r"""
Exchange parameter class.
"""
# SELF is introduced in python 3.11, it is too fresh for my taste
from typing import TypeVar, Union
Self = TypeVar("Self", bound="ExchangeParameter")
import numpy as np
from radtools.routines import print_2d_array
[docs]
class ExchangeParameter:
r"""
Exchange parameter (:math:`\boldsymbol{J}`) class.
Basically it is a wrapper around :numpy:`ndarray`
with predefined exchange-specific attributes.
Any function, which work on :numpy:`ndarray` should work on
:py:class:`.ExchangeParameter` as well. It will act on the
:py:attr:`.matrix` attribute.
If ``matrix`` is specified then ``iso``, ``aniso`` and ``dmi`` are
ignored and derived from ``matrix``. If ``matrix`` is not specified
then it is derived from ``iso``, ``aniso`` and ``dmi``.
If nothing is provided exchange matrix is set to zero matrix.
Parameters
----------
iso : int or float, optional
Value of isotropic exchange parameter.
aniso : (3, 3) |array_like|_, optional
3 x 3 matrix of symmetric anisotropic exchange.
dmi : (3,) |array_like|_, optional
Dzyaroshinsky-Moria interaction vector :math:`(D_x, D_y, D_z)`.
matrix : (3, 3) |array_like|_, optional
Exchange matrix.
"""
def __init__(self, matrix=None, iso=None, aniso=None, dmi=None) -> None:
self._matrix = np.zeros((3, 3), dtype=float)
self._iso = 0.0
self._aniso = np.zeros((3, 3), dtype=float)
self._dmi = np.zeros(3, dtype=float)
if matrix is None:
if iso is not None:
self.iso = iso
if dmi is not None:
self.dmi = dmi
if aniso is not None:
self.aniso = aniso
else:
self.matrix = matrix
def __format__(self, fmt):
return self.__str__(fmt=fmt)
def __str__(self, fmt=".4f"):
return print_2d_array(self.matrix, fmt=fmt, print_result=False, borders=False)
def __repr__(self):
return f"ExchangeParameter({self.matrix.__repr__()})"
@property
def __array_interface__(self):
return self.matrix.__array_interface__
@property
def T(self):
r"""
Transposes a matrix of the exchange parameter.
It returns new instance of the :py:class`.ExchangeParameter`
with transposed matrix.
Returns
-------
ExchangeParameter : :py:class`.ExchangeParameter`
New instance of the :py:class`.ExchangeParameter`
with transposed matrix.
"""
return ExchangeParameter(matrix=self.matrix.T)
@property
def matrix(self) -> np.ndarray:
r"""
Full exchange matrix.
.. code-block:: python
[[J_xx, J_xy, J_xz],
[J_yx, J_yy, J_yz],
[J_zx, J_zy, J_zz]]
Returns
-------
matrix : (3, 3) :numpy:`ndarray`
Full exchange matrix.
See Also
--------
symm_matrix
Symmetric part.
asymm_matrix
Asymmetric part.
"""
return self._matrix
@matrix.setter
def matrix(self, new_matrix):
try:
new_matrix = np.array(new_matrix, dtype=float)
except:
raise ValueError(f"New matrix is not array_like: \n{new_matrix}")
if new_matrix.shape != (3, 3):
raise ValueError("Matrix shape has to be equal to (3, 3)")
self._matrix = new_matrix
@property
def symm_matrix(self) -> np.ndarray:
r"""
Symmetric part of exchange :py:attr:`.matrix`.
.. math::
J_{symm} = \dfrac{J + J^T}{2}
Returns
-------
symm_matrix : (3, 3) :numpy:`ndarray`
Symmetric part of exchange matrix.
See Also
--------
asymm_matrix
Asymmetric part.
matrix
Full matrix.
"""
return (self.matrix + self.matrix.T) / 2
@property
def asymm_matrix(self) -> np.ndarray:
"""
Asymmetric part of exchange :py:attr:`.matrix`.
.. math::
J_{asymm} = \dfrac{J - J^T}{2}
Returns
-------
asymm_matrix : (3, 3) :numpy:`ndarray`
Asymmetric part of exchange matrix.
See Also
--------
symm_matrix
Symmetric part.
matrix
Full matrix.
"""
return (self.matrix - self.matrix.T) / 2
@property
def iso(self) -> float:
r"""
Value of isotropic exchange parameter.
Derived from the exchange matrix (:math:`\mathbf{J}`) as
.. math::
J_{iso} = \dfrac{1}{3}Tr(\mathbf{J})
Returns
-------
iso : float
Value of isotropic exchange parameter.
See Also
--------
iso_matrix
Isotropic exchange in a matrix form.
"""
return np.trace(self.symm_matrix) / 3
@iso.setter
def iso(self, new_iso):
new_iso = new_iso - self.iso
self.matrix = self.matrix + (new_iso) * np.identity(3, dtype=float)
@property
def iso_matrix(self) -> np.ndarray:
r"""
Isotropic part of the exchange :py:attr:`.matrix`.
