From 231c0189f643763f256f3a5657babb5ca265bee7 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=ED=99=A9=EC=84=A0=EC=9A=B0?= Date: Thu, 11 Jul 2024 00:48:40 +0900 Subject: [PATCH 01/22] updated power_spectrum function --- .../ellipsoidal_density_projection.py | 27 +++++++++++++++++++ 1 file changed, 27 insertions(+) diff --git a/anisoap/representations/ellipsoidal_density_projection.py b/anisoap/representations/ellipsoidal_density_projection.py index be5fa45..b9399a0 100644 --- a/anisoap/representations/ellipsoidal_density_projection.py +++ b/anisoap/representations/ellipsoidal_density_projection.py @@ -646,3 +646,30 @@ def transform(self, frames, show_progress=False, normalize=True): return normalized_features else: return features + def power_spectrum(self, ell_frames, AniSOAP_HYPERS=None, mycg=None): + calculator = EllipsoidalDensityProjection(**AniSOAP_HYPERS) + if ell_frames is None: + raise ValueError("ell_frames cannot be none") + required_attributes = [ + 'c_diameter[1]', + 'c_diameter[2]', + 'c_diameter[3]', + 'c_q', + 'positions', + 'species' + ] + for index, frame in enumerate(ell_frames): + for attr in required_attributes: + if attr not in frame: + raise ValueError(f"ell_frame at index {index} is missing a required attribute '{attr}'") + + mvg_coeffs = calculator.transform(ell_frames, show_progress=True) + mvg_nu1 = standardize_keys(mvg_coeffs) + mvg_nu2 = cg_combine( + mvg_nu1, + mvg_nu1, + clebsch_gordan=mycg, + lcut=0, + other_keys_match=["types_center"] + ) + return mvg_nu2 From 907587efe58a00c73841a2a6932828ccb5e73e98 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=ED=99=A9=EC=84=A0=EC=9A=B0?= Date: Thu, 18 Jul 2024 22:57:20 +0900 Subject: [PATCH 02/22] updates for power_spectrum function --- .../ellipsoidal_density_projection.py | 19 ++++++++++++++++--- notebooks/anisotropic_representations.ipynb | 8 ++++---- 2 files changed, 20 insertions(+), 7 deletions(-) diff --git a/anisoap/representations/ellipsoidal_density_projection.py b/anisoap/representations/ellipsoidal_density_projection.py index b9399a0..e2bd190 100644 --- a/anisoap/representations/ellipsoidal_density_projection.py +++ b/anisoap/representations/ellipsoidal_density_projection.py @@ -1,5 +1,6 @@ import sys import warnings +import metatensor from itertools import product import numpy as np @@ -11,6 +12,7 @@ from rascaline import NeighborList from scipy.spatial.transform import Rotation from tqdm.auto import tqdm +from skmatter.preprocessing import StandardFlexibleScaler from anisoap.representations.radial_basis import ( GTORadialBasis, @@ -18,7 +20,11 @@ ) from anisoap.utils.moment_generator import * from anisoap.utils.spherical_to_cartesian import spherical_to_cartesian - +from anisoap.utils.metatensor_utils import ( + cg_combine, + standardize_keys, + ClebschGordanReal +) def pairwise_ellip_expansion( lmax, @@ -656,7 +662,8 @@ def power_spectrum(self, ell_frames, AniSOAP_HYPERS=None, mycg=None): 'c_diameter[3]', 'c_q', 'positions', - 'species' + 'species', + 'quaternion' ] for index, frame in enumerate(ell_frames): for attr in required_attributes: @@ -672,4 +679,10 @@ def power_spectrum(self, ell_frames, AniSOAP_HYPERS=None, mycg=None): lcut=0, other_keys_match=["types_center"] ) - return mvg_nu2 + + x_asoap_raw = metatensor.sum_over_samples(mvg_nu2, sample_names="center") + x_asoap_raw = x_asoap_raw.block().values.squeeze() + x_asoap_scaler = StandardFlexibleScaler(column_wise=False).fit(x_asoap_raw) + x_asoap = x_asoap_scaler.transform(x_asoap_raw) + + return x_asoap diff --git a/notebooks/anisotropic_representations.ipynb b/notebooks/anisotropic_representations.ipynb index f2c4e1e..d79a71a 100644 --- a/notebooks/anisotropic_representations.ipynb +++ b/notebooks/anisotropic_representations.ipynb @@ -344,10 +344,10 @@ "evalue": "No module named 'anisoap.representations.projection_coefficients_modified'", "output_type": "error", "traceback": [ - "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[0;31mModuleNotFoundError\u001b[0m Traceback (most recent call last)", - "Cell \u001b[0;32mIn [47], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01manisoap\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mrepresentations\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mprojection_coefficients_modified\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;241m*\u001b[39m\n", - "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'anisoap.representations.projection_coefficients_modified'" + "\u001B[0;31m---------------------------------------------------------------------------\u001B[0m", + "\u001B[0;31mModuleNotFoundError\u001B[0m Traceback (most recent call last)", + "Cell \u001B[0;32mIn [47], line 1\u001B[0m\n\u001B[0;32m----> 1\u001B[0m \u001B[38;5;28;01mfrom\u001B[39;00m \u001B[38;5;21;01manisoap\u001B[39;00m\u001B[38;5;21;01m.\u001B[39;00m\u001B[38;5;21;01mrepresentations\u001B[39;00m\u001B[38;5;21;01m.\u001B[39;00m\u001B[38;5;21;01mprojection_coefficients_modified\u001B[39;00m \u001B[38;5;28;01mimport\u001B[39;00m \u001B[38;5;241m*\u001B[39m\n", + "\u001B[0;31mModuleNotFoundError\u001B[0m: No module named 'anisoap.representations.projection_coefficients_modified'" ] } ], From 40e3a2c06798d2dffc5631d495344e909dde15bb Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=ED=99=A9=EC=84=A0=EC=9A=B0?= Date: Thu, 25 Jul 2024 02:39:42 +0900 Subject: [PATCH 03/22] final update of power_spectrum function --- .../ellipsoidal_density_projection.py | 36 ++++++++++++------- setup.py | 3 +- 2 files changed, 25 insertions(+), 14 deletions(-) diff --git a/anisoap/representations/ellipsoidal_density_projection.py b/anisoap/representations/ellipsoidal_density_projection.py index e2bd190..bf3d0fb 100644 --- a/anisoap/representations/ellipsoidal_density_projection.py +++ b/anisoap/representations/ellipsoidal_density_projection.py @@ -23,9 +23,10 @@ from anisoap.utils.metatensor_utils import ( cg_combine, standardize_keys, - ClebschGordanReal + ClebschGordanReal, ) + def pairwise_ellip_expansion( lmax, neighbor_list, @@ -652,23 +653,32 @@ def transform(self, frames, show_progress=False, normalize=True): return normalized_features else: return features - def power_spectrum(self, ell_frames, AniSOAP_HYPERS=None, mycg=None): + + def power_spectrum(self, ell_frames, AniSOAP_HYPERS=None): + mycg = ClebschGordanReal(AniSOAP_HYPERS["max_angular"]) calculator = EllipsoidalDensityProjection(**AniSOAP_HYPERS) - if ell_frames is None: + if ell_frames[0].arrays is None: raise ValueError("ell_frames cannot be none") required_attributes = [ - 'c_diameter[1]', - 'c_diameter[2]', - 'c_diameter[3]', - 'c_q', - 'positions', - 'species', - 'quaternion' + "c_diameter[1]", + "c_diameter[2]", + "c_diameter[3]", + "c_q", + "positions", + "numbers", ] + for index, frame in enumerate(ell_frames): + array = frame.arrays for attr in required_attributes: - if attr not in frame: - raise ValueError(f"ell_frame at index {index} is missing a required attribute '{attr}'") + if attr not in array: + raise ValueError( + f"ell_frame at index {index} is missing a required attribute '{attr}'" + ) + if "quaternion" in array: + raise ValueError( + f"ell_frame should contain c_q rather than quaternion" + ) mvg_coeffs = calculator.transform(ell_frames, show_progress=True) mvg_nu1 = standardize_keys(mvg_coeffs) @@ -677,7 +687,7 @@ def power_spectrum(self, ell_frames, AniSOAP_HYPERS=None, mycg=None): mvg_nu1, clebsch_gordan=mycg, lcut=0, - other_keys_match=["types_center"] + other_keys_match=["types_center"], ) x_asoap_raw = metatensor.sum_over_samples(mvg_nu2, sample_names="center") diff --git a/setup.py b/setup.py index a93d3b6..cff2f1e 100644 --- a/setup.py +++ b/setup.py @@ -1,7 +1,8 @@ #!/usr/bin/env python3 -from setuptools import setup import re +from setuptools import setup + __version__ = re.search( r'__version__\s*=\s*[\'"]([^\'"]*)[\'"]', open("anisoap/__init__.py").read() ).group(1) From e517f37abe4753eb1c34e61f309d5aa93ad61c93 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=ED=99=A9=EC=84=A0=EC=9A=B0?= Date: Thu, 25 Jul 2024 02:52:45 +0900 Subject: [PATCH 04/22] last update --- .../ellipsoidal_density_projection.py | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/anisoap/representations/ellipsoidal_density_projection.py b/anisoap/representations/ellipsoidal_density_projection.py index bf3d0fb..f1f4039 100644 --- a/anisoap/representations/ellipsoidal_density_projection.py +++ b/anisoap/representations/ellipsoidal_density_projection.py @@ -1,8 +1,8 @@ import sys import warnings -import metatensor from itertools import product +import metatensor import numpy as np from metatensor import ( Labels, @@ -11,20 +11,20 @@ ) from rascaline import NeighborList from scipy.spatial.transform import Rotation -from tqdm.auto import tqdm from skmatter.preprocessing import StandardFlexibleScaler +from tqdm.auto import tqdm from anisoap.representations.radial_basis import ( GTORadialBasis, MonomialBasis, ) -from anisoap.utils.moment_generator import * -from anisoap.utils.spherical_to_cartesian import spherical_to_cartesian from anisoap.utils.metatensor_utils import ( + ClebschGordanReal, cg_combine, standardize_keys, - ClebschGordanReal, ) +from anisoap.utils.moment_generator import * +from anisoap.utils.spherical_to_cartesian import spherical_to_cartesian def pairwise_ellip_expansion( @@ -667,7 +667,7 @@ def power_spectrum(self, ell_frames, AniSOAP_HYPERS=None): "positions", "numbers", ] - + for index, frame in enumerate(ell_frames): array = frame.arrays for attr in required_attributes: From 8ef7696a314345d7f6ea127d9392a4f16ed41c28 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=ED=99=A9=EC=84=A0=EC=9A=B0?= Date: Fri, 6 Sep 2024 00:06:50 +0900 Subject: [PATCH 05/22] added docstrings and modified the function --- .../ellipsoidal_density_projection.py | 43 ++++++++++++++++--- 1 file changed, 36 insertions(+), 7 deletions(-) diff --git a/anisoap/representations/ellipsoidal_density_projection.py b/anisoap/representations/ellipsoidal_density_projection.py index f1f4039..ae58aed 100644 --- a/anisoap/representations/ellipsoidal_density_projection.py +++ b/anisoap/representations/ellipsoidal_density_projection.py @@ -654,7 +654,36 @@ def transform(self, frames, show_progress=False, normalize=True): else: return features - def power_spectrum(self, ell_frames, AniSOAP_HYPERS=None): + def power_spectrum(self, ell_frames, AniSOAP_HYPERS=None, sum_over_samples=True): + + """Function to compute the power spectrum of AniSOAP + + computes the power spectrum of AniSOAP with the inputs of AniSOAP hyperparameters + and ellipsoidal frames using ellipsoidal density projection. It checks if + each ellipsoidal frame contains all required attributes and processes + Clebsch-Gordan coefficients for the angular component of the AniSOAP descriptors. + + Parameters + ---------- + + ell_frames: list + a list of ellipsoidal frames, where each frame contains attributes: + 'c_diameter[1]', 'c_diameter[2]', 'c_diameter[3]', 'c_q', 'positions', and 'numbers'. + It only accepts c_q for the angular attribute of each frame. + + AniSOAP_HYPERS : keyword arguments + A dictionary of hyperparameters for the power spectrum calculation, including 'max_angular' + 'max_radial', 'radial_basis_name', 'rotation_type', 'rotation_key', 'cutoff_radius', 'radial_gaussian_width', + 'basis_rcond', and 'basis_tol'. + + sum_over_sample: bool + A function that returns the sum of coefficients of all the samples (frames) + + Returns + ------- + x_asoap_raw, a power spectrum that can be visualized using jupyter notebook. + + """ mycg = ClebschGordanReal(AniSOAP_HYPERS["max_angular"]) calculator = EllipsoidalDensityProjection(**AniSOAP_HYPERS) if ell_frames[0].arrays is None: @@ -689,10 +718,10 @@ def power_spectrum(self, ell_frames, AniSOAP_HYPERS=None): lcut=0, other_keys_match=["types_center"], ) + if sum_over_samples: + x_asoap_raw = metatensor.sum_over_samples(mvg_nu2, sample_names="center") + x_asoap_raw = x_asoap_raw.block().values.squeeze() + return x_asoap_raw + else: + mvg_nu2.block().values - x_asoap_raw = metatensor.sum_over_samples(mvg_nu2, sample_names="center") - x_asoap_raw = x_asoap_raw.block().values.squeeze() - x_asoap_scaler = StandardFlexibleScaler(column_wise=False).fit(x_asoap_raw) - x_asoap = x_asoap_scaler.transform(x_asoap_raw) - - return x_asoap From bcc4605c547717be89100cbc2fa18e5f99ae72b0 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=ED=99=A9=EC=84=A0=EC=9A=B0?= Date: Thu, 11 Jul 2024 00:48:40 +0900 Subject: [PATCH 06/22] updated power_spectrum function --- .../ellipsoidal_density_projection.py | 27 +++++++++++++++++++ 1 file changed, 27 insertions(+) diff --git a/anisoap/representations/ellipsoidal_density_projection.py b/anisoap/representations/ellipsoidal_density_projection.py index a88a4d9..d4e2f0f 100644 --- a/anisoap/representations/ellipsoidal_density_projection.py +++ b/anisoap/representations/ellipsoidal_density_projection.py @@ -658,3 +658,30 @@ def transform(self, frames, show_progress=False, normalize=True, rust_moments=Tr return normalized_features else: return features + def power_spectrum(self, ell_frames, AniSOAP_HYPERS=None, mycg=None): + calculator = EllipsoidalDensityProjection(**AniSOAP_HYPERS) + if ell_frames is None: + raise ValueError("ell_frames cannot be none") + required_attributes = [ + 'c_diameter[1]', + 'c_diameter[2]', + 'c_diameter[3]', + 'c_q', + 'positions', + 'species' + ] + for index, frame in enumerate(ell_frames): + for attr in required_attributes: + if attr not in frame: + raise ValueError(f"ell_frame at index {index} is missing a required attribute '{attr}'") + + mvg_coeffs = calculator.transform(ell_frames, show_progress=True) + mvg_nu1 = standardize_keys(mvg_coeffs) + mvg_nu2 = cg_combine( + mvg_nu1, + mvg_nu1, + clebsch_gordan=mycg, + lcut=0, + other_keys_match=["types_center"] + ) + return mvg_nu2 From 8425aef07b10b0670b8dcef6040ce25b99b79d9b Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=ED=99=A9=EC=84=A0=EC=9A=B0?= Date: Thu, 18 Jul 2024 22:57:20 +0900 Subject: [PATCH 07/22] updates for power_spectrum function --- .../ellipsoidal_density_projection.py | 19 ++++++++++++++++--- notebooks/anisotropic_representations.ipynb | 8 ++++---- 2 files changed, 20 insertions(+), 7 deletions(-) diff --git a/anisoap/representations/ellipsoidal_density_projection.py b/anisoap/representations/ellipsoidal_density_projection.py index d4e2f0f..1637670 100644 --- a/anisoap/representations/ellipsoidal_density_projection.py +++ b/anisoap/representations/ellipsoidal_density_projection.py @@ -1,5 +1,6 @@ import sys import warnings +import metatensor from itertools import product import numpy as np @@ -12,6 +13,7 @@ from rascaline import NeighborList from scipy.spatial.transform import Rotation from tqdm.auto import tqdm +from skmatter.preprocessing import StandardFlexibleScaler from anisoap.representations.radial_basis import ( GTORadialBasis, @@ -19,7 +21,11 @@ ) from anisoap.utils.moment_generator import * from anisoap.utils.spherical_to_cartesian import spherical_to_cartesian - +from anisoap.utils.metatensor_utils import ( + cg_combine, + standardize_keys, + ClebschGordanReal +) def pairwise_ellip_expansion( lmax, @@ -668,7 +674,8 @@ def power_spectrum(self, ell_frames, AniSOAP_HYPERS=None, mycg=None): 'c_diameter[3]', 'c_q', 'positions', - 'species' + 'species', + 'quaternion' ] for index, frame in enumerate(ell_frames): for attr in required_attributes: @@ -684,4 +691,10 @@ def power_spectrum(self, ell_frames, AniSOAP_HYPERS=None, mycg=None): lcut=0, other_keys_match=["types_center"] ) - return mvg_nu2 + + x_asoap_raw = metatensor.sum_over_samples(mvg_nu2, sample_names="center") + x_asoap_raw = x_asoap_raw.block().values.squeeze() + x_asoap_scaler = StandardFlexibleScaler(column_wise=False).fit(x_asoap_raw) + x_asoap = x_asoap_scaler.transform(x_asoap_raw) + + return x_asoap diff --git a/notebooks/anisotropic_representations.ipynb b/notebooks/anisotropic_representations.ipynb index f2c4e1e..d79a71a 100644 --- a/notebooks/anisotropic_representations.ipynb +++ b/notebooks/anisotropic_representations.ipynb @@ -344,10 +344,10 @@ "evalue": "No module named 'anisoap.representations.projection_coefficients_modified'", "output_type": "error", "traceback": [ - "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[0;31mModuleNotFoundError\u001b[0m Traceback (most recent call last)", - "Cell \u001b[0;32mIn [47], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01manisoap\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mrepresentations\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mprojection_coefficients_modified\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;241m*\u001b[39m\n", - "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'anisoap.representations.projection_coefficients_modified'" + "\u001B[0;31m---------------------------------------------------------------------------\u001B[0m", + "\u001B[0;31mModuleNotFoundError\u001B[0m Traceback (most recent call last)", + "Cell \u001B[0;32mIn [47], line 1\u001B[0m\n\u001B[0;32m----> 1\u001B[0m \u001B[38;5;28;01mfrom\u001B[39;00m \u001B[38;5;21;01manisoap\u001B[39;00m\u001B[38;5;21;01m.\u001B[39;00m\u001B[38;5;21;01mrepresentations\u001B[39;00m\u001B[38;5;21;01m.\u001B[39;00m\u001B[38;5;21;01mprojection_coefficients_modified\u001B[39;00m \u001B[38;5;28;01mimport\u001B[39;00m \u001B[38;5;241m*\u001B[39m\n", + "\u001B[0;31mModuleNotFoundError\u001B[0m: No module named 'anisoap.representations.projection_coefficients_modified'" ] } ], From 24c06b2df4ca5379f82b28c49e8f8a53e0666e21 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=ED=99=A9=EC=84=A0=EC=9A=B0?= Date: Thu, 25 Jul 2024 02:39:42 +0900 Subject: [PATCH 08/22] final update of power_spectrum function --- .../ellipsoidal_density_projection.py | 36 ++++++++++++------- 1 file changed, 23 insertions(+), 13 deletions(-) diff --git a/anisoap/representations/ellipsoidal_density_projection.py b/anisoap/representations/ellipsoidal_density_projection.py index 1637670..128fef7 100644 --- a/anisoap/representations/ellipsoidal_density_projection.py +++ b/anisoap/representations/ellipsoidal_density_projection.py @@ -24,9 +24,10 @@ from anisoap.utils.metatensor_utils import ( cg_combine, standardize_keys, - ClebschGordanReal + ClebschGordanReal, ) + def pairwise_ellip_expansion( lmax, neighbor_list, @@ -664,23 +665,32 @@ def transform(self, frames, show_progress=False, normalize=True, rust_moments=Tr return normalized_features else: return features - def power_spectrum(self, ell_frames, AniSOAP_HYPERS=None, mycg=None): + + def power_spectrum(self, ell_frames, AniSOAP_HYPERS=None): + mycg = ClebschGordanReal(AniSOAP_HYPERS["max_angular"]) calculator = EllipsoidalDensityProjection(**AniSOAP_HYPERS) - if ell_frames is None: + if ell_frames[0].arrays is None: raise ValueError("ell_frames cannot be none") required_attributes = [ - 'c_diameter[1]', - 'c_diameter[2]', - 'c_diameter[3]', - 'c_q', - 'positions', - 'species', - 'quaternion' + "c_diameter[1]", + "c_diameter[2]", + "c_diameter[3]", + "c_q", + "positions", + "numbers", ] + for index, frame in enumerate(ell_frames): + array = frame.arrays for attr in required_attributes: - if attr not in frame: - raise ValueError(f"ell_frame at index {index} is missing a required attribute '{attr}'") + if attr not in array: + raise ValueError( + f"ell_frame at index {index} is missing a required attribute '{attr}'" + ) + if "quaternion" in array: + raise ValueError( + f"ell_frame should contain c_q rather than quaternion" + ) mvg_coeffs = calculator.transform(ell_frames, show_progress=True) mvg_nu1 = standardize_keys(mvg_coeffs) @@ -689,7 +699,7 @@ def power_spectrum(self, ell_frames, AniSOAP_HYPERS=None, mycg=None): mvg_nu1, clebsch_gordan=mycg, lcut=0, - other_keys_match=["types_center"] + other_keys_match=["types_center"], ) x_asoap_raw = metatensor.sum_over_samples(mvg_nu2, sample_names="center") From 407febfc60c121bc1a44e0af0da32ba72aad8746 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=ED=99=A9=EC=84=A0=EC=9A=B0?= Date: Thu, 25 Jul 2024 02:52:45 +0900 Subject: [PATCH 09/22] last update --- .../ellipsoidal_density_projection.py | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/anisoap/representations/ellipsoidal_density_projection.py b/anisoap/representations/ellipsoidal_density_projection.py index 128fef7..d827eae 100644 --- a/anisoap/representations/ellipsoidal_density_projection.py +++ b/anisoap/representations/ellipsoidal_density_projection.py @@ -1,8 +1,8 @@ import sys import warnings -import metatensor from itertools import product +import metatensor import numpy as np from anisoap_rust_lib import compute_moments from metatensor import ( @@ -12,20 +12,20 @@ ) from rascaline import NeighborList from scipy.spatial.transform import Rotation -from tqdm.auto import tqdm from skmatter.preprocessing import StandardFlexibleScaler +from tqdm.auto import tqdm from anisoap.representations.radial_basis import ( GTORadialBasis, MonomialBasis, ) -from anisoap.utils.moment_generator import * -from anisoap.utils.spherical_to_cartesian import spherical_to_cartesian from anisoap.utils.metatensor_utils import ( + ClebschGordanReal, cg_combine, standardize_keys, - ClebschGordanReal, ) +from anisoap.utils.moment_generator import * +from anisoap.utils.spherical_to_cartesian import spherical_to_cartesian def pairwise_ellip_expansion( @@ -679,7 +679,7 @@ def power_spectrum(self, ell_frames, AniSOAP_HYPERS=None): "positions", "numbers", ] - + for index, frame in enumerate(ell_frames): array = frame.arrays for attr in required_attributes: From 20fb1f12eefdc4b1036ade8802f972d4581d74af Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=ED=99=A9=EC=84=A0=EC=9A=B0?= Date: Fri, 6 Sep 2024 00:06:50 +0900 Subject: [PATCH 10/22] added docstrings and modified the function --- .../ellipsoidal_density_projection.py | 43 ++++++++++++++++--- 1 file changed, 36 insertions(+), 7 deletions(-) diff --git a/anisoap/representations/ellipsoidal_density_projection.py b/anisoap/representations/ellipsoidal_density_projection.py index d827eae..1ae5b2a 100644 --- a/anisoap/representations/ellipsoidal_density_projection.py +++ b/anisoap/representations/ellipsoidal_density_projection.py @@ -666,7 +666,36 @@ def transform(self, frames, show_progress=False, normalize=True, rust_moments=Tr else: return features - def power_spectrum(self, ell_frames, AniSOAP_HYPERS=None): + def power_spectrum(self, ell_frames, AniSOAP_HYPERS=None, sum_over_samples=True): + + """Function to compute the power spectrum of AniSOAP + + computes the power spectrum of AniSOAP with the inputs of AniSOAP hyperparameters + and ellipsoidal frames using ellipsoidal density projection. It checks if + each ellipsoidal frame contains all required attributes and processes + Clebsch-Gordan coefficients for the angular component of the AniSOAP descriptors. + + Parameters + ---------- + + ell_frames: list + a list of ellipsoidal frames, where each frame contains attributes: + 'c_diameter[1]', 'c_diameter[2]', 'c_diameter[3]', 'c_q', 'positions', and 'numbers'. + It only accepts c_q for the angular attribute of each frame. + + AniSOAP_HYPERS : keyword arguments + A dictionary of hyperparameters for the power spectrum calculation, including 'max_angular' + 'max_radial', 'radial_basis_name', 'rotation_type', 'rotation_key', 'cutoff_radius', 'radial_gaussian_width', + 'basis_rcond', and 'basis_tol'. + + sum_over_sample: bool + A function that returns the sum of coefficients of all the samples (frames) + + Returns + ------- + x_asoap_raw, a power spectrum that can be visualized using jupyter notebook. + + """ mycg = ClebschGordanReal(AniSOAP_HYPERS["max_angular"]) calculator = EllipsoidalDensityProjection(**AniSOAP_HYPERS) if ell_frames[0].arrays is None: @@ -701,10 +730,10 @@ def power_spectrum(self, ell_frames, AniSOAP_HYPERS=None): lcut=0, other_keys_match=["types_center"], ) + if sum_over_samples: + x_asoap_raw = metatensor.sum_over_samples(mvg_nu2, sample_names="center") + x_asoap_raw = x_asoap_raw.block().values.squeeze() + return x_asoap_raw + else: + mvg_nu2.block().values - x_asoap_raw = metatensor.sum_over_samples(mvg_nu2, sample_names="center") - x_asoap_raw = x_asoap_raw.block().values.squeeze() - x_asoap_scaler = StandardFlexibleScaler(column_wise=False).fit(x_asoap_raw) - x_asoap = x_asoap_scaler.transform(x_asoap_raw) - - return x_asoap From 2260b7df1b7b3eba68dbdabca670bd6f56a87963 Mon Sep 17 00:00:00 2001 From: Arthur Lin Date: Tue, 10 Sep 2024 13:53:45 -0500 Subject: [PATCH 11/22] added skmatter --- tests/requirements.txt | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/tests/requirements.txt b/tests/requirements.txt index f526634..e303a0a 100644 --- a/tests/requirements.txt +++ b/tests/requirements.txt @@ -9,4 +9,5 @@ tqdm metatensor wigners matplotlib -Sphinx \ No newline at end of file +Sphinx +skmatter \ No newline at end of file From b8d7e81bb5a3e22b364d53db9770de4b9a344056 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=ED=99=A9=EC=84=A0=EC=9A=B0?