import torch
from torch import Tensor
import torch.utils.data
import math
from collections import defaultdict
from typing import Tuple, NamedTuple, Optional, Sequence, List, Dict
from torchani.units import sqrt_mhessian2invcm, sqrt_mhessian2milliev, mhessian2fconst
from .nn import SpeciesEnergies
def stack_with_padding(properties, padding):
output = defaultdict(list)
for p in properties:
for k, v in p.items():
output[k].append(torch.as_tensor(v))
for k, v in output.items():
if v[0].dim() == 0:
output[k] = torch.stack(v)
else:
output[k] = torch.nn.utils.rnn.pad_sequence(v, True, padding[k])
return output
def broadcast_first_dim(properties):
num_molecule = 1
for k, v in properties.items():
shape = list(v.shape)
n = shape[0]
if num_molecule != 1:
assert n == 1 or n == num_molecule, "unable to broadcast"
else:
num_molecule = n
for k, v in properties.items():
shape = list(v.shape)
shape[0] = num_molecule
properties[k] = v.expand(shape)
return properties
[docs]def pad_atomic_properties(properties, padding_values=defaultdict(lambda: 0.0, species=-1)):
"""Put a sequence of atomic properties together into single tensor.
Inputs are `[{'species': ..., ...}, {'species': ..., ...}, ...]` and the outputs
are `{'species': padded_tensor, ...}`
Arguments:
properties (:class:`collections.abc.Sequence`): sequence of properties.
padding_values (dict): the value to fill to pad tensors to same size
"""
vectors = [k for k in properties[0].keys() if properties[0][k].dim() > 1]
scalars = [k for k in properties[0].keys() if properties[0][k].dim() == 1]
padded_sizes = {k: max(x[k].shape[1] for x in properties) for k in vectors}
num_molecules = [x[vectors[0]].shape[0] for x in properties]
total_num_molecules = sum(num_molecules)
output = {}
for k in scalars:
output[k] = torch.stack([x[k] for x in properties])
for k in vectors:
tensor = properties[0][k]
shape = list(tensor.shape)
device = tensor.device
dtype = tensor.dtype
shape[0] = total_num_molecules
shape[1] = padded_sizes[k]
output[k] = torch.full(shape, padding_values[k], device=device, dtype=dtype)
index0 = 0
for n, x in zip(num_molecules, properties):
original_size = x[k].shape[1]
output[k][index0: index0 + n, 0: original_size, ...] = x[k]
index0 += n
return output
[docs]def present_species(species):
"""Given a vector of species of atoms, compute the unique species present.
Arguments:
species (:class:`torch.Tensor`): 1D vector of shape ``(atoms,)``
Returns:
:class:`torch.Tensor`: 1D vector storing present atom types sorted.
"""
# present_species, _ = species.flatten()._unique(sorted=True)
present_species = species.flatten().unique(sorted=True)
if present_species[0].item() == -1:
present_species = present_species[1:]
return present_species
[docs]def strip_redundant_padding(atomic_properties):
"""Strip trailing padding atoms.
Arguments:
atomic_properties (dict): properties to strip
Returns:
dict: same set of properties with redundant padding atoms stripped.
"""
species = atomic_properties['species']
non_padding = (species >= 0).any(dim=0).nonzero().squeeze()
for k in atomic_properties:
atomic_properties[k] = atomic_properties[k].index_select(1, non_padding)
return atomic_properties
[docs]def map2central(cell, coordinates, pbc):
"""Map atoms outside the unit cell into the cell using PBC.
Arguments:
cell (:class:`torch.Tensor`): tensor of shape (3, 3) of the three
vectors defining unit cell:
.. code-block:: python
tensor([[x1, y1, z1],
[x2, y2, z2],
[x3, y3, z3]])
coordinates (:class:`torch.Tensor`): Tensor of shape
``(molecules, atoms, 3)``.
pbc (:class:`torch.Tensor`): boolean vector of size 3 storing
if pbc is enabled for that direction.
Returns:
:class:`torch.Tensor`: coordinates of atoms mapped back to unit cell.
"""
# Step 1: convert coordinates from standard cartesian coordinate to unit
# cell coordinates
inv_cell = torch.inverse(cell)
coordinates_cell = torch.matmul(coordinates, inv_cell)
# Step 2: wrap cell coordinates into [0, 1)
coordinates_cell -= coordinates_cell.floor() * pbc
# Step 3: convert from cell coordinates back to standard cartesian
# coordinate
return torch.matmul(coordinates_cell, cell)
[docs]class EnergyShifter(torch.nn.Module):
"""Helper class for adding and subtracting self atomic energies
This is a subclass of :class:`torch.nn.Module`, so it can be used directly
in a pipeline as ``[input->AEVComputer->ANIModel->EnergyShifter->output]``.
