q)= 0.0d0
+ end do
+ end do
+ do p = 1, size(dohat_dinputs)
+ do q = 1, size(delta(layer)%onedarray)
+ doutput_dinputsdweights(p, q) = &
+ doutput_dinputsdweights(p, q) + &
+ dohat_dinputs(p) * delta(layer)%onedarray(q) + &
+ ohat(layer)%onedarray(p)* &
+ ddelta_dinputs(layer)%onedarray(q)
+ end do
+ end do
+ do p = 1, size(ohat(layer)%onedarray)
+ do q = 1, size(delta(layer)%onedarray)
+ unraveled_dforce_dparameters(element)%weights(&
+ layer)%twodarray(p, q) = &
+ unraveled_parameters(element)%slope * &
+ doutput_dinputsdweights(p, q)
+ ! force is multiplied by -1, because it is -dE/dx and
+ ! not dE/dx.
+ unraveled_dforce_dparameters(element)%weights(&
+ layer)%twodarray(p, q) = &
+ -1.0d0 * unraveled_dforce_dparameters(element)%weights(&
+ layer)%twodarray(p, q)
+ end do
+ end do
+ deallocate(dohat_dinputs)
+ deallocate(doutput_dinputsdweights)
+ end do
+
+! deallocating neural network
+ deallocate(hiddensizes)
+ do p = 1, size(o)
+ deallocate(o(p)%onedarray)
+ end do
+ deallocate(o)
+ do p = 1, size(ohat)
+ deallocate(ohat(p)%onedarray)
+ end do
+ deallocate(ohat)
+ do p = 1, size(delta)
+ deallocate(delta(p)%onedarray)
+ end do
+ deallocate(delta)
+ do p = 1, size(D)
+ deallocate(D(p)%onedarray)
+ end do
+ deallocate(D)
+ do p = 1, size(doutputs_dinputs)
+ deallocate(doutputs_dinputs(p)%onedarray)
+ end do
+ deallocate(doutputs_dinputs)
+ do p = 1, size(ddelta_dinputs)
+ deallocate(ddelta_dinputs(p)%onedarray)
+ end do
+ deallocate(ddelta_dinputs)
+ do p = 1, size(dD_dinputs)
+ deallocate(dD_dinputs(p)%onedarray)
+ end do
+ deallocate(dD_dinputs)
+
+ k = 0
+ l = 0
+ do element = 1, num_elements
+ if (element > 1) then
+ k = k + no_layers_of_elements(element - 1)
+ end if
+ do j = 1, no_layers_of_elements(element) - 1
+ num_rows = no_nodes_of_elements(k + j) + 1
+ num_cols = no_nodes_of_elements(k + j + 1)
+ do p = 1, num_rows
+ do q = 1, num_cols
+ calculate_dforce_dparameters(&
+ l + (p - 1) * num_cols + q) = &
+ unraveled_dforce_dparameters(&
+ element)%weights(j)%twodarray(p, q)
+ end do
+ end do
+ l = l + num_rows * num_cols
+ end do
+ end do
+ do element = 1, num_elements
+ calculate_dforce_dparameters(l + 2 * element - 1) = &
+ unraveled_dforce_dparameters(element)%intercept
+ calculate_dforce_dparameters(l + 2 * element) = &
+ unraveled_dforce_dparameters(element)%slope
+ end do
+
+! deallocating derived-type parameters
+ do element = 1, num_elements
+ deallocate(unraveled_parameters(element)%weights)
+ deallocate(unraveled_dforce_dparameters(element)%weights)
+ end do
+
+ end function calculate_dforce_dparameters
+
+ !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+
+ end module neuralnetwork
+
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
diff --git a/amp/model/neuralnetwork.py b/amp/model/neuralnetwork.py
new file mode 100644
index 0000000..e2a3e39
--- /dev/null
+++ b/amp/model/neuralnetwork.py
@@ -0,0 +1,1208 @@
+import os
+import numpy as np
+from collections import OrderedDict
+from ase.calculators.calculator import Parameters
+
+from . import LossFunction, calculate_fingerprints_range, Model
+from ..regression import Regressor
+from ..utilities import Logger, hash_images, make_filename
+
+
+class NeuralNetwork(Model):
+
+ """Class that implements a basic feed-forward neural network.
+
+ Parameters
+ ----------
+ hiddenlayers : dict
+ Dictionary of chemical element symbols and architectures of their
+ corresponding hidden layers of the conventional neural network. Number
+ of nodes of last layer is always one corresponding to energy. However,
+ number of nodes of first layer is equal to three times number of atoms
+ in the system in the case of no descriptor, and is equal to length of
+ symmetry functions of the descriptor. Can be fed using tuples as:
+
+ >>> hiddenlayers = (3, 2,)
+
+ for example, in which a neural network with two hidden layers, the
+ first one having three nodes and the second one having two nodes is
+ assigned (to the whole atomic system in the no descriptor case, and to
+ each chemical element in the atom-centered mode). When setting only one
+ hidden layer, the dictionary can be fed as:
+
+ >>> hiddenlayers = (3,)
+
+ In the atom-centered mode, neural network for each species can be
+ assigned seperately, as:
+
+ >>> hiddenlayers = {"O":(3,5), "Au":(5,6)}
+
+ for example.
+
+ activation : str
+ Assigns the type of activation funtion. "linear" refers to linear
+ function, "tanh" refers to tanh function, and "sigmoid" refers to
+ sigmoid function.
+ weights : dict
+ In the case of no descriptor, keys correspond to layers and values are
+ two dimensional arrays of network weight. In the atom-centered mode,
+ keys correspond to chemical elements and values are dictionaries with
+ layer keys and network weight two dimensional arrays as values. Arrays
+ are set up to connect node i in the previous layer with node j in the
+ current layer with indices w[i,j]. The last value for index i
+ corresponds to bias. If weights is not given, arrays will be randomly
+ generated.
+ scalings : dict
+ In the case of no descriptor, keys are "intercept" and "slope" and
+ values are real numbers. In the fingerprinting scheme, keys correspond
+ to chemical elements and values are dictionaries with "intercept" and
+ "slope" keys and real number values. If scalings is not given, it will
+ be randomly generated.
+ fprange : dict
+ Range of fingerprints of each chemical species. Should be fed as
+ a dictionary of chemical species and a list of minimum and maximun,
+ e.g.:
+
+ >>> fprange={"Pd": [0.31, 0.59], "O":[0.56, 0.72]}
+
+ regressor : object
+ Regressor object for finding best fit model parameters, e.g. by loss
+ function optimization via amp.regression.Regressor.
+ mode : str
+ Can be either 'atom-centered' or 'image-centered'.
+ lossfunction : object
+ Loss function object, if at all desired by the user.
+ version : object
+ Version of this class.
+ fortran : bool
+ If True, allows for extrapolation, if False, does not allow.
+ checkpoints : int
+ Frequency with which to save parameter checkpoints upon training. E.g.,
+ 100 saves a checkpoint on each 100th training setp. Specify None for
+ no checkpoints. Note: You can make this negative to not overwrite
+ previous checkpoints.
+
+ .. note:: Dimensions of weight two dimensional arrays should be consistent
+ with hiddenlayers.
+
+ Raises
+ ------
+ RuntimeError, NotImplementedError
+ """
+
+ def __init__(self, hiddenlayers=(5, 5), activation='tanh', weights=None,
+ scalings=None, fprange=None, regressor=None, mode=None,
+ lossfunction=None, version=None, fortran=True,
+ checkpoints=100):
+
+ # Version check, particularly if restarting.
+ compatibleversions = ['2015.12', ]
+ if (version is not None) and version not in compatibleversions:
+ raise RuntimeError('Error: Trying to use NeuralNetwork'
+ ' version %s, but this module only supports'
+ ' versions %s. You may need an older or '
+ 'newer version of Amp.' %
+ (version, compatibleversions))
+ else:
+ version = compatibleversions[-1]
+
+ # The parameters dictionary contains the minimum information
+ # to produce a compatible model; e.g., one that gives
+ # the identical energy (and/or forces) when fed a fingerprint.
+ p = self.parameters = Parameters()
+ p.importname = '.model.neuralnetwork.NeuralNetwork'
+ p.version = version
+ p.hiddenlayers = hiddenlayers
+ p.weights = weights
+ p.scalings = scalings
+ p.fprange = fprange
+ p.activation = activation
+ p.mode = mode
+
+ # Checking that the activation function is given correctly:
+ if activation not in ['linear', 'tanh', 'sigmoid']:
+ _ = ('Unknown activation function %s; must be one of '
+ '"linear", "tanh", or "sigmoid".' % activation)
+ raise NotImplementedError(_)
+
+ self.regressor = regressor
+ self.parent = None # Can hold a reference to main Amp instance.
+ self.lossfunction = lossfunction
+ self.fortran = fortran
+ self.checkpoints = checkpoints
+ if self.lossfunction is None:
+ self.lossfunction = LossFunction()
+
+ def fit(self,
+ trainingimages,
+ descriptor,
+ log,
+ parallel,
+ only_setup=False,
+ ):
+ """Fit the model parameters such that the fingerprints can be used to
+ describe the energies in trainingimages. log is the logging object.
+ descriptor is a descriptor object, as would be in calc.descriptor.
+
+ Parameters
+ ----------
+ trainingimages : dict
+ Hashed dictionary of training images.
+ descriptor : object
+ Class representing local atomic environment.
+ log : Logger object
+ Write function at which to log data. Note this must be a callable
+ function.
+ parallel: dict
+ Parallel configuration dictionary. Takes the same form as in
+ amp.Amp.
+ only_setup : bool
+ only_setup is primarily for debugging. It initializes all
+ variables but skips the last line of starting the regressor.
+ """
+
+ # Set all parameters and report to logfile.
+ self._parallel = parallel
+ self._log = log
+
+ if self.regressor is None:
+ self.regressor = Regressor()
+
+ p = self.parameters
+ tp = self.trainingparameters = Parameters()
+ tp.trainingimages = trainingimages
+ tp.descriptor = descriptor
+
+ if p.mode is None:
+ p.mode = descriptor.parameters.mode
+ else:
+ assert p.mode == descriptor.parameters.mode
+ log('Regression in %s mode.' % p.mode)
+
+ if 'fprange' not in p or p.fprange is None:
+ log('Calculating new fingerprint range; this range is part '
+ 'of the model.')
+ p.fprange = calculate_fingerprints_range(descriptor,
+ trainingimages)
+
+ if p.mode == 'atom-centered':
+ # If hiddenlayers is a tuple/list, convert to a dictionary.
+ if not hasattr(p.hiddenlayers, 'keys'):
+ p.hiddenlayers = {element: p.hiddenlayers
+ for element in p.fprange.keys()}
+
+ log('Hidden-layer structure:')
+ if p.mode == 'image-centered':
+ log(' %s' % str(p.hiddenlayers))
+ elif p.mode == 'atom-centered':
+ for item in p.hiddenlayers.items():
+ log(' %2s: %s' % item)
+
+ if p.weights is None:
+ log('Initializing with random weights.')
+ if p.mode == 'image-centered':
+ raise NotImplementedError('Needs to be coded.')
+ elif p.mode == 'atom-centered':
+ p.weights = get_random_weights(p.hiddenlayers, p.activation,
+ None, p.fprange)
+ else:
+ log('Initial weights already present.')
+
+ if p.scalings is None:
+ log('Initializing with random scalings.')
+ if p.mode == 'image-centered':
+ raise NotImplementedError('Need to code.')
+ elif p.mode == 'atom-centered':
+ p.scalings = get_random_scalings(trainingimages, p.activation,
+ p.fprange.keys())
+ else:
+ log('Initial scalings already present.')
+
+ if only_setup:
+ return
+
+ # Regress the model.
+ self.step = 0
+ result = self.regressor.regress(model=self, log=log)
+ return result # True / False
+
+ @property
+ def forcetraining(self):
+ """Returns true if forcetraining is turned on (as determined by
+ examining the convergence criteria in the loss function), else
+ returns False.
+ """
+ if self.lossfunction.parameters['force_coefficient'] is None:
+ forcetraining = False
+ elif self.lossfunction.parameters['force_coefficient'] > 0.:
+ forcetraining = True
+ return forcetraining
+
+ @property
+ def vector(self):
+ """Access to get or set the model parameters (weights, scaling for
+ each network) as a single vector, useful in particular for
+ regression.
+
+ Parameters
+ ----------
+ vector : list
+ Parameters of the regression model in the form of a list.
+ """
+ if self.parameters['weights'] is None:
+ return None
+ p = self.parameters
+ if not hasattr(self, 'ravel'):
+ self.ravel = Raveler(p.weights, p.scalings)
+ return self.ravel.to_vector(weights=p.weights, scalings=p.scalings)
+
+ @vector.setter
+ def vector(self, vector):
+ p = self.parameters
+ if not hasattr(self, 'ravel'):
+ self.ravel = Raveler(p.weights, p.scalings)
+ weights, scalings = self.ravel.to_dicts(vector)
+ p['weights'] = weights
+ p['scalings'] = scalings
+
+ def get_loss(self, vector):
+ """Method to be called by the regression master.
+
+ Takes one and only one input, a vector of parameters.
+ Returns one output, the value of the loss (cost) function.
+
+ Parameters
+ ----------
+ vector : list
+ Parameters of the regression model in the form of a list.
+ """
+ if self.step == 0:
+ filename = make_filename(self.parent.label,
+ '-initial-parameters.amp')
+ filename = self.parent.save(filename, overwrite=True)
+ if self.checkpoints:
+ if self.step % self.checkpoints == 0:
+ self._log('Saving checkpoint data.')
+ if self.checkpoints < 0:
+ path = os.path.join(self.parent.label + '-checkpoints')
+ if self.step == 0:
+ if not os.path.exists(path):
+ os.mkdir(path)
+ filename = os.path.join(path,
+ '{}.amp'.format(int(self.step)))
+ else:
+ filename = make_filename(self.parent.label,
+ '-checkpoint.amp')
+ self.parent.save(filename, overwrite=True)
+ loss = self.lossfunction.get_loss(vector, lossprime=False)['loss']
+ if hasattr(self, 'observer'):
+ self.observer(self, vector, loss)
+ self.step += 1
+ return loss
+
+ def get_lossprime(self, vector):
+ """Method to be called by the regression master.
+
+ Takes one and only one input, a vector of parameters. Returns one
+ output, the value of the derivative of the loss function with respect
+ to model parameters.
+
+ Parameters
+ ----------
+ vector : list
+ Parameters of the regression model in the form of a list.
+ """
+ return self.lossfunction.get_loss(vector,
+ lossprime=True)['dloss_dparameters']
+
+ @property
+ def lossfunction(self):
+ """Allows the user to set a custom loss function.
+
+ For example,
+ >>> from amp.model import LossFunction
+ >>> lossfxn = LossFunction(energy_tol=0.0001)
+ >>> calc.model.lossfunction = lossfxn
+
+ Parameters
+ ----------
+ lossfunction : object
+ Loss function object, if at all desired by the user.
+ """
+ return self._lossfunction
+
+ @lossfunction.setter
+ def lossfunction(self, lossfunction):
+ if hasattr(lossfunction, 'attach_model'):
+ lossfunction.attach_model(self) # Allows access to methods.
+ self._lossfunction = lossfunction
+
+ def calculate_atomic_energy(self, afp, index, symbol,):
+ """
+ Given input to the neural network, output (which corresponds to energy)
+ is calculated about the specified atom. The sum of these for all
+ atoms is the total energy (in atom-centered mode).
+
+ Parameters
+ ---------
+ afp : list
+ Atomic fingerprints in the form of a list to be used as input to
+ the neural network.
+ index: int
+ Index of the atom for which atomic energy is calculated (only used
+ in the atom-centered mode).
+ symbol : str
+ Symbol of the atom for which atomic energy is calculated (only used
+ in the atom-centered mode).
+
+ Returns
+ -------
+ float
+ Energy.
+ """
+ if self.parameters.mode != 'atom-centered':
+ raise AssertionError('calculate_atomic_energy should only be '
+ ' called in atom-centered mode.')
+
+ scaling = self.parameters.scalings[symbol]
+ outputs = calculate_nodal_outputs(self.parameters, afp, symbol,)
+ atomic_amp_energy = scaling['slope'] * \
+ float(outputs[len(outputs) - 1]) + \
+ scaling['intercept']
+
+ return atomic_amp_energy
+
+ def calculate_force(self, afp, derafp,
+ direction,
+ nindex=None, nsymbol=None,):
+ """Given derivative of input to the neural network, derivative of output
+ (which corresponds to forces) is calculated.
+
+ Parameters
+ ----------
+ afp : list
+ Atomic fingerprints in the form of a list to be used as input to
+ the neural network.
+ derafp : list
+ Derivatives of atomic fingerprints in the form of a list to be used
+ as input to the neural network.
+ direction : int
+ Direction of force.
+ nindex : int
+ Index of the neighbor atom which force is acting at. (only used in
+ the atom-centered mode)
+ nsymbol : str
+ Symbol of the neighbor atom which force is acting at. (only used
+ in the atom-centered mode)
+
+ Returns
+ -------
+ float
+ Force.
+ """
+
+ scaling = self.parameters.scalings[nsymbol]
+ outputs = calculate_nodal_outputs(self.parameters, afp, nsymbol,)
+ dOutputs_dInputs = calculate_dOutputs_dInputs(self.parameters, derafp,
+ outputs, nsymbol,)
+
+ force = float((scaling['slope'] *
+ dOutputs_dInputs[len(dOutputs_dInputs) - 1][0]))
+ # force is multiplied by -1, because it is -dE/dx and not dE/dx.
+ force *= -1.
+
+ return force
+
+ def calculate_dAtomicEnergy_dParameters(self, afp, index=None,
+ symbol=None):
+ """Returns the derivative of energy square error with respect to
+ variables.
+
+ Parameters
+ ----------
+ afp : list
+ Atomic fingerprints in the form of a list to be used as input to
+ the neural network.
+ index : int
+ Index of the atom for which atomic energy is calculated (only used
+ in the atom-centered mode)
+ symbol : str
+ Symbol of the atom for which atomic energy is calculated (only used
+ in the atom-centered mode)
+
+ Returns
+ -------
+ list of float
+ The value of the derivative of energy square error with respect to
+ variables.
+ """
+ p = self.parameters
+ scaling = p.scalings[symbol]
+ # self.W dictionary initiated.
+ self.W = {}
+ for elm in p.weights.keys():
+ self.W[elm] = {}
+ weight = p.weights[elm]
+ for _ in range(len(weight)):
+ self.W[elm][_ + 1] = np.delete(weight[_ + 1], -1, 0)
+ W = self.W[symbol]
+
+ dAtomicEnergy_dParameters = np.zeros(self.ravel.count)
+ dAtomicEnergy_dWeights, dAtomicEnergy_dScalings = \
+ self.ravel.to_dicts(dAtomicEnergy_dParameters)
+
+ outputs = calculate_nodal_outputs(self.parameters, afp, symbol,)
+ ohat, D, delta = calculate_ohat_D_delta(self.parameters, outputs, W)
+
+ dAtomicEnergy_dScalings[symbol]['intercept'] = 1.
+ dAtomicEnergy_dScalings[symbol][
+ 'slope'] = float(outputs[len(outputs) - 1])
+ for k in range(1, len(outputs)):
+ dAtomicEnergy_dWeights[symbol][k] = float(scaling['slope']) * \
+ np.dot(np.matrix(ohat[k - 1]).T, np.matrix(delta[k]).T)
+
+ dAtomicEnergy_dParameters = \
+ self.ravel.to_vector(
+ dAtomicEnergy_dWeights, dAtomicEnergy_dScalings)
+
+ return dAtomicEnergy_dParameters
+
+ def calculate_dForce_dParameters(self, afp, derafp,
+ direction,
+ nindex=None, nsymbol=None,):
+ """Returns the derivative of force square error with respect to
+ variables.
+
+ Parameters
+ ----------
+ afp : list
+ Atomic fingerprints in the form of a list to be used as input to
+ the neural network.
+ derafp : list
+ Derivatives of atomic fingerprints in the form of a list to be used
+ as input to the neural network.
+ direction : int
+ Direction of force.
+ nindex : int
+ Index of the neighbor atom which force is acting at. (only used in
+ the atom-centered mode)
+ nsymbol : str
+ Symbol of the neighbor atom which force is acting at. (only used
+ in the atom-centered mode)
+
+ Returns
+ -------
+ list of float
+ The value of the derivative of force square error with respect to
+ variables.
+ """
+ p = self.parameters
+ scaling = p.scalings[nsymbol]
+ activation = p.activation
+ # self.W dictionary initiated.
+ self.W = {}
+ for elm in p.weights.keys():
+ self.W[elm] = {}
+ weight = p.weights[elm]
+ for _ in range(len(weight)):
+ self.W[elm][_ + 1] = np.delete(weight[_ + 1], -1, 0)
+ W = self.W[nsymbol]
+
+ dForce_dParameters = np.zeros(self.ravel.count)
+
+ dForce_dWeights, dForce_dScalings = \
+ self.ravel.to_dicts(dForce_dParameters)
+
+ outputs = calculate_nodal_outputs(self.parameters, afp, nsymbol,)
+ ohat, D, delta = calculate_ohat_D_delta(self.parameters, outputs, W)
+ dOutputs_dInputs = calculate_dOutputs_dInputs(self.parameters, derafp,
+ outputs, nsymbol,)
+
+ N = len(outputs) - 2
+ dD_dInputs = {}
+ for k in range(1, N + 2):
+ # Calculating coordinate derivative of D matrix
+ dD_dInputs[k] = np.zeros(shape=(np.size(outputs[k]),
+ np.size(outputs[k])))
+ for j in range(np.size(outputs[k])):
+ if activation == 'linear': # linear
+ dD_dInputs[k][j, j] = 0.
+ elif activation == 'tanh': # tanh
+ dD_dInputs[k][j, j] = \
+ - 2. * outputs[k][0, j] * dOutputs_dInputs[k][j]
+ elif activation == 'sigmoid': # sigmoid
+ dD_dInputs[k][j, j] = dOutputs_dInputs[k][j] - \
+ 2. * outputs[k][0, j] * dOutputs_dInputs[k][j]
+ # Calculating coordinate derivative of delta
+ dDelta_dInputs = {}
+ # output layer
+ dDelta_dInputs[N + 1] = dD_dInputs[N + 1]
+ # hidden layers
+ temp1 = {}
+ temp2 = {}
+ for k in range(N, 0, -1):
+ temp1[k] = np.dot(W[k + 1], delta[k + 1])
+ temp2[k] = np.dot(W[k + 1], dDelta_dInputs[k + 1])
+ dDelta_dInputs[k] = \
+ np.dot(dD_dInputs[k], temp1[k]) + np.dot(D[k], temp2[k])
+ # Calculating coordinate derivative of ohat and
+ # coordinates weights derivative of atomic_output
+ dOhat_dInputs = {}
+ dOutput_dInputsdWeights = {}
+ for k in range(1, N + 2):
+ dOhat_dInputs[k - 1] = [None] * (1 + len(dOutputs_dInputs[k - 1]))
+ bound = len(dOutputs_dInputs[k - 1])
+ for count in range(bound):
+ dOhat_dInputs[k - 1][count] = dOutputs_dInputs[k - 1][count]
+ dOhat_dInputs[k - 1][count + 1] = 0.
+ dOutput_dInputsdWeights[k] = \
+ np.dot(np.matrix(dOhat_dInputs[k - 1]).T,
+ np.matrix(delta[k]).T) + \
+ np.dot(np.matrix(ohat[k - 1]).T,
+ np.matrix(dDelta_dInputs[k]).T)
+
+ for k in range(1, N + 2):
+ dForce_dWeights[nsymbol][k] = float(scaling['slope']) * \
+ dOutput_dInputsdWeights[k]
+ dForce_dScalings[nsymbol]['slope'] = dOutputs_dInputs[N + 1][0]
+ dForce_dParameters = self.ravel.to_vector(dForce_dWeights,
+ dForce_dScalings)
+ # force is multiplied by -1, because it is -dE/dx and not dE/dx.
+ dForce_dParameters *= -1.
+
+ return dForce_dParameters
+
+# Auxiliary functions #########################################################
+
+
+def calculate_nodal_outputs(parameters, afp, symbol,):
+ """
+ Given input to the neural network, output (which corresponds to energy)
+ is calculated about the specified atom. The sum of these for all
+ atoms is the total energy (in atom-centered mode).
+
+ Parameters
+ ----------
+ parameters : dict
+ ASE dictionary object.
+ afp : list
+ Atomic fingerprints in the form of a list to be used as input to the
+ neural network.
+ symbol : str
+ Symbol of the atom for which atomic energy is calculated (only used in
+ the atom-centered mode)
+
+ Returns
+ -------
+ dict
+ Outputs of neural network nodes
+ """
+
+ _afp = np.array(afp).copy()
+ hiddenlayers = parameters.hiddenlayers[symbol]
+ weight = parameters.weights[symbol]
+ activation = parameters.activation
+
+ fprange = parameters.fprange[symbol]
+ # Scale the fingerprints to be in [-1, 1] range.
+ for _ in range(np.shape(_afp)[0]):
+ if (fprange[_][1] - fprange[_][0]) > (10.**(-8.)):
+ _afp[_] = -1.0 + 2.0 * ((_afp[_] - fprange[_][0]) /
+ (fprange[_][1] - fprange[_][0]))
+
+ # Calculate node values.
+ o = {} # node values
+ layer = 1 # input layer
+ net = {} # excitation
+ ohat = {} # ohat is the nodal output matrix o concatenated by 1 for biases
+
+ len_of_afp = len(_afp)
+ # a temp variable is defined to construct the output matix o
+ temp = np.zeros((1, len_of_afp + 1))
+ for _ in range(len_of_afp):
+ temp[0, _] = _afp[_]
+ temp[0, len(_afp)] = 1.0
+ ohat[0] = temp
+ net[1] = np.dot(ohat[0], weight[1])
+ if activation == 'linear':
+ o[1] = net[1] # linear activation
+ elif activation == 'tanh':
+ o[1] = np.tanh(net[1]) # tanh activation
+ elif activation == 'sigmoid': # sigmoid activation
+ o[1] = 1. / (1. + np.exp(-net[1]))
+ temp = np.zeros((1, np.shape(o[1])[1] + 1))
+ bound = np.shape(o[1])[1]
+ for _ in range(bound):
+ temp[0, _] = o[1][0, _]
+ temp[0, np.shape(o[1])[1]] = 1.0
+ ohat[1] = temp
+ for hiddenlayer in hiddenlayers[1:]:
+ layer += 1
+ net[layer] = np.dot(ohat[layer - 1], weight[layer])
+ if activation == 'linear':
+ o[layer] = net[layer] # linear activation
+ elif activation == 'tanh':
+ o[layer] = np.tanh(net[layer]) # tanh activation
+ elif activation == 'sigmoid':
+ # sigmoid activation
+ o[layer] = 1. / (1. + np.exp(-net[layer]))
+ temp = np.zeros((1, np.size(o[layer]) + 1))
+ bound = np.size(o[layer])
+ for _ in range(bound):
+ temp[0, _] = o[layer][0, _]
+ temp[0, np.size(o[layer])] = 1.0
+ ohat[layer] = temp
+ layer += 1 # output layer
+ net[layer] = np.dot(ohat[layer - 1], weight[layer])
+ if activation == 'linear':
+ o[layer] = net[layer] # linear activation
+ elif activation == 'tanh':
+ o[layer] = np.tanh(net[layer]) # tanh activation
+ elif activation == 'sigmoid':
+ # sigmoid activation
+ o[layer] = 1. / (1. + np.exp(-net[layer]))
+
+ del hiddenlayers, weight, ohat, net
+
+ len_of_afp = len(_afp)
+ temp = np.zeros((1, len_of_afp))
+ for _ in range(len_of_afp):
+ temp[0, _] = _afp[_]
+ o[0] = temp
+
+ return o
+
+
+def calculate_dOutputs_dInputs(parameters, derafp, outputs, nsymbol,):
+ """
+ Parameters
+ ----------
+ parameters : dict
+ ASE dictionary object.
+ derafp : list
+ Derivatives of atomic fingerprints in the form of a list to be used as
+ input to the neural network.
+ outputs : dict
+ Outputs of neural network nodes.
+ nsymbol : str
+ Symbol of the atom for which atomic energy is calculated (only used in
+ the atom-centered mode)
+
+ Returns
+ -------
+ dict
+ Derivatives of outputs of neural network nodes w.r.t. inputs.
+ """
+
+ _derafp = np.array(derafp).copy()
+ hiddenlayers = parameters.hiddenlayers[nsymbol]
+ weight = parameters.weights[nsymbol]
+ activation = parameters.activation
+
+ fprange = parameters.fprange[nsymbol]
+ # Scaling derivative of fingerprints.
+ for _ in range(len(_derafp)):
+ if (fprange[_][1] - fprange[_][0]) > (10.**(-8.)):
+ _derafp[_] = 2.0 * (_derafp[_] / (fprange[_][1] - fprange[_][0]))
+
+ dOutputs_dInputs = {} # node values
+ dOutputs_dInputs[0] = _derafp
+ layer = 0 # input layer
+ for hiddenlayer in hiddenlayers[0:]:
+ layer += 1
+ temp = np.dot(np.matrix(dOutputs_dInputs[layer - 1]),
+ np.delete(weight[layer], -1, 0))
+ dOutputs_dInputs[layer] = [None] * np.size(outputs[layer])
+ bound = np.size(outputs[layer])
+ for j in range(bound):
+ if activation == 'linear': # linear function
+ dOutputs_dInputs[layer][j] = float(temp[0, j])
+ elif activation == 'sigmoid': # sigmoid function
+ dOutputs_dInputs[layer][j] = float(temp[0, j]) * \
+ float(outputs[layer][0, j] * (1. - outputs[layer][0, j]))
+ elif activation == 'tanh': # tanh function
+ dOutputs_dInputs[layer][j] = float(temp[0, j]) * \
+ float(1. - outputs[layer][0, j] * outputs[layer][0, j])
+ layer += 1 # output layer
+ temp = np.dot(np.matrix(dOutputs_dInputs[layer - 1]),
+ np.delete(weight[layer], -1, 0))
+ if activation == 'linear': # linear function
+ dOutputs_dInputs[layer] = float(temp)
+ elif activation == 'sigmoid': # sigmoid function
+ dOutputs_dInputs[layer] = \
+ float(outputs[layer] * (1. - outputs[layer]) * temp)
+ elif activation == 'tanh': # tanh function
+ dOutputs_dInputs[layer] = \
+ float((1. - outputs[layer] * outputs[layer]) * temp)
+
+ dOutputs_dInputs[layer] = [dOutputs_dInputs[layer]]
+
+ return dOutputs_dInputs
+
+
+def calculate_ohat_D_delta(parameters, outputs, W):
+ """Calculates extra matrices ohat, D, delta needed in mathematical
+ manipulations.
+
+ Notations are consistent with those of 'Rojas, R. Neural Networks
+ - A Systematic Introduction. Springer-Verlag, Berlin, first edition 1996'
+
+ Parameters
+ ----------
+ parameters : dict
+ ASE dictionary object.
+ outputs : dict
+ Outputs of neural network nodes.
+ W : dict
+ The same as weight dictionary, but the last rows associated with biases
+ are deleted in W.
+ """
+
+ activation = parameters.activation
+
+ N = len(outputs) - 2 # number of hiddenlayers
+ D = {}
+ for k in range(N + 2):
+ D[k] = np.zeros(shape=(np.size(outputs[k]), np.size(outputs[k])))
+ for j in range(np.size(outputs[k])):
+ if activation == 'linear': # linear
+ D[k][j, j] = 1.
+ elif activation == 'sigmoid': # sigmoid
+ D[k][j, j] = float(outputs[k][0, j]) * \
+ float((1. - outputs[k][0, j]))
+ elif activation == 'tanh': # tanh
+ D[k][j, j] = float(1. - outputs[k][0, j] * outputs[k][0, j])
+ # Calculating delta
+ delta = {}
+ # output layer
+ delta[N + 1] = D[N + 1]
+ # hidden layers
+
+ for k in range(N, 0, -1): # backpropagate starting from output layer
+ delta[k] = np.dot(D[k], np.dot(W[k + 1], delta[k + 1]))
+ # Calculating ohat
+ ohat = {}
+ for k in range(1, N + 2):
+ bound = np.size(outputs[k - 1])
+ ohat[k - 1] = np.zeros(shape=(1, bound + 1))
+ for j in range(bound):
+ ohat[k - 1][0, j] = outputs[k - 1][0, j]
+ ohat[k - 1][0, bound] = 1.0
+
+ return ohat, D, delta
+
+
+def get_random_weights(hiddenlayers, activation, no_of_atoms=None,
+ fprange=None):
+ """Generates random weight arrays from variables.
+
+ hiddenlayers: dict
+ Dictionary of chemical element symbols and architectures of their
+ corresponding hidden layers of the conventional neural network. Number
+ of nodes of last layer is always one corresponding to energy. However,
+ number of nodes of first layer is equal to three times number of atoms
+ in the system in the case of no descriptor, and is equal to length of
+ symmetry functions in the atom-centered mode. Can be fed as:
+
+ >>> hiddenlayers = (3, 2,)
+
+ for example, in which a neural network with two hidden
+ layers, the first one having three nodes and the
+ second one having two nodes is assigned (to the whole
+ atomic system in the case of no descriptor, and to
+ each chemical element in the atom-centered mode). In
+ the atom-centered mode, neural network for each
+ species can be assigned seperately, as:
+
+ >>> hiddenlayers = {"O":(3,5), "Au":(5,6)}
+
+ for example.
+ activation : str
+ Assigns the type of activation funtion. "linear" refers to linear
+ function, "tanh" refers to tanh function, and "sigmoid" refers to
+ sigmoid function.
+ no_of_atoms : int
+ Number of atoms in atomic systems; used only in the case of no
+ descriptor.
+
+ fprange : dict
+ Range of fingerprints of each chemical species. Should be fed as
+ a dictionary of chemical species and a list of minimum and maximun,
+ e.g:
+
+ >>> fprange={"Pd": [0.31, 0.59], "O":[0.56, 0.72]}
+
+ Returns
+ -------
+ float
+ weights
+ """
+
+ weight = {}
+ nn_structure = {}
+
+ if no_of_atoms is not None: # pure atomic-coordinates scheme
+
+ if isinstance(hiddenlayers, int):
+ nn_structure = ([3 * no_of_atoms] + [hiddenlayers] + [1])
+ else:
+ nn_structure = (
+ [3 * no_of_atoms] +
+ [layer for layer in hiddenlayers] + [1])
+ weight = {}
+ # Instead try Andrew Ng coursera approach. +/- epsilon
+ # epsilon = sqrt(6./(n_i + n_o))
+ # where the n's are the number of input and output nodes.
+ # Note: need to double that here with the math below.
+ epsilon = np.sqrt(6. / (nn_structure[0] +
+ nn_structure[1]))
+ normalized_arg_range = 2. * epsilon
+ weight[1] = np.random.random((3 * no_of_atoms + 1,
+ nn_structure[1])) * \
+ normalized_arg_range - \
+ normalized_arg_range / 2.
+ len_of_hiddenlayers = len(list(nn_structure)) - 3
+ for layer in range(len_of_hiddenlayers):
+ epsilon = np.sqrt(6. / (nn_structure[layer + 1] +
+ nn_structure[layer + 2]))
+ normalized_arg_range = 2. * epsilon
+ weight[layer + 2] = np.random.random(
+ (nn_structure[layer + 1] + 1,
+ nn_structure[layer + 2])) * \
+ normalized_arg_range - normalized_arg_range / 2.
+
+ epsilon = np.sqrt(6. / (nn_structure[-2] +
+ nn_structure[-1]))
+ normalized_arg_range = 2. * epsilon
+ weight[len(list(nn_structure)) - 1] = \
+ np.random.random((nn_structure[-2] + 1, 1)) \
+ * normalized_arg_range - normalized_arg_range / 2.
+
+ if False: # This seemed to be setting all biases to zero?
+ len_of_weight = len(weight)
+ for _ in range(len_of_weight): # biases
+ size = weight[_ + 1][-1].size
+ for __ in range(size):
+ weight[_ + 1][-1][__] = 0.
+
+ else:
+ elements = fprange.keys()
+
+ for element in sorted(elements):
+ len_of_fps = len(fprange[element])
+ if isinstance(hiddenlayers[element], int):
+ nn_structure[element] = ([len_of_fps] +
+ [hiddenlayers[element]] + [1])
+ else:
+ nn_structure[element] = (
+ [len_of_fps] +
+ [layer for layer in hiddenlayers[element]] + [1])
+ weight[element] = {}
+ # Instead try Andrew Ng coursera approach. +/- epsilon
+ # epsilon = sqrt(6./(n_i + n_o))
+ # where the n's are the number of input and output nodes.
+ # Note: need to double that here with the math below.
+ epsilon = np.sqrt(6. / (nn_structure[element][0] +
+ nn_structure[element][1]))
+ normalized_arg_range = 2. * epsilon
+ weight[element][1] = np.random.random((len(fprange[element]) + 1,
+ nn_structure[
+ element][1])) * \
+ normalized_arg_range - \
+ normalized_arg_range / 2.
+ len_of_hiddenlayers = len(list(nn_structure[element])) - 3
+ for layer in range(len_of_hiddenlayers):
+ epsilon = np.sqrt(6. / (nn_structure[element][layer + 1] +
+ nn_structure[element][layer + 2]))
+ normalized_arg_range = 2. * epsilon
+ weight[element][layer + 2] = np.random.random(
+ (nn_structure[element][layer + 1] + 1,
+ nn_structure[element][layer + 2])) * \
+ normalized_arg_range - normalized_arg_range / 2.
+
+ epsilon = np.sqrt(6. / (nn_structure[element][-2] +
+ nn_structure[element][-1]))
+ normalized_arg_range = 2. * epsilon
+ weight[element][len(list(nn_structure[element])) - 1] = \
+ np.random.random((nn_structure[element][-2] + 1, 1)) \
+ * normalized_arg_range - normalized_arg_range / 2.
+
+ if False: # This seemed to be setting all biases to zero?
+ len_of_weight = len(weight[element])
+ for _ in range(len_of_weight): # biases
+ size = weight[element][_ + 1][-1].size
+ for __ in range(size):
+ weight[element][_ + 1][-1][__] = 0.
+
+ return weight
+
+
+def get_random_scalings(images, activation, elements=None):
+ """Generates initial scaling matrices, such that the range of activation is
+ scaled to the range of actual energies.
+
+ images : dict
+ ASE atoms objects (the training set).
+ activation: str
+ Assigns the type of activation funtion. "linear" refers to linear
+ function, "tanh" refers to tanh function, and "sigmoid" refers to
+ sigmoid function.
+ elements: list of str
+ List of atom symbols; used in the atom-centered mode only.
+
+ Returns
+ -------
+ float
+ scalings
+ """
+ hashs = list(images.keys())
+
+ no_of_images = len(hashs)
+
+ max_act_energy = max(image.get_potential_energy(apply_constraint=False)
+ for image in images.values())
+ min_act_energy = min(image.get_potential_energy(apply_constraint=False)
+ for image in images.values())
+
+ for count in range(no_of_images):
+ hash = hashs[count]
+ image = images[hash]
+ no_of_atoms = len(image)
+ if image.get_potential_energy(apply_constraint=False) == \
+ max_act_energy:
+ no_atoms_of_max_act_energy = no_of_atoms
+ if image.get_potential_energy(apply_constraint=False) == \
+ min_act_energy:
+ no_atoms_of_min_act_energy = no_of_atoms
+
+ max_act_energy_per_atom = max_act_energy / no_atoms_of_max_act_energy
+ min_act_energy_per_atom = min_act_energy / no_atoms_of_min_act_energy
+
+ scaling = {}
+
+ if elements is None: # pure atomic-coordinates scheme
+
+ scaling = {}
+ if activation == 'sigmoid': # sigmoid activation function
+ scaling['intercept'] = min_act_energy_per_atom
+ scaling['slope'] = (max_act_energy_per_atom -
+ min_act_energy_per_atom)
+ elif activation == 'tanh': # tanh activation function
+ scaling['intercept'] = (max_act_energy_per_atom +
+ min_act_energy_per_atom) / 2.
+ scaling['slope'] = (max_act_energy_per_atom -
+ min_act_energy_per_atom) / 2.
+ elif activation == 'linear': # linear activation function
+ scaling['intercept'] = (max_act_energy_per_atom +
+ min_act_energy_per_atom) / 2.
+ scaling['slope'] = (10. ** (-10.)) * \
+ (max_act_energy_per_atom -
+ min_act_energy_per_atom) / 2.
+
+ else: # atom-centered mode
+
+ for element in elements:
+ scaling[element] = {}
+ if activation == 'sigmoid': # sigmoid activation function
+ scaling[element]['intercept'] = min_act_energy_per_atom
+ scaling[element]['slope'] = (max_act_energy_per_atom -
+ min_act_energy_per_atom)
+ elif activation == 'tanh': # tanh activation function
+ scaling[element]['intercept'] = (max_act_energy_per_atom +
+ min_act_energy_per_atom) / 2.
+ scaling[element]['slope'] = (max_act_energy_per_atom -
+ min_act_energy_per_atom) / 2.
+ elif activation == 'linear': # linear activation function
+ scaling[element]['intercept'] = (max_act_energy_per_atom +
+ min_act_energy_per_atom) / 2.
+ scaling[element]['slope'] = (10. ** (-10.)) * \
+ (max_act_energy_per_atom -
+ min_act_energy_per_atom) / 2.
+
+ return scaling
+
+
+class Raveler:
+
+ """Class to ravel and unravel variable values into a single vector.
+
+ This is used for feeding into the optimizer. Feed in a list of dictionaries
+ to initialize the shape of the transformation. Note no data is saved in the
+ class; each time it is used it is passed either the dictionaries or vector.
+ The dictionaries for initialization should be two levels deep.
+
+ weights, scalings are the variables to ravel and unravel
+ """
+
+ def __init__(self, weights, scalings):
+
+ self.count = 0
+ self.weightskeys = []
+ self.scalingskeys = []
+ for key1 in sorted(weights.keys()): # element
+ for key2 in sorted(weights[key1].keys()): # layer
+ value = weights[key1][key2]
+ self.weightskeys.append({'key1': key1,
+ 'key2': key2,
+ 'shape': np.array(value).shape,
+ 'size': np.array(value).size})
+ self.count += np.array(weights[key1][key2]).size
+ for key1 in sorted(scalings.keys()): # element
+ for key2 in sorted(scalings[key1].keys()): # slope / intercept
+ self.scalingskeys.append({'key1': key1,
+ 'key2': key2})
+ self.count += 1
+ self.vector = np.zeros(self.count)
+
+ def to_vector(self, weights, scalings):
+ """Puts the weights and scalings embedded dictionaries into a single
+ vector and returns it. The dictionaries need to have the identical
+ structure to those it was initialized with."""
+
+ vector = np.zeros(self.count)
+ count = 0
+
+ for k in self.weightskeys:
+ lweights = np.array(weights[k['key1']][k['key2']]).ravel()
+ vector[count:(count + lweights.size)] = lweights
+ count += lweights.size
+ for k in self.scalingskeys:
+ vector[count] = scalings[k['key1']][k['key2']]
+ count += 1
+
+ return vector
+
+ def to_dicts(self, vector):
+ """Puts the vector back into weights and scalings dictionaries of the
+ form initialized. vector must have same length as the output of
+ unravel."""
+
+ assert len(vector) == self.count
+ count = 0
+ weights = OrderedDict()
+ scalings = OrderedDict()
+
+ for k in self.weightskeys:
+ if k['key1'] not in weights.keys():
+ weights[k['key1']] = OrderedDict()
+ matrix = vector[count:count + k['size']]
+ matrix = matrix.flatten()
+ matrix = np.matrix(matrix.reshape(k['shape']))
+ weights[k['key1']][k['key2']] = matrix.tolist()
+ count += k['size']
+ for k in self.scalingskeys:
+ if k['key1'] not in scalings.keys():
+ scalings[k['key1']] = OrderedDict()
+ scalings[k['key1']][k['key2']] = vector[count]
+ count += 1
+ return weights, scalings
+
+# Analysis tools ##############################################################
+
+
+class NodePlot:
+
+ """Creates plots to visualize the output of the nodes in the neural
+ networks.
+
+ initialize with a calculator that has parameters; e.g. a trained
+ calculator or else one in which fit has been called with the setup_only
+ flag turned on.
+
+ Call with the 'plot' method, which takes as argment a list of images
+ """
+
+ def __init__(self, calc):
+ self.calc = calc
+ self.data = {} # For accumulating the data.
+ # Local imports; these are not package-wide dependencies.
+ from matplotlib import pyplot
+ from matplotlib.backends.backend_pdf import PdfPages
+ self.pyplot = pyplot
+ self.PdfPages = PdfPages
+
+ def plot(self, images, filename='nodeplot.pdf'):
+ """ Creates a plot of the output of each node, as a violin plot.
+ """
+ calc = self.calc
+ log = Logger('develop.log')
+ images = hash_images(images, log=log)
+ calc.descriptor.calculate_fingerprints(images=images,
+ parallel={'cores': 1},
+ log=log,
+ calculate_derivatives=False)
+ for hash in images.keys():
+ fingerprints = calc.descriptor.fingerprints[hash]
+ for fp in fingerprints:
+ outputs = calculate_nodal_outputs(calc.model.parameters,
+ afp=fp[1],
+ symbol=fp[0])
+ self._accumulate(symbol=fp[0], output=outputs)
+
+ self._finalize_table()
+
+ with self.PdfPages(filename) as pdf:
+ for symbol in self.data.keys():
+ fig = self._makefig(symbol)
+ pdf.savefig(fig)
+ self.pyplot.close(fig)
+
+ def _makefig(self, symbol, save=False):
+ """Makes a figure for one element."""
+
+ fig = self.pyplot.figure(figsize=(8.5, 11.0))
+ lm = 0.1
+ rm = 0.05
+ bm = 0.05
+ tm = 0.05
+ vg = 0.05
+ numplots = 1 + self.data[symbol]['header'][-1][0]
+ axwidth = 1. - lm - rm
+ axheight = (1. - bm - tm - (numplots - 1) * vg) / numplots
+
+ d = self.data[symbol]
+ for layer in range(1 + d['header'][-1][0]):
+ ax = fig.add_axes((lm,
+ 1. - tm - axheight - (axheight + vg) * layer,
+ axwidth, axheight))
+ indices = [_ for _, label in enumerate(d['header'])
+ if label[0] == layer]
+ sub = d['table'][:, indices]
+ ax.violinplot(dataset=sub, positions=range(len(indices)))
+ ax.set_ylim(-1.2, 1.2)
+ ax.set_xlim(-0.5, len(indices) - 0.5)
+ ax.set_ylabel('Layer %i' % layer)
+ ax.set_xlabel('node')
+ fig.text(0.5, 1. - 0.5 * tm, 'Node outputs for %s' % symbol,
+ ha='center', va='center')
+
+ if save:
+ fig.savefig(save)
+ return fig
+
+ def _accumulate(self, symbol, output):
+ """Accumulates the data for the symbol."""
+ data = self.data
+ layerkeys = list(output.keys()) # Correspond to layers.
+
+ if symbol not in data:
+ # Create headers, structure.
+ data[symbol] = {'header': [],
+ 'table': []}
+ for layerkey in layerkeys:
+ v = output[layerkey]
+ v = v.reshape(v.size).tolist()
+ data[symbol]['header'].extend([(layerkey, _) for _ in
+ range(len(v))])
+ # Add as a row to data table.
+ row = []
+ for layerkey in layerkeys:
+ v = output[layerkey]
+ v = v.reshape(v.size).tolist()
+ row.extend(v)
+ data[symbol]['table'].append(row)
+
+ def _finalize_table(self):
+ """Converts the data table into a numpy array."""
+ for symbol in self.data:
+ self.data[symbol]['table'] = np.array(self.data[symbol]['table'])
diff --git a/amp/model/tflow.py b/amp/model/tflow.py
new file mode 100644
index 0000000..48e2d53
--- /dev/null
+++ b/amp/model/tflow.py
@@ -0,0 +1,1766 @@
+# This module was contributed by:
+# Zachary Ulissi
+# Department of Chemical Engineering
+# Stanford University
+# zulissi at gmail.com
+# Help/testing/discussions: Andrew Doyle (Stanford) and
+# the AMP development team
+
+# This module implements energy- and force- training using Google's
+# TensorFlow library. In doing so, the training is multithreaded and GPU
+# accelerated.
+
+import numpy as np
+import uuid
+
+from . import LossFunction
+from ..utilities import ConvergenceOccurred
+
+try:
+ import tensorflow as tf
+ from tensorflow.contrib.opt import ScipyOptimizerInterface
+except ImportError:
+ # A warning is raised instead of an error so that documentation can
+ # build without tensorflow installed.
+ import warnings
+ warnings.warn('Please install tensorflow if you plan to use this '
+ 'Amp module.')
+
+
+class NeuralNetwork:
+
+ """TensorFlow-based Neural Network model.
+
+ Uses Google's machine-learning code to construct a neural network. This
+ method also allows for GPU acceleration.
+
+ Parameters
+ ----------
+ hiddenlayers
+ Structure of the neural network. Can either be in the format
+ (int,int,int), where each element represnts the size of a
+ layer and there and the length of the list is the number of
+ layers, or dictionary format of the network structure for each
+ element type. E.g. {'Cu': (5, 5), 'O': (10, 5)}
+
+ activation
+ Activation type. (XXX Provide list of possibilities.)
+
+ keep_prob : float
+ Dropout rate for the neural network to reduce overfitting.
+ (keep_prob=1. uses all nodes, keep_prob~0.5-0.8 better for training)
+
+ maxTrainingEpochs : int
+ Maximum number of times to loop through the training data before
+ giving up.
+
+ batchsize : int
+ Batch size for minibatch (if miniBatch is set to True).
+
+ initialTrainingRate
+ Initial training rate for SGD optimizers like ADAM. See the TF
+ documentation for choose this value. Likely between 1e-2 and 1e-5,
+ depending on use case, whether mini-batch is on, etc.
+
+ miniBatch : bool
+ Whether to use minibatches in training.
+
+ tfVars
+ Tensorflow variables (used if restoring from a previous save).
+
+ saveVariableName : str
+ Name used for the internal tensorflow variable naming scheme.