= Date: Wed, 18 Sep 2024 23:37:15 +0900 Subject: [PATCH 12/22] Added a few comments --- .../ellipsoidal_density_projection.py | 17 +++++++++++++++-- 1 file changed, 15 insertions(+), 2 deletions(-) diff --git a/anisoap/representations/ellipsoidal_density_projection.py b/anisoap/representations/ellipsoidal_density_projection.py index ae58aed..cc31a96 100644 --- a/anisoap/representations/ellipsoidal_density_projection.py +++ b/anisoap/representations/ellipsoidal_density_projection.py @@ -677,15 +677,21 @@ def power_spectrum(self, ell_frames, AniSOAP_HYPERS=None, sum_over_samples=True) 'basis_rcond', and 'basis_tol'. sum_over_sample: bool - A function that returns the sum of coefficients of all the samples (frames) + A function that returns the sum of coefficients of the frames in the sample. Returns ------- - x_asoap_raw, a power spectrum that can be visualized using jupyter notebook. + x_asoap_raw, a power spectrum of AniSOAP descriptor that can be visualized using jupyter notebook. """ + + # Initialize the Clebsch Gordan calculator for the angular component. mycg = ClebschGordanReal(AniSOAP_HYPERS["max_angular"]) + + # Initialize the ellipsoidal density projection calculator using the AniSOAP hyperparameters. calculator = EllipsoidalDensityProjection(**AniSOAP_HYPERS) + + # Checks that the sample's first frame is not empty if ell_frames[0].arrays is None: raise ValueError("ell_frames cannot be none") required_attributes = [ @@ -697,6 +703,7 @@ def power_spectrum(self, ell_frames, AniSOAP_HYPERS=None, sum_over_samples=True) "numbers", ] + # Checks if the sample contains all necessary information for computation of power spectrum for index, frame in enumerate(ell_frames): array = frame.arrays for attr in required_attributes: @@ -709,8 +716,11 @@ def power_spectrum(self, ell_frames, AniSOAP_HYPERS=None, sum_over_samples=True) f"ell_frame should contain c_q rather than quaternion" ) + # Executes ellipsoidal density projection on the frames of sample using the calculator. mvg_coeffs = calculator.transform(ell_frames, show_progress=True) mvg_nu1 = standardize_keys(mvg_coeffs) + + # Combines the mvg_nu1 with itself using the Clebsch-Gordan coefficients. This combines the angular and radial components of the sample. mvg_nu2 = cg_combine( mvg_nu1, mvg_nu1, @@ -718,6 +728,9 @@ def power_spectrum(self, ell_frames, AniSOAP_HYPERS=None, sum_over_samples=True) lcut=0, other_keys_match=["types_center"], ) + + # If sum_over_samples = True, it returns simplified form of coefficients with fewer dimensions in the tensormap for subsequent visualization. If not, it returns raw numerical data of coefficients contained within a specific block of the mvg_nu2 tensor + if sum_over_samples: x_asoap_raw = metatensor.sum_over_samples(mvg_nu2, sample_names="center") x_asoap_raw = x_asoap_raw.block().values.squeeze() From bf8437e7f2fc21b42d07f209196866585fca6302 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=ED=99=A9=EC=84=A0=EC=9A=B0?= Date: Thu, 19 Sep 2024 00:02:44 +0900 Subject: [PATCH 13/22] added a few comments --- anisoap/representations/ellipsoidal_density_projection.py | 2 -- 1 file changed, 2 deletions(-) diff --git a/anisoap/representations/ellipsoidal_density_projection.py b/anisoap/representations/ellipsoidal_density_projection.py index cc31a96..949b5a2 100644 --- a/anisoap/representations/ellipsoidal_density_projection.py +++ b/anisoap/representations/ellipsoidal_density_projection.py @@ -655,7 +655,6 @@ def transform(self, frames, show_progress=False, normalize=True): return features def power_spectrum(self, ell_frames, AniSOAP_HYPERS=None, sum_over_samples=True): - """Function to compute the power spectrum of AniSOAP computes the power spectrum of AniSOAP with the inputs of AniSOAP hyperparameters @@ -737,4 +736,3 @@ def power_spectrum(self, ell_frames, AniSOAP_HYPERS=None, sum_over_samples=True) return x_asoap_raw else: mvg_nu2.block().values - From f522793a55e8d87a400d12acfe4d8b4a346a320b Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=ED=99=A9=EC=84=A0=EC=9A=B0?= Date: Fri, 20 Sep 2024 10:11:24 +0900 Subject: [PATCH 14/22] adding the invarience of powerspectrum notebook --- Invariances_of_powerspectrum.ipynb | 1175 ++++++++++++++++++++++++++++ 1 file changed, 1175 insertions(+) create mode 100644 Invariances_of_powerspectrum.ipynb diff --git a/Invariances_of_powerspectrum.ipynb b/Invariances_of_powerspectrum.ipynb new file mode 100644 index 0000000..d09e3b4 --- /dev/null +++ b/Invariances_of_powerspectrum.ipynb @@ -0,0 +1,1175 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 22, + "id": "9a0205c7-a5d9-49d8-9b65-afc6b9f02562", + "metadata": {}, + "outputs": [], + "source": [ + "import sys\n", + "import warnings\n", + "import metatensor\n", + "from itertools import product\n", + "from ase.io import read\n", + "\n", + "import numpy as np\n", + "from metatensor import (\n", + " Labels,\n", + " TensorBlock,\n", + " TensorMap,\n", + ")\n", + "\n", + "from scipy.spatial.transform import Rotation as R\n", + "from tqdm.auto import tqdm\n", + "from skmatter.preprocessing import StandardFlexibleScaler\n", + "\n", + "from anisoap.representations.radial_basis import (\n", + " GTORadialBasis,\n", + " MonomialBasis,\n", + ")\n", + "from anisoap.representations.ellipsoidal_density_projection import (\n", + " EllipsoidalDensityProjection,\n", + ")\n", + "\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "34f7cffd-2d19-455c-aaf7-9ed6f4ce62b4", + "metadata": {}, + "outputs": [], + "source": [ + "ell_frames = read(\"ellipsoids.xyz\", \"0:2\")\n", + "ell_frames_translation = read(\"ellipsoids.xyz\", \"0:2\")\n", + "ell_frames_rotation = read(\"ellipsoids.xyz\", \"0:2\")\n", + "\n", + "# This is to make sure the ell_frames list calls c_diameter[] rather than c_diameter and to update the diameters of ellipsoids to be 3,3, and 1.\n", + "\n", + "\n", + "def update_diameters_and_variablename(frames):\n", + " for frame in frames:\n", + " for i in range(1, 4):\n", + " old = f\"c_diameter{i}\"\n", + " new = f\"c_diameter[{i}]\"\n", + " if old in frame.arrays:\n", + " frame.arrays[new] = frame.arrays[old]\n", + " frame.arrays[new] = np.ones(len(frame)) * (3.0 if i < 3 else 1.0)\n", + "\n", + "\n", + "update_diameters_and_variablename(ell_frames)\n", + "update_diameters_and_variablename(ell_frames_translation)\n", + "update_diameters_and_variablename(ell_frames_rotation)" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "c6d137d4-a26b-42fb-b620-26d2c3ba482f", + "metadata": {}, + "outputs": [], + "source": [ + "# Translation vector is used to demonstrate the power spectrum of ellipsoidal representations are invariant of translation in positions.\n", + "\n", + "translation_vector = np.array([2.0, 2.0, 2.0])\n", + "for frame in ell_frames_translation:\n", + " frame.arrays[\"positions\"] += translation_vector" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "1b433389-6910-4b18-b4e4-ed56bd4b584a", + "metadata": {}, + "outputs": [], + "source": [ + "lmax = 5\n", + "nmax = 3\n", + "\n", + "AniSOAP_HYPERS = {\n", + " \"max_angular\": lmax,\n", + " \"max_radial\": nmax,\n", + " \"radial_basis_name\": \"gto\",\n", + " \"rotation_type\": \"quaternion\",\n", + " \"rotation_key\": \"c_q\",\n", + " \"cutoff_radius\": 7.0,\n", + " \"radial_gaussian_width\": 1.5,\n", + " \"basis_rcond\": 1e-8,\n", + " \"basis_tol\": 1e-4,\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "7ca6c85f-571d-4abe-97a0-2c6dda70c1de", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/PrettyBoy/Desktop/AniSOAP/AniSOAP/anisoap/representations/ellipsoidal_density_projection.py:547: UserWarning: In quaternion mode, quaternions are assumed to be in (w,x,y,z) format.\n", + " warnings.warn(\n" + ] + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "ecef6d3abc694e16acbfcc7f12730a52", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "Computing neighborlist: 0%| | 0/2 [00:00 Date: Fri, 20 Sep 2024 10:18:45 +0900 Subject: [PATCH 15/22] linter --- anisoap/representations/ellipsoidal_density_projection.py | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/anisoap/representations/ellipsoidal_density_projection.py b/anisoap/representations/ellipsoidal_density_projection.py index fded18c..32daa2f 100644 --- a/anisoap/representations/ellipsoidal_density_projection.py +++ b/anisoap/representations/ellipsoidal_density_projection.py @@ -667,7 +667,6 @@ def transform(self, frames, show_progress=False, normalize=True, rust_moments=Tr return features def power_spectrum(self, ell_frames, AniSOAP_HYPERS=None, sum_over_samples=True): - """Function to compute the power spectrum of AniSOAP computes the power spectrum of AniSOAP with the inputs of AniSOAP hyperparameters @@ -732,7 +731,8 @@ def power_spectrum(self, ell_frames, AniSOAP_HYPERS=None, sum_over_samples=True) mvg_coeffs = calculator.transform(ell_frames, show_progress=True) mvg_nu1 = standardize_keys(mvg_coeffs) - # Combines the mvg_nu1 with itself using the Clebsch-Gordan coefficients. This combines the angular and radial components of the sample. + # Combines the mvg_nu1 with itself using the Clebsch-Gordan coefficients. + # This combines the angular and radial components of the sample. mvg_nu2 = cg_combine( mvg_nu1, mvg_nu1, @@ -741,11 +741,11 @@ def power_spectrum(self, ell_frames, AniSOAP_HYPERS=None, sum_over_samples=True) other_keys_match=["types_center"], ) - # If sum_over_samples = True, it returns simplified form of coefficients with fewer dimensions in the tensormap for subsequent visualization. If not, it returns raw numerical data of coefficients contained within a specific block of the mvg_nu2 tensor + # If sum_over_samples = True, it returns simplified form of coefficients with fewer dimensions in the tensormap for subsequent visualization. + # If not, it returns raw numerical data of coefficients contained within a specific block of the mvg_nu2 tensor if sum_over_samples: x_asoap_raw = metatensor.sum_over_samples(mvg_nu2, sample_names="center") x_asoap_raw = x_asoap_raw.block().values.squeeze() return x_asoap_raw else: mvg_nu2.block().values - From 53dacdc6afbbe0e3b919ffeee94d3fe5fda577ae Mon Sep 17 00:00:00 2001 From: SeonwooH <158118187+SeonwooH@users.noreply.github.com> Date: Fri, 20 Sep 2024 10:24:09 +0900 Subject: [PATCH 16/22] Update tests.yml removed python 3.8 rascaline requires python ver >=3.9 --- .github/workflows/tests.yml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml index 4c2b08d..bb5443a 100644 --- a/.github/workflows/tests.yml +++ b/.github/workflows/tests.yml @@ -11,7 +11,7 @@ jobs: runs-on: ubuntu-latest strategy: matrix: - python-version: ["3.8", "3.9", "3.10"] + python-version: ["3.9", "3.10"] steps: - uses: actions/checkout@v2 From 159a5f5edb1d42916d23bdca0320933dba608976 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=ED=99=A9=EC=84=A0=EC=9A=B0?= Date: Fri, 27 Sep 2024 16:13:21 +0900 Subject: [PATCH 17/22] few changes after feedback --- .../AvailableRadialBases.ipynb | 2 +- .../ellipsoidal_density_projection.py | 33 +- .../GTO Orthogonalization Demonstration.ipynb | 94 ++- notebooks/aniso_descriptor.ipynb | 190 +++--- notebooks/anisotropic_gaussian.ipynb | 289 +++++---- notebooks/anisotropic_representations.ipynb | 549 +++++++++++------- 6 files changed, 694 insertions(+), 463 deletions(-) diff --git a/anisoap/representations/AvailableRadialBases.ipynb b/anisoap/representations/AvailableRadialBases.ipynb index 37db375..1ef789a 100644 --- a/anisoap/representations/AvailableRadialBases.ipynb +++ b/anisoap/representations/AvailableRadialBases.ipynb @@ -70,7 +70,7 @@ " radial_gaussian_width=width,\n", " # radial_gaussian_shift = shift,\n", " tol=1e-1,\n", - " **shared_params\n", + " **shared_params,\n", ")\n", "shiftedgto.plot_basis()" ] diff --git a/anisoap/representations/ellipsoidal_density_projection.py b/anisoap/representations/ellipsoidal_density_projection.py index 32daa2f..0deec0b 100644 --- a/anisoap/representations/ellipsoidal_density_projection.py +++ b/anisoap/representations/ellipsoidal_density_projection.py @@ -666,7 +666,7 @@ def transform(self, frames, show_progress=False, normalize=True, rust_moments=Tr else: return features - def power_spectrum(self, ell_frames, AniSOAP_HYPERS=None, sum_over_samples=True): + def power_spectrum(self, ell_frames, sum_over_samples=True): """Function to compute the power spectrum of AniSOAP computes the power spectrum of AniSOAP with the inputs of AniSOAP hyperparameters @@ -678,29 +678,23 @@ def power_spectrum(self, ell_frames, AniSOAP_HYPERS=None, sum_over_samples=True) ---------- ell_frames: list - a list of ellipsoidal frames, where each frame contains attributes: - 'c_diameter[1]', 'c_diameter[2]', 'c_diameter[3]', 'c_q', 'positions', and 'numbers'. - It only accepts c_q for the angular attribute of each frame. - - AniSOAP_HYPERS : keyword arguments - A dictionary of hyperparameters for the power spectrum calculation, including 'max_angular' - 'max_radial', 'radial_basis_name', 'rotation_type', 'rotation_key', 'cutoff_radius', 'radial_gaussian_width', - 'basis_rcond', and 'basis_tol'. + A list of ellipsoidal frames, where each frame contains attributes: + 'c_diameter[1]', 'c_diameter[2]', 'c_diameter[3]', 'c_q', 'positions', and 'numbers'. + It only accepts c_q for the angular attribute of each frame. sum_over_sample: bool - A function that returns the sum of coefficients of the frames in the sample. + A function that returns the sum of coefficients of the frames in the sample. Returns ------- - x_asoap_raw, a power spectrum of AniSOAP descriptor that can be visualized using jupyter notebook. + x_asoap_raw when kwarg sum_over_samples=True or mvg_nu2 when sum_over_samples=False: + x_asoap_raw: A 2-dimensional np.array with shape (n_samples, n_features). This AniSOAP power spectrum aggregates (sums) over each sample. + mvg_nu2: a TensorMap of unaggregated power spectrum features. """ # Initialize the Clebsch Gordan calculator for the angular component. - mycg = ClebschGordanReal(AniSOAP_HYPERS["max_angular"]) - - # Initialize the ellipsoidal density projection calculator using the AniSOAP hyperparameters. - calculator = EllipsoidalDensityProjection(**AniSOAP_HYPERS) + mycg = ClebschGordanReal(self.max_angular) # Checks that the sample's first frame is not empty if ell_frames[0].arrays is None: @@ -727,8 +721,7 @@ def power_spectrum(self, ell_frames, AniSOAP_HYPERS=None, sum_over_samples=True) f"ell_frame should contain c_q rather than quaternion" ) - # Executes ellipsoidal density projection on the frames of sample using the calculator. - mvg_coeffs = calculator.transform(ell_frames, show_progress=True) + mvg_coeffs = self.transform(ell_frames, show_progress=True) mvg_nu1 = standardize_keys(mvg_coeffs) # Combines the mvg_nu1 with itself using the Clebsch-Gordan coefficients. @@ -741,11 +734,11 @@ def power_spectrum(self, ell_frames, AniSOAP_HYPERS=None, sum_over_samples=True) other_keys_match=["types_center"], ) - # If sum_over_samples = True, it returns simplified form of coefficients with fewer dimensions in the tensormap for subsequent visualization. - # If not, it returns raw numerical data of coefficients contained within a specific block of the mvg_nu2 tensor + # If sum_over_samples = True, it returns simplified form of coefficients with fewer dimensions in the TensorMap for subsequent visualization. + # If not, it returns raw numerical data of coefficients in mvg_nu2 TensorMap if sum_over_samples: x_asoap_raw = metatensor.sum_over_samples(mvg_nu2, sample_names="center") x_asoap_raw = x_asoap_raw.block().values.squeeze() return x_asoap_raw else: - mvg_nu2.block().values + return mvg_nu2 diff --git a/notebooks/GTO Orthogonalization Demonstration.ipynb b/notebooks/GTO Orthogonalization Demonstration.ipynb index dcd1903..e705090 100644 --- a/notebooks/GTO Orthogonalization Demonstration.ipynb +++ b/notebooks/GTO Orthogonalization Demonstration.ipynb @@ -52,24 +52,30 @@ "\n", "# Visualize a set of 3 normalized GTOs, with random widths and orders\n", "\n", + "\n", "def gto_norm(r, n, sigma_n):\n", - " I_n = 0.5 * sigma_n**(2 * n + 3) * gamma(n + 1.5)\n", - " N_n = 1/np.sqrt(I_n)\n", - " return N_n * r**n * np.exp(-r**2 / (2 * sigma_n**2))\n", + " I_n = 0.5 * sigma_n ** (2 * n + 3) * gamma(n + 1.5)\n", + " N_n = 1 / np.sqrt(I_n)\n", + " return N_n * r**n * np.exp(-(r**2) / (2 * sigma_n**2))\n", + "\n", "\n", "sigma_n_arr = np.array([1, 0.8, 0.5])\n", "n_arr = np.array([1, 6, 4])\n", "\n", - "r_grid = np.linspace(0,10,1000)\n", + "r_grid = np.linspace(0, 10, 1000)\n", "\n", "for i in range(3):\n", " sigma_n = sigma_n_arr[i]\n", " n = n_arr[i]\n", " plt.plot(r_grid, gto_norm(r_grid, n, sigma_n))\n", "\n", - "plt.legend([f\"n = {n_arr[0]}, sigma_n = {sigma_n_arr[0]}\",\n", - " f\"n = {n_arr[1]}, sigma_n = {sigma_n_arr[1]}\",\n", - " f\"n = {n_arr[2]}, sigma_n = {sigma_n_arr[2]}\"])\n", + "plt.legend(\n", + " [\n", + " f\"n = {n_arr[0]}, sigma_n = {sigma_n_arr[0]}\",\n", + " f\"n = {n_arr[1]}, sigma_n = {sigma_n_arr[1]}\",\n", + " f\"n = {n_arr[2]}, sigma_n = {sigma_n_arr[2]}\",\n", + " ]\n", + ")\n", "\n", "plt.show()" ] @@ -101,12 +107,14 @@ "source": [ "import scipy.integrate as integrate\n", "\n", - "# Note that the integral of a product of the same GTOs (i.e. overlap of same GTOs) have square norm of 1 \n", + "# Note that the integral of a product of the same GTOs (i.e. overlap of same GTOs) have square norm of 1\n", "# (i.e. the normalization factor is correct)\n", "n1 = n2 = n_arr[0]\n", "sigma_n1 = sigma_n2 = sigma_n_arr[0]\n", "\n", - "result_identical = np.trapz(gto_norm(r_grid, n1, sigma_n1) * gto_norm(r_grid, n2, sigma_n2) * r_grid**2, r_grid)\n", + "result_identical = np.trapz(\n", + " gto_norm(r_grid, n1, sigma_n1) * gto_norm(r_grid, n2, sigma_n2) * r_grid**2, r_grid\n", + ")\n", "print(\"overlap of identical GTOs\", result_identical)\n", "\n", "# But are not yet orthoganol: Here, we are looking at the overlap of two GTOs\n", @@ -116,9 +124,10 @@ "sigma_n1 = sigma_n_arr[0]\n", "sigma_n2 = sigma_n_arr[1]\n", "\n", - "result_nonidentical = np.trapz(gto_norm(r_grid, n1, sigma_n1) * gto_norm(r_grid, n2, sigma_n2) * r_grid**2, r_grid)\n", - "print(\"overlap of nonidentical GTOs\", result_nonidentical)\n", - "\n" + "result_nonidentical = np.trapz(\n", + " gto_norm(r_grid, n1, sigma_n1) * gto_norm(r_grid, n2, sigma_n2) * r_grid**2, r_grid\n", + ")\n", + "print(\"overlap of nonidentical GTOs\", result_nonidentical)" ] }, { @@ -147,7 +156,8 @@ "outputs": [], "source": [ "def gto(r, n, sigma_n):\n", - " return r**n * np.exp(-r**2 / (2 * sigma_n**2))\n", + " return r**n * np.exp(-(r**2) / (2 * sigma_n**2))\n", + "\n", "\n", "def inverse_matrix_sqrt(matrix: np.array):\n", " \"\"\"\n", @@ -167,8 +177,10 @@ " eva, eve = np.linalg.eigh(matrix)\n", "\n", " if (eva < 0).all():\n", - " raise ValueError(\"Matrix is not positive semidefinite. Check that a valid gram matrix is passed.\")\n", - " return eve @ np.diag(1/np.sqrt(eva)) @ eve.T\n", + " raise ValueError(\n", + " \"Matrix is not positive semidefinite. Check that a valid gram matrix is passed.\"\n", + " )\n", + " return eve @ np.diag(1 / np.sqrt(eva)) @ eve.T\n", "\n", "\n", "def gto_square_norm(n, sigma):\n", @@ -184,7 +196,7 @@ " Returns:\n", " square norm: The square norm of the GTO\n", " \"\"\"\n", - " return 0.5 * sigma**(2 * n + 3) * gamma(n + 1.5)\n", + " return 0.5 * sigma ** (2 * n + 3) * gamma(n + 1.5)\n", "\n", "\n", "def gto_prefactor(n, sigma):\n", @@ -254,20 +266,30 @@ } ], "source": [ - "overlap_matrix = gto_overlap(n_arr[:, np.newaxis],\n", - " n_arr[np.newaxis, :],\n", - " sigma_n_arr[:, np.newaxis],\n", - " sigma_n_arr[np.newaxis, :])\n", + "overlap_matrix = gto_overlap(\n", + " n_arr[:, np.newaxis],\n", + " n_arr[np.newaxis, :],\n", + " sigma_n_arr[:, np.newaxis],\n", + " sigma_n_arr[np.newaxis, :],\n", + ")\n", "orthonormalization_matrix = inverse_matrix_sqrt(overlap_matrix)\n", "\n", "# The original nonorthonormalized basis set is (these aren't normalized either!):\n", - "original_gto = np.array([gto(r_grid, n_arr[0], sigma_n_arr[0]),\n", - " gto(r_grid, n_arr[1], sigma_n_arr[1]),\n", - " gto(r_grid, n_arr[2], sigma_n_arr[2])])\n", + "original_gto = np.array(\n", + " [\n", + " gto(r_grid, n_arr[0], sigma_n_arr[0]),\n", + " gto(r_grid, n_arr[1], sigma_n_arr[1]),\n", + " gto(r_grid, n_arr[2], sigma_n_arr[2]),\n", + " ]\n", + ")\n", "plt.plot(r_grid, original_gto.T)\n", - "plt.legend([f\"n = {n_arr[0]}, sigma_n = {sigma_n_arr[0]}\",\n", - " f\"n = {n_arr[1]}, sigma_n = {sigma_n_arr[1]}\",\n", - " f\"n = {n_arr[2]}, sigma_n = {sigma_n_arr[2]}\"])\n", + "plt.legend(\n", + " [\n", + " f\"n = {n_arr[0]}, sigma_n = {sigma_n_arr[0]}\",\n", + " f\"n = {n_arr[1]}, sigma_n = {sigma_n_arr[1]}\",\n", + " f\"n = {n_arr[2]}, sigma_n = {sigma_n_arr[2]}\",\n", + " ]\n", + ")\n", "\n", "plt.show()\n", "\n", @@ -275,9 +297,13 @@ "orthonormal_gto = orthonormalization_matrix @ original_gto\n", "\n", "plt.plot(r_grid, orthonormal_gto.T)\n", - "plt.legend([f\"n = {n_arr[0]}, sigma_n = {sigma_n_arr[0]}\",\n", - " f\"n = {n_arr[1]}, sigma_n = {sigma_n_arr[1]}\",\n", - " f\"n = {n_arr[2]}, sigma_n = {sigma_n_arr[2]}\"])\n", + "plt.legend(\n", + " [\n", + " f\"n = {n_arr[0]}, sigma_n = {sigma_n_arr[0]}\",\n", + " f\"n = {n_arr[1]}, sigma_n = {sigma_n_arr[1]}\",\n", + " f\"n = {n_arr[2]}, sigma_n = {sigma_n_arr[2]}\",\n", + " ]\n", + ")\n", "plt.show()" ] }, @@ -309,13 +335,17 @@ "\n", "# Two identical functions have a overlap of 1:\n", "\n", - "result_identical = np.trapz(orthonormal_gto[0, :] * orthonormal_gto[0, :] * r_grid**2, r_grid)\n", + "result_identical = np.trapz(\n", + " orthonormal_gto[0, :] * orthonormal_gto[0, :] * r_grid**2, r_grid\n", + ")\n", "print(\"overlap of identical orthonormalized GTOs\", result_identical)\n", "\n", "# Nonidentical functions have an overlap of 0:\n", "\n", - "result_nonidentical = np.trapz(orthonormal_gto[0, :] * orthonormal_gto[1, :] * r_grid**2, r_grid)\n", - "print(\"overlap of nonidentical orthonormalized GTOs\", result_nonidentical)\n" + "result_nonidentical = np.trapz(\n", + " orthonormal_gto[0, :] * orthonormal_gto[1, :] * r_grid**2, r_grid\n", + ")\n", + "print(\"overlap of nonidentical orthonormalized GTOs\", result_nonidentical)" ] }, { diff --git a/notebooks/aniso_descriptor.ipynb b/notebooks/aniso_descriptor.ipynb index b710d6c..5b956dc 100644 --- a/notebooks/aniso_descriptor.ipynb +++ b/notebooks/aniso_descriptor.ipynb @@ -10,13 +10,13 @@ "import numpy as np\n", "import metatensor\n", "from ase.io import read\n", - "from metatensor import TensorBlock, TensorMap,Labels\n", + "from metatensor import TensorBlock, TensorMap, Labels\n", "from itertools import product\n", "import ase\n", "\n", "from rascaline import NeighborList\n", "\n", - "# from anisotropic_gaussian_moments_expansion import * " + "# from anisotropic_gaussian_moments_expansion import *" ] }, { @@ -41,70 +41,90 @@ " Contains the position vector for the center of the trivariate Gaussian.\n", " - maxdeg: int\n", " Maximum degree for which the moments need to be computed.\n", - " \n", + "\n", " Returns:\n", " - The list of moments defined as\n", " = integral (x^n0 * y^n1 * z^n2) * exp(-0.5*(r-a).T@cov@(r-a)) dxdydz\n", " Note that the term \"moments\" in probability theory are defined for normalized Gaussian distributions.\n", - " Here, we take the Gaussian \n", + " Here, we take the Gaussian\n", " \"\"\"\n", " # Make sure that the provided arrays have the correct dimensions and properties\n", - " assert A.shape == (3,3), \"Dilation matrix needs to be 3x3\"\n", - " assert np.sum((A-A.T)**2) < 1e-14, \"Dilation matrix needs to be symmetric\"\n", - " assert a.shape == (3,1), \"Center of Gaussian has to be given by a 3-dim. vector\"\n", + " assert A.shape == (3, 3), \"Dilation matrix needs to be 3x3\"\n", + " assert np.sum((A - A.T) ** 2) < 1e-14, \"Dilation matrix needs to be symmetric\"\n", + " assert a.shape == (3, 1), \"Center of Gaussian has to be given by a 3-dim. vector\"\n", " assert maxdeg > 0, \"The maximum degree needs to be at least 1\"\n", - " cov = np.linalg.inv(A) # the covariance matrix is the inverse of the matrix A\n", - " global_factor = (2*np.pi)**1.5 / np.sqrt(np.linalg.det(A)) # normalization of Gaussian\n", - " \n", + " cov = np.linalg.inv(A) # the covariance matrix is the inverse of the matrix A\n", + " global_factor = (2 * np.pi) ** 1.5 / np.sqrt(\n", + " np.linalg.det(A)\n", + " ) # normalization of Gaussian\n", + "\n", " # Initialize the array in which to store the moments\n", " # moments[n0, n1, n2] will be set to \n", " # This representation is memory inefficient, since only about 1/3 of the\n", " # array elements will actually be relevant.\n", " # The advantage, however, is the simplicity in later use.\n", - " moments = np.zeros((maxdeg+1, maxdeg+1, maxdeg+1))\n", - " \n", + " moments = np.zeros((maxdeg + 1, maxdeg + 1, maxdeg + 1))\n", + "\n", " # Initialize the first few elements\n", - " moments[0,0,0] = 1.