Implementation of a 3D matrix. More...

#include <Matrix.h>

Public Member Functions
	Matrix3D ()
	default constructor More...

	Matrix3D (Mdouble xx, Mdouble xy, Mdouble xz, Mdouble yx, Mdouble yy, Mdouble yz, Mdouble zx, Mdouble zy, Mdouble zz)
	Alternative constructor, which let you define all elements. More...

	Matrix3D (const SmallMatrix< 3, 3 > &matrix)
	Alternative constructor, which takes a matrix of the same size. More...

void	setZero ()
	Sets all elements to zero. More...

double	trace () const
	Sum of the diagonal elements. More...

Vec3D	diag () const
	The diagonal elements. More...

double	determinant () const

double	deviator () const
	Deviator. More...

Matrix3D	operator+ (const Matrix3D &A) const
	Matrix addition. More...

Matrix3D	operator- (const Matrix3D &A) const
	Matrix subtraction. More...

Matrix3D	operator+ (Mdouble a) const
	Scalar addition. More...

Matrix3D	operator- (Mdouble a) const
	Scalar subtraction. More...

Matrix3D	operator* (Mdouble a) const
	Scalar multiplication. More...

Vec3D	operator* (const Vec3D &a) const
	Vector multiplication. More...

Matrix3D	operator* (const Matrix3D &a) const
	Matrix multiplication. More...

Matrix3D	operator/ (Mdouble a) const
	Scalar division. More...

Matrix3D &	operator+= (const Matrix3D &A)
	Matrix addition. More...

Matrix3D &	operator-= (const Matrix3D &A)
	Matrix substraction. More...

Matrix3D &	operator/= (Mdouble a)
	Scalar division. More...

Vec3D	ldivide (const Vec3D &b)
	A.ldivide(b) computes the solution x to A*x=b. More...

Matrix3D	getCylindricalTensorField (const Vec3D &p) const
	Returns the matrix in cylindrical coordinates. More...

Static Public Member Functions
static Matrix3D	square (const Matrix3D &A)
	Calculates the pointwise square. More...

static Matrix3D	sqrt (const Matrix3D &A)
	Calculates the pointwise square root. More...

static Matrix3D	dyadic (const Vec3D &a, const Vec3D &b)
	Calculates the dyadic product of a two Vec3D: \(a \otimes b\). More...

static Matrix3D	cross (const Vec3D &a, const Matrix3D &b)
	'Special' cross product; CP of vector with each column of a matrix More...

static Matrix3D	inverse (const Matrix3D &A)
	Computes the inverse of a matrix. More...

Public Attributes
Mdouble	XX
	all nine matrix elements More...

Mdouble	XY

Mdouble	XZ

Mdouble	YX

Mdouble	YY

Mdouble	YZ

Mdouble	ZX

Mdouble	ZY

Mdouble	ZZ

Friends
std::ostream &	operator<< (std::ostream &os, const Matrix3D &A)
	Add elements to ostream. More...

std::istream &	operator>> (std::istream &is, Matrix3D &A)
	Add elements to istream. More...

Detailed Description

Implementation of a 3D matrix.

Constructor & Destructor Documentation

◆ Matrix3D() [1/3]

Matrix3D::Matrix3D ( )

default constructor

default constructor, which is empty (i.e., only creates the object)

 {
     setZero();
 }

References setZero().

Referenced by cross(), dyadic(), getCylindricalTensorField(), operator*(), operator+(), operator-(), operator/(), sqrt(), and square().

◆ Matrix3D() [2/3]

Matrix3D::Matrix3D	(	Mdouble	xx,
		Mdouble	xy,
		Mdouble	xz,
		Mdouble	yx,
		Mdouble	yy,
		Mdouble	yz,
		Mdouble	zx,
		Mdouble	zy,
		Mdouble	zz
	)

Alternative constructor, which let you define all elements.

Alternative constructor. Let's you specify ALL 9 elements of the 3x3 matrix.