+ If variables have the same name as another model in the same
+ tensorflow session, there will be collisions.
+
+ parameters
+ Dictionary of parameters to be used in initialization. Mostly these
+ are the same keywords as the keyword arguments in this function. This
+ is primarily used to make saving/loading easier.
+
+ sess
+ tensorflow session to use (None means start a new session)
+
+ maxAtomsForces : int
+ Number of atoms to be used in the force training. It sets the upper
+ bound on the number of atoms that can be used to calculate the force
+ for. E.g., if maxAtomsForces=40, then forces can only be calculated
+ for images with less than 40 atoms.
+
+ energy_coefficient : float
+ Used to adjust the loss function; this is the weight applied to the
+ energy component.
+
+ force_coefficient : float or None
+ Used to adjust the loss function; this is the weight applied to the
+ force component. Note you can turn off force training by setting
+ this to None.
+
+ convergenceCriteria: dict
+ Dictionary of convergence criteria, analagous to the main AMP
+ convergence criteria dictionary.
+
+ optimizationMethod: string
+ Set the optimization method for the NN parameters. Currently either
+ 'ADAM' for the ADAM optimizer in tensorflow, of 'l-BFGS-b' for the
+ deterministic l-BFGS-b method. ADAM is usually faster per training
+ step, has all of the benefits of being a stochastic optimizer, and
+ allows for mini-batch operation, but has more tunable parameters and
+ can be harder to get working well. l-BFGS-b usually works for
+ small/moderate network sizes.
+
+ input_keep_prob
+ Dropout ratio on the first layer (from fingerprints to the neural
+ network. Rule of thumb is this should be 0 to 0.2. Only applies when
+ using a SGD optimizer like ADAM. BFGS ignores this.
+
+ ADAM_optimizer_params
+ Dictionary of parameters to pass to the ADAM optimizer. See
+ https://www.tensorflow.org/versions/r0.11/api_docs/python/
+ train.html#AdamOptimizer for documentation
+
+ regularization_strength
+ Weight for L2-regularization in the cost function
+
+ fprange: dict
+ This is a dictionary that contains the minimum and maximum values seen
+ for each fingerprint of each element. These
+
+ weights: np array
+ Input that allows the NN weights (and biases) to be set directly. This
+ is only used for verifying that the calculation is working correctly
+ in the CuOPd test case. In general, don't use this except for testing
+ the code. This argument is analagous to the original AMP NeuralNetwork
+ module.
+
+ scalings
+ Input that allows the NN final scaling o be set directly. This
+ is only used for verifying that the calculation is working correctly
+ in the CuOPd test case. In general, don't use this except for testing
+ the code. This argument is analagous to the original AMP NeuralNetwork
+ module.
+
+ unit_type: string
+ Sets the internal datatype of the tensorflow model. Either "float"
+ for 32-bit FP precision, or "double" for 64-bit FP precision.
+
+ preLoadTrainingData: bool
+ Decides whether to run the training by preloading all training data
+ into tensorflow. Doing so results in faster training if the entire
+ dataset can fit into memory. This only works when not using mini-batch.
+
+ relativeForceCutoff: float
+ Parameter for controlling whether the force contribution to the trained
+ cost function is absolute (just differences of force compared to
+ training forces) or relative for large values of the force. This
+ basically sets the upper limit on the forces that should be fitted
+ (e.g. if the force is >A, then the force is scaled). This helps when a
+ small number of images have very large forces that don't need to be
+ reconstructed perfectly.
+ """
+
+ def __init__(self,
+ hiddenlayers=(5, 5),
+ activation='tanh',
+ keep_prob=1.,
+ maxTrainingEpochs=10000,
+ importname=None,
+ batchsize=2,
+ initialTrainingRate=1e-4,
+ miniBatch=False,
+ tfVars=None,
+ saveVariableName=None,
+ parameters=None,
+ sess=None,
+ energy_coefficient=1.0,
+ force_coefficient=0.04,
+ scikit_model=None,
+ convergenceCriteria=None,
+ optimizationMethod='l-BFGS-b',
+ input_keep_prob=0.8,
+ ADAM_optimizer_params={'beta1': 0.9},
+ regularization_strength=None,
+ numTrainingImages={},
+ elementFingerprintLengths=None,
+ fprange=None,
+ weights=None,
+ scalings=None,
+ unit_type="float",
+ preLoadTrainingData=True,
+ relativeForceCutoff=None
+ ):
+ self.parameters = {} if parameters is None else parameters
+ for prop in ['energyMeanScale',
+ 'energyPerElement']:
+ if prop not in self.parameters:
+ self.parameters[prop] = 0.
+ for prop in ['energyProdScale']:
+ if prop not in self.parameters:
+ self.parameters[prop] = 1.
+
+ if 'convergence' in self.parameters:
+ 1
+ elif convergenceCriteria is None:
+ self.parameters['convergence'] = {'energy_rmse': 0.001,
+ 'energy_maxresid': None,
+ 'force_rmse': 0.005,
+ 'force_maxresid': None}
+ else:
+ self.parameters['convergence'] = convergenceCriteria
+
+ if 'energy_coefficient' not in self.parameters:
+ self.parameters['energy_coefficient'] = energy_coefficient
+ if 'force_coefficient' not in self.parameters:
+ self.parameters['force_coefficient'] = force_coefficient
+ if 'ADAM_optimizer_params' not in self.parameters:
+ self.parameters['ADAM_optimizer_params'] = ADAM_optimizer_params
+ if 'regularization_strength' not in self.parameters:
+ self.parameters['regularization_strength'] =\
+ regularization_strength
+ if 'relativeForceCutoff' not in self.parameters:
+ self.parameters['relativeForceCutoff'] = relativeForceCutoff
+ if 'unit_type' not in self.parameters:
+ self.parameters['unit_type'] = unit_type
+ if 'preLoadTrainingData' not in self.parameters:
+ self.parameters['preLoadTrainingData'] = preLoadTrainingData
+ if 'fprange' not in self.parameters and fprange is not None:
+ self.parameters['fprange'] = {}
+ for element in fprange:
+ _ = np.array([map(lambda x: x[0], fprange[element]),
+ map(lambda x: x[1], fprange[element])])
+ self.parameters['fprange'][element] = _
+
+ self.hiddenlayers = hiddenlayers
+
+ if isinstance(activation, basestring):
+ self.activationName = activation
+ self.activation = eval('tf.nn.' + activation)
+ else:
+ self.activation = activation
+ self.activationName = activation.__name__
+ self.keep_prob = keep_prob
+ self.input_keep_prob = input_keep_prob
+
+ if saveVariableName is None:
+ self.saveVariableName = str(uuid.uuid4())[:8]
+ else:
+ self.saveVariableName = saveVariableName
+
+ if elementFingerprintLengths is not None:
+ self.elements = elementFingerprintLengths.keys()
+ self.elements.sort()
+ self.elementFingerprintLengths = {}
+ for element in self.elements:
+ self.elementFingerprintLengths[element] =\
+ elementFingerprintLengths[element]
+ self.weights = weights
+ self.scalings = scalings
+
+ self.sess = sess
+ self.graph = None
+ if tfVars is not None:
+ self.constructSessGraphModel(tfVars, self.sess)
+
+ if weights is not None:
+ self.elementFingerprintLengths = {}
+ self.elements = weights.keys()
+ for element in self.elements:
+ self.elementFingerprintLengths[element] =\
+ weights[element][1].shape[0] - 1
+
+ self.constructSessGraphModel(tfVars, self.sess)
+ self.tfVars = tfVars
+
+ self.maxTrainingEpochs = maxTrainingEpochs
+ self.importname = '.model.neuralnetwork.tflow'
+ self.batchsize = batchsize
+ self.initialTrainingRate = initialTrainingRate
+ self.miniBatch = miniBatch
+
+ # Optimizer can be 'ADAM' or 'l-BFGS-b'.
+ self.optimizationMethod = optimizationMethod
+
+ # self.forcetraining is queried by the main Amp instance.
+ if self.parameters['force_coefficient'] is None:
+ self.forcetraining = False
+ self.parameters['convergence']['force_rmse'] = None
+ self.parameters['convergence']['force_maxresid'] = None
+ else:
+ self.forcetraining = True
+
+ def constructSessGraphModel(self, tfVars, sess, trainOnly=False,
+ numElements=None, numTrainingImages=None,
+ num_dgdx_Eindices=None, numTrainingAtoms=None):
+ self.graph = tf.Graph()
+ with self.graph.as_default():
+ if sess is None:
+ self.sess = tf.InteractiveSession()
+ else:
+ self.sess = sess
+ if trainOnly:
+ self.constructModel(self.sess, self.graph, trainOnly,
+ numElements, numTrainingImages,
+ num_dgdx_Eindices, numTrainingAtoms)
+ else:
+ self.constructModel(self.sess, self.graph)
+ trainvarlist = tf.trainable_variables()
+ trainvarlist = [a for a in trainvarlist
+ if a.name[:8] == self.saveVariableName]
+ self.saver = tf.train.Saver(trainvarlist)
+ if tfVars is not None:
+ self.sess.run(tf.initialize_all_variables())
+ with open('tfAmpNN-checkpoint-restore', 'w') as fhandle:
+ fhandle.write(tfVars)
+ self.saver.restore(self.sess, 'tfAmpNN-checkpoint-restore')
+ else:
+ self.sess.run(tf.initialize_all_variables())
+
+ # This function is used to test the code by pre-setting the weights in the
+ # model for each element, so that results can be checked against
+ # pre-computed exact estimates
+ def setWeightsScalings(self, feedinput, weights, scalings):
+ with self.graph.as_default():
+ namefun = lambda x: '%s_%s_' % (self.saveVariableName, element) + x
+ for element in weights:
+ for layer in weights[element]:
+ weight = weights[element][layer][0:-1]
+ bias = weights[element][layer][-1]
+ bias = np.array(bias).reshape(bias.size)
+ feedinput[self.graph.get_tensor_by_name(
+ namefun('Wfc%d:0' % (layer - 1)))] = weight
+ feedinput[self.graph.get_tensor_by_name(
+ namefun('bfc%d:0' % (layer - 1)))] = bias
+ feedinput[
+ self.graph.get_tensor_by_name(namefun('Wfcout:0'))] = \
+ np.array(scalings[element]['slope']).reshape((1, 1))
+ feedinput[
+ self.graph.get_tensor_by_name(namefun('bfcout:0'))] = \
+ np.array(scalings[element]['intercept']).reshape((1,))
+
+ def constructModel(self, sess, graph, preLoadData=False, numElements=None,
+ numTrainingImages=None, num_dgdx_Eindices=None,
+ numTrainingAtoms=None):
+ """Sets up the tensorflow neural networks for each atom type."""
+
+ with sess.as_default(), graph.as_default():
+ # Make tensorflow inputs for each element.
+ tensordict = {}
+ indsdict = {}
+ maskdict = {}
+ dgdx_dict = {}
+ dgdx_Eindices_dict = {}
+ dgdx_Xindices_dict = {}
+ if preLoadData:
+ tensordictInitializer = {}
+ dgdx_dict_initializer = {}
+ dgdx_Eindices_dict_initializer = {}
+ dgdx_Xindices_dict_initializer = {}
+ indsdictInitializer = {}
+ maskdictInitializer = {}
+ for element in self.elements:
+ if preLoadData:
+ tensordictInitializer[element] = \
+ tf.placeholder(self.parameters['unit_type'],
+ shape=[numElements[element],
+ self.elementFingerprintLengths[
+ element]],
+ name='tensor_%s' % element,)
+
+ dgdx_dict_initializer[element] = \
+ tf.placeholder(self.parameters['unit_type'],
+ shape=[num_dgdx_Eindices[element],
+ self.elementFingerprintLengths[
+ element], 3],
+ name='dgdx_%s' % element,)
+ dgdx_Eindices_dict_initializer[element] = \
+ tf.placeholder("int64",
+ shape=[num_dgdx_Eindices[element]],
+ name='dgdx_Eindices_%s' % element,)
+ dgdx_Xindices_dict_initializer[element] = \
+ tf.placeholder("int64",
+ shape=[num_dgdx_Eindices[element]],
+ name='dgdx_Xindices_%s' % element,)
+
+ indsdictInitializer[element] = \
+ tf.placeholder("int64",
+ shape=[numElements[element]],
+ name='indsdict_%s' % element,)
+ maskdictInitializer[element] = \
+ tf.placeholder(self.parameters['unit_type'],
+ shape=[numTrainingImages, 1],
+ name='maskdict_%s' % element,)
+ tensordict[element] = \
+ tf.Variable(tensordictInitializer[element],
+ trainable=False,
+ collections=[],)
+ dgdx_dict[element] = \
+ tf.Variable(dgdx_dict_initializer[element],
+ trainable=False,
+ collections=[],)
+ dgdx_Eindices_dict[element] = \
+ tf.Variable(dgdx_Eindices_dict_initializer[element],
+ trainable=False,
+ collections=[],)
+ dgdx_Xindices_dict[element] = \
+ tf.Variable(dgdx_Xindices_dict_initializer[element],
+ trainable=False,
+ collections=[])
+ indsdict[element] = \
+ tf.Variable(indsdictInitializer[element],
+ trainable=False,
+ collections=[])
+ maskdict[element] = \
+ tf.Variable(maskdictInitializer[element],
+ trainable=False,
+ collections=[])
+ else:
+ tensordict[element] = \
+ tf.placeholder(self.parameters['unit_type'],
+ shape=[None,
+ self.elementFingerprintLengths[
+ element]],
+ name='tensor_%s' % element,)
+ dgdx_dict[element] = \
+ tf.placeholder(self.parameters['unit_type'],
+ shape=[None,
+ self.elementFingerprintLengths[
+ element],
+ 3],
+ name='dgdx_%s' % element)
+ dgdx_Eindices_dict[element] = \
+ tf.placeholder("int64",
+ shape=[None],
+ name='dgdx_Eindices_%s' % element)
+ dgdx_Xindices_dict[element] = \
+ tf.placeholder("int64",
+ shape=[None],
+ name='dgdx_Xindices_%s' % element)
+
+ indsdict[element] = \
+ tf.placeholder("int64",
+ shape=[None],
+ name='indsdict_%s' % element)
+ maskdict[element] = \
+ tf.placeholder(self.parameters['unit_type'],
+ shape=[None, 1],
+ name='maskdict_%s' % element)
+
+ self.indsdict = indsdict
+
+ self.tensordict = tensordict
+ self.maskdict = maskdict
+ self.dgdx_dict = dgdx_dict
+ self.dgdx_Eindices_dict = dgdx_Eindices_dict
+ self.dgdx_Xindices_dict = dgdx_Xindices_dict
+
+ # y_ is the input energy for each configuration.
+
+ if preLoadData:
+ y_Initializer = \
+ tf.placeholder(self.parameters['unit_type'],
+ shape=[numTrainingImages, 1],
+ name='y_')
+ input_keep_prob_inInitializer = \
+ tf.placeholder(self.parameters['unit_type'],
+ shape=[],
+ name='input_keep_prob_in')
+ keep_prob_inInitializer = \
+ tf.placeholder(self.parameters['unit_type'],
+ shape=[],
+ name='keep_prob_in')
+ nAtoms_inInitializer = \
+ tf.placeholder(self.parameters['unit_type'],
+ shape=[numTrainingImages, 1],
+ name='nAtoms_in')
+ nAtoms_forces_Initializer = \
+ tf.placeholder(self.parameters['unit_type'],
+ shape=[numTrainingAtoms, 1],
+ name='nAtoms_forces')
+ batchsizeInputInitializer = \
+ tf.placeholder("int32",
+ shape=[],
+ name='batchsizeInput')
+ learningrateInitializer = \
+ tf.placeholder(self.parameters['unit_type'],
+ shape=[],
+ name='learningrate')
+ forces_inInitializer = \
+ tf.placeholder(self.parameters['unit_type'],
+ shape=[numTrainingAtoms, 3],
+ name='forces_in')
+ energycoefficientInitializer = \
+ tf.placeholder(self.parameters['unit_type'],
+ shape=[])
+ forcecoefficientInitializer = \
+ tf.placeholder(self.parameters['unit_type'],
+ shape=[])
+ energyProdScaleInitializer = \
+ tf.placeholder(self.parameters['unit_type'],
+ shape=[],
+ name='energyProdScale')
+ totalNumAtomsInitializer = \
+ tf.placeholder("int32",
+ shape=[],
+ name='totalNumAtoms')
+
+ self.y_ = \
+ tf.Variable(y_Initializer,
+ trainable=False,
+ collections=[])
+ self.input_keep_prob_in = \
+ tf.Variable(input_keep_prob_inInitializer,
+ trainable=False,
+ collections=[])
+ self.keep_prob_in = \
+ tf.Variable(keep_prob_inInitializer,
+ trainable=False,
+ collections=[])
+ self.nAtoms_in = \
+ tf.Variable(nAtoms_inInitializer,
+ trainable=False,
+ collections=[])
+ self.batchsizeInput = \
+ tf.Variable(batchsizeInputInitializer,
+ trainable=False,
+ collections=[])
+ self.learningrate = \
+ tf.Variable(learningrateInitializer,
+ trainable=False,
+ collections=[])
+ self.forces_in = \
+ tf.Variable(forces_inInitializer,
+ trainable=False,
+ collections=[])
+ self.energycoefficient = \
+ tf.Variable(energycoefficientInitializer,
+ trainable=False,
+ collections=[])
+ self.forcecoefficient = \
+ tf.Variable(forcecoefficientInitializer,
+ trainable=False,
+ collections=[])
+ self.energyProdScale = \
+ tf.Variable(energyProdScaleInitializer,
+ trainable=False,
+ collections=[])
+ self.totalNumAtoms = \
+ tf.Variable(totalNumAtomsInitializer,
+ trainable=False,
+ collections=[])
+ self.nAtoms_forces = \
+ tf.Variable(nAtoms_forces_Initializer,
+ trainable=False,
+ collections=[])
+ self.initializers = \
+ {'indsdict': indsdictInitializer,
+ 'dgdx_dict': dgdx_dict_initializer,
+ 'dgdx_Xindices_dict': dgdx_Xindices_dict_initializer,
+ 'dgdx_Eindices_dict': dgdx_Eindices_dict_initializer,
+ 'maskdict': maskdictInitializer,
+ 'tensordict': tensordictInitializer,
+ 'y_': y_Initializer,
+ 'input_keep_prob_in': input_keep_prob_inInitializer,
+ 'keep_prob_in': keep_prob_inInitializer,
+ 'nAtoms_in': nAtoms_inInitializer,
+ 'batchsizeInput': batchsizeInputInitializer,
+ 'learningrate': learningrateInitializer,
+ 'forces_in': forces_inInitializer,
+ 'energycoefficient': energycoefficientInitializer,
+ 'forcecoefficient': forcecoefficientInitializer,
+ 'energyProdScale': energyProdScaleInitializer,
+ 'totalNumAtoms': totalNumAtomsInitializer,
+ 'nAtoms_forces': nAtoms_forces_Initializer}
+ else:
+ self.y_ = \
+ tf.placeholder(self.parameters['unit_type'],
+ shape=[None, 1],
+ name='y_')
+ self.input_keep_prob_in = \
+ tf.placeholder(self.parameters['unit_type'],
+ name='input_keep_prob_in')
+ self.keep_prob_in = \
+ tf.placeholder(self.parameters['unit_type'],
+ name='keep_prob_in')
+ self.nAtoms_in = \
+ tf.placeholder(self.parameters['unit_type'],
+ shape=[None, 1],
+ name='nAtoms_in')
+ self.batchsizeInput = \
+ tf.placeholder("int32",
+ name='batchsizeInput')
+ self.learningrate = \
+ tf.placeholder(self.parameters['unit_type'],
+ name='learningrate')
+ self.forces_in = \
+ tf.placeholder(self.parameters['unit_type'],
+ shape=[None, None, 3],
+ name='forces_in')
+ self.energycoefficient = \
+ tf.placeholder(self.parameters['unit_type'])
+ self.forcecoefficient = \
+ tf.placeholder(self.parameters['unit_type'])
+ self.energyProdScale = \
+ tf.placeholder(self.parameters['unit_type'],
+ name='energyProdScale')
+ self.totalNumAtoms = \
+ tf.placeholder("int32",
+ name='totalNumAtoms')
+ self.nAtoms_forces = \
+ tf.placeholder(self.parameters['unit_type'],
+ shape=[None, 1],
+ name='totalNumAtoms')
+ # Generate a multilayer neural network for each element type.
+ outdict = {}
+ forcedict = {}
+ l2_regularization_dict = {}
+ for element in self.elements:
+ if isinstance(self.hiddenlayers, dict):
+ networkListToUse = self.hiddenlayers[element]
+ else:
+ networkListToUse = self.hiddenlayers
+ (outdict[element],
+ forcedict[element],
+ l2_regularization_dict[element]) = \
+ model(tensordict[element],
+ indsdict[element],
+ self.keep_prob_in,
+ self.input_keep_prob_in,
+ self.batchsizeInput,
+ networkListToUse,
+ self.activation,
+ self.elementFingerprintLengths[
+ element],
+ mask=maskdict[
+ element],
+ name=self.saveVariableName,
+ dgdx=self.dgdx_dict[
+ element],
+ dgdx_Eindices=self.dgdx_Eindices_dict[
+ element],
+ dgdx_Xindices=self.dgdx_Xindices_dict[
+ element],
+ element=element,
+ unit_type=self.parameters[
+ 'unit_type'],
+ totalNumAtoms=self.totalNumAtoms)
+ self.outdict = outdict
+
+ # The total energy is the sum of the energies over each atom type.
+ keylist = self.elements
+ ytot = outdict[keylist[0]]
+ for i in range(1, len(keylist)):
+ ytot = ytot + outdict[keylist[i]]
+ self.energy = ytot * self.energyProdScale
+
+ # The total force is the sum of the forces over each atom type.
+ Ftot = forcedict[keylist[0]]
+ for i in range(1, len(keylist)):
+ Ftot = Ftot + forcedict[keylist[i]]
+ self.forcedict = forcedict
+ self.forces = -Ftot * self.energyProdScale
+
+ l2_regularization = l2_regularization_dict[keylist[0]]
+ for i in range(1, len(keylist)):
+ l2_regularization = l2_regularization + \
+ l2_regularization_dict[keylist[i]]
+ # Define output nodes for the energy of a configuration, a loss
+ # function, and the loss per atom (which is what we usually track)
+ # self.loss = tf.sqrt(tf.reduce_sum(
+ # tf.square(tf.sub(self.energy, self.y_))))
+ # self.lossPerAtom = tf.reduce_sum(
+ # tf.square(tf.div(tf.sub(self.energy, self.y_), self.nAtoms_in)))
+
+ # loss function, as included in model/__init__.py
+ self.energy_loss = tf.reduce_sum(
+ tf.square(tf.div(tf.sub(self.energy, self.y_),
+ self.nAtoms_in)))
+ # Define the training step for energy training.
+
+ # self.loss_forces = self.forcecoefficient * \
+ # tf.sqrt(tf.reduce_mean(tf.square(tf.sub(self.forces_in,
+ # self.forces))))
+ # force loss function, as included in model/__init__.py
+ if self.parameters['relativeForceCutoff'] is None:
+ self.force_loss = tf.reduce_sum(
+ tf.div(tf.square(tf.sub(self.forces_in, self.forces)),
+ self.nAtoms_forces)) / 3.
+ # tf.reduce_sum(tf.div(
+ # tf.reduce_mean(tf.square(tf.sub(self.forces_in,
+ # self.forces)), 2), self.nAtoms_in))
+ else:
+ relativeA = self.parameters['relativeForceCutoff']
+ self.force_loss = \
+ tf.reduce_sum(tf.div(tf.div(
+ tf.square(
+ tf.sub(
+ self.forces_in, self.forces)),
+ tf.square(
+ self.forces_in) +
+ relativeA**2.) *
+ relativeA**2.,
+ self.nAtoms_forces)) / 3.
+
+ # tf.reduce_sum(tf.div(tf.reduce_mean(
+ # tf.div(tf.square(tf.sub(self.forces_in, self.forces)),
+ # tf.square(self.forces_in)+relativeA**2.)*relativeA**2.,2),
+ # self.nAtoms_in))
+
+ # Define max residuals
+ self.energy_maxresid = tf.reduce_max(
+ tf.abs(tf.div(tf.sub(self.energy, self.y_), self.nAtoms_in)))
+ self.force_maxresid = tf.reduce_max(
+ tf.abs(tf.sub(self.forces_in, self.forces)))
+
+ # Define the training step for force training.
+ if self.parameters['regularization_strength'] is not None:
+ self.loss = self.forcecoefficient * self.force_loss + \
+ self.energycoefficient * self.energy_loss + \
+ self.parameters[
+ 'regularization_strength'] * l2_regularization
+ self.energy_loss_regularized = self.energy_loss + \
+ self.parameters[
+ 'regularization_strength'] * l2_regularization
+ else:
+ self.loss = self.forcecoefficient * self.force_loss + \
+ self.energycoefficient * self.energy_loss
+ self.energy_loss_regularized = self.energy_loss
+
+ self.adam_optimizer_instance = \
+ tf.train.AdamOptimizer(self.learningrate,
+ **self.parameters[
+ 'ADAM_optimizer_params'])
+ self.train_step = \
+ self.adam_optimizer_instance.minimize(
+ self.energy_loss_regularized)
+ self.train_step_forces = \
+ self.adam_optimizer_instance.minimize(self.loss)
+
+ # self.loss_forces_relative = \
+ # self.forcecoefficient * \
+ # tf.sqrt(tf.reduce_mean(tf.square(tf.div(tf.sub(self.forces_in,
+ # self.forces),self.forces_in+0.0001))))
+ # self.force_loss_relative = \
+ # tf.reduce_sum(tf.div(tf.reduce_mean(
+ # tf.div(tf.square(tf.sub(self.forces_in,
+ # self.forces)),tf.square(self.forces_in)+0.005**2.),2),
+ # self.nAtoms_in))
+ # self.loss_relative = \
+ # self.forcecoefficient*self.loss_forces_relative + \
+ # self.energycoefficient*self.energy_loss
+ # self.train_step_forces =
+ # tf.adam_optimizer_instance.minimize(self.loss_relative)
+
+ def initializeVariables(self):
+ """Resets all of the variables in the current tensorflow model."""
+ self.sess.run(tf.initialize_all_variables())
+
+ def generateFeedInput(self, curinds,
+ energies,
+ atomArraysAll,
+ dgdx, dgdx_Eindices, dgdx_Xindices,
+ nAtomsDict,
+ atomsIndsReverse,
+ batchsize,
+ trainingrate,
+ keepprob, inputkeepprob, natoms,
+ forcesExp=0.,
+ forces=False,
+ energycoefficient=1.,
+ forcecoefficient=None, training=True):
+ """Generates the input dictionary that maps various inputs on
+ the python side to placeholders for the tensorflow model."""
+
+ (atomArraysFinal,
+ dgdx_batch,
+ dgdx_Eindices_batch,
+ dgdx_Xindices_batch,
+ atomInds) = \
+ generateBatch(curinds,
+ self.elements,
+ atomArraysAll,
+ nAtomsDict,
+ atomsIndsReverse,
+ dgdx,
+ dgdx_Eindices,
+ dgdx_Xindices)
+ feedinput = {}
+
+ for element in self.elements:
+ if len(atomArraysFinal[element]) > 0:
+ aAF = atomArraysFinal[element].copy()
+ for i in range(len(aAF)):
+ for j in range(len(aAF[i])):
+ if (self.parameters['fprange'][element][1][j] -
+ self.parameters['fprange'][element][0][j]) > 10.**-8:
+ aAF[i][j] = -1. + \
+ 2. * (atomArraysFinal[element][i][j] -
+ self.parameters['fprange'][element][0][j]) / (
+ self.parameters['fprange'][element][1][j] -
+ self.parameters['fprange'][element][0][j])
+ feedinput[self.tensordict[element]] = aAF
+
+ feedinput[self.indsdict[element]] = atomInds[element]
+ feedinput[self.maskdict[element]] = np.ones((batchsize, 1))
+ if forcecoefficient > 1.e-5:
+
+ dgdx_to_scale = dgdx_batch[element]
+ for i in range(dgdx_to_scale.shape[0]):
+ for l in range(dgdx_to_scale.shape[1]):
+ if (self.parameters['fprange'][element][1][l] -
+ self.parameters['fprange'][element][0][l]) > 10.**-8:
+ dgdx_to_scale[i][l][:] = \
+ 2. * dgdx_to_scale[i][l][:] / \
+ (self.parameters['fprange'][element][1][l] -
+ self.parameters['fprange'][element][0][l])
+ feedinput[self.dgdx_dict[element]] = dgdx_to_scale
+ feedinput[self.dgdx_Eindices_dict[
+ element]] = dgdx_Eindices_batch[element]
+ feedinput[self.dgdx_Xindices_dict[
+ element]] = dgdx_Xindices_batch[element]
+ else:
+ feedinput[self.dgdx_dict[element]] = \
+ np.zeros((len(dgdx_Eindices[element]),
+ self.elementFingerprintLengths[element], 3))
+ feedinput[self.dgdx_Eindices_dict[element]] = []
+ feedinput[self.dgdx_Xindices_dict[element]] = []
+ else:
+ feedinput[self.tensordict[element]] = np.zeros(
+ (1, self.elementFingerprintLengths[element]))
+ feedinput[self.indsdict[element]] = [0]
+ feedinput[self.maskdict[element]] = np.zeros((batchsize, 1))
+ feedinput[self.dgdx_dict[element]] = \
+ np.zeros((len(dgdx_Eindices[element]),
+ self.elementFingerprintLengths[element], 3))
+ feedinput[self.dgdx_Eindices_dict[element]] = []
+ feedinput[self.dgdx_Xindices_dict[element]] = []
+
+ feedinput[self.batchsizeInput] = batchsize
+ feedinput[self.learningrate] = trainingrate
+ feedinput[self.keep_prob_in] = keepprob
+ feedinput[self.input_keep_prob_in] = inputkeepprob
+ natoms_forces = []
+ for natom in natoms[curinds]:
+ for i in range(natom):
+ natoms_forces.append(natom)
+ natoms_forces = np.array(natoms_forces)
+ feedinput[self.nAtoms_forces] = natoms_forces
+ feedinput[self.nAtoms_in] = natoms[curinds]
+ feedinput[self.totalNumAtoms] = np.sum(natoms[curinds])
+ if training:
+ feedinput[self.y_] = energies[curinds]
+ if forcecoefficient > 1.e-5:
+ feedinput[self.forces_in] = np.concatenate(
+ forcesExp[curinds], axis=0)
+ feedinput[self.forcecoefficient] = forcecoefficient
+ feedinput[self.energycoefficient] = energycoefficient
+ feedinput[self.energyProdScale] = self.parameters['energyProdScale']
+ return feedinput
+
+ def fit(self, trainingimages, descriptor, parallel, log=None):
+ """Fit takes a bunch of training images (which are assumed to have a
+ working calculator attached), and fits the internal variables to the
+ training images.
+ """
+
+ # if self.graph is None, the module hasn't been initialized
+ if self.graph is None:
+ self.elementFingerprintLengths = {}
+ for element in descriptor.parameters.Gs:
+ self.elementFingerprintLengths[element] = len(
+ descriptor.parameters.Gs[element])
+ self.elements = self.elementFingerprintLengths.keys()
+ self.elements.sort()
+ self.constructSessGraphModel(self.tfVars, self.sess)
+
+ self.log = log
+
+ params = self.parameters
+ lf = LossFunction(convergence=params['convergence'],
+ energy_coefficient=params['energy_coefficient'],
+ force_coefficient=params['force_coefficient'],
+ parallel={'cores': 1})
+ if params['force_coefficient'] is not None:
+ lf.attach_model(self,
+ images=trainingimages,
+ fingerprints=descriptor.fingerprints,
+ fingerprintprimes=descriptor.fingerprintprimes)
+ else:
+ lf.attach_model(self,
+ images=trainingimages,
+ fingerprints=descriptor.fingerprints)
+ lf._initialize()
+ # Inputs:
+ # trainingimages:
+ batchsize = self.batchsize
+ if self.parameters['force_coefficient'] is None:
+ fingerprintDerDB = None
+ else:
+ fingerprintDerDB = descriptor.fingerprintprimes
+ images = trainingimages
+ keylist = images.keys()
+ fingerprintDB = descriptor.fingerprints
+ self.parameters['numTrainingImages'] = len(keylist)
+ (atomArraysAll,
+ nAtomsDict,
+ atomsIndsReverse,
+ natoms,
+ dgdx,
+ dgdx_Eindices,
+ dgdx_Xindices) = \
+ generateTensorFlowArrays(fingerprintDB,
+ self.elements,
+ keylist,
+ fingerprintDerDB)
+ energies = map(
+ lambda x: [images[x].get_potential_energy(apply_constraint=False)],
+ keylist)
+ energies = np.array(energies)
+
+ if self.parameters['preLoadTrainingData'] and not(self.miniBatch):
+ numElements = {}
+ for element in nAtomsDict:
+ numElements[element] = sum(nAtomsDict[element])
+ self.saver.save(self.sess, 'tfAmpNN-checkpoint')
+ with open('tfAmpNN-checkpoint') as fhandle:
+ tfvars = fhandle.read()
+ self.sess.close()
+ numTrainingAtoms = np.sum(map(lambda x: len(images[x]), keylist))
+ num_dgdx_Eindices = {}
+ num_dgdx_Xindices = {}
+ for element in self.elements:
+ num_dgdx_Eindices[element] = sum(
+ map(len, dgdx_Eindices[element]))
+ num_dgdx_Xindices[element] = sum(
+ map(len, dgdx_Xindices[element]))
+
+ self.constructSessGraphModel(tfvars,
+ None,
+ trainOnly=True,
+ numElements=numElements,
+ numTrainingImages=len(keylist),
+ num_dgdx_Eindices=num_dgdx_Eindices,
+ numTrainingAtoms=numTrainingAtoms)
+
+ natomsArray = np.zeros((len(keylist), len(self.elements)))
+ for i in range(len(images)):
+ for j in range(len(self.elements)):
+ natomsArray[i][j] = nAtomsDict[self.elements[j]][i]
+
+ (atomArraysAll,
+ nAtomsDict,
+ atomsIndsReverse,
+ natoms,
+ dgdx,
+ dgdx_Eindices,
+ dgdx_Xindices) = generateTensorFlowArrays(fingerprintDB,
+ self.elements,
+ keylist,
+ fingerprintDerDB)
+
+ self.parameters['energyMeanScale'] = np.mean(energies)
+ energies = energies - self.parameters['energyMeanScale']
+ self.parameters['energyProdScale'] = np.mean(np.abs(energies))
+ self.parameters['fprange'] = {}
+ for element in self.elements:
+ if len(atomArraysAll[element]) == 0:
+ self.parameters['fprange'][element] = []
+ else:
+ self.parameters['fprange'][element] = \
+ [np.min(atomArraysAll[element], axis=0),
+ np.max(atomArraysAll[element], axis=0)]
+
+ if self.parameters['force_coefficient'] is not None:
+ # forces = map(lambda x: images[x].get_forces(
+ # apply_constraint=False), keylist)
+ # forces = np.zeros((len(keylist), self.maxAtomsForces, 3))
+ forces = []
+ for i in range(len(keylist)):
+ atoms = images[keylist[i]]
+ forces.append(atoms.get_forces(apply_constraint=False))
+ forces = np.array(forces)
+ else:
+ forces = 0.
+
+ if not(self.miniBatch):
+ batchsize = len(keylist)
+
+ def trainmodel(trainingrate, keepprob, inputkeepprob, maxepochs):
+ icount = 1
+ icount_global = 1
+ indlist = np.arange(len(keylist))
+ converge_save = []
+
+ # continue taking training steps as long as we haven't hit the RMSE
+ # minimum of the max number of epochs
+ while (icount < maxepochs):
+
+ # if we're in minibatch mode, shuffle the index list
+ if self.miniBatch:
+ np.random.shuffle(indlist)
+
+ for i in range(int(len(keylist) / batchsize)):
+
+ # if we're doing minibatch, construct a new set of inputs
+ if self.miniBatch or (not(self.miniBatch)and(icount == 1)):
+ if self.miniBatch:
+ curinds = indlist[
+ np.arange(batchsize) + i * batchsize]
+ else:
+ curinds = range(len(keylist))
+
+ feedinput = self.generateFeedInput(
+ curinds,
+ energies,
+ atomArraysAll,
+ dgdx,
+ dgdx_Eindices,
+ dgdx_Xindices,
+ nAtomsDict,
+ atomsIndsReverse,
+ batchsize,
+ trainingrate,
+ keepprob,
+ inputkeepprob,
+ natoms,
+ forcesExp=forces,
+ energycoefficient=self.parameters[
+ 'energy_coefficient'],
+ forcecoefficient=self.parameters[
+ 'force_coefficient'])
+ if (self.parameters['preLoadTrainingData'] and
+ not(self.miniBatch)):
+ self.preLoadFeed(feedinput)
+
+ # run a training step with the inputs.
+ if self.parameters['force_coefficient'] is None:
+ self.sess.run(self.train_step, feed_dict=feedinput)
+ else:
+ self.sess.run(self.train_step_forces,
+ feed_dict=feedinput)
+
+ # Print the loss function every 100 evals.
+ # if (self.miniBatch)and(icount % 100 == 0):
+ # feed_keepprob_save=feedinput[self.keep_prob_in]
+ # feed_keepprob_save_input=\
+ # feedinput[self.input_keep_prob_in]
+ # feedinput[self.keep_prob_in]=1.
+ # feedinput[self.keep_prob_in]=feed_keepprob_save
+ icount += 1
+
+ # Every 10 epochs, report the RMSE on the entire training set
+ if icount_global % 10 == 0:
+ if self.miniBatch:
+ feedinput = self.generateFeedInput(
+ range(len(keylist)),
+ energies,
+ atomArraysAll,
+ dgdx,
+ dgdx_Eindices,
+ dgdx_Xindices,
+ nAtomsDict,
+ atomsIndsReverse,
+ len(keylist),
+ trainingrate,
+ 1.,
+ 1.,
+ natoms,
+ forcesExp=forces,
+ energycoefficient=self.parameters[
+ 'energy_coefficient'],
+ forcecoefficient=self.parameters[
+ 'force_coefficient'],
+ )
+ feed_keepprob_save = feedinput[self.keep_prob_in]
+ feed_keepprob_save_input = feedinput[
+ self.input_keep_prob_in]
+ feedinput[self.keep_prob_in] = 1.
+ feedinput[self.input_keep_prob_in] = 1.
+ if self.parameters['force_coefficient'] is not None:
+ converge_save.append(
+ [self.sess.run(self.loss, feed_dict=feedinput),
+ self.sess.run(
+ self.energy_loss, feed_dict=feedinput),
+ self.sess.run(
+ self.force_loss, feed_dict=feedinput),
+ self.sess.run(
+ self.energy_maxresid, feed_dict=feedinput),
+ self.sess.run(self.force_maxresid,
+ feed_dict=feedinput)])
+ if len(converge_save) > 2:
+ converge_save.pop(0)
+ convergence_vals = np.mean(converge_save, 0)
+ converged = lf.check_convergence(*convergence_vals)
+ if converged:
+ raise ConvergenceOccurred()
+ else:
+ converged = \
+ lf.check_convergence(
+ self.sess.run(self.energy_loss,
+ feed_dict=feedinput),
+ self.sess.run(self.energy_loss,
+ feed_dict=feedinput),
+ 0.,
+ self.sess.run(self.energy_maxresid,
+ feed_dict=feedinput),
+ 0.)
+ if converged:
+ raise ConvergenceOccurred()
+ feedinput[self.keep_prob_in] = keepprob
+ feedinput[self.input_keep_prob_in] = inputkeepprob
+ icount_global += 1
+ return
+
+ def trainmodelBFGS(maxEpochs):
+ curinds = range(len(keylist))
+ feedinput = self.generateFeedInput(
+ curinds,
+ energies,
+ atomArraysAll,
+ dgdx,
+ dgdx_Eindices,
+ dgdx_Xindices,
+ nAtomsDict,
+ atomsIndsReverse,
+ batchsize,
+ 1.,
+ 1.,
+ 1.,
+ natoms,
+ forcesExp=forces,
+ energycoefficient=self.parameters[
+ 'energy_coefficient'],
+ forcecoefficient=self.parameters['force_coefficient'])
+
+ def step_callbackfun_forces(x):
+ evalvarlist = map(lambda y: float(np.array(y(x))), varlist)
+ converged = lf.check_convergence(*evalvarlist)
+ if converged:
+ raise ConvergenceOccurred()
+
+ def step_callbackfun_noforces(x):
+ converged = \
+ lf.check_convergence(float(np.array(varlist[1](x))),
+ float(np.array(varlist[1](x))),
+ 0.,
+ float(np.array(varlist[3](x))),
+ 0.)
+ if converged:
+ raise ConvergenceOccurred()
+
+ if self.parameters['force_coefficient'] is None:
+ step_callbackfun = step_callbackfun_noforces
+ curloss = self.energy_loss
+ else:
+ step_callbackfun = step_callbackfun_forces
+ curloss = self.loss
+
+ if self.parameters['preLoadTrainingData'] and not(self.miniBatch):
+ self.preLoadFeed(feedinput)
+
+ extOpt = \
+ ScipyOptimizerInterface(curloss,
+ method='l-BFGS-b',
+ options={'maxiter': maxEpochs,
+ 'ftol': 1.e-10,
+ 'gtol': 1.e-10,
+ 'factr': 1.e4})
+ varlist = []
+ for var in [self.loss,
+ self.energy_loss,
+ self.force_loss,
+ self.energy_maxresid,
+ self.force_maxresid]:
+ if (self.parameters['preLoadTrainingData'] and
+ (not self.miniBatch)):
+ varlist.append(
+ extOpt._make_eval_func(var, self.sess, {}, []))
+ else:
+ varlist.append(extOpt._make_eval_func(var,
+ self.sess,
+ feedinput,
+ []))
+
+ extOpt.minimize(self.sess,
+ feed_dict=feedinput,
+ step_callback=step_callbackfun)
+
+ return
+
+ try:
+ if self.optimizationMethod == 'l-BFGS-b':
+ with self.graph.as_default():
+ trainmodelBFGS(self.maxTrainingEpochs)
+ elif self.optimizationMethod == 'ADAM':
+ trainmodel(self.initialTrainingRate,
+ self.keep_prob,
+ self.input_keep_prob,
+ self.maxTrainingEpochs)
+ else:
+ log('uknown optimizer!')
+ except ConvergenceOccurred:
+ if self.parameters['preLoadTrainingData'] and not(self.miniBatch):
+ self.saver.save(self.sess, 'tfAmpNN-checkpoint')
+ with open('tfAmpNN-checkpoint') as fhandle:
+ tfvars = fhandle.read()
+ self.constructSessGraphModel(tfvars, None, trainOnly=False)
+ return True
+ return False
+
+ def preLoadFeed(self, feedinput):
+ for element in self.dgdx_dict:
+ if self.dgdx_dict[element] in feedinput:
+ self.sess.run(self.dgdx_dict[element].initializer,
+ feed_dict={
+ self.initializers['dgdx_dict'][element]:
+ feedinput[self.dgdx_dict[element]]})
+ self.sess.run(self.dgdx_Eindices_dict[element].initializer,
+ feed_dict={
+ self.initializers['dgdx_Eindices_dict'][element]:
+ feedinput[self.dgdx_Eindices_dict[element]]})
+ self.sess.run(self.dgdx_Xindices_dict[element].initializer,
+ feed_dict={
+ self.initializers['dgdx_Xindices_dict'][element]:
+ feedinput[self.dgdx_Xindices_dict[element]]})
+ del feedinput[self.dgdx_dict[element]]
+ del feedinput[self.dgdx_Eindices_dict[element]]
+ del feedinput[self.dgdx_Xindices_dict[element]]
+ self.sess.run(self.tensordict[element].initializer,
+ feed_dict={
+ self.initializers['tensordict'][element]:
+ feedinput[self.tensordict[element]]})
+ self.sess.run(self.indsdict[element].initializer,
+ feed_dict={
+ self.initializers['indsdict'][element]:
+ feedinput[self.indsdict[element]]})
+ self.sess.run(self.maskdict[element].initializer,
+ feed_dict={
+ self.initializers['maskdict'][element]:
+ feedinput[self.maskdict[element]]})
+ del feedinput[self.tensordict[element]]
+ del feedinput[self.indsdict[element]]
+ del feedinput[self.maskdict[element]]
+ self.sess.run(self.y_.initializer,
+ feed_dict={
+ self.initializers['y_']:
+ feedinput[self.y_]})
+ self.sess.run(self.input_keep_prob_in.initializer,
+ feed_dict={
+ self.initializers['input_keep_prob_in']:
+ feedinput[self.input_keep_prob_in]})
+ self.sess.run(self.keep_prob_in.initializer,
+ feed_dict={
+ self.initializers['keep_prob_in']:
+ feedinput[self.keep_prob_in]})
+ self.sess.run(self.nAtoms_in.initializer,
+ feed_dict={
+ self.initializers['nAtoms_in']:
+ feedinput[self.nAtoms_in]})
+ self.sess.run(self.batchsizeInput.initializer,
+ feed_dict={
+ self.initializers['batchsizeInput']:
+ feedinput[self.batchsizeInput]})
+ self.sess.run(self.learningrate.initializer,
+ feed_dict={
+ self.initializers['learningrate']:
+ feedinput[self.learningrate]})
+ self.sess.run(self.totalNumAtoms.initializer,
+ feed_dict={
+ self.initializers['totalNumAtoms']:
+ feedinput[self.totalNumAtoms]})
+ self.sess.run(self.nAtoms_forces.initializer,
+ feed_dict={
+ self.initializers['nAtoms_forces']:
+ feedinput[self.nAtoms_forces]})
+ if self.forces_in in feedinput:
+ self.sess.run(self.forces_in.initializer,
+ feed_dict={
+ self.initializers['forces_in']:
+ feedinput[self.forces_in]})
+ self.sess.run(self.energycoefficient.initializer,
+ feed_dict={
+ self.initializers['energycoefficient']:
+ feedinput[self.energycoefficient]})
+ self.sess.run(self.forcecoefficient.initializer,
+ feed_dict={
+ self.initializers['forcecoefficient']:
+ feedinput[self.forcecoefficient]})
+ self.sess.run(self.energyProdScale.initializer,
+ feed_dict={
+ self.initializers['energyProdScale']:
+ feedinput[self.energyProdScale]})
+ # feeedinput={}
+
+ def get_energy_list(self, hashs, fingerprintDB, fingerprintDerDB=None,
+ keep_prob=1., input_keep_prob=1.,
+ forces=False, nsamples=1):
+ """Methods to get the energy and forces for a set of
+ configurations."""
+
+ # Make images a list in case we've been passed a single hash to
+ # calculate.
+ if not(isinstance(hashs, list)):
+ hashs = [hashs]
+
+ # Reformat the image and fingerprint data into something we can pass
+ # into tensorflow.
+
+ (atomArraysAll, nAtomsDict, atomsIndsReverse,
+ natoms, dgdx, dgdx_Eindices, dgdx_Xindices) = \
+ generateTensorFlowArrays(fingerprintDB,
+ self.elements,
+ hashs,
+ fingerprintDerDB)
+
+ energies = np.zeros(len(hashs))
+ forcelist = np.zeros(len(hashs))
+ curinds = range(len(hashs))
+ (atomArraysFinal,
+ dgdx_batch,
+ dgdx_Eindices_batch,
+ dgdx_Xindices_batch,
+ atomInds) = generateBatch(curinds,
+ self.elements,
+ atomArraysAll,
+ nAtomsDict,
+ atomsIndsReverse,
+ dgdx,
+ dgdx_Eindices,
+ dgdx_Xindices)
+
+ feedinput = self.generateFeedInput(curinds,
+ energies,
+ atomArraysAll,
+ dgdx,
+ dgdx_Eindices,
+ dgdx_Xindices,
+ nAtomsDict,
+ atomsIndsReverse,
+ len(hashs),
+ 1.,
+ 1.,
+ 1.,
+ natoms,
+ forcesExp=forcelist,
+ energycoefficient=1.,
+ forcecoefficient=int(forces),
+ training=False)
+
+ if self.weights is not None:
+ self.setWeightsScalings(feedinput, self.weights, self.scalings)
+ if nsamples == 1:
+ energies = \
+ np.array(self.sess.run(self.energy, feed_dict=feedinput)) + \
+ self.parameters['energyMeanScale']
+
+ # Add in the per-atom base energy.
+ natomsArray = np.zeros((len(hashs), len(self.elements)))
+ for i in range(len(hashs)):
+ for j in range(len(self.elements)):
+ natomsArray[i][j] = nAtomsDict[self.elements[j]][i]
+ if forces:
+ force = self.sess.run(self.forces,
+ feed_dict=feedinput)
+ force = reorganizeForces(force, natoms)
+
+ else:
+ force = []
+ else:
+ energysave = []
+ forcesave = []
+ # Add in the per-atom base energy.
+ natomsArray = np.zeros((len(hashs), len(self.elements)))
+ for i in range(len(hashs)):
+ for j in range(len(self.elements)):
+ natomsArray[i][j] = nAtomsDict[self.elements[j]][i]
+ for samplenum in range(nsamples):
+ energies = \
+ np.array(self.sess.run(self.energy,
+ feed_dict=feedinput)) + \
+ self.parameters['energyMeanScale']
+ energysave.append(map(lambda x: x[0], energies))
+ if forces:
+ force = self.sess.run(self.forces,
+ feed_dict=feedinput)
+ forcesave.append(reorganizeForces(force, natoms))
+ energies = np.array(energysave)
+ force = np.array(forcesave)
+
+ return energies, force
+
+ def calculate_energy(self, fingerprint):
+ """Get the energy by feeding in a list to the get_list version (which
+ is more efficient for anything greater than 1 image)."""
+ key = '1'
+ energies, forces = self.get_energy_list([key], {key: fingerprint})
+ return energies[0]
+
+ def getVariance(self, fingerprint, nSamples=10, l=1.):
+ key = '1'
+ # energies=[]
+ # for i in range(nSamples):
+ # energies.append(self.get_energy_list([key], {key:
+ # fingerprint},keep_prob=self.keep_prob)[0])
+ energies, force = \
+ self.get_energy_list([key],
+ {key: fingerprint},
+ keep_prob=self.keep_prob,
+ nsamples=nSamples)
+ if (('regularization_strength' in self.parameters) and
+ (self.parameters['regularization_strength'] is not None)):
+ tau = l**2. * self.keep_prob / \
+ (2 * self.parameters['numTrainingImages'] *
+ self.parameters['regularization_strength'])
+ var = np.var(energies) + tau**-1.
