Contains operations for operating on compile time sized vectors and matrices. More...

Functions
Fixed size square matrix operations
Functions that are overloaded to operate square matrices of a fixed size. Note Currently all functions only support matrices of sizes 2x2 and 3x3.
template<std::ptrdiff_t M, typename MATRIX >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK auto	determinant (MATRIX const &matrix)

template<std::ptrdiff_t M, typename DST_MATRIX , typename SRC_MATRIX >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK auto	invert (DST_MATRIX &&LVARRAY_RESTRICT_REF dstMatrix, SRC_MATRIX const &LVARRAY_RESTRICT_REF srcMatrix)
	Invert the source matrix `srcMatrix` and store the result in `dstMatrix`. More...

template<std::ptrdiff_t M, typename MATRIX >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK auto	invert (MATRIX &&matrix)
	Invert the matrix `matrix` overwritting it. More...

Fixed size symmetric matrix operations
Functions that are overloaded to operate symmetric matrices of a fixed size. Note Currently all functions only support matrices of sizes 2x2 and 3x3.
template<std::ptrdiff_t M, typename DST_VECTOR , typename SYM_MATRIX_A , typename VECTOR_B >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	Ri_eq_symAijBj (DST_VECTOR &&LVARRAY_RESTRICT_REF dstVector, SYM_MATRIX_A const &LVARRAY_RESTRICT_REF symMatrixA, VECTOR_B const &LVARRAY_RESTRICT_REF vectorB)
	Multiply the vector `vectorB` by the symmetric matrix `symMatrixA` and store the result in `dstVector`. More...

template<std::ptrdiff_t M, typename DST_VECTOR , typename SYM_MATRIX_A , typename VECTOR_B >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	Ri_add_symAijBj (DST_VECTOR &&LVARRAY_RESTRICT_REF dstVector, SYM_MATRIX_A const &LVARRAY_RESTRICT_REF symMatrixA, VECTOR_B const &LVARRAY_RESTRICT_REF vectorB)
	Multiply the vector `vectorB` by the symmetric matrix `symMatrixA` and add the result to `dstVector`. More...

template<std::ptrdiff_t M, typename DST_MATRIX , typename SYM_MATRIX_A , typename MATRIX_B >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	Rij_eq_symAikBjk (DST_MATRIX &&LVARRAY_RESTRICT_REF dstMatrix, SYM_MATRIX_A const &LVARRAY_RESTRICT_REF symMatrixA, MATRIX_B const &LVARRAY_RESTRICT_REF matrixB)
	Multiply the transpose of matrix `matrixB` by the symmetric matrix `symMatrixA` and store the result in `dstMatrix`. More...

template<std::ptrdiff_t M, typename DST_SYM_MATRIX , typename MATRIX_A , typename SYM_MATRIX_B >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	Rij_eq_AikSymBklAjl (DST_SYM_MATRIX &&LVARRAY_RESTRICT_REF dstSymMatrix, MATRIX_A const &LVARRAY_RESTRICT_REF matrixA, SYM_MATRIX_B const &LVARRAY_RESTRICT_REF symMatrixB)
	Multiply the transpose of matrix `matrixA` by the symmetric matrix `symMatrixB` then by `matrixA` and store the result in `dstSymMatrix`. More...

template<std::ptrdiff_t M, typename DST_SYM_MATRIX , typename VECTOR_A >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	symRij_eq_AiAj (DST_SYM_MATRIX &&LVARRAY_RESTRICT_REF dstMatrix, VECTOR_A const &LVARRAY_RESTRICT_REF vectorA)
	Perform the outer product of `vectorA` with itself writing the result to `dstMatrix`. More...

template<std::ptrdiff_t M, typename DST_SYM_MATRIX , typename VECTOR_A , typename VECTOR_B >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	symRij_eq_AiBj_plus_AjBi (DST_SYM_MATRIX &&LVARRAY_RESTRICT_REF dstMatrix, VECTOR_A const &LVARRAY_RESTRICT_REF vectorA, VECTOR_B const &LVARRAY_RESTRICT_REF vectorB)
	Perform the unscaled symmetric outer product of `vectorA` and `vectorB` with itself writing the result to `dstMatrix`. More...

