# Copyright (c) 2012-2024, 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 dataclasses import dataclass
from typing import Literal
from ogstools.variables import tensor_math
from ogstools.variables.variable import Scalar, Variable
from ogstools.variables.vector import Vector, VectorList
[docs]
@dataclass
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"]
) -> Scalar:
"A scalar variable as a matrix component."
int_index = (
index
if isinstance(index, int)
else ["xx", "yy", "zz", "xy", "yz", "xz"].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,
)
@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{{Mises}}",
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,
)