+ # forcevar=np.var(forces,)
+ else:
+ tau = 1
+ var = np.var(energies)
+ return var
+
+ def calculate_forces(self, fingerprint, derfingerprint):
+ # calculate_forces function still needs to be implemented. Can't do
+ # this without the fingerprint derivates working properly though
+ key = '1'
+ energies, forces = \
+ self.get_energy_list([key],
+ {key: fingerprint},
+ fingerprintDerDB={key: derfingerprint},
+ forces=True)
+ return forces[0][0:len(fingerprint)]
+
+ def tostring(self):
+ """Dummy tostring to make things work."""
+ params = {}
+
+ params['hiddenlayers'] = self.hiddenlayers
+ params['keep_prob'] = self.keep_prob
+ params['input_keep_prob'] = self.input_keep_prob
+ params['elementFingerprintLengths'] = self.elementFingerprintLengths
+ params['batchsize'] = self.batchsize
+ params['maxTrainingEpochs'] = self.maxTrainingEpochs
+ params['importname'] = self.importname
+ params['initialTrainingRate'] = self.initialTrainingRate
+ params['activation'] = self.activationName
+ params['saveVariableName'] = self.saveVariableName
+ params['parameters'] = self.parameters
+ params['miniBatch'] = self.miniBatch
+ params['optimizationMethod'] = self.optimizationMethod
+
+ # Create a string format of the tensorflow variables.
+ self.saver.save(self.sess, 'tfAmpNN-checkpoint')
+ with open('tfAmpNN-checkpoint') as fhandle:
+ params['tfVars'] = fhandle.read()
+
+ return str(params)
+
+
+def model(x, segmentinds, keep_prob, input_keep_prob, batchsize,
+ neuronList, activationType, fplength, mask, name, dgdx,
+ dgdx_Xindices, dgdx_Eindices, element, unit_type, totalNumAtoms):
+ """Generates a multilayer neural network with variable number
+ of neurons, so that we have a template for each atom's NN."""
+ namefun = lambda x: '%s_%s_' % (name, element) + x
+ nNeurons = neuronList[0]
+ # Pass the input tensors through the first soft-plus layer
+ W_fc = weight_variable(
+ [fplength, nNeurons], name=namefun('Wfc0'), unit_type=unit_type)
+ b_fc = bias_variable([nNeurons], name=namefun('bfc0'), unit_type=unit_type)
+ input_dropout = tf.nn.dropout(x, input_keep_prob)
+ # h_fc = activationType(tf.matmul(x, W_fc) + b_fc)
+ h_fc = tf.nn.dropout(
+ activationType(tf.matmul(input_dropout, W_fc) + b_fc), keep_prob)
+ # l2_regularization=\
+ # tf.reduce_sum(tf.square(W_fc))+tf.reduce_sum(tf.square(b_fc))
+ l2_regularization = tf.reduce_sum(tf.square(W_fc))
+ if len(neuronList) > 1:
+ for i in range(1, len(neuronList)):
+ nNeurons = neuronList[i]
+ nNeuronsOld = neuronList[i - 1]
+ W_fc = weight_variable([nNeuronsOld, nNeurons],
+ name=namefun('Wfc%d' % i),
+ unit_type=unit_type)
+ b_fc = bias_variable([nNeurons],
+ name=namefun('bfc%d' % i),
+ unit_type=unit_type)
+ h_fc = tf.nn.dropout(activationType(
+ tf.matmul(h_fc, W_fc) + b_fc), keep_prob)
+ l2_regularization += tf.reduce_sum(
+ tf.square(W_fc)) + tf.reduce_sum(tf.square(b_fc))
+
+ W_fc_out = weight_variable(
+ [neuronList[-1], 1], name=namefun('Wfcout'), unit_type=unit_type)
+ b_fc_out = bias_variable([1], name=namefun('bfcout'), unit_type=unit_type)
+ y_out = tf.matmul(h_fc, W_fc_out) + b_fc_out
+ l2_regularization += tf.reduce_sum(
+ tf.square(W_fc_out)) + tf.reduce_sum(tf.square(b_fc_out))
+ # l2_regularization+=tf.reduce_sum(tf.square(W_fc_out)))
+
+ # Sum the predicted energy for each molecule
+ reducedSum = tf.unsorted_segment_sum(y_out, segmentinds, batchsize)
+
+ dEjdgj = tf.gradients(y_out, x)[0]
+
+ # expand for 3 components (x,y,z)
+ # dEjdgj1 = tf.expand_dims(dEjdgj, 2)
+ # dEjdgjtile = tf.tile(dEjdgj1, [1,1,3])
+
+ # Gather rows necessary based on the given partial derivatives (dg/dx)
+ dEdg_arranged = tf.gather(dEjdgj, dgdx_Eindices)
+
+ dEdg_arranged_expand = tf.expand_dims(dEdg_arranged, 2)
+ dEdg_arranged_tile = tf.tile(dEdg_arranged_expand, [1, 1, 3])
+
+ # multiply through with the dg/dx tensor, and sum along the components of g
+ # to get a tensor of dE/dx (one row per atom considered, second dim =3)
+ dEdx = tf.reduce_sum(tf.mul(dEdg_arranged_tile, dgdx), 1)
+
+ # this should be a tensor of size (total atoms in training set)x3,
+ # representing the contribution of each atom to the total energy via
+ # interactions with elements of the current atom type
+ dEdx_arranged = tf.unsorted_segment_sum(dEdx, dgdx_Xindices, totalNumAtoms)
+
+ return tf.mul(reducedSum, mask), dEdx_arranged, l2_regularization
+# dEg
+# dEjdgj1 = tf.expand_dims(dEjdgj, 1)
+# dEjdgj2 = tf.expand_dims(dEjdgj1, 1)
+# dEjdgjtile = tf.tile(dEjdgj2, tilederiv)
+# dEdxik = tf.mul(dxdxik, dEjdgjtile)
+# dEdxikReduce = tf.reduce_sum(dEdxik, 3)
+# dEdxik_reduced = tf.unsorted_segment_sum(
+# dEdxikReduce, segmentinds, batchsize)
+# return tf.mul(reducedSum, mask), dEdxik_reduced,l2_regularization
+
+
+def weight_variable(shape, name, unit_type, stddev=0.1):
+ """Helper functions taken from the MNIST tutorial to generate weight and
+ bias variables with random initial weights."""
+ initial = tf.truncated_normal(shape, stddev=stddev, dtype=unit_type)
+ return tf.Variable(initial, name=name)
+
+
+def bias_variable(shape, name, unit_type, a=0.1):
+ """Helper functions taken from the MNIST tutorial to generate weight and
+ bias variables with random initial weights."""
+ initial = tf.truncated_normal(stddev=a, shape=shape, dtype=unit_type)
+ return tf.Variable(initial, name=name)
+
+
+def generateBatch(curinds, elements, atomArraysAll, nAtomsDict,
+ atomsIndsReverse, dgdx, dgdx_Eindices, dgdx_Xindices,):
+ """This method generates batches from a large dataset using a set of
+ selected indices curinds."""
+ # inputs:
+
+ atomArraysFinal = {}
+ for element in elements:
+ validKeys = np.in1d(atomsIndsReverse[element], curinds)
+ if len(validKeys) > 0:
+ atomArraysFinal[element] = atomArraysAll[element][validKeys]
+ else:
+ atomArraysFinal[element] = []
+
+ dgdx_out = {}
+ dgdx_Eindices_out = {}
+ dgdx_Xindices_out = {}
+ for element in elements:
+ if len(dgdx[element]) > 0:
+ dgdx_out[element] = []
+ dgdx_Eindices_out[element] = []
+ dgdx_Xindices_out[element] = []
+ cursumE = 0
+ cursumX = 0
+ for curind in curinds:
+ natomsElement = nAtomsDict[element][curind]
+ natomsTotal = np.sum(
+ map(lambda x: nAtomsDict[x][curind], elements))
+ if len(dgdx_Eindices[element][curind]) > 0:
+ dgdx_out[element].append(dgdx[element][curind])
+ dgdx_Eindices_out[element].append(
+ dgdx_Eindices[element][curind] + cursumE)
+ dgdx_Xindices_out[element].append(
+ dgdx_Xindices[element][curind] + cursumX)
+ cursumE += natomsElement
+ cursumX += natomsTotal
+ if len(dgdx_out[element]) > 0:
+ dgdx_out[element] = np.concatenate(dgdx_out[element], axis=0)
+ dgdx_Eindices_out[element] = np.concatenate(
+ dgdx_Eindices_out[element], axis=0)
+ dgdx_Xindices_out[element] = np.concatenate(
+ dgdx_Xindices_out[element], axis=0)
+ else:
+ dgdx_out[element] = np.array([[]])
+ dgdx_Eindices_out[element] = np.array([])
+ dgdx_Xindices_out[element] = np.array([])
+ else:
+ dgdx_out[element] = np.array([[[]]])
+ dgdx_Eindices_out[element] = np.array([])
+ dgdx_Xindices_out[element] = np.array([])
+ atomInds = {}
+ for element in elements:
+ validKeys = np.in1d(atomsIndsReverse[element], curinds)
+ if len(validKeys) > 0:
+ atomIndsTemp = np.sum(atomsIndsReverse[element][validKeys], 1)
+ atomInds[element] = atomIndsTemp * 0.
+ for i in range(len(curinds)):
+ atomInds[element][atomIndsTemp == curinds[i]] = i
+ else:
+ atomInds[element] = []
+
+ return (atomArraysFinal, dgdx_out,
+ dgdx_Eindices_out, dgdx_Xindices_out, atomInds)
+
+
+def generateTensorFlowArrays(fingerprintDB, elements, keylist,
+ fingerprintDerDB=None):
+ """
+ This function generates the inputs to the tensorflow graph for the selected
+ images.
+ The essential problem is that each neural network is associated with a
+ specific element type. Thus, atoms in each ASE image need to be sent to
+ different networks.
+
+ Inputs:
+
+ fingerprintDB: a database of fingerprints, as taken from the descriptor
+
+ elements: a list of element types (e.g. 'C','O', etc)
+
+ keylist: a list of hashs into the fingerprintDB that we want to create
+ inputs for
+
+ fingerprintDerDB: a database of fingerprint derivatives, as taken from the
+ descriptor
+
+ maxAtomsForces: the maximum length of the atoms
+
+ Outputs:
+
+ atomArraysAll: a dictionary of fingerprint inputs to each element's neural
+ network
+
+ nAtomsDict: a dictionary for each element with lists of the number of
+ atoms of each type in each image
+
+ atomsIndsReverse: a dictionary that contains the index of each atom into
+ the original keylist
+
+ nAtoms: the number of atoms in each image
+
+ atomArraysAllDerivs: dictionary of fingerprint derivates for each
+ element's neural network
+ """
+
+ nAtomsDict = {}
+ for element in elements:
+ nAtomsDict[element] = np.zeros(len(keylist))
+
+ for j in range(len(keylist)):
+ fp = fingerprintDB[keylist[j]]
+ atomSymbols, fpdata = zip(*fp)
+ for i in range(len(fp)):
+ nAtomsDict[atomSymbols[i]][j] += 1
+
+ atomsPositions = {}
+ for element in elements:
+ atomsPositions[element] = np.cumsum(
+ nAtomsDict[element]) - nAtomsDict[element]
+
+ atomsIndsReverse = {}
+ for element in elements:
+ atomsIndsReverse[element] = []
+ for i in range(len(keylist)):
+ if nAtomsDict[element][i] > 0:
+ atomsIndsReverse[element].append(
+ np.ones((nAtomsDict[element][i].astype(np.int64), 1)) * i)
+ if len(atomsIndsReverse[element]) > 0:
+ atomsIndsReverse[element] = np.concatenate(
+ atomsIndsReverse[element])
+
+ atomArraysAll = {}
+ for element in elements:
+ atomArraysAll[element] = []
+
+ natoms = np.zeros((len(keylist), 1))
+ for j in range(len(keylist)):
+ fp = fingerprintDB[keylist[j]]
+ atomSymbols, fpdata = zip(*fp)
+ atomdata = zip(atomSymbols, range(len(atomSymbols)))
+ for element in elements:
+ atomArraysTemp = []
+ curatoms = [atom for atom in atomdata if atom[0] == element]
+ for i in range(len(curatoms)):
+ atomArraysTemp.append(fp[curatoms[i][1]][1])
+ if len(atomArraysTemp) > 0:
+ atomArraysAll[element].append(atomArraysTemp)
+ natoms[j] = len(atomSymbols)
+
+ natomsposition = np.cumsum(natoms) - natoms[0]
+
+ for element in elements:
+ if len(atomArraysAll[element]) > 0:
+ atomArraysAll[element] = np.concatenate(atomArraysAll[element])
+ else:
+ atomArraysAll[element] = []
+
+ # Set up the array for atom-based fingerprint derivatives.
+
+ dgdx = {}
+ dgdx_Eindices = {}
+ dgdx_Xindices = {}
+ for element in elements:
+ dgdx[element] = [] # Nxlen(fp)x3 array
+ dgdx_Eindices[element] = [] # Nx1 array of which dE/dg to pull
+ dgdx_Xindices[element] = []
+ # Nx1 array representing which atom this force will represent
+ if fingerprintDerDB is not None:
+ for j in range(len(keylist)):
+ fp = fingerprintDB[keylist[j]]
+ fpDer = fingerprintDerDB[keylist[j]]
+ atomSymbols, fpdata = zip(*fp)
+ atomdata = zip(atomSymbols, range(len(atomSymbols)))
+
+ for element in elements:
+ curatoms = [atom for atom in atomdata if atom[0] == element]
+ dgdx_temp = []
+ dgdx_Eindices_temp = []
+ dgdx_Xindices_temp = []
+ if len(curatoms) > 0:
+ for i in range(len(curatoms)):
+ for k in range(len(atomdata)):
+ # check if fp derivative is present
+ dictkeys = [(k, atomdata[k][0], curatoms[
+ i][1], curatoms[i][0], 0),
+ (k, atomdata[k][0], curatoms[
+ i][1], curatoms[i][0], 1),
+ (k, atomdata[k][0], curatoms[
+ i][1], curatoms[i][0], 2)]
+ if ((dictkeys[0] in fpDer) or
+ (dictkeys[1] in fpDer) or
+ (dictkeys[2] in fpDer)):
+ fptemp = []
+ for ix in range(3):
+ dictkey = (k, atomdata[k][0], curatoms[
+ i][1], curatoms[i][0], ix)
+ fptemp.append(fpDer[dictkey])
+ dgdx_temp.append(np.array(fptemp).transpose())
+ dgdx_Eindices_temp.append(i)
+ dgdx_Xindices_temp.append(k)
+ if len(dgdx_Eindices_temp) > 0:
+ dgdx[element].append(np.array(dgdx_temp))
+ dgdx_Eindices[element].append(np.array(dgdx_Eindices_temp))
+ dgdx_Xindices[element].append(np.array(dgdx_Xindices_temp))
+ else:
+ dgdx[element].append([])
+ dgdx_Eindices[element].append([])
+ dgdx_Xindices[element].append([])
+ return (atomArraysAll, nAtomsDict, atomsIndsReverse,
+ natoms, dgdx, dgdx_Eindices, dgdx_Xindices)
+
+
+def reorganizeForces(forces, natoms):
+ curoffset = 0
+ forcelist = []
+ for N in natoms:
+ forcelist.append(forces[curoffset:curoffset + N[0].astype(np.int64)])
+ curoffset += N[0]
+ return forcelist
diff --git a/amp/regression/__init__.py b/amp/regression/__init__.py
new file mode 100644
index 0000000..b1f0933
--- /dev/null
+++ b/amp/regression/__init__.py
@@ -0,0 +1,100 @@
+from ..utilities import ConvergenceOccurred
+
+
+class Regressor:
+
+ """Class to manage the regression of a generic model. That is, for a
+ given parameter set, calculates the cost function (the difference in
+ predicted energies and actual energies across training images), then
+ decides how to adjust the parameters to reduce this cost function.
+ Global optimization conditioners (e.g., simulated annealing, etc.) can
+ be built into this class.
+
+ Parameters
+ ----------
+ optimizer : str
+ The optimizer to use. Several defaults are available including
+ 'L-BFGS-B', 'BFGS', 'TNC', or 'NCG'. Alternatively, any function can
+ be supplied which behaves like scipy.optimize.fmin_bfgs.
+ optimizer_kwargs : dict
+ Optional keywords for the corresponding optimizer.
+ lossprime : boolean
+ Decides whether or not the regressor needs to be fed in by gradient of
+ the loss function as well as the loss function itself.
+ """
+
+ def __init__(self, optimizer='BFGS', optimizer_kwargs=None,
+ lossprime=True):
+ """optimizer can be specified; it should behave like a
+ scipy.optimize optimizer. That is, it should take as its first two
+ arguments the function to be optimized and the initial guess of the
+ optimal paramters. Additional keyword arguments can be fed through
+ the optimizer_kwargs dictionary."""
+
+ user_kwargs = optimizer_kwargs
+ optimizer_kwargs = {}
+ if optimizer == 'BFGS':
+ from scipy.optimize import fmin_bfgs as optimizer
+ optimizer_kwargs = {'gtol': 1e-15, }
+ elif optimizer == 'L-BFGS-B':
+ from scipy.optimize import fmin_l_bfgs_b as optimizer
+ optimizer_kwargs = {'factr': 1e+02,
+ 'pgtol': 1e-08,
+ 'maxfun': 1000000,
+ 'maxiter': 1000000}
+ import scipy
+ from distutils.version import StrictVersion
+ if StrictVersion(scipy.__version__) >= StrictVersion('0.17.0'):
+ optimizer_kwargs['maxls'] = 2000
+ elif optimizer == 'TNC':
+ from scipy.optimize import fmin_tnc as optimizer
+ optimizer_kwargs = {'ftol': 0.,
+ 'xtol': 0.,
+ 'pgtol': 1e-08,
+ 'maxfun': 1000000, }
+ elif optimizer == 'NCG':
+ from scipy.optimize import fmin_ncg as optimizer
+ optimizer_kwargs = {'avextol': 1e-15, }
+
+ if user_kwargs:
+ optimizer_kwargs.update(user_kwargs)
+ self.optimizer = optimizer
+ self.optimizer_kwargs = optimizer_kwargs
+ self.lossprime = lossprime
+
+ def regress(self, model, log):
+ """Performs the regression. Calls model.get_loss,
+ which should return the current value of the loss function
+ until convergence has been reached, at which point it should
+ raise a amp.utilities.ConvergenceException.
+
+ Parameters
+ ----------
+ model : object
+ Class representing the regression model.
+ log : str
+ Name of script to log progress.
+ """
+ log('Starting parameter optimization.', tic='opt')
+ log(' Optimizer: %s' % self.optimizer)
+ log(' Optimizer kwargs: %s' % self.optimizer_kwargs)
+ x0 = model.vector.copy()
+ try:
+ if self.lossprime:
+ self.optimizer(model.get_loss, x0, model.get_lossprime,
+ **self.optimizer_kwargs)
+ else:
+ self.optimizer(model.get_loss, x0, **self.optimizer_kwargs)
+
+ except ConvergenceOccurred:
+ log('...optimization successful.', toc='opt')
+ return True
+ else:
+ log('...optimization unsuccessful.', toc='opt')
+ if self.lossprime:
+ max_lossprime = \
+ max(abs(max(model.lossfunction.dloss_dparameters)),
+ abs(min(model.lossfunction.dloss_dparameters)))
+ log('...maximum absolute value of loss prime: %.3e'
+ % max_lossprime)
+ return False
diff --git a/amp/stats/__init__.py b/amp/stats/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/amp/stats/bootstrap.py b/amp/stats/bootstrap.py
new file mode 100644
index 0000000..87ca3c0
--- /dev/null
+++ b/amp/stats/bootstrap.py
@@ -0,0 +1,400 @@
+import os
+import sys
+import shutil
+import numpy as np
+from string import Template
+import time
+import json
+from StringIO import StringIO
+from scipy.stats.mstats import mquantiles
+import tarfile
+import tempfile
+
+import ase.io
+
+from ..utilities import hash_images, Logger
+from .. import Amp
+
+
+calc_text = """
+from amp import Amp
+from amp.descriptor.gaussian import Gaussian
+from amp.model.neuralnetwork import NeuralNetwork
+
+
+calc = Amp(descriptor=Gaussian(),
+ model=NeuralNetwork(),
+ dblabel='../amp-db')
+"""
+
+train_line = "calc.train(images=hashed_images)"
+
+script = """#!/usr/bin/env python
+${headerlines}
+
+from amp.utilities import TrainingConvergenceError, hash_images
+from ase.parallel import paropen
+from bunquant.bootstrap import hash_with_duplicates
+import os
+
+${calc_text}
+
+ensemble_index = int(os.path.split(os.getcwd())[-1])
+trainfile = '../training-images/%i.traj' % ensemble_index
+hashed_images = hash_with_duplicates(trainfile)
+
+converged = True
+try:
+ ${train_line}
+except TrainingConvergenceError:
+ converged = False
+
+f = paropen('converged', 'w')
+f.write(str(converged))
+f.close()
+"""
+
+
+class BootStrap:
+ """A bootstrap ensemble calculator which serves as a wrapper around and
+ Amp calculator. Initiate with an amp.utilities.Logger instance as log.
+
+ If an existing trained bootstrap calculator is available, it can be
+ loaded by providing its filename to the load keyword.
+
+ Note that the 'train' method is meant to be a job-submission and
+ -management script;
+ e.g., it will typically be run at the command line to both submit jobs
+ and monitor their convergence.
+ """
+
+ def __init__(self, load=None, log=None):
+ if log is None:
+ log = Logger(sys.stdout)
+ self.log = log
+ if load is None:
+ return
+
+ with open(load) as f:
+ calctexts = json.load(f)
+ self.ensemble = []
+ for calctext in calctexts:
+ f = StringIO(calctext)
+ calc = Amp.load(file=f)
+ calc.log = Logger(None)
+ self.ensemble.append(calc)
+ log('Loaded ensemble of %i calculators.' % len(self.ensemble))
+
+ def train(self, images, n=50, calc_text=calc_text, headerlines='',
+ start_command='python run.py', sleep=0.1,
+ train_line=train_line, label='bootstrap'):
+ """Trains a bootstrap ensemble of calculators.
+ This is set up to enable the submision of each as a job through
+ the local queuing system, but can also run in serial.
+ On first call to this method, jobs are created/submitted.
+ On subsequent calls, jobs are analyzed for convergence.
+ If all are converged, an ensemble is created and the training
+ directory is archived.
+
+ Creates a lot of individual runs in directories
+
+ n: int
+ size of ensemble (number of calculators to train)
+ calc_text: text
+ text that is used to initiate the Amp calculator.
+ see the example in this module in calc_text; must produce
+ a 'calc' object
+ headerlines: text
+ lines in the top of the python script that will be submitted
+ this would typically contain comment lines for the batching
+ system, such as '#SBATCH -n=3\n #SBATCH -cores=8\n...'
+ start_command: text
+ command to start the job in the current queuing system,
+ such as 'sbatch run.py' ('run.py' is the scriptname here)
+ for serial operation use 'python run.py'
+ sleep : float
+ time (s) to sleep between job submissions
+ train_line: text
+ line to use to train each amp instance; usually the default is
+ fine but user may want to use this to insert additional keywords
+ such as train_forces=False
+ label: string
+ label to give final trained calculator
+ """
+
+ log = self.log
+ trainingpath = '-'.join((label, 'training'))
+ if os.path.exists(trainingpath):
+ log('Path exists. Checking for which jobs are finished.')
+ n_unfinished = 0
+ n_converged = 0
+ n_unconverged = 0
+ pwd = os.getcwd()
+ os.chdir(trainingpath)
+ fulltrainingpath = os.getcwd()
+ for index in range(n):
+ os.chdir('%i' % index)
+ if not os.path.exists('converged'):
+ log('%i: Still running? No converged file.' % index)
+ os.chdir(fulltrainingpath)
+ n_unfinished += 1
+ continue
+ with open('converged') as f:
+ converged = f.read()
+
+ if converged == 'True':
+ log('%i: Converged.' % index)
+ n_converged += 1
+ else:
+ log('%i: Not converged. Cleaning up directory to '
+ ' restart job.' % index)
+ n_unconverged += 1
+ for _ in os.listdir(os.getcwd()):
+ if _ != 'run.py':
+ if os.path.isdir(_):
+ shutil.rmtree(_)
+ else:
+ os.remove(_)
+ os.system(start_command)
+ time.sleep(sleep)
+ log('%i: Restarted.')
+
+ os.chdir(fulltrainingpath)
+ log('')
+ log('Stats:')
+ log('%10i converged' % n_converged)
+ log('%10i did not converge, restarted' % n_unconverged)
+ log('%10i apparently still running' % n_unfinished)
+ log('=' * 10)
+ log('%10i total' % n)
+ log('\n')
+
+ if n_converged < n:
+ log('Not all runs converged; not creating bundled amp '
+ 'calculator.')
+ return
+
+ log('Creating bundled amp calculator.')
+ ensemble = []
+ for index in range(n):
+ os.chdir('%i' % index)
+ with open('amp.amp') as f:
+ text = f.read()
+ ensemble.append(text)
+ os.chdir(fulltrainingpath)
+ os.chdir(pwd)
+ with open('%s.ensemble' % label, 'w') as f:
+ json.dump(ensemble, f)
+ log('Saved in json format as "%s.ensemble".' % label)
+ log('Converting training directory into tar archive...')
+ archive_directory(trainingpath)
+ log('...converted.')
+ return
+
+ log('Training set: ' + str(images))
+ images = hash_images(images)
+ log('%i images in training set after hashing.' % len(images))
+ image_keys = images.keys()
+
+ originalpath = os.getcwd()
+ trajpath = os.path.join(trainingpath, 'training-images')
+ os.mkdir(trainingpath)
+ os.mkdir(trajpath)
+
+ log('Creating bootstrapped training images in %s.' % trajpath)
+ for index in range(n):
+ log(' Choosing images for %i.' % index)
+ chosen = bootstrap(image_keys)
+ log(' Writing trajectory for %i.' % index)
+ traj = ase.io.Trajectory(
+ os.path.join(trajpath, '%i.traj' % index), 'w')
+ for key in chosen:
+ traj.write(images[key])
+
+ log('Creating and submitting jobs.')
+ os.chdir(trainingpath)
+ template = Template(script)
+ pwd = os.getcwd()
+
+ for index in range(n):
+ os.mkdir('%i' % index)
+ os.chdir('%i' % index)
+ with open('run.py', 'w') as f:
+ f.write(template.substitute({'headerlines': headerlines,
+ 'calc_text': calc_text,
+ 'train_line': train_line}))
+ os.system(start_command)
+ time.sleep(sleep)
+ os.chdir(pwd)
+ os.chdir(originalpath)
+
+ def get_potential_energy(self, atoms, output=(.5,)):
+ """Returns the potential energy from the ensemble for the atoms
+ object.
+ By default only returns the median prediction (50th percentile)
+ of the ensemble, such that it works like a normal ASE calculator.
+ To get uncertainty information, use the output keyword with the
+ following codes:
+ <q>: (where <q> is a float) return the q quantile of the
+ ensemble (where the quantile is a decimal, as in 0.5 for 50th
+ percentile)
+ e: return the whole ensemble prediction as a list
+ Join the arguments with commas. For example, to return the median
+ prediction plus a centered spread covering 90% of the ensemble
+ prediction, use output=[.5, .05, .95].
+ If the ensemble is requested, it must be the last argument, e.g.,
+ output=[.5, .025, .97.5, 'e'].
+ Note a list is typically returned, but if only one attribute is
+ requested it returns it as a float, so that it's ASE-like.
+ """
+ energies = [calc.get_potential_energy(atoms) for calc in self.ensemble]
+ if output[-1] == 'e':
+ quantiles = output[:-1]
+ return_ensemble = True
+ else:
+ quantiles = output
+ return_ensemble = False
+ for quantile in quantiles:
+ if (quantile > 1.0) or (quantile < 0.0):
+ raise RuntimeError('Quantiles must be between 0 and 1.')
+ result = mquantiles(energies, prob=quantiles)
+ result = list(result)
+ if return_ensemble:
+ result.append(energies)
+ if len(result) == 1:
+ result == result[0]
+ return result
+
+ def get_forces(self, atoms, output=(.5,)):
+ """Returns the atomic forces from the ensemble for the atoms
+ object.
+ By default only returns the median prediction (50th percentile)
+ of the ensemble, such that it works like a normal ASE calculator.
+ To get uncertainty information, use the output keyword with the
+ following codes:
+ <q>: (where <q> is a float) return the q quantile of the
+ ensemble (where the quantile is a decimal, as in 0.5 for 50th
+ percentile)
+ e: return the whole ensemble prediction as a list
+ Join the arguments with commas. For example, to return the median
+ prediction plus a centered spread covering 90% of the ensemble
+ prediction, use output=[.5, .05, .95].
+ If the ensemble is requested, it must be the last argument, e.g.,
+ output=[.5, .025, .97.5, 'e'].
+ Note a list is typically returned, but if only one attribute is
+ requested it returns it as a float, so that it's ASE-like.
+ """
+ forces = [calc.get_forces(atoms) for calc in self.ensemble]
+ forces = np.array(forces)
+ if output[-1] == 'e':
+ quantiles = output[:-1]
+ return_ensemble = True
+ else:
+ quantiles = output
+ return_ensemble = False
+ for quantile in quantiles:
+ if (quantile > 1.0) or (quantile < 0.0):
+ raise RuntimeError('Quantiles must be between 0 and 1.')
+ # FIXME/ap: Had to switch to np.percentile from scipy mquantiles.
+ # Because mquantiles doesn't support higher dimensions.
+ # Should probably switch to percentiles throughout the code as
+ # it's easier to read.
+ percentiles = np.array(quantiles) * 100.
+ result = np.percentile(forces, percentiles, axis=0)
+ result = list(result)
+ if return_ensemble:
+ result.append(forces)
+ if len(result) == 1:
+ result == result[0]
+ return result
+
+ def get_atomic_energies(self, atoms, output=(.5,)):
+ """ Returns the energy per atom from ensemble.
+ The output parameter works as get_potential_energy."""
+ if output[-1] == 'e':
+ quantiles = output[:-1]
+ return_ensemble = True
+ else:
+ quantiles = output
+ return_ensemble = False
+ for quantile in quantiles:
+ if (quantile > 1.0) or (quantile < 0.0):
+ raise RuntimeError('Percentiles must be between 0 and 1.')
+ self.get_potential_energy(atoms) # Assure calculation is fresh.
+ atomic_energies = np.array([calc.model.atomic_energies for calc in
+ self.ensemble])
+ result = mquantiles(atomic_energies, prob=quantiles, axis=0)
+ result = list(result)
+ if return_ensemble:
+ result.append(atomic_energies)
+ if len(result) == 1:
+ result == result[0]
+ return result
+
+
+def bootstrap(vector, size=None, return_missing=False):
+ """Returns a randomly chosen, with replacement, version of the data
+ set. If size is None returns a vector of same length.
+ To pull from sample from multiple vectors, zip and unzip them like:
+
+ >>> xsbs, ysbs = zip(*bootstrap(zip(xs, ys)))
+
+ If return_missing == True, also finds and returns the missing elements
+ not sampled from the vector as a second output.
+ """
+
+ size = len(vector) if size is None else size
+ ids = np.random.choice(len(vector), size=size, replace=True)
+ chosen = [vector[_] for _ in ids]
+ if return_missing is False:
+ return chosen
+ unchosen = set(range(len(vector))).difference(set(ids))
+ unchosen = [vector[_] for _ in unchosen]
+ return chosen, unchosen
+
+
+def hash_with_duplicates(images):
+ """Creates new hash id's for duplicate images; new dictionary contains
+ a redundant copy of each atoms object, so that the lossfunctions can be
+ used as-is. Note will typically waste ~30% of the computational cost;
+ it would be more efficient to update the calls inside the loss
+ functions."""
+ if not hasattr(images, 'keys'):
+ images = hash_images(images)
+ duplicates = images.metadata['duplicates']
+ dict_images = dict(images)
+ for oldhash, repititions in duplicates.iteritems():
+ for repitition in range(repititions - 1):
+ newhash = '-'.join([oldhash, '%i' % (repitition + 1)])
+ assert newhash not in dict_images
+ dict_images[newhash] = images[oldhash]
+ return dict_images
+
+
+def archive_directory(source_dir):
+ """Turns <source_dir> into a .tar.gz file and removes the original
+ directory."""
+ outputname = source_dir + '.tar.gz'
+ if os.path.exists(outputname):
+ raise RuntimeError('%s exists.' % outputname)
+ with tarfile.open(outputname, 'w:gz') as tar:
+ tar.add(source_dir)
+ shutil.rmtree(source_dir)
+
+
+class TrainingArchive:
+ """Helper to get training trajectories and Amp calc instances from the
+ training tar ball. Initialize with archive name. The get commands use
+ the path the file would have had if the archive were extracted."""
+
+ def __init__(self, name):
+ self.tf = tarfile.open(name)
+
+ def get_trajectory(self, path):
+ # Doesn't work with extractfile because of numpy bug.
+ tempdir = tempfile.mkdtemp()
+ self.tf.extract(member=path, path=tempdir)
+ return ase.io.Trajectory(os.path.join(tempdir, path))
+
+ def get_amp_calc(self, path):
+ return Amp.load(self.tf.extractfile(path))
diff --git a/amp/utilities.py b/amp/utilities.py
new file mode 100644
index 0000000..1742250
--- /dev/null
+++ b/amp/utilities.py
@@ -0,0 +1,1195 @@
+#!/usr/bin/env python
+
+import numpy as np
+import hashlib
+import time
+import os
+import sys
+import copy
+import math
+import random
+import signal
+import tarfile
+import traceback
+from datetime import datetime
+from getpass import getuser
+from ase import io as aseio
+from ase.db import connect
+from ase.calculators.calculator import PropertyNotImplementedError
+try:
+ import cPickle as pickle # Python2
+except ImportError:
+ import pickle # Python3
+
+
+# Parallel processing ########################################################
+
+def assign_cores(cores, log=None):
+ """Tries to guess cores from environment.
+
+ If fed a log object, will write its progress.
+ """
+ log = Logger(None) if log is None else log
+
+ def fail(q, traceback_text=None):
+ msg = ('Auto core detection is either not set up or not working for'
+ ' your version of %s. You are invited to submit a patch to '
+ 'return a dictionary of the form {nodename: ncores} for this'
+ ' batching system. The environment contents were dumped to '
+ 'the log file, as well as any traceback that caused the '
+ 'error.')
+ log(msg % q)
+ log('Environment dump:')
+ for key, value in os.environ.items():
+ log('%s: %s' % (key, value))
+ if traceback_text:
+ log('\n' + '='*70 + '\nTraceback of last error encountered:')
+ log(traceback_text)
+ raise NotImplementedError(msg % q)
+
+ def success(q, cores, log):
+ log('Parallel configuration determined from environment for %s:' % q)
+ for key, value in cores.items():
+ log(' %s: %i' % (key, value))
+
+ if cores is not None:
+ q = '<user-specified>'
+ if cores == 1:
+ log('Serial operation on one core specified.')
+ return cores
+ else:
+ try:
+ cores = int(cores)
+ except TypeError:
+ cores = cores
+ success(q, cores, log)
+ return cores
+ else:
+ cores = {'localhost': cores}
+ success(q, cores, log)
+ return cores
+
+ if 'SLURM_NODELIST' in os.environ.keys():
+ q = 'SLURM'
+ try:
+ nnodes = int(os.environ['SLURM_NNODES'])
+ taskspernode = int(os.environ['SLURM_NTASKS_PER_NODE'])
+ if nnodes == 1:
+ cores = {'localhost': taskspernode}
+ else:
+ nodes = os.environ['SLURM_NODELIST']
+ if '[' in nodes:
+ # Formatted funny like 'node[572,578]'.
+ prename, numbers = nodes.split('[')
+ numbers = numbers[:-1].split(',')
+ nodes = [prename + _ for _ in numbers]
+ else:
+ nodes = nodes.split(',')
+ cores = {node: taskspernode for node in nodes}
+ except:
+ # Get the traceback to log it.
+ fail(q, traceback_text=traceback.format_exc())
+ elif 'PBS_NODEFILE' in os.environ.keys():
+ fail(q='PBS')
+ elif 'LOADL_PROCESSOR_LIST' in os.environ.keys():
+ fail(q='LOADL')
+ elif 'PE_HOSTFILE' in os.environ.keys():
+ q = 'SGE'
+ try:
+ hostfile = os.getenv('PE_HOSTFILE')
+ cores = {}
+ with open(hostfile) as f:
+ for i, istr in enumerate(f):
+ hostname, nc = istr.split()[0:2]
+ nc = int(nc)
+ cores[hostname] = nc
+ except:
+ # Get the traceback to log it.
+ fail(q, traceback_text=traceback.format_exc())
+ else:
+ import multiprocessing
+ ncores = multiprocessing.cpu_count()
+ cores = {'localhost': ncores}
+ log('No queuing system detected; single machine assumed.')
+ q = '<single machine>'
+ success(q, cores, log)
+ return cores
+
+
+class MessageDictionary:
+ """Standard container for all messages (typically requests, via
+ zmq.context.socket.send_pyobj) sent from the workers to the master.
+
+ This returns a simple dictionary. This is roughly email format.
+ Initialize with process id (e.g., 'from'). Call with subject and data
+ (body).
+ """
+
+ def __init__(self, process_id):
+ self._process_id = process_id
+
+ def __call__(self, subject, data=None):
+ d = {'id': self._process_id,
+ 'subject': subject,
+ 'data': data}
+ return d
+
+
+def make_sublists(masterlist, n):
+ """Randomly divides the masterlist into n sublists of roughly
+ equal size.
+
+ The intended use is to divide a keylist and assign
+ keys to each task in parallel processing. This also destroys
+ the masterlist (to save some memory).
+ """
+ masterlist = list(masterlist)
+ np.random.shuffle(masterlist)
+ N = len(masterlist)
+ sublist_lengths = [
+ N // n if _ >= (N % n) else N // n + 1 for _ in range(n)]
+ sublists = []
+ for sublist_length in sublist_lengths:
+ sublists.append([masterlist.pop() for _ in range(sublist_length)])
+ return sublists
+
+
+def setup_parallel(parallel, workercommand, log):
+ """Starts the worker processes and the master to control them.
+
+ This makes an SSH connection to each node (including the one the master
+ process runs on), then creates the specified number of processes on each
+ node through its SSH connection. Then sets up ZMQ for efficienty
+ communication between the worker processes and the master process.
+
+ Uses the parallel dictionary as defined in amp.Amp. log is an Amp logger.
+ module is the name of the module to be called, which is usually
+ given by self.calc.__module, etc.
+ workercommand is stub of the command used to start the servers,
+ typically like "python -m amp.descriptor.gaussian". Appended to
+ this will be " <pid> <serversocket> &" where <pid> is the unique ID
+ assigned to each process and <serversocket> is the address of the
+ server, like 'node321:34292'.
+
+ Returns
+ -------
+ server : (a ZMQ socket)
+ The ssh connections (pxssh instances; if these objects are destroyed
+ pxssh will close the sessions)
+
+ the pid_count, which is the total number of workers started. Each
+ worker can be communicated directly through its PID, an integer
+ between 0 and pid_count
+ """
+ import zmq
+ from socket import gethostname
+
+ log(' Parallel processing.')
+ serverhostname = gethostname()
+
+ # Establish server session.
+ context = zmq.Context()
+ server = context.socket(zmq.REP)
+ port = server.bind_to_random_port('tcp://*')
+ serversocket = '%s:%s' % (serverhostname, port)
+ log(' Established server at %s.' % serversocket)
+
+ workercommand += ' %s ' + serversocket
+
+ log(' Establishing worker sessions.')
+ connections = []
+ pid_count = 0
+ for workerhostname, nprocesses in parallel['cores'].items():
+ pids = range(pid_count, pid_count + nprocesses)
+ pid_count += nprocesses
+ connections.append(start_workers(pids,
+ workerhostname,
+ workercommand,
+ log,
+ parallel['envcommand']))
+
+ return server, connections, pid_count
+
+
+def start_workers(process_ids, workerhostname, workercommand, log,
+ envcommand):
+ """A function to start a new SSH session and establish processes on
+ that session.
+ """
+ if workerhostname != 'localhost':
+ workercommand += ' &'
+ log(' Starting non-local connections.')
+ pxssh = importer('pxssh')
+ ssh = pxssh.pxssh()
+ ssh.login(workerhostname, getuser())
+ if envcommand is not None:
+ log('Environment command: %s' % envcommand)
+ ssh.sendline(envcommand)
+ ssh.readline()
+ for process_id in process_ids:
+ ssh.sendline(workercommand % process_id)
+ ssh.expect('<amp-connect>')
+ ssh.expect('<stderr>')
+ log(' Session %i (%s): %s' %
+ (process_id, workerhostname, ssh.before.strip()))
+ return ssh
+ import pexpect
+ log(' Starting local connections.')
+ children = []
+ for process_id in process_ids:
+ child = pexpect.spawn(workercommand % process_id)
+ child.expect('<amp-connect>')
+ child.expect('<stderr>')
+ log(' Session %i (%s): %s' %
+ (process_id, workerhostname, child.before.strip()))
+ children.append(child)
+ return children
+
+
+# Data and logging ###########################################################
+
+
+class FileDatabase:
+ """Using a database file, such as shelve or sqlitedict, that can handle
+ multiple processes writing to the file is hard.
+
+ Therefore, we take the stupid approach of having each database entry be
+ a separate file. This class behaves essentially like shelve, but saves each
+ dictionary entry as a plain pickle file within the directory, with the
+ filename corresponding to the dictionary key (which must be a string).
+
+ Like shelve, this also keeps an internal (memory dictionary) representation
+ of the variables that have been accessed.
+
+ Also includes an archive feature, where files are instead added to a file
+ called 'archive.tar.gz' to save disk space. If an entry exists in both the
+ loose and archive formats, the loose is taken to be the new (correct)
+ value.
+ """
+
+ def __init__(self, filename):
+ """Open the filename at specified location. flag is ignored; this
+ format is always capable of both reading and writing."""
+ if not filename.endswith(os.extsep + 'ampdb'):
+ filename += os.extsep + 'ampdb'
+ self.path = filename
+ self.loosepath = os.path.join(self.path, 'loose')
+ self.tarpath = os.path.join(self.path, 'archive.tar.gz')
+ if not os.path.exists(self.path):
+ os.mkdir(self.path)
+ os.mkdir(self.loosepath)
+ self._memdict = {} # Items already accessed; stored in memory.
+
+ @classmethod
+ def open(Cls, filename, flag=None):
+ """Open present for compatibility with shelve. flag is ignored; this
+ format is always capable of both reading and writing.
+ """
+ return Cls(filename=filename)
+
+ def close(self):
+ """Only present for compatibility with shelve.
+ """
+ return
+
+ def keys(self):
+ """Return list of keys, both of in-memory and out-of-memory
+ items.
+ """
+ keys = os.listdir(self.loosepath)
+ if os.path.exists(self.tarpath):
+ with tarfile.open(self.tarpath) as tf:
+ keys = list(set(keys + tf.getnames()))
+ return keys
+
+ def values(self):
+ """Return list of values, both of in-memory and out-of-memory
+ items. This moves all out-of-memory items into memory.
+ """
+ keys = self.keys()
+ return [self[key] for key in keys]
+
+ def __len__(self):
+ return len(self.keys())
+
+ def __setitem__(self, key, value):
+ self._memdict[key] = value
+ path = os.path.join(self.loosepath, str(key))
+ if os.path.exists(path):
+ with open(path, 'r') as f:
+ if f.read() == pickle.dumps(value):
+ return # Nothing to update.
+ with open(path, 'wb') as f:
+ pickle.dump(value, f)
+
+ def __getitem__(self, key):
+ if key in self._memdict:
+ return self._memdict[key]
+ keypath = os.path.join(self.loosepath, key)
+ if os.path.exists(keypath):
+ with open(keypath, 'rb') as f:
+ return pickle.load(f)
+ elif os.path.exists(self.tarpath):
+ with tarfile.open(self.tarpath) as tf:
+ return pickle.load(tf.extractfile(key))
+ else:
+ raise KeyError(str(key))
+
+ def update(self, newitems):
+ for key, value in newitems.items():
+ self.__setitem__(key, value)
+
+ def archive(self):
+ """Cleans up to save disk space and reduce huge number of files.
+
+ That is, puts all files into an archive. Compresses all files in
+ <path>/loose and places them in <path>/archive.tar.gz. If archive
+ exists, appends/modifies.
+ """
+ loosefiles = os.listdir(self.loosepath)
+ print('Contains %i loose entries.' % len(loosefiles))
+ if len(loosefiles) == 0:
+ print(' -> No action taken.')
+ return
+ if os.path.exists(self.tarpath):
+ with tarfile.open(self.tarpath) as tf:
+ names = [_ for _ in tf.getnames() if _ not in
+ os.listdir(self.loosepath)]
+ for name in names:
+ tf.extract(member=name, path=self.loosepath)
+ loosefiles = os.listdir(self.loosepath)
+ print('Compressing %i entries.' % len(loosefiles))
+ with tarfile.open(self.tarpath, 'w:gz') as tf:
+ for file in loosefiles:
+ tf.add(name=os.path.join(self.loosepath, file),
+ arcname=file)
+ print('Cleaning up: removing %i files.' % len(loosefiles))
+ for file in loosefiles:
+ os.remove(os.path.join(self.loosepath, file))
+
+
+class Data:
+ """Serves as a container (dictionary-like) for (key, value) pairs that
+ also serves to calculate them.
+
+ Works by default with python's shelve module, but something that is built
+ to share the same commands as shelve will work fine; just specify this in
+ dbinstance.
+
+ Designed to hold things like neighborlists, which have a hash, value
+ format.
+
+ This will work like a dictionary in that items can be accessed with
+ data[key], but other advanced dictionary functions should be accessed with
+ through the .d attribute:
+
+ >>> data = Data(...)
+ >>> data.open()
+ >>> keys = data.d.keys()
+ >>> values = data.d.values()
+ """
+
+ def __init__(self, filename, db=FileDatabase, calculator=None):
+ self.calc = calculator
+ self.db = db
+ self.filename = filename
+ self.d = None
+
+ def calculate_items(self, images, parallel, log=None):
+ """Calculates the data value with 'calculator' for the specified
+ images.
+
+ images is a dictionary, and the same keys will be used for the current
+ database.
+ """
+ if log is None:
+ log = Logger(None)
+ if self.d is not None:
+ self.d.close()
+ self.d = None
+ log(' Data stored in file %s.' % self.filename)
+ d = self.db.open(self.filename, 'r')
+ calcs_needed = list(set(images.keys()).difference(d.keys()))
+ dblength = len(d)
+ d.close()
+ log(' File exists with %i total images, %i of which are needed.' %
+ (dblength, len(images) - len(calcs_needed)))
+ log(' %i new calculations needed.' % len(calcs_needed))
+ if len(calcs_needed) == 0:
+ return
+ if parallel['cores'] == 1:
+ d = self.db.open(self.filename, 'c')
+ for key in calcs_needed:
+ d[key] = self.calc.calculate(images[key], key)
+ d.close() # Necessary to get out of write mode and unlock?
+ log(' Calculated %i new images.' % len(calcs_needed))
+ else:
+ python = sys.executable
+ workercommand = '%s -m %s' % (python, self.calc.__module__)
+ server, connections, n_pids = setup_parallel(parallel,
+ workercommand, log)
+
+ globals = self.calc.globals
+ keyed = self.calc.keyed
+
+ keys = make_sublists(calcs_needed, n_pids)
+ results = {}
+
+ # All incoming requests will be dictionaries with three keys.
+ # d['id']: process id number, assigned when process created above.
+ # d['subject']: what the message is asking for / telling you
+ # d['data']: optional data passed from the worker.
+
+ active = 0 # count of processes actively calculating
+ log(' Parallel calculations starting...', tic='parallel')
+ while True:
+ message = server.recv_pyobj()
+ if message['subject'] == '<purpose>':
+ server.send_pyobj(self.calc.parallel_command)
+ active += 1
+ elif message['subject'] == '<request>':
+ request = message['data'] # Variable name.
+ if request == 'images':
+ server.send_pyobj({k: images[k] for k in
+ keys[int(message['id'])]})
+ elif request in keyed:
+ server.send_pyobj({k: keyed[request][k] for k in
+ keys[int(message['id'])]})
+ else:
+ server.send_pyobj(globals[request])
+ elif message['subject'] == '<result>':
+ result = message['data']
+ server.send_string('meaningless reply')
+ active -= 1
+ log(' Process %s returned %i results.' %
+ (message['id'], len(result)))
+ results.update(result)
+ elif message['subject'] == '<info>':
+ server.send_string('meaningless reply')
+ if active == 0:
+ break
+ log(' %i new results.' % len(results))
+ log(' ...parallel calculations finished.', toc='parallel')
+ log(' Adding new results to database.')
+ d = self.db.open(self.filename, 'c')
+ d.update(results)
+ d.close() # Necessary to get out of write mode and unlock?
+
+ self.d = None
+
+ def __getitem__(self, key):
+ self.open()
+ return self.d[key]
+
+ def close(self):
+ """Safely close the database.
+ """
+ if self.d:
+ self.d.close()
+ self.d = None
+
+ def open(self, mode='r'):
+ """Open the database connection with mode specified.
+ """
+ if self.d is None:
+ self.d = self.db.open(self.filename, mode)
+
+ def __del__(self):
+ self.close()
+
+
+class Logger:
+
+ """Logger that can also deliver timing information.
+
+ Parameters
+ ----------
+ file : str
+ File object or path to the file to write to. Or set to None for
+ a logger that does nothing.
+ """
+
+ def __init__(self, file):
+ if file is None:
+ self.file = None
+ return
+ if isinstance(file, str):
+ self.filename = file
+ file = open(file, 'a')
+ self.file = file
+ self.tics = {}
+
+ def tic(self, label=None):
+ """Start a timer.