template<std::ptrdiff_t M, typename SYM_MATRIX >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK auto	symDeterminant (SYM_MATRIX const &symMatrix)

template<std::ptrdiff_t M, typename DST_SYM_MATRIX , typename SRC_SYM_MATRIX >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK auto	symInvert (DST_SYM_MATRIX &&LVARRAY_RESTRICT_REF dstSymMatrix, SRC_SYM_MATRIX const &LVARRAY_RESTRICT_REF srcSymMatrix)
	Invert the symmetric matrix `srcSymMatrix` and store the result in `dstSymMatrix`. More...

template<std::ptrdiff_t M, typename SYM_MATRIX >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK auto	symInvert (SYM_MATRIX &&symMatrix)
	Invert the symmetric matrix `symMatrix` overwritting it. More...

template<std::ptrdiff_t M, typename DST_VECTOR , typename SYM_MATRIX >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	symEigenvalues (DST_VECTOR &&LVARRAY_RESTRICT_REF eigenvalues, SYM_MATRIX const &LVARRAY_RESTRICT_REF symMatrix)
	Compute the eigenvalues of the symmetric matrix `symMatrix`. More...

template<std::ptrdiff_t M, typename DST_VECTOR , typename DST_MATRIX , typename SYM_MATRIX >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	symEigenvectors (DST_VECTOR &&LVARRAY_RESTRICT_REF eigenvalues, DST_MATRIX &&LVARRAY_RESTRICT_REF eigenvectors, SYM_MATRIX const &LVARRAY_RESTRICT_REF symMatrix)
	Compute the eigenvalues and eigenvectors of the symmetric matrix `symMatrix`. More...

template<std::ptrdiff_t M, typename DST_SYM_MATRIX , typename SRC_MATRIX >
LVARRAY_HOST_DEVICE constexpr void	denseToSymmetric (DST_SYM_MATRIX &&dstSymMatrix, SRC_MATRIX const &srcMatrix)
	Convert the upper triangular part of `srcMatrix` to a symmetric matrix. More...

template<std::ptrdiff_t M, typename DST_MATRIX , typename SRC_SYM_MATRIX >
LVARRAY_HOST_DEVICE constexpr void	symmetricToDense (DST_MATRIX &&dstMatrix, SRC_SYM_MATRIX const &srcSymMatrix)
	Convert the `srcSymMatrix` into a dense matrix. More...

Generic operations
Functions that are overloaded to operate on both vectors and matrices. Note Not all of the functions have been overloaded to operate on both vectors and matrices.
template<std::ptrdiff_t ISIZE, typename VECTOR >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK auto	maxAbsoluteEntry (VECTOR &&vector)

template<std::ptrdiff_t ISIZE, typename VECTOR >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	fill (VECTOR &&vector, std::remove_reference_t< decltype(vector[0]) > const value)
	Set the entries of `vector` to `value`. More...

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, typename MATRIX >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	fill (MATRIX &&matrix, std::remove_reference_t< decltype(matrix[0][0]) > const value)
	Set the entries of `matrix` to `value`. More...

template<std::ptrdiff_t ISIZE, typename DST_VECTOR , typename SRC_VECTOR >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	copy (DST_VECTOR &&LVARRAY_RESTRICT_REF dstVector, SRC_VECTOR const &LVARRAY_RESTRICT_REF srcVector)
	Copy `srcVector` into `dstVector`. More...

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, typename DST_MATRIX , typename SRC_MATRIX >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	copy (DST_MATRIX &&LVARRAY_RESTRICT_REF dstMatrix, SRC_MATRIX const &LVARRAY_RESTRICT_REF srcMatrix)
	Copy `srcMatrix` into `dstMatrix`. More...

template<std::ptrdiff_t ISIZE, typename VECTOR >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	scale (VECTOR &&vector, std::remove_reference_t< decltype(vector[0]) > const scale)
	Multiply the entries of `vector` by `scale`. More...

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, typename MATRIX >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	scale (MATRIX &&matrix, std::remove_reference_t< decltype(matrix[0][0]) > const scale)
	Multiply the entries of `matrix` by `scale`. More...

template<std::ptrdiff_t ISIZE, typename DST_VECTOR , typename SRC_VECTOR >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	scaledCopy (DST_VECTOR &&LVARRAY_RESTRICT_REF dstVector, SRC_VECTOR const &LVARRAY_RESTRICT_REF srcVector, std::remove_reference_t< decltype(srcVector[0]) > const scale)
	Copy `srcVector` scaled by `scale` into `dstVector`. More...