\n", - " moments[1,0,0] = a[0] # \n", - " moments[0,1,0] = a[1] # \n", - " moments[0,0,1] = a[2] # \n", + " moments[0, 0, 0] = 1.0\n", + " moments[1, 0, 0] = a[0] # \n", + " moments[0, 1, 0] = a[1] # \n", + " moments[0, 0, 1] = a[2] # \n", " if maxdeg == 1:\n", " return global_factor * moments\n", - " \n", + "\n", " # Initialize the quadratic elements\n", - " moments[2,0,0] = cov[0,0] + a[0]**2\n", - " moments[0,2,0] = cov[1,1] + a[1]**2\n", - " moments[0,0,2] = cov[2,2] + a[2]**2\n", - " moments[1,1,0] = cov[0,1] + a[0]*a[1]\n", - " moments[0,1,1] = cov[1,2] + a[1]*a[2]\n", - " moments[1,0,1] = cov[2,0] + a[2]*a[0]\n", + " moments[2, 0, 0] = cov[0, 0] + a[0] ** 2\n", + " moments[0, 2, 0] = cov[1, 1] + a[1] ** 2\n", + " moments[0, 0, 2] = cov[2, 2] + a[2] ** 2\n", + " moments[1, 1, 0] = cov[0, 1] + a[0] * a[1]\n", + " moments[0, 1, 1] = cov[1, 2] + a[1] * a[2]\n", + " moments[1, 0, 1] = cov[2, 0] + a[2] * a[0]\n", " if maxdeg == 2:\n", " return global_factor * moments\n", - " \n", + "\n", " # Iterate over all possible exponents to generate all moments\n", " # Instead of iterating over n1, n2 and n3, we iterate over the total degree of the monomials\n", " # which will allow us to simplify certain edge cases.\n", " for deg in range(2, maxdeg):\n", - " for n0 in range(deg+1):\n", - " for n1 in range(deg+1-n0):\n", + " for n0 in range(deg + 1):\n", + " for n1 in range(deg + 1 - n0):\n", " # We consider monomials of degree \"deg\", and generate moments of degree deg+1.\n", " n2 = deg - n0 - n1\n", - " \n", + "\n", " # Run the x-iteration\n", - " moments[n0+1,n1,n2] = a[0]*moments[n0,n1,n2] + cov[0,0]*n0*moments[n0-1,n1,n2]\n", - " moments[n0+1,n1,n2] += cov[0,1]*n1*moments[n0,n1-1,n2] + cov[0,2]*n2*moments[n0,n1,n2-1]\n", - " \n", + " moments[n0 + 1, n1, n2] = (\n", + " a[0] * moments[n0, n1, n2]\n", + " + cov[0, 0] * n0 * moments[n0 - 1, n1, n2]\n", + " )\n", + " moments[n0 + 1, n1, n2] += (\n", + " cov[0, 1] * n1 * moments[n0, n1 - 1, n2]\n", + " + cov[0, 2] * n2 * moments[n0, n1, n2 - 1]\n", + " )\n", + "\n", " # If n0 is equal to zero, we also need the y- and z-iterations\n", " if n0 == 0:\n", " # Run the y-iteration\n", - " moments[n0,n1+1,n2] = a[1]*moments[n0,n1,n2] + cov[1,0]*n0*moments[n0-1,n1,n2]\n", - " moments[n0,n1+1,n2] += cov[1,1]*n1*moments[n0,n1-1,n2] + cov[1,2]*n2*moments[n0,n1,n2-1]\n", - " \n", + " moments[n0, n1 + 1, n2] = (\n", + " a[1] * moments[n0, n1, n2]\n", + " + cov[1, 0] * n0 * moments[n0 - 1, n1, n2]\n", + " )\n", + " moments[n0, n1 + 1, n2] += (\n", + " cov[1, 1] * n1 * moments[n0, n1 - 1, n2]\n", + " + cov[1, 2] * n2 * moments[n0, n1, n2 - 1]\n", + " )\n", + "\n", " if n0 == 0 and n1 == 0:\n", " # Run the z-iteration\n", - " moments[n0,n1,n2+1] = a[2]*moments[n0,n1,n2] + cov[2,0]*n0*moments[n0-1,n1,n2]\n", - " moments[n0,n1,n2+1] += cov[2,1]*n1*moments[n0,n1-1,n2] + cov[2,2]*n2*moments[n0,n1,n2-1]\n", - " \n", + " moments[n0, n1, n2 + 1] = (\n", + " a[2] * moments[n0, n1, n2]\n", + " + cov[2, 0] * n0 * moments[n0 - 1, n1, n2]\n", + " )\n", + " moments[n0, n1, n2 + 1] += (\n", + " cov[2, 1] * n1 * moments[n0, n1 - 1, n2]\n", + " + cov[2, 2] * n2 * moments[n0, n1, n2 - 1]\n", + " )\n", + "\n", " return global_factor * moments" ] }, @@ -116,9 +136,9 @@ "outputs": [], "source": [ "hypers = {\n", - " \"interaction_cutoff\": 4.5, # need to define the neighborlist \n", - " \"A\": np.eye(3),#anisotropy/dilation matrix\n", - " \"maxdeg\":5 # max degree of expansion \n", + " \"interaction_cutoff\": 4.5, # need to define the neighborlist\n", + " \"A\": np.eye(3), # anisotropy/dilation matrix\n", + " \"maxdeg\": 5, # max degree of expansion\n", "}" ] }, @@ -129,9 +149,12 @@ "metadata": {}, "outputs": [], "source": [ - "frames = read('/Users/jigyasa/scratch/data_papers/data/water/dataset/water_randomized_1000.xyz', ':2')\n", - "for f in frames: \n", - " f.pbc=False\n", + "frames = read(\n", + " \"/Users/jigyasa/scratch/data_papers/data/water/dataset/water_randomized_1000.xyz\",\n", + " \":2\",\n", + ")\n", + "for f in frames:\n", + " f.pbc = False\n", "# f.pbc=True\n", "# f.cell = [5,5,5]\n", "# f.center()\n", @@ -145,12 +168,12 @@ "metadata": {}, "outputs": [], "source": [ - "#use rascaline to get the full neighborlist \n", + "# use rascaline to get the full neighborlist\n", "nl = NeighborList(hypers[\"interaction_cutoff\"], True).compute(frames)\n", "\n", - "#nl is a tensormap with keys ('species_first_atom', 'species_second_atom')\n", - "#depending on the cutoff some species pairs may not appear \n", - "#self pairs are not present but in PBC pairs between copies of the same atom are accounted for\n", + "# nl is a tensormap with keys ('species_first_atom', 'species_second_atom')\n", + "# depending on the cutoff some species pairs may not appear\n", + "# self pairs are not present but in PBC pairs between copies of the same atom are accounted for\n", "\n", "# nl.keys_to_properties('species_second_atom')" ] @@ -162,8 +185,8 @@ "metadata": {}, "outputs": [], "source": [ - "sigma =0.3\n", - "A = hypers[\"A\"]*sigma**2\n", + "sigma = 0.3\n", + "A = hypers[\"A\"] * sigma**2\n", "maxdeg = hypers[\"maxdeg\"]" ] }, @@ -185,7 +208,7 @@ } ], "source": [ - "sample_value.reshape((sample_value.shape)+(1,)).shape" + "sample_value.reshape((sample_value.shape) + (1,)).shape" ] }, { @@ -195,30 +218,40 @@ "metadata": {}, "outputs": [], "source": [ - "#accumulate the blocks for the pairwise expansion - \n", - "desc_blocks=[]\n", + "# accumulate the blocks for the pairwise expansion -\n", + "desc_blocks = []\n", "for center_species in global_species:\n", " for neighbor_species in global_species:\n", " if (center_species, neighbor_species) in nl.keys:\n", - " nl_block = nl.block(species_first_atom=center_species, species_second_atom=neighbor_species)\n", + " nl_block = nl.block(\n", + " species_first_atom=center_species, species_second_atom=neighbor_species\n", + " )\n", " desc_block_values = []\n", " for isample, nl_sample in enumerate(nl_block.samples):\n", - " x,y,z = nl_block.values[isample,0], nl_block.values[isample,1],nl_block.values[isample,2]\n", - " sample_value=compute_moments_inefficient_implementation(A, np.array([x,y,z]), maxdeg) #moments for the pair\n", - " #this is a (maxdeg+1, maxdeg+1, maxdeg+1) matrix\n", - " desc_block_values.append(sample_value.reshape((sample_value.shape)+(1,)))\n", - " \n", + " x, y, z = (\n", + " nl_block.values[isample, 0],\n", + " nl_block.values[isample, 1],\n", + " nl_block.values[isample, 2],\n", + " )\n", + " sample_value = compute_moments_inefficient_implementation(\n", + " A, np.array([x, y, z]), maxdeg\n", + " ) # moments for the pair\n", + " # this is a (maxdeg+1, maxdeg+1, maxdeg+1) matrix\n", + " desc_block_values.append(\n", + " sample_value.reshape((sample_value.shape) + (1,))\n", + " )\n", + "\n", "# print(sample_value.shape)\n", "# desc_blocks.append(TensorBlock(values = np.asarray(desc_block_values),\n", "# samples = nl_block.samples,\n", "# components = [Labels(),Labels(),Labels()]\n", "# properties = [Labels([\"dummy\"], [\"0\"])]\n", - " \n", - " \n", + "\n", + "\n", "# )\n", - " \n", + "\n", "# )\n", - "# pair_aniso_desc = TensorMap(nl.keys, desc_blocks)\n" + "# pair_aniso_desc = TensorMap(nl.keys, desc_blocks)" ] }, { @@ -240,30 +273,45 @@ } ], "source": [ - "# To get the final descriptor, we just need to sum over the neighbor species \n", + "# To get the final descriptor, we just need to sum over the neighbor species\n", "\n", "desc_blocks = []\n", "for center_species in global_species:\n", " for neighbor_species in global_species:\n", " if (center_species, neighbor_species) in pair_aniso_desc.keys:\n", - " desc_samples=[]\n", - " pair_block = pair_aniso_desc.block(species_first_atom=center_species, species_second_atom=neighbor_species)\n", + " desc_samples = []\n", + " pair_block = pair_aniso_desc.block(\n", + " species_first_atom=center_species, species_second_atom=neighbor_species\n", + " )\n", " desc_block_values = []\n", - " desc_samples = list(product(np.unique(block.samples['structure']), np.unique(block.samples['center'])))\n", + " desc_samples = list(\n", + " product(\n", + " np.unique(block.samples[\"structure\"]),\n", + " np.unique(block.samples[\"center\"]),\n", + " )\n", + " )\n", " for isample, sample in enumerate(desc_samples):\n", - " sample_idx = [idx for idx, tup in enumerate(nl_block.samples) if tup['structure']==sample[0] and tup['center']==sample[1]]\n", - " \n", - " sample_value+= desc_block_values.append(nl_block.values[sample_idx].sum(axis=0))\n", + " sample_idx = [\n", + " idx\n", + " for idx, tup in enumerate(nl_block.samples)\n", + " if tup[\"structure\"] == sample[0] and tup[\"center\"] == sample[1]\n", + " ]\n", + "\n", + " sample_value += desc_block_values.append(\n", + " nl_block.values[sample_idx].sum(axis=0)\n", + " )\n", " desc_block_values.append(sample_value)\n", "# desc_blocks.append(TensorBlock(values = np.asarray(desc_block_values),\n", "# samples = Labels([\"structure\", \"central_atom\"], desc_samples),\n", "# components = [Labels()]\n", "# properties = [Labels()]\n", - " \n", - " \n", + "\n", + "\n", "# )\n", "\n", - "aniso_desc = TensorMap(Labels(\"center_species\", np.asarray(global_species, dtype=int32)), desc_blocks)" + "aniso_desc = TensorMap(\n", + " Labels(\"center_species\", np.asarray(global_species, dtype=int32)), desc_blocks\n", + ")" ] }, { diff --git a/notebooks/anisotropic_gaussian.ipynb b/notebooks/anisotropic_gaussian.ipynb index 0d9028b..e16a3de 100644 --- a/notebooks/anisotropic_gaussian.ipynb +++ b/notebooks/anisotropic_gaussian.ipynb @@ -36,70 +36,90 @@ " Contains the position vector for the center of the trivariate Gaussian.\n", " - maxdeg: int\n", " Maximum degree for which the moments need to be computed.\n", - " \n", + "\n", " Returns:\n", " - The list of moments defined as\n", " = integral (x^n0 * y^n1 * z^n2) * exp(-0.5*(r-a).T@cov@(r-a)) dxdydz\n", " Note that the term \"moments\" in probability theory are defined for normalized Gaussian distributions.\n", - " Here, we take the Gaussian \n", + " Here, we take the Gaussian\n", " \"\"\"\n", " # Make sure that the provided arrays have the correct dimensions and properties\n", - " assert A.shape == (3,3), \"Dilation matrix needs to be 3x3\"\n", - " assert np.sum((A-A.T)**2) < 1e-14, \"Dilation matrix needs to be symmetric\"\n", + " assert A.shape == (3, 3), \"Dilation matrix needs to be 3x3\"\n", + " assert np.sum((A - A.T) ** 2) < 1e-14, \"Dilation matrix needs to be symmetric\"\n", " assert a.shape == (3,), \"Center of Gaussian has to be given by a 3-dim. vector\"\n", " assert maxdeg > 0, \"The maximum degree needs to be at least 1\"\n", - " cov = np.linalg.inv(A) # the covariance matrix is the inverse of the matrix A\n", - " global_factor = (2*np.pi)**1.5 / np.sqrt(np.linalg.det(A)) # normalization of Gaussian\n", - " \n", + " cov = np.linalg.inv(A) # the covariance matrix is the inverse of the matrix A\n", + " global_factor = (2 * np.pi) ** 1.5 / np.sqrt(\n", + " np.linalg.det(A)\n", + " ) # normalization of Gaussian\n", + "\n", " # Initialize the array in which to store the moments\n", " # moments[n0, n1, n2] will be set to \n", " # This representation is memory inefficient, since only about 1/3 of the\n", " # array elements will actually be relevant.\n", " # The advantage, however, is the simplicity in later use.\n", - " moments = np.zeros((maxdeg+1, maxdeg+1, maxdeg+1))\n", - " \n", + " moments = np.zeros((maxdeg + 1, maxdeg + 1, maxdeg + 1))\n", + "\n", " # Initialize the first few elements\n", - " moments[0,0,0] = 1.\n", - " moments[1,0,0] = a[0] # \n", - " moments[0,1,0] = a[1] # \n", - " moments[0,0,1] = a[2] # \n", + " moments[0, 0, 0] = 1.0\n", + " moments[1, 0, 0] = a[0] # \n", + " moments[0, 1, 0] = a[1] # \n", + " moments[0, 0, 1] = a[2] # \n", " if maxdeg == 1:\n", " return global_factor * moments\n", - " \n", + "\n", " # Initialize the quadratic elements\n", - " moments[2,0,0] = cov[0,0] + a[0]**2\n", - " moments[0,2,0] = cov[1,1] + a[1]**2\n", - " moments[0,0,2] = cov[2,2] + a[2]**2\n", - " moments[1,1,0] = cov[0,1] + a[0]*a[1]\n", - " moments[0,1,1] = cov[1,2] + a[1]*a[2]\n", - " moments[1,0,1] = cov[2,0] + a[2]*a[0]\n", + " moments[2, 0, 0] = cov[0, 0] + a[0] ** 2\n", + " moments[0, 2, 0] = cov[1, 1] + a[1] ** 2\n", + " moments[0, 0, 2] = cov[2, 2] + a[2] ** 2\n", + " moments[1, 1, 0] = cov[0, 1] + a[0] * a[1]\n", + " moments[0, 1, 1] = cov[1, 2] + a[1] * a[2]\n", + " moments[1, 0, 1] = cov[2, 0] + a[2] * a[0]\n", " if maxdeg == 2:\n", " return global_factor * moments\n", - " \n", + "\n", " # Iterate over all possible exponents to generate all moments\n", " # Instead of iterating over n1, n2 and n3, we iterate over the total degree of the monomials\n", " # which will allow us to simplify certain edge cases.\n", " for deg in range(2, maxdeg):\n", - " for n0 in range(deg+1):\n", - " for n1 in range(deg+1-n0):\n", + " for n0 in range(deg + 1):\n", + " for n1 in range(deg + 1 - n0):\n", " # We consider monomials of degree \"deg\", and generate moments of degree deg+1.\n", " n2 = deg - n0 - n1\n", - " \n", + "\n", " # Run the x-iteration\n", - " moments[n0+1,n1,n2] = a[0]*moments[n0,n1,n2] + cov[0,0]*n0*moments[n0-1,n1,n2]\n", - " moments[n0+1,n1,n2] += cov[0,1]*n1*moments[n0,n1-1,n2] + cov[0,2]*n2*moments[n0,n1,n2-1]\n", - " \n", + " moments[n0 + 1, n1, n2] = (\n", + " a[0] * moments[n0, n1, n2]\n", + " + cov[0, 0] * n0 * moments[n0 - 1, n1, n2]\n", + " )\n", + " moments[n0 + 1, n1, n2] += (\n", + " cov[0, 1] * n1 * moments[n0, n1 - 1, n2]\n", + " + cov[0, 2] * n2 * moments[n0, n1, n2 - 1]\n", + " )\n", + "\n", " # If n0 is equal to zero, we also need the y- and z-iterations\n", " if n0 == 0:\n", " # Run the y-iteration\n", - " moments[n0,n1+1,n2] = a[1]*moments[n0,n1,n2] + cov[1,0]*n0*moments[n0-1,n1,n2]\n", - " moments[n0,n1+1,n2] += cov[1,1]*n1*moments[n0,n1-1,n2] + cov[1,2]*n2*moments[n0,n1,n2-1]\n", - " \n", + " moments[n0, n1 + 1, n2] = (\n", + " a[1] * moments[n0, n1, n2]\n", + " + cov[1, 0] * n0 * moments[n0 - 1, n1, n2]\n", + " )\n", + " moments[n0, n1 + 1, n2] += (\n", + " cov[1, 1] * n1 * moments[n0, n1 - 1, n2]\n", + " + cov[1, 2] * n2 * moments[n0, n1, n2 - 1]\n", + " )\n", + "\n", " if n0 == 0 and n1 == 0:\n", " # Run the z-iteration\n", - " moments[n0,n1,n2+1] = a[2]*moments[n0,n1,n2] + cov[2,0]*n0*moments[n0-1,n1,n2]\n", - " moments[n0,n1,n2+1] += cov[2,1]*n1*moments[n0,n1-1,n2] + cov[2,2]*n2*moments[n0,n1,n2-1]\n", - " \n", + " moments[n0, n1, n2 + 1] = (\n", + " a[2] * moments[n0, n1, n2]\n", + " + cov[2, 0] * n0 * moments[n0 - 1, n1, n2]\n", + " )\n", + " moments[n0, n1, n2 + 1] += (\n", + " cov[2, 1] * n1 * moments[n0, n1 - 1, n2]\n", + " + cov[2, 2] * n2 * moments[n0, n1, n2 - 1]\n", + " )\n", + "\n", " return global_factor * moments" ] }, @@ -133,23 +153,23 @@ " - a: center\n", " - maxdeg: int\n", " Maximum degree for which the moments need to be computed.\n", - " \n", + "\n", " Returns:\n", " - A numpy array of size (maxdeg+1, ) containing the moments defined as\n", " = integral x^n exp(-A(x-a)^2/2) dx\n", " \"\"\"\n", " assert maxdeg > 0\n", - " moments = np.zeros((maxdeg+1, ))\n", - " moments[0] = np.sqrt(2*np.pi/A)\n", + " moments = np.zeros((maxdeg + 1,))\n", + " moments[0] = np.sqrt(2 * np.pi / A)\n", " moments[1] = a * moments[0]\n", - " \n", + "\n", " # If maxdeg = 1, there is nothing more to do\n", " if maxdeg == 1:\n", " return moments\n", - " \n", + "\n", " for deg in range(1, maxdeg):\n", - " moments[deg+1] = a*moments[deg] + deg*moments[deg-1] / A\n", - " \n", + " moments[deg + 1] = a * moments[deg] + deg * moments[deg - 1] / A\n", + "\n", " return moments" ] }, @@ -163,7 +183,9 @@ "# Define function to compute all moments for a diagonal dilation matrix.\n", "# The implementation focuses on conceptual simplicity, while sacrifizing\n", "# memory efficiency.\n", - "def compute_moments_diagonal_inefficient_implementation(principcal_components, a, maxdeg):\n", + "def compute_moments_diagonal_inefficient_implementation(\n", + " principcal_components, a, maxdeg\n", + "):\n", " \"\"\"\n", " Parameters:\n", " - principal_components: np.ndarray of shape (3,)\n", @@ -172,34 +194,34 @@ " Contains the information about the center of the trivariate Gaussian.\n", " - maxdeg: int\n", " Maximum degree for which the moments need to be computed.\n", - " \n", + "\n", " Returns:\n", " - The list of moments defined as\n", " = integral (x^n0 * y^n1 * z^n2) * exp(-0.5*(r-a).T@cov@(r-a)) dxdydz\n", " Note that the term \"moments\" in probability theory are defined for normalized Gaussian distributions.\n", - " Here, we take the Gaussian \n", + " Here, we take the Gaussian\n", " \"\"\"\n", " # Initialize the array in which to store the moments\n", " # moments[n0, n1, n2] will be set to \n", " # This representation is very inefficient, since only about 1/6 of the\n", " # array elements will actually be relevant.\n", " # The advantage, however, is the simplicity in later use.\n", - " moments = np.zeros((maxdeg+1, maxdeg+1, maxdeg+1))\n", - " \n", + " moments = np.zeros((maxdeg + 1, maxdeg + 1, maxdeg + 1))\n", + "\n", " # Precompute the single variable moments in x- y- and z-directions:\n", " moments_x = compute_moments_single_variable(principal_components[0], a[0], maxdeg)\n", " moments_y = compute_moments_single_variable(principal_components[1], a[1], maxdeg)\n", " moments_z = compute_moments_single_variable(principal_components[2], a[2], maxdeg)\n", "\n", " # Compute values for all relevant components for which the monomial degree is <= maxdeg\n", - " for n0 in range(maxdeg+1):\n", - " for n1 in range(maxdeg+1):\n", - " for n2 in range(maxdeg+1):\n", + " for n0 in range(maxdeg + 1):\n", + " for n1 in range(maxdeg + 1):\n", + " for n2 in range(maxdeg + 1):\n", " # Make sure that the degree is not above the maximal degree\n", " deg = n0 + n1 + n2\n", " if deg > maxdeg:\n", " continue\n", - " \n", + "\n", " # If not, the moment is a product of the x- y- and z-integrals\n", " moments[n0, n1, n2] = moments_x[n0] * moments_y[n1] * moments_z[n2]\n", " return moments" @@ -229,9 +251,9 @@ "outputs": [], "source": [ "sigma = 0.32\n", - "a = 0.\n", + "a = 0.0\n", "maxdeg = 5\n", - "A = 1/sigma**2\n", + "A = 1 / sigma**2\n", "moments_single = compute_moments_single_variable(A, a, maxdeg)" ] }, @@ -242,12 +264,12 @@ "metadata": {}, "outputs": [], "source": [ - "exact_values = np.zeros((maxdeg+1,))\n", - "for deg in range(maxdeg+1):\n", + "exact_values = np.zeros((maxdeg + 1,))\n", + "for deg in range(maxdeg + 1):\n", " exact_value = 0\n", " if deg % 2 == 0:\n", " neff = (deg + 1) / 2\n", - " exact_value = (2 * sigma**2)**neff * gamma(neff)\n", + " exact_value = (2 * sigma**2) ** neff * gamma(neff)\n", " exact_values[deg] = exact_value" ] }, @@ -258,7 +280,7 @@ "metadata": {}, "outputs": [], "source": [ - "assert_allclose(exact_values, moments_single,atol=1e-15)" + "assert_allclose(exact_values, moments_single, atol=1e-15)" ] }, { @@ -277,7 +299,7 @@ "outputs": [], "source": [ "sigma = 0.23\n", - "A = 1/sigma**2\n", + "A = 1 / sigma**2\n", "a = 0.5\n", "maxdeg = 5\n", "moments_single = compute_moments_single_variable(A, a, maxdeg)" @@ -292,25 +314,25 @@ "source": [ "def test_non_centered_moments(A, a, maxdeg):\n", " # Compute the exact moments for the centered moments\n", - " centered_moments = np.zeros((maxdeg+1,))\n", - " for deg in range(maxdeg+1):\n", + " centered_moments = np.zeros((maxdeg + 1,))\n", + " for deg in range(maxdeg + 1):\n", " exact_value = 0\n", " if deg % 2 == 0:\n", " neff = (deg + 1) / 2\n", - " exact_value = (2 * sigma**2)**neff * gamma(neff)\n", + " exact_value = (2 * sigma**2) ** neff * gamma(neff)\n", " centered_moments[deg] = exact_value\n", - " \n", + "\n", " # Compute the moments from the binomial theorem\n", - " moments = np.zeros((maxdeg+1,))\n", - " for deg in range(maxdeg+1):\n", + " moments = np.zeros((maxdeg + 1,))\n", + " for deg in range(maxdeg + 1):\n", " moments[deg] += centered_moments[deg]\n", - " \n", + "\n", " # Get the correction from the centered moment\n", " for k in range(deg):\n", - " moments[deg] -= comb(deg, k) * (-a)**(deg-k) * moments[k]\n", - " \n", + " moments[deg] -= comb(deg, k) * (-a) ** (deg - k) * moments[k]\n", + "\n", " moments_from_code = compute_moments_single_variable(A, a, maxdeg)\n", - " \n", + "\n", " assert_allclose(moments_from_code, moments)" ] }, @@ -337,13 +359,15 @@ "metadata": {}, "outputs": [], "source": [ - "principal_components = np.array([2.8,0.4,1.1])\n", + "principal_components = np.array([2.8, 0.4, 1.1])\n", "A = np.diag(principal_components)\n", "a = np.array([3.1, -2.3, 5.92])\n", - "#a *= 0\n", + "# a *= 0\n", "maxdeg = 3\n", "moments_general = compute_moments_inefficient_implementation(A, a, maxdeg)\n", - "moments_diagonal = compute_moments_diagonal_inefficient_implementation(principal_components, a, maxdeg)" + "moments_diagonal = compute_moments_diagonal_inefficient_implementation(\n", + " principal_components, a, maxdeg\n", + ")" ] }, { @@ -354,39 +378,41 @@ "outputs": [], "source": [ "def get_exact_moments(A, a, maxdeg=3):\n", - " global_factor = (2*np.pi)**1.5 / np.sqrt(np.linalg.det(A))\n", - " assert maxdeg in [1,2,3]\n", - " \n", - " moments_exact = np.zeros((maxdeg+1, maxdeg+1, maxdeg+1))\n", - " moments_exact[0,0,0] = 1.\n", + " global_factor = (2 * np.pi) ** 1.5 / np.sqrt(np.linalg.det(A))\n", + " assert maxdeg in [1, 2, 3]\n", + "\n", + " moments_exact = np.zeros((maxdeg + 1, maxdeg + 1, maxdeg + 1))\n", + " moments_exact[0, 0, 0] = 1.0\n", " # Exact expressions for degree 1\n", - " moments_exact[1,0,0] = a[0]\n", - " moments_exact[0,1,0] = a[1]\n", - " moments_exact[0,0,1] = a[2]\n", + " moments_exact[1, 0, 0] = a[0]\n", + " moments_exact[0, 1, 0] = a[1]\n", + " moments_exact[0, 0, 1] = a[2]\n", " if maxdeg == 1:\n", " return global_factor * moments_exact\n", "\n", " # Exact expressions for degree 2\n", - " moments_exact[2,0,0] = cov[0,0] + a[0]**2\n", - " moments_exact[0,2,0] = cov[1,1] + a[1]**2\n", - " moments_exact[0,0,2] = cov[2,2] + a[2]**2\n", - " moments_exact[1,1,0] = a[0]*a[1]\n", - " moments_exact[0,1,1] = a[1]*a[2]\n", - " moments_exact[1,0,1] = a[0]*a[2]\n", + " moments_exact[2, 0, 0] = cov[0, 0] + a[0] ** 2\n", + " moments_exact[0, 2, 0] = cov[1, 1] + a[1] ** 2\n", + " moments_exact[0, 0, 2] = cov[2, 2] + a[2] ** 2\n", + " moments_exact[1, 1, 0] = a[0] * a[1]\n", + " moments_exact[0, 1, 1] = a[1] * a[2]\n", + " moments_exact[1, 0, 1] = a[0] * a[2]\n", " if maxdeg == 2:\n", " return global_factor * moments_exact\n", "\n", " # Exact expressions for degree 3\n", - " moments_exact[3,0,0] = 3*a[0]*cov[0,0] + a[0]**3\n", - " moments_exact[0,3,0] = 3*a[1]*cov[1,1] + a[1]**3\n", - " moments_exact[0,0,3] = 3*a[2]*cov[2,2] + a[2]**3\n", - " moments_exact[2,1,0] = a[1]*(cov[0,0] + a[0]**2) + 2*a[0]*cov[0,1]\n", - " moments_exact[2,0,1] = a[2]*(cov[0,0] + a[0]**2) + 2*a[0]*cov[0,2]\n", - " moments_exact[1,2,0] = a[0]*(cov[1,1] + a[1]**2) + 2*a[1]*cov[1,0]\n", - " moments_exact[0,2,1] = a[2]*(cov[1,1] + a[1]**2) + 2*a[1]*cov[1,2]\n", - " moments_exact[1,0,2] = a[0]*(cov[2,2] + a[2]**2) + 2*a[2]*cov[2,0]\n", - " moments_exact[0,1,2] = a[1]*(cov[2,2] + a[2]**2) + 2*a[2]*cov[2,1]\n", - " moments_exact[1,1,1] = a[0]*a[1]*a[2] + a[0]*cov[1,2] + a[1]*cov[0,2] + a[2]*cov[0,1]\n", + " moments_exact[3, 0, 0] = 3 * a[0] * cov[0, 0] + a[0] ** 3\n", + " moments_exact[0, 3, 0] = 3 * a[1] * cov[1, 1] + a[1] ** 3\n", + " moments_exact[0, 0, 3] = 3 * a[2] * cov[2, 2] + a[2] ** 3\n", + " moments_exact[2, 1, 0] = a[1] * (cov[0, 0] + a[0] ** 2) + 2 * a[0] * cov[0, 1]\n", + " moments_exact[2, 0, 1] = a[2] * (cov[0, 0] + a[0] ** 2) + 2 * a[0] * cov[0, 2]\n", + " moments_exact[1, 2, 0] = a[0] * (cov[1, 1] + a[1] ** 2) + 2 * a[1] * cov[1, 0]\n", + " moments_exact[0, 2, 1] = a[2] * (cov[1, 1] + a[1] ** 2) + 2 * a[1] * cov[1, 2]\n", + " moments_exact[1, 0, 2] = a[0] * (cov[2, 2] + a[2] ** 2) + 2 * a[2] * cov[2, 0]\n", + " moments_exact[0, 1, 2] = a[1] * (cov[2, 2] + a[2] ** 2) + 2 * a[2] * cov[2, 1]\n", + " moments_exact[1, 1, 1] = (\n", + " a[0] * a[1] * a[2] + a[0] * cov[1, 2] + a[1] * cov[0, 2] + a[2] * cov[0, 1]\n", + " )\n", " if maxdeg == 3:\n", " return global_factor * moments_exact" ] @@ -398,34 +424,36 @@ "metadata": {}, "outputs": [], "source": [ - "moments_exact = np.zeros((4,4,4))\n", - "moments_exact[0,0,0] = 1.