Parameters

[in] [all] xx/xy/xz /yx/yy/yz /zx/zy/zz are all nine elements (left-to-right, top-to-bottom) of the 3D matrix.

 {
     XX = xx;
     XY = xy;
     XZ = xz;
     YX = yx;
     YY = yy;
     YZ = yz;
     ZX = zx;
     ZY = zy;
     ZZ = zz;
 }

References XX, xy, XY, XZ, YX, YY, YZ, ZX, ZY, and ZZ.

◆ Matrix3D() [3/3]

Matrix3D::Matrix3D ( const SmallMatrix< 3, 3 > & matrix )

Alternative constructor, which takes a matrix of the same size.

 {
     XX = matrix(0, 0);
     XY = matrix(0, 1);
     XZ = matrix(0, 2);
     YX = matrix(1, 0);
     YY = matrix(1, 1);
     YZ = matrix(1, 2);
     ZX = matrix(2, 0);
     ZY = matrix(2, 1);
     ZZ = matrix(2, 2);
 }

References matrix(), XX, XY, XZ, YX, YY, YZ, ZX, ZY, and ZZ.

Member Function Documentation

◆ cross()

Matrix3D Matrix3D::cross	(	const Vec3D &	a,
		const Matrix3D &	B
	)

static

'Special' cross product; CP of vector with each column of a matrix

Returns a matrix, who's columns are the inner product of a given vector with the corresponding columns of a given matrix

Parameters

[in]	a	vector
[in]	B	matrix

Returns: Resulting matrix

 {
     return Matrix3D(
             a.Y * B.ZX - a.Z * B.YX, a.Y * B.ZY - a.Z * B.YY, a.Y * B.ZZ - a.Z * B.YZ,
             a.Z * B.XX - a.X * B.ZX, a.Z * B.XY - a.X * B.ZY, a.Z * B.XZ - a.X * B.ZZ,
             a.X * B.YX - a.Y * B.XX, a.X * B.YY - a.Y * B.XY, a.X * B.YZ - a.Y * B.XZ);
 }

References a, and Matrix3D().

◆ determinant()

double Matrix3D::determinant ( ) const

inline

Returns the determinant of this matrix https://www.mathsisfun.com/algebra/matrix-determinant.html

                                {
         return XX*(YY*ZZ-YZ*ZY) - XY*(YX*ZZ-YZ*ZX) + XZ*(YX*ZY-YY*ZX);
     }

References XX, XY, XZ, YX, YY, YZ, ZX, ZY, and ZZ.

◆ deviator()

Mdouble Matrix3D::deviator ( ) const

Deviator.

Returns an invariant of the deviatoric tensor, scaled such that it is equal to shear stress for the stress tensor.

Returns: resulting scalar

 {
     const Mdouble P = trace() / 3.0;
     return std::sqrt(0.5 * (mathsFunc::square(XX - P) + mathsFunc::square(YY - P) + mathsFunc::square(ZZ - P)) +
                      0.25 * (mathsFunc::square(XY + YX) + mathsFunc::square(XZ + ZX) + mathsFunc::square(YZ + ZY)));
 }

References Global_Physical_Variables::P, sqrt(), mathsFunc::square(), trace(), XX, XY, XZ, YX, YY, YZ, ZX, ZY, and ZZ.

◆ diag()

Vec3D Matrix3D::diag ( ) const

The diagonal elements.

Returns the sum of the diagonal elements of the matrix.

Returns: The trace of the matrix divided by 3 as an Mdouble

 {
     return Vec3D(XX, YY, ZZ);
 }

References XX, YY, and ZZ.

◆ dyadic()

Matrix3D Matrix3D::dyadic	(	const Vec3D &	a,
		const Vec3D &	b
	)

static

Calculates the dyadic product of a two Vec3D: \(a \otimes b\).