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, typename DST_MATRIX , typename SRC_MATRIX >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	scaledCopy (DST_MATRIX &&LVARRAY_RESTRICT_REF dstMatrix, SRC_MATRIX const &LVARRAY_RESTRICT_REF srcMatrix, std::remove_reference_t< decltype(srcMatrix[0][0]) > const scale)
	Copy `srcMatrix` scaled by `scale` into `dstMatrix`. More...

template<std::ptrdiff_t M, typename DST_VECTOR >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	addScalar (DST_VECTOR &&LVARRAY_RESTRICT_REF dstVector, std::remove_reference_t< decltype(dstVector[0]) > const value)
	Add `value` to `dstVector`. More...

template<std::ptrdiff_t ISIZE, typename DST_VECTOR , typename SRC_VECTOR >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	add (DST_VECTOR &&LVARRAY_RESTRICT_REF dstVector, SRC_VECTOR const &LVARRAY_RESTRICT_REF srcVector)
	Add `srcVector` to `dstVector`. More...

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, typename DST_MATRIX , typename SRC_MATRIX >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	add (DST_MATRIX &&LVARRAY_RESTRICT_REF dstMatrix, SRC_MATRIX const &LVARRAY_RESTRICT_REF srcMatrix)
	Add `srcMatrix` to `dstMatrix`. More...

template<std::ptrdiff_t ISIZE, typename DST_VECTOR , typename SRC_VECTOR >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	subtract (DST_VECTOR &&LVARRAY_RESTRICT_REF dstVector, SRC_VECTOR const &LVARRAY_RESTRICT_REF srcVector)
	Subtract `srcVector` from `dstVector`. More...

template<std::ptrdiff_t ISIZE, typename DST_VECTOR , typename SRC_VECTOR >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	scaledAdd (DST_VECTOR &&LVARRAY_RESTRICT_REF dstVector, SRC_VECTOR const &LVARRAY_RESTRICT_REF srcVector, std::remove_reference_t< decltype(srcVector[0]) > const scale)
	Add `srcVector` scaled by `scale` to `dstVector`. More...

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, typename DST_MATRIX , typename SRC_MATRIX >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	scaledAdd (DST_MATRIX &&LVARRAY_RESTRICT_REF dstMatrix, SRC_MATRIX const &LVARRAY_RESTRICT_REF srcMatrix, std::remove_reference_t< decltype(srcMatrix[0][0]) > const scale)
	Add `srcMatrix` scaled by `scale` to `dstMatrix`. More...

template<std::ptrdiff_t ISIZE, typename DST_VECTOR , typename VECTOR_A , typename VECTOR_B >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	hadamardProduct (DST_VECTOR &&LVARRAY_RESTRICT_REF dstVector, VECTOR_A const &LVARRAY_RESTRICT_REF vectorA, VECTOR_B const &LVARRAY_RESTRICT_REF vectorB)
	Multiply the elements of `vectorA` and `vectorB` putting the result into `dstVector`. More...

Vector operations
Functions that operate on vectors.
template<std::ptrdiff_t ISIZE, typename VECTOR >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK auto	l2NormSquared (VECTOR const &vector)

template<std::ptrdiff_t ISIZE, typename VECTOR >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK auto	l2Norm (VECTOR const &vector)

template<std::ptrdiff_t ISIZE, typename VECTOR >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK auto	normalize (VECTOR &&vector)
	Scale `vector` to a unit vector. More...

template<std::ptrdiff_t JSIZE, typename VECTOR_A , typename VECTOR_B >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK auto	AiBi (VECTOR_A const &LVARRAY_RESTRICT_REF vectorA, VECTOR_B const &LVARRAY_RESTRICT_REF vectorB)

template<typename DST_VECTOR , typename VECTOR_A , typename VECTOR_B >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	crossProduct (DST_VECTOR &&LVARRAY_RESTRICT_REF dstVector, VECTOR_A const &LVARRAY_RESTRICT_REF vectorA, VECTOR_B const &LVARRAY_RESTRICT_REF vectorB)
	Compute the cross product of `vectorA` and `vectorB` and put it in `dstVector`. More...