\n", + "moments_exact = np.zeros((4, 4, 4))\n", + "moments_exact[0, 0, 0] = 1.0\n", "# Exact expressions for degree 1\n", - "moments_exact[1,0,0] = a[0]\n", - "moments_exact[0,1,0] = a[1]\n", - "moments_exact[0,0,1] = a[2]\n", + "moments_exact[1, 0, 0] = a[0]\n", + "moments_exact[0, 1, 0] = a[1]\n", + "moments_exact[0, 0, 1] = a[2]\n", "\n", "# Exact expressions for degree 2\n", - "moments_exact[2,0,0] = cov[0,0] + a[0]**2\n", - "moments_exact[0,2,0] = cov[1,1] + a[1]**2\n", - "moments_exact[0,0,2] = cov[2,2] + a[2]**2\n", - "moments_exact[1,1,0] = a[0]*a[1]\n", - "moments_exact[0,1,1] = a[1]*a[2]\n", - "moments_exact[1,0,1] = a[0]*a[2]\n", + "moments_exact[2, 0, 0] = cov[0, 0] + a[0] ** 2\n", + "moments_exact[0, 2, 0] = cov[1, 1] + a[1] ** 2\n", + "moments_exact[0, 0, 2] = cov[2, 2] + a[2] ** 2\n", + "moments_exact[1, 1, 0] = a[0] * a[1]\n", + "moments_exact[0, 1, 1] = a[1] * a[2]\n", + "moments_exact[1, 0, 1] = a[0] * a[2]\n", "\n", "# Exact expressions for degree 3\n", - "moments_exact[3,0,0] = 3*a[0]*cov[0,0] + a[0]**3\n", - "moments_exact[0,3,0] = 3*a[1]*cov[1,1] + a[1]**3\n", - "moments_exact[0,0,3] = 3*a[2]*cov[2,2] + a[2]**3\n", - "moments_exact[2,1,0] = a[1]*(cov[0,0] + a[0]**2) + 2*a[0]*cov[0,1]\n", - "moments_exact[2,0,1] = a[2]*(cov[0,0] + a[0]**2) + 2*a[0]*cov[0,2]\n", - "moments_exact[1,2,0] = a[0]*(cov[1,1] + a[1]**2) + 2*a[1]*cov[1,0]\n", - "moments_exact[0,2,1] = a[2]*(cov[1,1] + a[1]**2) + 2*a[1]*cov[1,2]\n", - "moments_exact[1,0,2] = a[0]*(cov[2,2] + a[2]**2) + 2*a[2]*cov[2,0]\n", - "moments_exact[0,1,2] = a[1]*(cov[2,2] + a[2]**2) + 2*a[2]*cov[2,1]\n", - "moments_exact[1,1,1] = a[0]*a[1]*a[2] + a[0]*cov[1,2] + a[1]*cov[0,2] + a[2]*cov[0,1]\n", + "moments_exact[3, 0, 0] = 3 * a[0] * cov[0, 0] + a[0] ** 3\n", + "moments_exact[0, 3, 0] = 3 * a[1] * cov[1, 1] + a[1] ** 3\n", + "moments_exact[0, 0, 3] = 3 * a[2] * cov[2, 2] + a[2] ** 3\n", + "moments_exact[2, 1, 0] = a[1] * (cov[0, 0] + a[0] ** 2) + 2 * a[0] * cov[0, 1]\n", + "moments_exact[2, 0, 1] = a[2] * (cov[0, 0] + a[0] ** 2) + 2 * a[0] * cov[0, 2]\n", + "moments_exact[1, 2, 0] = a[0] * (cov[1, 1] + a[1] ** 2) + 2 * a[1] * cov[1, 0]\n", + "moments_exact[0, 2, 1] = a[2] * (cov[1, 1] + a[1] ** 2) + 2 * a[1] * cov[1, 2]\n", + "moments_exact[1, 0, 2] = a[0] * (cov[2, 2] + a[2] ** 2) + 2 * a[2] * cov[2, 0]\n", + "moments_exact[0, 1, 2] = a[1] * (cov[2, 2] + a[2] ** 2) + 2 * a[2] * cov[2, 1]\n", + "moments_exact[1, 1, 1] = (\n", + " a[0] * a[1] * a[2] + a[0] * cov[1, 2] + a[1] * cov[0, 2] + a[2] * cov[0, 1]\n", + ")\n", "\n", - "moments_exact *= (2*np.pi)**1.5 / np.sqrt(np.prod(principal_components))" + "moments_exact *= (2 * np.pi) ** 1.5 / np.sqrt(np.prod(principal_components))" ] }, { @@ -461,7 +489,9 @@ "a0 = 3.2\n", "a = a0 * np.ones((3,))\n", "maxdeg = 8\n", - "moments_diagonal = compute_moments_diagonal_inefficient_implementation(principal_components, a, maxdeg)" + "moments_diagonal = compute_moments_diagonal_inefficient_implementation(\n", + " principal_components, a, maxdeg\n", + ")" ] }, { @@ -472,16 +502,25 @@ "outputs": [], "source": [ "eps = 1e-12\n", - "for n0 in range(maxdeg+1):\n", - " for n1 in range(maxdeg+1):\n", - " for n2 in range(maxdeg+1):\n", + "for n0 in range(maxdeg + 1):\n", + " for n1 in range(maxdeg + 1):\n", + " for n2 in range(maxdeg + 1):\n", " deg = n0 + n1 + n2\n", " if deg > maxdeg:\n", " assert moments_diagonal[n0, n1, n2] == 0\n", " else:\n", - " assert abs(moments_diagonal[n0,n1,n2]-moments_diagonal[n1,n0,n2]) < eps\n", - " assert abs(moments_diagonal[n0,n1,n2]-moments_diagonal[n2,n1,n0]) < eps\n", - " assert abs(moments_diagonal[n0,n1,n2]-moments_diagonal[n0,n2,n1]) < eps" + " assert (\n", + " abs(moments_diagonal[n0, n1, n2] - moments_diagonal[n1, n0, n2])\n", + " < eps\n", + " )\n", + " assert (\n", + " abs(moments_diagonal[n0, n1, n2] - moments_diagonal[n2, n1, n0])\n", + " < eps\n", + " )\n", + " assert (\n", + " abs(moments_diagonal[n0, n1, n2] - moments_diagonal[n0, n2, n1])\n", + " < eps\n", + " )" ] }, { @@ -507,12 +546,14 @@ "metadata": {}, "outputs": [], "source": [ - "principal_components = np.array([2.8,0.4,1.1])\n", + "principal_components = np.array([2.8, 0.4, 1.1])\n", "A = np.diag(principal_components)\n", "a = np.array([3.1, -2.3, 5.92])\n", "maxdeg = 3\n", "moments_general = compute_moments_inefficient_implementation(A, a, maxdeg)\n", - "moments_diagonal = compute_moments_diagonal_inefficient_implementation(principal_components, a, maxdeg)\n", + "moments_diagonal = compute_moments_diagonal_inefficient_implementation(\n", + " principal_components, a, maxdeg\n", + ")\n", "assert_allclose(moments_general, moments_diagonal, rtol=1e-15, atol=3e-16)" ] }, diff --git a/notebooks/anisotropic_representations.ipynb b/notebooks/anisotropic_representations.ipynb index d79a71a..70b7201 100644 --- a/notebooks/anisotropic_representations.ipynb +++ b/notebooks/anisotropic_representations.ipynb @@ -25,36 +25,50 @@ "from math import comb\n", "from anisoap.utils import monomial_iterator\n", "\n", - "#We are implementing iterations of the form R_{l} = prefact_minus1* z * R_{l-1} + prefact_minus2* r^2 * R_{l-2}\n", + "\n", + "# We are implementing iterations of the form R_{l} = prefact_minus1* z * R_{l-1} + prefact_minus2* r^2 * R_{l-2}\n", "def prefact_minus1(l):\n", " \"\"\"\n", " Parameters:\n", - " - l: int \n", - " \n", + " - l: int\n", + "\n", " Returns:\n", - " - A list of size (2*l -1) corresponding to the prefactor that multiplies the \n", - " \n", - " For m in [-l, -l+2, ..., l], compute the factor as : \n", - " sqrt(factorial(l+1-m)/ factorial(l+1+m)) sqrt(factorial(l+m)/ factorial(l-m)) (2*l+1)/(l+1-m) \n", - " \n", + " - A list of size (2*l -1) corresponding to the prefactor that multiplies the\n", + "\n", + " For m in [-l, -l+2, ..., l], compute the factor as :\n", + " sqrt(factorial(l+1-m)/ factorial(l+1+m)) sqrt(factorial(l+m)/ factorial(l-m)) (2*l+1)/(l+1-m)\n", + "\n", " \"\"\"\n", - " m=np.arange(-l,l+1)\n", - " return np.sqrt(factorial(l+1-m)/factorial(l+1+m)) * np.sqrt(factorial(l+m)/factorial(l-m)) * (2*l+1)/(l+1-m)\n", - " \n", + " m = np.arange(-l, l + 1)\n", + " return (\n", + " np.sqrt(factorial(l + 1 - m) / factorial(l + 1 + m))\n", + " * np.sqrt(factorial(l + m) / factorial(l - m))\n", + " * (2 * l + 1)\n", + " / (l + 1 - m)\n", + " )\n", + "\n", + "\n", "def prefact_minus2(l):\n", " \"\"\"\n", - " For m in [-l+1, -l+2, ..., l-1], compute the factor as : \n", - " sqrt(factorial(l+1-m)/ factorial(l+1+m)) sqrt(factorial(l-1+m)/ factorial(l-1-m)) (l+m)/(l-m+1) \n", + " For m in [-l+1, -l+2, ..., l-1], compute the factor as :\n", + " sqrt(factorial(l+1-m)/ factorial(l+1+m)) sqrt(factorial(l-1+m)/ factorial(l-1-m)) (l+m)/(l-m+1)\n", " \"\"\"\n", - " m=np.arange(-l+1,l)\n", - " return -1* np.sqrt(factorial(l+1-m)/factorial(l+1+m)) * np.sqrt(factorial(l-1+m)/factorial(l-1-m)) * (l+m)/(l+1-m)\n", + " m = np.arange(-l + 1, l)\n", + " return (\n", + " -1\n", + " * np.sqrt(factorial(l + 1 - m) / factorial(l + 1 + m))\n", + " * np.sqrt(factorial(l - 1 + m) / factorial(l - 1 - m))\n", + " * (l + m)\n", + " / (l + 1 - m)\n", + " )\n", + "\n", "\n", "def binom(n, k):\n", " \"\"\"\n", " returns binomial coefficient nCk = math.factorial(n) / (math.factorial(k) * math.factorial(n - k))\n", - " We use math.comb utility to compute this \n", + " We use math.comb utility to compute this\n", " \"\"\"\n", - " return comb(n, k)\n" + " return comb(n, k)" ] }, { @@ -69,13 +83,13 @@ "def spherical_to_cartesian2(lmax, num_ns):\n", " \"\"\"\n", " Parameters:\n", - " - lmax: int \n", - " \n", + " - lmax: int\n", + "\n", " - num_ns: list of ints\n", - " \n", + "\n", " Returns:\n", " - A list with as many entries as in num_ns (corresponding to l=0,1,... lmax+1). Each corresponding entry is an\n", - " array of size (2*l+1, num_ns[l], maxdeg, maxdeg, maxdeg) \n", + " array of size (2*l+1, num_ns[l], maxdeg, maxdeg, maxdeg)\n", " where maxdeg = l + 2* max(num_ns[l]) and the last three axes correspond to n0, n1, n2 respectively such that\n", " the entries of the array form the coefficient of the x^n0 y^n1 z^n2 monomial in the expansion of R_l^m\n", " \"\"\"\n", @@ -87,71 +101,75 @@ " # Usage T_l[m,n,n0,n1,n2]\n", " T = []\n", " for l, num_n in enumerate(num_ns):\n", - " maxdeg = l + 2*(num_n-1)\n", - " T_l = np.zeros((2*l+1,num_n,maxdeg+1,maxdeg+1,maxdeg+1))\n", + " maxdeg = l + 2 * (num_n - 1)\n", + " T_l = np.zeros((2 * l + 1, num_n, maxdeg + 1, maxdeg + 1, maxdeg + 1))\n", " T.append(T_l)\n", "\n", " # Initialize array in which to store all coefficients for each l\n", " # Usage T_l[m,n,n0,n1,n2]\n", - " T[0][0,0,0,0,0] = 1\n", - " for l in range(1,lmax+1):\n", - " prefact = np.sqrt(2) * factorial2(2*l-1) / np.sqrt(factorial(2*l))\n", - " for k in range(l//2+1):\n", - " n1 = 2*k\n", - " n0 = l-n1\n", - " T[l][2*l,0, n0, n1,0] = binom(l, n1) *(-1)**k \n", - " for k in range((l-1)//2+1):\n", - " n1 = 2*k+1\n", - " n0 = l-n1\n", - " T[l][0,0,n0,n1,0] = binom(l, n1) *(-1)**k\n", - " T[l]*= prefact\n", + " T[0][0, 0, 0, 0, 0] = 1\n", + " for l in range(1, lmax + 1):\n", + " prefact = np.sqrt(2) * factorial2(2 * l - 1) / np.sqrt(factorial(2 * l))\n", + " for k in range(l // 2 + 1):\n", + " n1 = 2 * k\n", + " n0 = l - n1\n", + " T[l][2 * l, 0, n0, n1, 0] = binom(l, n1) * (-1) ** k\n", + " for k in range((l - 1) // 2 + 1):\n", + " n1 = 2 * k + 1\n", + " n0 = l - n1\n", + " T[l][0, 0, n0, n1, 0] = binom(l, n1) * (-1) ** k\n", + " T[l] *= prefact\n", "\n", " # Run iteration over (l,m) to generate all coefficients for n=0.\n", - " for l in range(1, lmax+1):\n", + " for l in range(1, lmax + 1):\n", " deg = l\n", " myiter = iter(monomial_iterator.TrivariateMonomialIndices(deg))\n", - " for idx,n0,n1,n2 in myiter:\n", + " for idx, n0, n1, n2 in myiter:\n", " print(l)\n", - " a = prefact_minus1(l-1) # length 2l+1 due to m dependence\n", - " b = prefact_minus2(l-1) # length 2l+1 due to m dependence\n", - " \n", - " #(-l+1)+2: (l+1) -2 gets contributions from T[l-1]\n", - " if n0-2>=0:\n", - " print(\"n0\",l)\n", - " T[l][2:2*l-1,0,n0,n1,n2] += b * T[l-2][:,0,n0-2,n1,n2]\n", - " if n1-2>=0:\n", - " print(\"n1\",l)\n", - " T[l][2:2*l-1,0,n0,n1,n2] += b * T[l-2][:,0,n0,n1-2,n2]\n", - " if n2-2>=0:\n", - " print(\"n2\",l)\n", - " T[l][2:2*l-1,0,n0,n1,n2] += b * T[l-2][:,0,n0,n1,n2-2]\n", - " #(-l+1)+1: (l+1) -1 gets contributions from T[l]\n", - " if n2-1>=0:\n", - " print(\"n2>1\",l)\n", - " print(T[l][1:2*l,0,n0,n1,n2].shape, a.shape,T[l-1][:,0,n0,n1,n2-1].shape )\n", - " T[l][1:2*l,0,n0,n1,n2] += a * T[l-1][:,0,n0,n1,n2-1]\n", - "# a's length needs to be fixed \n", - " \n", + " a = prefact_minus1(l - 1) # length 2l+1 due to m dependence\n", + " b = prefact_minus2(l - 1) # length 2l+1 due to m dependence\n", + "\n", + " # (-l+1)+2: (l+1) -2 gets contributions from T[l-1]\n", + " if n0 - 2 >= 0:\n", + " print(\"n0\", l)\n", + " T[l][2 : 2 * l - 1, 0, n0, n1, n2] += b * T[l - 2][:, 0, n0 - 2, n1, n2]\n", + " if n1 - 2 >= 0:\n", + " print(\"n1\", l)\n", + " T[l][2 : 2 * l - 1, 0, n0, n1, n2] += b * T[l - 2][:, 0, n0, n1 - 2, n2]\n", + " if n2 - 2 >= 0:\n", + " print(\"n2\", l)\n", + " T[l][2 : 2 * l - 1, 0, n0, n1, n2] += b * T[l - 2][:, 0, n0, n1, n2 - 2]\n", + " # (-l+1)+1: (l+1) -1 gets contributions from T[l]\n", + " if n2 - 1 >= 0:\n", + " print(\"n2>1\", l)\n", + " print(\n", + " T[l][1 : 2 * l, 0, n0, n1, n2].shape,\n", + " a.shape,\n", + " T[l - 1][:, 0, n0, n1, n2 - 1].shape,\n", + " )\n", + " T[l][1 : 2 * l, 0, n0, n1, n2] += a * T[l - 1][:, 0, n0, n1, n2 - 1]\n", + " # a's length needs to be fixed\n", + "\n", " # Run the iteration over n\n", - "# B_{n+1,lm} = r^2 B_{nlm} = (x^2+y^2+z^2)B_{nlm}\n", - "# T^{n+1,lm}_{n_0+2,n_1,n_2} += T^{n,lm}_{n_0,n_1n_2}\n", - "# T^{n+1,lm}_{n_0,n_1+2,n_2} += T^{n,lm}_{n_0,n_1n_2}\n", - "# T^{n+1,lm}_{n_0,n_1,n_2+2} += T^{n,lm}_{n_0,n_1n_2}\n", - " for l in range(lmax+1):\n", - " for n in range(1,num_ns[l]):\n", - " deg = l + 2*n # degree of polynomial\n", + " # B_{n+1,lm} = r^2 B_{nlm} = (x^2+y^2+z^2)B_{nlm}\n", + " # T^{n+1,lm}_{n_0+2,n_1,n_2} += T^{n,lm}_{n_0,n_1n_2}\n", + " # T^{n+1,lm}_{n_0,n_1+2,n_2} += T^{n,lm}_{n_0,n_1n_2}\n", + " # T^{n+1,lm}_{n_0,n_1,n_2+2} += T^{n,lm}_{n_0,n_1n_2}\n", + " for l in range(lmax + 1):\n", + " for n in range(1, num_ns[l]):\n", + " deg = l + 2 * n # degree of polynomial\n", " myiter = iter(monomial_iterator.TrivariateMonomialIndices(deg))\n", - " for idx,n0,n1,n2 in myiter:\n", + " for idx, n0, n1, n2 in myiter:\n", " # Use recurrence relation to update\n", " # Warning, if n0-2, n1-2 or n2-2 are negative\n", " # it might be necessary to add if statements\n", " # to avoid.\n", - " if n0>=2:\n", - " T[l][:,n,n0,n1,n2] += T[l][:,n-1,n0-2,n1,n2]\n", - " if n1>=2:\n", - " T[l][:,n,n0,n1,n2] += T[l][:,n-1,n0,n1-2,n2]\n", - " if n2>=2:\n", - " T[l][:,n,n0,n1,n2] += T[l][:,n-1,n0,n1,n2-2]\n", + " if n0 >= 2:\n", + " T[l][:, n, n0, n1, n2] += T[l][:, n - 1, n0 - 2, n1, n2]\n", + " if n1 >= 2:\n", + " T[l][:, n, n0, n1, n2] += T[l][:, n - 1, n0, n1 - 2, n2]\n", + " if n2 >= 2:\n", + " T[l][:, n, n0, n1, n2] += T[l][:, n - 1, n0, n1, n2 - 2]\n", "\n", " return T" ] @@ -192,8 +210,8 @@ } ], "source": [ - "lmax=2\n", - "num_ns=[1,1,2]\n", + "lmax = 2\n", + "num_ns = [1, 1, 2]\n", "test = spherical_to_cartesian2(lmax, num_ns)" ] }, @@ -207,7 +225,8 @@ "outputs": [], "source": [ "from anisoap.utils.spherical_to_cartesian import spherical_to_cartesian\n", - "ref = spherical_to_cartesian(lmax, num_ns)\n" + "\n", + "ref = spherical_to_cartesian(lmax, num_ns)" ] }, { @@ -230,7 +249,7 @@ ], "source": [ "for i in range(len(ref)):\n", - " print(np.linalg.norm(ref[i]-test[i]))" + " print(np.linalg.norm(ref[i] - test[i]))" ] }, { @@ -261,17 +280,18 @@ "source": [ "from anisoap.utils.spherical_to_cartesian import spherical_to_cartesian\n", "import numpy as np\n", + "\n", "try:\n", " from tqdm import tqdm\n", "except ImportError:\n", - " tqdm = (lambda i, **kwargs: i)\n", + " tqdm = lambda i, **kwargs: i\n", "\n", "from anisoap.utils import compute_moments_diagonal_inefficient_implementation\n", "from anisoap.utils import quaternion_to_rotation_matrix\n", "from anisoap.representations.radial_basis import RadialBasis\n", "from anisoap.utils import compute_moments_inefficient_implementation\n", "\n", - "from metatensor import TensorBlock, TensorMap,Labels" + "from metatensor import TensorBlock, TensorMap, Labels" ] }, { @@ -284,13 +304,20 @@ "from ase.io import read\n", "from rascaline import NeighborList\n", "import ase\n", - "frames = read('/Users/jigyasa/scratch/data_papers/data/water/dataset/water_randomized_1000.xyz', ':2')\n", - "frames2 = read(\"/Users/jigyasa/scratch/metatensor-examples/data/hamiltonian/ethanol-hamiltonian/ethanol_4500.xyz\",\":1\")\n", - "frames3= [ase.build.molecule('NH3')]\n", - "frames = frames+frames2+frames3\n", - "for f in frames: \n", - " f.pbc=True\n", - " f.cell=[4,4,4]" + "\n", + "frames = read(\n", + " \"/Users/jigyasa/scratch/data_papers/data/water/dataset/water_randomized_1000.xyz\",\n", + " \":2\",\n", + ")\n", + "frames2 = read(\n", + " \"/Users/jigyasa/scratch/metatensor-examples/data/hamiltonian/ethanol-hamiltonian/ethanol_4500.xyz\",\n", + " \":1\",\n", + ")\n", + "frames3 = [ase.build.molecule(\"NH3\")]\n", + "frames = frames + frames2 + frames3\n", + "for f in frames:\n", + " f.pbc = True\n", + " f.cell = [4, 4, 4]" ] }, { @@ -301,7 +328,7 @@ "outputs": [], "source": [ "from anisoap.utils.moment_generator import *\n", - "from anisoap.utils.quaternion_to_rotation_matrix import quaternion_to_rotation_matrix\n", + "from anisoap.utils.quaternion_to_rotation_matrix import quaternion_to_rotation_matrix\n", "from anisoap.representations.radial_basis import RadialBasis\n", "from anisoap.utils import compute_moments_inefficient_implementation\n", "from itertools import product\n", @@ -315,20 +342,20 @@ "metadata": {}, "outputs": [], "source": [ - "#hypers\n", + "# hypers\n", "rcut = 4\n", "lmax = 4\n", - "radial_basis_name = 'monomial'\n", - "radial_hypers={}\n", - "radial_hypers['radial_basis'] = radial_basis_name.lower() # lower case\n", - "radial_hypers['radial_gaussian_width'] = 0.2\n", - "radial_hypers['max_angular'] = lmax\n", + "radial_basis_name = \"monomial\"\n", + "radial_hypers = {}\n", + "radial_hypers[\"radial_basis\"] = radial_basis_name.lower() # lower case\n", + "radial_hypers[\"radial_gaussian_width\"] = 0.2\n", + "radial_hypers[\"max_angular\"] = lmax\n", "\n", "radial_basis = RadialBasis(**radial_hypers)\n", "\n", "num_ns = []\n", - "for l in range(lmax+1):\n", - "# num_ns.append(lmax + 1 - l)\n", + "for l in range(lmax + 1):\n", + " # num_ns.append(lmax + 1 - l)\n", " num_ns.append(1)\n", "sph_to_cart = spherical_to_cartesian(lmax, num_ns)" ] @@ -344,10 +371,10 @@ "evalue": "No module named 'anisoap.representations.projection_coefficients_modified'", "output_type": "error", "traceback": [ - "\u001B[0;31m---------------------------------------------------------------------------\u001B[0m", - "\u001B[0;31mModuleNotFoundError\u001B[0m Traceback (most recent call last)", - "Cell \u001B[0;32mIn [47], line 1\u001B[0m\n\u001B[0;32m----> 1\u001B[0m \u001B[38;5;28;01mfrom\u001B[39;00m \u001B[38;5;21;01manisoap\u001B[39;00m\u001B[38;5;21;01m.\u001B[39;00m\u001B[38;5;21;01mrepresentations\u001B[39;00m\u001B[38;5;21;01m.\u001B[39;00m\u001B[38;5;21;01mprojection_coefficients_modified\u001B[39;00m \u001B[38;5;28;01mimport\u001B[39;00m \u001B[38;5;241m*\u001B[39m\n", - "\u001B[0;31mModuleNotFoundError\u001B[0m: No module named 'anisoap.representations.projection_coefficients_modified'" + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mModuleNotFoundError\u001b[0m Traceback (most recent call last)", + "Cell \u001b[0;32mIn [47], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01manisoap\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mrepresentations\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mprojection_coefficients_modified\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;241m*\u001b[39m\n", + "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'anisoap.representations.projection_coefficients_modified'" ] } ], @@ -370,10 +397,10 @@ "outputs": [], "source": [ "num_frames = len(frames)\n", - "num_atoms_per_frame = np.zeros((num_frames),int)\n", + "num_atoms_per_frame = np.zeros((num_frames), int)\n", "species = set()\n", "\n", - "for i,f in enumerate(frames):\n", + "for i, f in enumerate(frames):\n", " num_atoms_per_frame[i] = len(f)\n", " for atom in f:\n", " species.add(atom.number)\n", @@ -389,9 +416,11 @@ "metadata": {}, "outputs": [], "source": [ - "frame_to_global_atom_idx = np.zeros((num_frames),int)\n", - "for n in range(1,num_frames):\n", - " frame_to_global_atom_idx[n] = num_atoms_per_frame[n-1] + frame_to_global_atom_idx[n-1]\n" + "frame_to_global_atom_idx = np.zeros((num_frames), int)\n", + "for n in range(1, num_frames):\n", + " frame_to_global_atom_idx[n] = (\n", + " num_atoms_per_frame[n - 1] + frame_to_global_atom_idx[n - 1]\n", + " )" ] }, { @@ -401,17 +430,17 @@ "metadata": {}, "outputs": [], "source": [ - "quaternions = np.zeros((num_atoms,4))\n", + "quaternions = np.zeros((num_atoms, 4))\n", "ellipsoid_lengths = np.zeros((num_atoms, 3))\n", "\n", "for i in range(num_atoms):\n", - " quaternions[i]= [0, 0, np.sin(np.pi/4), np.cos(np.pi/4)]\n", - " ellipsoid_lengths[i] = [0.5,0.3,0.4]\n", + " quaternions[i] = [0, 0, np.sin(np.pi / 4), np.cos(np.pi / 4)]\n", + " ellipsoid_lengths[i] = [0.5, 0.3, 0.4]\n", "\n", "# Convert quaternions to rotation matrices\n", - "rotation_matrices = np.zeros((num_atoms,3,3))\n", + "rotation_matrices = np.zeros((num_atoms, 3, 3))\n", "for i, quat in enumerate(quaternions):\n", - " rotation_matrices[i] = quaternion_to_rotation_matrix(quat)\n" + " rotation_matrices[i] = quaternion_to_rotation_matrix(quat)" ] }, { @@ -422,8 +451,8 @@ "outputs": [], "source": [ "nl = NeighborList(rcut, True).compute(frames)\n", - "keys=np.array(nl.keys.asarray(), dtype=int)\n", - "keys=[tuple(i)+(l,) for i in keys for l in range(lmax+1)]" + "keys = np.array(nl.keys.asarray(), dtype=int)\n", + "keys = [tuple(i) + (l,) for i in keys for l in range(lmax + 1)]" ] }, { @@ -454,82 +483,123 @@ "metadata": {}, "outputs": [], "source": [ - "def pairwise_aniso_expansion(neighbor_list, species, frame_to_global_atom_idx, rotation_matrices, ellipsoid_lengths, radial_basis):\n", + "def pairwise_aniso_expansion(\n", + " neighbor_list,\n", + " species,\n", + " frame_to_global_atom_idx,\n", + " rotation_matrices,\n", + " ellipsoid_lengths,\n", + " radial_basis,\n", + "):\n", " \"\"\"\n", - " Function to compute the pairwise expansion by combining the moments and the spherical to Cartesian \n", + " Function to compute the pairwise expansion by combining the moments and the spherical to Cartesian\n", " transformation\n", " --------------------------------------------------------\n", " Parameters:\n", - " \n", - " neighbor_list : Equistore TensorMap \n", + "\n", + " neighbor_list : Equistore TensorMap\n", " Full neighborlist with keys (species_1, species_2) enumerating the possible species pairs.\n", " Each block contains as samples, the atom indices of (first_atom, second_atom) that correspond to the key,\n", - " and block.value is a 3D array of the form (num_samples, num_components,properties), with num_components=3 \n", + " and block.value is a 3D array of the form (num_samples, num_components,properties), with num_components=3\n", " corresponding to the (x,y,z) components of the vector from first_atom to second_atom.\n", " Depending on the cutoff some species pairs may not appear. Self pairs are not present but in PBC,\n", " pairs between copies of the same atom are accounted for.\n", - " \n", + "\n", " species: list of ints\n", - " List of atomic numbers present across the data frames \n", - " \n", + " List of atomic numbers present across the data frames\n", + "\n", " frame_to_global_atom_idx: list of ints\n", " The length of the list equals the number of frames, each entry enumerating the number of atoms in\n", " corresponding frame\n", - " \n", + "\n", " rotation_matrices: np.array of dimension ((num_atoms,3,3))\n", - " \n", + "\n", " ellipsoid_lengths: np.array of dimension ((num_atoms,3))\n", - " \n", + "\n", " radial_basis : Instance of the RadialBasis Class\n", - " anisoap.representations.radial_basis.RadialBasis that has been instantiated appropriately with the \n", + " anisoap.representations.radial_basis.RadialBasis that has been instantiated appropriately with the\n", " cutoff radius, radial basis type.\n", " -----------------------------------------------------------\n", - " Returns: \n", - " An Equistore TensorMap with keys (species_1, species_2, l) where (\"species_1\", \"species_2\") is key in the \n", + " Returns:\n", + " An Equistore TensorMap with keys (species_1, species_2, l) where (\"species_1\", \"species_2\") is key in the\n", " neighbor_list and \"l\" is the angular channel.\n", " Each block of this tensormap has the same samples as the corresponding block of the neighbor_list.\n", - " block.value is a 3D array of the form (num_samples, num_components, properties) where num_components \n", - " form the 2*l+1 values for the corresponding angular channel and the properties dimension corresponds to \n", + " block.value is a 3D array of the form (num_samples, num_components, properties) where num_components\n", + " form the 2*l+1 values for the corresponding angular channel and the properties dimension corresponds to\n", " the radial channel.\n", - " \n", - " \"\"\" \n", + "\n", + " \"\"\"\n", " tensorblock_list = []\n", " tensormap_keys = []\n", "\n", " for center_species in species:\n", " for neighbor_species in species:\n", " if (center_species, neighbor_species) in neighbor_list.keys:\n", - " values_ldict = {l:[] for l in range(lmax+1)}\n", - " nl_block = neighbor_list.block(species_first_atom=center_species, species_second_atom=neighbor_species)\n", + " values_ldict = {l: [] for l in range(lmax + 1)}\n", + " nl_block = neighbor_list.block(\n", + " species_first_atom=center_species,\n", + " species_second_atom=neighbor_species,\n", + " )\n", "\n", " for isample, nl_sample in enumerate(nl_block.samples):\n", - " frame_idx, i,j = nl_sample[\"structure\"], nl_sample[\"first_atom\"], nl_sample[\"second_atom\"]\n", - " i_global = frame_to_global_atom_idx[frame_idx] +i\n", - " j_global = frame_to_global_atom_idx[frame_idx] +j\n", + " frame_idx, i, j = (\n", + " nl_sample[\"structure\"],\n", + " nl_sample[\"first_atom\"],\n", + " nl_sample[\"second_atom\"],\n", + " )\n", + " i_global = frame_to_global_atom_idx[frame_idx] + i\n", + " j_global = frame_to_global_atom_idx[frame_idx] + j\n", "\n", - " r_ij = np.asarray([nl_block.values[isample,0], nl_block.values[isample,1],nl_block.values[isample,2]]).reshape(3,)\n", - " # r_ij = pos_i - positions[j_global]\n", + " r_ij = np.asarray(\n", + " [\n", + " nl_block.values[isample, 0],\n", + " nl_block.values[isample, 1],\n", + " nl_block.values[isample, 2],\n", + " ]\n", + " ).reshape(\n", + " 3,\n", + " )\n", + " # r_ij = pos_i - positions[j_global]\n", "\n", " rot = rotation_matrices[j_global]\n", " lengths = ellipsoid_lengths[j_global]\n", - " precision, center = radial_basis.compute_gaussian_parameters(r_ij, lengths, rot)\n", - " # moments = compute_moments_inefficient_implementation(precision, center, maxdeg=lmax)\n", + " precision, center = radial_basis.compute_gaussian_parameters(\n", + " r_ij, lengths, rot\n", + " )\n", + " # moments = compute_moments_inefficient_implementation(precision, center, maxdeg=lmax)\n", "\n", - " for l in range(lmax+1):\n", + " for l in range(lmax + 1):\n", " moments = np.ones(sph_to_cart[l].shape[-3:])\n", - " values_ldict[l].append(np.einsum(\"mnpqr, pqr->mn\", sph_to_cart[l], moments))\n", + " values_ldict[l].append(\n", + " np.einsum(\"mnpqr, pqr->mn\", sph_to_cart[l], moments)\n", + " )\n", "\n", - "\n", - " for l in range(lmax+1):\n", - " block = TensorBlock(values = np.asarray(values_ldict[l]), \n", - " samples = nl_block.samples, #as many rows as samples\n", - " components = [Labels(['spherical_component_m'], np.asarray([list(range(-l,l+1))], np.int32).reshape(-1,1) )],\n", - " properties = Labels(['n'],np.asarray(list(range(num_ns[l])), np.int32).reshape(-1,1))\n", - " )\n", + " for l in range(lmax + 1):\n", + " block = TensorBlock(\n", + " values=np.asarray(values_ldict[l]),\n", + " samples=nl_block.samples, # as many rows as samples\n", + " components=[\n", + " Labels(\n", + " [\"spherical_component_m\"],\n", + " np.asarray([list(range(-l, l + 1))], np.int32).reshape(\n", + " -1, 1\n", + " ),\n", + " )\n", + " ],\n", + " properties=Labels(\n", + " [\"n\"],\n", + " np.asarray(list(range(num_ns[l])), np.int32).reshape(-1, 1),\n", + " ),\n", + " )\n", " tensorblock_list.append(block)\n", "\n", - "\n", - " pairwise_aniso_feat = TensorMap(Labels([\"species_center\", \"species_neighbor\", \"angular_channel\"],np.asarray(keys, dtype=np.int32)), tensorblock_list)\n", + " pairwise_aniso_feat = TensorMap(\n", + " Labels(\n", + " [\"species_center\", \"species_neighbor\", \"angular_channel\"],\n", + " np.asarray(keys, dtype=np.int32),\n", + " ),\n", + " tensorblock_list,\n", + " )\n", " return pairwise_aniso_feat" ] }, @@ -540,7 +610,14 @@ "metadata": {}, "outputs": [], "source": [ - "pairwise_aniso_feat = pairwise_aniso_expansion(nl, species, frame_to_global_atom_idx, rotation_matrices, ellipsoid_lengths, radial_basis)" + "pairwise_aniso_feat = pairwise_aniso_expansion(\n", + " nl,\n", + " species,\n", + " frame_to_global_atom_idx,\n", + " rotation_matrices,\n", + " ellipsoid_lengths,\n", + " radial_basis,\n", + ")" ] }, { @@ -626,119 +703,161 @@ " Function to sum over the pairwise expansion \\sum_{j in a} = \n", " --------------------------------------------------------\n", " Parameters:\n", - " \n", - " pair_aniso_feat : Equistore TensorMap \n", - " TensorMap returned from \"pairwise_aniso_expansion()\" with keys (species_1, species_2,l) enumerating \n", + "\n", + " pair_aniso_feat : Equistore TensorMap\n", + " TensorMap returned from \"pairwise_aniso_expansion()\" with keys (species_1, species_2,l) enumerating\n", " the possible species pairs and the angular channels.