Dyadic product of two vectors

Parameters

[in]	a	first vector
[in]	b	second vector

Returns: Resulting matrix

 {
     return Matrix3D(a.X * b.X, a.X * b.Y, a.X * b.Z,
                     a.Y * b.X, a.Y * b.Y, a.Y * b.Z,
                     a.Z * b.X, a.Z * b.Y, a.Z * b.Z);
 }

References a, b, and Matrix3D().

Referenced by CGFields::GradVelocityField::addParticleDifferentialStatistics(), DPMBase::getKineticStress(), DPMBase::getStaticStress(), main(), CGFields::StandardFields::setFields(), and CGFields::StandardFieldsBinning::setFields().

◆ getCylindricalTensorField()

Matrix3D Matrix3D::getCylindricalTensorField ( const Vec3D & p ) const

Returns the matrix in cylindrical coordinates.

Transforms the (Cartesian) vector to cylindrical coordinates. See https://en.wikipedia.org/wiki/Vector_fields_in_cylindrical_and_spherical_coordinates

Returns: Transformed vector

 {
     //define sin(A)=y/r, cos(A)=x/r
     const Mdouble r = std::sqrt(p.X * p.X + p.Y * p.Y);
     Mdouble s = p.Y / r;
     Mdouble c = p.X / r;
     if (r == 0)
     {
         s = 0;
         c = 1;
     }
     const Matrix3D M = Matrix3D(XX * c + XY * s, -XX * s + XY * c, XZ,
                                 YX * c + YY * s, -YX * s + YY * c, YZ,
                                 ZX * c + ZY * s, -ZX * s + ZY * c, ZZ);
     return Matrix3D(M.XX * c + M.YX * s, -M.XX * s + M.YX * c, M.ZX,
                     M.XY * c + M.YY * s, -M.XY * s + M.YY * c, M.ZY,
                     M.XZ * c + M.YZ * s, -M.XZ * s + M.YZ * c, M.ZZ);
 }

References calibrate::c, Matrix3D(), p, UniformPSDSelfTest::r, s, sqrt(), XX, XY, XZ, YX, YY, YZ, ZX, ZY, and ZZ.

Referenced by main(), and CGFields::StandardFields::setCylindricalFields().

◆ inverse()

Matrix3D Matrix3D::inverse ( const Matrix3D & A )

static

Computes the inverse of a matrix.

Parameters

[in] A Matrix that should be inverted.

Returns: Inverse of matrix A.

 {
     Matrix3D result;
     Mdouble det;
     det = 1. / (A.XX * (A.YY * A.ZZ - A.YZ * A.ZY)
                 + A.XY * (A.YZ * A.ZX - A.YX * A.ZZ)
                 + A.XZ * (A.YX * A.ZY - A.YY * A.ZX));
     result.XX = (A.YY * A.ZZ - A.YZ * A.ZY) * det;
     result.XY = -(A.XY * A.ZZ - A.XZ * A.ZY) * det;
     result.XZ = (A.XY * A.YZ - A.XZ * A.YY) * det;
     result.YX = -(A.YX * A.ZZ - A.YZ * A.ZX) * det;
     result.YY = (A.XX * A.ZZ - A.XZ * A.ZX) * det;
     result.YZ = -(A.XX * A.YZ - A.XZ * A.YX) * det;
     result.ZX = (A.YX * A.ZY - A.YY * A.ZX) * det;
     result.ZY = -(A.XX * A.ZY - A.XY * A.ZX) * det;
     result.ZZ = (A.XX * A.YY - A.XY * A.YX) * det;
     return result;
 }

References XX, XY, XZ, YX, YY, YZ, ZX, ZY, and ZZ.

◆ ldivide()

Vec3D Matrix3D::ldivide ( const Vec3D & b )

A.ldivide(b) computes the solution x to A*x=b.

Solve the linear system Ax = b: A.ldivide(b) computes the solution x to A*x=b.

Parameters

[in] b Right-handside in Ax = b, as a const-reference to a Vec3D

Returns: The solution x of Ax = b as a Vec3D.

