# SPDX-FileCopyrightText: Copyright (c) OpenGeoSys Community (opengeosys.org)
# SPDX-License-Identifier: BSD-3-Clause
from __future__ import annotations
from collections.abc import Sequence
from functools import partial
from typing import Literal
from ogstools.mesh.utils import angles, azimuth
from ogstools.variables import tensor_math
from ogstools.variables.variable import Scalar, Variable
from ogstools.variables.vector import Vector, VectorList
from .func import Function
[docs]
class Matrix(Variable):
"""Represent a matrix variable.
Matrix variables should contain either 4 (2D) or 6 (3D) components.
Matrix components can be accesses with brackets e.g. stress[0]
"""
[docs]
def __getitem__(
self,
index: (
int
| Literal["xx", "yy", "zz", "xy", "yz", "xz"]
| Literal["rr", "tt", "pp", "rt", "tp", "rp"]
),
) -> Scalar:
"""A scalar variable as a matrix component.
The following index values correspond to a polar coordinate system:
rr: radial component
tt: angular component in theta (azimuthal) direction
pp: angular component in phi (polar) direction
rt: shear component in the radial-azimuthal plane
tp: shear component in the azimuthal-polar plane
rp: shear component in the radial-polar plane
"""
cartesian_keys = {"xx": 0, "yy": 1, "zz": 2, "xy": 3, "yz": 4, "xz": 5}
polar_keys = {"rr": 0, "tt": 1, "pp": 2, "rt": 3, "tp": 4, "rp": 5}
key_map = cartesian_keys | polar_keys
if not isinstance(index, int) and index not in key_map:
allowed = list(key_map.keys())
msg = f"Matrix index can only be an int or one of {allowed}."
raise KeyError(msg)
int_index = key_map.get(str(index), index)
return Scalar.from_variable(
self,
output_name=self.output_name + f"_{index}",
symbol=f"{{{self.symbol}}}_{{{index}}}",
func=lambda x: x[..., int_index],
bilinear_cmap=True,
)
[docs]
def to_polar(
self, center: Sequence = (0, 0, 0), normal: Sequence = (0, 0, 1)
) -> Matrix:
"""Return the Matrix converted to a polar coordinate system.
For 3D only spherical coordinate system is implemented for now.
"""
return Matrix.from_variable(
self,
func=Function(
tensor_math.to_polar,
[partial(angles, center=center, normal=normal), azimuth],
),
)
@property
def magnitude(self) -> Scalar:
"A scalar variable as the frobenius norm of the matrix."
return Scalar.from_variable(
self,
output_name=self.output_name + "_magnitude",
symbol=rf"||{{{self.symbol}}}||_\mathrm{{F}}",
func=tensor_math.frobenius_norm,
)
@property
def trace(self) -> Scalar:
"A scalar variable as the trace of the matrix."
return Scalar.from_variable(
self,
output_name=self.output_name + "_trace",
symbol=rf"\mathrm{{tr}}({{{self.symbol}}})",
func=tensor_math.trace,
)
@property
def eigenvalues(self) -> Vector:
"A vector variable as the eigenvalues of the matrix."
return Vector.from_variable(
self,
output_name=self.output_name + "_eigenvalues",
symbol=r"\lambda",
func=tensor_math.eigenvalues,
)
@property
def eigenvectors(self) -> VectorList:
"A vector variable as the eigenvectors of the matrix."
return VectorList.from_variable(
self,
output_name=self.output_name + "_eigenvectors",
symbol="v",
data_unit="",
output_unit="",
func=tensor_math.eigenvectors,
)
@property
def det(self) -> Scalar:
"A scalar variable as the determinant of the matrix."
return Scalar.from_variable(
self,
output_name=self.output_name + "_det",
output_unit=self.output_unit + "^2",
symbol=rf"\mathrm{{det}} {{{self.symbol}}}",
process_with_units=True,
func=tensor_math.det,
)
@property
def invariant_1(self) -> Scalar:
"A scalar variable as the first invariant of the matrix."
return Scalar.from_variable(
self,
output_name=self.output_name + "_I1",
func=tensor_math.invariant_1,
)
@property
def invariant_2(self) -> Scalar:
"A scalar variable as the second invariant of the matrix."
return Scalar.from_variable(
self,
output_unit=self.output_unit + "^2",
output_name=self.output_name + "_I2",
func=tensor_math.invariant_2,
process_with_units=True,
)
@property
def invariant_3(self) -> Scalar:
"A scalar variable as the third invariant of the matrix."
return Scalar.from_variable(
self,
output_name=self.output_name + "_I3",
func=tensor_math.invariant_3,
)
@property
def tensor_mean(self) -> Scalar:
"A scalar variable as the mean value of the matrix."
return Scalar.from_variable(
self,
output_name="mean_" + self.output_name,
symbol=r"\pi",
func=tensor_math.mean,
)
@property
def hydrostatic_component(self) -> Matrix:
"A vector variable as the effective pressure of the matrix."
return Matrix.from_variable(
self,
output_name="hydrostatic_" + self.output_name + "_component",
symbol=rf"p^{{{self.symbol}}}",
func=tensor_math.hydrostatic_component,
)
@property
def deviator(self) -> Matrix:
"A vector variable as the deviator of the matrix."
return Matrix.from_variable(
self,
output_name=self.output_name + "_deviator",
symbol=rf"s^{{{self.symbol}}}",
func=tensor_math.deviator,
)
@property
def deviator_invariant_1(self) -> Scalar:
"A scalar variable as the first invariant of the matrix deviator."
return Scalar.from_variable(
self,
output_name=self.output_name + "_J1",
func=tensor_math.deviator_invariant_1,
)
@property
def deviator_invariant_2(self) -> Scalar:
"A scalar variable as the second invariant of the matrix deviator."
return Scalar.from_variable(
self,
output_name=self.output_name + "_J2",
func=tensor_math.deviator_invariant_2,
)
@property
def deviator_invariant_3(self) -> Scalar:
"A scalar variable as the third invariant of the matrix deviator."
return Scalar.from_variable(
self,
output_name=self.output_name + "_J3",
func=tensor_math.deviator_invariant_3,
)
@property
def octahedral_shear(self) -> Scalar:
"A scalar variable as the octahedral shear component of the matrix."
return Scalar.from_variable(
self,
output_name="octahedral_shear_" + self.output_name,
symbol=r"\tau_\mathrm{oct}",
func=tensor_math.octahedral_shear,
)
@property
def von_Mises(self) -> Scalar:
"A scalar variable as the von Mises stress."
return Scalar.from_variable(
self,
output_name="von_Mises_" + self.output_name,
symbol=rf"{{{self.symbol}}}_\mathrm{{v}}",
func=tensor_math.von_mises,
)
@property
def qp_ratio(self) -> Scalar:
"A scalar variable as the qp stress ratio."
return Scalar.from_variable(
self,
output_name="qp_ratio",
output_unit="%",
symbol="qp",
func=tensor_math.qp_ratio,
process_with_units=True,
)