\n", - " \n", + "\n", " species: list of ints\n", - " List of atomic numbers present across the data frames \n", - " \n", + " List of atomic numbers present across the data frames\n", + "\n", " -----------------------------------------------------------\n", - " Returns: \n", - " An Equistore TensorMap with keys (species, l) \"species\" takes the value of the atomic numbers present \n", + " Returns:\n", + " An Equistore TensorMap with keys (species, l) \"species\" takes the value of the atomic numbers present\n", " in the dataset and \"l\" is the angular channel.\n", - " Each block of this tensormap has as samples (\"structure\", \"center\") yielding the indices of the frames \n", + " Each block of this tensormap has as samples (\"structure\", \"center\") yielding the indices of the frames\n", " and atoms that correspond to \"species\" are present.\n", - " block.value is a 3D array of the form (num_samples, num_components, properties) where num_components \n", - " take on the same values as in the pair_aniso_feat_feat.block . block.properties now has an additional index \n", + " block.value is a 3D array of the form (num_samples, num_components, properties) where num_components\n", + " take on the same values as in the pair_aniso_feat_feat.block . block.properties now has an additional index\n", " for neighbor_species that corresponds to \"a\" in \n", - " \n", - " \"\"\" \n", - " aniso_keys = list(set([tuple(list(x)[:1]+list(x)[2:]) for x in keys]))\n", - " # Select the unique combinations of pair_aniso_feat.keys[\"species_center\"] and \n", - " # pair_aniso_feat.keys[\"angular_channel\"] to form the keys of the single particle centered feature \n", + "\n", + " \"\"\"\n", + " aniso_keys = list(set([tuple(list(x)[:1] + list(x)[2:]) for x in keys]))\n", + " # Select the unique combinations of pair_aniso_feat.keys[\"species_center\"] and\n", + " # pair_aniso_feat.keys[\"angular_channel\"] to form the keys of the single particle centered feature\n", " aniso_keys.sort()\n", " aniso_blocks = []\n", - " property_names = pair_aniso_feat.property_names + ('neighbor_species',)\n", - " \n", + " property_names = pair_aniso_feat.property_names + (\"neighbor_species\",)\n", + "\n", " for key in aniso_keys:\n", - " contract_blocks=[]\n", - " contract_properties=[]\n", - " contract_samples=[]\n", + " contract_blocks = []\n", + " contract_properties = []\n", + " contract_samples = []\n", " # these collect the values, properties and samples of the blocks when contracted over neighbor_species.\n", - " # All these lists have as many entries as len(species). \n", - " \n", + " # All these lists have as many entries as len(species).\n", + "\n", " for ele in species:\n", - " blockidx = pair_aniso_feat.blocks_matching(species_neighbor= ele)\n", + " blockidx = pair_aniso_feat.blocks_matching(species_neighbor=ele)\n", " # indices of the blocks in pair_aniso_feat with neighbor species = ele\n", - " sel_blocks = [pair_aniso_feat.block(i) for i in blockidx if key==tuple(list(pair_aniso_feat.keys[i])[:1]+list(pair_aniso_feat.keys[i])[2:])]\n", + " sel_blocks = [\n", + " pair_aniso_feat.block(i)\n", + " for i in blockidx\n", + " if key\n", + " == tuple(\n", + " list(pair_aniso_feat.keys[i])[:1]\n", + " + list(pair_aniso_feat.keys[i])[2:]\n", + " )\n", + " ]\n", " if not len(sel_blocks):\n", - "# print(key, ele, \"skipped\") # this block is not found in the pairwise feat\n", + " # print(key, ele, \"skipped\") # this block is not found in the pairwise feat\n", " continue\n", - " assert len(sel_blocks)==1 \n", - " \n", - " # sel_blocks is the corresponding block in the pairwise feat with the same (species_center, l) and \n", + " assert len(sel_blocks) == 1\n", + "\n", + " # sel_blocks is the corresponding block in the pairwise feat with the same (species_center, l) and\n", " # species_neighbor = ele thus there can be only one block corresponding to the triplet (species_center, species_neighbor, l)\n", " block = sel_blocks[0]\n", - " \n", - " pair_block_sample = list(zip(block.samples['structure'], block.samples['first_atom']))\n", + "\n", + " pair_block_sample = list(\n", + " zip(block.samples[\"structure\"], block.samples[\"first_atom\"])\n", + " )\n", " # Takes the structure and first atom index from the current pair_block sample. There might be repeated\n", " # entries here because for example (0,0,1) (0,0,2) might be samples of the pair block (the index of the\n", - " # neighbor atom is changing but for both of these we are keeping (0,0) corresponding to the structure and \n", - " #first atom. \n", + " # neighbor atom is changing but for both of these we are keeping (0,0) corresponding to the structure and\n", + " # first atom.\n", "\n", - " struct, center = np.unique(block.samples['structure']), np.unique(block.samples['first_atom'])\n", - " possible_block_samples = list(product(struct,center))\n", + " struct, center = np.unique(block.samples[\"structure\"]), np.unique(\n", + " block.samples[\"first_atom\"]\n", + " )\n", + " possible_block_samples = list(product(struct, center))\n", " # possible block samples contains all *unique* possible pairwise products between structure and atom index\n", " # From here we choose the entries that are actually present in the block to form the final sample\n", - " \n", - " block_samples=[]\n", + "\n", + " block_samples = []\n", " block_values = []\n", "\n", " for isample, sample in enumerate(possible_block_samples):\n", - " sample_idx = [idx for idx, tup in enumerate(pair_block_sample) if tup[0] ==sample[0] and tup[1] == sample[1]]\n", - " # all samples of the pair block that match the current sample \n", - " # in the example above, for sample = (0,0) we would identify sample_idx = [(0,0,1), (0,0,2)] \n", - " if len(sample_idx)==0:\n", + " sample_idx = [\n", + " idx\n", + " for idx, tup in enumerate(pair_block_sample)\n", + " if tup[0] == sample[0] and tup[1] == sample[1]\n", + " ]\n", + " # all samples of the pair block that match the current sample\n", + " # in the example above, for sample = (0,0) we would identify sample_idx = [(0,0,1), (0,0,2)]\n", + " if len(sample_idx) == 0:\n", " continue\n", - " # #print(key, ele, sample, block.samples[sample_idx])\n", + " # #print(key, ele, sample, block.samples[sample_idx])\n", " block_samples.append(sample)\n", - " block_values.append(block.values[sample_idx].sum(axis=0)) #sum over \"j\" for given ele\n", - " \n", - " # block_values has as many entries as samples satisfying (key, neighbor_species=ele). \n", + " block_values.append(\n", + " block.values[sample_idx].sum(axis=0)\n", + " ) # sum over \"j\" for given ele\n", + "\n", + " # block_values has as many entries as samples satisfying (key, neighbor_species=ele).\n", " # When we iterate over neighbor species, not all (structure, center) would be present\n", - " # Example: (0,0,1) might be present in a block with neighbor_species = 1 but no other pair block \n", + " # Example: (0,0,1) might be present in a block with neighbor_species = 1 but no other pair block\n", " # ever has (0,0,x) present as a sample- so (0,0) doesnt show up in a block_sample for all ele\n", " # so in general we have a ragged list of contract_blocks\n", - " \n", + "\n", " contract_blocks.append(block_values)\n", " contract_samples.append(block_samples)\n", - " contract_properties.append([tuple(p)+(ele,) for p in block.properties])\n", - " #this adds the \"ele\" (i.e. neighbor_species) to the properties dimension\n", - " \n", - "# print(len(contract_samples))\n", - " all_block_samples= sorted(list(set().union(*contract_samples))) \n", + " contract_properties.append([tuple(p) + (ele,) for p in block.properties])\n", + " # this adds the \"ele\" (i.e. neighbor_species) to the properties dimension\n", + "\n", + " # print(len(contract_samples))\n", + " all_block_samples = sorted(list(set().union(*contract_samples)))\n", " # Selects the set of samples from all the block_samples we collected by iterating over the neighbor_species\n", - " # These form the final samples of the block! \n", + " # These form the final samples of the block!\n", "\n", - " all_block_values = np.zeros(((len(all_block_samples),)+ block.values.shape[1:]+(len(contract_blocks),)))\n", - " # Create storage for the final values - we need as many rows as all_block_samples, \n", + " all_block_values = np.zeros(\n", + " (\n", + " (len(all_block_samples),)\n", + " + block.values.shape[1:]\n", + " + (len(contract_blocks),)\n", + " )\n", + " )\n", + " # Create storage for the final values - we need as many rows as all_block_samples,\n", " # block.values.shape[1:] accounts for \"components\" and \"properties\" that are already part of the pair blocks\n", " # and we dont alter these\n", - " # len(contract_blocks) - adds the additional dimension for the neighbor_species since we accumulated \n", + " # len(contract_blocks) - adds the additional dimension for the neighbor_species since we accumulated\n", " # values for each of them as \\sum_{j in ele} <|rho_ij>\n", " # Thus - all_block_values.shape = (num_final_samples, components_pair, properties_pair, num_species)\n", - " \n", + "\n", " for iele, elem_cont_samples in enumerate(contract_samples):\n", " # This effectively loops over the species of the neighbors\n", " # Now we just need to add the contributions to the final samples and values from this species to the right\n", " # samples\n", - " nzidx=[i for i in range(len(all_block_samples)) if all_block_samples[i] in elem_cont_samples]\n", + " nzidx = [\n", + " i\n", + " for i in range(len(all_block_samples))\n", + " if all_block_samples[i] in elem_cont_samples\n", + " ]\n", " # identifies where the samples that this species contributes to, are present in the final samples\n", - "# print(apecies[ib],key, bb, all_block_samples)\n", - " all_block_values[nzidx,:,:,iele] = contract_blocks[iele]\n", + " # print(apecies[ib],key, bb, all_block_samples)\n", + " all_block_values[nzidx, :, :, iele] = contract_blocks[iele]\n", "\n", - " new_block = TensorBlock(values = all_block_values.reshape(all_block_values.shape[0],all_block_values.shape[1] ,-1),\n", - " samples = Labels(['structure', 'center'], np.asarray(all_block_samples, np.int32)), \n", - " components = block.components,\n", - " properties= Labels(list(property_names), np.asarray(np.vstack(contract_properties),np.int32))\n", - " )\n", + " new_block = TensorBlock(\n", + " values=all_block_values.reshape(\n", + " all_block_values.shape[0], all_block_values.shape[1], -1\n", + " ),\n", + " samples=Labels(\n", + " [\"structure\", \"center\"], np.asarray(all_block_samples, np.int32)\n", + " ),\n", + " components=block.components,\n", + " properties=Labels(\n", + " list(property_names),\n", + " np.asarray(np.vstack(contract_properties), np.int32),\n", + " ),\n", + " )\n", "\n", " aniso_blocks.append(new_block)\n", - " aniso = TensorMap(Labels(['species_center','angular_channel'],np.asarray(aniso_keys,dtype=np.int32)), aniso_blocks)\n", + " aniso = TensorMap(\n", + " Labels(\n", + " [\"species_center\", \"angular_channel\"],\n", + " np.asarray(aniso_keys, dtype=np.int32),\n", + " ),\n", + " aniso_blocks,\n", + " )\n", "\n", - " return aniso\n" + " return aniso" ] }, { From a8603c82b52093907d114f1074640f10c7ad570c Mon Sep 17 00:00:00 2001 From: Arthur Lin Date: Thu, 3 Oct 2024 19:54:01 -0500 Subject: [PATCH 18/22] undo linting changes in notebooks --- .../AvailableRadialBases.ipynb | 2 +- .../GTO Orthogonalization Demonstration.ipynb | 94 +-- notebooks/aniso_descriptor.ipynb | 190 +++--- notebooks/anisotropic_gaussian.ipynb | 289 ++++----- notebooks/anisotropic_representations.ipynb | 549 +++++++----------- 5 files changed, 443 insertions(+), 681 deletions(-) diff --git a/anisoap/representations/AvailableRadialBases.ipynb b/anisoap/representations/AvailableRadialBases.ipynb index 1ef789a..37db375 100644 --- a/anisoap/representations/AvailableRadialBases.ipynb +++ b/anisoap/representations/AvailableRadialBases.ipynb @@ -70,7 +70,7 @@ " radial_gaussian_width=width,\n", " # radial_gaussian_shift = shift,\n", " tol=1e-1,\n", - " **shared_params,\n", + " **shared_params\n", ")\n", "shiftedgto.plot_basis()" ] diff --git a/notebooks/GTO Orthogonalization Demonstration.ipynb b/notebooks/GTO Orthogonalization Demonstration.ipynb index e705090..dcd1903 100644 --- a/notebooks/GTO Orthogonalization Demonstration.ipynb +++ b/notebooks/GTO Orthogonalization Demonstration.ipynb @@ -52,30 +52,24 @@ "\n", "# Visualize a set of 3 normalized GTOs, with random widths and orders\n", "\n", - "\n", "def gto_norm(r, n, sigma_n):\n", - " I_n = 0.5 * sigma_n ** (2 * n + 3) * gamma(n + 1.5)\n", - " N_n = 1 / np.sqrt(I_n)\n", - " return N_n * r**n * np.exp(-(r**2) / (2 * sigma_n**2))\n", - "\n", + " I_n = 0.5 * sigma_n**(2 * n + 3) * gamma(n + 1.5)\n", + " N_n = 1/np.sqrt(I_n)\n", + " return N_n * r**n * np.exp(-r**2 / (2 * sigma_n**2))\n", "\n", "sigma_n_arr = np.array([1, 0.8, 0.5])\n", "n_arr = np.array([1, 6, 4])\n", "\n", - "r_grid = np.linspace(0, 10, 1000)\n", + "r_grid = np.linspace(0,10,1000)\n", "\n", "for i in range(3):\n", " sigma_n = sigma_n_arr[i]\n", " n = n_arr[i]\n", " plt.plot(r_grid, gto_norm(r_grid, n, sigma_n))\n", "\n", - "plt.legend(\n", - " [\n", - " f\"n = {n_arr[0]}, sigma_n = {sigma_n_arr[0]}\",\n", - " f\"n = {n_arr[1]}, sigma_n = {sigma_n_arr[1]}\",\n", - " f\"n = {n_arr[2]}, sigma_n = {sigma_n_arr[2]}\",\n", - " ]\n", - ")\n", + "plt.legend([f\"n = {n_arr[0]}, sigma_n = {sigma_n_arr[0]}\",\n", + " f\"n = {n_arr[1]}, sigma_n = {sigma_n_arr[1]}\",\n", + " f\"n = {n_arr[2]}, sigma_n = {sigma_n_arr[2]}\"])\n", "\n", "plt.show()" ] @@ -107,14 +101,12 @@ "source": [ "import scipy.integrate as integrate\n", "\n", - "# Note that the integral of a product of the same GTOs (i.e. overlap of same GTOs) have square norm of 1\n", + "# Note that the integral of a product of the same GTOs (i.e. overlap of same GTOs) have square norm of 1 \n", "# (i.e. the normalization factor is correct)\n", "n1 = n2 = n_arr[0]\n", "sigma_n1 = sigma_n2 = sigma_n_arr[0]\n", "\n", - "result_identical = np.trapz(\n", - " gto_norm(r_grid, n1, sigma_n1) * gto_norm(r_grid, n2, sigma_n2) * r_grid**2, r_grid\n", - ")\n", + "result_identical = np.trapz(gto_norm(r_grid, n1, sigma_n1) * gto_norm(r_grid, n2, sigma_n2) * r_grid**2, r_grid)\n", "print(\"overlap of identical GTOs\", result_identical)\n", "\n", "# But are not yet orthoganol: Here, we are looking at the overlap of two GTOs\n", @@ -124,10 +116,9 @@ "sigma_n1 = sigma_n_arr[0]\n", "sigma_n2 = sigma_n_arr[1]\n", "\n", - "result_nonidentical = np.trapz(\n", - " gto_norm(r_grid, n1, sigma_n1) * gto_norm(r_grid, n2, sigma_n2) * r_grid**2, r_grid\n", - ")\n", - "print(\"overlap of nonidentical GTOs\", result_nonidentical)" + "result_nonidentical = np.trapz(gto_norm(r_grid, n1, sigma_n1) * gto_norm(r_grid, n2, sigma_n2) * r_grid**2, r_grid)\n", + "print(\"overlap of nonidentical GTOs\", result_nonidentical)\n", + "\n" ] }, { @@ -156,8 +147,7 @@ "outputs": [], "source": [ "def gto(r, n, sigma_n):\n", - " return r**n * np.exp(-(r**2) / (2 * sigma_n**2))\n", - "\n", + " return r**n * np.exp(-r**2 / (2 * sigma_n**2))\n", "\n", "def inverse_matrix_sqrt(matrix: np.array):\n", " \"\"\"\n", @@ -177,10 +167,8 @@ " eva, eve = np.linalg.eigh(matrix)\n", "\n", " if (eva < 0).all():\n", - " raise ValueError(\n", - " \"Matrix is not positive semidefinite. Check that a valid gram matrix is passed.\"\n", - " )\n", - " return eve @ np.diag(1 / np.sqrt(eva)) @ eve.T\n", + " raise ValueError(\"Matrix is not positive semidefinite. Check that a valid gram matrix is passed.\")\n", + " return eve @ np.diag(1/np.sqrt(eva)) @ eve.T\n", "\n", "\n", "def gto_square_norm(n, sigma):\n", @@ -196,7 +184,7 @@ " Returns:\n", " square norm: The square norm of the GTO\n", " \"\"\"\n", - " return 0.5 * sigma ** (2 * n + 3) * gamma(n + 1.5)\n", + " return 0.5 * sigma**(2 * n + 3) * gamma(n + 1.5)\n", "\n", "\n", "def gto_prefactor(n, sigma):\n", @@ -266,30 +254,20 @@ } ], "source": [ - "overlap_matrix = gto_overlap(\n", - " n_arr[:, np.newaxis],\n", - " n_arr[np.newaxis, :],\n", - " sigma_n_arr[:, np.newaxis],\n", - " sigma_n_arr[np.newaxis, :],\n", - ")\n", + "overlap_matrix = gto_overlap(n_arr[:, np.newaxis],\n", + " n_arr[np.newaxis, :],\n", + " sigma_n_arr[:, np.newaxis],\n", + " sigma_n_arr[np.newaxis, :])\n", "orthonormalization_matrix = inverse_matrix_sqrt(overlap_matrix)\n", "\n", "# The original nonorthonormalized basis set is (these aren't normalized either!):\n", - "original_gto = np.array(\n", - " [\n", - " gto(r_grid, n_arr[0], sigma_n_arr[0]),\n", - " gto(r_grid, n_arr[1], sigma_n_arr[1]),\n", - " gto(r_grid, n_arr[2], sigma_n_arr[2]),\n", - " ]\n", - ")\n", + "original_gto = np.array([gto(r_grid, n_arr[0], sigma_n_arr[0]),\n", + " gto(r_grid, n_arr[1], sigma_n_arr[1]),\n", + " gto(r_grid, n_arr[2], sigma_n_arr[2])])\n", "plt.plot(r_grid, original_gto.T)\n", - "plt.legend(\n", - " [\n", - " f\"n = {n_arr[0]}, sigma_n = {sigma_n_arr[0]}\",\n", - " f\"n = {n_arr[1]}, sigma_n = {sigma_n_arr[1]}\",\n", - " f\"n = {n_arr[2]}, sigma_n = {sigma_n_arr[2]}\",\n", - " ]\n", - ")\n", + "plt.legend([f\"n = {n_arr[0]}, sigma_n = {sigma_n_arr[0]}\",\n", + " f\"n = {n_arr[1]}, sigma_n = {sigma_n_arr[1]}\",\n", + " f\"n = {n_arr[2]}, sigma_n = {sigma_n_arr[2]}\"])\n", "\n", "plt.show()\n", "\n", @@ -297,13 +275,9 @@ "orthonormal_gto = orthonormalization_matrix @ original_gto\n", "\n", "plt.plot(r_grid, orthonormal_gto.T)\n", - "plt.legend(\n", - " [\n", - " f\"n = {n_arr[0]}, sigma_n = {sigma_n_arr[0]}\",\n", - " f\"n = {n_arr[1]}, sigma_n = {sigma_n_arr[1]}\",\n", - " f\"n = {n_arr[2]}, sigma_n = {sigma_n_arr[2]}\",\n", - " ]\n", - ")\n", + "plt.legend([f\"n = {n_arr[0]}, sigma_n = {sigma_n_arr[0]}\",\n", + " f\"n = {n_arr[1]}, sigma_n = {sigma_n_arr[1]}\",\n", + " f\"n = {n_arr[2]}, sigma_n = {sigma_n_arr[2]}\"])\n", "plt.show()" ] }, @@ -335,17 +309,13 @@ "\n", "# Two identical functions have a overlap of 1:\n", "\n", - "result_identical = np.trapz(\n", - " orthonormal_gto[0, :] * orthonormal_gto[0, :] * r_grid**2, r_grid\n", - ")\n", + "result_identical = np.trapz(orthonormal_gto[0, :] * orthonormal_gto[0, :] * r_grid**2, r_grid)\n", "print(\"overlap of identical orthonormalized GTOs\", result_identical)\n", "\n", "# Nonidentical functions have an overlap of 0:\n", "\n", - "result_nonidentical = np.trapz(\n", - " orthonormal_gto[0, :] * orthonormal_gto[1, :] * r_grid**2, r_grid\n", - ")\n", - "print(\"overlap of nonidentical orthonormalized GTOs\", result_nonidentical)" + "result_nonidentical = np.trapz(orthonormal_gto[0, :] * orthonormal_gto[1, :] * r_grid**2, r_grid)\n", + "print(\"overlap of nonidentical orthonormalized GTOs\", result_nonidentical)\n" ] }, { diff --git a/notebooks/aniso_descriptor.ipynb b/notebooks/aniso_descriptor.ipynb index 5b956dc..b710d6c 100644 --- a/notebooks/aniso_descriptor.ipynb +++ b/notebooks/aniso_descriptor.ipynb @@ -10,13 +10,13 @@ "import numpy as np\n", "import metatensor\n", "from ase.io import read\n", - "from metatensor import TensorBlock, TensorMap, Labels\n", + "from metatensor import TensorBlock, TensorMap,Labels\n", "from itertools import product\n", "import ase\n", "\n", "from rascaline import NeighborList\n", "\n", - "# from anisotropic_gaussian_moments_expansion import *" + "# from anisotropic_gaussian_moments_expansion import * " ] }, { @@ -41,90 +41,70 @@ " Contains the position vector for the center of the trivariate Gaussian.\n", " - maxdeg: int\n", " Maximum degree for which the moments need to be computed.\n", - "\n", + " \n", " Returns:\n", " - The list of moments defined as\n", " = integral (x^n0 * y^n1 * z^n2) * exp(-0.5*(r-a).T@cov@(r-a)) dxdydz\n", " Note that the term \"moments\" in probability theory are defined for normalized Gaussian distributions.\n", - " Here, we take the Gaussian\n", + " Here, we take the Gaussian \n", " \"\"\"\n", " # Make sure that the provided arrays have the correct dimensions and properties\n", - " assert A.shape == (3, 3), \"Dilation matrix needs to be 3x3\"\n", - " assert np.sum((A - A.T) ** 2) < 1e-14, \"Dilation matrix needs to be symmetric\"\n", - " assert a.shape == (3, 1), \"Center of Gaussian has to be given by a 3-dim. vector\"\n", + " assert A.shape == (3,3), \"Dilation matrix needs to be 3x3\"\n", + " assert np.sum((A-A.T)**2) < 1e-14, \"Dilation matrix needs to be symmetric\"\n", + " assert a.shape == (3,1), \"Center of Gaussian has to be given by a 3-dim. vector\"\n", " assert maxdeg > 0, \"The maximum degree needs to be at least 1\"\n", - " cov = np.linalg.inv(A) # the covariance matrix is the inverse of the matrix A\n", - " global_factor = (2 * np.pi) ** 1.5 / np.sqrt(\n", - " np.linalg.det(A)\n", - " ) # normalization of Gaussian\n", - "\n", + " cov = np.linalg.inv(A) # the covariance matrix is the inverse of the matrix A\n", + " global_factor = (2*np.pi)**1.5 / np.sqrt(np.linalg.det(A)) # normalization of Gaussian\n", + " \n", " # Initialize the array in which to store the moments\n", " # moments[n0, n1, n2] will be set to \n", " # This representation is memory inefficient, since only about 1/3 of the\n", " # array elements will actually be relevant.\n", " # The advantage, however, is the simplicity in later use.\n", - " moments = np.zeros((maxdeg + 1, maxdeg + 1, maxdeg + 1))\n", - "\n", + " moments = np.zeros((maxdeg+1, maxdeg+1, maxdeg+1))\n", + " \n", " # Initialize the first few elements\n", - " moments[0, 0, 0] = 1.0\n", - " moments[1, 0, 0] = a[0] # \n", - " moments[0, 1, 0] = a[1] # \n", - " moments[0, 0, 1] = a[2] # \n", + " moments[0,0,0] = 1.\n", + " moments[1,0,0] = a[0] # \n", + " moments[0,1,0] = a[1] # \n", + " moments[0,0,1] = a[2] # \n", " if maxdeg == 1:\n", " return global_factor * moments\n", - "\n", + " \n", " # Initialize the quadratic elements\n", - " moments[2, 0, 0] = cov[0, 0] + a[0] ** 2\n", - " moments[0, 2, 0] = cov[1, 1] + a[1] ** 2\n", - " moments[0, 0, 2] = cov[2, 2] + a[2] ** 2\n", - " moments[1, 1, 0] = cov[0, 1] + a[0] * a[1]\n", - " moments[0, 1, 1] = cov[1, 2] + a[1] * a[2]\n", - " moments[1, 0, 1] = cov[2, 0] + a[2] * a[0]\n", + " moments[2,0,0] = cov[0,0] + a[0]**2\n", + " moments[0,2,0] = cov[1,1] + a[1]**2\n", + " moments[0,0,2] = cov[2,2] + a[2]**2\n", + " moments[1,1,0] = cov[0,1] + a[0]*a[1]\n", + " moments[0,1,1] = cov[1,2] + a[1]*a[2]\n", + " moments[1,0,1] = cov[2,0] + a[2]*a[0]\n", " if maxdeg == 2:\n", " return global_factor * moments\n", - "\n", + " \n", " # Iterate over all possible exponents to generate all moments\n", " # Instead of iterating over n1, n2 and n3, we iterate over the total degree of the monomials\n", " # which will allow us to simplify certain edge cases.\n", " for deg in range(2, maxdeg):\n", - " for n0 in range(deg + 1):\n", - " for n1 in range(deg + 1 - n0):\n", + " for n0 in range(deg+1):\n", + " for n1 in range(deg+1-n0):\n", " # We consider monomials of degree \"deg\", and generate moments of degree deg+1.