Arguments:
self_energies (:class:`collections.abc.Sequence`): Sequence of floating
numbers for the self energy of each atom type. The numbers should
be in order, i.e. ``self_energies[i]`` should be atom type ``i``.
fit_intercept (bool): Whether to calculate the intercept during the LSTSQ
fit. The intercept will also be taken into account to shift energies.
"""
def __init__(self, self_energies, fit_intercept=False):
super().__init__()
self.fit_intercept = fit_intercept
if self_energies is not None:
self_energies = torch.tensor(self_energies, dtype=torch.double)
self.register_buffer('self_energies', self_energies)
[docs] def sae(self, species):
"""Compute self energies for molecules.
Padding atoms will be automatically excluded.
Arguments:
species (:class:`torch.Tensor`): Long tensor in shape
``(conformations, atoms)``.
Returns:
:class:`torch.Tensor`: 1D vector in shape ``(conformations,)``
for molecular self energies.
"""
intercept = 0.0
if self.fit_intercept:
intercept = self.self_energies[-1]
self_energies = self.self_energies[species]
self_energies[species == torch.tensor(-1, device=species.device)] = torch.tensor(0, device=species.device, dtype=torch.double)
return self_energies.sum(dim=1) + intercept
[docs] def forward(self, species_energies: Tuple[Tensor, Tensor],
cell: Optional[Tensor] = None,
pbc: Optional[Tensor] = None) -> SpeciesEnergies:
"""(species, molecular energies)->(species, molecular energies + sae)
"""
species, energies = species_energies
sae = self.sae(species)
return SpeciesEnergies(species, energies + sae)
[docs]class ChemicalSymbolsToInts(torch.nn.Module):
r"""Helper that can be called to convert chemical symbol string to integers
On initialization the class should be supplied with a :class:`list` (or in
general :class:`collections.abc.Sequence`) of :class:`str`. The returned
instance is a callable object, which can be called with an arbitrary list
of the supported species that is converted into a tensor of dtype
:class:`torch.long`. Usage example:
.. code-block:: python
from torchani.utils import ChemicalSymbolsToInts
# We initialize ChemicalSymbolsToInts with the supported species
species_to_tensor = ChemicalSymbolsToInts(['H', 'C', 'Fe', 'Cl'])
# We have a species list which we want to convert to an index tensor
index_tensor = species_to_tensor(['H', 'C', 'H', 'H', 'C', 'Cl', 'Fe'])
# index_tensor is now [0 1 0 0 1 3 2]
.. warning::
If the input is a string python will iterate over
characters, this means that a string such as 'CHClFe' will be
intepreted as 'C' 'H' 'C' 'l' 'F' 'e'. It is recommended that you
input either a :class:`list` or a :class:`numpy.ndarray` ['C', 'H', 'Cl', 'Fe'],
and not a string. The output of a call does NOT correspond to a
tensor of atomic numbers.
Arguments:
all_species (:class:`collections.abc.Sequence` of :class:`str`):
sequence of all supported species, in order (it is recommended to order
according to atomic number).
"""
_dummy: Tensor
rev_species: Dict[str, int]
def __init__(self, all_species: Sequence[str]):
super().__init__()
self.rev_species = {s: i for i, s in enumerate(all_species)}
# dummy tensor to hold output device
self.register_buffer('_dummy', torch.empty(0), persistent=False)
[docs] def forward(self, species: List[str]) -> Tensor:
r"""Convert species from sequence of strings to 1D tensor"""
rev = [self.rev_species[s] for s in species]
return torch.tensor(rev, dtype=torch.long, device=self._dummy.device)
def __len__(self):
return len(self.rev_species)
def _get_derivatives_not_none(x: Tensor, y: Tensor, retain_graph: Optional[bool] = None, create_graph: bool = False) -> Tensor:
ret = torch.autograd.grad([y.sum()], [x], retain_graph=retain_graph, create_graph=create_graph)[0]
assert ret is not None
return ret
[docs]def hessian(coordinates: Tensor, energies: Optional[Tensor] = None, forces: Optional[Tensor] = None) -> Tensor:
"""Compute analytical hessian from the energy graph or force graph.