+
+ Parameters
+ ----------
+ label : str
+ Label for managing multiple timers.
+ """
+ if self.file is None:
+ return
+ if label:
+ self.tics[label] = time.time()
+ else:
+ self._tic = time.time()
+
+ def __call__(self, message, toc=None, tic=False):
+ """Writes message to the log file.
+
+ Parameters
+ ---------
+ message : str
+ Message to be written.
+ toc : bool or str
+ If toc=True or toc=label, it will append timing information in
+ minutes to the timer.
+ tic : bool or str
+ If tic=True or tic=label, will start the generic timer or a timer
+ associated with label. Equivalent to self.tic(label).
+ """
+ if self.file is None:
+ return
+ dt = ''
+ if toc:
+ if toc is True:
+ tic = self._tic
+ else:
+ tic = self.tics[toc]
+ dt = (time.time() - tic) / 60.
+ dt = ' %.1f min.' % dt
+ if self.file.closed:
+ self.file = open(self.filename, 'a')
+ self.file.write(message + dt + '\n')
+ self.file.flush()
+ if tic:
+ if tic is True:
+ self.tic()
+ else:
+ self.tic(label=tic)
+
+
+def make_filename(label, base_filename):
+ """Creates a filename from the label and the base_filename which should be
+ a string.
+
+ Returns None if label is None; that is, it only saves output if a label is
+ specified.
+
+ Parameters
+ ----------
+ label : str
+ Prefix.
+ base_filename : str
+ Basic name of the file.
+ """
+
+ if label is None:
+ return None
+ if not label:
+ filename = base_filename
+ else:
+ filename = os.path.join(label + base_filename)
+
+ return filename
+
+
+# Images and hashing #########################################################
+
+def get_hash(atoms):
+ """Creates a unique signature for a particular ASE atoms object.
+
+ This is used to check whether an image has been seen before. This is just
+ an md5 hash of a string representation of the atoms object.
+
+ Parameters
+ ----------
+ atoms : ASE dict
+ ASE atoms object.
+
+ Returns
+ -------
+ Hash string key of 'atoms'.
+ """
+ string = str(atoms.pbc)
+ for number in atoms.cell.flatten():
+ string += '%.15f' % number
+ string += str(atoms.get_atomic_numbers())
+ for number in atoms.get_positions().flatten():
+ string += '%.15f' % number
+
+ md5 = hashlib.md5(string.encode('utf-8'))
+ hash = md5.hexdigest()
+ return hash
+
+
+def hash_images(images, log=None, ordered=False):
+ """ Converts input images -- which may be a list, a trajectory file, or
+ a database -- into a dictionary indexed by their hashes.
+
+ Returns this dictionary. If ordered is True, returns an OrderedDict. When
+ duplicate images are encountered (based on encountering an identical hash),
+ a warning is written to the logfile. The number of duplicates of each image
+ can be accessed by examinging dict_images.metadata['duplicates'], where
+ dict_images is the returned dictionary.
+ """
+ if log is None:
+ log = Logger(None)
+ if images is None:
+ return
+ elif hasattr(images, 'keys'):
+ log(' %i unique images after hashing.' % len(images))
+ return images # Apparently already hashed.
+ else:
+ # Need to be hashed, and possibly read from file.
+ if isinstance(images, str):
+ log('Attempting to read images from file %s.' %
+ images)
+ extension = os.path.splitext(images)[1]
+ from ase import io
+ if extension == '.traj':
+ images = io.Trajectory(images, 'r')
+ elif extension == '.db':
+ images = [row.toatoms() for row in
+ connect(images, 'db').select(None)]
+
+ # images converted to dictionary form; key is hash of image.
+ log('Hashing images...', tic='hash')
+ dict_images = MetaDict()
+ dict_images.metadata['duplicates'] = {}
+ dup = dict_images.metadata['duplicates']
+ if ordered is True:
+ from collections import OrderedDict
+ dict_images = OrderedDict()
+ for image in images:
+ hash = get_hash(image)
+ if hash in dict_images.keys():
+ log('Warning: Duplicate image (based on identical hash).'
+ ' Was this expected? Hash: %s' % hash)
+ if hash in dup.keys():
+ dup[hash] += 1
+ else:
+ dup[hash] = 2
+ dict_images[hash] = image
+ log(' %i unique images after hashing.' % len(dict_images))
+ log('...hashing completed.', toc='hash')
+ return dict_images
+
+
+def check_images(images, forces):
+ """Checks that all images have energies, and optionally forces,
+ calculated, so that they can be used for training. Raises a
+ MissingDataError if any are missing."""
+ missing_energies, missing_forces = 0, 0
+ for index, image in enumerate(images.values()):
+ try:
+ image.get_potential_energy()
+ except PropertyNotImplementedError:
+ missing_energies += 1
+ if forces is True:
+ try:
+ image.get_forces()
+ except PropertyNotImplementedError:
+ missing_forces += 1
+ if missing_energies + missing_forces == 0:
+ return
+ msg = ''
+ if missing_energies > 0:
+ msg += 'Missing energy in {} image(s).'.format(missing_energies)
+ if missing_forces > 0:
+ msg += ' Missing forces in {} image(s).'.format(missing_forces)
+ raise MissingDataError(msg)
+
+
+def randomize_images(images, fraction=0.8):
+ """Randomly assigns 'fraction' of the images to a training set and (1
+ - 'fraction') to a test set. Returns two lists of ASE images.
+
+ Parameters
+ ----------
+ images : list or str
+ List of ASE atoms objects in ASE format. This can also be the path to
+ an ASE trajectory (.traj) or database (.db) file.
+ fraction : float
+ Portion of train_images to all images.
+
+ Returns
+ -------
+ train_images, test_images : list
+ Lists of train and test images.
+ """
+ file_opened = False
+ if type(images) == str:
+ extension = os.path.splitext(images)[1]
+ if extension == '.traj':
+ images = aseio.Trajectory(images, 'r')
+ elif extension == '.db':
+ images = aseio.read(images)
+ file_opened = True
+
+ trainingsize = int(fraction * len(images))
+ testsize = len(images) - trainingsize
+ testindices = []
+ while len(testindices) < testsize:
+ next = np.random.randint(len(images))
+ if next not in testindices:
+ testindices.append(next)
+ testindices.sort()
+ trainindices = [index for index in range(len(images)) if index not in
+ testindices]
+ train_images = [images[index] for index in trainindices]
+ test_images = [images[index] for index in testindices]
+ if file_opened:
+ images.close()
+ return train_images, test_images
+
+# Custom exceptions ##########################################################
+
+
+class ConvergenceOccurred(Exception):
+ """ Kludge to decide when scipy's optimizers are complete.
+ """
+ pass
+
+
+class TrainingConvergenceError(Exception):
+ """Error to be raised if training does not converge.
+ """
+ pass
+
+
+class MissingDataError(Exception):
+ """Error to be raised if any images are missing key data,
+ like energy or forces."""
+ pass
+
+
+# Miscellaneous ##############################################################
+
+def string2dict(text):
+ """Converts a string into a dictionary.
+
+ Basically just calls `eval` on it, but supplies words like OrderedDict and
+ matrix.
+ """
+ try:
+ dictionary = eval(text)
+ except NameError:
+ from collections import OrderedDict
+ from numpy import array, matrix
+ dictionary = eval(text)
+ return dictionary
+
+
+def now(with_utc=False):
+ """
+ Returns
+ -------
+ String of current time.
+ """
+ local = datetime.now().isoformat().split('.')[0]
+ utc = datetime.utcnow().isoformat().split('.')[0]
+ if with_utc:
+ return '%s (%s UTC)' % (local, utc)
+ else:
+ return local
+
+
+logo = """
+ oo o o oooooo
+ o o oo oo o o
+ o o o o o o o o
+o o o o o o o o
+oooooooo o o o oooooo
+o o o o o
+o o o o o
+o o o o o
+"""
+
+
+def importer(name):
+ """Handles strange import cases, like pxssh which might show
+ up in eithr the package pexpect or pxssh.
+ """
+
+ if name == 'pxssh':
+ try:
+ import pxssh
+ except ImportError:
+ try:
+ from pexpect import pxssh
+ except ImportError:
+ raise ImportError('pxssh not found!')
+ return pxssh
+ elif name == 'NeighborList':
+ try:
+ from ase.neighborlist import NeighborList
+ except ImportError:
+ # We're on ASE 3.10 or older
+ from ase.calculators.neighborlist import NeighborList
+ return NeighborList
+
+
+# Amp Simulated Annealer ######################################################
+
+
+class Annealer(object):
+
+ """
+ Inspired by the simulated annealing implementation of
+ Richard J. Wagner <wagnerr at umich.edu> and
+ Matthew T. Perry <perrygeo at gmail.com> at
+ https://github.com/perrygeo/simanneal.
+
+ Performs simulated annealing by calling functions to calculate loss and
+ make moves on a state. The temperature schedule for annealing may be
+ provided manually or estimated automatically.
+
+ Can be used by something like:
+
+ >>> from amp import Amp
+ >>> from amp.descriptor.gaussian import Gaussian
+ >>> from amp.model.neuralnetwork import NeuralNetwork
+ >>> calc = Amp(descriptor=Gaussian(), model=NeuralNetwork())
+
+ which will initialize tha calc object as usual, and then
+
+ >>> from amp.utilities import Annealer
+ >>> Annealer(calc=calc, images=images)
+
+ which will perform simulated annealing global search in parameters space,
+ and finally
+
+ >>> calc.train(images=images)
+
+ for gradient descent optimization.
+ """
+
+ Tmax = 20.0 # Max (starting) temperature
+ Tmin = 2.5 # Min (ending) temperature
+ steps = 10000 # Number of iterations
+ updates = steps / 200 # Number of updates (an update prints to log)
+ copy_strategy = 'copy'
+ user_exit = False
+ save_state_on_exit = False
+
+ def __init__(self, calc, images,
+ Tmax=None, Tmin=None, steps=None, updates=None):
+ if Tmax is not None:
+ self.Tmax = Tmax
+ if Tmin is not None:
+ self.Tmin = Tmin
+ if steps is not None:
+ self.steps = steps
+ if updates is not None:
+ self.updates = updates
+ self.calc = calc
+
+ self.calc._log('\nAmp simulated annealer started. ' + now() + '\n')
+ self.calc._log('Descriptor: %s' %
+ self.calc.descriptor.__class__.__name__)
+ self.calc._log('Model: %s' % self.calc.model.__class__.__name__)
+
+ images = hash_images(images, log=self.calc._log)
+
+ self.calc._log('\nDescriptor\n==========')
+ # Derivatives of fingerprints need to be calculated if train_forces is
+ # True.
+ calculate_derivatives = True
+ self.calc.descriptor.calculate_fingerprints(
+ images=images,
+ parallel=self.calc._parallel,
+ log=self.calc._log,
+ calculate_derivatives=calculate_derivatives)
+ # Setting up calc.model.vector()
+ self.calc.model.fit(trainingimages=images,
+ descriptor=self.calc.descriptor,
+ log=self.calc._log,
+ parallel=self.calc._parallel,
+ only_setup=True,)
+ # Truning off ConvergenceOccured exception and log_losses
+ initial_raise_ConvergenceOccurred = \
+ self.calc.model.lossfunction.raise_ConvergenceOccurred
+ initial_log_losses = self.calc.model.lossfunction.log_losses
+ self.calc.model.lossfunction.log_losses = False
+ self.calc.model.lossfunction.raise_ConvergenceOccurred = False
+ initial_state = self.calc.model.vector.copy()
+ self.state = self.copy_state(initial_state)
+
+ signal.signal(signal.SIGINT, self.set_user_exit)
+ self.calc._log('\nAnnealing\n=========\n')
+ bestState, bestLoss = self.anneal()
+ # Taking the best state
+ self.calc.model.vector = np.array(bestState)
+ # Returning back the changed arguments
+ self.calc.model.lossfunction.log_losses = initial_log_losses
+ self.calc.model.lossfunction.raise_ConvergenceOccurred = \
+ initial_raise_ConvergenceOccurred
+ # cleaning up sessions
+ self.calc.model.lossfunction._step = 0
+ self.calc.model.lossfunction._cleanup()
+ calc = self.calc
+
+ @staticmethod
+ def round_figures(x, n):
+ """Returns x rounded to n significant figures."""
+ return round(x, int(n - math.ceil(math.log10(abs(x)))))
+
+ @staticmethod
+ def time_string(seconds):
+ """Returns time in seconds as a string formatted HHHH:MM:SS."""
+ s = int(round(seconds)) # round to nearest second
+ h, s = divmod(s, 3600) # get hours and remainder
+ m, s = divmod(s, 60) # split remainder into minutes and seconds
+ return '%4i:%02i:%02i' % (h, m, s)
+
+ def save_state(self, fname=None):
+ """Saves state
+ """
+ if not fname:
+ date = datetime.datetime.now().isoformat().split(".")[0]
+ fname = date + "_loss_" + str(self.get_loss()) + ".state"
+ print("Saving state to: %s" % fname)
+ with open(fname, "w") as fh:
+ pickle.dump(self.state, fh)
+
+ def move(self, state):
+ """Create a state change
+ """
+ move_step = np.random.rand(len(state)) * 2. - 1.
+ move_step *= 0.0005
+ for _ in range(len(state)):
+ state[_] = state[_] * (1 + move_step[_])
+ return state
+
+ def get_loss(self, state):
+ """Calculate state's loss
+ """
+ lossfxn = \
+ self.calc.model.lossfunction.get_loss(np.array(state),
+ lossprime=False,)['loss']
+ return lossfxn
+
+ def set_user_exit(self, signum, frame):
+ """Raises the user_exit flag, further iterations are stopped
+ """
+ self.user_exit = True
+
+ def set_schedule(self, schedule):
+ """Takes the output from `auto` and sets the attributes
+ """
+ self.Tmax = schedule['tmax']
+ self.Tmin = schedule['tmin']
+ self.steps = int(schedule['steps'])
+
+ def copy_state(self, state):
+ """Returns an exact copy of the provided state Implemented according to
+ self.copy_strategy, one of
+
+ * deepcopy : use copy.deepcopy (slow but reliable)
+ * slice: use list slices (faster but only works if state is list-like)
+ * method: use the state's copy() method
+ """
+ if self.copy_strategy == 'deepcopy':
+ return copy.deepcopy(state)
+ elif self.copy_strategy == 'slice':
+ return state[:]
+ elif self.copy_strategy == 'copy':
+ return state.copy()
+
+ def update(self, step, T, L, acceptance, improvement):
+ """Prints the current temperature, loss, acceptance rate, improvement
+ rate, elapsed time, and remaining time.
+
+ The acceptance rate indicates the percentage of moves since the last
+ update that were accepted by the Metropolis algorithm. It includes
+ moves that decreased the loss, moves that left the loss unchanged, and
+ moves that increased the loss yet were reached by thermal excitation.
+
+ The improvement rate indicates the percentage of moves since the last
+ update that strictly decreased the loss. At high temperatures it will
+ include both moves that improved the overall state and moves that
+ simply undid previously accepted moves that increased the loss by
+ thermal excititation. At low temperatures it will tend toward zero as
+ the moves that can decrease the loss are exhausted and moves that would
+ increase the loss are no longer thermally accessible.
+ """
+
+ elapsed = time.time() - self.start
+ if step == 0:
+ self.calc._log('\n')
+ header = ' %5s %12s %12s %7s %7s %10s %10s'
+ self.calc._log(header % ('Step', 'Temperature', 'Loss (SSD)',
+ 'Accept', 'Improve', 'Elapsed',
+ 'Remaining'))
+ self.calc._log(header % ('=' * 5, '=' * 12, '=' * 12,
+ '=' * 7, '=' * 7, '=' * 10,
+ '=' * 10,))
+ self.calc._log(
+ ' %5i %12.2e %12.4e %s '
+ % (step, T, L, self.time_string(elapsed)))
+ else:
+ remain = (self.steps - step) * (elapsed / step)
+ self.calc._log(' %5i %12.2e %12.4e %7.2f%% %7.2f%% %s %s' %
+ (step, T, L,
+ 100.0 * acceptance, 100.0 * improvement,
+ self.time_string(elapsed),
+ self.time_string(remain)))
+
+ def anneal(self):
+ """Minimizes the loss of a system by simulated annealing.
+
+ Parameters
+ ---------
+ state
+ An initial arrangement of the system
+
+ Returns
+ -------
+ state, loss
+ The best state and loss found.
+ """
+ step = 0
+ self.start = time.time()
+
+ # Precompute factor for exponential cooling from Tmax to Tmin
+ if self.Tmin <= 0.0:
+ raise Exception('Exponential cooling requires a minimum "\
+ "temperature greater than zero.')
+ Tfactor = -math.log(self.Tmax / self.Tmin)
+
+ # Note initial state
+ T = self.Tmax
+ L = self.get_loss(self.state)
+ prevState = self.copy_state(self.state)
+ prevLoss = L
+ bestState = self.copy_state(self.state)
+ bestLoss = L
+ trials, accepts, improves = 0, 0, 0
+ if self.updates > 0:
+ updateWavelength = self.steps / self.updates
+ self.update(step, T, L, None, None)
+
+ # Attempt moves to new states
+ while step < (self.steps - 1) and not self.user_exit:
+ step += 1
+ T = self.Tmax * math.exp(Tfactor * step / self.steps)
+ self.state = self.move(self.state)
+ L = self.get_loss(self.state)
+ dL = L - prevLoss
+ trials += 1
+ if dL > 0.0 and math.exp(-dL / T) < random.random():
+ # Restore previous state
+ self.state = self.copy_state(prevState)
+ L = prevLoss
+ else:
+ # Accept new state and compare to best state
+ accepts += 1
+ if dL < 0.0:
+ improves += 1
+ prevState = self.copy_state(self.state)
+ prevLoss = L
+ if L < bestLoss:
+ bestState = self.copy_state(self.state)
+ bestLoss = L
+ if self.updates > 1:
+ if step // updateWavelength > (step - 1) // updateWavelength:
+ self.update(
+ step, T, L, accepts / trials, improves / trials)
+ trials, accepts, improves = 0, 0, 0
+
+ # line break after progress output
+ print('')
+
+ self.state = self.copy_state(bestState)
+ if self.save_state_on_exit:
+ self.save_state()
+ # Return best state and loss
+ return bestState, bestLoss
+
+ def auto(self, minutes, steps=2000):
+ """Minimizes the loss of a system by simulated annealing with automatic
+ selection of the temperature schedule.
+
+ Keyword arguments:
+ state -- an initial arrangement of the system
+ minutes -- time to spend annealing (after exploring temperatures)
+ steps -- number of steps to spend on each stage of exploration
+
+ Returns the best state and loss found.
+ """
+
+ def run(T, steps):
+ """Anneals a system at constant temperature and returns the state,
+ loss, rate of acceptance, and rate of improvement.
+ """
+ L = self.get_loss()
+ prevState = self.copy_state(self.state)
+ prevLoss = L
+ accepts, improves = 0, 0
+ for step in range(steps):
+ self.move()
+ L = self.get_loss()
+ dL = L - prevLoss
+ if dL > 0.0 and math.exp(-dL / T) < random.random():
+ self.state = self.copy_state(prevState)
+ L = prevLoss
+ else:
+ accepts += 1
+ if dL < 0.0:
+ improves += 1
+ prevState = self.copy_state(self.state)
+ prevLoss = L
+ return L, float(accepts) / steps, float(improves) / steps
+
+ step = 0
+ self.start = time.time()
+
+ # Attempting automatic simulated anneal...
+ # Find an initial guess for temperature
+ T = 0.0
+ L = self.get_loss()
+ self.update(step, T, L, None, None)
+ while T == 0.0:
+ step += 1
+ self.move()
+ T = abs(self.get_loss() - L)
+
+ # Search for Tmax - a temperature that gives 98% acceptance
+ L, acceptance, improvement = run(T, steps)
+
+ step += steps
+ while acceptance > 0.98:
+ T = self.round_figures(T / 1.5, 2)
+ L, acceptance, improvement = run(T, steps)
+ step += steps
+ self.update(step, T, L, acceptance, improvement)
+ while acceptance < 0.98:
+ T = self.round_figures(T * 1.5, 2)
+ L, acceptance, improvement = run(T, steps)
+ step += steps
+ self.update(step, T, L, acceptance, improvement)
+ Tmax = T
+
+ # Search for Tmin - a temperature that gives 0% improvement
+ while improvement > 0.0:
+ T = self.round_figures(T / 1.5, 2)
+ L, acceptance, improvement = run(T, steps)
+ step += steps
+ self.update(step, T, L, acceptance, improvement)
+ Tmin = T
+
+ # Calculate anneal duration
+ elapsed = time.time() - self.start
+ duration = self.round_figures(int(60.0 * minutes * step / elapsed), 2)
+
+ print('') # New line after auto() output
+ # Don't perform anneal, just return params
+ return {'tmax': Tmax, 'tmin': Tmin, 'steps': duration}
+
+
+class MetaDict(dict):
+ """Dictionary that can also store metadata. Useful for images dictionary
+ so that images can still be iterated by keys.
+ """
+ metadata = {}
diff --git a/docs/README b/docs/README
new file mode 100644
index 0000000..ebc21df
--- /dev/null
+++ b/docs/README
@@ -0,0 +1,2 @@
+For instructions on how to build this documentation, please see the
+"Documentation" section of the file "develop.rst".
diff --git a/docs/_static/amp-logo.svg b/docs/_static/amp-logo.svg
new file mode 100644
index 0000000..a74a7f0
--- /dev/null
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diff --git a/docs/_static/completeexample.py b/docs/_static/completeexample.py
new file mode 100644
index 0000000..f0e262e
--- /dev/null
+++ b/docs/_static/completeexample.py
@@ -0,0 +1,70 @@
+from ase.lattice.surface import fcc110
+from ase import Atom, Atoms
+from ase.constraints import FixAtoms
+from ase.calculators.emt import EMT
+from ase.md import VelocityVerlet
+from ase.md.velocitydistribution import MaxwellBoltzmannDistribution
+from ase import units
+from ase import io
+
+from amp.utilities import randomize_images
+from amp import Amp
+from amp.descriptor import *
+from amp.regression import *
+
+###############################################################################
+
+
+def test():
+
+ # Generate atomic system to create test data.
+ atoms = fcc110('Cu', (2, 2, 2), vacuum=7.)
+ adsorbate = Atoms([Atom('H', atoms[7].position + (0., 0., 2.)),
+ Atom('H', atoms[7].position + (0., 0., 5.))])
+ atoms.extend(adsorbate)
+ atoms.set_constraint(FixAtoms(indices=[0, 2]))
+ calc = EMT() # cheap calculator
+ atoms.set_calculator(calc)
+
+ # Run some molecular dynamics to generate data.
+ trajectory = io.Trajectory('data.traj', 'w', atoms=atoms)
+ MaxwellBoltzmannDistribution(atoms, temp=300. * units.kB)
+ dynamics = VelocityVerlet(atoms, dt=1. * units.fs)
+ dynamics.attach(trajectory)
+ for step in range(50):
+ dynamics.run(5)
+ trajectory.close()
+
+ # Train the calculator.
+ train_images, test_images = randomize_images('data.traj')
+
+ calc = Amp(descriptor=Behler(),
+ regression=NeuralNetwork())
+ calc.train(train_images, energy_goal=0.001, force_goal=None)
+
+ # Plot and test the predictions.
+ import matplotlib
+ matplotlib.use('Agg')
+ from matplotlib import pyplot
+
+ fig, ax = pyplot.subplots()
+
+ for image in train_images:
+ actual_energy = image.get_potential_energy()
+ predicted_energy = calc.get_potential_energy(image)
+ ax.plot(actual_energy, predicted_energy, 'b.')
+
+ for image in test_images:
+ actual_energy = image.get_potential_energy()
+ predicted_energy = calc.get_potential_energy(image)
+ ax.plot(actual_energy, predicted_energy, 'r.')
+
+ ax.set_xlabel('Actual energy, eV')
+ ax.set_ylabel('Amp energy, eV')
+
+ fig.savefig('parityplot.png')
+
+###############################################################################
+
+if __name__ == '__main__':
+ test()
\ No newline at end of file
diff --git a/docs/_static/convergence.svg b/docs/_static/convergence.svg
new file mode 100644
index 0000000..d0b0383
--- /dev/null
+++ b/docs/_static/convergence.svg
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diff --git a/docs/analysis.rst b/docs/analysis.rst
new file mode 100644
index 0000000..5e5df06
--- /dev/null
+++ b/docs/analysis.rst
@@ -0,0 +1,31 @@
+.. _Analysis:
+
+
+==================================
+Analysis
+==================================
+
+----------------------------------
+Convergence plots
+----------------------------------
+
+You can use the tool called `amp-plotconvergence` to help you examine the output of an Amp log file. Run `amp-plotconvergence -h` for help at the command line.
+
+You can also access this tool as :func:`~amp.analysis.plot_convergence` from the :mod:`amp.analysis` module.
+
+ .. image:: _static/convergence.svg
+ :width: 600 px
+ :align: center
+
+----------------------------------
+Other plots
+----------------------------------
+
+There are several other plotting tools within the :mod:`amp.analysis` module, including :func:`~amp.analysis.plot_parity` for making parity plots, :func:`~amp.analysis.plot_error` for making error plots, and :func:`~amp.analysis.plot_sensitivity` for examining the sensitivity of the model output to the model parameters.
+These modules should produce plots like below; in the order parity, error, and sensitivity from left to right.
+See the module autodocumentation for details.
+
+ .. image:: _static/parity_error_sensitivity.svg
+ :width: 1000 px
+ :align: center
+
diff --git a/docs/building.rst b/docs/building.rst
new file mode 100644
index 0000000..e0bb671
--- /dev/null
+++ b/docs/building.rst
@@ -0,0 +1,187 @@
+.. _Building:
+
+==================================
+Building modules
+==================================
+
+Amp is designed to be modular, so if you think you have a great descriptor scheme or machine-learning model, you can try it out.
+This page describes how to add your own modules; starting with the bare-bones requirements to make it work, and building up with how to construct it so it integrates with respect to parallelization, etc.
+
+----------------------------------
+Descriptor: minimal requirements
+----------------------------------
+
+To build your own descriptor, it needs to have certain minimum requirements met, in order to play with *Amp*. The below code illustrates these minimum requirements::
+
+ from ase.calculators.calculator import Parameters
+
+ class MyDescriptor(object):
+
+ def __init__(self, parameter1, parameter2):
+ self.parameters = Parameters({'mode': 'atom-centered',})
+ self.parameters.parameter1 = parameter1
+ self.parameters.parameter2 = parameter2
+
+ def tostring(self):
+ return self.parameters.tostring()
+
+ def calculate_fingerprints(self, images, cores, log):
+ # Do the calculations...
+ self.fingerprints = fingerprints # A dictionary.
+
+
+The specific requirements, illustrated above, are:
+
+* Has a parameters attribute (of type `ase.calculators.calculator.Parameters`), which holds the minimum information needed to re-build your module.
+ That is, if your descriptor has user-settable parameters such as a cutoff radius, etc., they should be stored in this dictionary.
+ Additionally, it must have the keyword "mode"; which must be set to either "atom-centered" or "image-centered".
+ (This keyword will be used by the model class.)
+
+* Has a "tostring" method, which converts the minimum parameters into a dictionary that can be re-constructed using `eval`.
+ If you used the ASE `Parameters` class above, this class is simple::
+
+ def tostring():
+ return self.parameters.tostring()
+
+* Has a "calculate_fingerprints" method.
+ The images argument is a dictionary of training images, with keys that are unique hashes of each image in the set produced with `amp.utilities.hash_images`.
+ The log is a `amp.utilities.Logger` instance, that the method can optionally use as `log('Message.')`.
+ The cores keyword describes parallelization, and can safely be ignored if serial operation is desired.
+ This method must save a sub-attribute `self.fingerprints` (which will be accessible in the main *Amp* instance as `calc.descriptor.fingerprints`) that contains a dictionary-like object of the fingerprints, indexed by the same keys that were in the images dictionary.
+ Ideally, `descriptor.fingerprints` is an instance of `amp.utilities.Data`, but probably any mapping (dictionary-like) object will do.
+
+ A fingerprint is a vector.
+ In **image-centered** mode, there is one fingerprint for each image.
+ This will generally be just the Cartesian positions of all the atoms in the system, but transformations are possible.
+ For example this could be accessed by the images key
+
+ >>> calc.descriptor.fingerprints[key]
+ >>> [3.223, 8.234, 0.0322, 8.33]
+
+ In **atom-centered** mode, there is a fingerprint for each atom in the image.
+ Therefore, calling `calc.descriptor.fingerprints[key]` returns a list of fingerprints, in the same order as the atom ordering in the original ASE atoms object.
+ So to access an individual atom's fingerprints one could do
+
+ >>> calc.descriptor.fingerprints[key][index]
+ >>> ('Cu', [8.832, 9.22, 7.118, 0.312])
+
+ That is, the first item is the element of the atom, and the second is a 1-dimensional array which is that atom's fingerprint.
+ Thus, `calc.descriptor.fingerprints[hash]` gives a list of fingerprints, in the same order the atoms appear in the image they were fingerprinted from.
+
+ If you want to train your model to forces also (besides energies), your "calculate_fingerprints" method needs to calculate derivatives of the fingerprints with respect to coordinates as well.
+ This is because forces (as the minus of coordinate-gradient of the potential energy) can be written, according to the chain rule of calculus, as the derivative of your model output (which represents energy here) with respect to model inputs (which is fingerprints) times the derivative of fingerprints with respect to spatial coordinates.
+ These derivatives are calculated for each image for each possible pair of atoms (within the cutoff distance in the **atom-centered** mode).
+ They can be calculated either analytically or simply numerically with finite-difference method.
+ If a piece of code is written to calculate coordinate-derivatives of fingerprints, then the "calculate_fingerprints" method can save it as a sub-attribute `self.fingerprintprimes` (which will be accessible in the main *Amp* instance as `calc.descriptor.fingerprintprimes`) along with `self.fingerprints`.
+ `self.fingerprintprimes` is a dictionary-like object, indexed by the same keys that were in the images dictionary.
+ Ideally, `descriptor.fingerprintprimes` is an instance of `amp.utilities.Data`, but probably any mapping (dictionary-like) object will do.
+
+ Calling `calc.descriptor.fingerprintprimes[key]` returns the derivatives of fingerprints for the image key of interest.
+ This is a dictionary where each key is a tuple representing the indices of the derivative, and each value is a list of finperprintprimes.
+ (This list has the same length as the fingerprints.)
+ For example, to retrieve derivatives of the fingerprints of atom indexed 2 (which is say Pt) with respect to :math:`x` coordinate of atom indexed 1 (which is say Cu), we should do
+
+ >>> calc.descriptor.fingerprintprimes[key][(1, 'Cu', 2, 'Pt', 0)]
+ >>> [-1.202, 0.130, 4.511, -0.721]
+
+ Or to retrieve derivatives of the fingerprints of atom indexed 1 with respect to :math:`z` coordinate of atom indexed 1, we do
+
+ >>> calc.descriptor.fingerprintprimes[key][(1, 'Cu', 1, 'Cu', 2)]
+ >>> [3.48, -1.343, -2.561, -8.412]
+
+----------------------------------
+Descriptor: standard practices
+----------------------------------
+
+The below describes standard practices we use in building modules. It is not necessary to use these, but it should make your life easier to follow standard practices. And, if your code is ultimately destined to be part of an Amp release, you should plan to make it follow these practices unless there is a compelling reason not to.
+
+We have an example of a minimal descriptor in `amp.descriptor.example`; it's probably easiest to copy this file and modify it to become your new descriptor. For a complete example of a working descriptor, see `amp.descriptor.gaussian`.
+
+The Data class
+^^^^^^^^^^^^^^^^^^^
+
+The key element we use to make our lives easier is the `Data` class. It should be noted that, in the development version, this is still a work in progress. The `Data` class acts like a dictionary in that items can be accessed by key, but also saves the data to disk (it is persistent), enables calculation of missing items, and can even parallelize these calculations across cores and nodes.
+
+It is recommended to first construct a pure python version that fits with the `Data` scheme for 1 core, then expanding it to work with multiple cores via the following procedure. See the Gaussian descriptor for an example of implementation.
+
+
+
+Basic data addition
+"""""""""""""""""""
+To make the descriptor work with the `Data` class, the `Data` class needs a keyword `calculator`. The simplest example of this is our `NeighborlistCalculator`, which is basically a wrapper around ASE's Neighborlist class::
+
+ class NeighborlistCalculator:
+ """For integration with .utilities.Data
+ For each image fed to calculate, a list of neighbors with offset
+ distances is returned.
+ """
+
+ def __init__(self, cutoff):
+ self.globals = Parameters({'cutoff': cutoff})
+ self.keyed = Parameters()
+ self.parallel_command = 'calculate_neighborlists'
+
+ def calculate(self, image, key):
+ cutoff = self.globals.cutoff
+ n = NeighborList(cutoffs=[cutoff / 2.] * len(image),
+ self_interaction=False,
+ bothways=True,
+ skin=0.)
+ n.update(image)
+ return [n.get_neighbors(index) for index in range(len(image))]
+
+Notice there are two categories of parameters saved in the init statement: `globals` and `keyed`. The first are parameters that apply to every image; here the cutoff radius is the same regardless of the image. The second category contains data that is specific to each image, in a dictionary format keyed by the image hash. In this example, there are no keyed parameters, but in the case of the fingerprint calculator, the dictionary of neighborlists is an example of a `keyed` parameter. The [...]
+
+Parallelization
+"""""""""""""""
+The parallelization should work provided the scheme is `embarassingly parallel <https://en.wikipedia.org/wiki/Embarrassingly_parallel>`_; that is, each image's fingerprint is independent of all other images' fingerprints. We implement this in building the `amp.utilities.Data` dictionaries, using a scheme of establishing SSH sessions (with pxssh) for each worker and passing messages with ZMQ.
+
+The `Data` class itself serves as the master, and the workers are instances of the specific module; that is, for the Gaussian scheme the workers are started with `python -m amp.descriptor.gaussian id hostname:port` where id is a unique identifier number assigned to each worker, and hostname:port is the socket at which the workers should open the connection to the mater (e.g., "node243:51247"). The master expects the worker to print two messages to the screen: "<amp-connect>" which confir [...]
+
+ if __name__ == "__main__":
+ import sys
+ import tempfile
+
+ hostsocket = sys.argv[-1]
+ proc_id = sys.argv[-2]
+
+ print('<amp-connect>')
+ sys.stderr = tempfile.NamedTemporaryFile(mode='w', delete=False,
+ suffix='.stderr')
+ print('stderr written to %s<stderr>' % sys.stderr.name)
+
+
+After this, the worker communicates with the master in request (from the worker) / reply (from the master) mode, via ZMQ. (It's worth checking out the `ZMQ Guide <http://zguide.zeromq.org/>`_; (ZMQ Guide examples). Each request from the worker needs to take the form of a dictionary with three entries: "id", "subject", and (optionally) "data". These are easily created with the `amp.utilities.MessageDictionary` class. The first thing the worker needs to do is establish the connection to th [...]
+
+ import zmq
+ from ..utilities import MessageDictionary
+ msg = MessageDictionary(proc_id)
+
+ # Establish client session via zmq; find purpose.
+ context = zmq.Context()
+ socket = context.socket(zmq.REQ)
+ socket.connect('tcp://%s' % hostsocket)
+ socket.send_pyobj(msg('<purpose>'))
+ purpose = socket.recv_pyobj()
+
+In the final line above, the master has sent a string with the `parallel_command` attribute mentioned above. You can have some if/elif statements to choose what to do next, but for the calculate_neighborlist example, the worker routine is as simple as requesting the variables, performing the calculations, and sending back the results, which happens in these few lines. This is all that is needed for parallelization (in pure python)::
+
+ # Request variables.
+ socket.send_pyobj(msg('<request>', 'cutoff'))
+ cutoff = socket.recv_pyobj()
+ socket.send_pyobj(msg('<request>', 'images'))
+ images = socket.recv_pyobj()
+
+ # Perform the calculations.
+ calc = NeighborlistCalculator(cutoff=cutoff)
+ neighborlist = {}
+ while len(images) > 0:
+ key, image = images.popitem() # Reduce memory.
+ neighborlist[key] = calc.calculate(image, key)
+
+ # Send the results.
+ socket.send_pyobj(msg('<result>', neighborlist))
+ socket.recv_string() # Needed to complete REQ/REP.
+
+
+
diff --git a/docs/community.rst b/docs/community.rst
new file mode 100644
index 0000000..ff2f992
--- /dev/null
+++ b/docs/community.rst
@@ -0,0 +1,33 @@
+.. _Community:
+
+
+==================================
+Community
+==================================
+
+----------------------------------
+Mailing list
+----------------------------------
+
+An amp-users listserv is available for general discussion, troubleshooting, suggestions, etc.
+It is available at
+
+https://listserv.brown.edu/?A0=AMP-USERS
+
+The archives of this list are also available to members of the list.
+
+
+----------------------------------
+Bugs and issues
+----------------------------------
+
+To report bugs, issues, works-in-progress, or feature requests (although those might best be first discussed on amp-users), please use our Issue Tracker on the repository page. It is available at
+
+https://bitbucket.org/andrewpeterson/amp/issues
+
+----------------------------------
+Contributions
+----------------------------------
+
+You are welcome to contribute to this project. See the :any:`Develop` page.
+
diff --git a/docs/conf.py b/docs/conf.py
new file mode 100644
index 0000000..62f2656
--- /dev/null
+++ b/docs/conf.py
@@ -0,0 +1,345 @@
+# -*- coding: utf-8 -*-
+#
+# AMP documentation build configuration file, created by
+# sphinx-quickstart on Thu Jul 30 17:27:50 2015.
+#
+# This file is execfile()d with the current directory set to its
+# containing dir.
+#
+# Note that not all possible configuration values are present in this
+# autogenerated file.
+#
+# All configuration values have a default; values that are commented out
+# serve to show the default.
+
+import sys
+import os
+
+# If extensions (or modules to document with autodoc) are in another directory,
+# add these directories to sys.path here. If the directory is relative to the
+# documentation root, use os.path.abspath to make it absolute, like shown here.
+#sys.path.insert(0, os.path.abspath('.'))
+#sys.path.insert(0, os.path.abspath('../'))
+
+# -- General configuration ------------------------------------------------
+
+# If your documentation needs a minimal Sphinx version, state it here.
+#needs_sphinx = '1.0'
+
+# Add any Sphinx extension module names here, as strings. They can be
+# extensions coming with Sphinx (named 'sphinx.ext.*') or your custom
+# ones.
+extensions = [
+ 'sphinx.ext.autodoc',
+ 'sphinx.ext.napoleon',
+ 'sphinx.ext.doctest',
+ 'sphinx.ext.intersphinx',
+ 'sphinx.ext.todo',
+ 'sphinx.ext.coverage',
+ 'sphinx.ext.mathjax',
+ 'sphinx.ext.ifconfig',
+ 'sphinx.ext.viewcode',
+]
+
+# Add any paths that contain templates here, relative to this directory.
+templates_path = ['_templates']
+
+# The suffix of source filenames.
+source_suffix = '.rst'
+
+# The encoding of source files.
+#source_encoding = 'utf-8-sig'
+
+# The master toctree document.
+master_doc = 'index'
+
+# General information about the project.
+project = u'Amp'
+copyright = u'2015--current, Andrew A. Peterson, Alireza Khorshidi'
+
+# The version info for the project you're documenting, acts as replacement for
+# |version| and |release|, also used in various other places throughout the
+# built documents.
+#
+# The short X.Y version.
+version = 'dev'
+# The full version, including alpha/beta/rc tags.
+release = 'development version'
+
+# The language for content autogenerated by Sphinx. Refer to documentation
+# for a list of supported languages.
+#language = None
+
+# There are two options for replacing |today|: either, you set today to some
+# non-false value, then it is used:
+#today = ''
+# Else, today_fmt is used as the format for a strftime call.
+#today_fmt = '%B %d, %Y'
+
+# List of patterns, relative to source directory, that match files and
+# directories to ignore when looking for source files.
+exclude_patterns = []
+
+# The reST default role (used for this markup: `text`) to use for all
+# documents.
+#default_role = None
+
+# If true, '()' will be appended to :func: etc. cross-reference text.
+#add_function_parentheses = True
+
+# If true, the current module name will be prepended to all description
+# unit titles (such as .. function::).
+#add_module_names = True
+
+# If true, sectionauthor and moduleauthor directives will be shown in the
+# output. They are ignored by default.
+#show_authors = False
+
+# The name of the Pygments (syntax highlighting) style to use.
+pygments_style = 'sphinx'
+
+# A list of ignored prefixes for module index sorting.
+#modindex_common_prefix = []
+
+# If true, keep warnings as "system message" paragraphs in the built documents.
+#keep_warnings = False
+
+
+# -- Options for HTML output ----------------------------------------------
+
+# The theme to use for HTML and HTML Help pages. See the documentation for
+# a list of builtin themes.
+html_theme = 'bizstyle'
+
+# Theme options are theme-specific and customize the look and feel of a theme
+# further. For a list of options available for each theme, see the
+# documentation.
+#html_theme_options = {}
+
+# Add any paths that contain custom themes here, relative to this directory.
+#html_theme_path = []
+
+# The name for this set of Sphinx documents. If None, it defaults to
+# "<project> v<release> documentation".
+#html_title = None
+
+# A shorter title for the navigation bar. Default is the same as html_title.
+#html_short_title = None
+
+# The name of an image file (relative to this directory) to place at the top
+# of the sidebar.
+#html_logo = '_static/amp.png'
+html_logo = '_static/amp-logo.svg'
+
+# The name of an image file (within the static path) to use as favicon of the
+# docs. This file should be a Windows icon file (.ico) being 16x16 or 32x32
+# pixels large.
+#html_favicon = None
+
+# Add any paths that contain custom static files (such as style sheets) here,
+# relative to this directory. They are copied after the builtin static files,
+# so a file named "default.css" will overwrite the builtin "default.css".
+html_static_path = ['_static']
+
+# Add any extra paths that contain custom files (such as robots.txt or
+# .htaccess) here, relative to this directory. These files are copied
+# directly to the root of the documentation.
+#html_extra_path = []
+
+# If not '', a 'Last updated on:' timestamp is inserted at every page bottom,
+# using the given strftime format.
+html_last_updated_fmt = '%b %d, %Y'
+#html_last_updated_fmt = '%a, %d %b %Y %H:%M:%S'
+
+# If true, SmartyPants will be used to convert quotes and dashes to
+# typographically correct entities.
+#html_use_smartypants = True
+
+# Custom sidebar templates, maps document names to template names.
+#html_sidebars = {}
+
+# Additional templates that should be rendered to pages, maps page names to
+# template names.
+#html_additional_pages = {}
+
+# If false, no module index is generated.
+#html_domain_indices = True
+
+# If false, no index is generated.
+#html_use_index = True
+
+# If true, the index is split into individual pages for each letter.
+#html_split_index = False
+
+# If true, links to the reST sources are added to the pages.
+#html_show_sourcelink = True
+
+# If true, "Created using Sphinx" is shown in the HTML footer. Default is True.
+#html_show_sphinx = True
+
+# If true, "(C) Copyright ..." is shown in the HTML footer. Default is True.
+#html_show_copyright = True
+
+# If true, an OpenSearch description file will be output, and all pages will
+# contain a <link> tag referring to it. The value of this option must be the
+# base URL from which the finished HTML is served.
+#html_use_opensearch = ''
+
+# This is the file name suffix for HTML files (e.g. ".xhtml").
+#html_file_suffix = None
+
+# Output file base name for HTML help builder.
+htmlhelp_basename = 'Ampdoc'
+
+
+# -- Options for LaTeX output ---------------------------------------------
+
+latex_elements = {
+# The paper size ('letterpaper' or 'a4paper').
+#'papersize': 'letterpaper',
+
+# The font size ('10pt', '11pt' or '12pt').
+#'pointsize': '10pt',
+
+# Additional stuff for the LaTeX preamble.
+#'preamble': '',
+}
+
+# Grouping the document tree into LaTeX files. List of tuples
+# (source start file, target name, title,
+# author, documentclass [howto, manual, or own class]).
+latex_documents = [
+ ('index', 'Amp.tex', u'Amp Documentation',
+ u'Andrew A. Peterson, Alireza Khorshidi', 'manual'),
+]
+
+# The name of an image file (relative to this directory) to place at the top of
+# the title page.
+#latex_logo = None
+
+# For "manual" documents, if this is true, then toplevel headings are parts,
+# not chapters.
+#latex_use_parts = False
+
+# If true, show page references after internal links.
+#latex_show_pagerefs = False
+
+# If true, show URL addresses after external links.
+#latex_show_urls = False
+
+# Documents to append as an appendix to all manuals.
+#latex_appendices = []
+
+# If false, no module index is generated.
+#latex_domain_indices = True
+
+
+# -- Options for manual page output ---------------------------------------
+
+# One entry per manual page. List of tuples
+# (source start file, name, description, authors, manual section).
+man_pages = [
+ ('index', 'amp', u'Amp Documentation',
+ [u'Alireza Khorshidi, Andrew A. Peterson'], 1)
+]
+
+# If true, show URL addresses after external links.
+#man_show_urls = False
+
+
+# -- Options for Texinfo output -------------------------------------------
+
+# Grouping the document tree into Texinfo files. List of tuples
+# (source start file, target name, title, author,
+# dir menu entry, description, category)
+texinfo_documents = [
+ ('index', 'Amp', u'Amp Documentation',
+ u'Andrew A. Peterson, Alireza Khorshidi', 'Amp', 'One line description of project.',
+ 'Miscellaneous'),
+]
+
+# Documents to append as an appendix to all manuals.
+#texinfo_appendices = []
+
+# If false, no module index is generated.
+#texinfo_domain_indices = True
+
+# How to display URL addresses: 'footnote', 'no', or 'inline'.
+#texinfo_show_urls = 'footnote'
+
+# If true, do not generate a @detailmenu in the "Top" node's menu.
+#texinfo_no_detailmenu = False
+
+
+# -- Options for Epub output ----------------------------------------------
+
+# Bibliographic Dublin Core info.
+epub_title = u'Amp'
+epub_author = u'Andrew A. Peterson, Alireza Khorshidi'
+epub_publisher = u'Andrew A. Peterson, Alireza Khorshidi'
+epub_copyright = u'2015--current, Andrew A. Peterson, Alireza Khorshidi'
+
+# The basename for the epub file. It defaults to the project name.
+#epub_basename = u'AMP'
+
+# The HTML theme for the epub output. Since the default themes are not optimized
+# for small screen space, using the same theme for HTML and epub output is
+# usually not wise. This defaults to 'epub', a theme designed to save visual
+# space.
+#epub_theme = 'epub'
+
+# The language of the text. It defaults to the language option
+# or en if the language is not set.
+#epub_language = ''
+
+# The scheme of the identifier. Typical schemes are ISBN or URL.
+#epub_scheme = ''
+
+# The unique identifier of the text. This can be a ISBN number
+# or the project homepage.
+#epub_identifier = ''
+
+# A unique identification for the text.
+#epub_uid = ''
+
+# A tuple containing the cover image and cover page html template filenames.
+#epub_cover = ()
+
+# A sequence of (type, uri, title) tuples for the guide element of content.opf.
+#epub_guide = ()
+
+# HTML files that should be inserted before the pages created by sphinx.
+# The format is a list of tuples containing the path and title.
+#epub_pre_files = []
+
+# HTML files shat should be inserted after the pages created by sphinx.
+# The format is a list of tuples containing the path and title.
+#epub_post_files = []
+
+# A list of files that should not be packed into the epub file.
+epub_exclude_files = ['search.html']
+
+# The depth of the table of contents in toc.ncx.
+#epub_tocdepth = 3
+
+# Allow duplicate toc entries.
+#epub_tocdup = True
+
+# Choose between 'default' and 'includehidden'.
+#epub_tocscope = 'default'
+
+# Fix unsupported image types using the PIL.
+#epub_fix_images = False
+
+# Scale large images.
+#epub_max_image_width = 0
+
+# How to display URL addresses: 'footnote', 'no', or 'inline'.
+#epub_show_urls = 'inline'
+
+# If false, no index is generated.
+#epub_use_index = True
+
+
+# Example configuration for intersphinx: refer to the Python standard library.
+intersphinx_mapping = {'http://docs.python.org/': None}
diff --git a/docs/credits.rst b/docs/credits.rst
new file mode 100644
index 0000000..d0face0
--- /dev/null
+++ b/docs/credits.rst
@@ -0,0 +1,41 @@
+.. Amp documentation master file, created by
+ sphinx-quickstart on Thu Jul 30 17:27:50 2015.
+ You can adapt this file completely to your liking, but it should at least
+ contain the root `toctree` directive.
+
+Credits
+=======
+
+People
+------
+
+This project is developed primarily by **Andrew Peterson** and **Alireza Khorshidi** in the Brown University School of Engineering. Specific credits:
+
+* Andrew Peterson: lead, PI, many modules
+* Alireza Khorshidi: many modules, Zernike descriptor
+* Zack Ulissi: tensorflow version of neural network
+* Muammar El Khatib: general contributions
+
+We are also indebted to Nongnuch Artrith (MIT) and Pedro Felzenszwalb (Brown) for inspiration and technical discussion.
+
+Citations
+---------
+
+We would appreciate if you cite the below publication for any use of Amp or its methods:
+
+ Khorshidi & Peterson, "Amp: A modular approach to machine learning in atomistic simulations", *Computer Physics Communications* 207:310-324, 2016. |amp_paper|
+
+
+.. |amp_paper| raw:: html
+
+ <a href="http://dx.doi.org/10.1016/j.cpc.2016.05.010" target="_blank">[doi:10.1016/j.cpc.2016.05.010] </a>
+
+
+If you use Amp for saddle-point searches or nudged elastic bands, please also cite:
+
+ Peterson, "Acceleration of saddle-point searches with machine learning", *Journal of Chemical Physics*, 145:074106, 2016. |mlneb_paper|
+
+
+.. |mlneb_paper| raw:: html
+
+ <a href="http://dx.doi.org/10.1063/1.4960708" target="_blank">[DOI:10.1063/1.4960708] </a>
diff --git a/docs/databases.rst b/docs/databases.rst
new file mode 100644
index 0000000..9035e36
--- /dev/null
+++ b/docs/databases.rst
@@ -0,0 +1,49 @@
+.. _Databases:
+
+==================================
+Fingerprint databases
+==================================
+
+Often, a user will want to train multiple calculators to a common set of images. This may be just in routine development of a trained calculator (e.g., trying different neural network sizes), in using multiple training instances trying to find a good initial guess of parameters, or in making a committee of calculators. In this case, it can be a waste of computational time to calculate the fingerprints (and more expensively, the fingerprint derivatives) more than once.