Matrix form:
.. code-block:: python
[[J, 0, 0],
[0, J, 0],
[0, 0, J]]
Returns
-------
iso_matrix : (3, 3) :numpy:`ndarray`
Isotropic part of the exchange matrix.
See Also
--------
iso
Isotropic exchange parameter.
"""
return self.iso * np.identity(3, dtype=float)
@property
def aniso(self) -> np.ndarray:
r"""
3 x 3 matrix of symmetric anisotropic exchange.
.. code-block:: python
[[J_xx, J_xy, J_xz],
[J_xy, J_yy, J_yz],
[J_xz, J_yz, J_zz]]
Derived from the exchange matrix (:math:`\mathbf{J}`) as
.. math::
\mathbf{J}_{aniso} = \mathbf{J}_{symm} - \dfrac{1}{3}Tr(\mathbf{J})
\cdot \mathbf{I}
where :math:`\mathbf{I}` is a :math:`3\times3` identity matrix.
Returns
-------
aniso : (3, 3) :numpy:`ndarray`
Matrix of symmetric anisotropic exchange.
See Also
--------
aniso_diagonal
Diagonal part of the symmetric anisotropic exchange.
aniso_diagonal_matrix
Diagonal part of the symmetric anisotropic exchange in a matrix form.
"""
return self.symm_matrix - self.iso * np.identity(3, dtype=float)
@aniso.setter
def aniso(self, new_aniso):
try:
new_aniso = np.array(new_aniso, dtype=float)
except:
raise ValueError(f"New aniso is not array_like: \n{new_aniso}")
if new_aniso.shape != (3, 3):
raise ValueError("Aniso matrix shape have " + "to be equal to (3, 3)")
# correction is correct (see matrix update)
new_aniso = new_aniso - self.aniso
self.matrix = self.matrix + new_aniso
@property
def aniso_diagonal(self) -> np.ndarray:
r"""
Diagonal part of the symmetric anisotropic exchange.
.. code-block:: python
[J_xx, J_yy, J_zz]
Returns
-------
aniso_diagonal : (3,) :numpy:`ndarray`
Diagonal part of the symmetric anisotropic exchange.
See Also
--------
aniso
3 x 3 matrix of symmetric anisotropic exchange.
aniso_diagonal_matrix
Diagonal part of the symmetric anisotropic exchange in a matrix form.
"""
return np.diag(self.aniso)
@property
def aniso_diagonal_matrix(self) -> np.ndarray:
r"""
Diagonal part of the symmetric anisotropic exchange.
.. code-block:: python
[[J_xx, 0, 0],
[0, J_yy, 0],
[0, 0, J_zz]]
Returns
-------
aniso_diagonal_matrix : (3, 3) :numpy:`ndarray`
Diagonal part of the symmetric anisotropic exchange in matrix form.
See Also
--------
aniso
3 x 3 matrix of symmetric anisotropic exchange.
aniso_diagonal
Diagonal part of the symmetric anisotropic exchange.
"""
return np.diag(np.diag(self.aniso))
@property
def dmi(self) -> np.ndarray:
r"""
Dzyaroshinsky-Moria interaction vector (Dx, Dy, Dz).
.. code-block:: python
[D_x, D_y, D_z]
Returns
-------
dmi : (3,) :numpy:`ndarray`
Dzyaroshinsky-Moria interaction vector.
See Also
--------
dmi_matrix
Dzyaroshinsky-Moria interaction in a matrix form.
dmi_module
Module of Dzyaroshinsky-Moria vector.
rel_dmi
Relative strength of Dzyaroshinsky-Moria interaction.
"""
return np.array(
[self.asymm_matrix[1][2], self.asymm_matrix[2][0], self.asymm_matrix[0][1]],
dtype=float,
)
@dmi.setter
def dmi(self, new_dmi):
try:
new_dmi = np.array(new_dmi, dtype=float)
except:
raise ValueError(f"New DMI is not array_like: \n{new_dmi}")
if new_dmi.shape != (3,):
raise ValueError(f"DMI have to be a 3 component vector. {new_dmi}")
new_dmi = new_dmi - self.dmi
dmi_matrix = np.array(
[
[0, new_dmi[2], -new_dmi[1]],
[-new_dmi[2], 0, new_dmi[0]],
[new_dmi[1], -new_dmi[0], 0],
],
dtype=float,
)
self.matrix = self.matrix + dmi_matrix
@property
def dmi_matrix(self) -> np.ndarray:
r"""
Asymmetric part of the exchange :py:attr:`.matrix`.
.. code-block:: python
[[0, D_z, -D_y],
[-D_z, 0, D_x],
[D_y, -D_x, 0]]
Returns
-------
dmi_matrix : (3, 3) :numpy:`ndarray`
Asymmetric part of the exchange matrix.