\n", " n2 = deg - n0 - n1\n", - "\n", + " \n", " # Run the x-iteration\n", - " moments[n0 + 1, n1, n2] = (\n", - " a[0] * moments[n0, n1, n2]\n", - " + cov[0, 0] * n0 * moments[n0 - 1, n1, n2]\n", - " )\n", - " moments[n0 + 1, n1, n2] += (\n", - " cov[0, 1] * n1 * moments[n0, n1 - 1, n2]\n", - " + cov[0, 2] * n2 * moments[n0, n1, n2 - 1]\n", - " )\n", - "\n", + " moments[n0+1,n1,n2] = a[0]*moments[n0,n1,n2] + cov[0,0]*n0*moments[n0-1,n1,n2]\n", + " moments[n0+1,n1,n2] += cov[0,1]*n1*moments[n0,n1-1,n2] + cov[0,2]*n2*moments[n0,n1,n2-1]\n", + " \n", " # If n0 is equal to zero, we also need the y- and z-iterations\n", " if n0 == 0:\n", " # Run the y-iteration\n", - " moments[n0, n1 + 1, n2] = (\n", - " a[1] * moments[n0, n1, n2]\n", - " + cov[1, 0] * n0 * moments[n0 - 1, n1, n2]\n", - " )\n", - " moments[n0, n1 + 1, n2] += (\n", - " cov[1, 1] * n1 * moments[n0, n1 - 1, n2]\n", - " + cov[1, 2] * n2 * moments[n0, n1, n2 - 1]\n", - " )\n", - "\n", + " moments[n0,n1+1,n2] = a[1]*moments[n0,n1,n2] + cov[1,0]*n0*moments[n0-1,n1,n2]\n", + " moments[n0,n1+1,n2] += cov[1,1]*n1*moments[n0,n1-1,n2] + cov[1,2]*n2*moments[n0,n1,n2-1]\n", + " \n", " if n0 == 0 and n1 == 0:\n", " # Run the z-iteration\n", - " moments[n0, n1, n2 + 1] = (\n", - " a[2] * moments[n0, n1, n2]\n", - " + cov[2, 0] * n0 * moments[n0 - 1, n1, n2]\n", - " )\n", - " moments[n0, n1, n2 + 1] += (\n", - " cov[2, 1] * n1 * moments[n0, n1 - 1, n2]\n", - " + cov[2, 2] * n2 * moments[n0, n1, n2 - 1]\n", - " )\n", - "\n", + " moments[n0,n1,n2+1] = a[2]*moments[n0,n1,n2] + cov[2,0]*n0*moments[n0-1,n1,n2]\n", + " moments[n0,n1,n2+1] += cov[2,1]*n1*moments[n0,n1-1,n2] + cov[2,2]*n2*moments[n0,n1,n2-1]\n", + " \n", " return global_factor * moments" ] }, @@ -136,9 +116,9 @@ "outputs": [], "source": [ "hypers = {\n", - " \"interaction_cutoff\": 4.5, # need to define the neighborlist\n", - " \"A\": np.eye(3), # anisotropy/dilation matrix\n", - " \"maxdeg\": 5, # max degree of expansion\n", + " \"interaction_cutoff\": 4.5, # need to define the neighborlist \n", + " \"A\": np.eye(3),#anisotropy/dilation matrix\n", + " \"maxdeg\":5 # max degree of expansion \n", "}" ] }, @@ -149,12 +129,9 @@ "metadata": {}, "outputs": [], "source": [ - "frames = read(\n", - " \"/Users/jigyasa/scratch/data_papers/data/water/dataset/water_randomized_1000.xyz\",\n", - " \":2\",\n", - ")\n", - "for f in frames:\n", - " f.pbc = False\n", + "frames = read('/Users/jigyasa/scratch/data_papers/data/water/dataset/water_randomized_1000.xyz', ':2')\n", + "for f in frames: \n", + " f.pbc=False\n", "# f.pbc=True\n", "# f.cell = [5,5,5]\n", "# f.center()\n", @@ -168,12 +145,12 @@ "metadata": {}, "outputs": [], "source": [ - "# use rascaline to get the full neighborlist\n", + "#use rascaline to get the full neighborlist \n", "nl = NeighborList(hypers[\"interaction_cutoff\"], True).compute(frames)\n", "\n", - "# nl is a tensormap with keys ('species_first_atom', 'species_second_atom')\n", - "# depending on the cutoff some species pairs may not appear\n", - "# self pairs are not present but in PBC pairs between copies of the same atom are accounted for\n", + "#nl is a tensormap with keys ('species_first_atom', 'species_second_atom')\n", + "#depending on the cutoff some species pairs may not appear \n", + "#self pairs are not present but in PBC pairs between copies of the same atom are accounted for\n", "\n", "# nl.keys_to_properties('species_second_atom')" ] @@ -185,8 +162,8 @@ "metadata": {}, "outputs": [], "source": [ - "sigma = 0.3\n", - "A = hypers[\"A\"] * sigma**2\n", + "sigma =0.3\n", + "A = hypers[\"A\"]*sigma**2\n", "maxdeg = hypers[\"maxdeg\"]" ] }, @@ -208,7 +185,7 @@ } ], "source": [ - "sample_value.reshape((sample_value.shape) + (1,)).shape" + "sample_value.reshape((sample_value.shape)+(1,)).shape" ] }, { @@ -218,40 +195,30 @@ "metadata": {}, "outputs": [], "source": [ - "# accumulate the blocks for the pairwise expansion -\n", - "desc_blocks = []\n", + "#accumulate the blocks for the pairwise expansion - \n", + "desc_blocks=[]\n", "for center_species in global_species:\n", " for neighbor_species in global_species:\n", " if (center_species, neighbor_species) in nl.keys:\n", - " nl_block = nl.block(\n", - " species_first_atom=center_species, species_second_atom=neighbor_species\n", - " )\n", + " nl_block = nl.block(species_first_atom=center_species, species_second_atom=neighbor_species)\n", " desc_block_values = []\n", " for isample, nl_sample in enumerate(nl_block.samples):\n", - " x, y, z = (\n", - " nl_block.values[isample, 0],\n", - " nl_block.values[isample, 1],\n", - " nl_block.values[isample, 2],\n", - " )\n", - " sample_value = compute_moments_inefficient_implementation(\n", - " A, np.array([x, y, z]), maxdeg\n", - " ) # moments for the pair\n", - " # this is a (maxdeg+1, maxdeg+1, maxdeg+1) matrix\n", - " desc_block_values.append(\n", - " sample_value.reshape((sample_value.shape) + (1,))\n", - " )\n", - "\n", + " x,y,z = nl_block.values[isample,0], nl_block.values[isample,1],nl_block.values[isample,2]\n", + " sample_value=compute_moments_inefficient_implementation(A, np.array([x,y,z]), maxdeg) #moments for the pair\n", + " #this is a (maxdeg+1, maxdeg+1, maxdeg+1) matrix\n", + " desc_block_values.append(sample_value.reshape((sample_value.shape)+(1,)))\n", + " \n", "# print(sample_value.shape)\n", "# desc_blocks.append(TensorBlock(values = np.asarray(desc_block_values),\n", "# samples = nl_block.samples,\n", "# components = [Labels(),Labels(),Labels()]\n", "# properties = [Labels([\"dummy\"], [\"0\"])]\n", - "\n", - "\n", + " \n", + " \n", "# )\n", - "\n", + " \n", "# )\n", - "# pair_aniso_desc = TensorMap(nl.keys, desc_blocks)" + "# pair_aniso_desc = TensorMap(nl.keys, desc_blocks)\n" ] }, { @@ -273,45 +240,30 @@ } ], "source": [ - "# To get the final descriptor, we just need to sum over the neighbor species\n", + "# To get the final descriptor, we just need to sum over the neighbor species \n", "\n", "desc_blocks = []\n", "for center_species in global_species:\n", " for neighbor_species in global_species:\n", " if (center_species, neighbor_species) in pair_aniso_desc.keys:\n", - " desc_samples = []\n", - " pair_block = pair_aniso_desc.block(\n", - " species_first_atom=center_species, species_second_atom=neighbor_species\n", - " )\n", + " desc_samples=[]\n", + " pair_block = pair_aniso_desc.block(species_first_atom=center_species, species_second_atom=neighbor_species)\n", " desc_block_values = []\n", - " desc_samples = list(\n", - " product(\n", - " np.unique(block.samples[\"structure\"]),\n", - " np.unique(block.samples[\"center\"]),\n", - " )\n", - " )\n", + " desc_samples = list(product(np.unique(block.samples['structure']), np.unique(block.samples['center'])))\n", " for isample, sample in enumerate(desc_samples):\n", - " sample_idx = [\n", - " idx\n", - " for idx, tup in enumerate(nl_block.samples)\n", - " if tup[\"structure\"] == sample[0] and tup[\"center\"] == sample[1]\n", - " ]\n", - "\n", - " sample_value += desc_block_values.append(\n", - " nl_block.values[sample_idx].sum(axis=0)\n", - " )\n", + " sample_idx = [idx for idx, tup in enumerate(nl_block.samples) if tup['structure']==sample[0] and tup['center']==sample[1]]\n", + " \n", + " sample_value+= desc_block_values.append(nl_block.values[sample_idx].sum(axis=0))\n", " desc_block_values.append(sample_value)\n", "# desc_blocks.append(TensorBlock(values = np.asarray(desc_block_values),\n", "# samples = Labels([\"structure\", \"central_atom\"], desc_samples),\n", "# components = [Labels()]\n", "# properties = [Labels()]\n", - "\n", - "\n", + " \n", + " \n", "# )\n", "\n", - "aniso_desc = TensorMap(\n", - " Labels(\"center_species\", np.asarray(global_species, dtype=int32)), desc_blocks\n", - ")" + "aniso_desc = TensorMap(Labels(\"center_species\", np.asarray(global_species, dtype=int32)), desc_blocks)" ] }, { diff --git a/notebooks/anisotropic_gaussian.ipynb b/notebooks/anisotropic_gaussian.ipynb index e16a3de..0d9028b 100644 --- a/notebooks/anisotropic_gaussian.ipynb +++ b/notebooks/anisotropic_gaussian.ipynb @@ -36,90 +36,70 @@ " Contains the position vector for the center of the trivariate Gaussian.\n", " - maxdeg: int\n", " Maximum degree for which the moments need to be computed.\n", - "\n", + " \n", " Returns:\n", " - The list of moments defined as\n", " = integral (x^n0 * y^n1 * z^n2) * exp(-0.5*(r-a).T@cov@(r-a)) dxdydz\n", " Note that the term \"moments\" in probability theory are defined for normalized Gaussian distributions.\n", - " Here, we take the Gaussian\n", + " Here, we take the Gaussian \n", " \"\"\"\n", " # Make sure that the provided arrays have the correct dimensions and properties\n", - " assert A.shape == (3, 3), \"Dilation matrix needs to be 3x3\"\n", - " assert np.sum((A - A.T) ** 2) < 1e-14, \"Dilation matrix needs to be symmetric\"\n", + " assert A.shape == (3,3), \"Dilation matrix needs to be 3x3\"\n", + " assert np.sum((A-A.T)**2) < 1e-14, \"Dilation matrix needs to be symmetric\"\n", " assert a.shape == (3,), \"Center of Gaussian has to be given by a 3-dim. vector\"\n", " assert maxdeg > 0, \"The maximum degree needs to be at least 1\"\n", - " cov = np.linalg.inv(A) # the covariance matrix is the inverse of the matrix A\n", - " global_factor = (2 * np.pi) ** 1.5 / np.sqrt(\n", - " np.linalg.det(A)\n", - " ) # normalization of Gaussian\n", - "\n", + " cov = np.linalg.inv(A) # the covariance matrix is the inverse of the matrix A\n", + " global_factor = (2*np.pi)**1.5 / np.sqrt(np.linalg.det(A)) # normalization of Gaussian\n", + " \n", " # Initialize the array in which to store the moments\n", " # moments[n0, n1, n2] will be set to \n", " # This representation is memory inefficient, since only about 1/3 of the\n", " # array elements will actually be relevant.\n", " # The advantage, however, is the simplicity in later use.\n", - " moments = np.zeros((maxdeg + 1, maxdeg + 1, maxdeg + 1))\n", - "\n", + " moments = np.zeros((maxdeg+1, maxdeg+1, maxdeg+1))\n", + " \n", " # Initialize the first few elements\n", - " moments[0, 0, 0] = 1.0\n", - " moments[1, 0, 0] = a[0] # \n", - " moments[0, 1, 0] = a[1] # \n", - " moments[0, 0, 1] = a[2] # \n", + " moments[0,0,0] = 1.\n", + " moments[1,0,0] = a[0] # \n", + " moments[0,1,0] = a[1] # \n", + " moments[0,0,1] = a[2] # \n", " if maxdeg == 1:\n", " return global_factor * moments\n", - "\n", + " \n", " # Initialize the quadratic elements\n", - " moments[2, 0, 0] = cov[0, 0] + a[0] ** 2\n", - " moments[0, 2, 0] = cov[1, 1] + a[1] ** 2\n", - " moments[0, 0, 2] = cov[2, 2] + a[2] ** 2\n", - " moments[1, 1, 0] = cov[0, 1] + a[0] * a[1]\n", - " moments[0, 1, 1] = cov[1, 2] + a[1] * a[2]\n", - " moments[1, 0, 1] = cov[2, 0] + a[2] * a[0]\n", + " moments[2,0,0] = cov[0,0] + a[0]**2\n", + " moments[0,2,0] = cov[1,1] + a[1]**2\n", + " moments[0,0,2] = cov[2,2] + a[2]**2\n", + " moments[1,1,0] = cov[0,1] + a[0]*a[1]\n", + " moments[0,1,1] = cov[1,2] + a[1]*a[2]\n", + " moments[1,0,1] = cov[2,0] + a[2]*a[0]\n", " if maxdeg == 2:\n", " return global_factor * moments\n", - "\n", + " \n", " # Iterate over all possible exponents to generate all moments\n", " # Instead of iterating over n1, n2 and n3, we iterate over the total degree of the monomials\n", " # which will allow us to simplify certain edge cases.\n", " for deg in range(2, maxdeg):\n", - " for n0 in range(deg + 1):\n", - " for n1 in range(deg + 1 - n0):\n", + " for n0 in range(deg+1):\n", + " for n1 in range(deg+1-n0):\n", " # We consider monomials of degree \"deg\", and generate moments of degree deg+1.\n", " n2 = deg - n0 - n1\n", - "\n", + " \n", " # Run the x-iteration\n", - " moments[n0 + 1, n1, n2] = (\n", - " a[0] * moments[n0, n1, n2]\n", - " + cov[0, 0] * n0 * moments[n0 - 1, n1, n2]\n", - " )\n", - " moments[n0 + 1, n1, n2] += (\n", - " cov[0, 1] * n1 * moments[n0, n1 - 1, n2]\n", - " + cov[0, 2] * n2 * moments[n0, n1, n2 - 1]\n", - " )\n", - "\n", + " moments[n0+1,n1,n2] = a[0]*moments[n0,n1,n2] + cov[0,0]*n0*moments[n0-1,n1,n2]\n", + " moments[n0+1,n1,n2] += cov[0,1]*n1*moments[n0,n1-1,n2] + cov[0,2]*n2*moments[n0,n1,n2-1]\n", + " \n", " # If n0 is equal to zero, we also need the y- and z-iterations\n", " if n0 == 0:\n", " # Run the y-iteration\n", - " moments[n0, n1 + 1, n2] = (\n", - " a[1] * moments[n0, n1, n2]\n", - " + cov[1, 0] * n0 * moments[n0 - 1, n1, n2]\n", - " )\n", - " moments[n0, n1 + 1, n2] += (\n", - " cov[1, 1] * n1 * moments[n0, n1 - 1, n2]\n", - " + cov[1, 2] * n2 * moments[n0, n1, n2 - 1]\n", - " )\n", - "\n", + " moments[n0,n1+1,n2] = a[1]*moments[n0,n1,n2] + cov[1,0]*n0*moments[n0-1,n1,n2]\n", + " moments[n0,n1+1,n2] += cov[1,1]*n1*moments[n0,n1-1,n2] + cov[1,2]*n2*moments[n0,n1,n2-1]\n", + " \n", " if n0 == 0 and n1 == 0:\n", " # Run the z-iteration\n", - " moments[n0, n1, n2 + 1] = (\n", - " a[2] * moments[n0, n1, n2]\n", - " + cov[2, 0] * n0 * moments[n0 - 1, n1, n2]\n", - " )\n", - " moments[n0, n1, n2 + 1] += (\n", - " cov[2, 1] * n1 * moments[n0, n1 - 1, n2]\n", - " + cov[2, 2] * n2 * moments[n0, n1, n2 - 1]\n", - " )\n", - "\n", + " moments[n0,n1,n2+1] = a[2]*moments[n0,n1,n2] + cov[2,0]*n0*moments[n0-1,n1,n2]\n", + " moments[n0,n1,n2+1] += cov[2,1]*n1*moments[n0,n1-1,n2] + cov[2,2]*n2*moments[n0,n1,n2-1]\n", + " \n", " return global_factor * moments" ] }, @@ -153,23 +133,23 @@ " - a: center\n", " - maxdeg: int\n", " Maximum degree for which the moments need to be computed.\n", - "\n", + " \n", " Returns:\n", " - A numpy array of size (maxdeg+1, ) containing the moments defined as\n", " = integral x^n exp(-A(x-a)^2/2) dx\n", " \"\"\"\n", " assert maxdeg > 0\n", - " moments = np.zeros((maxdeg + 1,))\n", - " moments[0] = np.sqrt(2 * np.pi / A)\n", + " moments = np.zeros((maxdeg+1, ))\n", + " moments[0] = np.sqrt(2*np.pi/A)\n", " moments[1] = a * moments[0]\n", - "\n", + " \n", " # If maxdeg = 1, there is nothing more to do\n", " if maxdeg == 1:\n", " return moments\n", - "\n", + " \n", " for deg in range(1, maxdeg):\n", - " moments[deg + 1] = a * moments[deg] + deg * moments[deg - 1] / A\n", - "\n", + " moments[deg+1] = a*moments[deg] + deg*moments[deg-1] / A\n", + " \n", " return moments" ] }, @@ -183,9 +163,7 @@ "# Define function to compute all moments for a diagonal dilation matrix.\n", "# The implementation focuses on conceptual simplicity, while sacrifizing\n", "# memory efficiency.\n", - "def compute_moments_diagonal_inefficient_implementation(\n", - " principcal_components, a, maxdeg\n", - "):\n", + "def compute_moments_diagonal_inefficient_implementation(principcal_components, a, maxdeg):\n", " \"\"\"\n", " Parameters:\n", " - principal_components: np.ndarray of shape (3,)\n", @@ -194,34 +172,34 @@ " Contains the information about the center of the trivariate Gaussian.\n", " - maxdeg: int\n", " Maximum degree for which the moments need to be computed.\n", - "\n", + " \n", " Returns:\n", " - The list of moments defined as\n", " = integral (x^n0 * y^n1 * z^n2) * exp(-0.5*(r-a).T@cov@(r-a)) dxdydz\n", " Note that the term \"moments\" in probability theory are defined for normalized Gaussian distributions.\n", - " Here, we take the Gaussian\n", + " Here, we take the Gaussian \n", " \"\"\"\n", " # Initialize the array in which to store the moments\n", " # moments[n0, n1, n2] will be set to \n", " # This representation is very inefficient, since only about 1/6 of the\n", " # array elements will actually be relevant.\n", " # The advantage, however, is the simplicity in later use.\n", - " moments = np.zeros((maxdeg + 1, maxdeg + 1, maxdeg + 1))\n", - "\n", + " moments = np.zeros((maxdeg+1, maxdeg+1, maxdeg+1))\n", + " \n", " # Precompute the single variable moments in x- y- and z-directions:\n", " moments_x = compute_moments_single_variable(principal_components[0], a[0], maxdeg)\n", " moments_y = compute_moments_single_variable(principal_components[1], a[1], maxdeg)\n", " moments_z = compute_moments_single_variable(principal_components[2], a[2], maxdeg)\n", "\n", " # Compute values for all relevant components for which the monomial degree is <= maxdeg\n", - " for n0 in range(maxdeg + 1):\n", - " for n1 in range(maxdeg + 1):\n", - " for n2 in range(maxdeg + 1):\n", + " for n0 in range(maxdeg+1):\n", + " for n1 in range(maxdeg+1):\n", + " for n2 in range(maxdeg+1):\n", " # Make sure that the degree is not above the maximal degree\n", " deg = n0 + n1 + n2\n", " if deg > maxdeg:\n", " continue\n", - "\n", + " \n", " # If not, the moment is a product of the x- y- and z-integrals\n", " moments[n0, n1, n2] = moments_x[n0] * moments_y[n1] * moments_z[n2]\n", " return moments" @@ -251,9 +229,9 @@ "outputs": [], "source": [ "sigma = 0.32\n", - "a = 0.0\n", + "a = 0.\n", "maxdeg = 5\n", - "A = 1 / sigma**2\n", + "A = 1/sigma**2\n", "moments_single = compute_moments_single_variable(A, a, maxdeg)" ] }, @@ -264,12 +242,12 @@ "metadata": {}, "outputs": [], "source": [ - "exact_values = np.zeros((maxdeg + 1,))\n", - "for deg in range(maxdeg + 1):\n", + "exact_values = np.zeros((maxdeg+1,))\n", + "for deg in range(maxdeg+1):\n", " exact_value = 0\n", " if deg % 2 == 0:\n", " neff = (deg + 1) / 2\n", - " exact_value = (2 * sigma**2) ** neff * gamma(neff)\n", + " exact_value = (2 * sigma**2)**neff * gamma(neff)\n", " exact_values[deg] = exact_value" ] }, @@ -280,7 +258,7 @@ "metadata": {}, "outputs": [], "source": [ - "assert_allclose(exact_values, moments_single, atol=1e-15)" + "assert_allclose(exact_values, moments_single,atol=1e-15)" ] }, { @@ -299,7 +277,7 @@ "outputs": [], "source": [ "sigma = 0.23\n", - "A = 1 / sigma**2\n", + "A = 1/sigma**2\n", "a = 0.5\n", "maxdeg = 5\n", "moments_single = compute_moments_single_variable(A, a, maxdeg)" @@ -314,25 +292,25 @@ "source": [ "def test_non_centered_moments(A, a, maxdeg):\n", " # Compute the exact moments for the centered moments\n", - " centered_moments = np.zeros((maxdeg + 1,))\n", - " for deg in range(maxdeg + 1):\n", + " centered_moments = np.zeros((maxdeg+1,))\n", + " for deg in range(maxdeg+1):\n", " exact_value = 0\n", " if deg % 2 == 0:\n", " neff = (deg + 1) / 2\n", - " exact_value = (2 * sigma**2) ** neff * gamma(neff)\n", + " exact_value = (2 * sigma**2)**neff * gamma(neff)\n", " centered_moments[deg] = exact_value\n", - "\n", + " \n", " # Compute the moments from the binomial theorem\n", - " moments = np.zeros((maxdeg + 1,))\n", - " for deg in range(maxdeg + 1):\n", + " moments = np.zeros((maxdeg+1,))\n", + " for deg in range(maxdeg+1):\n", " moments[deg] += centered_moments[deg]\n", - "\n", + " \n", " # Get the correction from the centered moment\n", " for k in range(deg):\n", - " moments[deg] -= comb(deg, k) * (-a) ** (deg - k) * moments[k]\n", - "\n", + " moments[deg] -= comb(deg, k) * (-a)**(deg-k) * moments[k]\n", + " \n", " moments_from_code = compute_moments_single_variable(A, a, maxdeg)\n", - "\n", + " \n", " assert_allclose(moments_from_code, moments)" ] }, @@ -359,15 +337,13 @@ "metadata": {}, "outputs": [], "source": [ - "principal_components = np.array([2.8, 0.4, 1.1])\n", + "principal_components = np.array([2.8,0.4,1.1])\n", "A = np.diag(principal_components)\n", "a = np.array([3.1, -2.3, 5.92])\n", - "# a *= 0\n", + "#a *= 0\n", "maxdeg = 3\n", "moments_general = compute_moments_inefficient_implementation(A, a, maxdeg)\n", - "moments_diagonal = compute_moments_diagonal_inefficient_implementation(\n", - " principal_components, a, maxdeg\n", - ")" + "moments_diagonal = compute_moments_diagonal_inefficient_implementation(principal_components, a, maxdeg)" ] }, { @@ -378,41 +354,39 @@ "outputs": [], "source": [ "def get_exact_moments(A, a, maxdeg=3):\n", - " global_factor = (2 * np.pi) ** 1.5 / np.sqrt(np.linalg.det(A))\n", - " assert maxdeg in [1, 2, 3]\n", - "\n", - " moments_exact = np.zeros((maxdeg + 1, maxdeg + 1, maxdeg + 1))\n", - " moments_exact[0, 0, 0] = 1.0\n", + " global_factor = (2*np.pi)**1.5 / np.sqrt(np.linalg.det(A))\n", + " assert maxdeg in [1,2,3]\n", + " \n", + " moments_exact = np.zeros((maxdeg+1, maxdeg+1, maxdeg+1))\n", + " moments_exact[0,0,0] = 1.\n", " # Exact expressions for degree 1\n", - " moments_exact[1, 0, 0] = a[0]\n", - " moments_exact[0, 1, 0] = a[1]\n", - " moments_exact[0, 0, 1] = a[2]\n", + " moments_exact[1,0,0] = a[0]\n", + " moments_exact[0,1,0] = a[1]\n", + " moments_exact[0,0,1] = a[2]\n", " if maxdeg == 1:\n", " return global_factor * moments_exact\n", "\n", " # Exact expressions for degree 2\n", - " moments_exact[2, 0, 0] = cov[0, 0] + a[0] ** 2\n", - " moments_exact[0, 2, 0] = cov[1, 1] + a[1] ** 2\n", - " moments_exact[0, 0, 2] = cov[2, 2] + a[2] ** 2\n", - " moments_exact[1, 1, 0] = a[0] * a[1]\n", - " moments_exact[0, 1, 1] = a[1] * a[2]\n", - " moments_exact[1, 0, 1] = a[0] * a[2]\n", + " moments_exact[2,0,0] = cov[0,0] + a[0]**2\n", + " moments_exact[0,2,0] = cov[1,1] + a[1]**2\n", + " moments_exact[0,0,2] = cov[2,2] + a[2]**2\n", + " moments_exact[1,1,0] = a[0]*a[1]\n", + " moments_exact[0,1,1] = a[1]*a[2]\n", + " moments_exact[1,0,1] = a[0]*a[2]\n", " if maxdeg == 2:\n", " return global_factor * moments_exact\n", "\n", " # Exact expressions for degree 3\n", - " moments_exact[3, 0, 0] = 3 * a[0] * cov[0, 0] + a[0] ** 3\n", - " moments_exact[0, 3, 0] = 3 * a[1] * cov[1, 1] + a[1] ** 3\n", - " moments_exact[0, 0, 3] = 3 * a[2] * cov[2, 2] + a[2] ** 3\n", - " moments_exact[2, 1, 0] = a[1] * (cov[0, 0] + a[0] ** 2) + 2 * a[0] * cov[0, 1]\n", - " moments_exact[2, 0, 1] = a[2] * (cov[0, 0] + a[0] ** 2) + 2 * a[0] * cov[0, 2]\n", - " moments_exact[1, 2, 0] = a[0] * (cov[1, 1] + a[1] ** 2) + 2 * a[1] * cov[1, 0]\n", - " moments_exact[0, 2, 1] = a[2] * (cov[1, 1] + a[1] ** 2) + 2 * a[1] * cov[1, 2]\n", - " moments_exact[1, 0, 2] = a[0] * (cov[2, 2] + a[2] ** 2) + 2 * a[2] * cov[2, 0]\n", - " moments_exact[0, 1, 2] = a[1] * (cov[2, 2] + a[2] ** 2) + 2 * a[2] * cov[2, 1]\n", - " moments_exact[1, 1, 1] = (\n", - " a[0] * a[1] * a[2] + a[0] * cov[1, 2] + a[1] * cov[0, 2] + a[2] * cov[0, 1]\n", - " )\n", + " moments_exact[3,0,0] = 3*a[0]*cov[0,0] + a[0]**3\n", + " moments_exact[0,3,0] = 3*a[1]*cov[1,1] + a[1]**3\n", + " moments_exact[0,0,3] = 3*a[2]*cov[2,2] + a[2]**3\n", + " moments_exact[2,1,0] = a[1]*(cov[0,0] + a[0]**2) + 2*a[0]*cov[0,1]\n", + " moments_exact[2,0,1] = a[2]*(cov[0,0] + a[0]**2) + 2*a[0]*cov[0,2]\n", + " moments_exact[1,2,0] = a[0]*(cov[1,1] + a[1]**2) + 2*a[1]*cov[1,0]\n", + " moments_exact[0,2,1] = a[2]*(cov[1,1] + a[1]**2) + 2*a[1]*cov[1,2]\n", + " moments_exact[1,0,2] = a[0]*(cov[2,2] + a[2]**2) + 2*a[2]*cov[2,0]\n", + " moments_exact[0,1,2] = a[1]*(cov[2,2] + a[2]**2) + 2*a[2]*cov[2,1]\n", + " moments_exact[1,1,1] = a[0]*a[1]*a[2] + a[0]*cov[1,2] + a[1]*cov[0,2] + a[2]*cov[0,1]\n", " if maxdeg == 3:\n", " return global_factor * moments_exact" ] @@ -424,36 +398,34 @@ "metadata": {}, "outputs": [], "source": [ - "moments_exact = np.zeros((4, 4, 4))\n", - "moments_exact[0, 0, 0] = 1.0\n", + "moments_exact = np.zeros((4,4,4))\n", + "moments_exact[0,0,0] = 1.