+
+To deal with this, Amp saves the fingerprints to a database, the location of which can be specified by the user. If you want multiple calculators to avoid re-fingerprinting the same images, just point them to the same database location.
+
+
+Format
+---------------------------------
+
+The database format is custom for Amp, and is designed to be as simple as possible.
+Amp databases end in the extension `.ampdb`.
+In its simplest form, it is just a directory with one file per image; that is, you will see something like below::
+
+ label-fingerprints.ampdb/
+ loose/
+ f60b3324f6001d810afbab9f85a6ea5f
+ aeaaa21e5faccc62bae94c5c48b04031
+
+In the above, each file in the directory "loose" is the hash of an image, and contains that image's fingerprint. We use a file-based "database" to avoid conflicts with multiple processes accessing a database at the same time, which can cause conflicts.
+
+However, for large training sets this can lead to lots of loose files, which can eat up a lot of memory, and with the large number of files slow down indexing jobs (like backups and scans). Therefore, you can compress the database with the `amp-compress` tool, described below.
+
+Compress
+---------------------------------
+
+To save disk space, you may periodically want to run the utility `amp-compress` (contained in the `tools` directory of the amp package; this should be on your path for normal installations). In this case, you would run `amp-compress <filename>`, which would result in the above `.ampdb` file being changed to::
+
+ label-fingerprints.ampdb/
+ archive.tar.gz
+ loose/
+
+That is, the two fingerprints that were in the "loose" directory are now in the file "archive.tar.gz".
+
+You can also use the `--recursive` (or `-r`) flag to compress all ampdb files in or below the specified directory.
+
+When Amp reads from the above database, it first looks in the "loose" directory for the fingerprint. If it is not there, it looks in "archive.tar.gz". If it is not there, it calculates the fingerprint and adds it to the "loose" directory.
+
+
+Future
+---------------------------------
+
+We plan to make the amp-compress tool more automated.
+If the user does not supply a separate `dblabel` keyword, then we assume that their process is the only process using the database, and it is safe to compress the database at the end of their training job.
+This would automatically clean up the loose files at the end of the job.
diff --git a/docs/develop.rst b/docs/develop.rst
new file mode 100644
index 0000000..0b5dbe6
--- /dev/null
+++ b/docs/develop.rst
@@ -0,0 +1,91 @@
+.. _Develop:
+
+==================================
+Development
+==================================
+
+This page contains standard practices for developing Amp, focusing on repositories and documentation.
+
+----------------------------------
+Repositories and branching
+----------------------------------
+
+The main Amp repository lives on bitbucket, `andrewpeterson/amp <https://bitbucket.org/andrewpeterson/amp>`_ .
+We employ a branching model where the `master` branch is the main development branch, containing day-to-day commits from the core developers and honoring merge requests from others.
+From time to time, we create a new branch that corresponds to a release.
+This release branch contains only the tagged release and any bug fixes.
+
+ .. image:: _static/branches.svg
+ :width: 400 px
+ :align: center
+
+
+----------------------------------
+Contributing
+----------------------------------
+
+You are welcome to contribute new features, bug fixes, better documentation, etc. to Amp.
+If you would like to contribute, please create a private fork and a branch for your new commits.
+When it is ready, send us a merge request.
+We follow the same basic model as ASE; please see the ASE documentation for complete instructions.
+
+As good coding practice, make sure your code passes both the pyflakes and pep8 tests.
+(On linux, you should be able to run `pyflakes file.py` and `pep8 file.py`, and then correct it by `autopep8 --in-place file.py`.)
+If adding a new feature: consider adding a (very brief) test to the tests folder to ensure your new code continues to work, and also be sure to write clear documentation.
+Finally, to make users aware of your new feature or change, add a bullet point to the release notes page of the documentation under the Development version heading.
+
+It is also a good idea to send us an email if you are planning something complicated.
+
+----------------------------------
+Documentation
+----------------------------------
+
+This documentation is built with sphinx.
+(Mkdocs doesn't seem to support autodocumentation.)
+To build a local copy, cd into the docs directory and try a command such as
+
+.. code-block:: bash
+
+ sphinx-build . /tmp/ampdocs
+ firefox /tmp/ampdocs/index.html & # View the local copy.
+
+This uses the style "bizstyle"; if you find this is missing on your system, you can likely install it with
+
+.. code-block:: bash
+
+ pip install --user sphinxjp.themes.bizstyle
+
+
+You should then be able to update the documentation rst files and see changes on your own machine.
+For line breaks, please use the style of containing each sentence on a new line.
+
+----------------------------------
+Releases
+----------------------------------
+
+To create a release, we go through the following steps.
+
+* Create a new branch on the bitbucket repository with the version name, as in `v0.5`.
+ (Don't create a separate branch if this is a bugfix release, e.g., 0.5.1 --- just add those to the v0.5 branch.)
+ All subsequent work is in the new branch.
+ Note the branch name starts with "v", while the tag names will not, to avoid naming conflicts.
+
+* Change `docs/conf.py`'s version information to match the new version number.
+
+* Change the version that prints out in the Amp headers by changing the `_ampversion` variable in `amp/__init__.py`.
+
+* Change revision history to include this release; generally the changes should have been catalogued under a "Development version" heading.
+
+* Commit and push the changes to the new branch on bitbucket.
+
+* Tag the release with the release number, e.g., '0.5' or '0.5.1', the latter being for bug fixes.
+ Do this on a local machine (on the correct branch) with `git tag -a 0.5`, followed by `git push origin --tags`.
+
+* Add the version to readthedocs' available versions; also set it as the default stable version.
+
+* Change the nightly tests to test this branch as the "stable" build.
+
+* Create a DOI for the release via zenodo.org.
+ Note that all the ".git" files and folders should be removed from the files before uploading to Zenodo.
+ The DOI can then be added to the development version's release notes.
+ (I don't think there's a way to get it into the archival version on Zenodo!)
diff --git a/docs/examplescripts.rst b/docs/examplescripts.rst
new file mode 100644
index 0000000..bb31b69
--- /dev/null
+++ b/docs/examplescripts.rst
@@ -0,0 +1,185 @@
+.. _ExampleScripts:
+
+
+==================================
+Example scripts
+==================================
+
+----------------------------------
+A basic fitting script
+----------------------------------
+
+The below script uses Gaussian descriptors with a neural network backend --- the Behler-Parrinello approach --- to train energies only to a training set made by the script. Note that most of the code is just generating the training data, and the training takes place in a couple of lines.
+
+
+.. code-block:: python
+
+ """Simple test of the Amp calculator, using Gaussian descriptors and neural
+ network model. Randomly generates data with the EMT potential in MD
+ simulations."""
+
+ import os
+ from ase import Atoms, Atom, units
+ import ase.io
+ from ase.calculators.emt import EMT
+ from ase.lattice.surface import fcc110
+ from ase.md.velocitydistribution import MaxwellBoltzmannDistribution
+ from ase.md import VelocityVerlet
+ from ase.constraints import FixAtoms
+
+ from amp import Amp
+ from amp.descriptor.gaussian import Gaussian
+ from amp.model.neuralnetwork import NeuralNetwork
+
+
+ def generate_data(count, filename='training.traj'):
+ """Generates test or training data with a simple MD simulation."""
+ if os.path.exists(filename):
+ return
+ traj = ase.io.Trajectory(filename, 'w')
+ atoms = fcc110('Pt', (2, 2, 2), vacuum=7.)
+ atoms.extend(Atoms([Atom('Cu', atoms[7].position + (0., 0., 2.5)),
+ Atom('Cu', atoms[7].position + (0., 0., 5.))]))
+ atoms.set_constraint(FixAtoms(indices=[0, 2]))
+ atoms.set_calculator(EMT())
+ atoms.get_potential_energy()
+ traj.write(atoms)
+ MaxwellBoltzmannDistribution(atoms, 300. * units.kB)
+ dyn = VelocityVerlet(atoms, dt=1. * units.fs)
+ for step in range(count - 1):
+ dyn.run(50)
+ traj.write(atoms)
+
+
+ generate_data(20)
+
+ calc = Amp(descriptor=Gaussian(),
+ model=NeuralNetwork(hiddenlayers=(10, 10, 10)))
+ calc.train(images='training.traj')
+
+
+Note you can monitor the progress of the training by typing `amp-plotconvergence amp-log.txt`, which will create a file called `convergence.pdf`.
+
+
+----------------------------------
+A basic script with forces
+----------------------------------
+
+The below script trains both energy and forces to the same training set as above. Note this may take some time to run, which will depend upon the initial guess for the neural network parameters that is randomly generated. Try decreasing the `force_rmse` convergence parameter if you would like faster results.
+
+
+.. code-block:: python
+
+ """Simple test of the Amp calculator, using Gaussian descriptors and neural
+ network model. Randomly generates data with the EMT potential in MD
+ simulations."""
+
+ import os
+ from ase import Atoms, Atom, units
+ import ase.io
+ from ase.calculators.emt import EMT
+ from ase.lattice.surface import fcc110
+ from ase.md.velocitydistribution import MaxwellBoltzmannDistribution
+ from ase.md import VelocityVerlet
+ from ase.constraints import FixAtoms
+
+ from amp import Amp
+ from amp.descriptor.gaussian import Gaussian
+ from amp.model.neuralnetwork import NeuralNetwork
+ from amp.model import LossFunction
+
+
+ def generate_data(count, filename='training.traj'):
+ """Generates test or training data with a simple MD simulation."""
+ if os.path.exists(filename):
+ return
+ traj = ase.io.Trajectory(filename, 'w')
+ atoms = fcc110('Pt', (2, 2, 2), vacuum=7.)
+ atoms.extend(Atoms([Atom('Cu', atoms[7].position + (0., 0., 2.5)),
+ Atom('Cu', atoms[7].position + (0., 0., 5.))]))
+ atoms.set_constraint(FixAtoms(indices=[0, 2]))
+ atoms.set_calculator(EMT())
+ atoms.get_potential_energy()
+ traj.write(atoms)
+ MaxwellBoltzmannDistribution(atoms, 300. * units.kB)
+ dyn = VelocityVerlet(atoms, dt=1. * units.fs)
+ for step in range(count - 1):
+ dyn.run(50)
+ traj.write(atoms)
+
+
+ generate_data(20)
+
+ calc = Amp(descriptor=Gaussian(),
+ model=NeuralNetwork(hiddenlayers=(10, 10, 10)))
+ calc.model.lossfunction = LossFunction(convergence={'energy_rmse': 0.02,
+ 'force_rmse': 0.02})
+ calc.train(images='training.traj')
+
+
+Note you can monitor the progress of the training by typing `amp-plotconvergence amp-log.txt`, which will create a file called `convergence.pdf`.
+
+
+
+----------------------------------
+Examining fingerprints
+----------------------------------
+
+With the modular nature, it's straightforward to analyze how fingerprints change with changes in images.
+The below script makes an animated GIF that shows how a fingerprint about the O atom in water changes as one of the O-H bonds is stretched.
+Note that most of the lines of code below are either making the atoms or making the figure; very little effort is needed to produce the fingerprints themselves---this is done in three lines.
+
+.. code-block:: python
+
+ # Make a series of images.
+ import numpy as np
+ from ase.structure import molecule
+ from ase import Atoms
+ atoms = molecule('H2O')
+ atoms.rotate('y', -np.pi/2.)
+ atoms.set_pbc(False)
+ displacements = np.linspace(0.9, 8.0, 20)
+ vec = atoms[2].position - atoms[0].position
+ images = []
+ for displacement in displacements:
+ atoms = Atoms(atoms)
+ atoms[2].position = (atoms[0].position + vec * displacement)
+ images.append(atoms)
+
+ # Fingerprint using Amp.
+ from amp.descriptor.gaussian import Gaussian
+ descriptor = Gaussian()
+ from amp.utilities import hash_images
+ images = hash_images(images, ordered=True)
+ descriptor.calculate_fingerprints(images)
+
+ # Plot the data.
+ from matplotlib import pyplot
+
+ def barplot(hash, name, title):
+ """Makes a barplot of the fingerprint about the O atom."""
+ fp = descriptor.fingerprints[hash][0]
+ fig, ax = pyplot.subplots()
+ ax.bar(range(len(fp[1])), fp[1])
+ ax.set_title(title)
+ ax.set_ylim(0., 2.)
+ ax.set_xlabel('fingerprint')
+ ax.set_ylabel('value')
+ fig.savefig(name)
+
+ for index, hash in enumerate(images.keys()):
+ barplot(hash, 'bplot-%02i.png' % index,
+ '%.2f$\\times$ equilibrium O-H bondlength'
+ % displacements[index])
+
+ # For fun, make an animated gif.
+ import os
+ filenames = ['bplot-%02i.png' % index for index in range(len(images))]
+ command = ('convert -delay 100 %s -loop 0 animation.gif' %
+ ' '.join(filenames))
+ os.system(command)
+
+
+.. image:: _static/animation.gif
+ :width: 600 px
+ :align: center
diff --git a/docs/gaussian.rst b/docs/gaussian.rst
new file mode 100644
index 0000000..abbe4be
--- /dev/null
+++ b/docs/gaussian.rst
@@ -0,0 +1,34 @@
+.. _Gaussian:
+
+
+Gaussian descriptor
+===================
+
+Custom parameters
+-----------------
+
+The Gaussian descriptor creates feature vectors based on the Behler scheme, and defaults to values used in Nano Letters 14:2670, 2014. You can specify custom parameters for the elements of the feature vectors as listed in the documentation of the :class:`~amp.descriptor.gaussian.Gaussian` class.
+
+There is also a helper function :func:`~amp.descriptor.gaussian.make_symmetry_functions` within the :mod:`amp.descriptor.gaussian` module to assist with this. An example of making a custom fingerprint is given below for a two-element system.
+
+.. code-block:: python
+
+ import numpy as np
+ from amp import Amp
+ from amp.descriptor.gaussian import Gaussian, make_symmetry_functions
+ from amp.model.neuralnetwork import NeuralNetwork
+
+ elements = ['Cu', 'Pt']
+ G = make_symmetry_functions(elements=elements, type='G2',
+ etas=np.logspace(np.log10(0.05), np.log10(80.),
+ num=4))
+ G += make_symmetry_functions(elements=elements, type='G4',
+ etas=[0.005],
+ zetas=[1., 4.],
+ gammas=[+1., -1.])
+
+ G = {'Cu': G,
+ 'Pt': G}
+ calc = Amp(descriptor=Gaussian(Gs=G),
+ model=NeuralNetwork())
+
diff --git a/docs/index.rst b/docs/index.rst
new file mode 100644
index 0000000..cee59ba
--- /dev/null
+++ b/docs/index.rst
@@ -0,0 +1,70 @@
+.. Amp documentation master file, created by
+ sphinx-quickstart on Thu Jul 30 17:27:50 2015.
+ You can adapt this file completely to your liking, but it should at least
+ contain the root `toctree` directive.
+
+Amp: Atomistic Machine-learning Package
+=======================================
+
+Amp is an open-source package designed to easily bring machine-learning to atomistic calculations.
+This project is being developed at Brown University in the School of Engineering, primarily by **Andrew Peterson** and **Alireza Khorshidi**, and is released under the GNU General Public License.
+
+The latest stable release of Amp is version 0.5, released on February 24, 2017; see the :ref:`ReleaseNotes` page for a download link.
+Please see the project's `git repository <https://bitbucket.org/andrewpeterson/amp>`_ for the latest development version or a place to report an issue.
+
+You can read about Amp in the below paper; if you find this project useful, we would appreciate if you cite this work:
+
+ Khorshidi & Peterson, "Amp: A modular approach to machine learning in atomistic simulations", *Computer Physics Communications* 207:310-324, 2016. |amp_paper|
+
+
+.. |amp_paper| raw:: html
+
+ <a href="http://dx.doi.org/10.1016/j.cpc.2016.05.010" target="_blank">DOI:10.1016/j.cpc.2016.05.010</a>
+
+**News**:
+
+An amp-users mailing list has been started, for general discussions about the use and development of Amp. You can subscribe via listserv at:
+
+https://listserv.brown.edu/?A0=AMP-USERS
+
+**Manual**:
+
+.. toctree::
+ :maxdepth: 1
+
+ introduction.rst
+ installation.rst
+ useamp.rst
+ community.rst
+ theory.rst
+ credits.rst
+ releasenotes.rst
+ examplescripts.rst
+ analysis.rst
+ building.rst
+ moredescriptor.rst
+ moremodel.rst
+ gaussian.rst
+ tensorflow.rst
+ databases.rst
+ develop.rst
+
+**Module autodocumentation**:
+
+.. toctree::
+ :maxdepth: 1
+
+ modules/main.rst
+ modules/descriptor.rst
+ modules/model.rst
+ modules/regression.rst
+ modules/utilities.rst
+ modules/analysis.rst
+
+
+**Indices and tables**
+
+* :ref:`genindex`
+* :ref:`modindex`
+* :ref:`search`
+
diff --git a/docs/installation.rst b/docs/installation.rst
new file mode 100644
index 0000000..8d21555
--- /dev/null
+++ b/docs/installation.rst
@@ -0,0 +1,142 @@
+.. _install:
+
+==================================
+Installation
+==================================
+
+AMP is python-based and is designed to integrate closely with the `Atomic Simulation Environment <https://wiki.fysik.dtu.dk/ase/>`_ (ASE).
+In its most basic form, it has few requirements:
+
+* Python, version 2.7 is recommended (it also supports Python3).
+* ASE.
+* NumPy.
+* SciPy.
+
+To get more features, such as parallelization in training, a few more packages are recommended:
+
+* Pexpect (or pxssh)
+* ZMQ (or PyZMQ, the python version of ØMQ).
+
+Certain advanced modules may contain dependencies that will be noted when they are used; for example Tensorflow for the tflow module or matplotlib for the plotting modules.
+
+Basic installation instructions follow.
+
+----------------------------------
+Install ASE
+----------------------------------
+
+We always test against the latest version (svn checkout) of ASE, but slightly older versions (>=3.9) are likely to work as well.
+Follow the instructions at the `ASE <https://wiki.fysik.dtu.dk/ase/download.html>`_ website.
+ASE itself depends upon python with the standard numeric and scientific packages.
+Verify that you have working versions of `NumPy <http://numpy.org>`_ and `SciPy <http://scipy.org>`_.
+We also recommend `matplotlib <http://matplotlib.org>`_ in order to generate plots.
+
+----------------------------------
+Get the code
+----------------------------------
+
+The latest stable release of Amp is version 0.5, which is permanently available at `https://doi.org/10.5281/zenodo.322427 <https://doi.org/10.5281/zenodo.322427>`_.
+If installing version 0.5, you should follow ignore the rest of this page and follow the instructions included with the download (see docs/installation.rst or look for v0.5 on `http://amp.readthedocs.io <http://amp.readthedocs.io>`_).
+
+We are constantly improving *Amp* and adding features, so depending on your needs it may be preferable to use the development version rather than "stable" releases.
+We run daily unit tests to try to make sure that our development code works as intended.
+We recommend checking out the latest version of the code via `the project's bitbucket page <https://bitbucket.org/andrewpeterson/amp/>`_.
+If you use git, check out the code with::
+
+ $ cd ~/path/to/my/codes
+ $ git clone git at bitbucket.org:andrewpeterson/amp.git
+
+where you should replace '~/path/to/my/codes' with wherever you would like the code to be located on your computer.
+If you do not use git, just download the code as a zip file from the project's `download <https://bitbucket.org/andrewpeterson/amp/downloads>`_ page, and extract it into '~/path/to/my/codes'.
+Please make sure that the folder '~/path/to/my/codes/amp' includes subdirectories 'amp', 'docs', 'tests', and 'tools'.
+
+----------------------------------
+Set the environment
+----------------------------------
+
+You need to let your python version know about the existence of the amp module. Add the following line to your '.bashrc'
+(or other appropriate spot), with the appropriate path substituted for '~/path/to/my/codes'::
+
+ $ export PYTHONPATH=~/path/to/my/codes/amp:$PYTHONPATH
+
+You can check that this works by starting python and typing the below command, verifying that the location listed from
+the second command is where you expect::
+
+ >>> import amp
+ >>> print(amp.__file__)
+
+See also the section on parallel processing for any issues that arise in making the environment work with Amp in parallel.
+
+---------------------------------------
+Recommended step: Build fortran modules
+---------------------------------------
+
+Amp works in pure python, however, it will be annoyingly slow unless the associated Fortran 90 modules are compiled to speed up several parts of the code.
+The compilation of the Fortran 90 code and integration with the python parts is accomplished with f2py, which is part of NumPy.
+A Fortran 90 compiler will also be necessary on the system; a reasonable open-source option is GNU Fortran, or gfortran.
+This compiler will generate Fortran modules (.mod).
+gfortran will also be used by f2py to generate extension module fmodules.so on Linux or fmodules.pyd on Windows.
+We have included a `Make` file that automatizes the building of Fortran modules.
+To use it, install `GNU Makefile <https://www.gnu.org/software/make/>`_
+on your Linux distribution or macOS.
+For Python2, then simply do::
+
+ $ cd <installation-directory>/amp/
+ $ make python2
+
+For Python3::
+
+ $ cd <installation-directory>/amp/
+ $ make python3
+
+If you do not have the GNU Makefile installed, you can prepare the Fortran extension modules manually in the following steps:
+
+1. Compile model Fortran subroutines inside the model and descriptor folders by::
+
+ $ cd <installation-directory>/amp/model
+
+ $ gfortran -c neuralnetwork.f90
+
+ $ cd ../descriptor
+
+ $ gfortran -c cutoffs.f90
+
+
+2. Move the modules "neuralnetwork.mod" and "cutoffs.mod" created in the last step, to the parent directory by::
+
+ $ cd ..
+
+ $ mv model/neuralnetwork.mod .
+
+ $ mv descriptor/cutoffs.mod .
+
+3. Compile the model Fortran subroutines in companion with the descriptor and neuralnetwork subroutines by something like::
+
+ $ f2py -c -m fmodules model.f90 descriptor/cutoffs.f90 descriptor/gaussian.f90 descriptor/zernike.f90 model/neuralnetwork.f90
+
+Note that for Python3, you need to use `f2py3` instead of `f2py`.
+
+or on a Windows machine by::
+
+ $ f2py -c -m fmodules model.f90 descriptor/cutoffs.f90 descriptor/gaussian.f90 descriptor/zernike.f90 model/neuralnetwork.f90 --fcompiler=gnu95 --compiler=mingw32
+
+Note that if you update your code (e.g., with 'git pull origin master') and the fortran code changes but your version of fmodules.f90 is not updated, an exception will be raised telling you to re-compile your fortran modules.
+
+----------------------------------
+Recommended step: Run the tests
+----------------------------------
+
+We include tests in the package to ensure that it still runs as intended as we continue our development; we run these
+tests on the latest build every night to try to keep bugs out. It is a good idea to run these tests after you install the
+package to see if your installation is working. The tests are in the folder `tests`; they are designed to run with
+`nose <https://nose.readthedocs.org/>`_.
+If you have nose and GNU Makefile installed, simply do::
+
+ $ make py2tests (for Python2)
+ $ make py3tests (for Python3)
+
+Otherwise, if you have only nose installed (and not GNU Makefile), run the commands below::
+
+ $ mkdir /tmp/amptests
+ $ cd /tmp/amptests
+ $ nosetests ~/path/to/my/codes/amp/tests
diff --git a/docs/introduction.rst b/docs/introduction.rst
new file mode 100644
index 0000000..999dce3
--- /dev/null
+++ b/docs/introduction.rst
@@ -0,0 +1,18 @@
+.. _introduction:
+
+==================================
+Introduction
+==================================
+
+Amp is an open-source package designed to easily bring machine-learning to atomistic calculations.
+This allows one to predict (or really, interpolate) calculations on the potential energy surface,
+by first building up a regression representation from a "training set" of atomic images.
+The Amp calculator works by first
+learning from any other calculator (usually quantum mechanical calculations) that can provide energy and forces as a
+function of atomic coordinates.
+Depending upon the model choice, the predictions from Amp can take place with arbitrary accuracy, approaching that of the original calculator.
+
+Amp is designed to integrate closely with the `Atomic Simulation Environment <https://wiki.fysik.dtu.dk/ase/>`_ (ASE).
+As such, the interface is in pure python, although several compute-heavy parts of the underlying codes also have fortran
+versions to accelerate the calculations. The close integration with ASE means that any calculator that works with ASE
+- including EMT, GPAW, DACAPO, VASP, NWChem, and Gaussian - can easily be used as the parent method.
diff --git a/docs/modules/analysis.rst b/docs/modules/analysis.rst
new file mode 100644
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+++ b/docs/modules/analysis.rst
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+Analysis
+==============
+
+Tools for analysis of output exist here.
+
+
+Module contents
+---------------
+
+.. automodule:: amp.analysis
+ :members:
+ :undoc-members:
+ :show-inheritance:
diff --git a/docs/modules/descriptor.rst b/docs/modules/descriptor.rst
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index 0000000..e7a08ec
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+++ b/docs/modules/descriptor.rst
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+Descriptor
+==============
+
+The descriptor module contains methods for describing the local atomic environment; that is, feature fectors that can be fed to machine-learning modules.
+
+
+Gaussian
+--------
+
+.. automodule:: amp.descriptor.gaussian
+ :members:
+ :undoc-members:
+ :show-inheritance:
+
+Zernike
+-------
+
+.. automodule:: amp.descriptor.zernike
+ :members:
+ :undoc-members:
+ :show-inheritance:
+
+Bispectrum
+----------
+
+.. automodule:: amp.descriptor.bispectrum
+ :members:
+ :undoc-members:
+ :show-inheritance:
+
+Cutoff functions
+----------------
+
+.. automodule:: amp.descriptor.cutoffs
+ :members:
+ :undoc-members:
+ :show-inheritance:
diff --git a/docs/modules/main.rst b/docs/modules/main.rst
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--- /dev/null
+++ b/docs/modules/main.rst
@@ -0,0 +1,13 @@
+Main
+==============
+
+This module is the main part of the Amp package.
+
+
+Module contents
+---------------
+
+.. automodule:: amp
+ :members:
+ :undoc-members:
+ :show-inheritance:
diff --git a/docs/modules/model.rst b/docs/modules/model.rst
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+++ b/docs/modules/model.rst
@@ -0,0 +1,34 @@
+Model
+=====
+
+This module is designed to include machine-learning models for interpolating
+energies and forces from either an atom-centered or image-centered fingerprint
+description.
+
+
+Model
+-----
+
+.. automodule:: amp.model
+ :members:
+ :undoc-members:
+ :show-inheritance:
+
+Neural Network
+--------------
+
+.. automodule:: amp.model.neuralnetwork
+ :members:
+ :undoc-members:
+ :show-inheritance:
+
+Tensorflow Neural Network
+-------------------------
+
+A work in progress, this module `amp.model.tflow` uses Google's TensorFlow package to implement a neural network, which may provide GPU acceleration and other advantages.
+
+.. automodule:: amp.model.tflow
+ :members:
+ :undoc-members:
+ :show-inheritance:
+
diff --git a/docs/modules/regression.rst b/docs/modules/regression.rst
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--- /dev/null
+++ b/docs/modules/regression.rst
@@ -0,0 +1,13 @@
+Regression
+==============
+
+This module includes a regressor object used to optimize the parameters of the machine-learning model.
+
+
+Module contents
+---------------
+
+.. automodule:: amp.regression
+ :members:
+ :undoc-members:
+ :show-inheritance:
diff --git a/docs/modules/utilities.rst b/docs/modules/utilities.rst
new file mode 100644
index 0000000..689d7b3
--- /dev/null
+++ b/docs/modules/utilities.rst
@@ -0,0 +1,14 @@
+Utilities
+==============
+
+This module contains utilities for use with various aspects of the Amp
+calculator.
+
+
+Module contents
+---------------
+
+.. automodule:: amp.utilities
+ :members:
+ :undoc-members:
+ :show-inheritance:
diff --git a/docs/moredescriptor.rst b/docs/moredescriptor.rst
new file mode 100644
index 0000000..99d361c
--- /dev/null
+++ b/docs/moredescriptor.rst
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+.. _MoreDescriptor:
+
+
+==================================
+More on descriptors
+==================================
+
+
+----------------------------------
+Fingerprint ranges
+----------------------------------
+
+It is often useful to examine your fingerprints more closely. There is a utility that can help with that, an example of its use is below. This assumes you have open a calculator called "calc.amp" and you want to examine the fingerprint ranges for your training data.
+
+.. code-block:: python
+
+
+ from ase import io
+ from amp.descriptor.analysis import FingerprintPlot
+ from amp import Amp
+
+ calc = Amp.load('calc.amp')
+ images = io.read('training.traj', index=':')
+
+ fpplot = FingerprintPlot(calc)
+ fpplot(images)
+
+This will create a plot that looks something like below, here showing the fingerprint ranges for the specified element.
+
+.. image:: _static/fpranges.svg
+ :width: 1000 px
+ :align: center
+
+You can also overlay a specific image's fingerprint on to the fingerprint plot by using the `overlay` keyword when calling fpplot.
diff --git a/docs/moremodel.rst b/docs/moremodel.rst
new file mode 100644
index 0000000..550cfcb
--- /dev/null
+++ b/docs/moremodel.rst
@@ -0,0 +1,41 @@
+.. _MoreModel:
+
+
+==================================
+More on models
+==================================
+
+Visualizing neural network outputs
+----------------------------------
+
+It can be useful to visualize the neural network model to see how it is behaving. For example, you may find nodes that are effectively shut off (e.g., always giving a constant value like 1) or that are acting as a binary switch (e.g., only returning 1 or -1). There is a tool to allow you to visualize the node outputs of a set of data.
+
+.. code-block:: python
+
+ from amp.model.neuralnetwork import NodePlot
+
+ nodeplot = NodePlot(calc)
+ nodeplot.plot(images, filename='nodeplottest.pdf')
+
+
+This will create a plot that looks something like below. Note that one such series of plots is made for each element. Here, Layer 0 is the input layer, from the fingerprints. Layer 1 and Layer 2 are the hidden layers. Layer 3 is the output layer; that is, the contribution of Pt to the potential energy (before it is multiplied by and added to a parameter to bring it to the correct magnitude).
+
+.. image:: _static/nodeplot-Pt.svg
+ :width: 1000 px
+ :align: center
+
+Calling an observer during training
+-----------------------------------
+It can be useful to call a function known as an "observer" during the training of the model. In the neural network implementation, this can be accomplished by attaching an observer directly to the model. The observer is executed at each call to `model.get_loss`, and is fed the arguments (self, vector, loss). An example of using the observer to print out one component of the parameter vector is shown below:
+
+
+.. code-block:: python
+
+ def observer(model, vector, loss):
+ """Prints out the first component of the parameter vector."""
+ print(vector[0])
+
+ calc.model.observer = observer
+ calc.train(images)
+
+With this approach, all kinds of fancy tricks are possible, like calling *another* Amp model that reports the loss function on a test set of images. This could be useful to implement training with early stopping, for example.
diff --git a/docs/releasenotes.rst b/docs/releasenotes.rst
new file mode 100644
index 0000000..73aa941
--- /dev/null
+++ b/docs/releasenotes.rst
@@ -0,0 +1,65 @@
+.. _ReleaseNotes:
+
+Release notes
+=============
+
+Development version
+-------------------
+
+(Significant changes since the last release are itemized here.)
+
+* A community page has been added with resources such as the new mailing list and issue tracker.
+* The default convergence parameters have been changed to energy-only training; force-training can be added by the user via the loss function.
+* Convergence plots show maximum residuals as well as root mean-squared error.
+* Parameters to make the Gaussian feature vectors are now output to the log file.
+* The helper function :func:`~amp.descriptor.gaussian.make_symmetry_functions` has been added to more easily customize Gaussian fingerprint parameters.
+* Amp has been ported to Python 3. The only module that is not yet ported is TensorFlow.
+
+0.5
+---
+Release date: February 24, 2017
+
+The code has been significantly restructured since the previous version, in order to increase the modularity; much of the code structure has been changed since v0.4. Specific changes below:
+
+* A parallelization scheme allowing for fast message passing with ZeroMQ.
+* A simpler database format based on files, which optionally can be compressed to save diskspace.
+* Incorporation of an experimental neural network model based on google's TensorFlow package. Requires TensorFlow version 0.11.0.
+* Incorporation of an experimental bootstrap module for uncertainty analysis.
+
+Permanently available at https://doi.org/10.5281/zenodo.322427
+
+0.4
+---
+Release date: February 29, 2016
+
+Corresponds to the publication of Khorshidi, A; Peterson*, AA. Amp: a modular approach to machine learning in atomistic simulations. Computer Physics Communications 207:310-324, 2016. http://dx.doi.org/10.1016/j.cpc.2016.05.010
+
+Permanently available at https://doi.org/10.5281/zenodo.46737
+
+0.3
+---
+Release date: July 13, 2015
+
+First release under the new name "Amp" (Atomistic Machine-Learning Package/Potentials).
+
+Permanently available at https://doi.org/10.5281/zenodo.20636
+
+
+0.2
+---
+Release date: July 13, 2015
+
+Last version under the name "Neural: Machine-learning for Atomistics". Future versions are named "Amp".
+
+Available as the v0.2 tag in https://bitbucket.org/andrewpeterson/neural/commits/tag/v0.2
+
+
+0.1
+---
+Release date: November 12, 2014
+
+(Package name: Neural: Machine-Learning for Atomistics)
+
+Permanently available at https://doi.org/10.5281/zenodo.12665.
+
+First public bitbucket release: September, 2014.
diff --git a/docs/tensorflow.rst b/docs/tensorflow.rst
new file mode 100644
index 0000000..844d7e6
--- /dev/null
+++ b/docs/tensorflow.rst
@@ -0,0 +1,106 @@
+.. _TensorFlow:
+
+==================================
+TensorFlow
+==================================
+
+Google has released an open-source version of its machine-learning software named Tensorflow, which can allow for efficient backpropagation of neural networks and utilization of GPUs for extra speed.
+
+We have incorporated an experimental module that uses a tensorflow back-end, which may provide an acceleration particularly through access to GPU systems.
+As of this writing, the tensorflow code is in flux (with version 1.0 anticipated shortly).
+
+
+Dependencies
+---------------------------------
+
+This package requires google's TensorFlow 0.11.0. You can install it as shown
+below for Linux::
+
+ export TF_BINARY_URL=https://storage.googleapis.com/tensorflow/linux/cpu/tensorflow-0.11.0-cp27-none-linux_x86_64.whl
+ pip install -U --upgrade $TF_BINARY_URL
+
+or macOS::
+
+ export TF_BINARY_URL=https://storage.googleapis.com/tensorflow/mac/cpu/tensorflow-0.11.0-py2-none-any.whl
+ pip install -U --upgrade $TF_BINARY_URL
+
+If you want more information, please see `tensorflow's website <https://www.tensorflow.org/versions/r0.11/get_started/os_setup#pip_installation>`_ for instructions
+for installation on your system.
+
+Example
+---------------------------------
+
+.. code-block:: python
+
+ #!/usr/bin/env python
+ """Simple test of the Amp calculator, using Gaussian descriptors and neural
+ network model. Randomly generates data with the EMT potential in MD
+ simulations."""
+
+ from ase.calculators.emt import EMT
+ from ase.lattice.surface import fcc110
+ from ase import Atoms, Atom
+ from ase.md.velocitydistribution import MaxwellBoltzmannDistribution
+ from ase import units
+ from ase.md import VelocityVerlet
+ from ase.constraints import FixAtoms
+
+ from amp import Amp
+ from amp.descriptor.gaussian import Gaussian
+ from amp.model.tflow import NeuralNetwork
+
+
+ def generate_data(count):
+ """Generates test or training data with a simple MD simulation."""
+ atoms = fcc110('Pt', (2, 2, 2), vacuum=7.)
+ adsorbate = Atoms([Atom('Cu', atoms[7].position + (0., 0., 2.5)),
+ Atom('Cu', atoms[7].position + (0., 0., 5.))])
+ atoms.extend(adsorbate)
+ atoms.set_constraint(FixAtoms(indices=[0, 2]))
+ atoms.set_calculator(EMT())
+ MaxwellBoltzmannDistribution(atoms, 300. * units.kB)
+ dyn = VelocityVerlet(atoms, dt=1. * units.fs)
+ newatoms = atoms.copy()
+ newatoms.set_calculator(EMT())
+ newatoms.get_potential_energy()
+ images = [newatoms]
+ for step in range(count - 1):
+ dyn.run(50)
+ newatoms = atoms.copy()
+ newatoms.set_calculator(EMT())
+ newatoms.get_potential_energy()
+ images.append(newatoms)
+ return images
+
+
+ def train_test():
+ label = 'train_test/calc'
+ train_images = generate_data(2)
+ convergence = {
+ 'energy_rmse': 0.02,
+ 'force_rmse': 0.02
+ }
+
+ calc = Amp(descriptor=Gaussian(),
+ model=NeuralNetwork(hiddenlayers=(3, 3), convergenceCriteria=convergence),
+ label=label,
+ cores=1)
+
+ calc.train(images=train_images,)
+ for image in train_images:
+ print "energy =", calc.get_potential_energy(image)
+ print "forces =", calc.get_forces(image)
+
+
+ if __name__ == '__main__':
+ train_test()
+
+Known issues
+---------------------------------
+- `tflow` module does not work for versions different from 0.11.0.
+
+About
+---------------------------------
+
+This module was contributed by Zachary Ulissi (Department of Chemical Engineering, Stanford University, zulissi at gmail.com) with help, testing, and discussions from Andrew Doyle (Stanford) and the Amp development team.
+
diff --git a/docs/theory.rst b/docs/theory.rst
new file mode 100644
index 0000000..3f890e2
--- /dev/null
+++ b/docs/theory.rst
@@ -0,0 +1,181 @@
+.. _theory:
+
+==================================
+Theory
+==================================
+
+According to the Born-Oppenheimer approximation, the ground-state potential energy of an atomic configuration is dictated solely by the nuclear coordinates (under certain conditions, such as the absence of external fields and constant charge).
+The potential energy is in general a very complicated function of the nuclear coordinates; it in theory can be calculated by directly solving the Schrodinger equation.
+However, in practice, an exact analytical solution to the many-body Schrodinger equation is very difficult (if not impossible), and most electronic structure codes provide a point-by-point approximation to the ground-state potential energy for given nuclear configurations.
+
+Given enough example calculations from any electronic structure calculator, the idea is then to approximate the potential energy with a regression model:
+
+.. math::
+ \textbf{R}\xrightarrow{\text{regression}}E=E(\textbf{R}),
+
+where :math:`\textbf{R}` is the position of atoms in the system.
+
+-----------------------------------------
+Atomic representation of potential energy
+-----------------------------------------
+
+In order to have a potential function which is simultaneously applicable to systems of
+different sizes, the total potential energy of the system can to be broken up into atomic
+energy contributions:
+
+.. math::
+ E(\textbf{R})=\sum_{\text{atom}=1}^{N}E_\text{atom}(\textbf{R}).
+
+The above expansion can be justified by assembling the atomic configuration by bringing
+atoms close to each other one by one. Then the atomic energy contributions (instead of the energy of the whole system at once) can be
+approximated using a regression method:
+
+.. math::
+ \textbf{R}\xrightarrow{\text{regression}}E_\text{atom}=E_\text{atom}\left(\textbf{R}\right).
+
+----------
+Descriptor
+----------
+
+A better interpolation can be achieved if an appropriate symmetry function :math:`\textbf{G}`
+of atomic coordinates, approximating the functional dependence of local energetics, is used
+as the input of the regression operator:
+
+.. math::
+ \textbf{R}\xrightarrow{\textbf{G}}\textbf{G}\left(\textbf{R}\right)\xrightarrow{\text{regression}}E_\text{atom}=E_\text{atom}\left(\textbf{G}\left(\textbf{R}\right)\right).
+
+********
+Gaussian
+********
+
+A Gaussian descriptor :math:`\textbf{G}` as a function of pair-atom distances and three-atom angles has been suggested by Behler [1], and is implemented within Amp.
+Radial fingerprints of the Gaussian type capture the interaction of atom :math:`i` with all atoms :math:`j` as the sum of Gaussians with width :math:`\eta` and center :math:`R_s`,
+
+.. math::
+ G_{i}^{I}=\sum^{\tiny{\begin{array}{c} \text{atoms j within }R_c\\
+ \text{ distance of atom i}
+ \end{array}}}_{j\ne i}{e^{-\eta(R_{ij}-R_s)^2/R_c^2}f_c\left(R_{ij}\right)}.
+
+By specifying many values of :math:`\eta` and :math:`R_s` we can begin to build a feature vector for regression.
+
+The next type is the angular fingerprint accounting for three-atom interactions.
+The Gaussian angular fingerprints are computed for all triplets of atoms :math:`i`, :math:`j`, and :math:`k` by summing over the cosine values of the angles :math:`\theta_{ijk}=\cos^{-1}\left(\displaystyle\frac{\textbf{R}_{ij}.\textbf{R}_{ik}}{R_{ij}R_{ik}}\right)`, (:math:`\textbf{R}_{ij}=\textbf{R}_{i}-\textbf{R}_{j}`), centered at atom :math:`i`, according to
+
+.. math::
+ G_{i}^{II}=2^{1-\zeta}\sum^{\tiny{\begin{array}{c} \text{atoms j, k within }R_c\\
+ \text{ distance of atom i}
+ \end{array}}}_{\scriptsize\begin{array}{c}
+ j,\,k\ne i \\
+ (j\ne k) \end{array}}{\left(1+\lambda \cos \theta_{ijk}\right)^\zeta
+ e^{-\eta\left(R_{ij}^2+R_{ik}^2+R_{jk}^2\right)/R_c^2}f_c\left(R_{ij}\right)f_c\left(R_{ik}\right)f_c\left(R_{jk}\right)},
+
+with parameters :math:`\lambda`, :math:`\eta`, and :math:`\zeta`, which again can be chosen to build more elements of a feature vector.
+
+The cutoff function :math:`f_c\left(R_{ij}\right)` in the above equations defines the energetically relevant local environment with value one at :math:`R_{ij}=0` and zero at :math:`R_{ij}=R_{c}`, where :math:`R_c` is the cutoff radius.
+In order to have a continuous force-field, the cutoff function :math:`f_c\left(R_{ij}\right)` as well as its first derivative should be continuous in :math:`R_{ij}\in\left[0,\infty\right)`. One possible expression for such a function as proposed by Behler [1] is
+
+.. math::
+ f_{c}\left(r\right)==
+ \begin{cases}
+ &0.5\left(1+\cos\left(\pi\displaystyle\frac{r}{R_c}\right)\right)\qquad \text{for}\;\: r\leq R_{c},\\
+ &0\qquad\qquad\qquad\qquad\quad\quad\quad\:\: \text{for}\;\: r> R_{c}.\\
+ \end{cases}
+
+Another more general choice for the cutoff function is the following polynomial [5]:
+
+.. math::
+ f_{c} \left( r \right)=
+ \begin{cases}
+ 1 + \gamma \cdot \left(r/R_c\right)^{\gamma + 1} - (\gamma + 1) \left(r/R_c\right)^{\gamma}\qquad\quad &\text{if}\;\: r\leq R_{c},\\
+ 0&\text{if}\;\: r> R_{c},\\
+ \end{cases}
+
+with a user-specified parameter :math:`\gamma` that determines the rate of decay of the cutoff function as it extends from :math:`r=0` to :math:`r=R_c`.
+
+The figure below shows how components of the fingerprints :math:`\textbf{G}_{i}^{I}` and :math:`\textbf{G}_{i}^{II}` change with, respectively, distance :math:`R_{ij}` between the pair of atoms :math:`i` and :math:`j` and the valence angle :math:`\theta_{ijk}` between the triplet of atoms :math:`i`, :math:`j`, and :math:`k` with central atom :math:`i`:
+
+.. image:: _static/gaussian.svg
+ :width: 800 px
+ :align: center
+
+*******
+Zernike
+*******
+
+A three-dimensional Zernike descriptor is also available inside Amp, and can be used as the atomic environment descriptor.
+The Zernike-type descriptor has been previously used in the machine-learning community extensively, but it has been suggested here for the first time for representing the local chemical environment.
+Zernike moments are basically a tensor product between spherical harmonics (complete and orthogonal on the surface of the unit sphere), and Zernike polynomials (complete and orthogonal within the unit sphere).
+Zernike descriptor components for each integer degree are then defined as the norm of Zernike moments with the same corresponding degree.
+For more details on the Zernike descriptor the reader is referred to the nice paper of Novotni and Klein [2].
+
+Inspired by Bartok et. al. [3], to represent the local chemical environment of atom :math:`i`, an atomic density function :math:`\rho_{i}(\mathbf{r})` is defined for each atomic local environment as the sum of delta distributions shifted to atomic positions:
+
+.. math::
+ \rho_{i}(\mathbf{r}) = \sum_{j\neq
+ i}^{\tiny{\begin{array}{c} \text{atoms j within }R_c\\
+ \text{ distance of atom i}
+ \end{array}}}\eta_{j}\delta\left(\mathbf{r}-\mathbf{R}_{ij}\right)f_{c}\left(\|\mathbf{R}_{ij}\|\right),
+
+Next, components of the Zernike descriptor are computed from Zernike moments of the above atomic density destribution for each atom :math:`i`.
+
+The figure below shows how components of the Zernike descriptor vary with pair-atom distance, three-atom angle, and four-atom dehidral angle.
+It is important to note that components of the Gaussian descriptor discussed above are non-sensitive to the four-atom dehidral angle of the following figure.
+
+.. image:: _static/zernike.svg
+ :width: 1200 px
+ :align: center
+
+**********
+Bispectrum
+**********
+
+Bispectrum of four-dimensional spherical harmonics have been suggested by Bartok et al. [3] to be invariant under rotation of the local atomic environment.
+In this approach, the atomic density distribution defined above is first mapped onto the surface of unit sphere in four dimensions.
+Consequently, Bartok et al. have shown that the bispectrum of this mapping can be used as atomic environment descriptor.
+We refer the reader to the original paper [3] for mathematical details.
+This approach of describing local environment is also available inside Amp.
+
+
+----------------
+Regression Model
+----------------
+
+The general purpose of the regression model :math:`x\xrightarrow{\text{regression}}y` with input :math:`x` and output :math:`y` is to approximate the function :math:`y=f(x)` by using sample training data points :math:`(x_i, y_i)`.
+The intent is to later use the approximated :math:`f` for input data :math:`x_j` (other than :math:`x_i` in the training data set), and make predictions for :math:`y_j`.
+Typical regression models include Gaussian processes, support vector regression, and neural network.
+
+********************
+Neural network model
+********************
+
+A neural network model is basically a very simple model of how the nervous system processes information.
+The first mathematical model was developed in 1943 by McCulloch and Pitts [4] for classification purposes; biological neurons either send or do not send a signal to the neighboring neuron.
+The model was soon extended to do linear and nonlinear regression, by replacing the binary activation function with a continuous function.
+The basic functional unit of a neural network is called "node".
+A number of parallel nodes constitute a layer.
+A feed-forward neural network consists of at least an input layer plus an output layer.
+When approximating the PES, the output layer has just one neuron representing the potential energy.
+For a more robust interpolation, a number of "hidden layers" may exist in the neural network as well; the word "hidden" refers to the fact that these layers have no physical meaning.
+A schematic of a typical feed-forward neural network is shown below.
+In each node a number of inputs is multiplied by the corresponding weights and summed up with a constant bias.
+An activation function then acts upon the summation and an output is generated.
+The output is finally sent to the neighboring neuron in the next layer.
+Typically used activation functions are hyperbolic tangent, sigmoid, Gaussian, and linear functions.
+The unbounded linear activation function is particularly useful in the last hidden layer to scale neural network outputs to the range of reference values.
+For our purpose, the output of neural network represents energy of atomic system.
+
+.. image:: _static/nn.svg
+ :width: 500 px
+ :align: center
+
+**References:**
+
+1. "Atom-centered symmetry functions for constructing high-dimensional neural network potentials", J. Behler, J. Chem. Phys. 134(7), 074106 (2011)
+
+2. "Shape retrieval using 3D Zernike descriptors", M. Novotni and R. Klein, Computer-Aided Design 36(11), 1047--1062 (2004)
+
+3. "Gaussian approximation potentials: The accuracy of quantum mechanics, without the electrons", A.P. Bart\'ok, M.C. Payne, R. Kondor and G. Csanyi, Physical Review Letters 104, 136403 (2010)
+
+4. "A logical calculus of the ideas immanent in nervous activity", W.S. McCulloch, and W.H. Pitts, Bull. Math. Biophys. 5, 115--133 (1943)
+
+5. "Amp: A modular approach to machine learning in atomistic simulations", A. Khorshidi, and A.A. Peterson, Comput. Phys. Commun. 207, 310--324 (2016)
diff --git a/docs/useamp.rst b/docs/useamp.rst
new file mode 100644
index 0000000..6aefdc2
--- /dev/null
+++ b/docs/useamp.rst
@@ -0,0 +1,208 @@
+.. _UseAmp:
+
+==================================
+Using Amp
+==================================
+
+If you are familiar with ASE, the use of Amp should be intuitive.
+At its most basic, Amp behaves like any other ASE calculator, except that it has a key extra method, called `train`, which allows you to fit the calculator to a set of atomic images.
+This means you can use Amp as a substitute for an expensive calculator in any atomistic routine, such as molecular dynamics, global optimization, transition-state searches, normal-mode analyses, phonon analyses, etc.
+
+----------------------------------
+Basic use
+----------------------------------
+
+To use Amp, you need to specify a `descriptor` and a `model`.
+The below shows a basic example of training :class:`~amp.Amp` with :class:`~amp.descriptor.gaussian.Gaussian` descriptors and a :class:`~amp.model.neuralnetwork.NeuralNetwork` model---the Behler-Parinello scheme.
+
+.. code-block:: python
+
+ from amp import Amp
+ from amp.descriptor.gaussian import Gaussian
+ from amp.model.neuralnetwork import NeuralNetwork
+
+ calc = Amp(descriptor=Gaussian(), model=NeuralNetwork(),
+ label='calc')
+ calc.train(images='my-images.traj')
+
+After training is successful you can use your trained calculator just like any other ASE calculator (although you should be careful that you can only trust it within the trained regime).