Arguments:
coordinates (:class:`torch.Tensor`): Tensor of shape `(molecules, atoms, 3)`
energies (:class:`torch.Tensor`): Tensor of shape `(molecules,)`, if specified,
then `forces` must be `None`. This energies must be computed from
`coordinates` in a graph.
forces (:class:`torch.Tensor`): Tensor of shape `(molecules, atoms, 3)`, if specified,
then `energies` must be `None`. This forces must be computed from
`coordinates` in a graph.
Returns:
:class:`torch.Tensor`: Tensor of shape `(molecules, 3A, 3A)` where A is the number of
atoms in each molecule
"""
if energies is None and forces is None:
raise ValueError('Energies or forces must be specified')
if energies is not None and forces is not None:
raise ValueError('Energies or forces can not be specified at the same time')
if forces is None:
assert energies is not None
forces = -_get_derivatives_not_none(coordinates, energies, create_graph=True)
flattened_force = forces.flatten(start_dim=1)
force_components = flattened_force.unbind(dim=1)
return -torch.stack([
_get_derivatives_not_none(coordinates, f, retain_graph=True).flatten(start_dim=1)
for f in force_components
], dim=1)
class FreqsModes(NamedTuple):
freqs: Tensor
modes: Tensor
class VibAnalysis(NamedTuple):
freqs: Tensor
modes: Tensor
fconstants: Tensor
rmasses: Tensor
[docs]def vibrational_analysis(masses, hessian, mode_type='MDU', unit='cm^-1'):
"""Computing the vibrational wavenumbers from hessian.
Note that normal modes in many popular software packages such as
Gaussian and ORCA are output as mass deweighted normalized (MDN).
Normal modes in ASE are output as mass deweighted unnormalized (MDU).
Some packages such as Psi4 let ychoose different normalizations.
Force constants and reduced masses are calculated as in Gaussian.
mode_type should be one of:
- MWN (mass weighted normalized)
- MDU (mass deweighted unnormalized)
- MDN (mass deweighted normalized)
MDU modes are not orthogonal, and not normalized,
MDN modes are not orthogonal, and normalized.
MWN modes are orthonormal, but they correspond
to mass weighted cartesian coordinates (x' = sqrt(m)x).
"""
if unit == 'meV':
unit_converter = sqrt_mhessian2milliev
elif unit == 'cm^-1':
unit_converter = sqrt_mhessian2invcm
else:
raise ValueError('Only meV and cm^-1 are supported right now')
assert hessian.shape[0] == 1, 'Currently only supporting computing one molecule a time'
# Solving the eigenvalue problem: Hq = w^2 * T q
# where H is the Hessian matrix, q is the normal coordinates,
# T = diag(m1, m1, m1, m2, m2, m2, ....) is the mass
# We solve this eigenvalue problem through Lowdin diagnolization:
# Hq = w^2 * Tq ==> Hq = w^2 * T^(1/2) T^(1/2) q
# Letting q' = T^(1/2) q, we then have
# T^(-1/2) H T^(-1/2) q' = w^2 * q'
inv_sqrt_mass = (1 / masses.sqrt()).repeat_interleave(3, dim=1) # shape (molecule, 3 * atoms)
mass_scaled_hessian = hessian * inv_sqrt_mass.unsqueeze(1) * inv_sqrt_mass.unsqueeze(2)
if mass_scaled_hessian.shape[0] != 1:
raise ValueError('The input should contain only one molecule')
mass_scaled_hessian = mass_scaled_hessian.squeeze(0)
eigenvalues, eigenvectors = torch.linalg.eigh(mass_scaled_hessian)
angular_frequencies = eigenvalues.sqrt()
frequencies = angular_frequencies / (2 * math.pi)
# converting from sqrt(hartree / (amu * angstrom^2)) to cm^-1 or meV
wavenumbers = unit_converter(frequencies)
# Note that the normal modes are the COLUMNS of the eigenvectors matrix
mw_normalized = eigenvectors.t()
md_unnormalized = mw_normalized * inv_sqrt_mass
norm_factors = 1 / torch.linalg.norm(md_unnormalized, dim=1) # units are sqrt(AMU)
md_normalized = md_unnormalized * norm_factors.unsqueeze(1)
rmasses = norm_factors**2 # units are AMU
# The conversion factor for Ha/(AMU*A^2) to mDyne/(A*AMU) is about 4.3597482
fconstants = mhessian2fconst(eigenvalues) * rmasses # units are mDyne/A
if mode_type == 'MDN':
modes = (md_normalized).reshape(frequencies.numel(), -1, 3)
elif mode_type == 'MDU':
modes = (md_unnormalized).reshape(frequencies.numel(), -1, 3)
elif mode_type == 'MWN':
modes = (mw_normalized).reshape(frequencies.numel(), -1, 3)
return VibAnalysis(wavenumbers, modes, fconstants, rmasses)
[docs]def get_atomic_masses(species):
r"""Convert a tensor of atomic numbers ("periodic table indices") into a tensor of atomic masses
Atomic masses supported are the first 119 elements, and are taken from:
Atomic weights of the elements 2013 (IUPAC Technical Report). Meija, J.,
Coplen, T., Berglund, M., et al. (2016). Pure and Applied Chemistry, 88(3), pp.