\n", "# Exact expressions for degree 1\n", - "moments_exact[1, 0, 0] = a[0]\n", - "moments_exact[0, 1, 0] = a[1]\n", - "moments_exact[0, 0, 1] = a[2]\n", + "moments_exact[1,0,0] = a[0]\n", + "moments_exact[0,1,0] = a[1]\n", + "moments_exact[0,0,1] = a[2]\n", "\n", "# Exact expressions for degree 2\n", - "moments_exact[2, 0, 0] = cov[0, 0] + a[0] ** 2\n", - "moments_exact[0, 2, 0] = cov[1, 1] + a[1] ** 2\n", - "moments_exact[0, 0, 2] = cov[2, 2] + a[2] ** 2\n", - "moments_exact[1, 1, 0] = a[0] * a[1]\n", - "moments_exact[0, 1, 1] = a[1] * a[2]\n", - "moments_exact[1, 0, 1] = a[0] * a[2]\n", + "moments_exact[2,0,0] = cov[0,0] + a[0]**2\n", + "moments_exact[0,2,0] = cov[1,1] + a[1]**2\n", + "moments_exact[0,0,2] = cov[2,2] + a[2]**2\n", + "moments_exact[1,1,0] = a[0]*a[1]\n", + "moments_exact[0,1,1] = a[1]*a[2]\n", + "moments_exact[1,0,1] = a[0]*a[2]\n", "\n", "# Exact expressions for degree 3\n", - "moments_exact[3, 0, 0] = 3 * a[0] * cov[0, 0] + a[0] ** 3\n", - "moments_exact[0, 3, 0] = 3 * a[1] * cov[1, 1] + a[1] ** 3\n", - "moments_exact[0, 0, 3] = 3 * a[2] * cov[2, 2] + a[2] ** 3\n", - "moments_exact[2, 1, 0] = a[1] * (cov[0, 0] + a[0] ** 2) + 2 * a[0] * cov[0, 1]\n", - "moments_exact[2, 0, 1] = a[2] * (cov[0, 0] + a[0] ** 2) + 2 * a[0] * cov[0, 2]\n", - "moments_exact[1, 2, 0] = a[0] * (cov[1, 1] + a[1] ** 2) + 2 * a[1] * cov[1, 0]\n", - "moments_exact[0, 2, 1] = a[2] * (cov[1, 1] + a[1] ** 2) + 2 * a[1] * cov[1, 2]\n", - "moments_exact[1, 0, 2] = a[0] * (cov[2, 2] + a[2] ** 2) + 2 * a[2] * cov[2, 0]\n", - "moments_exact[0, 1, 2] = a[1] * (cov[2, 2] + a[2] ** 2) + 2 * a[2] * cov[2, 1]\n", - "moments_exact[1, 1, 1] = (\n", - " a[0] * a[1] * a[2] + a[0] * cov[1, 2] + a[1] * cov[0, 2] + a[2] * cov[0, 1]\n", - ")\n", + "moments_exact[3,0,0] = 3*a[0]*cov[0,0] + a[0]**3\n", + "moments_exact[0,3,0] = 3*a[1]*cov[1,1] + a[1]**3\n", + "moments_exact[0,0,3] = 3*a[2]*cov[2,2] + a[2]**3\n", + "moments_exact[2,1,0] = a[1]*(cov[0,0] + a[0]**2) + 2*a[0]*cov[0,1]\n", + "moments_exact[2,0,1] = a[2]*(cov[0,0] + a[0]**2) + 2*a[0]*cov[0,2]\n", + "moments_exact[1,2,0] = a[0]*(cov[1,1] + a[1]**2) + 2*a[1]*cov[1,0]\n", + "moments_exact[0,2,1] = a[2]*(cov[1,1] + a[1]**2) + 2*a[1]*cov[1,2]\n", + "moments_exact[1,0,2] = a[0]*(cov[2,2] + a[2]**2) + 2*a[2]*cov[2,0]\n", + "moments_exact[0,1,2] = a[1]*(cov[2,2] + a[2]**2) + 2*a[2]*cov[2,1]\n", + "moments_exact[1,1,1] = a[0]*a[1]*a[2] + a[0]*cov[1,2] + a[1]*cov[0,2] + a[2]*cov[0,1]\n", "\n", - "moments_exact *= (2 * np.pi) ** 1.5 / np.sqrt(np.prod(principal_components))" + "moments_exact *= (2*np.pi)**1.5 / np.sqrt(np.prod(principal_components))" ] }, { @@ -489,9 +461,7 @@ "a0 = 3.2\n", "a = a0 * np.ones((3,))\n", "maxdeg = 8\n", - "moments_diagonal = compute_moments_diagonal_inefficient_implementation(\n", - " principal_components, a, maxdeg\n", - ")" + "moments_diagonal = compute_moments_diagonal_inefficient_implementation(principal_components, a, maxdeg)" ] }, { @@ -502,25 +472,16 @@ "outputs": [], "source": [ "eps = 1e-12\n", - "for n0 in range(maxdeg + 1):\n", - " for n1 in range(maxdeg + 1):\n", - " for n2 in range(maxdeg + 1):\n", + "for n0 in range(maxdeg+1):\n", + " for n1 in range(maxdeg+1):\n", + " for n2 in range(maxdeg+1):\n", " deg = n0 + n1 + n2\n", " if deg > maxdeg:\n", " assert moments_diagonal[n0, n1, n2] == 0\n", " else:\n", - " assert (\n", - " abs(moments_diagonal[n0, n1, n2] - moments_diagonal[n1, n0, n2])\n", - " < eps\n", - " )\n", - " assert (\n", - " abs(moments_diagonal[n0, n1, n2] - moments_diagonal[n2, n1, n0])\n", - " < eps\n", - " )\n", - " assert (\n", - " abs(moments_diagonal[n0, n1, n2] - moments_diagonal[n0, n2, n1])\n", - " < eps\n", - " )" + " assert abs(moments_diagonal[n0,n1,n2]-moments_diagonal[n1,n0,n2]) < eps\n", + " assert abs(moments_diagonal[n0,n1,n2]-moments_diagonal[n2,n1,n0]) < eps\n", + " assert abs(moments_diagonal[n0,n1,n2]-moments_diagonal[n0,n2,n1]) < eps" ] }, { @@ -546,14 +507,12 @@ "metadata": {}, "outputs": [], "source": [ - "principal_components = np.array([2.8, 0.4, 1.1])\n", + "principal_components = np.array([2.8,0.4,1.1])\n", "A = np.diag(principal_components)\n", "a = np.array([3.1, -2.3, 5.92])\n", "maxdeg = 3\n", "moments_general = compute_moments_inefficient_implementation(A, a, maxdeg)\n", - "moments_diagonal = compute_moments_diagonal_inefficient_implementation(\n", - " principal_components, a, maxdeg\n", - ")\n", + "moments_diagonal = compute_moments_diagonal_inefficient_implementation(principal_components, a, maxdeg)\n", "assert_allclose(moments_general, moments_diagonal, rtol=1e-15, atol=3e-16)" ] }, diff --git a/notebooks/anisotropic_representations.ipynb b/notebooks/anisotropic_representations.ipynb index 70b7201..d79a71a 100644 --- a/notebooks/anisotropic_representations.ipynb +++ b/notebooks/anisotropic_representations.ipynb @@ -25,50 +25,36 @@ "from math import comb\n", "from anisoap.utils import monomial_iterator\n", "\n", - "\n", - "# We are implementing iterations of the form R_{l} = prefact_minus1* z * R_{l-1} + prefact_minus2* r^2 * R_{l-2}\n", + "#We are implementing iterations of the form R_{l} = prefact_minus1* z * R_{l-1} + prefact_minus2* r^2 * R_{l-2}\n", "def prefact_minus1(l):\n", " \"\"\"\n", " Parameters:\n", - " - l: int\n", - "\n", + " - l: int \n", + " \n", " Returns:\n", - " - A list of size (2*l -1) corresponding to the prefactor that multiplies the\n", - "\n", - " For m in [-l, -l+2, ..., l], compute the factor as :\n", - " sqrt(factorial(l+1-m)/ factorial(l+1+m)) sqrt(factorial(l+m)/ factorial(l-m)) (2*l+1)/(l+1-m)\n", - "\n", + " - A list of size (2*l -1) corresponding to the prefactor that multiplies the \n", + " \n", + " For m in [-l, -l+2, ..., l], compute the factor as : \n", + " sqrt(factorial(l+1-m)/ factorial(l+1+m)) sqrt(factorial(l+m)/ factorial(l-m)) (2*l+1)/(l+1-m) \n", + " \n", " \"\"\"\n", - " m = np.arange(-l, l + 1)\n", - " return (\n", - " np.sqrt(factorial(l + 1 - m) / factorial(l + 1 + m))\n", - " * np.sqrt(factorial(l + m) / factorial(l - m))\n", - " * (2 * l + 1)\n", - " / (l + 1 - m)\n", - " )\n", - "\n", - "\n", + " m=np.arange(-l,l+1)\n", + " return np.sqrt(factorial(l+1-m)/factorial(l+1+m)) * np.sqrt(factorial(l+m)/factorial(l-m)) * (2*l+1)/(l+1-m)\n", + " \n", "def prefact_minus2(l):\n", " \"\"\"\n", - " For m in [-l+1, -l+2, ..., l-1], compute the factor as :\n", - " sqrt(factorial(l+1-m)/ factorial(l+1+m)) sqrt(factorial(l-1+m)/ factorial(l-1-m)) (l+m)/(l-m+1)\n", + " For m in [-l+1, -l+2, ..., l-1], compute the factor as : \n", + " sqrt(factorial(l+1-m)/ factorial(l+1+m)) sqrt(factorial(l-1+m)/ factorial(l-1-m)) (l+m)/(l-m+1) \n", " \"\"\"\n", - " m = np.arange(-l + 1, l)\n", - " return (\n", - " -1\n", - " * np.sqrt(factorial(l + 1 - m) / factorial(l + 1 + m))\n", - " * np.sqrt(factorial(l - 1 + m) / factorial(l - 1 - m))\n", - " * (l + m)\n", - " / (l + 1 - m)\n", - " )\n", - "\n", + " m=np.arange(-l+1,l)\n", + " return -1* np.sqrt(factorial(l+1-m)/factorial(l+1+m)) * np.sqrt(factorial(l-1+m)/factorial(l-1-m)) * (l+m)/(l+1-m)\n", "\n", "def binom(n, k):\n", " \"\"\"\n", " returns binomial coefficient nCk = math.factorial(n) / (math.factorial(k) * math.factorial(n - k))\n", - " We use math.comb utility to compute this\n", + " We use math.comb utility to compute this \n", " \"\"\"\n", - " return comb(n, k)" + " return comb(n, k)\n" ] }, { @@ -83,13 +69,13 @@ "def spherical_to_cartesian2(lmax, num_ns):\n", " \"\"\"\n", " Parameters:\n", - " - lmax: int\n", - "\n", + " - lmax: int \n", + " \n", " - num_ns: list of ints\n", - "\n", + " \n", " Returns:\n", " - A list with as many entries as in num_ns (corresponding to l=0,1,... lmax+1). Each corresponding entry is an\n", - " array of size (2*l+1, num_ns[l], maxdeg, maxdeg, maxdeg)\n", + " array of size (2*l+1, num_ns[l], maxdeg, maxdeg, maxdeg) \n", " where maxdeg = l + 2* max(num_ns[l]) and the last three axes correspond to n0, n1, n2 respectively such that\n", " the entries of the array form the coefficient of the x^n0 y^n1 z^n2 monomial in the expansion of R_l^m\n", " \"\"\"\n", @@ -101,75 +87,71 @@ " # Usage T_l[m,n,n0,n1,n2]\n", " T = []\n", " for l, num_n in enumerate(num_ns):\n", - " maxdeg = l + 2 * (num_n - 1)\n", - " T_l = np.zeros((2 * l + 1, num_n, maxdeg + 1, maxdeg + 1, maxdeg + 1))\n", + " maxdeg = l + 2*(num_n-1)\n", + " T_l = np.zeros((2*l+1,num_n,maxdeg+1,maxdeg+1,maxdeg+1))\n", " T.append(T_l)\n", "\n", " # Initialize array in which to store all coefficients for each l\n", " # Usage T_l[m,n,n0,n1,n2]\n", - " T[0][0, 0, 0, 0, 0] = 1\n", - " for l in range(1, lmax + 1):\n", - " prefact = np.sqrt(2) * factorial2(2 * l - 1) / np.sqrt(factorial(2 * l))\n", - " for k in range(l // 2 + 1):\n", - " n1 = 2 * k\n", - " n0 = l - n1\n", - " T[l][2 * l, 0, n0, n1, 0] = binom(l, n1) * (-1) ** k\n", - " for k in range((l - 1) // 2 + 1):\n", - " n1 = 2 * k + 1\n", - " n0 = l - n1\n", - " T[l][0, 0, n0, n1, 0] = binom(l, n1) * (-1) ** k\n", - " T[l] *= prefact\n", + " T[0][0,0,0,0,0] = 1\n", + " for l in range(1,lmax+1):\n", + " prefact = np.sqrt(2) * factorial2(2*l-1) / np.sqrt(factorial(2*l))\n", + " for k in range(l//2+1):\n", + " n1 = 2*k\n", + " n0 = l-n1\n", + " T[l][2*l,0, n0, n1,0] = binom(l, n1) *(-1)**k \n", + " for k in range((l-1)//2+1):\n", + " n1 = 2*k+1\n", + " n0 = l-n1\n", + " T[l][0,0,n0,n1,0] = binom(l, n1) *(-1)**k\n", + " T[l]*= prefact\n", "\n", " # Run iteration over (l,m) to generate all coefficients for n=0.\n", - " for l in range(1, lmax + 1):\n", + " for l in range(1, lmax+1):\n", " deg = l\n", " myiter = iter(monomial_iterator.TrivariateMonomialIndices(deg))\n", - " for idx, n0, n1, n2 in myiter:\n", + " for idx,n0,n1,n2 in myiter:\n", " print(l)\n", - " a = prefact_minus1(l - 1) # length 2l+1 due to m dependence\n", - " b = prefact_minus2(l - 1) # length 2l+1 due to m dependence\n", - "\n", - " # (-l+1)+2: (l+1) -2 gets contributions from T[l-1]\n", - " if n0 - 2 >= 0:\n", - " print(\"n0\", l)\n", - " T[l][2 : 2 * l - 1, 0, n0, n1, n2] += b * T[l - 2][:, 0, n0 - 2, n1, n2]\n", - " if n1 - 2 >= 0:\n", - " print(\"n1\", l)\n", - " T[l][2 : 2 * l - 1, 0, n0, n1, n2] += b * T[l - 2][:, 0, n0, n1 - 2, n2]\n", - " if n2 - 2 >= 0:\n", - " print(\"n2\", l)\n", - " T[l][2 : 2 * l - 1, 0, n0, n1, n2] += b * T[l - 2][:, 0, n0, n1, n2 - 2]\n", - " # (-l+1)+1: (l+1) -1 gets contributions from T[l]\n", - " if n2 - 1 >= 0:\n", - " print(\"n2>1\", l)\n", - " print(\n", - " T[l][1 : 2 * l, 0, n0, n1, n2].shape,\n", - " a.shape,\n", - " T[l - 1][:, 0, n0, n1, n2 - 1].shape,\n", - " )\n", - " T[l][1 : 2 * l, 0, n0, n1, n2] += a * T[l - 1][:, 0, n0, n1, n2 - 1]\n", - " # a's length needs to be fixed\n", - "\n", + " a = prefact_minus1(l-1) # length 2l+1 due to m dependence\n", + " b = prefact_minus2(l-1) # length 2l+1 due to m dependence\n", + " \n", + " #(-l+1)+2: (l+1) -2 gets contributions from T[l-1]\n", + " if n0-2>=0:\n", + " print(\"n0\",l)\n", + " T[l][2:2*l-1,0,n0,n1,n2] += b * T[l-2][:,0,n0-2,n1,n2]\n", + " if n1-2>=0:\n", + " print(\"n1\",l)\n", + " T[l][2:2*l-1,0,n0,n1,n2] += b * T[l-2][:,0,n0,n1-2,n2]\n", + " if n2-2>=0:\n", + " print(\"n2\",l)\n", + " T[l][2:2*l-1,0,n0,n1,n2] += b * T[l-2][:,0,n0,n1,n2-2]\n", + " #(-l+1)+1: (l+1) -1 gets contributions from T[l]\n", + " if n2-1>=0:\n", + " print(\"n2>1\",l)\n", + " print(T[l][1:2*l,0,n0,n1,n2].shape, a.shape,T[l-1][:,0,n0,n1,n2-1].shape )\n", + " T[l][1:2*l,0,n0,n1,n2] += a * T[l-1][:,0,n0,n1,n2-1]\n", + "# a's length needs to be fixed \n", + " \n", " # Run the iteration over n\n", - " # B_{n+1,lm} = r^2 B_{nlm} = (x^2+y^2+z^2)B_{nlm}\n", - " # T^{n+1,lm}_{n_0+2,n_1,n_2} += T^{n,lm}_{n_0,n_1n_2}\n", - " # T^{n+1,lm}_{n_0,n_1+2,n_2} += T^{n,lm}_{n_0,n_1n_2}\n", - " # T^{n+1,lm}_{n_0,n_1,n_2+2} += T^{n,lm}_{n_0,n_1n_2}\n", - " for l in range(lmax + 1):\n", - " for n in range(1, num_ns[l]):\n", - " deg = l + 2 * n # degree of polynomial\n", + "# B_{n+1,lm} = r^2 B_{nlm} = (x^2+y^2+z^2)B_{nlm}\n", + "# T^{n+1,lm}_{n_0+2,n_1,n_2} += T^{n,lm}_{n_0,n_1n_2}\n", + "# T^{n+1,lm}_{n_0,n_1+2,n_2} += T^{n,lm}_{n_0,n_1n_2}\n", + "# T^{n+1,lm}_{n_0,n_1,n_2+2} += T^{n,lm}_{n_0,n_1n_2}\n", + " for l in range(lmax+1):\n", + " for n in range(1,num_ns[l]):\n", + " deg = l + 2*n # degree of polynomial\n", " myiter = iter(monomial_iterator.TrivariateMonomialIndices(deg))\n", - " for idx, n0, n1, n2 in myiter:\n", + " for idx,n0,n1,n2 in myiter:\n", " # Use recurrence relation to update\n", " # Warning, if n0-2, n1-2 or n2-2 are negative\n", " # it might be necessary to add if statements\n", " # to avoid.\n", - " if n0 >= 2:\n", - " T[l][:, n, n0, n1, n2] += T[l][:, n - 1, n0 - 2, n1, n2]\n", - " if n1 >= 2:\n", - " T[l][:, n, n0, n1, n2] += T[l][:, n - 1, n0, n1 - 2, n2]\n", - " if n2 >= 2:\n", - " T[l][:, n, n0, n1, n2] += T[l][:, n - 1, n0, n1, n2 - 2]\n", + " if n0>=2:\n", + " T[l][:,n,n0,n1,n2] += T[l][:,n-1,n0-2,n1,n2]\n", + " if n1>=2:\n", + " T[l][:,n,n0,n1,n2] += T[l][:,n-1,n0,n1-2,n2]\n", + " if n2>=2:\n", + " T[l][:,n,n0,n1,n2] += T[l][:,n-1,n0,n1,n2-2]\n", "\n", " return T" ] @@ -210,8 +192,8 @@ } ], "source": [ - "lmax = 2\n", - "num_ns = [1, 1, 2]\n", + "lmax=2\n", + "num_ns=[1,1,2]\n", "test = spherical_to_cartesian2(lmax, num_ns)" ] }, @@ -225,8 +207,7 @@ "outputs": [], "source": [ "from anisoap.utils.spherical_to_cartesian import spherical_to_cartesian\n", - "\n", - "ref = spherical_to_cartesian(lmax, num_ns)" + "ref = spherical_to_cartesian(lmax, num_ns)\n" ] }, { @@ -249,7 +230,7 @@ ], "source": [ "for i in range(len(ref)):\n", - " print(np.linalg.norm(ref[i] - test[i]))" + " print(np.linalg.norm(ref[i]-test[i]))" ] }, { @@ -280,18 +261,17 @@ "source": [ "from anisoap.utils.spherical_to_cartesian import spherical_to_cartesian\n", "import numpy as np\n", - "\n", "try:\n", " from tqdm import tqdm\n", "except ImportError:\n", - " tqdm = lambda i, **kwargs: i\n", + " tqdm = (lambda i, **kwargs: i)\n", "\n", "from anisoap.utils import compute_moments_diagonal_inefficient_implementation\n", "from anisoap.utils import quaternion_to_rotation_matrix\n", "from anisoap.representations.radial_basis import RadialBasis\n", "from anisoap.utils import compute_moments_inefficient_implementation\n", "\n", - "from metatensor import TensorBlock, TensorMap, Labels" + "from metatensor import TensorBlock, TensorMap,Labels" ] }, { @@ -304,20 +284,13 @@ "from ase.io import read\n", "from rascaline import NeighborList\n", "import ase\n", - "\n", - "frames = read(\n", - " \"/Users/jigyasa/scratch/data_papers/data/water/dataset/water_randomized_1000.xyz\",\n", - " \":2\",\n", - ")\n", - "frames2 = read(\n", - " \"/Users/jigyasa/scratch/metatensor-examples/data/hamiltonian/ethanol-hamiltonian/ethanol_4500.xyz\",\n", - " \":1\",\n", - ")\n", - "frames3 = [ase.build.molecule(\"NH3\")]\n", - "frames = frames + frames2 + frames3\n", - "for f in frames:\n", - " f.pbc = True\n", - " f.cell = [4, 4, 4]" + "frames = read('/Users/jigyasa/scratch/data_papers/data/water/dataset/water_randomized_1000.xyz', ':2')\n", + "frames2 = read(\"/Users/jigyasa/scratch/metatensor-examples/data/hamiltonian/ethanol-hamiltonian/ethanol_4500.xyz\",\":1\")\n", + "frames3= [ase.build.molecule('NH3')]\n", + "frames = frames+frames2+frames3\n", + "for f in frames: \n", + " f.pbc=True\n", + " f.cell=[4,4,4]" ] }, { @@ -328,7 +301,7 @@ "outputs": [], "source": [ "from anisoap.utils.moment_generator import *\n", - "from anisoap.utils.quaternion_to_rotation_matrix import quaternion_to_rotation_matrix\n", + "from anisoap.utils.quaternion_to_rotation_matrix import quaternion_to_rotation_matrix\n", "from anisoap.representations.radial_basis import RadialBasis\n", "from anisoap.utils import compute_moments_inefficient_implementation\n", "from itertools import product\n", @@ -342,20 +315,20 @@ "metadata": {}, "outputs": [], "source": [ - "# hypers\n", + "#hypers\n", "rcut = 4\n", "lmax = 4\n", - "radial_basis_name = \"monomial\"\n", - "radial_hypers = {}\n", - "radial_hypers[\"radial_basis\"] = radial_basis_name.lower() # lower case\n", - "radial_hypers[\"radial_gaussian_width\"] = 0.2\n", - "radial_hypers[\"max_angular\"] = lmax\n", + "radial_basis_name = 'monomial'\n", + "radial_hypers={}\n", + "radial_hypers['radial_basis'] = radial_basis_name.lower() # lower case\n", + "radial_hypers['radial_gaussian_width'] = 0.2\n", + "radial_hypers['max_angular'] = lmax\n", "\n", "radial_basis = RadialBasis(**radial_hypers)\n", "\n", "num_ns = []\n", - "for l in range(lmax + 1):\n", - " # num_ns.append(lmax + 1 - l)\n", + "for l in range(lmax+1):\n", + "# num_ns.append(lmax + 1 - l)\n", " num_ns.append(1)\n", "sph_to_cart = spherical_to_cartesian(lmax, num_ns)" ] @@ -371,10 +344,10 @@ "evalue": "No module named 'anisoap.representations.projection_coefficients_modified'", "output_type": "error", "traceback": [ - "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[0;31mModuleNotFoundError\u001b[0m Traceback (most recent call last)", - "Cell \u001b[0;32mIn [47], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01manisoap\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mrepresentations\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mprojection_coefficients_modified\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;241m*\u001b[39m\n", - "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'anisoap.representations.projection_coefficients_modified'" + "\u001B[0;31m---------------------------------------------------------------------------\u001B[0m", + "\u001B[0;31mModuleNotFoundError\u001B[0m Traceback (most recent call last)", + "Cell \u001B[0;32mIn [47], line 1\u001B[0m\n\u001B[0;32m----> 1\u001B[0m \u001B[38;5;28;01mfrom\u001B[39;00m \u001B[38;5;21;01manisoap\u001B[39;00m\u001B[38;5;21;01m.\u001B[39;00m\u001B[38;5;21;01mrepresentations\u001B[39;00m\u001B[38;5;21;01m.\u001B[39;00m\u001B[38;5;21;01mprojection_coefficients_modified\u001B[39;00m \u001B[38;5;28;01mimport\u001B[39;00m \u001B[38;5;241m*\u001B[39m\n", + "\u001B[0;31mModuleNotFoundError\u001B[0m: No module named 'anisoap.representations.projection_coefficients_modified'" ] } ], @@ -397,10 +370,10 @@ "outputs": [], "source": [ "num_frames = len(frames)\n", - "num_atoms_per_frame = np.zeros((num_frames), int)\n", + "num_atoms_per_frame = np.zeros((num_frames),int)\n", "species = set()\n", "\n", - "for i, f in enumerate(frames):\n", + "for i,f in enumerate(frames):\n", " num_atoms_per_frame[i] = len(f)\n", " for atom in f:\n", " species.add(atom.number)\n", @@ -416,11 +389,9 @@ "metadata": {}, "outputs": [], "source": [ - "frame_to_global_atom_idx = np.zeros((num_frames), int)\n", - "for n in range(1, num_frames):\n", - " frame_to_global_atom_idx[n] = (\n", - " num_atoms_per_frame[n - 1] + frame_to_global_atom_idx[n - 1]\n", - " )" + "frame_to_global_atom_idx = np.zeros((num_frames),int)\n", + "for n in range(1,num_frames):\n", + " frame_to_global_atom_idx[n] = num_atoms_per_frame[n-1] + frame_to_global_atom_idx[n-1]\n" ] }, { @@ -430,17 +401,17 @@ "metadata": {}, "outputs": [], "source": [ - "quaternions = np.zeros((num_atoms, 4))\n", + "quaternions = np.zeros((num_atoms,4))\n", "ellipsoid_lengths = np.zeros((num_atoms, 3))\n", "\n", "for i in range(num_atoms):\n", - " quaternions[i] = [0, 0, np.sin(np.pi / 4), np.cos(np.pi / 4)]\n", - " ellipsoid_lengths[i] = [0.5, 0.3, 0.4]\n", + " quaternions[i]= [0, 0, np.sin(np.pi/4), np.cos(np.pi/4)]\n", + " ellipsoid_lengths[i] = [0.5,0.3,0.4]\n", "\n", "# Convert quaternions to rotation matrices\n", - "rotation_matrices = np.zeros((num_atoms, 3, 3))\n", + "rotation_matrices = np.zeros((num_atoms,3,3))\n", "for i, quat in enumerate(quaternions):\n", - " rotation_matrices[i] = quaternion_to_rotation_matrix(quat)" + " rotation_matrices[i] = quaternion_to_rotation_matrix(quat)\n" ] }, { @@ -451,8 +422,8 @@ "outputs": [], "source": [ "nl = NeighborList(rcut, True).compute(frames)\n", - "keys = np.array(nl.keys.asarray(), dtype=int)\n", - "keys = [tuple(i) + (l,) for i in keys for l in range(lmax + 1)]" + "keys=np.array(nl.keys.asarray(), dtype=int)\n", + "keys=[tuple(i)+(l,) for i in keys for l in range(lmax+1)]" ] }, { @@ -483,123 +454,82 @@ "metadata": {}, "outputs": [], "source": [ - "def pairwise_aniso_expansion(\n", - " neighbor_list,\n", - " species,\n", - " frame_to_global_atom_idx,\n", - " rotation_matrices,\n", - " ellipsoid_lengths,\n", - " radial_basis,\n", - "):\n", + "def pairwise_aniso_expansion(neighbor_list, species, frame_to_global_atom_idx, rotation_matrices, ellipsoid_lengths, radial_basis):\n", " \"\"\"\n", - " Function to compute the pairwise expansion by combining the moments and the spherical to Cartesian\n", + " Function to compute the pairwise expansion by combining the moments and the spherical to Cartesian \n", " transformation\n", " --------------------------------------------------------\n", " Parameters:\n", - "\n", - " neighbor_list : Equistore TensorMap\n", + " \n", + " neighbor_list : Equistore TensorMap \n", " Full neighborlist with keys (species_1, species_2) enumerating the possible species pairs.\n", " Each block contains as samples, the atom indices of (first_atom, second_atom) that correspond to the key,\n", - " and block.value is a 3D array of the form (num_samples, num_components,properties), with num_components=3\n", + " and block.value is a 3D array of the form (num_samples, num_components,properties), with num_components=3 \n", " corresponding to the (x,y,z) components of the vector from first_atom to second_atom.\n", " Depending on the cutoff some species pairs may not appear. Self pairs are not present but in PBC,\n", " pairs between copies of the same atom are accounted for.\n", - "\n", + " \n", " species: list of ints\n", - " List of atomic numbers present across the data frames\n", - "\n", + " List of atomic numbers present across the data frames \n", + " \n", " frame_to_global_atom_idx: list of ints\n", " The length of the list equals the number of frames, each entry enumerating the number of atoms in\n", " corresponding frame\n", - "\n", + " \n", " rotation_matrices: np.array of dimension ((num_atoms,3,3))\n", - "\n", + " \n", " ellipsoid_lengths: np.array of dimension ((num_atoms,3))\n", - "\n", + " \n", " radial_basis : Instance of the RadialBasis Class\n", - " anisoap.representations.radial_basis.RadialBasis that has been instantiated appropriately with the\n", + " anisoap.representations.radial_basis.RadialBasis that has been instantiated appropriately with the \n", " cutoff radius, radial basis type.\n", " -----------------------------------------------------------\n", - " Returns:\n", - " An Equistore TensorMap with keys (species_1, species_2, l) where (\"species_1\", \"species_2\") is key in the\n", + " Returns: \n", + " An Equistore TensorMap with keys (species_1, species_2, l) where (\"species_1\", \"species_2\") is key in the \n", " neighbor_list and \"l\" is the angular channel.\n", " Each block of this tensormap has the same samples as the corresponding block of the neighbor_list.\n", - " block.value is a 3D array of the form (num_samples, num_components, properties) where num_components\n", - " form the 2*l+1 values for the corresponding angular channel and the properties dimension corresponds to\n", + " block.value is a 3D array of the form (num_samples, num_components, properties) where num_components \n", + " form the 2*l+1 values for the corresponding angular channel and the properties dimension corresponds to \n", " the radial channel.\n", - "\n", - " \"\"\"\n", + " \n", + " \"\"\" \n", " tensorblock_list = []\n", " tensormap_keys = []\n", "\n", " for center_species in species:\n", " for neighbor_species in species:\n", " if (center_species, neighbor_species) in neighbor_list.keys:\n", - " values_ldict = {l: [] for l in range(lmax + 1)}\n", - " nl_block = neighbor_list.block(\n", - " species_first_atom=center_species,\n", - " species_second_atom=neighbor_species,\n", - " )\n", + " values_ldict = {l:[] for l in range(lmax+1)}\n", + " nl_block = neighbor_list.block(species_first_atom=center_species, species_second_atom=neighbor_species)\n", "\n", " for isample, nl_sample in enumerate(nl_block.samples):\n", - " frame_idx, i, j = (\n", - " nl_sample[\"structure\"],\n", - " nl_sample[\"first_atom\"],\n", - " nl_sample[\"second_atom\"],\n", - " )\n", - " i_global = frame_to_global_atom_idx[frame_idx] + i\n", - " j_global = frame_to_global_atom_idx[frame_idx] + j\n", + " frame_idx, i,j = nl_sample[\"structure\"], nl_sample[\"first_atom\"], nl_sample[\"second_atom\"]\n", + " i_global = frame_to_global_atom_idx[frame_idx] +i\n", + " j_global = frame_to_global_atom_idx[frame_idx] +j\n", "\n", - " r_ij = np.asarray(\n", - " [\n", - " nl_block.values[isample, 0],\n", - " nl_block.values[isample, 1],\n", - " nl_block.values[isample, 2],\n", - " ]\n", - " ).reshape(\n", - " 3,\n", - " )\n", - " # r_ij = pos_i - positions[j_global]\n", + " r_ij = np.asarray([nl_block.values[isample,0], nl_block.values[isample,1],nl_block.values[isample,2]]).reshape(3,)\n", + " # r_ij = pos_i - positions[j_global]\n", "\n", " rot = rotation_matrices[j_global]\n", " lengths = ellipsoid_lengths[j_global]\n", - " precision, center = radial_basis.compute_gaussian_parameters(\n", - " r_ij, lengths, rot\n", - " )\n", - " # moments = compute_moments_inefficient_implementation(precision, center, maxdeg=lmax)\n", + " precision, center = radial_basis.compute_gaussian_parameters(r_ij, lengths, rot)\n", + " # moments = compute_moments_inefficient_implementation(precision, center, maxdeg=lmax)\n", "\n", - " for l in range(lmax + 1):\n", + " for l in range(lmax+1):\n", " moments = np.ones(sph_to_cart[l].shape[-3:])\n", - " values_ldict[l].append(\n", - " np.einsum(\"mnpqr, pqr->mn\", sph_to_cart[l], moments)\n", - " )\n", + " values_ldict[l].append(np.einsum(\"mnpqr, pqr->mn\", sph_to_cart[l], moments))\n", "\n", - " for l in range(lmax + 1):\n", - " block = TensorBlock(\n", - " values=np.asarray(values_ldict[l]),\n", - " samples=nl_block.samples, # as many rows as samples\n", - " components=[\n", - " Labels(\n", - " [\"spherical_component_m\"],\n", - " np.asarray([list(range(-l, l + 1))], np.int32).reshape(\n", - " -1, 1\n", - " ),\n", - " )\n", - " ],\n", - " properties=Labels(\n", - " [\"n\"],\n", - " np.asarray(list(range(num_ns[l])), np.int32).reshape(-1, 1),\n", - " ),\n", - " )\n", + "\n", + " for l in range(lmax+1):\n", + " block = TensorBlock(values = np.asarray(values_ldict[l]), \n", + " samples = nl_block.samples, #as many rows as samples\n", + " components = [Labels(['spherical_component_m'], np.asarray([list(range(-l,l+1))], np.int32).reshape(-1,1) )],\n", + " properties = Labels(['n'],np.asarray(list(range(num_ns[l])), np.int32).reshape(-1,1))\n", + " )\n", " tensorblock_list.append(block)\n", "\n", - " pairwise_aniso_feat = TensorMap(\n", - " Labels(\n", - " [\"species_center\", \"species_neighbor\", \"angular_channel\"],\n", - " np.asarray(keys, dtype=np.int32),\n", - " ),\n", - " tensorblock_list,\n", - " )\n", + "\n", + " pairwise_aniso_feat = TensorMap(Labels([\"species_center\", \"species_neighbor\", \"angular_channel\"],np.asarray(keys, dtype=np.int32)), tensorblock_list)\n", " return pairwise_aniso_feat" ] }, @@ -610,14 +540,7 @@ "metadata": {}, "outputs": [], "source": [ - "pairwise_aniso_feat = pairwise_aniso_expansion(\n", - " nl,\n", - " species,\n", - " frame_to_global_atom_idx,\n", - " rotation_matrices,\n", - " ellipsoid_lengths,\n", - " radial_basis,\n", - ")" + "pairwise_aniso_feat = pairwise_aniso_expansion(nl, species, frame_to_global_atom_idx, rotation_matrices, ellipsoid_lengths, radial_basis)" ] }, { @@ -703,161 +626,119 @@ " Function to sum over the pairwise expansion \\sum_{j in a} = \n", " --------------------------------------------------------\n", " Parameters:\n", - "\n", - " pair_aniso_feat : Equistore TensorMap\n", - " TensorMap returned from \"pairwise_aniso_expansion()\" with keys (species_1, species_2,l) enumerating\n", + " \n", + " pair_aniso_feat : Equistore TensorMap \n", + " TensorMap returned from \"pairwise_aniso_expansion()\" with keys (species_1, species_2,l) enumerating \n", " the possible species pairs and the angular channels.\n", - "\n", + " \n", " species: list of ints\n", - " List of atomic numbers present across the data frames\n", - "\n", + " List of atomic numbers present across the data frames \n", + " \n", " -----------------------------------------------------------\n", - " Returns:\n", - " An Equistore TensorMap with keys (species, l) \"species\" takes the value of the atomic numbers present\n", + " Returns: \n", + " An Equistore TensorMap with keys (species, l) \"species\" takes the value of the atomic numbers present \n", " in the dataset and \"l\" is the angular channel.