 {
     Mdouble invdet = 1. / (XX * (YY * ZZ - YZ * ZY)
                            + XY * (YZ * ZX - YX * ZZ)
                            + XZ * (YX * ZY - YY * ZX));
     return Vec3D(+(XY * YZ - YY * XZ) * b.Z
                  - (ZY * YZ - ZZ * YY) * b.X
                  + (ZY * XZ - ZZ * XY) * b.Y,
                  -(XX * YZ - XZ * YX) * b.Z
                  + (ZX * YZ - ZZ * YX) * b.X
                  - (ZX * XZ - XX * ZZ) * b.Y,
                  +(XX * YY - YX * XY) * b.Z
                  - (ZX * YY - YX * ZY) * b.X
                  + (ZX * XY - XX * ZY) * b.Y) * invdet;
 }

References b, XX, XY, XZ, YX, YY, YZ, ZX, ZY, and ZZ.

◆ operator*() [1/3]

Matrix3D Matrix3D::operator* ( const Matrix3D & a ) const

Matrix multiplication.

Todo:: check

 {
     return Matrix3D(XX * a.XX + XY * a.YX + XZ * a.ZX,
                     XX * a.XY + XY * a.YY + XZ * a.ZY,
                     XX * a.XZ + XY * a.YZ + XZ * a.ZZ,
                     YX * a.XX + YY * a.YX + YZ * a.ZX,
                     YX * a.XY + YY * a.YY + YZ * a.ZY,
                     YX * a.XZ + YY * a.YZ + YZ * a.ZZ,
                     ZX * a.XX + ZY * a.YX + ZZ * a.ZX,
                     ZX * a.XY + ZY * a.YY + ZZ * a.ZY,
                     ZX * a.XZ + ZY * a.YZ + ZZ * a.ZZ
     );
 }

References a, Matrix3D(), XX, XY, XZ, YX, YY, YZ, ZX, ZY, and ZZ.

◆ operator*() [2/3]

Vec3D Matrix3D::operator* ( const Vec3D & a ) const

Vector multiplication.

Multiplication with vector

Parameters

[in] a Vector to be multiplied with

Returns: Resulting vector

 {
     return Vec3D(XX * a.X + XY * a.Y + XZ * a.Z,
                  YX * a.X + YY * a.Y + YZ * a.Z,
                  ZX * a.X + ZY * a.Y + ZZ * a.Z);
 }

References a, XX, XY, XZ, YX, YY, YZ, ZX, ZY, and ZZ.

◆ operator*() [3/3]

Matrix3D Matrix3D::operator* ( Mdouble a ) const

Scalar multiplication.

Multiplication with scalar

Parameters

[in] a Scalar to be multiplied with

Returns: resulting matrix

 {
     return Matrix3D(XX * a, XY * a, XZ * a,
                     YX * a, YY * a, YZ * a,
                     ZX * a, ZY * a, ZZ * a);
 }

References a, Matrix3D(), XX, XY, XZ, YX, YY, YZ, ZX, ZY, and ZZ.

◆ operator+() [1/2]

Matrix3D Matrix3D::operator+ ( const Matrix3D & A ) const

Matrix addition.

Addition of this matrix with given one

Parameters

[in] A Matrix to be added

Returns: resulting matrix

 {
     return Matrix3D(XX + A.XX, XY + A.XY, XZ + A.XZ,
                     YX + A.YX, YY + A.YY, YZ + A.YZ,
                     ZX + A.ZX, ZY + A.ZY, ZZ + A.ZZ);
 }

References Matrix3D(), XX, XY, XZ, YX, YY, YZ, ZX, ZY, and ZZ.

◆ operator+() [2/2]

Matrix3D Matrix3D::operator+ ( Mdouble a ) const

Scalar addition.