Matrix-vector operations
Functions that operate on matrices and vectors.
template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, typename DST_MATRIX , typename VECTOR_A , typename VECTOR_B >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	Rij_eq_AiBj (DST_MATRIX &&LVARRAY_RESTRICT_REF dstMatrix, VECTOR_A const &LVARRAY_RESTRICT_REF vectorA, VECTOR_B const &LVARRAY_RESTRICT_REF vectorB)
	Perform the outer product of `vectorA` and `vectorB` writing the result to `dstMatrix`. More...

template<std::ptrdiff_t JSIZE, std::ptrdiff_t ISIZE, typename DST_MATRIX , typename VECTOR_A , typename VECTOR_B >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	Rij_add_AiBj (DST_MATRIX &&LVARRAY_RESTRICT_REF dstMatrix, VECTOR_A const &LVARRAY_RESTRICT_REF vectorA, VECTOR_B const &LVARRAY_RESTRICT_REF vectorB)
	Perform the outer product of `vectorA` and `vectorB` adding the result to `dstMatrix`. More...

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, typename DST_VECTOR , typename MATRIX_A , typename VECTOR_B >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	Ri_eq_AijBj (DST_VECTOR &&LVARRAY_RESTRICT_REF dstVector, MATRIX_A const &LVARRAY_RESTRICT_REF matrixA, VECTOR_B const &LVARRAY_RESTRICT_REF vectorB)
	Perform the matrix vector multiplication of `matrixA` and `vectorB` writing the result to `dstVector`. More...

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, typename DST_VECTOR , typename MATRIX_A , typename VECTOR_B >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	Ri_add_AijBj (DST_VECTOR &&LVARRAY_RESTRICT_REF dstVector, MATRIX_A const &LVARRAY_RESTRICT_REF matrixA, VECTOR_B const &LVARRAY_RESTRICT_REF vectorB)
	Perform the matrix vector multiplication of `matrixA` and `vectorB` adding the result to `dstVector`. More...

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, typename DST_VECTOR , typename MATRIX_A , typename VECTOR_B >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	Ri_eq_AjiBj (DST_VECTOR &&LVARRAY_RESTRICT_REF dstVector, MATRIX_A const &LVARRAY_RESTRICT_REF matrixA, VECTOR_B const &LVARRAY_RESTRICT_REF vectorB)
	Perform the matrix vector multiplication of the transpose of `matrixA` and `vectorB` writing the result to `dstVector`. More...

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, typename DST_VECTOR , typename MATRIX_A , typename VECTOR_B >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	Ri_add_AjiBj (DST_VECTOR &&LVARRAY_RESTRICT_REF dstVector, MATRIX_A const &LVARRAY_RESTRICT_REF matrixA, VECTOR_B const &LVARRAY_RESTRICT_REF vectorB)
	Perform the matrix vector multiplication of the transpose of `matrixA` and `vectorB` adding the result to `dstVector`. More...

Matrix operations
Functions that operate matrices of any shape.
template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, typename DST_MATRIX , typename SRC_MATRIX >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	transpose (DST_MATRIX &&LVARRAY_RESTRICT_REF dstMatrix, SRC_MATRIX const &LVARRAY_RESTRICT_REF srcMatrix)
	Store the transpose of the NxM matrix `srcMatrix` in `dstMatrix`. More...

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, std::ptrdiff_t KSIZE, typename DST_MATRIX , typename MATRIX_A , typename MATRIX_B >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	Rij_eq_AikBkj (DST_MATRIX &&LVARRAY_RESTRICT_REF dstMatrix, MATRIX_A const &LVARRAY_RESTRICT_REF matrixA, MATRIX_B const &LVARRAY_RESTRICT_REF matrixB)
	Multiply `matrixA` with `matrixB` and put the result into `dstMatrix`. More...

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, std::ptrdiff_t KSIZE, typename DST_MATRIX , typename MATRIX_A , typename MATRIX_B >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	Rij_add_AikBkj (DST_MATRIX &&LVARRAY_RESTRICT_REF dstMatrix, MATRIX_A const &LVARRAY_RESTRICT_REF matrixA, MATRIX_B const &LVARRAY_RESTRICT_REF matrixB)
	Multiply `matrixA` with `matrixB` and add the result to `dstMatrix`. More...

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, std::ptrdiff_t KSIZE, typename DST_MATRIX , typename MATRIX_A , typename MATRIX_B >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	Rij_eq_AikBjk (DST_MATRIX &&LVARRAY_RESTRICT_REF dstMatrix, MATRIX_A const &LVARRAY_RESTRICT_REF matrixA, MATRIX_B const &LVARRAY_RESTRICT_REF matrixB)
	Multiply `matrixA` with the transpose of `matrixB` and put the result into `dstMatrix`. More...