See Also
--------
dmi
Dzyaroshinsky-Moria interaction vector.
dmi_module
Module of Dzyaroshinsky-Moria vector.
rel_dmi
Relative strength of Dzyaroshinsky-Moria interaction.
"""
return self.asymm_matrix
@property
def dmi_module(self) -> float:
r"""
Length of the DMI vector in the units of exchange interaction.
Returns
-------
dmi_module : float
Length of the DMI vector in the units of exchange interaction.
See Also
--------
dmi
Dzyaroshinsky-Moria interaction vector.
dmi_matrix
Dzyaroshinsky-Moria interaction in a matrix form.
rel_dmi
Relative strength of Dzyaroshinsky-Moria interaction.
"""
return np.linalg.norm(self.dmi)
@property
def rel_dmi(self) -> float:
r"""
Relative value of DMI.
.. math::
\frac{\vert DMI\vert}{\vert J\vert}
Returns
-------
rel_dmi : float
Relative value of DMI.
See Also
--------
dmi
Dzyaroshinsky-Moria interaction vector.
dmi_matrix
Dzyaroshinsky-Moria interaction in a matrix form.
dmi_module
Module of Dzyaroshinsky-Moria vector.
"""
return self.dmi_module / abs(self.iso)
# Definition of arithmetic operations5t
# + (add)
def __add__(self, other) -> Self:
if isinstance(other, ExchangeParameter):
matrix = self.matrix + other.matrix
else:
raise TypeError(
f"TypeError: unsupported operand type(s) "
+ f"for +: 'ExchangeParameter' and '{other.__class__.__name__}'"
)
return ExchangeParameter(matrix=matrix)
# - (sub)
def __sub__(self, other) -> Self:
if isinstance(other, ExchangeParameter):
matrix = self.matrix - other.matrix
else:
raise TypeError(
f"TypeError: unsupported operand type(s) "
+ f"for -: 'ExchangeParameter' and '{other.__class__.__name__}'"
)
return ExchangeParameter(matrix=matrix)
# *
def __mul__(self, number) -> Self:
try:
matrix = self.matrix * number
except:
raise TypeError(
f"TypeError: unsupported operand type(s) "
+ f"for *: 'ExchangeParameter' and '{number.__class__.__name__}'"
)
return ExchangeParameter(matrix=matrix)
# @
def __matmul__(self, other) -> np.ndarray:
try:
result = self.matrix @ other
except:
raise TypeError(
f"TypeError: unsupported operand type(s) "
+ f"for @: 'ExchangeParameter' and '{other.__class__.__name__}'"
)
return result
# /
def __truediv__(self, number) -> Self:
try:
matrix = self.matrix / number
except:
raise TypeError(
f"TypeError: unsupported operand type(s) "
+ f"for /: 'ExchangeParameter' and '{number.__class__.__name__}'"
)
return ExchangeParameter(matrix=matrix)
# //
def __floordiv__(self, number) -> Self:
try:
matrix = self.matrix // number
except:
raise TypeError(
f"TypeError: unsupported operand type(s) "
+ f"for //: 'ExchangeParameter' and '{number.__class__.__name__}'"
)
return ExchangeParameter(matrix=matrix)
# %
def __mod__(self, number) -> Self:
try:
matrix = self.matrix % number
except:
raise TypeError(
f"TypeError: unsupported operand type(s) "
+ f"for %: 'ExchangeParameter' and '{number.__class__.__name__}'"
)
return ExchangeParameter(matrix=matrix)
# *
def __rmul__(self, number) -> Self:
try:
matrix = number * self.matrix
except:
raise TypeError(
f"TypeError: unsupported operand type(s) "
+ f"for *: '{number.__class__.__name__}' and 'ExchangeParameter'"
)
return ExchangeParameter(matrix=matrix)
# @
def __rmatmul__(self, other) -> np.ndarray:
try:
result = other @ self.matrix
except:
raise TypeError(
f"TypeError: unsupported operand type(s) "
+ f"for @: '{other.__class__.__name__}' and 'ExchangeParameter'"
)
return result
# - (neg)
def __neg__(self) -> Self:
return ExchangeParameter(matrix=-self.matrix)
# + (pos)
def __pos__(self) -> Self:
return ExchangeParameter(matrix=self.matrix)
# abs()
def __abs__(self) -> Self:
return ExchangeParameter(matrix=np.abs(self.matrix))
# ==
def __eq__(self, other):
if isinstance(other, ExchangeParameter):
return (self.matrix == other.matrix).all()
try:
other = np.array(other, dtype=float)
except:
raise ValueError(f"Other is not array_like: \n{other}")
if other.shape != (3, 3):
raise ValueError("Other has to be equal to (3, 3)")
return (self.matrix == other).all()
# !=
def __neq__(self, other):
return not self == other