Addition of scalar

Parameters

[in] a Scalar to be added

Returns: resulting matrix

 {
     return Matrix3D(XX + a, XY + a, XZ + a,
                     YX + a, YY + a, YZ + a,
                     ZX + a, ZY + a, ZZ + a);
 }

References a, Matrix3D(), XX, XY, XZ, YX, YY, YZ, ZX, ZY, and ZZ.

◆ operator+=()

Matrix3D & Matrix3D::operator+= ( const Matrix3D & A )

Matrix addition.

Adds all elements of a given matrix to its own

Parameters

[in] A 3D matrix to be added

Returns: (reference to) resulting (this) matrix

 {
     XX += A.XX;
     XY += A.XY;
     XZ += A.XZ;
     YX += A.YX;
     YY += A.YY;
     YZ += A.YZ;
     ZX += A.ZX;
     ZY += A.ZY;
     ZZ += A.ZZ;
     return *this;
 }

References XX, XY, XZ, YX, YY, YZ, ZX, ZY, and ZZ.

◆ operator-() [1/2]

Matrix3D Matrix3D::operator- ( const Matrix3D & A ) const

Matrix subtraction.

Substraction of given matrix from this one

Parameters

[in] A Matrix to be subtracted

Returns: resulting matrix

 {
     return Matrix3D(XX - A.XX, XY - A.XY, XZ - A.XZ,
                     YX - A.YX, YY - A.YY, YZ - A.YZ,
                     ZX - A.ZX, ZY - A.ZY, ZZ - A.ZZ);
 }

References Matrix3D(), XX, XY, XZ, YX, YY, YZ, ZX, ZY, and ZZ.

◆ operator-() [2/2]

Matrix3D Matrix3D::operator- ( Mdouble a ) const

Scalar subtraction.

Substraction of scalar

Parameters

[in] a Scalar to be subtracted

Returns: resulting matrix

 {
     return Matrix3D(XX - a, XY - a, XZ - a,
                     YX - a, YY - a, YZ - a,
                     ZX - a, ZY - a, ZZ - a);
 }

References a, Matrix3D(), XX, XY, XZ, YX, YY, YZ, ZX, ZY, and ZZ.

◆ operator-=()

Matrix3D & Matrix3D::operator-= ( const Matrix3D & A )

Matrix substraction.

Substract all elements of a given matrix from its own

Parameters

[in] A 3D matrix to be subtracted

Returns: (reference to) resulting (this) matrix

 {
     XX -= A.XX;
     XY -= A.XY;
     XZ -= A.XZ;
     YX -= A.YX;
     YY -= A.YY;
     YZ -= A.YZ;
     ZX -= A.ZX;
     ZY -= A.ZY;
     ZZ -= A.ZZ;
     return *this;
 }

References XX, XY, XZ, YX, YY, YZ, ZX, ZY, and ZZ.

◆ operator/()

Matrix3D Matrix3D::operator/ ( Mdouble a ) const

Scalar division.

Division by a scalar

Parameters

[in] a scalar to be divided by

Returns: resulting matrix

 {
     return Matrix3D(XX / a, XY / a, XZ / a,
                     YX / a, YY / a, YZ / a,
                     ZX / a, ZY / a, ZZ / a);
 }

References a, Matrix3D(), XX, XY, XZ, YX, YY, YZ, ZX, ZY, and ZZ.

◆ operator/=()

Matrix3D & Matrix3D::operator/= ( Mdouble a )

Scalar division.

Division by a scalar

Parameters

[in] a scalar to be divided by

Returns: (reference to) resulting (this) matrix

 {
     XX /= a;
     XY /= a;
     XZ /= a;
     YX /= a;
     YY /= a;
     YZ /= a;
     ZX /= a;
     ZY /= a;
     ZZ /= a;
     return *this;
 }

References a, XX, XY, XZ, YX, YY, YZ, ZX, ZY, and ZZ.

◆ setZero()

void Matrix3D::setZero ( )

Sets all elements to zero.