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, std::ptrdiff_t KSIZE, typename DST_MATRIX , typename MATRIX_A , typename MATRIX_B >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	Rij_add_AikBjk (DST_MATRIX &&LVARRAY_RESTRICT_REF dstMatrix, MATRIX_A const &LVARRAY_RESTRICT_REF matrixA, MATRIX_B const &LVARRAY_RESTRICT_REF matrixB)
	Multiply `matrixA` with the transpose of `matrixB` and put the result into `dstMatrix`. More...

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, typename DST_MATRIX , typename MATRIX_A >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	Rij_add_AikAjk (DST_MATRIX &&LVARRAY_RESTRICT_REF dstMatrix, MATRIX_A const &LVARRAY_RESTRICT_REF matrixA)
	Multiply `matrixA` with the transpose of itself and put the result into `dstMatrix`. More...

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, std::ptrdiff_t KSIZE, typename DST_MATRIX , typename MATRIX_A , typename MATRIX_B >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	Rij_eq_AkiBkj (DST_MATRIX &&LVARRAY_RESTRICT_REF dstMatrix, MATRIX_A const &LVARRAY_RESTRICT_REF matrixA, MATRIX_B const &LVARRAY_RESTRICT_REF matrixB)
	Multiply the transpose of `matrixA` with `matrixB` and put the result into `dstMatrix`. More...

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, typename DST_MATRIX , typename MATRIX_A >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	Rij_eq_AkiAkj (DST_MATRIX &&LVARRAY_RESTRICT_REF dstMatrix, MATRIX_A const &LVARRAY_RESTRICT_REF matrixA)
	Multiply the transpose of `matrixA` with `matrixA` and put the result into `dstMatrix`. More...

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, std::ptrdiff_t KSIZE, typename DST_MATRIX , typename MATRIX_A , typename MATRIX_B >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	Rij_add_AkiBkj (DST_MATRIX &&LVARRAY_RESTRICT_REF dstMatrix, MATRIX_A const &LVARRAY_RESTRICT_REF matrixA, MATRIX_B const &LVARRAY_RESTRICT_REF matrixB)
	Multiply the transpose of `matrixA` with `matrixB` and add the result into `dstMatrix`. More...

Square matrix operations
Functions that operate on square matrices of any size.
template<std::ptrdiff_t ISIZE, typename MATRIX >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	transpose (MATRIX &&LVARRAY_RESTRICT_REF matrix)
	Transpose the MxM matrix `matrix`. More...

template<std::ptrdiff_t ISIZE, typename MATRIX >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	addIdentity (MATRIX &&matrix, std::remove_reference_t< decltype(matrix[0][0]) > const scale)
	Add `scale` times the identity matrix to `matrix`. More...

template<std::ptrdiff_t ISIZE, typename MATRIX >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK auto	trace (MATRIX const &matrix)

Symmetric matrix operations
Functions that operate on symmetric matrices of any size.
template<std::ptrdiff_t ISIZE, typename SYM_MATRIX >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void	symAddIdentity (SYM_MATRIX &&symMatrix, std::remove_reference_t< decltype(symMatrix[0]) > const scale)
	Add `scale` times the identity matrix to `symMatrix`. More...

template<std::ptrdiff_t ISIZE, typename SYM_MATRIX >
LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK auto	symTrace (SYM_MATRIX const &symMatrix)

Variables
template<std::ptrdiff_t ISIZE>
constexpr std::ptrdiff_t	SYM_SIZE = ( ISIZE * ( ISIZE + 1 ) ) / 2
	The size of a symmetric MxM matrix in Voigt notation.

Detailed Description

Contains operations for operating on compile time sized vectors and matrices.

LvArray::tensorOps functions accept four differnet types of arguments

Scalars
Vectors: These can either be a one dimensional c-array such as double[ 3 ] or a one dimensional LvArray::Array, LvArray::ArrayView, or LvArray::ArraySlice.
Matrices: These can either be a two dimensional c-array such as int[ 5 ][ 2 ] or a two dimensional LvArray::Array, LvArray::ArrayView, or LvArray::ArraySlice.
Symmetric matrices: These are represented in Voigt notation as a vector.

Each function takes in the size of the objects as template parameters. As an example to take the dot product of two vectors of length 3 you'd call

LvArray::tensorOps::AiBi< 3 >( x, y )

Function Documentation

◆ add() [1/2]

template<std::ptrdiff_t ISIZE, typename DST_VECTOR , typename SRC_VECTOR >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::add	(	DST_VECTOR &&LVARRAY_RESTRICT_REF	dstVector,
		SRC_VECTOR const &LVARRAY_RESTRICT_REF	srcVector
	)

inline

Add srcVector to dstVector.