+This will also result in the saving the calculator parameters to "<label>.amp", which can be used to re-load the calculator in a future session:
+
+.. code-block:: python
+
+ calc = Amp.load('calc.amp')
+
+
+The modular nature of Amp is meant such that you can easily mix-and-match different descriptor and model schemes.
+See the theory section for more details.
+
+----------------------------------
+Adjusting convergence parameters
+----------------------------------
+
+To control how tightly the energy and/or forces are converged, you can adjust the :class:`~amp.model.LossFunction`. Just insert before the `calc.train` line some code like:
+
+.. code-block:: python
+
+ from amp.model import LossFunction
+
+ convergence = {'energy_rmse': 0.02, 'force_rmse': 0.04}
+ calc.model.lossfunction = LossFunction(convergence=convergence)
+
+You can see the adjustable parameters and their default values in the dictionary :attr:`~amp.model.LossFunction.default_parameters`:
+
+.. code-block:: python
+
+ >>> LossFunction.default_parameters
+ {'convergence': {'energy_rmse': 0.001, 'force_rmse': None, 'energy_maxresid': None, 'force_maxresid': None}}
+
+Note that you can also set a maximum residual of any energy or force prediction with the appropriate keywords above.
+
+To change how the code manages the regression process, you can use the :class:`~amp.regression.Regressor` class. For example, to switch from the scipy's fmin_bfgs optimizer (the default) to scipy's basin hopping optimizer, try inserting the following lines before initializing training:
+
+.. code-block:: python
+
+ from amp.regression import Regressor
+ from scipy.optimize import basinhopping
+
+ regressor = Regressor(optimizer=basinhopping)
+ calc.model.regressor = regressor
+
+----------------------------------
+Turning on/off force training
+----------------------------------
+
+Most electronic structure codes also give forces (in addition to potential energy) for each image, and you can get a much more predictive fit if you include this information while training.
+However, this can create issues: training will tend to be slower than training energies only, convergence will be more difficult, and if there are inconsistencies in the training data (say if the calculator reports 0K-extrapolated energies rather than force-consistent ones, or if there are egg-box errors), you might not be able to train at all.
+For this reason, Amp defaults to energy-only training, but you can turn on force-training via the convergence dictionary as noted above.
+Note that there is a `force_coefficient` keyword also fed to the :class:`~amp.model.LossFunction` class which can control the relative weighting of the energy and force RMSEs used in the path to convergence.
+
+.. code-block:: python
+
+ from amp.model import LossFunction
+
+ convergence = {'energy_rmse': 0.02, 'force_rmse': 0.04}
+ calc.model.lossfunction = LossFunction(convergence=convergence,
+ force_coefficient=0.04)
+
+----------------------------------
+Parallel processing
+----------------------------------
+
+Most tasks in Amp are "embarrassingly parallel" and thus you should see a performance boost by specifying more cores.
+Our standard parallel processing approach requires the modules ZMQ (to pass messages between processes) and pxssh (to establish SSH connections across nodes, and is only needed if parallelizing on more than one node).
+
+The code will try to automatically guess the parallel configuration from the environment variables that your batching system produces, using the function :func:`amp.utilities.assign_cores`.
+(We only use SLURM on our system, so we welcome patches to get this utility working on other systems!)
+If you want to override the automatic guess, use the `cores` keyword when initializing Amp.
+To specify serial operation, use `cores=1`; to specify (for example) 8 cores on only a single node, use `cores=8` or `cores={'localhost': 8}`.
+For parallel operation, cores should be a dictionary where the keys are the hostnames and the values are the number of processors (cores) available on that node; e.g.,
+
+.. code-block:: python
+
+ cores = {'node241': 16,
+ 'node242': 16}
+
+(One of the keys in the dictionary could also be `localhost`, as in the single-node example. Using `localhost` just prevents it from establishing an extra SSH connection.)
+
+For this to work on multiple nodes, you need to be able to freely SSH between nodes on your system.
+Typically, this means that once you are logged in to your cluster you have public/private keys in use to ssh between nodes.
+If you can run `ssh localhost` without it asking you for a password, this is likely to work for you.
+
+This also assumes that your environment is identical each time you SSH into a node; that is, all the packages such as ASE, Amp, ZMQ, etc., are available in the same version.
+Generally, if you are setting your environment with a .bashrc or .modules file this will just work.
+However, if you need to set your environment variables on the machine that is being ssh'd to, you can do so with the `envcommand` keyword, which you might set to
+
+.. code-block:: python
+
+ envcommand = 'export PYTHONPATH=/path/to/amp:$PYTHONPATH'
+
+This envcommand can be passed as a keyword to the initialization of the :class:`~amp.Amp` class.
+Ultimately, Amp stores these and passes them around in a configuration dictionary called `parallel`, so if you are calling descriptor or model functions directly you may need to construct this dictionary, which has the form `parallel={'cores': ..., 'envcommand': ...}`.
+
+
+----------------------------------
+Advanced use
+----------------------------------
+
+Under the hood, the train function is pretty simple; it just runs:
+
+.. code-block:: python
+
+ images = hash_images(images, ...)
+ self.descriptor.calculate_fingerprints(images, ...)
+ result = self.model.fit(images, self.descriptor, ...)
+ if result is True:
+ self.save(filename)
+
+* In the first line, the images are read and converted to a dictionary, addressed by a hash.
+ This makes addressing the images simpler across modules and eliminates duplicate images.
+ This also facilitates keeping a database of fingerprints, such that in future scripts you do not need to re-fingerprint images you have already encountered.
+
+* In the second line, the descriptor converts the images into fingerprints, one fingerprint per image. There are two possible modes a descriptor can operate in: "image-centered" in which one vector is produced per image, and "atom-centered" in which one vector is produced per atom. That is, in atom-centered mode the image's fingerprint will be a list of lists. The resulting fingerprint is stored in `self.descriptor.fingerprints`, and the mode is stored in `self.parameters.mode`.
+
+* In the third line, the model (e.g., a neural network) is fit to the data. As it is passed a reference to `self.descriptor`, it has access to the fingerprints as well as the mode. Many options are available to customize this in terms of the loss function, the regression method, etc.
+
+* In the final pair of lines, if the target fit was achieved, the model is saved to disk.
+
+----------------------------------
+Re-training
+----------------------------------
+
+If training is successful, Amp saves the parameters into an '<label>.amp' file (by default the label is 'amp', so this file is 'amp.amp'). You can load the pretrained calculator and re-train it further with tighter convergence criteria. You can specify if the pre-trained amp.amp will be overwritten by the re-trained one through the key word 'overwrite' (default is False).
+
+.. code-block:: python
+
+ calc = Amp.load('amp.amp')
+ calc.model.lossfunction = LossFunction(convergence=convergence)
+ calc.train(overwrite=True)
+
+If training does not succeed, Amp raises a :exc:`~amp.utilities.TrainingConvergenceError`.
+You can use this within your scripts to catch when training succeeds or fails, for example:
+
+.. code-block:: python
+
+ from amp.utilities import TrainingConvergenceError
+
+ ...
+
+ try:
+ calc.train(images)
+ except TrainingConvergenceError:
+ # Whatever you want to happen if training fails;
+ # e.g., refresh parameters and train again.
+
+------------------------------------
+Global search in the parameter space
+------------------------------------
+
+If the model is trained with minimizing a loss function which has a non-convex form, it might be desirable to perform a global search in the parameter space in prior to a gradient-descent optimization algorithm.
+That is, in the first step we do a random search in an area of parameter space including multiple basins (each basin has a local minimum).
+Next we take the parameters corresponding to the minimum loss function found, and start a gradient-descent optimization to find the local minimum of the basin found in the first step.
+Currently there exists a built-in global-search optimizer inside Amp which uses simulated-annealing algorithm.
+The module is based on the open-source simulated-annealing code of Wagner and Perry [1], but has been brought into the context of Amp.
+To use this module, the calculator object should be initiated as usual:
+
+.. code-block:: python
+
+ from amp import Amp
+ calc = Amp(descriptor=..., model=...)
+ images = ...
+
+Then the calculator object and the images are passed to the :class:`~amp.utilities.Annealer` module and the simulated-annealing search is performed by reducing the temperature from the initial maximum value `Tmax` to the final minimum value `Tmin` in number of steps `steps`:
+
+.. code-block:: python
+
+ from amp.utilities import Annealer
+ Annealer(calc=calc, images=images, Tmax=20, Tmin=1, steps=4000)
+
+If `Tmax` takes a small value (greater than zero), then the algorithm reduces to the simple random-walk search.
+Finally the usual :meth:`~amp.Amp.train` method is called to continue from the best parameters found in the last step:
+
+.. code-block:: python
+
+ calc.train(images=images,)
+
+**References:**
+
+1. https://github.com/perrygeo/simanneal.
diff --git a/setup.py b/setup.py
new file mode 100644
index 0000000..6601b95
--- /dev/null
+++ b/setup.py
@@ -0,0 +1,21 @@
+#!/usr/bin/env
+
+from setuptools import setup
+
+setup(
+ name = 'amp',
+ version = 'dev',
+ long_description = open('README.md').read(),
+ packages = ['amp', 'amp.descriptor', 'amp.regression', 'amp.model'],
+ package_dir = {'amp': 'amp',
+ 'descriptor' : 'descriptor',
+ 'regression' : 'regression',
+ 'model' : 'model',},
+ classifiers = [
+ 'Programming Language :: Python',
+ 'Programming Language :: Python :: 2.6',
+ 'Programming Language :: Python :: 2.7',
+ 'Programming Language :: Python :: 3',
+ 'Programming Language :: Python :: 3.3',
+ ],
+ install_requires=['numpy>=1.7.0', 'matplotlib', 'ase'])
diff --git a/tests/CuOPd_test/gaussian_neural_test/force_call_test.py b/tests/CuOPd_test/gaussian_neural_test/force_call_test.py
new file mode 100644
index 0000000..1317cd3
--- /dev/null
+++ b/tests/CuOPd_test/gaussian_neural_test/force_call_test.py
@@ -0,0 +1,340 @@
+"""
+Exact Gaussian-neural scheme forces and energies of five different non-periodic
+configurations and three different periodic configurations have been calculated
+in Mathematica, and are given below. This script checks the values calculated
+by the code with and without fortran modules.
+
+"""
+
+import numpy as np
+from ase import Atoms
+from collections import OrderedDict
+from amp import Amp
+from amp.descriptor.gaussian import Gaussian
+from amp.model.neuralnetwork import NeuralNetwork
+
+# The test function for non-periodic systems
+
+
+def non_periodic_test():
+
+ # Making the list of non-periodic images
+ images = [Atoms(symbols='PdOPd2',
+ pbc=np.array([False, False, False], dtype=bool),
+ cell=np.array(
+ [[1., 0., 0.],
+ [0., 1., 0.],
+ [0., 0., 1.]]),
+ positions=np.array(
+ [[0., 0., 0.],
+ [0., 2., 0.],
+ [0., 0., 3.],
+ [1., 0., 0.]])),
+ Atoms(symbols='PdOPd2',
+ pbc=np.array([False, False, False], dtype=bool),
+ cell=np.array(
+ [[1., 0., 0.],
+ [0., 1., 0.],
+ [0., 0., 1.]]),
+ positions=np.array(
+ [[0., 1., 0.],
+ [1., 2., 1.],
+ [-1., 1., 2.],
+ [1., 3., 2.]])),
+ Atoms(symbols='PdO',
+ pbc=np.array([False, False, False], dtype=bool),
+ cell=np.array(
+ [[1., 0., 0.],
+ [0., 1., 0.],
+ [0., 0., 1.]]),
+ positions=np.array(
+ [[2., 1., -1.],
+ [1., 2., 1.]])),
+ Atoms(symbols='Pd2O',
+ pbc=np.array([False, False, False], dtype=bool),
+ cell=np.array(
+ [[1., 0., 0.],
+ [0., 1., 0.],
+ [0., 0., 1.]]),
+ positions=np.array(
+ [[-2., -1., -1.],
+ [1., 2., 1.],
+ [3., 4., 4.]])),
+ Atoms(symbols='Cu',
+ pbc=np.array([False, False, False], dtype=bool),
+ cell=np.array(
+ [[1., 0., 0.],
+ [0., 1., 0.],
+ [0., 0., 1.]]),
+ positions=np.array(
+ [[0., 0., 0.]]))]
+
+ # Correct energies and forces
+ correct_energies = [14.231186811226152, 14.327219917287948,
+ 5.5742510565528285, 9.41456771216968,
+ -0.5019297954597407]
+ correct_forces = \
+ [[[-0.05095024246182649, -0.10709193432146558, -0.09734321482638622],
+ [-0.044550772904033635, 0.2469763195486647, -0.07617425912869778],
+ [-0.02352490951707703, -0.050782839419131864, 0.24409220250631508],
+ [0.11902592488293715, -0.08910154580806727, -0.07057472855123109]],
+ [[-0.024868720575099375, -0.07417891957113862,
+ -0.12121240797223251],
+ [0.060156158438252574, 0.017517013378773042,
+ -0.020047135079325505],
+ [-0.10901144291312388, -0.06671262448352767, 0.06581556263014315],
+ [0.07372400504997068, 0.12337453067589325, 0.07544398042141486]],
+ [[0.10151747265164626, -0.10151747265164626, -0.20303494530329252],
+ [-0.10151747265164626, 0.10151747265164626, 0.20303494530329252]],
+ [[-0.00031177673224312745, -0.00031177673224312745,
+ -0.0002078511548287517],
+ [0.004823209772264884, 0.004823209772264884,
+ 0.006975000714861393],
+ [-0.004511433040021756, -0.004511433040021756,
+ -0.006767149560032641]],
+ [[0.0, 0.0, 0.0]]]
+
+ # Parameters
+ Gs = {'O': [{'type': 'G2', 'element': 'Pd', 'eta': 0.8},
+ {'type': 'G4', 'elements': [
+ 'Pd', 'Pd'], 'eta':0.2, 'gamma':0.3, 'zeta':1},
+ {'type': 'G4', 'elements': ['O', 'Pd'], 'eta':0.3, 'gamma':0.6,
+ 'zeta':0.5}],
+ 'Pd': [{'type': 'G2', 'element': 'Pd', 'eta': 0.2},
+ {'type': 'G4', 'elements': ['Pd', 'Pd'],
+ 'eta':0.9, 'gamma':0.75, 'zeta':1.5},
+ {'type': 'G4', 'elements': ['O', 'Pd'], 'eta':0.4,
+ 'gamma':0.3, 'zeta':4}],
+ 'Cu': [{'type': 'G2', 'element': 'Cu', 'eta': 0.8},
+ {'type': 'G4', 'elements': ['Cu', 'O'],
+ 'eta':0.2, 'gamma':0.3, 'zeta':1},
+ {'type': 'G4', 'elements': ['Cu', 'Cu'], 'eta':0.3,
+ 'gamma':0.6, 'zeta':0.5}]}
+
+ hiddenlayers = {'O': (2,), 'Pd': (2,), 'Cu': (2,)}
+
+ weights = OrderedDict([('O', OrderedDict([(1, np.matrix([[-2.0, 6.0],
+ [3.0, -3.0],
+ [1.5, -0.9],
+ [-2.5, -1.5]])),
+ (2, np.matrix([[5.5],
+ [3.6],
+ [1.4]]))])),
+ ('Pd', OrderedDict([(1, np.matrix([[-1.0, 3.0],
+ [2.0, 4.2],
+ [1.0, -0.7],
+ [-3.0, 2.0]])),
+ (2, np.matrix([[4.0],
+ [0.5],
+ [3.0]]))])),
+ ('Cu', OrderedDict([(1, np.matrix([[0.0, 1.0],
+ [-1.0, -2.0],
+ [2.5, -1.9],
+ [-3.5, 0.5]])),
+ (2, np.matrix([[0.5],
+ [1.6],
+ [-1.4]]))]))])
+
+ scalings = OrderedDict([('O', OrderedDict([('intercept', -2.3),
+ ('slope', 4.5)])),
+ ('Pd', OrderedDict([('intercept', 1.6),
+ ('slope', 2.5)])),
+ ('Cu', OrderedDict([('intercept', -0.3),
+ ('slope', -0.5)]))])
+
+ fingerprints_range = {"Cu": np.array([[0.0, 0.0], [0.0, 0.0], [0.0, 0.0]]),
+ "O": np.array([[0.2139617720858539,
+ 2.258090276328769],
+ [0.0, 1.085656080548734],
+ [0.0, 0.0]]),
+ "Pd": np.array([[0.0, 1.4751761770313006],
+ [0.0, 0.28464992134267897],
+ [0.0, 0.20167521020630502]])}
+
+ # Testing pure-python and fortran versions of Gaussian-neural force call
+ for fortran in [False, True]:
+ for cores in range(1, 6):
+ label = 'call-nonperiodic/%s-%i' % (fortran, cores)
+ calc = Amp(descriptor=Gaussian(cutoff=6.5,
+ Gs=Gs,
+ fortran=fortran),
+ model=NeuralNetwork(hiddenlayers=hiddenlayers,
+ weights=weights,
+ scalings=scalings,
+ activation='sigmoid',
+ fprange=fingerprints_range,
+ mode='atom-centered',
+ fortran=fortran),
+ label=label,
+ dblabel=label,
+ cores=cores)
+
+ predicted_energies = [calc.get_potential_energy(image) for image in
+ images]
+
+ for image_no in range(len(predicted_energies)):
+ diff = abs(predicted_energies[image_no] -
+ correct_energies[image_no])
+ assert (diff < 10.**(-15.)), \
+ 'The predicted energy of image %i is wrong!' % (
+ image_no + 1)
+
+ predicted_forces = [calc.get_forces(image) for image in images]
+
+ for image_no in range(len(predicted_forces)):
+ for index in range(np.shape(predicted_forces[image_no])[0]):
+ for direction in range(
+ np.shape(predicted_forces[image_no])[1]):
+ diff = abs(predicted_forces[image_no][index][
+ direction] -
+ correct_forces[image_no][index][direction])
+ assert (diff < 10.**(-15.)), \
+ 'The predicted %i force of atom %i of image %i ' \
+ 'is wrong!' % (direction, index, image_no + 1)
+
+
+# The test function for periodic systems
+def periodic_test():
+
+ # Making the list of periodic images
+ images = [Atoms(symbols='PdOPd',
+ pbc=np.array([True, False, False], dtype=bool),
+ cell=np.array(
+ [[2., 0., 0.],
+ [0., 2., 0.],
+ [0., 0., 2.]]),
+ positions=np.array(
+ [[0.5, 1., 0.5],
+ [1., 0.5, 1.],
+ [1.5, 1.5, 1.5]])),
+ Atoms(symbols='PdO',
+ pbc=np.array([True, True, False], dtype=bool),
+ cell=np.array(
+ [[2., 0., 0.],
+ [0., 2., 0.],
+ [0., 0., 2.]]),
+ positions=np.array(
+ [[0.5, 1., 0.5],
+ [1., 0.5, 1.]])),
+ Atoms(symbols='Cu',
+ pbc=np.array([True, True, False], dtype=bool),
+ cell=np.array(
+ [[1.8, 0., 0.],
+ [0., 1.8, 0.],
+ [0., 0., 1.8]]),
+ positions=np.array(
+ [[0., 0., 0.]]))]
+
+ # Correct energies and forces
+ correct_energies = [3.8560954326995978, 1.6120748520627273,
+ 0.19433107801410093]
+ correct_forces = \
+ [[[0.14747720528015523, -3.3010645563584973, 3.3008168318984463],
+ [0.03333579762326405, 9.050780376599887, -0.42608278400777605],
+ [-0.1808130029034193, -5.7497158202413905, -2.8747340478906698]],
+ [[6.5035267996045045 * (10.**(-6.)),
+ -6.503526799604495 * (10.**(-6.)),
+ 0.00010834689201069249],
+ [-6.5035267996045045 * (10.**(-6.)),
+ 6.503526799604495 * (10.**(-6.)),
+ -0.00010834689201069249]],
+ [[0.0, 0.0, 0.0]]]
+
+ # Parameters
+ Gs = {'O': [{'type': 'G2', 'element': 'Pd', 'eta': 0.8},
+ {'type': 'G4', 'elements': ['O', 'Pd'], 'eta':0.3, 'gamma':0.6,
+ 'zeta':0.5}],
+ 'Pd': [{'type': 'G2', 'element': 'Pd', 'eta': 0.2},
+ {'type': 'G4', 'elements': ['Pd', 'Pd'],
+ 'eta':0.9, 'gamma':0.75, 'zeta':1.5}],
+ 'Cu': [{'type': 'G2', 'element': 'Cu', 'eta': 0.8},
+ {'type': 'G4', 'elements': ['Cu', 'Cu'], 'eta':0.3,
+ 'gamma':0.6, 'zeta':0.5}]}
+
+ hiddenlayers = {'O': (2,), 'Pd': (2,), 'Cu': (2,)}
+
+ weights = OrderedDict([('O', OrderedDict([(1, np.matrix([[-2.0, 6.0],
+ [3.0, -3.0],
+ [1.5, -0.9]])),
+ (2, np.matrix([[5.5],
+ [3.6],
+ [1.4]]))])),
+ ('Pd', OrderedDict([(1, np.matrix([[-1.0, 3.0],
+ [2.0, 4.2],
+ [1.0, -0.7]])),
+ (2, np.matrix([[4.0],
+ [0.5],
+ [3.0]]))])),
+ ('Cu', OrderedDict([(1, np.matrix([[0.0, 1.0],
+ [-1.0, -2.0],
+ [2.5, -1.9]])),
+ (2, np.matrix([[0.5],
+ [1.6],
+ [-1.4]]))]))])
+
+ scalings = OrderedDict([('O', OrderedDict([('intercept', -2.3),
+ ('slope', 4.5)])),
+ ('Pd', OrderedDict([('intercept', 1.6),
+ ('slope', 2.5)])),
+ ('Cu', OrderedDict([('intercept', -0.3),
+ ('slope', -0.5)]))])
+
+ fingerprints_range = {"Cu": np.array([[2.8636310860653253,
+ 2.8636310860653253],
+ [1.5435994865298275,
+ 1.5435994865298275]]),
+ "O": np.array([[2.9409056366723028,
+ 2.972494902604392],
+ [1.9522542722823606,
+ 4.0720361595017245]]),
+ "Pd": np.array([[2.4629488092411096,
+ 2.6160138774087125],
+ [0.27127576524253594,
+ 0.5898312261433813]])}
+
+ # Testing pure-python and fortran versions of Gaussian-neural force call
+ for fortran in [False, True]:
+ for cores in range(1, 4):
+ label = 'call-periodic/%s-%i' % (fortran, cores)
+ calc = Amp(descriptor=Gaussian(cutoff=4.,
+ Gs=Gs,
+ fortran=fortran),
+ model=NeuralNetwork(hiddenlayers=hiddenlayers,
+ weights=weights,
+ scalings=scalings,
+ activation='tanh',
+ fprange=fingerprints_range,
+ mode='atom-centered',
+ fortran=fortran),
+ label=label,
+ dblabel=label,
+ cores=cores)
+
+ predicted_energies = [calc.get_potential_energy(image) for image in
+ images]
+
+ for image_no in range(len(predicted_energies)):
+ diff = abs(predicted_energies[image_no] -
+ correct_energies[image_no])
+ assert (diff < 10.**(-14.)), \
+ 'The predicted energy of image %i is wrong!' % (
+ image_no + 1)
+
+ predicted_forces = [calc.get_forces(image) for image in images]
+
+ for image_no in range(len(predicted_forces)):
+ for index in range(np.shape(predicted_forces[image_no])[0]):
+ for direction in range(
+ np.shape(predicted_forces[image_no])[1]):
+ diff = abs(predicted_forces[image_no][index][
+ direction] -
+ correct_forces[image_no][index][direction])
+ assert (diff < 10.**(-11.)), \
+ 'The predicted %i force of atom %i of image' \
+ ' %i is wrong!' % (direction,
+ index,
+ image_no + 1)
+
+if __name__ == '__main__':
+ non_periodic_test()
+ periodic_test()
diff --git a/tests/CuOPd_test/gaussian_neural_test/force_call_test_tflow.py b/tests/CuOPd_test/gaussian_neural_test/force_call_test_tflow.py
new file mode 100644
index 0000000..b77006f
--- /dev/null
+++ b/tests/CuOPd_test/gaussian_neural_test/force_call_test_tflow.py
@@ -0,0 +1,373 @@
+"""
+Exact Gaussian-neural scheme forces and energies of five different non-periodic
+configurations and three different periodic configurations have been calculated
+in Mathematica, and are given below. This script checks the values calculated
+by the code with and without fortran modules.
+
+"""
+
+import sys
+import numpy as np
+from collections import OrderedDict
+from ase import Atoms
+
+from amp import Amp
+from amp.descriptor.gaussian import Gaussian
+
+
+def perform_test():
+ """Determines whether or not to perform the test.
+ This should only perform the test if the python version is 2.x
+ and tensorflow is installed. If returns False (meaning don't
+ peform test), also supplies the reason."""
+ if sys.version_info >= (3,):
+ return False, 'amp.model.tflow not supported in python3.'
+ try:
+ import tensorflow
+ except ImportError:
+ return False, 'Tensorflow not installed.'
+ return True, ''
+
+
+def non_periodic_test():
+ """The test function for non-periodic systems."""
+ perform, reason = perform_test()
+ if not perform:
+ print('Skipping this test because {}'.format(reason))
+ return
+
+ from amp.model.tflow import NeuralNetwork
+ # Making the list of non-periodic images
+ images = [Atoms(symbols='PdOPd2',
+ pbc=np.array([False, False, False], dtype=bool),
+ cell=np.array(
+ [[1., 0., 0.],
+ [0., 1., 0.],
+ [0., 0., 1.]]),
+ positions=np.array(
+ [[0., 0., 0.],
+ [0., 2., 0.],
+ [0., 0., 3.],
+ [1., 0., 0.]])),
+ Atoms(symbols='PdOPd2',
+ pbc=np.array([False, False, False], dtype=bool),
+ cell=np.array(
+ [[1., 0., 0.],
+ [0., 1., 0.],
+ [0., 0., 1.]]),
+ positions=np.array(
+ [[0., 1., 0.],
+ [1., 2., 1.],
+ [-1., 1., 2.],
+ [1., 3., 2.]])),
+ Atoms(symbols='PdO',
+ pbc=np.array([False, False, False], dtype=bool),
+ cell=np.array(
+ [[1., 0., 0.],
+ [0., 1., 0.],
+ [0., 0., 1.]]),
+ positions=np.array(
+ [[2., 1., -1.],
+ [1., 2., 1.]])),
+ Atoms(symbols='Pd2O',
+ pbc=np.array([False, False, False], dtype=bool),
+ cell=np.array(
+ [[1., 0., 0.],
+ [0., 1., 0.],
+ [0., 0., 1.]]),
+ positions=np.array(
+ [[-2., -1., -1.],
+ [1., 2., 1.],
+ [3., 4., 4.]])),
+ Atoms(symbols='Cu',
+ pbc=np.array([False, False, False], dtype=bool),
+ cell=np.array(
+ [[1., 0., 0.],
+ [0., 1., 0.],
+ [0., 0., 1.]]),
+ positions=np.array(
+ [[0., 0., 0.]]))]
+
+ # Correct energies and forces
+ correct_energies = [14.231186811226152, 14.327219917287948,
+ 5.5742510565528285, 9.41456771216968,
+ -0.5019297954597407]
+ correct_forces = \
+ [[[-0.05095024246182649, -0.10709193432146558, -0.09734321482638622],
+ [-0.044550772904033635, 0.2469763195486647, -0.07617425912869778],
+ [-0.02352490951707703, -0.050782839419131864, 0.24409220250631508],
+ [0.11902592488293715, -0.08910154580806727, -0.07057472855123109]],
+ [[-0.024868720575099375, -0.07417891957113862,
+ -0.12121240797223251],
+ [0.060156158438252574, 0.017517013378773042,
+ -0.020047135079325505],
+ [-0.10901144291312388, -0.06671262448352767, 0.06581556263014315],
+ [0.07372400504997068, 0.12337453067589325, 0.07544398042141486]],
+ [[0.10151747265164626, -0.10151747265164626, -0.20303494530329252],
+ [-0.10151747265164626, 0.10151747265164626, 0.20303494530329252]],
+ [[-0.00031177673224312745, -0.00031177673224312745,
+ -0.0002078511548287517],
+ [0.004823209772264884, 0.004823209772264884,
+ 0.006975000714861393],
+ [-0.004511433040021756, -0.004511433040021756,
+ -0.006767149560032641]],
+ [[0.0, 0.0, 0.0]]]
+
+ # Parameters
+ Gs = {'O': [{'type': 'G2', 'element': 'Pd', 'eta': 0.8},
+ {'type': 'G4', 'elements': [
+ 'Pd', 'Pd'], 'eta':0.2, 'gamma':0.3, 'zeta':1},
+ {'type': 'G4', 'elements': ['O', 'Pd'], 'eta':0.3, 'gamma':0.6,
+ 'zeta':0.5}],
+ 'Pd': [{'type': 'G2', 'element': 'Pd', 'eta': 0.2},
+ {'type': 'G4', 'elements': ['Pd', 'Pd'],
+ 'eta':0.9, 'gamma':0.75, 'zeta':1.5},
+ {'type': 'G4', 'elements': ['O', 'Pd'], 'eta':0.4,
+ 'gamma':0.3, 'zeta':4}],
+ 'Cu': [{'type': 'G2', 'element': 'Cu', 'eta': 0.8},
+ {'type': 'G4', 'elements': ['Cu', 'O'],
+ 'eta':0.2, 'gamma':0.3, 'zeta':1},
+ {'type': 'G4', 'elements': ['Cu', 'Cu'], 'eta':0.3,
+ 'gamma':0.6, 'zeta':0.5}]}
+
+ hiddenlayers = {'O': (2, 1), 'Pd': (2, 1), 'Cu': (2, 1)}
+
+ weights = OrderedDict([('O', OrderedDict([(1, np.matrix([[-2.0, 6.0],
+ [3.0, -3.0],
+ [1.5, -0.9],
+ [-2.5, -1.5]])),
+ (2, np.matrix([[5.5],
+ [3.6],
+ [1.4]]))])),
+ ('Pd', OrderedDict([(1, np.matrix([[-1.0, 3.0],
+ [2.0, 4.2],
+ [1.0, -0.7],
+ [-3.0, 2.0]])),
+ (2, np.matrix([[4.0],
+ [0.5],
+ [3.0]]))])),
+ ('Cu', OrderedDict([(1, np.matrix([[0.0, 1.0],
+ [-1.0, -2.0],
+ [2.5, -1.9],
+ [-3.5, 0.5]])),
+ (2, np.matrix([[0.5],
+ [1.6],
+ [-1.4]]))]))])
+
+ scalings = OrderedDict([('O', OrderedDict([('intercept', -2.3),
+ ('slope', 4.5)])),
+ ('Pd', OrderedDict([('intercept', 1.6),
+ ('slope', 2.5)])),
+ ('Cu', OrderedDict([('intercept', -0.3),
+ ('slope', -0.5)]))])
+
+ fingerprints_range = {"Cu": np.array([[0.0, 0.0], [0.0, 0.0], [0.0, 0.0]]),
+ "O": np.array([[0.2139617720858539,
+ 2.258090276328769],
+ [0.0, 1.085656080548734],
+ [0.0, 0.0]]),
+ "Pd": np.array([[0.0, 1.4751761770313006],
+ [0.0, 0.28464992134267897],
+ [0.0, 0.20167521020630502]])}
+
+ # Testing pure-python and fortran versions of Gaussian-neural force call
+ for fortran in [False, True]:
+ for cores in range(1, 6):
+ label = 'call-nonperiodic/%s-%i' % (fortran, cores)
+ calc = Amp(descriptor=Gaussian(cutoff=6.5,
+ Gs=Gs,
+ fortran=fortran),
+ model=NeuralNetwork(hiddenlayers=hiddenlayers,
+ weights=weights,
+ scalings=scalings,
+ activation='sigmoid',
+ fprange=fingerprints_range),
+ label=label,
+ dblabel=label,
+ cores=cores)
+
+ predicted_energies = [calc.get_potential_energy(image) for image in
+ images]
+
+ for image_no in range(len(predicted_energies)):
+ print(predicted_energies[image_no])
+ print(correct_energies[image_no])
+ diff = abs(predicted_energies[image_no] -
+ correct_energies[image_no])
+ assert (diff < 10.**(-3.)), \
+ 'The predicted energy of image %i is wrong!' % (
+ image_no + 1)
+
+ predicted_forces = [calc.get_forces(image) for image in images]
+
+ for image_no in range(len(predicted_forces)):
+ print('predicted forces:')
+ print(predicted_forces[image_no])
+ print('correct forces:')
+ print(np.array(correct_forces[image_no]))
+ for index in range(np.shape(predicted_forces[image_no])[0]):
+ for direction in range(
+ np.shape(predicted_forces[image_no])[1]):
+ diff = abs(predicted_forces[image_no][index][
+ direction] -
+ correct_forces[image_no][index][direction])
+ assert (diff < 10.**(-3.)), \
+ 'The predicted %i force of atom %i of image %i ' \
+ 'is wrong!' % (direction, index, image_no + 1)
+
+
+def periodic_test():
+ """The test function for periodic systems."""
+ perform, reason = perform_test()
+ if not perform:
+ print('Skipping this test because {}'.format(reason))
+ return
+
+ from amp.model.tflow import NeuralNetwork
+ # Making the list of periodic images
+ images = [Atoms(symbols='PdOPd',
+ pbc=np.array([True, False, False], dtype=bool),
+ cell=np.array(
+ [[2., 0., 0.],
+ [0., 2., 0.],
+ [0., 0., 2.]]),
+ positions=np.array(
+ [[0.5, 1., 0.5],
+ [1., 0.5, 1.],
+ [1.5, 1.5, 1.5]])),
+ Atoms(symbols='PdO',
+ pbc=np.array([True, True, False], dtype=bool),
+ cell=np.array(
+ [[2., 0., 0.],
+ [0., 2., 0.],
+ [0., 0., 2.]]),
+ positions=np.array(
+ [[0.5, 1., 0.5],
+ [1., 0.5, 1.]])),
+ Atoms(symbols='Cu',
+ pbc=np.array([True, True, False], dtype=bool),
+ cell=np.array(
+ [[1.8, 0., 0.],
+ [0., 1.8, 0.],
+ [0., 0., 1.8]]),
+ positions=np.array(
+ [[0., 0., 0.]]))]
+
+ # Correct energies and forces
+ correct_energies = [3.8560954326995978, 1.6120748520627273,
+ 0.19433107801410093]
+ correct_forces = \
+ [[[0.14747720528015523, -3.3010645563584973, 3.3008168318984463],
+ [0.03333579762326405, 9.050780376599887, -0.42608278400777605],
+ [-0.1808130029034193, -5.7497158202413905, -2.8747340478906698]],
+ [[6.5035267996045045 * (10.**(-6.)),
+ -6.503526799604495 * (10.**(-6.)),
+ 0.00010834689201069249],
+ [-6.5035267996045045 * (10.**(-6.)),
+ 6.503526799604495 * (10.**(-6.)),
+ -0.00010834689201069249]],
+ [[0.0, 0.0, 0.0]]]
+
+ # Parameters
+ Gs = {'O': [{'type': 'G2', 'element': 'Pd', 'eta': 0.8},
+ {'type': 'G4', 'elements': ['O', 'Pd'], 'eta':0.3, 'gamma':0.6,
+ 'zeta':0.5}],
+ 'Pd': [{'type': 'G2', 'element': 'Pd', 'eta': 0.2},
+ {'type': 'G4', 'elements': ['Pd', 'Pd'],
+ 'eta':0.9, 'gamma':0.75, 'zeta':1.5}],
+ 'Cu': [{'type': 'G2', 'element': 'Cu', 'eta': 0.8},
+ {'type': 'G4', 'elements': ['Cu', 'Cu'], 'eta':0.3,
+ 'gamma':0.6, 'zeta':0.5}]}
+
+ hiddenlayers = {'O': (2, 1), 'Pd': (2, 1), 'Cu': (2, 1)}
+
+ weights = OrderedDict([('O', OrderedDict([(1, np.matrix([[-2.0, 6.0],
+ [3.0, -3.0],
+ [1.5, -0.9]])),
+ (2, np.matrix([[5.5],
+ [3.6],
+ [1.4]]))])),
+ ('Pd', OrderedDict([(1, np.matrix([[-1.0, 3.0],
+ [2.0, 4.2],
+ [1.0, -0.7]])),
+ (2, np.matrix([[4.0],
+ [0.5],
+ [3.0]]))])),
+ ('Cu', OrderedDict([(1, np.matrix([[0.0, 1.0],
+ [-1.0, -2.0],
+ [2.5, -1.9]])),
+ (2, np.matrix([[0.5],
+ [1.6],
+ [-1.4]]))]))])
+
+ scalings = OrderedDict([('O', OrderedDict([('intercept', -2.3),
+ ('slope', 4.5)])),
+ ('Pd', OrderedDict([('intercept', 1.6),
+ ('slope', 2.5)])),
+ ('Cu', OrderedDict([('intercept', -0.3),
+ ('slope', -0.5)]))])
+
+ fingerprints_range = {"Cu": np.array([[2.8636310860653253,
+ 2.8636310860653253],
+ [1.5435994865298275,
+ 1.5435994865298275]]),
+ "O": np.array([[2.9409056366723028,
+ 2.972494902604392],
+ [1.9522542722823606,
+ 4.0720361595017245]]),
+ "Pd": np.array([[2.4629488092411096,
+ 2.6160138774087125],
+ [0.27127576524253594,
+ 0.5898312261433813]])}
+
+ # Testing pure-python and fortran versions of Gaussian-neural force call
+ for fortran in [False, True]:
+ for cores in range(1, 4):
+ label = 'call-periodic/%s-%i' % (fortran, cores)
+ calc = Amp(descriptor=Gaussian(cutoff=4.,
+ Gs=Gs,
+ fortran=fortran),
+ model=NeuralNetwork(hiddenlayers=hiddenlayers,
+ weights=weights,
+ scalings=scalings,
+ activation='tanh',
+ fprange=fingerprints_range,
+ unit_type="double"),
+ label=label,
+ dblabel=label,
+ cores=cores)
+
+ predicted_energies = [calc.get_potential_energy(image) for image in
+ images]
+
+ for image_no in range(len(predicted_energies)):
+ print(predicted_energies[image_no])
+ print(correct_energies[image_no])
+ diff = abs(predicted_energies[image_no] -
+ correct_energies[image_no])
+ assert (diff < 10.**(-14.)), \
+ 'The predicted energy of image %i is wrong!' % (
+ image_no + 1)
+
+ predicted_forces = [calc.get_forces(image) for image in images]
+
+ for image_no in range(len(predicted_forces)):
+ print('predicted forces:')
+ print(predicted_forces[image_no])
+ print('correct forces:')
+ print(np.array(correct_forces[image_no]))
+ for index in range(np.shape(predicted_forces[image_no])[0]):
+ for direction in range(
+ np.shape(predicted_forces[image_no])[1]):
+ diff = abs(predicted_forces[image_no][index][
+ direction] -
+ correct_forces[image_no][index][direction])
+ assert (diff < 10.**(-11.)), \
+ 'The predicted %i force of atom %i of image' \
+ ' %i is wrong!' % (direction,
+ index,
+ image_no + 1)
+
+if __name__ == '__main__':
+ non_periodic_test()
+ periodic_test()
diff --git a/tests/CuOPd_test/gaussian_neural_test/train_test.py b/tests/CuOPd_test/gaussian_neural_test/train_test.py
new file mode 100644
index 0000000..f762c38
--- /dev/null
+++ b/tests/CuOPd_test/gaussian_neural_test/train_test.py
@@ -0,0 +1,556 @@
+"""
+Exact Gaussian-neural scheme loss function, energy loss and force loss
+for five different non-periodic configurations and three three different
+periodic configurations have been calculated in Mathematica. This script
+checks the values calculated by the code during training with and without
+fortran modules and also on different number of cores.
+
+"""
+
+
+import numpy as np
+from collections import OrderedDict
+from ase import Atoms
+from ase.calculators.emt import EMT
+from amp import Amp
+from amp.descriptor.gaussian import Gaussian
+from amp.model.neuralnetwork import NeuralNetwork
+from amp.model import LossFunction
+from amp.regression import Regressor
+try:
+ from ase import __version__ as aseversion
+except ImportError:
+ # We're on ASE 3.10 or older
+ from ase.version import version as aseversion
+aseversion = int(aseversion.split('.')[-2])
+
+
+# The test function for non-periodic systems
+
+convergence = {'energy_rmse': 10.**10.,
+ 'energy_maxresid': 10.**10.,
+ 'force_rmse': 10.**10.,
+ 'force_maxresid': 10.**10., }
+
+regressor = Regressor(optimizer='BFGS')
+
+
+def non_periodic_0th_bfgs_step_test():
+
+ # Making the list of periodic image
+
+ images = [Atoms(symbols='PdOPd2',
+ pbc=np.array([False, False, False], dtype=bool),
+ cell=np.array(
+ [[1., 0., 0.],
+ [0., 1., 0.],
+ [0., 0., 1.]]),
+ positions=np.array(
+ [[0., 0., 0.],
+ [0., 2., 0.],
+ [0., 0., 3.],
+ [1., 0., 0.]])),
+ Atoms(symbols='PdOPd2',
+ pbc=np.array([False, False, False], dtype=bool),
+ cell=np.array(
+ [[1., 0., 0.],
+ [0., 1., 0.],
+ [0., 0., 1.]]),
+ positions=np.array(
+ [[0., 1., 0.],
+ [1., 2., 1.],
+ [-1., 1., 2.],
+ [1., 3., 2.]])),
+ Atoms(symbols='PdO',
+ pbc=np.array([False, False, False], dtype=bool),
+ cell=np.array(
+ [[1., 0., 0.],
+ [0., 1., 0.],
+ [0., 0., 1.]]),
+ positions=np.array(
+ [[2., 1., -1.],
+ [1., 2., 1.]])),
+ Atoms(symbols='Pd2O',
+ pbc=np.array([False, False, False], dtype=bool),
+ cell=np.array(
+ [[1., 0., 0.],
+ [0., 1., 0.],
+ [0., 0., 1.]]),
+ positions=np.array(
+ [[-2., -1., -1.],
+ [1., 2., 1.],
+ [3., 4., 4.]])),
+ Atoms(symbols='Cu',
+ pbc=np.array([False, False, False], dtype=bool),
+ cell=np.array(
+ [[1., 0., 0.],
+ [0., 1., 0.],
+ [0., 0., 1.]]),
+ positions=np.array(
+ [[0., 0., 0.]]))]
+
+ for image in images:
+ image.set_calculator(EMT())
+ image.get_potential_energy(apply_constraint=False)
+ image.get_forces(apply_constraint=False)
+
+ # Parameters
+
+ Gs = {'O': [{'type': 'G2', 'element': 'Pd', 'eta': 0.8},
+ {'type': 'G4', 'elements': [
+ 'Pd', 'Pd'], 'eta':0.2, 'gamma':0.3, 'zeta':1},
+ {'type': 'G4', 'elements': ['O', 'Pd'], 'eta':0.3, 'gamma':0.6,
+ 'zeta':0.5}],
+ 'Pd': [{'type': 'G2', 'element': 'Pd', 'eta': 0.2},
+ {'type': 'G4', 'elements': ['Pd', 'Pd'],
+ 'eta':0.9, 'gamma':0.75, 'zeta':1.5},
+ {'type': 'G4', 'elements': ['O', 'Pd'], 'eta':0.4,
+ 'gamma':0.3, 'zeta':4}],
+ 'Cu': [{'type': 'G2', 'element': 'Cu', 'eta': 0.8},
+ {'type': 'G4', 'elements': ['Cu', 'O'],
+ 'eta':0.2, 'gamma':0.3, 'zeta':1},
+ {'type': 'G4', 'elements': ['Cu', 'Cu'], 'eta':0.3,
+ 'gamma':0.6, 'zeta':0.5}]}
+
+ hiddenlayers = {'O': (2,), 'Pd': (2,), 'Cu': (2,)}
+
+ weights = OrderedDict([('O', OrderedDict([(1, np.matrix([[-2.0, 6.0],
+ [3.0, -3.0],
+ [1.5, -0.9],
+ [-2.5, -1.5]])),
+ (2, np.matrix([[5.5],
+ [3.6],
+ [1.4]]))])),
+ ('Pd', OrderedDict([(1, np.matrix([[-1.0, 3.0],
+ [2.0, 4.2],
+ [1.0, -0.7],
+ [-3.0, 2.0]])),
+ (2, np.matrix([[4.0],
+ [0.5],
+ [3.0]]))])),
+ ('Cu', OrderedDict([(1, np.matrix([[0.0, 1.0],
+ [-1.0, -2.0],
+ [2.5, -1.9],
+ [-3.5, 0.5]])),
+ (2, np.matrix([[0.5],
+ [1.6],
+ [-1.4]]))]))])
+
+ scalings = OrderedDict([('O', OrderedDict([('intercept', -2.3),
+ ('slope', 4.5)])),
+ ('Pd', OrderedDict([('intercept', 1.6),
+ ('slope', 2.5)])),
+ ('Cu', OrderedDict([('intercept', -0.3),
+ ('slope', -0.5)]))])
+
+ # Correct values
+ if aseversion < 12: # EMT values have changed from 3.12.0 version
+ ref_loss = 7144.8107853579895
+ ref_energyloss = (24.318837496016506 ** 2.) * 5
+ ref_forceloss = (144.70282477494519 ** 2.) * 5
+ ref_dloss_dparameters = np.array([0, 0, 0, 0, 0, 0,
+ 0.01374139170953901,
+ 0.36318423812749656,
+ 0.028312691567496464,
+ 0.6012336354445753,
+ 0.9659002689921986,
+ -1.289777005924742,
+ -0.5718960934643078,
+ -2.642566722179569,
+ -1.196039924610482, 0, 0,
+ -2.72563797131018,
+ -0.9080181024866707,
+ -0.7739948323226851,
+ -0.29157894253717415,
+ -2.0599829042717404,
+ -0.6156374289895887,
+ -0.006086517460749253,
+ -0.829678548408266,
+ 0.0008092646745710161,
+ 0.04161302703491613,
+ 0.0034264690790135606,
+ -0.957800456897051,
+ -0.006281929606579444,
+ -0.2883588477371198,
+ -4.245777410962108,
+ -4.3174120941045535,
+ -8.02385959091948,
+ -3.240512651984099,
+ -27.289862194988853,
+ -26.8177742762544,
+ -82.45107056051073,
+ -80.68167683508715])
+ ref_energy_maxresid = 54.21915548269209
+ ref_force_maxresid = 791.6736436232306
+ else:
+ ref_loss = 7144.807220773296
+ ref_energyloss = (24.318829702548342 ** 2.) * 5
+ ref_forceloss = (144.70279593472887 ** 2.) * 5
+ ref_dloss_dparameters = np.array([0,
+ 0,
+ 0,
+ 0,
+ 0,
+ 0,
+ 0.01374139170953901,
+ 0.36318423812749656,
+ 0.028312691567496464,
+ 0.6012336354445753,
+ 0.9659002689921986,
+ -1.2897765357544038,
+ -0.5718958286530584,
+ -2.642565840915077,
+ -1.1960394346870424,
+ 0,
+ 0,
+ -2.7256370964673238,
+ -0.9080177898160631,
+ -0.7739945904033205,
+ -0.29157882294526083,
+ -2.0599825024556027,
+ -0.6156371996742152,
+ -0.006086514109432934,
+ -0.8296782839032163,
+ 0.0008092653341775424,
+ 0.04161306816722683,
+ 0.0034264692325982156,
+ -0.9578001030483714,
+ -0.006281927374160914,
+ -0.28835874344086,
+ -4.245775886469167,
+ -4.317410633818672,
+ -8.02385959091948,
+ -3.240512651984099,
+ -27.289853042932705,
+ -26.81776520493048,
+ -82.45104200076496,
+ -80.68164887277251])
+ ref_energy_maxresid = 54.21913802238612
+ ref_force_maxresid = 791.6734866205463
+
+ # Testing pure-python and fortran versions of Gaussian-neural on different
+ # number of processes
+
+ for fortran in [False, True]:
+ for cores in range(1, 6):
+ label = 'train-nonperiodic/%s-%i' % (fortran, cores)
+ print(label)
+ calc = Amp(descriptor=Gaussian(cutoff=6.5,
+ Gs=Gs,
+ fortran=fortran,),
+ model=NeuralNetwork(hiddenlayers=hiddenlayers,
+ weights=weights,
+ scalings=scalings,
+ activation='sigmoid',
+ regressor=regressor,
+ fortran=fortran,),
+ label=label,
+ dblabel=label,
+ cores=cores)
+
+ lossfunction = LossFunction(convergence=convergence)
+ calc.model.lossfunction = lossfunction
+ calc.train(images=images,)
+ diff = abs(calc.model.lossfunction.loss - ref_loss)
+ print("diff at 204 =", diff)
+ assert (diff < 10.**(-10.)), \
+ 'Calculated value of loss function is wrong!'
+ diff = abs(calc.model.lossfunction.energy_loss - ref_energyloss)
+ assert (diff < 10.**(-10.)), \
+ 'Calculated value of energy per atom RMSE is wrong!'
+ diff = abs(calc.model.lossfunction.force_loss - ref_forceloss)
+ assert (diff < 10 ** (-10.)), \
+ 'Calculated value of force RMSE is wrong!'
+ diff = abs(calc.model.lossfunction.energy_maxresid -
+ ref_energy_maxresid)
+ assert (diff < 10.**(-10.)), \
+ 'Calculated value of energy per atom max residual is wrong!'
+ diff = abs(calc.model.lossfunction.force_maxresid -
+ ref_force_maxresid)
+ assert (diff < 10 ** (-10.)), \
+ 'Calculated value of force max residual is wrong!'
+
+ for _ in range(len(ref_dloss_dparameters)):
+ diff = abs(calc.model.lossfunction.dloss_dparameters[_] -
+ ref_dloss_dparameters[_])
+ assert(diff < 10 ** (-12.)), \
+ "Calculated value of loss function derivative is wrong!"