 {
     XX = XY = XZ = YX = YY = YZ = ZX = ZY = ZZ = 0.0;
 }

References XX, XY, XZ, YX, YY, YZ, ZX, ZY, and ZZ.

Referenced by CylinderInsertionBoundary::CylinderInsertionBoundary(), Matrix3D(), CGFields::GradVelocityField::setZero(), CGFields::StandardFields::setZero(), and StressStrainControlBoundary::StressStrainControlBoundary().

◆ sqrt()

Matrix3D Matrix3D::sqrt ( const Matrix3D & A )

static

Calculates the pointwise square root.

Takes the square root of all the elements in given matrix

Parameters

[in] A Matrix to be pointwise square rooted

Returns: Resulting matrix

 {
     return Matrix3D(std::sqrt(A.XX), std::sqrt(A.XY), std::sqrt(A.XZ),
                     std::sqrt(A.YX), std::sqrt(A.YY), std::sqrt(A.YZ),
                     std::sqrt(A.ZX), std::sqrt(A.ZY), std::sqrt(A.ZZ));
 }

References Matrix3D(), and sqrt().

◆ square()

Matrix3D Matrix3D::square ( const Matrix3D & A )

static

Calculates the pointwise square.

Squares all the elements in given matrix

Parameters

[in] A Matrix to be pointwise squared

Returns: Resulting matrix

 {
     return Matrix3D(mathsFunc::square(A.XX), mathsFunc::square(A.XY), mathsFunc::square(A.XZ),
                     mathsFunc::square(A.YX), mathsFunc::square(A.YY), mathsFunc::square(A.YZ),
                     mathsFunc::square(A.ZX), mathsFunc::square(A.ZY), mathsFunc::square(A.ZZ));
 }

References Matrix3D(), and mathsFunc::square().

Referenced by CGFields::GradVelocityField::getSquared(), and CGFields::StandardFields::getSquared().

◆ trace()

Mdouble Matrix3D::trace ( ) const

Sum of the diagonal elements.

Returns the sum of the diagonal elements of the matrix.

Returns: The trace of the matrix divided by 3 as an Mdouble

 {
     return XX + YY + ZZ;
 }

References XX, YY, and ZZ.

Referenced by deviator().

Friends And Related Function Documentation

◆ operator<<

std::ostream& operator<<	(	std::ostream &	os,
		const Matrix3D &	A
	)

friend

Add elements to ostream.

Adds all elements of a matrix to an ostream

Parameters

[out]	os	output stream
[in]	A	3D matrix

Returns: output stream with matrix elements added

 {
     os << A.XX << ' ' << A.XY << ' ' << A.XZ << ' '
        << A.YX << ' ' << A.YY << ' ' << A.YZ << ' '
        << A.ZX << ' ' << A.ZY << ' ' << A.ZZ;
     return os;
 }

◆ operator>>

std::istream& operator>>	(	std::istream &	is,
		Matrix3D &	A
	)

friend

Add elements to istream.

Reads the elements of a matrix from an istream

Parameters

[in,out]	is	input stream
[out]	A	3D matrix

Returns: is input stream after the read operation.

 {
     is >> A.XX >> A.XY >> A.XZ >> A.YX >> A.YY >> A.YZ >> A.ZX >> A.ZY >> A.ZZ;
     return is;
 }

Member Data Documentation

◆ XX

Mdouble Matrix3D::XX

all nine matrix elements

Referenced by StressStrainControlBoundary::activateStrainRateControl(), StressStrainControlBoundary::checkBoundaryAfterParticlesMove(), StressStrainControlBoundary::computeStrainRate(), StressStrainControlBoundary::computeStressError(), determinant(), deviator(), diag(), getCylindricalTensorField(), ClumpParticle::getInitPrincipalDirections_e1(), ClumpParticle::getPrincipalDirections_e1(), CylinderInsertionBoundary::getRotationMatrixX(), CylinderInsertionBoundary::getRotationMatrixY(), CylinderInsertionBoundary::getRotationMatrixZ(), inverse(), ldivide(), main(), Matrix3D(), operator*(), operator+(), operator+=(), operator-(), operator-=(), operator/(), operator/=(), StressStrainControlBoundary::set(), ClumpParticle::setPrincipalDirections_e1(), setZero(), Packing::test(), ShapeGradientHessianTester::testCushion(), ShapeGradientHessianTester::testEllipsoid(), ShapeGradientHessianTester::testRoundedBeam(), ShapeGradientHessianTester::testSphere(), trace(), and StressStrainControlBoundary::updateDomainSize().

