# Copyright (c) 2012-2025, OpenGeoSys Community (http://www.opengeosys.org)
# Distributed under a Modified BSD License.
# See accompanying file LICENSE.txt or
# http://www.opengeosys.org/project/license
#
from __future__ import annotations
from collections.abc import Sequence
from typing import Literal
import numpy as np
from pyvista import UnstructuredGrid
from typeguard import typechecked
from ogstools.variables import tensor_math
from ogstools.variables.mesh_dependent import angles
from ogstools.variables.variable import Scalar, Variable
from ogstools.variables.vector import Vector, VectorList
[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]
@typechecked
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
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: self.func(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.
"""
def theta(mesh: UnstructuredGrid) -> np.ndarray | None:
"Calculate the azimuth angle with regards to the z-axis"
if np.shape(mesh[self.data_name])[-1] == 4: # 2D
return None
pts, z = (mesh.points, mesh.points[:, 2])
r = np.hypot(*pts[:, [0, 1]].T)
return np.arctan(
np.divide(r, z, out=np.ones_like(z) * 1e12, where=z != 0.0)
)
return self.replace(
mesh_dependent=True,
func=lambda mesh: (
tensor_math.to_polar(
self.func(self._get_data(mesh)),
angles(mesh, center, normal),
theta(mesh),
)
),
)
@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=lambda x: tensor_math.frobenius_norm(self.func(x)),
)
@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=lambda x: tensor_math.eigenvalues(self.func(x)),
)
@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=lambda x: tensor_math.eigenvectors(self.func(x)),
)
@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",
symbol=rf"\mathrm{{det}} {{{self.symbol}}}",
func=lambda x: tensor_math.det(self.func(x)),
)
@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=lambda x: tensor_math.invariant_1(self.func(x)),
)
@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=lambda x: tensor_math.invariant_2(self.func(x)),
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=lambda x: tensor_math.invariant_3(self.func(x)),
)
@property
def 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=lambda x: tensor_math.mean(self.func(x)),
)
@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=lambda x: tensor_math.hydrostatic_component(self.func(x)),
)
@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=lambda x: tensor_math.deviator(self.func(x)),
)
@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=lambda x: tensor_math.deviator_invariant_1(self.func(x)),
)
@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=lambda x: tensor_math.deviator_invariant_2(self.func(x)),
)
@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=lambda x: tensor_math.deviator_invariant_3(self.func(x)),
)
@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=lambda x: tensor_math.octahedral_shear(self.func(x)),
)
@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=lambda x: tensor_math.von_mises(self.func(x)),
)
@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="percent",
symbol="qp",
func=lambda x: tensor_math.qp_ratio(self.func(x)),
process_with_units=True,
)