+
+ dblabel = label
+ secondlabel = '_' + label
+
+ calc = Amp(descriptor=Gaussian(cutoff=6.5,
+ Gs=Gs,
+ fortran=fortran,),
+ model=NeuralNetwork(hiddenlayers=hiddenlayers,
+ weights=weights,
+ scalings=scalings,
+ activation='sigmoid',
+ regressor=regressor,
+ fortran=fortran,),
+ label=secondlabel,
+ dblabel=dblabel,
+ cores=cores)
+
+ lossfunction = LossFunction(convergence=convergence)
+ calc.model.lossfunction = lossfunction
+ calc.train(images=images,)
+ diff = abs(calc.model.lossfunction.loss - ref_loss)
+ assert (diff < 10.**(-10.)), \
+ 'Calculated value of loss function is wrong!'
+ diff = abs(calc.model.lossfunction.energy_loss - ref_energyloss)
+ assert (diff < 10.**(-10.)), \
+ 'Calculated value of energy per atom RMSE is wrong!'
+ diff = abs(calc.model.lossfunction.force_loss - ref_forceloss)
+ assert (diff < 10 ** (-10.)), \
+ 'Calculated value of force RMSE is wrong!'
+ diff = abs(calc.model.lossfunction.energy_maxresid -
+ ref_energy_maxresid)
+ assert (diff < 10.**(-10.)), \
+ 'Calculated value of energy per atom max residual is wrong!'
+ diff = abs(calc.model.lossfunction.force_maxresid -
+ ref_force_maxresid)
+ assert (diff < 10 ** (-10.)), \
+ 'Calculated value of force max residual is wrong!'
+
+ for _ in range(len(ref_dloss_dparameters)):
+ diff = abs(calc.model.lossfunction.dloss_dparameters[_] -
+ ref_dloss_dparameters[_])
+ assert(diff < 10 ** (-12.)), \
+ 'Calculated value of loss function derivative is wrong!'
+
+
+# The test function for periodic systems and first BFGS step
+
+def periodic_0th_bfgs_step_test():
+
+ # Making the list of images
+
+ images = [Atoms(symbols='PdOPd',
+ pbc=np.array([True, False, False], dtype=bool),
+ cell=np.array(
+ [[2., 0., 0.],
+ [0., 2., 0.],
+ [0., 0., 2.]]),
+ positions=np.array(
+ [[0.5, 1., 0.5],
+ [1., 0.5, 1.],
+ [1.5, 1.5, 1.5]])),
+ Atoms(symbols='PdO',
+ pbc=np.array([True, True, False], dtype=bool),
+ cell=np.array(
+ [[2., 0., 0.],
+ [0., 2., 0.],
+ [0., 0., 2.]]),
+ positions=np.array(
+ [[0.5, 1., 0.5],
+ [1., 0.5, 1.]])),
+ Atoms(symbols='Cu',
+ pbc=np.array([True, True, False], dtype=bool),
+ cell=np.array(
+ [[1.8, 0., 0.],
+ [0., 1.8, 0.],
+ [0., 0., 1.8]]),
+ positions=np.array(
+ [[0., 0., 0.]]))]
+
+ for image in images:
+ image.set_calculator(EMT())
+ image.get_potential_energy(apply_constraint=False)
+ image.get_forces(apply_constraint=False)
+
+ # Parameters
+
+ Gs = {'O': [{'type': 'G2', 'element': 'Pd', 'eta': 0.8},
+ {'type': 'G4', 'elements': ['O', 'Pd'], 'eta':0.3, 'gamma':0.6,
+ 'zeta':0.5}],
+ 'Pd': [{'type': 'G2', 'element': 'Pd', 'eta': 0.2},
+ {'type': 'G4', 'elements': ['Pd', 'Pd'],
+ 'eta':0.9, 'gamma':0.75, 'zeta':1.5}],
+ 'Cu': [{'type': 'G2', 'element': 'Cu', 'eta': 0.8},
+ {'type': 'G4', 'elements': ['Cu', 'Cu'], 'eta':0.3,
+ 'gamma':0.6, 'zeta':0.5}]}
+
+ hiddenlayers = {'O': (2,), 'Pd': (2,), 'Cu': (2,)}
+
+ weights = OrderedDict([('O', OrderedDict([(1, np.matrix([[-2.0, 6.0],
+ [3.0, -3.0],
+ [1.5, -0.9]])),
+ (2, np.matrix([[5.5],
+ [3.6],
+ [1.4]]))])),
+ ('Pd', OrderedDict([(1, np.matrix([[-1.0, 3.0],
+ [2.0, 4.2],
+ [1.0, -0.7]])),
+ (2, np.matrix([[4.0],
+ [0.5],
+ [3.0]]))])),
+ ('Cu', OrderedDict([(1, np.matrix([[0.0, 1.0],
+ [-1.0, -2.0],
+ [2.5, -1.9]])),
+ (2, np.matrix([[0.5],
+ [1.6],
+ [-1.4]]))]))])
+
+ scalings = OrderedDict([('O', OrderedDict([('intercept', -2.3),
+ ('slope', 4.5)])),
+ ('Pd', OrderedDict([('intercept', 1.6),
+ ('slope', 2.5)])),
+ ('Cu', OrderedDict([('intercept', -0.3),
+ ('slope', -0.5)]))])
+
+ # Correct values
+ if aseversion < 12: # EMT values have changed from 3.12.0 version
+ ref_loss = 8004.292841411172
+ ref_energyloss = (43.7360019403031 ** 2.) * 3
+ ref_forceloss = (137.40994760947325 ** 2.) * 3
+ ref_dloss_dparameters = np.array([0.08141668748130322,
+ 0.03231235582925534,
+ 0.04388650395738586,
+ 0.017417514465922313,
+ 0.028431276597563077,
+ 0.011283700608814465,
+ 0.0941695726576061,
+ -0.12322258890990219,
+ 0.12679918754154568,
+ 63.53960075374332,
+ 0.01624770019548904,
+ -86.6263955859162,
+ -0.01777752828707744,
+ 86.22415217526024,
+ 0.017745913074496918,
+ 104.58358033298292,
+ -96.73280209888215,
+ -99.09843648905876,
+ -8.302880631972338,
+ -1.2590007162074357,
+ 8.302877346883133,
+ 1.25875988418134,
+ -8.302866610678247,
+ -1.2563833805675353,
+ 28.324298392680998,
+ 28.093155094726413,
+ -29.37874455931869,
+ -11.247473567044866,
+ 11.119951466664787,
+ -87.08582317481387,
+ -20.939485239182346,
+ -125.73267675705365,
+ -35.138524407482116])
+ else:
+ ref_loss = 8004.287750978173
+ ref_energyloss = (43.73598563177581 ** 2.) * 3
+ ref_forceloss = (137.409923023214 ** 2.) * 3
+ ref_dloss_dparameters = np.array([0.08141663280688925,
+ 0.03231233413027478,
+ 0.043886474485922956,
+ 0.01741750276939638,
+ 0.02843125750487539,
+ 0.011283693031378718,
+ 0.09416950941914284,
+ -0.12322250616122936,
+ 0.1267991023910503,
+ 63.53958764057119,
+ 0.016247696749304368,
+ -86.62637753054923,
+ -0.01777752451341436,
+ 86.22413420485914,
+ 0.01774590930723711,
+ 104.58353326982777,
+ -96.73275667196937,
+ -99.09839026204304,
+ -8.302877823431269,
+ -1.2590002903842232,
+ 8.302874538343092,
+ 1.2587594584335775,
+ -8.302863802141216,
+ -1.2563829555383859,
+ 28.32428881173613,
+ 28.093145591893936,
+ -29.37873462156934,
+ -11.24746601393696,
+ 11.11994399919284,
+ -87.08579155328007,
+ -20.93947792122797,
+ -125.73262989900473,
+ -35.13850819392253])
+
+ # Testing pure-python and fortran versions of Gaussian-neural on different
+ # number of processes
+
+ for fortran in [False, True]:
+ for cores in range(1, 4):
+ label = 'train-periodic/%s-%i' % (fortran, cores)
+ print(label)
+ calc = Amp(descriptor=Gaussian(cutoff=4.,
+ Gs=Gs,
+ fortran=fortran,),
+ model=NeuralNetwork(hiddenlayers=hiddenlayers,
+ weights=weights,
+ scalings=scalings,
+ activation='tanh',
+ regressor=regressor,
+ fortran=fortran,),
+ label=label,
+ dblabel=label,
+ cores=cores)
+
+ lossfunction = LossFunction(convergence=convergence)
+ calc.model.lossfunction = lossfunction
+ calc.train(images=images,)
+ diff = abs(calc.model.lossfunction.loss - ref_loss)
+ print("diff at 414 =", diff)
+ assert (diff < 10.**(-10.)), \
+ 'Calculated value of loss function is wrong!'
+ diff = abs(calc.model.lossfunction.energy_loss - ref_energyloss)
+ assert (diff < 10.**(-10.)), \
+ 'Calculated value of energy per atom RMSE is wrong!'
+ diff = abs(calc.model.lossfunction.force_loss - ref_forceloss)
+ assert (diff < 10 ** (-9.)), \
+ 'Calculated value of force RMSE is wrong!'
+
+ for _ in range(len(ref_dloss_dparameters)):
+ diff = abs(calc.model.lossfunction.dloss_dparameters[_] -
+ ref_dloss_dparameters[_])
+ assert(diff < 10 ** (-10.)), \
+ 'Calculated value of loss function derivative is wrong!'
+
+ dblabel = label
+ secondlabel = '_' + label
+
+ calc = Amp(descriptor=Gaussian(cutoff=4.,
+ Gs=Gs,
+ fortran=fortran),
+ model=NeuralNetwork(hiddenlayers=hiddenlayers,
+ weights=weights,
+ scalings=scalings,
+ activation='tanh',
+ regressor=regressor,
+ fortran=fortran,),
+ label=secondlabel,
+ dblabel=dblabel,
+ cores=cores)
+
+ lossfunction = LossFunction(convergence=convergence)
+ calc.model.lossfunction = lossfunction
+ calc.train(images=images,)
+ diff = abs(calc.model.lossfunction.loss - ref_loss)
+ assert (diff < 10.**(-10.)), \
+ 'Calculated value of loss function is wrong!'
+ diff = abs(calc.model.lossfunction.energy_loss - ref_energyloss)
+ assert (diff < 10.**(-10.)), \
+ 'Calculated value of energy per atom RMSE is wrong!'
+ diff = abs(calc.model.lossfunction.force_loss - ref_forceloss)
+ assert (diff < 10 ** (-9.)), \
+ 'Calculated value of force RMSE is wrong!'
+
+ for _ in range(len(ref_dloss_dparameters)):
+ diff = abs(calc.model.lossfunction.dloss_dparameters[_] -
+ ref_dloss_dparameters[_])
+ assert(diff < 10 ** (-10.)), \
+ 'Calculated value of loss function derivative is wrong!'
+
+
+if __name__ == '__main__':
+ non_periodic_0th_bfgs_step_test()
+ periodic_0th_bfgs_step_test()
diff --git a/tests/consistency_test/gaussian_neural_test/force_call_test.py b/tests/consistency_test/gaussian_neural_test/force_call_test.py
new file mode 100644
index 0000000..d514527
--- /dev/null
+++ b/tests/consistency_test/gaussian_neural_test/force_call_test.py
@@ -0,0 +1,560 @@
+"""
+This script creates a list of three images. It then calculates behler-neural
+scheme forces and energies of different combinations of them with and without
+fortran modules, and check consistency between them.
+
+"""
+
+#
+
+import numpy as np
+from ase import Atoms
+from amp import Amp
+from amp.descriptor.gaussian import Gaussian
+from amp.model.neuralnetwork import NeuralNetwork
+
+#
+# Making the list of images
+
+
+def make_images():
+ """Makes test images."""
+
+ images = [Atoms(symbols='Pd4O2',
+ pbc=np.array([True, True, False], dtype=bool),
+ cell=np.array(
+ [[7.78, 0., 0.],
+ [0., 5.50129076, 0.],
+ [0., 0., 15.37532269]]),
+ positions=np.array(
+ [[0., 0., 8.37532269],
+ [3.89, 0., 8.37532269],
+ [0., 2.75064538, 8.37532269],
+ [3.89, 2.75064538, 8.37532269],
+ [5.835, 1.37532269, 8.5],
+ [5.835, 7.12596807, 8.]])),
+ Atoms(symbols='Pd4O2',
+ pbc=np.array([True, True, False], dtype=bool),
+ cell=np.array(
+ [[7.78, 0., 0.],
+ [0., 5.50129076, 0.],
+ [0., 0., 15.37532269]]),
+ positions=np.array(
+ [[8.43409903e-03, -4.40430259e-03,
+ 8.37107726e+00],
+ [3.88430768e+00, 5.28005966e-03,
+ 8.36678641e+00],
+ [-1.01122240e-02, 2.74577426e+00,
+ 8.37861758e+00],
+ [3.88251383e+00, 2.74138906e+00,
+ 8.37087611e+00],
+ [5.82067191e+00, 1.19156898e+00,
+ 8.97714483e+00],
+ [5.83355445e+00, 7.53318593e+00,
+ 8.50142020e+00]])),
+ Atoms(symbols='Pd4O2',
+ pbc=np.array([True, True, False], dtype=bool),
+ cell=np.array(
+ [[7.78, 0., 0.],
+ [0., 5.50129076, 0.],
+ [0., 0., 15.37532269]]),
+ positions=np.array(
+ [[1.84507759e-02, -9.96620379e-03,
+ 8.36465110e+00],
+ [3.87691266e+00, 9.29708987e-03,
+ 8.35604207e+00],
+ [-1.29700138e-02, 2.74373753e+00,
+ 8.37941484e+00],
+ [3.86813484e+00, 2.73488653e+00,
+ 8.36395999e+00],
+ [5.80386111e+00, 7.98192190e-01,
+ 9.74324179e+00],
+ [5.83223956e+00, 8.23855393e+00,
+ 9.18295137e+00]]))]
+
+ return images
+
+#
+# Parameters
+
+cutoff = 6.5
+activation = 'tanh'
+hiddenlayers = {'O': (5, 5), 'Pd': (5, 5)}
+
+Gs = {'O': [{'eta': 0.05, 'type': 'G2', 'element': 'O'},
+ {'eta': 0.05, 'type': 'G2', 'element': 'Pd'},
+ {'eta': 2.0, 'type': 'G2', 'element': 'O'},
+ {'eta': 2.0, 'type': 'G2', 'element': 'Pd'},
+ {'eta': 4.0, 'type': 'G2', 'element': 'O'},
+ {'eta': 4.0, 'type': 'G2', 'element': 'Pd'},
+ {'eta': 8.0, 'type': 'G2', 'element': 'O'},
+ {"eta": 8.0, "type": "G2", "element": "Pd"},
+ {"eta": 20.0, "type": "G2", "element": "O"},
+ {"eta": 20.0, "type": "G2", "element": "Pd"},
+ {"eta": 40.0, "type": "G2", "element": "O"},
+ {"eta": 40.0, "type": "G2", "element": "Pd"},
+ {"eta": 80.0, "type": "G2", "element": "O"},
+ {"eta": 80.0, "type": "G2", "element": "Pd"},
+ {"zeta": 1.0, "elements": ["O", "O"], "type": "G4", "gamma": 1.0,
+ "eta": 0.005},
+ {"zeta": 1.0, "elements": ["O", "Pd"], "type": "G4", "gamma": 1.0,
+ "eta": 0.005},
+ {"zeta": 1.0, "elements": ["Pd", "Pd"], "type": "G4",
+ "gamma": 1.0, "eta": 0.005},
+ {"zeta": 1.0, "elements": ["O", "O"],
+ "type": "G4", "gamma": -1.0, "eta": 0.005},
+ {"zeta": 1.0, "elements": ["O", "Pd"],
+ "type": "G4", "gamma": -1.0, "eta": 0.005},
+ {"zeta": 1.0, "elements": ["Pd", "Pd"], "type": "G4",
+ "gamma": -1.0,
+ "eta": 0.005}, {"zeta": 2.0, "elements": ["O", "O"], "type": "G4",
+ "gamma": 1.0, "eta": 0.005},
+ {"zeta": 2.0, "elements": ["O", "Pd"],
+ "type": "G4", "gamma": 1.0, "eta": 0.005},
+ {"zeta": 2.0,
+ "elements": ["Pd", "Pd"], "type": "G4",
+ "gamma": 1.0, "eta": 0.005},
+ {"zeta": 2.0, "elements": ["O", "O"], "type": "G4", "gamma": -1.0,
+ "eta": 0.005},
+ {"zeta": 2.0, "elements": ["O", "Pd"], "type": "G4",
+ "gamma": -1.0, "eta": 0.005}, {"zeta": 2.0,
+ "elements": ["Pd", "Pd"],
+ "type": "G4", "gamma": -1.0,
+ "eta": 0.005},
+ {"zeta": 4.0,
+ "elements": ["O", "O"],
+ "type": "G4",
+ "gamma": 1.0, "eta": 0.005},
+ {"zeta": 4.0, "elements": ["O", "Pd"], "type": "G4", "gamma": 1.0,
+ "eta": 0.005}, {"zeta": 4.0, "elements": ["Pd", "Pd"],
+ "type": "G4", "gamma": 1.0, "eta": 0.005},
+ {"zeta": 4.0, "elements": ["O", "O"], "type": "G4", "gamma": -1.0,
+ "eta": 0.005}, {"zeta": 4.0, "elements": ["O", "Pd"],
+ "type": "G4", "gamma": -1.0, "eta": 0.005},
+ {"zeta": 4.0, "elements": ["Pd", "Pd"],
+ "type": "G4", "gamma": -1.0,
+ "eta": 0.005}],
+ "Pd": [{"eta": 0.05, "type": "G2", "element": "O"},
+ {"eta": 0.05, "type": "G2", "element": "Pd"},
+ {"eta": 2.0, "type": "G2", "element": "O"},
+ {"eta": 2.0, "type": "G2", "element": "Pd"},
+ {"eta": 4.0, "type": "G2", "element": "O"},
+ {"eta": 4.0, "type": "G2", "element": "Pd"},
+ {"eta": 8.0, "type": "G2", "element": "O"},
+ {"eta": 8.0, "type": "G2", "element": "Pd"},
+ {"eta": 20.0, "type": "G2", "element": "O"},
+ {"eta": 20.0, "type": "G2", "element": "Pd"},
+ {"eta": 40.0, "type": "G2", "element": "O"},
+ {"eta": 40.0, "type": "G2", "element": "Pd"},
+ {"eta": 80.0, "type": "G2", "element": "O"},
+ {"eta": 80.0, "type": "G2", "element": "Pd"},
+ {"zeta": 1.0, "elements": ["O", "O"], "type": "G4", "gamma": 1.0,
+ "eta": 0.005},
+ {"zeta": 1.0, "elements": ["O", "Pd"], "type": "G4", "gamma": 1.0,
+ "eta": 0.005}, {"zeta": 1.0,
+ "elements": ["Pd", "Pd"],
+ "type": "G4",
+ "gamma": 1.0, "eta": 0.005},
+ {"zeta": 1.0, "elements": ["O", "O"], "type": "G4",
+ "gamma": -1.0, "eta": 0.005}, {"zeta": 1.0,
+ "elements": ["O", "Pd"],
+ "type": "G4", "gamma": -1.0,
+ "eta": 0.005},
+ {"zeta": 1.0, "elements": ["Pd", "Pd"], "type": "G4",
+ "gamma": -1.0,
+ "eta": 0.005}, {"zeta": 2.0, "elements": ["O", "O"],
+ "type": "G4",
+ "gamma": 1.0, "eta": 0.005},
+ {"zeta": 2.0,
+ "elements": ["O", "Pd"], "type": "G4",
+ "gamma": 1.0, "eta": 0.005}, {"zeta": 2.0,
+ "elements": ["Pd", "Pd"],
+ "type": "G4",
+ "gamma": 1.0, "eta": 0.005},
+ {"zeta": 2.0, "elements": ["O", "O"], "type": "G4", "gamma": -1.0,
+ "eta": 0.005}, {"zeta": 2.0, "elements": ["O", "Pd"],
+ "type": "G4",
+ "gamma": -1.0, "eta": 0.005},
+ {"zeta": 2.0, "elements": ["Pd", "Pd"],
+ "type": "G4", "gamma": -1.0, "eta": 0.005},
+ {"zeta": 4.0, "elements": ["O", "O"],
+ "type": "G4", "gamma": 1.0, "eta": 0.005},
+ {"zeta": 4.0, "elements": ["O", "Pd"], "type": "G4", "gamma": 1.0,
+ "eta": 0.005}, {"zeta": 4.0, "elements": ["Pd", "Pd"],
+ "type": "G4",
+ "gamma": 1.0, "eta": 0.005},
+ {"zeta": 4.0,
+ "elements": ["O", "O"],
+ "type": "G4", "gamma": -1.0, "eta": 0.005},
+ {"zeta": 4.0, "elements": ["O", "Pd"],
+ "type": "G4", "gamma": -1.0, "eta": 0.005},
+ {"zeta": 4.0, "elements": ["Pd", "Pd"], "type": "G4",
+ "gamma": -1.0,
+ "eta": 0.005}]}
+
+fingerprints_range = {"O": [[1.2034320541645842, 1.2325033032109112],
+ [6.126415779807456, 6.978993471872114],
+ [0.9968712422847974, 1.0238339591857768],
+ [3.8381486000216656, 4.6059867092450295],
+ [0.895627825206874, 0.9671954702902308],
+ [2.583663009213816, 3.2975746566094606],
+ [0.7964913272920149, 0.9263856740488036],
+ [1.3358420027866575, 1.987698731796872],
+ [0.6086945405610695, 0.8469928578399282],
+ [0.2529142293461268, 0.7771634549572402],
+ [0.3914378098148111, 0.7306361163848886],
+ [0.020116896658220102, 0.35759863784953067],
+ [0.16188160578588526, 0.5436809953654286],
+ [0.00018177869062004963, 0.12577780799256955],
+ [2.9283890234835495, 2.960848034649544],
+ [30.849062520667466, 34.34079115772228],
+ [74.38292698900159, 81.77213709053859],
+ [1.6948136646289693, 1.803559109943061],
+ [20.032647223918715, 25.204662559464523],
+ [46.30668067734771, 58.99262463422656],
+ [2.37554239540103, 2.7402971203873707],
+ [21.915472638677855, 25.585727302527907],
+ [54.57445823130601, 61.34907477324089],
+ [1.109508025380456, 1.6154672068468818],
+ [11.916848644888729, 17.04495978743268],
+ [27.88887260037905, 39.18415587653102],
+ [1.8928302257282086, 2.5827385383035284],
+ [14.565545948279196, 17.941552668205755],
+ [36.94672253980532, 42.672289485060745],
+ [0.6553641770222022, 1.4212816597490932],
+ [6.00446500499159, 10.95563925572871],
+ [15.456097104319266, 24.846009591495683]],
+ "Pd": [[0.8893801678132963, 2.186742268993366],
+ [5.681935730435191, 5.801357868163544],
+ [0.28325235730086895, 1.7195167772827762],
+ [3.319274384132528, 3.4278827090091513],
+ [0.08915750058756017, 1.5653576140941878],
+ [2.053165118375831, 2.1493466057807606],
+ [0.009285644347874652, 1.3396267483639697],
+ [0.8813449647319378, 0.949755776664418],
+ [1.4022708468796206e-05, 0.8694356341233072],
+ [0.08961848129998626, 0.10519747021560875],
+ [2.5350651988745783e-10, 0.4474694168207284],
+ [0.002199096348873827, 0.002942664869970825],
+ [1.3547037121993997e-19, 0.13803579787982578],
+ [1.3829812001140997e-06, 2.3283471452833342e-06],
+ [2.245260381205755, 6.506711057752208],
+ [30.80688145836148, 46.62802877467697],
+ [63.159691665137835, 63.42318872782115],
+ [1.4470182218367846, 3.5407788975262466],
+ [16.920091949041364, 27.974461180856085],
+ [43.372163387951744, 45.106267442742194],
+ [2.1007039650495236, 5.235507846017004],
+ [24.98117242089699, 38.28678610359639],
+ [47.903805932396644, 48.16729306561395],
+ [0.8039272162816901, 2.5404648021947756],
+ [11.094382911576862, 19.43921017240714],
+ [28.14489163971961, 29.853649179126506],
+ [2.0677437396917027, 3.980577524358615],
+ [18.507476335936385, 30.408978128204563],
+ [33.915660566694726, 34.201570710274964],
+ [0.2569160731561561, 1.5411619576089908],
+ [4.8043897598894185, 13.387133883397796],
+ [17.225764659147405, 18.83859512207448]]}
+
+weights = {"O": {1: np.matrix([[0.00036942165470836563, 0.022852891328080965,
+ -0.007763989520407272, 0.0017904084613678817,
+ -0.04680830976127531],
+ [-0.011220619170475267, -0.031465481900468384,
+ -0.0185587250581268, 0.00029876794872765733,
+ -0.03270538302430687],
+ [0.009269384571647388, -0.004439491584362951,
+ 0.02041622613407708, -0.04075220241750707,
+ -0.004384443250886716],
+ [-0.02045226889653854, -0.04085271674587569,
+ -0.0007470148939682439, 0.017448937916376722,
+ -0.03247360282480993],
+ [0.014076539841285075, -0.0006001148651055555,
+ -0.011206188631385075, 0.036131770356541804,
+ 0.04019195568663911], [0.04438555375359607,
+ -0.03630318854778723, -
+ 0.011787189723001579,
+ 0.03403384156560013,
+ 0.015653363757362176],
+ [0.02134038436971622, 0.000554719592425923,
+ -0.04353602059838731, 0.02829112575071807,
+ -0.010315738192632054],
+ [-0.009864186941597866, 0.025867111325423034,
+ -0.030222981254973712, -0.009255262808615411,
+ -0.0047940678082599025],
+ [0.009775595855839286, -0.004398102065676125,
+ -0.00195136837351699, -0.0015883410280669308,
+ 0.03528054083271703],
+ [0.0088457892425432, -0.0017778202887624855,
+ -0.030182606288789264, 0.03153096931177092,
+ -0.02709527292127762], [-0.02911935923819357,
+ -0.011844856703362105,
+ 0.03358589444051113,
+ 0.007149386960731488,
+ -0.007590532737964187],
+ [-0.03944400124516653, 0.03562647918045643,
+ -0.041584201666104756, -0.03482985747462908,
+ -0.045374395214468496],
+ [0.019057890033725933, -0.012580031773554046,
+ 0.04290707878850142, 0.04177600131985214,
+ -0.03500384259370384],
+ [-0.02033084113684249, -0.01111345650394805,
+ -0.005485434669132497, 0.03554246348547074,
+ 0.031421467582530324],
+ [-0.03310168568774624, 0.04617363212275834,
+ 0.03868456178440169, 0.012151585419746959,
+ -0.007359447003748548],
+ [0.044255356329426065, 0.036122120043098505,
+ 0.001842950538131695, -0.01615761183192349,
+ -0.03771427943410247],
+ [-0.0381118034639101, -0.04643318160382238,
+ 0.02900519652241655, -0.008475138348622263,
+ 0.021893066028991853],
+ [0.016038314042298385, 0.03545540262812917,
+ -0.031220884269865096, -0.033670838618425646,
+ 0.04684810506588663],
+ [0.037697271308168634, -0.04250612661317486,
+ 0.0028173761257807364, 0.04503591051281573,
+ -0.005888259820159045],
+ [-0.01688674535740177, 0.03765441774468983,
+ 0.040162723331136185, 0.023291060425779497,
+ 0.01875483057892434],
+ [0.009559969717541077, -0.010986361005406543,
+ 0.017717618257908102, 0.021594452542040676,
+ 0.00668490554203105],
+ [0.02899572788647327, 0.03884753546552183,
+ 0.0334345646492913, -0.0009724588802520473,
+ 0.008901825903656319],
+ [0.04472782971579241, 0.020125743534124996,
+ 0.018466622131502394, 0.014248370483492187,
+ 0.02954224116911444],
+ [0.018038582886592464, 0.007882237781735343,
+ -0.005639481686277245, -0.030317048204748388,
+ 0.011443284253329196],
+ [-0.014574589075944028, 0.027312879897418138,
+ -0.0052516221359138054, -0.02858166510190807,
+ -0.0218508786228111],
+ [-0.019062166466149163, -0.0421343628780219,
+ -0.0292511219030615, -0.04063165343284807,
+ -0.026551753085291934],
+ [-0.006973189792228912, 0.018725587327618767,
+ 0.037936857142053707, 0.011375377365914208,
+ -0.03823975980860963],
+ [-0.03087795180506949, -0.002166181826768615,
+ -0.009411940441267343, 0.008062289773496219,
+ 0.03143133615872179],
+ [0.022767389458292583, -0.032719990839286985,
+ 0.010234126834754581, -0.0025988597425086815,
+ 0.012893424785935387],
+ [0.03729503214821439, -0.04055234881977389,
+ -0.033180455803208164, -0.003962067731434399,
+ -0.04089277483943934],
+ [-0.005215540749534078, 0.013163002568367034,
+ 0.03980552568163612, 0.00803385354609431,
+ 7.658166702390057e-05],
+ [0.013936695364567375, 0.017657437899754047,
+ 0.027548202328624413, -0.0008692880197060243,
+ 0.032762776542753225],
+ [0.0, 0.0, 0.0, 0.0, 0.0]]),
+ 2: np.matrix([[-0.13315704861614908, 0.21616481887190436,
+ 0.07102546888848049, -0.2758348650926486,
+ -0.12434812671933795], [-0.024314957289090222,
+ -0.16392515185308187,
+ 0.2058922926890992,
+ 0.2154935160814611,
+ 0.11014812360618259],
+ [-0.08133895309316427, -0.1937923029504461,
+ 0.206977413616443, 0.03575405386811248,
+ -0.10559013113242327],
+ [0.1469937256217183, 0.07621742865022896,
+ 0.08882575726900893, -0.2577928927812111,
+ 0.2670748892517893],
+ [-0.141370342762172, -0.23738939477247786,
+ -0.06633785630500305, -0.24779722808875726,
+ 0.17677488447247947],
+ [0.0, 0.0, 0.0, 0.0, 0.0]]),
+ 3: np.matrix([[0.0377280558085506], [0.013842778159018243],
+ [-0.29408570195900635],
+ [0.19529036441834974], [-0.16745509851929688],
+ [0.0]])},
+ "Pd": {1: np.matrix([[0.008070279669324429, -0.04006333630883027,
+ -0.04312742429320118,
+ -0.03942171198922403, -0.04540662900302544],
+ [0.01339814716182161, -0.022961503636403632,
+ -0.006969046155031772, 0.01539617792272549,
+ -0.02587844848147742],
+ [0.045033334892680674, 0.0034430687137840393,
+ 0.02405223418836909, -0.035506042140031155,
+ 0.021328894351546446],
+ [-0.04416667286322164, -0.03993519399665675,
+ 0.032311654583997304, -0.03745738975064494,
+ 0.006061355326268905],
+ [-0.043438846516273555, 0.020424466564239616,
+ -0.03712722505187403, -0.04417848105963802,
+ -0.008777813735156417],
+ [0.03965347387678732, -0.01799472378269024,
+ 0.0362866746012956, 0.009704740166992,
+ 0.0004118619760827419],
+ [-0.03180969154106336, -0.006918591959222585,
+ 0.014099398062742227, -0.022931651589221756,
+ 0.03148626725702887],
+ [0.04573128229126357, 0.016654751576744925,
+ -0.028910689496630722,
+ 0.02242435838167882, -0.02783084152657823],
+ [0.030147617474449384, -0.009580788002314114,
+ 0.026913224902892594, -0.006350898911528513,
+ -0.01580260272955647],
+ [-0.03128280563473111, -0.044359797916295726,
+ -0.0455871021838766, -0.022323871191166217,
+ -0.025520059574284607],
+ [-0.004213681746207731, -0.027963910926939888,
+ -0.03734025976436221, -0.029904058599404374,
+ -0.023362113055890702],
+ [0.03140805808988659, -0.01625862158802977,
+ -0.012926251592534549, 0.0199950518624378,
+ 0.00017000814436556738],
+ [0.03611338398893238, -0.04064588225668243,
+ -0.03548786885528668, -0.034119876099748085,
+ -0.03249791207428783],
+ [0.04302813264222295, -0.031784410672976354,
+ -0.0018505347572984332, -0.02619493567773821,
+ -0.009963146880811465],
+ [-0.00382761556441661, 0.02051612655974898,
+ -0.015084868592703193, 0.036644660445905974,
+ 0.024267396930057042],
+ [0.0027419126458524262, -0.01875730493117643,
+ 0.042029556463568374, -0.033491496522005004,
+ 0.04664358315093048],
+ [-0.00857053904710025, 0.004386575075249165,
+ -0.03681921382606547, 0.024055769666913862,
+ -0.006710822409842235],
+ [0.01600071354805395, -0.03619212782962617,
+ -0.007657861036073181, 0.04579883161005442,
+ -0.027272703382017247],
+ [0.024782613292205463, 0.02454697361926271,
+ 0.014219326292126383, -0.03120859763819632,
+ 0.019746899921596867],
+ [-0.008107835898640163, -0.02411112524744128,
+ 0.01680784294783398, -0.03942450668164303,
+ -0.02148968897141828],
+ [0.006160769106771449, -0.02608742029162942,
+ -0.03445574192255718, 0.011100495475242236,
+ -0.011890887277678633],
+ [0.019265102424069563, -0.019510992393145597,
+ -0.039330197040643305, 0.028930252847621296,
+ 0.04535579375056527],
+ [0.0003841258275426168, -0.03140536534416318,
+ 0.004402540856303851, -0.006596225898408456,
+ -0.012287524451218383],
+ [0.032434589752896065,
+ -0.038422865723774166,
+ 0.04121673691259908,
+ 0.026471126594987765,
+ -0.045659510547159485],
+ [0.016693221128737612, 0.033475787637348264,
+ -0.01216104367054778, -0.04682497168901334,
+ -0.025748662607038442],
+ [-0.030035984906774393, 0.03528987279339724,
+ 0.01842649225978525, 0.013967345908646303,
+ 0.030368471307811548],
+ [-0.004245382943207754, 0.004346310546406856,
+ 0.04395403376516939, -0.03528225866346128,
+ 0.040526584371759225],
+ [-0.026240373867317947, -0.02790624801091845,
+ 0.033248579584558235, -0.03456761843589754,
+ -0.00921953855906435],
+ [-0.04029772119462781, 0.03944849938380114,
+ 0.03367466933743388, -0.04654081205741553,
+ -0.02559442696348037],
+ [-0.019162242379646047,
+ -0.0074198239538341496, -0.03481645962457279,
+ 0.0023221563528588313,
+ -0.01362951107641086],
+ [-0.04359327067093935, 0.008182459343197494,
+ -0.004311982184810589, 0.013459029430653538,
+ -0.02593952116632298],
+ [0.03419829018664716, -0.02909906291417496,
+ 0.0450381809975251,
+ 0.04636855435694584, 0.004474211596899327],
+ [0.0, 0.0, 0.0, 0.0, 0.0]]),
+ 2: np.matrix([[0.07339646055942084, -0.22682470946032204,
+ -0.07464451676678477, -0.21765816530655968,
+ 0.10447399748556846],
+ [-0.07339330664074986, -0.2620525555813218,
+ -0.010761218306725495, 0.07390075065002266,
+ 0.11039186125577433],
+ [-0.17516748044584285, -0.2837828871933906,
+ -0.02085650668287642, 0.08755824083276131,
+ 0.07220039658405131],
+ [0.23974597425595473, 0.24760019759492297,
+ -0.22060915253115443, -0.28310518337421325,
+ -0.016857214958102662],
+ [0.11687787432599622, -0.10151689213238121,
+ 0.18735099239621017, 0.21356695418645139,
+ -0.240568272158666],
+ [0.0, 0.0, 0.0, 0.0, 0.0]]),
+ 3: np.matrix([[0.05906457619187622], [-0.29300196568707426],
+ [-0.018802515167880285],
+ [-0.2723126668305828], [0.22668984898833738],
+ [0.0]])}}
+
+scalings = {"O": {"intercept": 4.2468934359280288,
+ "slope": 3.1965614888424687},
+ "Pd": {"intercept": 4.2468934359280288,
+ "slope": 3.1965614888424687}}
+
+#
+# Testing pure-python and fortran versions of gaussian-neural force call
+
+
+def test():
+
+ images = make_images()
+
+ for fortran in [False, True]:
+ label = 'forcecall/%s' % fortran
+ calc = Amp(descriptor=Gaussian(cutoff=cutoff,
+ Gs=Gs,
+ fortran=fortran,),
+ model=NeuralNetwork(hiddenlayers=hiddenlayers,
+ weights=weights,
+ scalings=scalings,
+ activation=activation,
+ mode='atom-centered',
+ fprange=fingerprints_range,
+ fortran=fortran,),
+ label=label,)
+
+ if fortran is False:
+ reference_energies = [calc.get_potential_energy(image)
+ for image in images]
+ else:
+ predicted_energies = [calc.get_potential_energy(image)
+ for image in images]
+ for image_no in range(len(predicted_energies)):
+ assert (abs(predicted_energies[image_no] -
+ reference_energies[image_no]) < 10.**(-5.)), \
+ 'Calculated energy value of image %i by \
+ fortran version is not consistent with the \
+ value of python version.' % (image_no + 1)
+
+ if fortran is False:
+ reference_forces = [calc.get_forces(image) for image in images]
+ else:
+ predicted_forces = [calc.get_forces(image) for image in images]
+
+ for image_no in range(len(predicted_forces)):
+ for index in range(np.shape(predicted_forces[image_no])[0]):
+ for k in range(np.shape(predicted_forces[image_no])[1]):
+ assert (abs(predicted_forces[image_no][index][k] -
+ reference_forces[image_no][index][k]) <
+ 10.**(-5.)), \
+ 'Calculated %i force of atom %i of \
+ image %i by fortran version is not \
+ consistent with the value of python \
+ version.' % (k, index, image_no + 1)
+
+#
+
+if __name__ == '__main__':
+ test()
diff --git a/tests/consistency_test/gaussian_neural_test/train_test.py b/tests/consistency_test/gaussian_neural_test/train_test.py
new file mode 100644
index 0000000..f846130
--- /dev/null
+++ b/tests/consistency_test/gaussian_neural_test/train_test.py
@@ -0,0 +1,603 @@
+"""
+This script creates a list of three images. It then calculates behler-neural
+scheme cost function, energy per atom RMSE and force RMSE of different
+combinations of images with and without fortran modules on different number of
+cores, and check consistency between them.
+
+"""
+
+import numpy as np
+from ase import Atoms
+from ase.calculators.emt import EMT
+from amp import Amp
+from amp.descriptor.gaussian import Gaussian
+from amp.model.neuralnetwork import NeuralNetwork
+from amp.model import LossFunction
+from amp.regression import Regressor
+
+# Making the list of images
+
+
+def make_images():
+ """Makes test images."""