◆ XY

Mdouble Matrix3D::XY

◆ XZ

◆ YX

◆ YY

Mdouble Matrix3D::YY

Referenced by ShearStage::actionsAfterTimeStep(), StressStrainControlBoundary::activateStrainRateControl(), StressStrainControlBoundary::checkBoundaryAfterParticlesMove(), StressStrainControlBoundary::computeStrainRate(), determinant(), deviator(), diag(), getCylindricalTensorField(), ClumpParticle::getInitPrincipalDirections_e2(), ClumpParticle::getPrincipalDirections_e2(), CylinderInsertionBoundary::getRotationMatrixX(), CylinderInsertionBoundary::getRotationMatrixY(), CylinderInsertionBoundary::getRotationMatrixZ(), inverse(), ldivide(), main(), Matrix3D(), operator*(), operator+(), operator+=(), operator-(), operator-=(), operator/(), operator/=(), ShearStage::printTime(), StressStrainControlBoundary::set(), ClumpParticle::setPrincipalDirections_e2(), setZero(), Packing::test(), ShapeGradientHessianTester::testCushion(), ShapeGradientHessianTester::testEllipsoid(), ShapeGradientHessianTester::testRoundedBeam(), ShapeGradientHessianTester::testSphere(), trace(), and StressStrainControlBoundary::updateDomainSize().

◆ YZ

◆ ZX

◆ ZY

◆ ZZ

Mdouble Matrix3D::ZZ

Referenced by StressStrainControlBoundary::activateStrainRateControl(), StressStrainControlBoundary::checkBoundaryAfterParticlesMove(), StressStrainControlBoundary::computeStrainRate(), determinant(), deviator(), diag(), getCylindricalTensorField(), ClumpParticle::getInitPrincipalDirections_e3(), ClumpParticle::getPrincipalDirections_e3(), CylinderInsertionBoundary::getRotationMatrixX(), CylinderInsertionBoundary::getRotationMatrixY(), CylinderInsertionBoundary::getRotationMatrixZ(), inverse(), ldivide(), main(), Matrix3D(), operator*(), operator+(), operator+=(), operator-(), operator-=(), operator/(), operator/=(), StressStrainControlBoundary::set(), ClumpParticle::setPrincipalDirections_e3(), setZero(), Packing::test(), ShapeGradientHessianTester::testCushion(), ShapeGradientHessianTester::testEllipsoid(), ShapeGradientHessianTester::testRoundedBeam(), ShapeGradientHessianTester::testSphere(), trace(), and StressStrainControlBoundary::updateDomainSize().

The documentation for this class was generated from the following files:

Public Member Functions

Static Public Member Functions

Public Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Matrix3D() [1/3]

◆ Matrix3D() [2/3]

◆ Matrix3D() [3/3]

Member Function Documentation

◆ cross()

◆ determinant()

◆ deviator()

◆ diag()

◆ dyadic()

◆ getCylindricalTensorField()

◆ inverse()

◆ ldivide()

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator+() [1/2]

◆ operator+() [2/2]

◆ operator+=()

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator-=()

◆ operator/()

◆ operator/=()

◆ setZero()

◆ sqrt()

◆ square()

◆ trace()

Friends And Related Function Documentation

◆ operator<<

◆ operator>>

Member Data Documentation

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◆ XY

◆ XZ

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◆ YZ

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