Source code for pairinteraction.system.green_tensor

# SPDX-FileCopyrightText: 2024 PairInteraction Developers
# SPDX-License-Identifier: LGPL-3.0-or-later
from __future__ import annotations

from typing import TYPE_CHECKING, TypeVar, overload

import numpy as np

from pairinteraction import _backend
from pairinteraction.units import QuantityArray, QuantityScalar

if TYPE_CHECKING:
    from collections.abc import Sequence

    from typing_extensions import Self

    from pairinteraction.units import Dimension, NDArray, PintArray, PintFloat

    Quantity = TypeVar("Quantity", float, "PintFloat")


[docs] class GreenTensor: """Green tensor for the multipole pair interactions. This class allows to define custom constant or frequency-dependent Green tensors, which can then be used for the interaction of a :class:`SystemPair` (see :meth:`SystemPair.set_green_tensor`). Examples: >>> import pairinteraction as pi >>> gt = pi.GreenTensor() >>> distance_mum = 5 >>> tensor = np.array([[1, 0, 0], [0, 1, 0], [0, 0, -2]]) / distance_mum**3 >>> tensor_unit = "hartree / (e^2 micrometer^3)" >>> gt.set_from_cartesian(1, 1, tensor, tensor_unit) GreenTensor(...) >>> print(gt.get_spherical(1, 1, unit=tensor_unit).diagonal()) [ 0.008 -0.016 0.008] """ _cpp: _backend.GreenTensorComplex _cpp_type = _backend.GreenTensorComplex
[docs] def __init__(self) -> None: """Initialize a new Green tensor object. The actual tensor can be set afterwards via the :meth:`set_from_cartesian` method. """ self._cpp = self._cpp_type()
def __repr__(self) -> str: return f"{type(self).__name__}(...)" def __str__(self) -> str: return self.__repr__() @overload def set_from_cartesian(self, kappa1: int, kappa2: int, tensor: NDArray, tensor_unit: str | None = None) -> Self: ... @overload def set_from_cartesian( self, kappa1: int, kappa2: int, tensor: Sequence[NDArray], tensor_unit: str | None, omegas: Sequence[float], omegas_unit: str | None = None, ) -> Self: ... @overload def set_from_cartesian( self, kappa1: int, kappa2: int, tensor: Sequence[NDArray], *, omegas: Sequence[float], omegas_unit: str | None = None, ) -> Self: ...
[docs] def set_from_cartesian( self, kappa1: int, kappa2: int, tensor: NDArray | Sequence[NDArray], tensor_unit: str | None = None, omegas: Sequence[float] | None = None, omegas_unit: str | None = None, ) -> Self: """Set the entries of the Green tensor. Args: kappa1: The rank of the first multipole operator. kappa2: The rank of the second multipole operator. tensor: The green tensor in cartesian coordinates. Either a single tensor to set a constant green tensor or a list of tensors to set a frequency-dependent green tensor. tensor_unit: The unit of the tensor. Default None, which means that the tensor must be given as pint object. omegas: Only needed if a list of tensors is given. The frequencies of the tensors. omegas_unit: The unit of the frequencies. Default None, which means that the frequencies must be given as pint object. """ dimension: list[Dimension] = self._get_unit_dimension(kappa1, kappa2) if omegas is None: tensor_au = QuantityArray.convert_user_to_au(np.array(tensor), tensor_unit, dimension) if tensor_au.shape != (3**kappa1, 3**kappa2) or tensor_au.ndim != 2: raise ValueError("The tensor must be a 2D array of shape (3**kappa1, 3**kappa2).") self._cpp.create_entries_from_cartesian(kappa1, kappa2, tensor_au) return self tensors_au = [QuantityArray.convert_user_to_au(np.array(t), tensor_unit, dimension) for t in tensor] if not all(t.ndim == 2 for t in tensors_au): raise ValueError("The tensor must be a list of 2D arrays.") if not all(t.shape == (3**kappa1, 3**kappa2) for t in tensors_au): raise ValueError("The tensors must be of shape (3**kappa1, 3**kappa2).") omegas_au = QuantityArray.convert_user_to_au(np.array(omegas), omegas_unit, "energy") self._cpp.create_entries_from_cartesian(kappa1, kappa2, tensors_au, omegas_au.tolist()) return self
@overload def get_spherical( self, kappa1: int, kappa2: int, omega: float | None = None, omega_unit: str | None = None, unit: None = None, ) -> PintArray: ... @overload def get_spherical( self, kappa1: int, kappa2: int, omega: float | None = None, omega_unit: str | None = None, *, unit: str ) -> NDArray: ...
[docs] def get_spherical( self, kappa1: int, kappa2: int, omega: float | None = None, omega_unit: str | None = None, unit: str | None = None, ) -> PintArray | NDArray: """Get the Green tensor in spherical coordinates for the given indices kappa1 and kappa2. For kappa == 1 the spherical basis is [p_{1,-1}, p_{1,0}, p_{1,1}]. For kappa == 2 the spherical basis is [p_{2,-2}, p_{2,-1}, p_{2,0}, p_{2,1}, p_{2,2}, p_{0,0}]. Args: kappa1: The rank of the first multipole operator. kappa2: The rank of the second multipole operator. omega: The frequency at which to evaluate the Green tensor. Only needed if the Green tensor is frequency dependent. omega_unit: The unit of the frequency. Default None, which means that the frequency must be given as pint object. unit: The unit to which to convert the result. Default None, which means that the result is returned as pint object. Returns: The Green tensor as a 2D array. """ entries_cpp = self._cpp.get_spherical_entries(kappa1, kappa2) omega_au = QuantityScalar.convert_user_to_au(omega, omega_unit, "energy") if omega is not None else None dim1 = 3 if kappa1 == 1 else 6 dim2 = 3 if kappa2 == 1 else 6 tensor_au = np.zeros((dim1, dim2), dtype=complex) for entry_cpp in entries_cpp: if isinstance(entry_cpp, (_backend.ConstantEntryReal, _backend.ConstantEntryComplex)): val = entry_cpp.val() else: if omega_au is None: raise ValueError("The Green tensor has omega dependent entries, please specify an omega.") val = entry_cpp.val(omega_au) tensor_au[entry_cpp.row(), entry_cpp.col()] = val tensor_au = np.real_if_close(tensor_au) return QuantityArray.convert_au_to_user(tensor_au, self._get_unit_dimension(kappa1, kappa2), unit)
def _get_unit_dimension(self, kappa1: int, kappa2: int) -> list[Dimension]: return ["green_tensor_00", *["inverse_distance" for _ in range(kappa1 + kappa2 + 1)]] # type: ignore [list-item]
class GreenTensorReal(GreenTensor): _cpp: _backend.GreenTensorReal # type: ignore [assignment] _cpp_type = _backend.GreenTensorReal # type: ignore [assignment]