+
+ images = [Atoms(symbols='Pd3O2',
+ pbc=np.array([True, True, False], dtype=bool),
+ cell=np.array(
+ [[7.78, 0., 0.],
+ [0., 5.50129076, 0.],
+ [0., 0., 15.37532269]]),
+ positions=np.array(
+ [[3.89, 0., 8.37532269],
+ [0., 2.75064538, 8.37532269],
+ [3.89, 2.75064538, 8.37532269],
+ [5.835, 1.37532269, 8.5],
+ [5.835, 7.12596807, 8.]])),
+ Atoms(symbols='Pd3O2',
+ pbc=np.array([True, True, False], dtype=bool),
+ cell=np.array(
+ [[7.78, 0., 0.],
+ [0., 5.50129076, 0.],
+ [0., 0., 15.37532269]]),
+ positions=np.array(
+ [[3.88430768e+00, 5.28005966e-03,
+ 8.36678641e+00],
+ [-1.01122240e-02, 2.74577426e+00,
+ 8.37861758e+00],
+ [3.88251383e+00, 2.74138906e+00,
+ 8.37087611e+00],
+ [5.82067191e+00, 1.19156898e+00,
+ 8.97714483e+00],
+ [5.83355445e+00, 7.53318593e+00,
+ 8.50142020e+00]])),
+ Atoms(symbols='Pd3O2',
+ pbc=np.array([True, True, False], dtype=bool),
+ cell=np.array(
+ [[7.78, 0., 0.],
+ [0., 5.50129076, 0.],
+ [0., 0., 15.37532269]]),
+ positions=np.array(
+ [[3.87691266e+00, 9.29708987e-03,
+ 8.35604207e+00],
+ [-1.29700138e-02, 2.74373753e+00,
+ 8.37941484e+00],
+ [3.86813484e+00, 2.73488653e+00,
+ 8.36395999e+00],
+ [5.80386111e+00, 7.98192190e-01,
+ 9.74324179e+00],
+ [5.83223956e+00, 8.23855393e+00,
+ 9.18295137e+00]]))]
+
+ for atoms in images:
+ atoms.set_calculator(EMT())
+ atoms.get_potential_energy(apply_constraint=False)
+ atoms.get_forces(apply_constraint=False)
+
+ return images
+
+
+# Parameters
+cutoff = 5.5
+activation = 'sigmoid'
+hiddenlayers = {'O': (5, 5), 'Pd': (5, 5)}
+
+Gs = {'O': [{'eta': 0.05, 'type': 'G2', 'element': 'O'},
+ {'eta': 0.05, 'type': 'G2', 'element': 'Pd'},
+ {'eta': 2.0, 'type': 'G2', 'element': 'O'},
+ {'eta': 2.0, 'type': 'G2', 'element': 'Pd'},
+ {'eta': 4.0, 'type': 'G2', 'element': 'O'},
+ {'eta': 4.0, 'type': 'G2', 'element': 'Pd'},
+ {'eta': 8.0, 'type': 'G2', 'element': 'O'},
+ {"eta": 8.0, "type": "G2", "element": "Pd"},
+ {"eta": 20.0, "type": "G2", "element": "O"},
+ {"eta": 20.0, "type": "G2", "element": "Pd"},
+ {"eta": 40.0, "type": "G2", "element": "O"},
+ {"eta": 40.0, "type": "G2", "element": "Pd"},
+ {"eta": 80.0, "type": "G2", "element": "O"},
+ {"eta": 80.0, "type": "G2", "element": "Pd"},
+ {"zeta": 1.0, "elements": ["O", "O"], "type": "G4", "gamma": 1.0,
+ "eta": 0.005},
+ {"zeta": 1.0, "elements": ["O", "Pd"], "type": "G4", "gamma": 1.0,
+ "eta": 0.005},
+ {"zeta": 1.0, "elements": ["Pd", "Pd"], "type": "G4",
+ "gamma": 1.0, "eta": 0.005},
+ {"zeta": 1.0, "elements": ["O", "O"],
+ "type": "G4", "gamma": -1.0, "eta": 0.005},
+ {"zeta": 1.0, "elements": ["O", "Pd"],
+ "type": "G4", "gamma": -1.0, "eta": 0.005},
+ {"zeta": 1.0, "elements": ["Pd", "Pd"], "type": "G4",
+ "gamma": -1.0,
+ "eta": 0.005}, {"zeta": 2.0, "elements": ["O", "O"], "type": "G4",
+ "gamma": 1.0, "eta": 0.005},
+ {"zeta": 2.0, "elements": ["O", "Pd"],
+ "type": "G4", "gamma": 1.0, "eta": 0.005},
+ {"zeta": 2.0,
+ "elements": ["Pd", "Pd"], "type": "G4",
+ "gamma": 1.0, "eta": 0.005},
+ {"zeta": 2.0, "elements": ["O", "O"], "type": "G4", "gamma": -1.0,
+ "eta": 0.005},
+ {"zeta": 2.0, "elements": ["O", "Pd"], "type": "G4",
+ "gamma": -1.0, "eta": 0.005}, {"zeta": 2.0,
+ "elements": ["Pd", "Pd"],
+ "type": "G4", "gamma": -1.0,
+ "eta": 0.005},
+ {"zeta": 4.0,
+ "elements": ["O", "O"],
+ "type": "G4",
+ "gamma": 1.0, "eta": 0.005},
+ {"zeta": 4.0, "elements": ["O", "Pd"], "type": "G4", "gamma": 1.0,
+ "eta": 0.005}, {"zeta": 4.0, "elements": ["Pd", "Pd"],
+ "type": "G4", "gamma": 1.0, "eta": 0.005},
+ {"zeta": 4.0, "elements": ["O", "O"], "type": "G4", "gamma": -1.0,
+ "eta": 0.005}, {"zeta": 4.0, "elements": ["O", "Pd"],
+ "type": "G4", "gamma": -1.0, "eta": 0.005},
+ {"zeta": 4.0, "elements": ["Pd", "Pd"],
+ "type": "G4", "gamma": -1.0,
+ "eta": 0.005}],
+ "Pd": [{"eta": 0.05, "type": "G2", "element": "O"},
+ {"eta": 0.05, "type": "G2", "element": "Pd"},
+ {"eta": 2.0, "type": "G2", "element": "O"},
+ {"eta": 2.0, "type": "G2", "element": "Pd"},
+ {"eta": 4.0, "type": "G2", "element": "O"},
+ {"eta": 4.0, "type": "G2", "element": "Pd"},
+ {"eta": 8.0, "type": "G2", "element": "O"},
+ {"eta": 8.0, "type": "G2", "element": "Pd"},
+ {"eta": 20.0, "type": "G2", "element": "O"},
+ {"eta": 20.0, "type": "G2", "element": "Pd"},
+ {"eta": 40.0, "type": "G2", "element": "O"},
+ {"eta": 40.0, "type": "G2", "element": "Pd"},
+ {"eta": 80.0, "type": "G2", "element": "O"},
+ {"eta": 80.0, "type": "G2", "element": "Pd"},
+ {"zeta": 1.0, "elements": ["O", "O"], "type": "G4", "gamma": 1.0,
+ "eta": 0.005},
+ {"zeta": 1.0, "elements": ["O", "Pd"], "type": "G4", "gamma": 1.0,
+ "eta": 0.005}, {"zeta": 1.0,
+ "elements": ["Pd", "Pd"],
+ "type": "G4",
+ "gamma": 1.0, "eta": 0.005},
+ {"zeta": 1.0, "elements": ["O", "O"], "type": "G4",
+ "gamma": -1.0, "eta": 0.005}, {"zeta": 1.0,
+ "elements": ["O", "Pd"],
+ "type": "G4", "gamma": -1.0,
+ "eta": 0.005},
+ {"zeta": 1.0, "elements": ["Pd", "Pd"], "type": "G4",
+ "gamma": -1.0,
+ "eta": 0.005}, {"zeta": 2.0, "elements": ["O", "O"],
+ "type": "G4",
+ "gamma": 1.0, "eta": 0.005},
+ {"zeta": 2.0,
+ "elements": ["O", "Pd"], "type": "G4",
+ "gamma": 1.0, "eta": 0.005}, {"zeta": 2.0,
+ "elements": ["Pd", "Pd"],
+ "type": "G4",
+ "gamma": 1.0, "eta": 0.005},
+ {"zeta": 2.0, "elements": ["O", "O"], "type": "G4", "gamma": -1.0,
+ "eta": 0.005}, {"zeta": 2.0, "elements": ["O", "Pd"],
+ "type": "G4",
+ "gamma": -1.0, "eta": 0.005},
+ {"zeta": 2.0, "elements": ["Pd", "Pd"],
+ "type": "G4", "gamma": -1.0, "eta": 0.005},
+ {"zeta": 4.0, "elements": ["O", "O"],
+ "type": "G4", "gamma": 1.0, "eta": 0.005},
+ {"zeta": 4.0, "elements": ["O", "Pd"], "type": "G4", "gamma": 1.0,
+ "eta": 0.005}, {"zeta": 4.0, "elements": ["Pd", "Pd"],
+ "type": "G4",
+ "gamma": 1.0, "eta": 0.005},
+ {"zeta": 4.0,
+ "elements": ["O", "O"],
+ "type": "G4", "gamma": -1.0, "eta": 0.005},
+ {"zeta": 4.0, "elements": ["O", "Pd"],
+ "type": "G4", "gamma": -1.0, "eta": 0.005},
+ {"zeta": 4.0, "elements": ["Pd", "Pd"], "type": "G4",
+ "gamma": -1.0,
+ "eta": 0.005}]}
+
+fingerprints_range = {"O": np.array([[0.9576297744816821, 0.9781635537721822],
+ [1.5965219624007356, 2.029991552829194],
+ [0.6490867939769083, 0.9554902891920712],
+ [0.8835113617162015, 1.385491645778086],
+ [0.45757754941615236, 0.9354370590550468],
+ [0.5038098795235629, 0.9704216656880006],
+ [0.24776862922895004, 0.8975120854112218],
+ [0.1778411370477522, 0.5033369040695346],
+ [0.04756795975972335, 0.7929693614866126],
+ [0.010678411893107285,
+ 0.08274205794992942],
+ [0.0032126590280589355,
+ 0.6450875782155161],
+ [0.00014810311804588016,
+ 0.004685139865518786],
+ [1.4684356130451328e-05,
+ 0.42691677760826546],
+ [3.687931521390313e-08,
+ 1.5871730901594423e-05],
+ [0.03019875732248386,
+ 0.20698709522424386],
+ [3.363261257762341, 5.363914410336563],
+ [2.262959763053792, 3.99309008637724],
+ [0.43931018496430263, 0.6100947886487761],
+ [3.048864359631384, 3.906027779282084],
+ [2.4759824537761026, 4.32175703694348],
+ [0.0014242919510283594,
+ 0.0662909452084825],
+ [2.1248328227888496, 4.238756592436429],
+ [1.4573759593003581, 2.815733155339926],
+ [0.2986140349485413, 0.5813203232773206],
+ [1.746995212759835, 2.3899513815298894],
+ [1.5256310348626507, 3.1071875821187103],
+ [3.1682461497983404e-06,
+ 0.006799486167343933],
+ [1.1510284000759108, 3.1879752591881956],
+ [0.8406198864990045, 1.7423917588951667],
+ [0.1379710925632159, 0.5277787358337935],
+ [0.6114872725198919, 1.340305590989966],
+ [0.7164066603703434,
+ 2.0891604176934395]]),
+ "Pd": np.array([[1.154607323053423, 1.3305487045981295],
+ [0.551759102399155, 1.3713637661332694],
+ [0.6469877982543076, 0.9038561263894056],
+ [0.1836383922219796, 0.7510644180086835],
+ [0.3706404542226067, 0.6308010197966096],
+ [0.061908829417001224,
+ 0.42094513726712196],
+ [0.13355181104922664,
+ 0.3205532867729253],
+ [0.0076308937151500725,
+ 0.14249172183309694],
+ [0.009302322319625642,
+ 0.048059061272533475],
+ [1.785148490055681e-05,
+ 0.006770671357855657],
+ [0.00014511169324163886,
+ 0.0025160536892603904],
+ [8.04287954299944e-10,
+ 4.599501555987974e-05],
+ [3.686778281930424e-08,
+ 8.524742995946123e-06],
+ [1.6422373031638726e-18,
+ 2.1846879428444836e-09],
+ [1.7383991321368732, 2.9347075860454988],
+ [4.544797763122505, 7.28152322128857],
+ [0.979596152457089, 1.9620028955131916],
+ [0.49196325681052067,
+ 1.0767938436994269],
+ [3.139828490686222, 4.524661360317331],
+ [1.23826020263128, 2.4316125030019147],
+ [1.4012907765627602, 2.476988108604277],
+ [3.4081270882827277, 6.0197611413153655],
+ [0.4897744167832538, 1.6851590166945567],
+ [0.15650247391327193,
+ 0.6306691375027177],
+ [2.2224602701293357, 3.262899280344123],
+ [0.9717045670826352, 1.815787153995498],
+ [0.9659634528285561, 2.163669429908823],
+ [2.3741505301983685, 4.8131425542358715],
+ [0.12244182821265122, 1.357426673243403],
+ [0.0326810274613218,
+ 0.22677866750542988],
+ [1.4047756390099746, 2.37308600253783],
+ [0.8248597322302271,
+ 1.3563088031163417]])}
+
+weights = {"O": {1: np.matrix([[0.00036942165470836563, 0.022852891328080965,
+ -0.007763989520407272, 0.0017904084613678817,
+ -0.04680830976127531],
+ [-0.011220619170475267, -0.031465481900468384,
+ -0.0185587250581268, 0.00029876794872765733,
+ -0.03270538302430687],
+ [0.009269384571647388, -0.004439491584362951,
+ 0.02041622613407708, -0.04075220241750707,
+ -0.004384443250886716],
+ [-0.02045226889653854, -0.04085271674587569,
+ -0.0007470148939682439, 0.017448937916376722,
+ -0.03247360282480993],
+ [0.014076539841285075, -0.0006001148651055555,
+ -0.011206188631385075, 0.036131770356541804,
+ 0.04019195568663911], [0.04438555375359607,
+ -0.03630318854778723, -
+ 0.011787189723001579,
+ 0.03403384156560013,
+ 0.015653363757362176],
+ [0.02134038436971622, 0.000554719592425923,
+ -0.04353602059838731, 0.02829112575071807,
+ -0.010315738192632054],
+ [-0.009864186941597866, 0.025867111325423034,
+ -0.030222981254973712, -0.009255262808615411,
+ -0.0047940678082599025],
+ [0.009775595855839286, -0.004398102065676125,
+ -0.00195136837351699, -0.0015883410280669308,
+ 0.03528054083271703],
+ [0.0088457892425432, -0.0017778202887624855,
+ -0.030182606288789264, 0.03153096931177092,
+ -0.02709527292127762], [-0.02911935923819357,
+ -0.011844856703362105,
+ 0.03358589444051113,
+ 0.007149386960731488,
+ -0.007590532737964187],
+ [-0.03944400124516653, 0.03562647918045643,
+ -0.041584201666104756, -0.03482985747462908,
+ -0.045374395214468496],
+ [0.019057890033725933, -0.012580031773554046,
+ 0.04290707878850142, 0.04177600131985214,
+ -0.03500384259370384],
+ [-0.02033084113684249, -0.01111345650394805,
+ -0.005485434669132497, 0.03554246348547074,
+ 0.031421467582530324],
+ [-0.03310168568774624, 0.04617363212275834,
+ 0.03868456178440169, 0.012151585419746959,
+ -0.007359447003748548],
+ [0.044255356329426065, 0.036122120043098505,
+ 0.001842950538131695, -0.01615761183192349,
+ -0.03771427943410247],
+ [-0.0381118034639101, -0.04643318160382238,
+ 0.02900519652241655, -0.008475138348622263,
+ 0.021893066028991853],
+ [0.016038314042298385, 0.03545540262812917,
+ -0.031220884269865096, -0.033670838618425646,
+ 0.04684810506588663],
+ [0.037697271308168634, -0.04250612661317486,
+ 0.0028173761257807364, 0.04503591051281573,
+ -0.005888259820159045],
+ [-0.01688674535740177, 0.03765441774468983,
+ 0.040162723331136185, 0.023291060425779497,
+ 0.01875483057892434],
+ [0.009559969717541077, -0.010986361005406543,
+ 0.017717618257908102, 0.021594452542040676,
+ 0.00668490554203105],
+ [0.02899572788647327, 0.03884753546552183,
+ 0.0334345646492913, -0.0009724588802520473,
+ 0.008901825903656319],
+ [0.04472782971579241, 0.020125743534124996,
+ 0.018466622131502394, 0.014248370483492187,
+ 0.02954224116911444],
+ [0.018038582886592464, 0.007882237781735343,
+ -0.005639481686277245, -0.030317048204748388,
+ 0.011443284253329196],
+ [-0.014574589075944028, 0.027312879897418138,
+ -0.0052516221359138054, -0.02858166510190807,
+ -0.0218508786228111],
+ [-0.019062166466149163, -0.0421343628780219,
+ -0.0292511219030615, -0.04063165343284807,
+ -0.026551753085291934],
+ [-0.006973189792228912, 0.018725587327618767,
+ 0.037936857142053707, 0.011375377365914208,
+ -0.03823975980860963],
+ [-0.03087795180506949, -0.002166181826768615,
+ -0.009411940441267343, 0.008062289773496219,
+ 0.03143133615872179],
+ [0.022767389458292583, -0.032719990839286985,
+ 0.010234126834754581, -0.0025988597425086815,
+ 0.012893424785935387],
+ [0.03729503214821439, -0.04055234881977389,
+ -0.033180455803208164, -0.003962067731434399,
+ -0.04089277483943934],
+ [-0.005215540749534078, 0.013163002568367034,
+ 0.03980552568163612, 0.00803385354609431,
+ 7.658166702390057e-05],
+ [0.013936695364567375, 0.017657437899754047,
+ 0.027548202328624413, -0.0008692880197060243,
+ 0.032762776542753225],
+ [0.0, 0.0, 0.0, 0.0, 0.0]]),
+ 2: np.matrix([[-0.13315704861614908, 0.21616481887190436,
+ 0.07102546888848049, -0.2758348650926486,
+ -0.12434812671933795], [-0.024314957289090222,
+ -0.16392515185308187,
+ 0.2058922926890992,
+ 0.2154935160814611,
+ 0.11014812360618259],
+ [-0.08133895309316427, -0.1937923029504461,
+ 0.206977413616443, 0.03575405386811248,
+ -0.10559013113242327],
+ [0.1469937256217183, 0.07621742865022896,
+ 0.08882575726900893, -0.2577928927812111,
+ 0.2670748892517893],
+ [-0.141370342762172, -0.23738939477247786,
+ -0.06633785630500305, -0.24779722808875726,
+ 0.17677488447247947],
+ [0.0, 0.0, 0.0, 0.0, 0.0]]),
+ 3: np.matrix([[0.0377280558085506], [0.013842778159018243],
+ [-0.29408570195900635],
+ [0.19529036441834974], [-0.16745509851929688],
+ [0.0]])},
+ "Pd": {1: np.matrix([[0.008070279669324429, -0.04006333630883027,
+ -0.04312742429320118,
+ -0.03942171198922403, -0.04540662900302544],
+ [0.01339814716182161, -0.022961503636403632,
+ -0.006969046155031772, 0.01539617792272549,
+ -0.02587844848147742],
+ [0.045033334892680674, 0.0034430687137840393,
+ 0.02405223418836909, -0.035506042140031155,
+ 0.021328894351546446],
+ [-0.04416667286322164, -0.03993519399665675,
+ 0.032311654583997304, -0.03745738975064494,
+ 0.006061355326268905],
+ [-0.043438846516273555, 0.020424466564239616,
+ -0.03712722505187403, -0.04417848105963802,
+ -0.008777813735156417],
+ [0.03965347387678732, -0.01799472378269024,
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+ 0.0004118619760827419],
+ [-0.03180969154106336, -0.006918591959222585,
+ 0.014099398062742227, -0.022931651589221756,
+ 0.03148626725702887],
+ [0.04573128229126357, 0.016654751576744925,
+ -0.028910689496630722,
+ 0.02242435838167882, -0.02783084152657823],
+ [0.030147617474449384, -0.009580788002314114,
+ 0.026913224902892594, -0.006350898911528513,
+ -0.01580260272955647],
+ [-0.03128280563473111, -0.044359797916295726,
+ -0.0455871021838766, -0.022323871191166217,
+ -0.025520059574284607],
+ [-0.004213681746207731, -0.027963910926939888,
+ -0.03734025976436221, -0.029904058599404374,
+ -0.023362113055890702],
+ [0.03140805808988659, -0.01625862158802977,
+ -0.012926251592534549, 0.0199950518624378,
+ 0.00017000814436556738],
+ [0.03611338398893238, -0.04064588225668243,
+ -0.03548786885528668, -0.034119876099748085,
+ -0.03249791207428783],
+ [0.04302813264222295, -0.031784410672976354,
+ -0.0018505347572984332, -0.02619493567773821,
+ -0.009963146880811465],
+ [-0.00382761556441661, 0.02051612655974898,
+ -0.015084868592703193, 0.036644660445905974,
+ 0.024267396930057042],
+ [0.0027419126458524262, -0.01875730493117643,
+ 0.042029556463568374, -0.033491496522005004,
+ 0.04664358315093048],
+ [-0.00857053904710025, 0.004386575075249165,
+ -0.03681921382606547, 0.024055769666913862,
+ -0.006710822409842235],
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+ -0.007657861036073181, 0.04579883161005442,
+ -0.027272703382017247],
+ [0.024782613292205463, 0.02454697361926271,
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+ 0.019746899921596867],
+ [-0.008107835898640163, -0.02411112524744128,
+ 0.01680784294783398, -0.03942450668164303,
+ -0.02148968897141828],
+ [0.006160769106771449, -0.02608742029162942,
+ -0.03445574192255718, 0.011100495475242236,
+ -0.011890887277678633],
+ [0.019265102424069563, -0.019510992393145597,
+ -0.039330197040643305, 0.028930252847621296,
+ 0.04535579375056527],
+ [0.0003841258275426168, -0.03140536534416318,
+ 0.004402540856303851, -0.006596225898408456,
+ -0.012287524451218383],
+ [0.032434589752896065,
+ -0.038422865723774166,
+ 0.04121673691259908,
+ 0.026471126594987765,
+ -0.045659510547159485],
+ [0.016693221128737612, 0.033475787637348264,
+ -0.01216104367054778, -0.04682497168901334,
+ -0.025748662607038442],
+ [-0.030035984906774393, 0.03528987279339724,
+ 0.01842649225978525, 0.013967345908646303,
+ 0.030368471307811548],
+ [-0.004245382943207754, 0.004346310546406856,
+ 0.04395403376516939, -0.03528225866346128,
+ 0.040526584371759225],
+ [-0.026240373867317947, -0.02790624801091845,
+ 0.033248579584558235, -0.03456761843589754,
+ -0.00921953855906435],
+ [-0.04029772119462781, 0.03944849938380114,
+ 0.03367466933743388, -0.04654081205741553,
+ -0.02559442696348037],
+ [-0.019162242379646047,
+ -0.0074198239538341496, -0.03481645962457279,
+ 0.0023221563528588313,
+ -0.01362951107641086],
+ [-0.04359327067093935, 0.008182459343197494,
+ -0.004311982184810589, 0.013459029430653538,
+ -0.02593952116632298],
+ [0.03419829018664716, -0.02909906291417496,
+ 0.0450381809975251,
+ 0.04636855435694584, 0.004474211596899327],
+ [0.0, 0.0, 0.0, 0.0, 0.0]]),
+ 2: np.matrix([[0.07339646055942084, -0.22682470946032204,
+ -0.07464451676678477, -0.21765816530655968,
+ 0.10447399748556846],
+ [-0.07339330664074986, -0.2620525555813218,
+ -0.010761218306725495, 0.07390075065002266,
+ 0.11039186125577433],
+ [-0.17516748044584285, -0.2837828871933906,
+ -0.02085650668287642, 0.08755824083276131,
+ 0.07220039658405131],
+ [0.23974597425595473, 0.24760019759492297,
+ -0.22060915253115443, -0.28310518337421325,
+ -0.016857214958102662],
+ [0.11687787432599622, -0.10151689213238121,
+ 0.18735099239621017, 0.21356695418645139,
+ -0.240568272158666],
+ [0.0, 0.0, 0.0, 0.0, 0.0]]),
+ 3: np.matrix([[0.05906457619187622], [-0.29300196568707426],
+ [-0.018802515167880285],
+ [-0.2723126668305828], [0.22668984898833738],
+ [0.0]])}}
+
+scalings = {"O": {"intercept": 4.2468934359280288,
+ "slope": 3.1965614888424687},
+ "Pd": {"intercept": 4.2468934359280288,
+ "slope": 3.1965614888424687}}
+
+
+# Testing pure-python and fortran versions of Gaussian-Neural on different
+# number of processes and different number of images
+
+def test():
+
+ images = make_images()
+
+ convergence = {'energy_rmse': 10.**10.,
+ 'energy_maxresid': 10.**10.,
+ 'force_rmse': 10.**10.,
+ 'force_maxresid': 10.**10., }
+
+ regressor = Regressor(optimizer='BFGS')
+
+ count = 0
+ for fortran in [False, True]:
+ for cores in range(1, 2):
+ string = 'consistgauss/%s-%i'
+ label = string % (fortran, cores)
+ calc = Amp(descriptor=Gaussian(cutoff=cutoff,
+ Gs=Gs,
+ fortran=fortran,),
+ model=NeuralNetwork(hiddenlayers=hiddenlayers,
+ weights=weights,
+ scalings=scalings,
+ activation=activation,
+ fprange=fingerprints_range,
+ regressor=regressor,),
+ label=label,
+ cores=1)
+
+ lossfunction = LossFunction(convergence=convergence)
+ calc.model.lossfunction = lossfunction
+ calc.train(images=images,)
+
+ if count == 0:
+ ref_loss = calc.model.lossfunction.loss
+ ref_energy_loss = calc.model.lossfunction.energy_loss
+ ref_force_loss = calc.model.lossfunction.force_loss
+ ref_dloss_dparameters = \
+ calc.model.lossfunction.dloss_dparameters
+ else:
+ assert (abs(calc.model.lossfunction.loss -
+ ref_loss) < 10.**(-10.)), \
+ '''Loss function value for %r fortran, and %i cores is
+ not consistent with the value of python version
+ on single core.''' % (fortran, cores)
+
+ assert (abs(calc.model.lossfunction.energy_loss -
+ ref_energy_loss) <
+ 10.**(-9.)), \
+ '''Energy rmse value for %r fortran, and %i cores is not
+ consistent with the value of python version on
+ single core.''' % (fortran, cores)
+
+ assert (abs(calc.model.lossfunction.force_loss -
+ ref_force_loss) <
+ 10.**(-9.)), \
+ '''Force rmse value for %r fortran, and %i cores is not
+ consistent with the value of python version on
+ single core.''' % (fortran, cores)
+
+ for _ in range(len(ref_dloss_dparameters)):
+ assert (calc.model.lossfunction.dloss_dparameters[_] -
+ ref_dloss_dparameters[_] < 10.**(-10.))
+ '''Derivative of the cost function for %r
+ fortran, and %i
+ cores is not consistent with the value of
+ python version on single
+ core. ''' % (fortran, cores)
+
+ count = count + 1
+
+if __name__ == '__main__':
+ test()
diff --git a/tests/consistency_test/gaussian_test.py b/tests/consistency_test/gaussian_test.py
new file mode 100644
index 0000000..bc5a926
--- /dev/null
+++ b/tests/consistency_test/gaussian_test.py
@@ -0,0 +1,114 @@
+"""
+This script creates a list of three images. It then calculates Gaussian
+fingerprints of images with and without fortran modules on different number of
+cores, and check consistency between them.
+
+"""
+
+import numpy as np
+from ase import Atoms
+from amp.descriptor.gaussian import Gaussian
+from amp.utilities import hash_images
+
+# Making the list of images
+
+
+def make_images():
+ """Makes test images."""
+
+ images = [Atoms(symbols='Pd3O2',
+ pbc=np.array([True, True, False], dtype=bool),
+ cell=np.array(
+ [[7.78, 0., 0.],
+ [0., 5.50129076, 0.],
+ [0., 0., 15.37532269]]),
+ positions=np.array(
+ [[3.89, 0., 8.37532269],
+ [0., 2.75064538, 8.37532269],
+ [3.89, 2.75064538, 8.37532269],
+ [5.835, 1.37532269, 8.5],
+ [5.835, 7.12596807, 8.]])),
+ Atoms(symbols='Pd3O2',
+ pbc=np.array([True, True, False], dtype=bool),
+ cell=np.array(
+ [[7.78, 0., 0.],
+ [0., 5.50129076, 0.],
+ [0., 0., 15.37532269]]),
+ positions=np.array(
+ [[3.88430768e+00, 5.28005966e-03,
+ 8.36678641e+00],
+ [-1.01122240e-02, 2.74577426e+00,
+ 8.37861758e+00],
+ [3.88251383e+00, 2.74138906e+00,
+ 8.37087611e+00],
+ [5.82067191e+00, 1.19156898e+00,
+ 8.97714483e+00],
+ [5.83355445e+00, 7.53318593e+00,
+ 8.50142020e+00]])),
+ Atoms(symbols='Pd3O2',
+ pbc=np.array([True, True, False], dtype=bool),
+ cell=np.array(
+ [[7.78, 0., 0.],
+ [0., 5.50129076, 0.],
+ [0., 0., 15.37532269]]),
+ positions=np.array(
+ [[3.87691266e+00, 9.29708987e-03,
+ 8.35604207e+00],
+ [-1.29700138e-02, 2.74373753e+00,
+ 8.37941484e+00],
+ [3.86813484e+00, 2.73488653e+00,
+ 8.36395999e+00],
+ [5.80386111e+00, 7.98192190e-01,
+ 9.74324179e+00],
+ [5.83223956e+00, 8.23855393e+00,
+ 9.18295137e+00]]))]
+
+ return images
+
+
+# Testing pure-python and fortran versions of Gaussian fingerprint on different
+# number of processes and different number of images
+
+def test():
+
+ images = make_images()
+ images = hash_images(images, ordered=True)
+
+ ref_fps = {}
+ ref_fp_primes = {}
+ count = 0
+ for fortran in [False, True]:
+ for cores in range(1, 2):
+ descriptor = Gaussian(fortran=fortran,
+ dblabel='Gaussian-%s-%d' % (fortran, cores))
+ descriptor.calculate_fingerprints(images,
+ parallel={'cores': cores},
+ log=None,
+ calculate_derivatives=True)
+ for hash, image in images.items():
+ if count == 0:
+ ref_fps[hash] = descriptor.fingerprints[hash]
+ ref_fp_primes[hash] = descriptor.fingerprintprimes[hash]
+ else:
+ fps = descriptor.fingerprints[hash]
+ # Checking consistency between fingerprints
+ for (element1, afp1), \
+ (element2, afp2) in zip(ref_fps[hash], fps):
+ assert element1 == element2, \
+ 'fortran-python consistency for Gaussian '
+ 'fingerprints broken!'
+ for _, __ in zip(afp1, afp2):
+ assert (abs(_ - __) < 10 ** (-15.)), \
+ 'fortran-python consistency for Gaussian '
+ 'fingerprints broken!'
+ # Checking consistency between fingerprint primes
+ fpprime = descriptor.fingerprintprimes[hash]
+ for key, value in ref_fp_primes[hash].items():
+ for _, __ in zip(value, fpprime[key]):
+ assert (abs(_ - __) < 10 ** (-15.)), \
+ 'fortran-python consistency for Gaussian '
+ 'fingerprint primes broken!'
+ count += 1
+
+if __name__ == '__main__':
+ test()
diff --git a/tests/consistency_test/zernike_test.py b/tests/consistency_test/zernike_test.py
new file mode 100644
index 0000000..d9fbeee
--- /dev/null
+++ b/tests/consistency_test/zernike_test.py
@@ -0,0 +1,80 @@
+"""
+This script creates a list of three images. It then calculates Zernike
+fingerprints of images with and without fortran modules on different number of
+cores, and checks consistency between them.
+
+"""
+
+import numpy as np
+from ase import Atoms
+from amp.descriptor.zernike import Zernike
+from amp.utilities import hash_images, assign_cores
+
+
+def make_images():
+ """Makes test images."""
+
+ images = [Atoms(symbols='Pd3O2',
+ pbc=np.array([True, True, False], dtype=bool),
+ cell=np.array(
+ [[7.78, 0., 0.],
+ [0., 5.50129076, 0.],
+ [0., 0., 15.37532269]]),
+ positions=np.array(
+ [[3.89, 0., 8.37532269],
+ [0., 2.75064538, 8.37532269],
+ [3.89, 2.75064538, 8.37532269],
+ [5.835, 1.37532269, 8.5],
+ [5.835, 7.12596807, 8.]]))]
+
+ return images
+
+
+def test():
+ """Testing pure-python and fortran versions of Zernike fingerprint on
+ different number of processes and different number of images.
+ """
+
+ images = make_images()
+ images = hash_images(images, ordered=True)
+
+ ref_fps = {}
+ ref_fp_primes = {}
+ count = 0
+ for fortran in [True, False]:
+ for ncores in range(1, 3):
+ cores = assign_cores(ncores)
+ descriptor = Zernike(fortran=fortran,
+ dblabel='Zernike-%s-%d' % (fortran, ncores))
+ descriptor.calculate_fingerprints(images,
+ parallel={'cores': cores,
+ 'envcommand': None},
+ log=None,
+ calculate_derivatives=True)
+ for hash, image in images.items():
+ if count == 0:
+ ref_fps[hash] = descriptor.fingerprints[hash]
+ ref_fp_primes[hash] = descriptor.fingerprintprimes[hash]
+ else:
+ fps = descriptor.fingerprints[hash]
+ # Checking consistency between fingerprints
+ for (element1, afp1), \
+ (element2, afp2) in zip(ref_fps[hash], fps):
+ assert element1 == element2, \
+ 'fortran-python consistency for Zernike '
+ 'fingerprints broken!'
+ for _, __ in zip(afp1, afp2):
+ assert (abs(_ - __) < (10 ** (-10.))), \
+ 'fortran-python consistency for Zernike '
+ 'fingerprints broken!'
+ # Checking consistency between fingerprint primes
+ fpprime = descriptor.fingerprintprimes[hash]
+ for key, value in ref_fp_primes[hash].items():
+ for _, __ in zip(value, fpprime[key]):
+ assert (abs(_ - __) < (10 ** (-10.))), \
+ 'fortran-python consistency for Zernike '
+ 'fingerprint primes broken!'
+ count += 1
+
+if __name__ == '__main__':
+ test()
diff --git a/tests/misc_test/displaced_atom_test.py b/tests/misc_test/displaced_atom_test.py
new file mode 100644
index 0000000..b23aab8
--- /dev/null
+++ b/tests/misc_test/displaced_atom_test.py
@@ -0,0 +1,116 @@
+"""
+An atom in an Atoms object is displaced a little bit and the potential energy
+both before and after displacement is calculated. The result should be
+different.
+
+"""
+
+###############################################################################
+
+import numpy as np
+from ase import Atoms
+from collections import OrderedDict
+from amp import Amp
+from amp.descriptor.gaussian import Gaussian
+from amp.model.neuralnetwork import NeuralNetwork
+
+###############################################################################
+
+
+def test():
+
+ ###########################################################################
+ # Parameters
+
+ atoms = Atoms(symbols='PdOPd2',
+ pbc=np.array([False, False, False], dtype=bool),
+ cell=np.array(
+ [[1., 0., 0.],
+ [0., 1., 0.],
+ [0., 0., 1.]]),
+ positions=np.array(
+ [[0., 1., 0.],
+ [1., 2., 1.],
+ [-1., 1., 2.],
+ [1., 3., 2.]]))
+
+ ###########################################################################
+ # Parameters
+
+ Gs = {'O': [{'type': 'G2', 'element': 'Pd', 'eta': 0.8},
+ {'type': 'G4', 'elements': [
+ 'Pd', 'Pd'], 'eta':0.2, 'gamma':0.3, 'zeta':1},
+ {'type': 'G4', 'elements': ['O', 'Pd'], 'eta':0.3, 'gamma':0.6,
+ 'zeta':0.5}],
+ 'Pd': [{'type': 'G2', 'element': 'Pd', 'eta': 0.2},
+ {'type': 'G4', 'elements': ['Pd', 'Pd'],
+ 'eta':0.9, 'gamma':0.75, 'zeta':1.5},
+ {'type': 'G4', 'elements': ['O', 'Pd'], 'eta':0.4,
+ 'gamma':0.3, 'zeta':4}]}
+
+ hiddenlayers = {'O': (2,), 'Pd': (2,)}
+
+ weights = OrderedDict([('O', OrderedDict([(1, np.matrix([[-2.0, 6.0],
+ [3.0, -3.0],
+ [1.5, -0.9],
+ [-2.5, -1.5]])),
+ (2, np.matrix([[5.5],
+ [3.6],
+ [1.4]]))])),
+ ('Pd', OrderedDict([(1, np.matrix([[-1.0, 3.0],
+ [2.0, 4.2],
+ [1.0, -0.7],
+ [-3.0, 2.0]])),
+ (2, np.matrix([[4.0],
+ [0.5],
+ [3.0]]))]))])
+
+ scalings = OrderedDict([('O', OrderedDict([('intercept', -2.3),
+ ('slope', 4.5)])),
+ ('Pd', OrderedDict([('intercept', 1.6),
+ ('slope', 2.5)]))])
+
+ fingerprints_range = {"O": np.array([[0.21396177208585404,
+ 2.258090276328769],
+ [0.0, 2.1579067008202975],
+ [0.0, 0.0]]),
+ "Pd": np.array([[0.0, 1.4751761770313006],
+ [0.0, 0.697686078889583],
+ [0.0, 0.37848964715610417]])}
+
+ ###########################################################################
+
+ calc = Amp(descriptor=Gaussian(cutoff=6.5,
+ Gs=Gs,
+ fortran=False,),
+ model=NeuralNetwork(hiddenlayers=hiddenlayers,
+ weights=weights,
+ scalings=scalings,
+ fprange=fingerprints_range,
+ mode='atom-centered'),
+ cores=1)
+
+ atoms.set_calculator(calc)
+
+ e1 = atoms.get_potential_energy(apply_constraint=False)
+ e2 = calc.get_potential_energy(atoms)
+ f1 = atoms.get_forces(apply_constraint=False)
+
+ atoms[0].x += 0.5
+
+ boolean = atoms.calc.calculation_required(atoms, properties=['energy'])
+
+ e3 = atoms.get_potential_energy(apply_constraint=False)
+ e4 = calc.get_potential_energy(atoms)
+ f2 = atoms.get_forces(apply_constraint=False)
+
+ assert (e1 == e2 and
+ e3 == e4 and
+ abs(e1 - e3) > 10. ** (-3.) and
+ (boolean is True) and
+ (not (f1 == f2).all())), 'Displaced-atom test broken!'
+
+###############################################################################
+
+if __name__ == '__main__':
+ test()
diff --git a/tests/misc_test/fpplot_test.py b/tests/misc_test/fpplot_test.py
new file mode 100644
index 0000000..d6fd919
--- /dev/null
+++ b/tests/misc_test/fpplot_test.py
@@ -0,0 +1,63 @@
+"""Simple test of the Amp calculator, using Gaussian descriptors and neural
+network model. Randomly generates data with the EMT potential in MD
+simulations."""
+
+import matplotlib
+# The 'Agg' command must be *before* all other matplotlib imports for
+# headless operation.
+matplotlib.use('Agg')
+
+import os
+from ase import Atoms, Atom, units
+import ase.io
+from ase.calculators.emt import EMT
+from ase.build import fcc110
+from ase.md.velocitydistribution import MaxwellBoltzmannDistribution
+from ase.md import VelocityVerlet
+from ase.constraints import FixAtoms
+
+from amp import Amp
+from amp.descriptor.gaussian import Gaussian
+from amp.model.neuralnetwork import NeuralNetwork
+from amp.model import LossFunction
+from amp.descriptor.analysis import FingerprintPlot
+
+
+def generate_data(count, filename='training.traj'):
+ """Generates test or training data with a simple MD simulation."""
+ if os.path.exists(filename):
+ return
+ traj = ase.io.Trajectory(filename, 'w')
+ atoms = fcc110('Pt', (2, 2, 2), vacuum=7.)
+ atoms.extend(Atoms([Atom('Cu', atoms[7].position + (0., 0., 2.5)),
+ Atom('Cu', atoms[7].position + (0., 0., 5.))]))
+ atoms.set_constraint(FixAtoms(indices=[0, 2]))
+ atoms.set_calculator(EMT())
+ atoms.get_potential_energy()
+ traj.write(atoms)
+ MaxwellBoltzmannDistribution(atoms, 300. * units.kB)
+ dyn = VelocityVerlet(atoms, dt=1. * units.fs)
+ for step in range(count - 1):
+ dyn.run(50)
+ traj.write(atoms)
+
+
+def test():
+ generate_data(2, filename='fpplot-training.traj')
+
+ calc = Amp(descriptor=Gaussian(),
+ model=NeuralNetwork(),
+ label='fpplot-test'
+ )
+ calc.model.lossfunction = LossFunction(convergence={'energy_rmse': 1.00,
+ 'force_rmse': 1.00})
+ calc.train(images='fpplot-training.traj')
+
+ images = ase.io.Trajectory('fpplot-training.traj')
+ fpplot = FingerprintPlot(calc)
+ fpplot(images)
+ fpplot(images, overlay=images[0])
+ fpplot(images, overlay=[images[1][2], images[0][-1]])
+
+if __name__ == '__main__':
+ test()
diff --git a/tests/misc_test/numeric_analytic_test.py b/tests/misc_test/numeric_analytic_test.py
new file mode 100644
index 0000000..009762c
--- /dev/null
+++ b/tests/misc_test/numeric_analytic_test.py
@@ -0,0 +1,133 @@
+#!/usr/bin/env python
+"""This test randomly generates data with the EMT potential in MD simulations,
+and then checks for consistency between analytical and numerical forces,
+as well as dloss_dparameters."""
+
+from ase.calculators.emt import EMT
+from ase.build import fcc110
+from ase import Atoms, Atom
+from ase.md.velocitydistribution import MaxwellBoltzmannDistribution
+from ase import units
+from ase.md import VelocityVerlet
+from ase.constraints import FixAtoms
+
+from amp import Amp
+from amp.descriptor.gaussian import Gaussian
+from amp.model.neuralnetwork import NeuralNetwork
+from amp.model import LossFunction
+from amp.regression import Regressor
+
+
+def generate_data(count):
+ """Generates test or training data with a simple MD simulation."""
+ atoms = fcc110('Pt', (2, 2, 1), vacuum=7.)
+ adsorbate = Atoms([Atom('Cu', atoms[3].position + (0., 0., 2.5)),
+ Atom('Cu', atoms[3].position + (0., 0., 5.))])
+ atoms.extend(adsorbate)
+ atoms.set_constraint(FixAtoms(indices=[0, 2]))
+ atoms.set_calculator(EMT())
+ MaxwellBoltzmannDistribution(atoms, 300. * units.kB)
+ dyn = VelocityVerlet(atoms, dt=1. * units.fs)
+ newatoms = atoms.copy()
+ newatoms.set_calculator(EMT())
+ newatoms.get_potential_energy()
+ images = [newatoms]
+ for step in range(count - 1):
+ dyn.run(50)
+ newatoms = atoms.copy()
+ newatoms.set_calculator(EMT())
+ newatoms.get_potential_energy()
+ del newatoms.constraints # See ASE issue #64.
+ images.append(newatoms)
+ return images
+
+
+def test():
+ images = generate_data(2)
+ regressor = Regressor(optimizer='BFGS')
+
+ calc = Amp(descriptor=Gaussian(),
+ model=NeuralNetwork(hiddenlayers=(3, 3),
+ regressor=regressor,),
+ cores=1)
+
+ step = 0
+ for d in [None, 0.00001]:
+ for fortran in [True, False]:
+ for cores in [1, 2]:
+ step += 1
+ label = \
+ 'numeric_analytic_test/analytic-%s-%i' % (fortran, cores) \
+ if d is None \
+ else 'numeric_analytic_test/numeric-%s-%i' \
+ % (fortran, cores)
+ print(label)
+
+ loss = LossFunction(convergence={'energy_rmse': 10 ** 10,
+ 'force_rmse': 10 ** 10},
+ d=d)
+ calc.set_label(label)
+ calc.dblabel = 'numeric_analytic_test/analytic-True-1'
+ calc.model.lossfunction = loss
+ calc.descriptor.fortran = fortran
+ calc.model.fortran = fortran
+ calc.cores = cores
+
+ calc.train(images=images,)
+
+ if step == 1:
+ ref_energies = []
+ ref_forces = []
+ for image in images:
+ ref_energies += [calc.get_potential_energy(image)]
+ ref_forces += [calc.get_forces(image)]
+ ref_dloss_dparameters = \
+ calc.model.lossfunction.dloss_dparameters
+ else:
+ energies = []
+ forces = []
+ for image in images:
+ energies += [calc.get_potential_energy(image)]
+ forces += [calc.get_forces(image)]
+ dloss_dparameters = \
+ calc.model.lossfunction.dloss_dparameters
+
+ for image_no in range(2):
+
+ diff = abs(energies[image_no] - ref_energies[image_no])
+ assert (diff < 10.**(-13.)), \
+ 'The calculated value of energy of image %i is ' \
+ 'wrong!' % (image_no + 1)
+
+ for atom_no in range(6):
+ for i in range(3):
+ diff = abs(forces[image_no][atom_no][i] -
+ ref_forces[image_no][atom_no][i])
+ assert (diff < 10.**(-10.)), \
+ 'The calculated %i force of atom %i of ' \
+ 'image %i is wrong!' \
+ % (i, atom_no, image_no + 1)
+ # Checks analytical and numerical dloss_dparameters
+ for _ in range(len(ref_dloss_dparameters)):
+ diff = abs(dloss_dparameters[_] -
+ ref_dloss_dparameters[_])
+ assert(diff < 10 ** (-10.)), \
+ 'The calculated value of loss function ' \
+ 'derivative is wrong!'
+ # Checks analytical and numerical forces
+ forces = []
+ for image in images:
+ image.set_calculator(calc)
+ forces += [calc.calculate_numerical_forces(image, d=d)]
+ for atom_no in range(6):
+ for i in range(3):
+ diff = abs(forces[image_no][atom_no][i] -
+ ref_forces[image_no][atom_no][i])
+ print("diff =", diff)
+ assert (diff < 10.**(-6.)), \
+ 'The calculated %i force of atom %i of ' \
+ 'image %i is wrong! (Diff = %f)' \
+ % (i, atom_no, image_no + 1, diff)
+
+if __name__ == '__main__':
+ test()
diff --git a/tests/misc_test/rotated_atoms_test.py b/tests/misc_test/rotated_atoms_test.py
new file mode 100644
index 0000000..5e0e88e
--- /dev/null
+++ b/tests/misc_test/rotated_atoms_test.py
@@ -0,0 +1,78 @@
+#!/usr/bin/env python
+"""This test checks rotation and translation invariance of descriptor schemes.
+Fingerprints both before and after a random rotation (+ translation) are
+calculated and compared."""
+
+import numpy as np
+from numpy import sin, cos
+from ase import Atom, Atoms
+from amp.descriptor.gaussian import Gaussian
+from amp.utilities import hash_images
+import random
+
+
+def rotate_atom(x, y, z, phi, theta, psi):
+ """Rotate atom in three dimensions."""
+
+ rotation_matrix = [
+ [cos(theta) * cos(psi),
+ cos(phi) * sin(psi) + sin(phi) * sin(theta) * cos(psi),
+ sin(phi) * sin(psi) - cos(phi) * sin(theta) * cos(psi)],
+ [-cos(theta) * sin(psi),
+ cos(phi) * cos(psi) - sin(phi) * sin(theta) * sin(psi),
+ sin(phi) * cos(psi) + cos(phi) * sin(theta) * sin(psi)],
+ [sin(theta),
+ -sin(phi) * cos(theta),
+ cos(phi) * cos(theta)]
+ ]
+
+ [[xprime], [yprime], [zprime]] = np.dot(rotation_matrix, [[x], [y], [z]])
+
+ return (xprime, yprime, zprime)
+
+
+def test():
+
+ for descriptor in [Gaussian(fortran=False), ]:
+
+ # Non-rotated atomic configuration
+ atoms = Atoms([Atom('Pt', (0., 0., 0.)),
+ Atom('Pt', (0., 0., 1.)),
+ Atom('Pt', (0., 2., 1.))])
+
+ images = hash_images([atoms], ordered=True)
+ descriptor1 = descriptor
+ descriptor1.calculate_fingerprints(images)
+ fp1 = descriptor1.fingerprints[list(images.keys())[0]]
+
+
+ # Randomly Rotated (and translated) atomic configuration
+ rot = [random.random(), random.random(), random.random()]
+ for i in range(1, len(atoms)):
+ (atoms[i].x,
+ atoms[i].y,
+ atoms[i].z) = rotate_atom(atoms[i].x,
+ atoms[i].y,
+ atoms[i].z,
+ rot[0] * np.pi,
+ rot[1] * np.pi,
+ rot[2] * np.pi)
+ disp = [random.random(), random.random(), random.random()]
+ for atom in atoms:
+ atom.x += disp[0]
+ atom.y += disp[1]
+ atom.z += disp[2]
+
+ images = hash_images([atoms], ordered=True)
+ descriptor2 = descriptor
+ descriptor2.calculate_fingerprints(images)
+ fp2 = descriptor2.fingerprints[list(images.keys())[0]]
+
+ for (element1, afp1), (element2, afp2) in zip(fp1, fp2):
+ assert element1 == element2, 'rotated atoms test broken!'
+ for _, __ in zip(afp1, afp2):
+ assert (abs(_ - __) < 10 ** (-10.)), \
+ 'rotated atoms test broken!'
+
+if __name__ == '__main__':
+ test()
diff --git a/tests/test_NN_nodeplot.py b/tests/test_NN_nodeplot.py
new file mode 100644
index 0000000..eb1b36f
--- /dev/null
+++ b/tests/test_NN_nodeplot.py
@@ -0,0 +1,82 @@
+import matplotlib
+matplotlib.use('Agg') # For headless operation.
+
+from ase.calculators.emt import EMT
+from ase.lattice.surface import fcc110
+from ase import Atoms, Atom
+from ase.md.velocitydistribution import MaxwellBoltzmannDistribution
+from ase import units
+from ase.md import VelocityVerlet
+from ase.constraints import FixAtoms
+
+from amp import Amp
+from amp.descriptor.gaussian import Gaussian
+from amp.model.neuralnetwork import NeuralNetwork
+from amp.model import LossFunction
+from amp.model.neuralnetwork import NodePlot
+from amp.utilities import hash_images
+
+
+def generate_data(count):
+ """Generates test or training data with a simple MD simulation."""
+ atoms = fcc110('Pt', (2, 2, 2), vacuum=7.)
+ adsorbate = Atoms([Atom('Cu', atoms[7].position + (0., 0., 2.5)),
+ Atom('Cu', atoms[7].position + (0., 0., 5.))])
+ atoms.extend(adsorbate)
+ atoms.set_constraint(FixAtoms(indices=[0, 2]))
+ atoms.set_calculator(EMT())
+ MaxwellBoltzmannDistribution(atoms, 300. * units.kB)
+ dyn = VelocityVerlet(atoms, dt=1. * units.fs)
+ newatoms = atoms.copy()
+ newatoms.set_calculator(EMT())
+ newatoms.get_potential_energy()
+ images = [newatoms]
+ for step in range(count - 1):
+ dyn.run(50)
+ newatoms = atoms.copy()
+ newatoms.set_calculator(EMT())
+ newatoms.get_potential_energy()
+ images.append(newatoms)
+ return images
+
+
+def train_data(images, setup_only=False):
+ label = 'nodeplot_test/calc'
+ train_images = images
+
+ calc = Amp(descriptor=Gaussian(),
+ model=NeuralNetwork(hiddenlayers=(5, 5)),
+ label=label,
+ cores=1)
+ loss = LossFunction(convergence={'energy_rmse': 0.02,
+ 'force_rmse': 0.02})
+ calc.model.lossfunction = loss
+
+ if not setup_only:
+ calc.train(images=train_images, )
+ for image in train_images:
+ print ("energy =", calc.get_potential_energy(image))
+ print ("forces =", calc.get_forces(image))
+ else:
+ images = hash_images(train_images)
+ calc.descriptor.calculate_fingerprints(images=images,
+ log=calc._log,
+ parallel={'cores': 1},
+ calculate_derivatives=False)
+ calc.model.fit(trainingimages=images,
+ descriptor=calc.descriptor,
+ log=calc._log,
+ parallel={'cores': 1},
+ only_setup=True)
+ return calc
+
+
+def test_nodeplot():
+ images = generate_data(2)
+ calc = train_data(images, setup_only=True)
+ nodeplot = NodePlot(calc)
+ nodeplot.plot(images, filename='nodeplottest.pdf')
+
+
+if __name__ == "__main__":
+ test_nodeplot()
diff --git a/tests/test_gaussian_neural.py b/tests/test_gaussian_neural.py
new file mode 100644
index 0000000..389bdf9
--- /dev/null
+++ b/tests/test_gaussian_neural.py
@@ -0,0 +1,69 @@
+#!/usr/bin/env python
+"""Simple test of the Amp calculator, using Gaussian descriptors and neural
+network model. Randomly generates data with the EMT potential in MD
+simulations."""
+
+from ase.calculators.emt import EMT
+from ase.build import fcc110
+from ase import Atoms, Atom
+from ase.md.velocitydistribution import MaxwellBoltzmannDistribution
+from ase import units
+from ase.md import VelocityVerlet
+from ase.constraints import FixAtoms
+
+from amp import Amp
+from amp.descriptor.gaussian import Gaussian
+from amp.model.neuralnetwork import NeuralNetwork
+from amp.model import LossFunction
+
+
+def generate_data(count):
+ """Generates test or training data with a simple MD simulation."""
+ atoms = fcc110('Pt', (2, 2, 2), vacuum=7.)
+ adsorbate = Atoms([Atom('Cu', atoms[7].position + (0., 0., 2.5)),
+ Atom('Cu', atoms[7].position + (0., 0., 5.))])
+ atoms.extend(adsorbate)
+ atoms.set_constraint(FixAtoms(indices=[0, 2]))
+ atoms.set_calculator(EMT())
+ MaxwellBoltzmannDistribution(atoms, 300. * units.kB)
+ dyn = VelocityVerlet(atoms, dt=1. * units.fs)
+ newatoms = atoms.copy()
+ newatoms.set_calculator(EMT())
+ newatoms.get_potential_energy()
+ images = [newatoms]
+ for step in range(count - 1):
+ dyn.run(50)
+ newatoms = atoms.copy()
+ newatoms.set_calculator(EMT())
+ newatoms.get_potential_energy()
+ images.append(newatoms)
+ return images
+
+
+def train_test():
+ label = 'train_test/calc'
+ train_images = generate_data(2)
+
+ calc = Amp(descriptor=Gaussian(),
+ model=NeuralNetwork(hiddenlayers=(3, 3)),
+ label=label,
+ cores=1)
+ loss = LossFunction(convergence={'energy_rmse': 0.02,
+ 'force_rmse': 0.02})
+ calc.model.lossfunction = loss
+
+ calc.train(images=train_images,)
+ for image in train_images:
+ print("energy = %s" % str(calc.get_potential_energy(image)))
+ print("forces = %s" % str(calc.get_forces(image)))
+
+ # Test that we can re-load this calculator and call it again.
+ del calc
+ calc2 = Amp.load(label + '.amp')
+ for image in train_images:
+ print("energy = %s" % str(calc2.get_potential_energy(image)))
+ print("forces = %s" % str(calc2.get_forces(image)))
+
+
+if __name__ == '__main__':
+ train_test()
diff --git a/tests/test_gaussian_tflow.py b/tests/test_gaussian_tflow.py
new file mode 100644
index 0000000..12b5c5f
--- /dev/null
+++ b/tests/test_gaussian_tflow.py
@@ -0,0 +1,83 @@
+#!/usr/bin/env python
+"""Simple test of the Amp calculator, using Gaussian descriptors and neural
+network model. Randomly generates data with the EMT potential in MD
+simulations."""
+
+import sys
+from ase.calculators.emt import EMT
+from ase.lattice.surface import fcc110
+from ase import Atoms, Atom
+from ase.md.velocitydistribution import MaxwellBoltzmannDistribution
+from ase import units
+from ase.md import VelocityVerlet
+from ase.constraints import FixAtoms
+
+from amp import Amp
+from amp.descriptor.gaussian import Gaussian
+
+
+def perform_test():
+ """Determines whether or not to perform the test.
+ This should only perform the test if the python version is 2.x
+ and tensorflow is installed. If returns False (meaning don't
+ peform test), also supplies the reason."""
+ if sys.version_info >= (3,):
+ return False, 'amp.model.tflow not supported in python3.'
+ try:
+ import tensorflow
+ except ImportError:
+ return False, 'Tensorflow not installed.'
+ return True, ''
+
+
+def generate_data(count):
+ """Generates test or training data with a simple MD simulation."""
+ atoms = fcc110('Pt', (2, 2, 2), vacuum=7.)
+ adsorbate = Atoms([Atom('Cu', atoms[7].position + (0., 0., 2.5)),
+ Atom('Cu', atoms[7].position + (0., 0., 5.))])
+ atoms.extend(adsorbate)
+ atoms.set_constraint(FixAtoms(indices=[0, 2]))
+ atoms.set_calculator(EMT())
+ MaxwellBoltzmannDistribution(atoms, 300. * units.kB)
+ dyn = VelocityVerlet(atoms, dt=1. * units.fs)
+ newatoms = atoms.copy()
+ newatoms.set_calculator(EMT())
+ newatoms.get_potential_energy()
+ images = [newatoms]
+ for step in range(count - 1):
+ dyn.run(50)
+ newatoms = atoms.copy()
+ newatoms.set_calculator(EMT())
+ newatoms.get_potential_energy()
+ images.append(newatoms)
+ return images
+
+
+def train_test():
+ perform, reason = perform_test()
+ if not perform:
+ print('Skipping this test because {}.'.format(reason))
+ return
+
+ from amp.model.tflow import NeuralNetwork
+ label = 'train_test/calc'
+ train_images = generate_data(2)
+ convergence = {
+ 'energy_rmse': 0.02,
+ 'force_rmse': 0.02
+ }
+
+ calc = Amp(descriptor=Gaussian(),
+ model=NeuralNetwork(hiddenlayers=(3, 3),
+ convergenceCriteria=convergence),
+ label=label,
+ cores=1)
+
+ calc.train(images=train_images,)
+ for image in train_images:
+ print("energy =", calc.get_potential_energy(image))
+ print("forces =", calc.get_forces(image))
+
+
+if __name__ == '__main__':
+ train_test()
diff --git a/tools/amp-compress b/tools/amp-compress
new file mode 100755
index 0000000..8ba51d1
--- /dev/null
+++ b/tools/amp-compress
@@ -0,0 +1,46 @@
+#!/usr/bin/env python
+"""Tool to compress Amp FileDatabase objects."""
+
+import os
+from optparse import OptionParser
+
+from amp.utilities import FileDatabase
+
+
+def compress_file(filename):
+ filename = filename.rstrip(os.path.sep)
+ assert filename.endswith('.ampdb')
+ assert 'loose' in os.listdir(filename)
+ FileDatabase(filename).archive()
+
+
+def parser():
+ parser = OptionParser(
+ usage='usage: %prog [options] [filename(s)]\n Compress .ampdb'
+ ' files(Amp FileDatabase objects).')
+ add = parser.add_option
+ add('-r', '--recursive', action='store_true',
+ default=False, help='recursively search and compress .ampdb files')
+ options, args = parser.parse_args()
+ return options, args
+
+
+options, args = parser()
+
+if not options.recursive:
+ for filename in args:
+ compress_file(filename)
+else:
+ if len(args) != 1:
+ raise AssertionError('A single argument (top directory) must be '
+ 'supplied with the recursive option.')
+ topdir = args[0]
+ if not os.path.isdir(topdir):
+ raise AssertionError('Argument must be a path with recursive option.')
+
+ for dirpath, dirnames, filenames in os.walk(topdir):
+ for dirname in dirnames:
+ if dirname.endswith('.ampdb'):
+ filename = os.path.join(dirpath, dirname)
+ print('Found %s.' % filename)
+ compress_file(filename)
diff --git a/tools/amp-plotconvergence b/tools/amp-plotconvergence
new file mode 100755
index 0000000..34b3c5b
--- /dev/null
+++ b/tools/amp-plotconvergence
@@ -0,0 +1,27 @@
+#!/usr/bin/env python
+"""Tool to create convergence plots for Amp."""
+
+import matplotlib
+# The 'Agg' command must be *before* all other matplotlib imports for
+# headless operation.
+matplotlib.use('Agg')
+
+from optparse import OptionParser
+
+from amp.analysis import plot_convergence
+
+
+parser = OptionParser(
+ usage='usage: %prog logfile [plotfile]\n Create convergence plot'
+ ' logfile is amp log file; plotfile is an optional filename '
+ ' for the output that takes any allowable matplotlib format.')
+options, args = parser.parse_args()
+
+if len(args) not in [1, 2]:
+ raise RuntimeError('Bad number of arguments.')
+plotfile = 'convergence.pdf'
+if len(args) == 2:
+ plotfile = args.pop(-1)
+logfile = args.pop(0)
+
+plot_convergence(logfile=logfile, plotfile=plotfile)
--
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