\n", - " Each block of this tensormap has as samples (\"structure\", \"center\") yielding the indices of the frames\n", + " Each block of this tensormap has as samples (\"structure\", \"center\") yielding the indices of the frames \n", " and atoms that correspond to \"species\" are present.\n", - " block.value is a 3D array of the form (num_samples, num_components, properties) where num_components\n", - " take on the same values as in the pair_aniso_feat_feat.block . block.properties now has an additional index\n", + " block.value is a 3D array of the form (num_samples, num_components, properties) where num_components \n", + " take on the same values as in the pair_aniso_feat_feat.block . block.properties now has an additional index \n", " for neighbor_species that corresponds to \"a\" in \n", - "\n", - " \"\"\"\n", - " aniso_keys = list(set([tuple(list(x)[:1] + list(x)[2:]) for x in keys]))\n", - " # Select the unique combinations of pair_aniso_feat.keys[\"species_center\"] and\n", - " # pair_aniso_feat.keys[\"angular_channel\"] to form the keys of the single particle centered feature\n", + " \n", + " \"\"\" \n", + " aniso_keys = list(set([tuple(list(x)[:1]+list(x)[2:]) for x in keys]))\n", + " # Select the unique combinations of pair_aniso_feat.keys[\"species_center\"] and \n", + " # pair_aniso_feat.keys[\"angular_channel\"] to form the keys of the single particle centered feature \n", " aniso_keys.sort()\n", " aniso_blocks = []\n", - " property_names = pair_aniso_feat.property_names + (\"neighbor_species\",)\n", - "\n", + " property_names = pair_aniso_feat.property_names + ('neighbor_species',)\n", + " \n", " for key in aniso_keys:\n", - " contract_blocks = []\n", - " contract_properties = []\n", - " contract_samples = []\n", + " contract_blocks=[]\n", + " contract_properties=[]\n", + " contract_samples=[]\n", " # these collect the values, properties and samples of the blocks when contracted over neighbor_species.\n", - " # All these lists have as many entries as len(species).\n", - "\n", + " # All these lists have as many entries as len(species). \n", + " \n", " for ele in species:\n", - " blockidx = pair_aniso_feat.blocks_matching(species_neighbor=ele)\n", + " blockidx = pair_aniso_feat.blocks_matching(species_neighbor= ele)\n", " # indices of the blocks in pair_aniso_feat with neighbor species = ele\n", - " sel_blocks = [\n", - " pair_aniso_feat.block(i)\n", - " for i in blockidx\n", - " if key\n", - " == tuple(\n", - " list(pair_aniso_feat.keys[i])[:1]\n", - " + list(pair_aniso_feat.keys[i])[2:]\n", - " )\n", - " ]\n", + " sel_blocks = [pair_aniso_feat.block(i) for i in blockidx if key==tuple(list(pair_aniso_feat.keys[i])[:1]+list(pair_aniso_feat.keys[i])[2:])]\n", " if not len(sel_blocks):\n", - " # print(key, ele, \"skipped\") # this block is not found in the pairwise feat\n", + "# print(key, ele, \"skipped\") # this block is not found in the pairwise feat\n", " continue\n", - " assert len(sel_blocks) == 1\n", - "\n", - " # sel_blocks is the corresponding block in the pairwise feat with the same (species_center, l) and\n", + " assert len(sel_blocks)==1 \n", + " \n", + " # sel_blocks is the corresponding block in the pairwise feat with the same (species_center, l) and \n", " # species_neighbor = ele thus there can be only one block corresponding to the triplet (species_center, species_neighbor, l)\n", " block = sel_blocks[0]\n", - "\n", - " pair_block_sample = list(\n", - " zip(block.samples[\"structure\"], block.samples[\"first_atom\"])\n", - " )\n", + " \n", + " pair_block_sample = list(zip(block.samples['structure'], block.samples['first_atom']))\n", " # Takes the structure and first atom index from the current pair_block sample. There might be repeated\n", " # entries here because for example (0,0,1) (0,0,2) might be samples of the pair block (the index of the\n", - " # neighbor atom is changing but for both of these we are keeping (0,0) corresponding to the structure and\n", - " # first atom.\n", + " # neighbor atom is changing but for both of these we are keeping (0,0) corresponding to the structure and \n", + " #first atom. \n", "\n", - " struct, center = np.unique(block.samples[\"structure\"]), np.unique(\n", - " block.samples[\"first_atom\"]\n", - " )\n", - " possible_block_samples = list(product(struct, center))\n", + " struct, center = np.unique(block.samples['structure']), np.unique(block.samples['first_atom'])\n", + " possible_block_samples = list(product(struct,center))\n", " # possible block samples contains all *unique* possible pairwise products between structure and atom index\n", " # From here we choose the entries that are actually present in the block to form the final sample\n", - "\n", - " block_samples = []\n", + " \n", + " block_samples=[]\n", " block_values = []\n", "\n", " for isample, sample in enumerate(possible_block_samples):\n", - " sample_idx = [\n", - " idx\n", - " for idx, tup in enumerate(pair_block_sample)\n", - " if tup[0] == sample[0] and tup[1] == sample[1]\n", - " ]\n", - " # all samples of the pair block that match the current sample\n", - " # in the example above, for sample = (0,0) we would identify sample_idx = [(0,0,1), (0,0,2)]\n", - " if len(sample_idx) == 0:\n", + " sample_idx = [idx for idx, tup in enumerate(pair_block_sample) if tup[0] ==sample[0] and tup[1] == sample[1]]\n", + " # all samples of the pair block that match the current sample \n", + " # in the example above, for sample = (0,0) we would identify sample_idx = [(0,0,1), (0,0,2)] \n", + " if len(sample_idx)==0:\n", " continue\n", - " # #print(key, ele, sample, block.samples[sample_idx])\n", + " # #print(key, ele, sample, block.samples[sample_idx])\n", " block_samples.append(sample)\n", - " block_values.append(\n", - " block.values[sample_idx].sum(axis=0)\n", - " ) # sum over \"j\" for given ele\n", - "\n", - " # block_values has as many entries as samples satisfying (key, neighbor_species=ele).\n", + " block_values.append(block.values[sample_idx].sum(axis=0)) #sum over \"j\" for given ele\n", + " \n", + " # block_values has as many entries as samples satisfying (key, neighbor_species=ele). \n", " # When we iterate over neighbor species, not all (structure, center) would be present\n", - " # Example: (0,0,1) might be present in a block with neighbor_species = 1 but no other pair block\n", + " # Example: (0,0,1) might be present in a block with neighbor_species = 1 but no other pair block \n", " # ever has (0,0,x) present as a sample- so (0,0) doesnt show up in a block_sample for all ele\n", " # so in general we have a ragged list of contract_blocks\n", - "\n", + " \n", " contract_blocks.append(block_values)\n", " contract_samples.append(block_samples)\n", - " contract_properties.append([tuple(p) + (ele,) for p in block.properties])\n", - " # this adds the \"ele\" (i.e. neighbor_species) to the properties dimension\n", - "\n", - " # print(len(contract_samples))\n", - " all_block_samples = sorted(list(set().union(*contract_samples)))\n", + " contract_properties.append([tuple(p)+(ele,) for p in block.properties])\n", + " #this adds the \"ele\" (i.e. neighbor_species) to the properties dimension\n", + " \n", + "# print(len(contract_samples))\n", + " all_block_samples= sorted(list(set().union(*contract_samples))) \n", " # Selects the set of samples from all the block_samples we collected by iterating over the neighbor_species\n", - " # These form the final samples of the block!\n", + " # These form the final samples of the block! \n", "\n", - " all_block_values = np.zeros(\n", - " (\n", - " (len(all_block_samples),)\n", - " + block.values.shape[1:]\n", - " + (len(contract_blocks),)\n", - " )\n", - " )\n", - " # Create storage for the final values - we need as many rows as all_block_samples,\n", + " all_block_values = np.zeros(((len(all_block_samples),)+ block.values.shape[1:]+(len(contract_blocks),)))\n", + " # Create storage for the final values - we need as many rows as all_block_samples, \n", " # block.values.shape[1:] accounts for \"components\" and \"properties\" that are already part of the pair blocks\n", " # and we dont alter these\n", - " # len(contract_blocks) - adds the additional dimension for the neighbor_species since we accumulated\n", + " # len(contract_blocks) - adds the additional dimension for the neighbor_species since we accumulated \n", " # values for each of them as \\sum_{j in ele} <|rho_ij>\n", " # Thus - all_block_values.shape = (num_final_samples, components_pair, properties_pair, num_species)\n", - "\n", + " \n", " for iele, elem_cont_samples in enumerate(contract_samples):\n", " # This effectively loops over the species of the neighbors\n", " # Now we just need to add the contributions to the final samples and values from this species to the right\n", " # samples\n", - " nzidx = [\n", - " i\n", - " for i in range(len(all_block_samples))\n", - " if all_block_samples[i] in elem_cont_samples\n", - " ]\n", + " nzidx=[i for i in range(len(all_block_samples)) if all_block_samples[i] in elem_cont_samples]\n", " # identifies where the samples that this species contributes to, are present in the final samples\n", - " # print(apecies[ib],key, bb, all_block_samples)\n", - " all_block_values[nzidx, :, :, iele] = contract_blocks[iele]\n", + "# print(apecies[ib],key, bb, all_block_samples)\n", + " all_block_values[nzidx,:,:,iele] = contract_blocks[iele]\n", "\n", - " new_block = TensorBlock(\n", - " values=all_block_values.reshape(\n", - " all_block_values.shape[0], all_block_values.shape[1], -1\n", - " ),\n", - " samples=Labels(\n", - " [\"structure\", \"center\"], np.asarray(all_block_samples, np.int32)\n", - " ),\n", - " components=block.components,\n", - " properties=Labels(\n", - " list(property_names),\n", - " np.asarray(np.vstack(contract_properties), np.int32),\n", - " ),\n", - " )\n", + " new_block = TensorBlock(values = all_block_values.reshape(all_block_values.shape[0],all_block_values.shape[1] ,-1),\n", + " samples = Labels(['structure', 'center'], np.asarray(all_block_samples, np.int32)), \n", + " components = block.components,\n", + " properties= Labels(list(property_names), np.asarray(np.vstack(contract_properties),np.int32))\n", + " )\n", "\n", " aniso_blocks.append(new_block)\n", - " aniso = TensorMap(\n", - " Labels(\n", - " [\"species_center\", \"angular_channel\"],\n", - " np.asarray(aniso_keys, dtype=np.int32),\n", - " ),\n", - " aniso_blocks,\n", - " )\n", + " aniso = TensorMap(Labels(['species_center','angular_channel'],np.asarray(aniso_keys,dtype=np.int32)), aniso_blocks)\n", "\n", - " return aniso" + " return aniso\n" ] }, { From 19322aa48427df2eeeae3f23c138f4bdacceb510 Mon Sep 17 00:00:00 2001 From: Arthur Lin Date: Thu, 3 Oct 2024 19:57:29 -0500 Subject: [PATCH 19/22] one more reset of linting changes in notebooks -- we want to keep this separate --- notebooks/anisotropic_representations.ipynb | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/notebooks/anisotropic_representations.ipynb b/notebooks/anisotropic_representations.ipynb index d79a71a..f2c4e1e 100644 --- a/notebooks/anisotropic_representations.ipynb +++ b/notebooks/anisotropic_representations.ipynb @@ -344,10 +344,10 @@ "evalue": "No module named 'anisoap.representations.projection_coefficients_modified'", "output_type": "error", "traceback": [ - "\u001B[0;31m---------------------------------------------------------------------------\u001B[0m", - "\u001B[0;31mModuleNotFoundError\u001B[0m Traceback (most recent call last)", - "Cell \u001B[0;32mIn [47], line 1\u001B[0m\n\u001B[0;32m----> 1\u001B[0m \u001B[38;5;28;01mfrom\u001B[39;00m \u001B[38;5;21;01manisoap\u001B[39;00m\u001B[38;5;21;01m.\u001B[39;00m\u001B[38;5;21;01mrepresentations\u001B[39;00m\u001B[38;5;21;01m.\u001B[39;00m\u001B[38;5;21;01mprojection_coefficients_modified\u001B[39;00m \u001B[38;5;28;01mimport\u001B[39;00m \u001B[38;5;241m*\u001B[39m\n", - "\u001B[0;31mModuleNotFoundError\u001B[0m: No module named 'anisoap.representations.projection_coefficients_modified'" + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mModuleNotFoundError\u001b[0m Traceback (most recent call last)", + "Cell \u001b[0;32mIn [47], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01manisoap\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mrepresentations\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mprojection_coefficients_modified\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;241m*\u001b[39m\n", + "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'anisoap.representations.projection_coefficients_modified'" ] } ], From cfeb979aac7b244019f58657b2b6eb631d82b9ad Mon Sep 17 00:00:00 2001 From: Arthur Lin Date: Mon, 25 Nov 2024 15:41:59 -0600 Subject: [PATCH 20/22] Slightly edited and organized Invarainces example --- Invariances_of_powerspectrum.ipynb | 1175 - .../Invariances_of_powerspectrum.ipynb | 1197 + notebooks/invariances_example/ellipsoids.xyz | 24646 ++++++++++++++++ 3 files changed, 25843 insertions(+), 1175 deletions(-) delete mode 100644 Invariances_of_powerspectrum.ipynb create mode 100644 notebooks/invariances_example/Invariances_of_powerspectrum.ipynb create mode 100644 notebooks/invariances_example/ellipsoids.xyz diff --git a/Invariances_of_powerspectrum.ipynb b/Invariances_of_powerspectrum.ipynb deleted file mode 100644 index d09e3b4..0000000 --- a/Invariances_of_powerspectrum.ipynb +++ /dev/null @@ -1,1175 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 22, - "id": "9a0205c7-a5d9-49d8-9b65-afc6b9f02562", - "metadata": {}, - "outputs": [], - "source": [ - "import sys\n", - "import warnings\n", - "import metatensor\n", - "from itertools import product\n", - "from ase.io import read\n", - "\n", - "import numpy as np\n", - "from metatensor import (\n", - " Labels,\n", - " TensorBlock,\n", - " TensorMap,\n", - ")\n", - "\n", - "from scipy.spatial.transform import Rotation as R\n", - "from tqdm.auto import tqdm\n", - "from skmatter.preprocessing import StandardFlexibleScaler\n", - "\n", - "from anisoap.representations.radial_basis import (\n", - " GTORadialBasis,\n", - " MonomialBasis,\n", - ")\n", - "from anisoap.representations.ellipsoidal_density_projection import (\n", - " EllipsoidalDensityProjection,\n", - ")\n", - "\n", - "import matplotlib.pyplot as plt" - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "id": "34f7cffd-2d19-455c-aaf7-9ed6f4ce62b4", - "metadata": {}, - "outputs": [], - "source": [ - "ell_frames = read(\"ellipsoids.xyz\", \"0:2\")\n", - "ell_frames_translation = read(\"ellipsoids.xyz\", \"0:2\")\n", - "ell_frames_rotation = read(\"ellipsoids.xyz\", \"0:2\")\n", - "\n", - "# This is to make sure the ell_frames list calls c_diameter[] rather than c_diameter and to update the diameters of ellipsoids to be 3,3, and 1.\n", - "\n", - "\n", - "def update_diameters_and_variablename(frames):\n", - " for frame in frames:\n", - " for i in range(1, 4):\n", - " old = f\"c_diameter{i}\"\n", - " new = f\"c_diameter[{i}]\"\n", - " if old in frame.arrays:\n", - " frame.arrays[new] = frame.arrays[old]\n", - " frame.arrays[new] = np.ones(len(frame)) * (3.0 if i < 3 else 1.0)\n", - "\n", - "\n", - "update_diameters_and_variablename(ell_frames)\n", - "update_diameters_and_variablename(ell_frames_translation)\n", - "update_diameters_and_variablename(ell_frames_rotation)" - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "id": "c6d137d4-a26b-42fb-b620-26d2c3ba482f", - "metadata": {}, - "outputs": [], - "source": [ - "# Translation vector is used to demonstrate the power spectrum of ellipsoidal representations are invariant of translation in positions.\n", - "\n", - "translation_vector = np.array([2.0, 2.0, 2.0])\n", - "for frame in ell_frames_translation:\n", - " frame.arrays[\"positions\"] += translation_vector" - ] - }, - { - "cell_type": "code", - "execution_count": 25, - "id": "1b433389-6910-4b18-b4e4-ed56bd4b584a", - "metadata": {}, - "outputs": [], - "source": [ - "lmax = 5\n", - "nmax = 3\n", - "\n", - "AniSOAP_HYPERS = {\n", - " \"max_angular\": lmax,\n", - " \"max_radial\": nmax,\n", - " \"radial_basis_name\": \"gto\",\n", - " \"rotation_type\": \"quaternion\",\n", - " \"rotation_key\": \"c_q\",\n", - " \"cutoff_radius\": 7.0,\n", - " \"radial_gaussian_width\": 1.5,\n", - " \"basis_rcond\": 1e-8,\n", - " \"basis_tol\": 1e-4,\n", - "}" - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "id": "7ca6c85f-571d-4abe-97a0-2c6dda70c1de", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/Users/PrettyBoy/Desktop/AniSOAP/AniSOAP/anisoap/representations/ellipsoidal_density_projection.py:547: UserWarning: In quaternion mode, quaternions are assumed to be in (w,x,y,z) format.\n", - " warnings.warn(\n" - ] - }, - { - "data": { - "application/vnd.jupyter.widget-view+json": { - "model_id": "ecef6d3abc694e16acbfcc7f12730a52", - "version_major": 2, - "version_minor": 0 - }, - "text/plain": [ - "Computing neighborlist: 0%| | 0/2 [00:00" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, axs = plt.subplots(1,2, figsize=(10,5))\n", + "axs[0].plot(power_spectrum_rotation.T[:,0])\n", + "axs[0].plot(power_spectrum_original.T[:,0])\n", + "axs[0].set_title(\"Frame 0, Original vs Rotated\")\n", + "axs[1].plot(power_spectrum_rotation.T[:,1])\n", + "axs[1].plot(power_spectrum_original.T[:,1])\n", + "axs[1].set_title(\"Frame 1, Original vs Rotated\")\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "64116b21-5af6-4e27-a48a-198438acfba1", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.14" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/notebooks/invariances_example/ellipsoids.xyz b/notebooks/invariances_example/ellipsoids.xyz new file mode 100644 index 0000000..c04f9e2 --- /dev/null +++ b/notebooks/invariances_example/ellipsoids.xyz @@ -0,0 +1,24646 @@ +2 +Lattice="5.724068709233237 3.504981211431003e-16 3.504981211431003e-16 0.0 9.775799214092565 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+2 +Lattice="8.000201839834528 -3.561642516266371 2.7650012491465796 0.0 6.152865221953651 1.2169064349032999 0.0 0.0 7.861752172194385" Properties=species:S:1:pos:R:3:c_q:R:4 1:R:1:c_diameter=T 2:R:1:c_diameter=T 3:R:1:corresponding_atoms:I:12=T signac_id=d6dc6c74fddc5e7acde0919214a444d9 pbc="T T T" +X 1.80027456 2.16382104 6.33022460 0.00518472 -0.03175524 -0.00121441 0.99948149 +X 6.19992728 0.42740166 5.51343526 0.95367032 0.01140089 -0.03030386 -0.29910636 +2 +Lattice="7.086630521671722 4.3393096925526063e-16 4.3393096925526063e-16 0.0 5.919417696812096 3.6245979676085657e-16 0.0 0.0 9.225266448727671" Properties=species:S:1:pos:R:3:c_q:R:4 1:R:1:c_diameter=T 2:R:1:c_diameter=T 3:R:1:corresponding_atoms:I:12=T signac_id=e4d46b5ab2fb909799f0a3d360afdb8b pbc="T T T" +X -0.00000000 2.95970885 0.00000000 0.23112140 0.86468830 -0.08885624 -0.43703731 +X 3.54331526 2.95970885 4.61263322 0.07483976 0.44475688 0.27716371 0.84839296 +1 +Lattice="5.448265694635889 3.3361005719200864e-16 3.3361005719200864e-16 0.0 6.315082224202058 3.866872616110699e-16 0.0 0.0 5.623807047096289" Properties=species:S:1:pos:R:3:c_q:R:4 1:R:1:c_diameter=T 2:R:1:c_diameter=T 3:R:1:corresponding_atoms:I:12=T signac_id=56d3b08464a61031ee20dc159b120186 pbc="T T T" +X 0.00000000 0.00000000 0.00000000 -0.15328864 0.06613699 -0.66528986 0.72767980 +1 +Lattice="6.246933733193326 3.8251437004204163e-16 3.8251437004204163e-16 0.0 4.789361859673506 2.932638335703787e-16 0.0 0.0 6.467302118699166" Properties=species:S:1:pos:R:3:c_q:R:4 1:R:1:c_diameter=T 2:R:1:c_diameter=T 3:R:1:corresponding_atoms:I:12=T signac_id=409a46081b2bb2586e7aedf04f2a18aa pbc="T T T" +X 0.00000000 -0.00000000 -0.00000000 -0.22366933 -0.19370706 -0.68403092 0.66674681 +2 +Lattice="9.336029000705627 4.534913971425249e-16 2.1814159895281526 0.0 8.690238606750272 5.321236446791737e-16 0.0 0.0 4.769839902162677" Properties=species:S:1:pos:R:3:c_q:R:4 1:R:1:c_diameter=T 2:R:1:c_diameter=T 3:R:1:corresponding_atoms:I:12=T signac_id=f155253c21c31848d1329dba1f9aa38a pbc="T T T" +X -0.00000000 4.34511930 0.00000000 0.32046248 0.29987160 0.18602793 0.87907590 +X 4.66801450 0.00000000 1.09070800 0.06237390 0.33153141 0.08843567 0.93721692 +1 +Lattice="6.8158523024000655 4.173505852797679e-16 4.173505852797679e-16 0.0 4.822171773043693 2.952728613398338e-16 0.0 0.0 5.887146624212287" Properties=species:S:1:pos:R:3:c_q:R:4 1:R:1:c_diameter=T 2:R:1:c_diameter=T 3:R:1:corresponding_atoms:I:12=T signac_id=7740a059adee0da452c8162c3e260d8a pbc="T T T" +X 3.40792615 2.41108588 2.94357331 -0.36885360 0.30922590 0.79344362 -0.37252326 +1 +Lattice="3.1816703790685685 0.7762992693425311 -0.9831854423567056 0.0 6.662185345099975 4.373427948604291 0.0 0.0 9.128424001979484" Properties=species:S:1:pos:R:3:c_q:R:4 1:R:1:c_diameter=T 2:R:1:c_diameter=T 3:R:1:corresponding_atoms:I:12=T signac_id=53da235548531189b081bed2e7c5cc00 pbc="T T T" +X 1.59083519 3.71924231 1.69512125 0.42721499 0.72339420 0.26835657 0.47135224 From e521e34c4d0fdb480d45584eb1b9bd17bba902ed Mon Sep 17 00:00:00 2001 From: "Rose K. Cersonsky" <47536110+rosecers@users.noreply.github.com> Date: Thu, 12 Dec 2024 16:05:52 -0600 Subject: [PATCH 21/22] Apply suggestions from code review --- .../ellipsoidal_density_projection.py | 16 ++++++++-------- 1 file changed, 8 insertions(+), 8 deletions(-) diff --git a/anisoap/representations/ellipsoidal_density_projection.py b/anisoap/representations/ellipsoidal_density_projection.py index f0162ba..77934bc 100644 --- a/anisoap/representations/ellipsoidal_density_projection.py +++ b/anisoap/representations/ellipsoidal_density_projection.py @@ -668,7 +668,7 @@ def transform(self, frames, show_progress=False, normalize=True, rust_moments=Tr else: return features - def power_spectrum(self, ell_frames, sum_over_samples=True): + def power_spectrum(self, frames, sum_over_samples=True): """Function to compute the power spectrum of AniSOAP computes the power spectrum of AniSOAP with the inputs of AniSOAP hyperparameters @@ -679,7 +679,7 @@ def power_spectrum(self, ell_frames, sum_over_samples=True): Parameters ---------- - ell_frames: list + frames: list A list of ellipsoidal frames, where each frame contains attributes: 'c_diameter[1]', 'c_diameter[2]', 'c_diameter[3]', 'c_q', 'positions', and 'numbers'. It only accepts c_q for the angular attribute of each frame. @@ -699,8 +699,8 @@ def power_spectrum(self, ell_frames, sum_over_samples=True): mycg = ClebschGordanReal(self.max_angular) # Checks that the sample's first frame is not empty - if ell_frames[0].arrays is None: - raise ValueError("ell_frames cannot be none") + if frames[0].arrays is None: + raise ValueError("frames cannot be none") required_attributes = [ "c_diameter[1]", "c_diameter[2]", @@ -711,19 +711,19 @@ def power_spectrum(self, ell_frames, sum_over_samples=True): ] # Checks if the sample contains all necessary information for computation of power spectrum - for index, frame in enumerate(ell_frames): + for index, frame in enumerate(frames): array = frame.arrays for attr in required_attributes: if attr not in array: raise ValueError( - f"ell_frame at index {index} is missing a required attribute '{attr}'" + f"frame at index {index} is missing a required attribute '{attr}'" ) if "quaternion" in array: raise ValueError( - f"ell_frame should contain c_q rather than quaternion" + f"frame should contain c_q rather than quaternion" ) - mvg_coeffs = self.transform(ell_frames, show_progress=True) + mvg_coeffs = self.transform(frames, show_progress=True) mvg_nu1 = standardize_keys(mvg_coeffs) # Combines the mvg_nu1 with itself using the Clebsch-Gordan coefficients. From 2aba961c76c71dbb5fefee8e17e53051ebd49790 Mon Sep 17 00:00:00 2001 From: "Rose K. Cersonsky" <47536110+rosecers@users.noreply.github.com> Date: Thu, 12 Dec 2024 16:09:43 -0600 Subject: [PATCH 22/22] Lint --- anisoap/representations/AvailableRadialBases.ipynb | 2 +- anisoap/representations/ellipsoidal_density_projection.py | 4 +--- 2 files changed, 2 insertions(+), 4 deletions(-) diff --git a/anisoap/representations/AvailableRadialBases.ipynb b/anisoap/representations/AvailableRadialBases.ipynb index 37db375..1ef789a 100644 --- a/anisoap/representations/AvailableRadialBases.ipynb +++ b/anisoap/representations/AvailableRadialBases.ipynb @@ -70,7 +70,7 @@ " radial_gaussian_width=width,\n", " # radial_gaussian_shift = shift,\n", " tol=1e-1,\n", - " **shared_params\n", + " **shared_params,\n", ")\n", "shiftedgto.plot_basis()" ] diff --git a/anisoap/representations/ellipsoidal_density_projection.py b/anisoap/representations/ellipsoidal_density_projection.py index 77934bc..1ed0569 100644 --- a/anisoap/representations/ellipsoidal_density_projection.py +++ b/anisoap/representations/ellipsoidal_density_projection.py @@ -719,9 +719,7 @@ def power_spectrum(self, frames, sum_over_samples=True): f"frame at index {index} is missing a required attribute '{attr}'" ) if "quaternion" in array: - raise ValueError( - f"frame should contain c_q rather than quaternion" - ) + raise ValueError(f"frame should contain c_q rather than quaternion") mvg_coeffs = self.transform(frames, show_progress=True) mvg_nu1 = standardize_keys(mvg_coeffs)