265-291. Retrieved 30 Nov. 2016, from doi:10.1515/pac-2015-0305
They are all consistent with those used in ASE
Arguments:
species (:class:`torch.Tensor`): tensor with atomic numbers
Returns:
:class:`torch.Tensor`: Tensor of dtype :class:`torch.double`, with
atomic masses, with the same shape as the input.
"""
# Note that there should not be any atoms with index zero, because that is
# not an element
assert len((species == 0).nonzero()) == 0
default_atomic_masses = torch.tensor(
[0. , 1.008 , 4.002602 , 6.94 , # noqa
9.0121831 , 10.81 , 12.011 , 14.007 , # noqa
15.999 , 18.99840316, 20.1797 , 22.98976928, # noqa
24.305 , 26.9815385 , 28.085 , 30.973762 , # noqa
32.06 , 35.45 , 39.948 , 39.0983 , # noqa
40.078 , 44.955908 , 47.867 , 50.9415 , # noqa
51.9961 , 54.938044 , 55.845 , 58.933194 , # noqa
58.6934 , 63.546 , 65.38 , 69.723 , # noqa
72.63 , 74.921595 , 78.971 , 79.904 , # noqa
83.798 , 85.4678 , 87.62 , 88.90584 , # noqa
91.224 , 92.90637 , 95.95 , 97.90721 , # noqa
101.07 , 102.9055 , 106.42 , 107.8682 , # noqa
112.414 , 114.818 , 118.71 , 121.76 , # noqa
127.6 , 126.90447 , 131.293 , 132.90545196, # noqa
137.327 , 138.90547 , 140.116 , 140.90766 , # noqa
144.242 , 144.91276 , 150.36 , 151.964 , # noqa
157.25 , 158.92535 , 162.5 , 164.93033 , # noqa
167.259 , 168.93422 , 173.054 , 174.9668 , # noqa
178.49 , 180.94788 , 183.84 , 186.207 , # noqa
190.23 , 192.217 , 195.084 , 196.966569 , # noqa
200.592 , 204.38 , 207.2 , 208.9804 , # noqa
208.98243 , 209.98715 , 222.01758 , 223.01974 , # noqa
226.02541 , 227.02775 , 232.0377 , 231.03588 , # noqa
238.02891 , 237.04817 , 244.06421 , 243.06138 , # noqa
247.07035 , 247.07031 , 251.07959 , 252.083 , # noqa
257.09511 , 258.09843 , 259.101 , 262.11 , # noqa
267.122 , 268.126 , 271.134 , 270.133 , # noqa
269.1338 , 278.156 , 281.165 , 281.166 , # noqa
285.177 , 286.182 , 289.19 , 289.194 , # noqa
293.204 , 293.208 , 294.214], # noqa
dtype=torch.double, device=species.device) # noqa
masses = default_atomic_masses[species]
return masses
# This constant, when indexed with the corresponding atomic number, gives the
# element associated with it. Note that there is no element with atomic number
# 0, so 'Dummy' returned in this case.
PERIODIC_TABLE = ['Dummy'] + """
H He
Li Be B C N O F Ne
Na Mg Al Si P S Cl Ar
K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr
Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe
Cs Ba La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn
Fr Ra Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr Rf Db Sg Bh Hs Mt Ds Rg Cn Nh Fl Mc Lv Ts Og
""".strip().split()
__all__ = ['pad_atomic_properties', 'present_species', 'hessian',
'vibrational_analysis', 'strip_redundant_padding',
'ChemicalSymbolsToInts', 'get_atomic_masses']