Template Parameters

ISIZE	The length of `dstVector` and `srcVector`.
DST_VECTOR	The type of `dstVector`.
SRC_VECTOR	The type of `srcVector`.

Parameters

dstVector	The destination vector, of length M.
srcVector	The source vector, of length M.

Performs the operation

dstVector[ i ] += srcVector[ i ]

◆ add() [2/2]

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, typename DST_MATRIX , typename SRC_MATRIX >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::add	(	DST_MATRIX &&LVARRAY_RESTRICT_REF	dstMatrix,
		SRC_MATRIX const &LVARRAY_RESTRICT_REF	srcMatrix
	)

inline

Add srcMatrix to dstMatrix.

Template Parameters

ISIZE	The size of the first dimension of `dstMatrix` and `srcMatrix`.
JSIZE	The size of the second dimension of `dstMatrix` and `srcMatrix`.
DST_MATRIX	The type of `dstMatrix`.
SRC_MATRIX	The type of `srcMatrix`.

Parameters

dstMatrix	The destination matrix, of size ISIZE x N.
srcMatrix	The source matrix, of size ISIZE x N.

Performs the operation

dstMatrix[ i ][ j ] += srcMatrix[ i ][ j ]

◆ addIdentity()

template<std::ptrdiff_t ISIZE, typename MATRIX >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::addIdentity	(	MATRIX &&	matrix,
		std::remove_reference_t< decltype(matrix[0][0]) > const	scale
	)

inline

Add scale times the identity matrix to matrix.

Template Parameters

ISIZE	The size of `matrix`.
MATRIX	The type of `matrix`.

Parameters

matrix	The ISIZE x ISIZE matrix to add the identity matrix to.
scale	The amount to scale the identity matrix by.

Performs the operations

matrix[ i ][ i ] += scale

◆ addScalar()

template<std::ptrdiff_t M, typename DST_VECTOR >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::addScalar	(	DST_VECTOR &&LVARRAY_RESTRICT_REF	dstVector,
		std::remove_reference_t< decltype(dstVector[0]) > const	value
	)

inline

Add value to dstVector.

Template Parameters

M	The length of `dstVector`.
DST_VECTOR	The type of `dstVector`.

Parameters

dstVector	The destination vector, of length M.
value	The value to add.

Performs the operation

dstVector[ i ] += value

◆ AiBi()

template<std::ptrdiff_t JSIZE, typename VECTOR_A , typename VECTOR_B >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK auto LvArray::tensorOps::AiBi	(	VECTOR_A const &LVARRAY_RESTRICT_REF	vectorA,
		VECTOR_B const &LVARRAY_RESTRICT_REF	vectorB
	)

inline

Returns: Return the inner product of vectorA and vectorB.

Template Parameters

ISIZE	The length of `vectorA` and `vectorB`.
VECTOR_A	The type of `vectorA`.
VECTOR_B	The type of `vectorB`.

Parameters

vectorA	The first vector in the inner product, of length M.
vectorB	The second vector in the inner product, of length M.

◆ copy() [1/2]

template<std::ptrdiff_t ISIZE, typename DST_VECTOR , typename SRC_VECTOR >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::copy	(	DST_VECTOR &&LVARRAY_RESTRICT_REF	dstVector,
		SRC_VECTOR const &LVARRAY_RESTRICT_REF	srcVector
	)

inline

Copy srcVector into dstVector.

Template Parameters

ISIZE	The length of `dstVector` and `srcVector`.
DST_VECTOR	The type of `dstVector`.
SRC_VECTOR	The type of `srcVector`.

Parameters

dstVector	The destination vector, of length ISIZE.
srcVector	The source vector, of length ISIZE.

Performs the operation

dstVector[ i ] = srcVector[ i ]

◆ copy() [2/2]

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, typename DST_MATRIX , typename SRC_MATRIX >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::copy	(	DST_MATRIX &&LVARRAY_RESTRICT_REF	dstMatrix,
		SRC_MATRIX const &LVARRAY_RESTRICT_REF	srcMatrix
	)

inline

Copy srcMatrix into dstMatrix.

Template Parameters

ISIZE	The size of the first dimension of `dstMatrix` and `srcMatrix`.
JSIZE	The size of the second dimension of `dstMatrix` and `srcMatrix`.
DST_MATRIX	The type of `dstMatrix`.
SRC_MATRIX	The type of `srcMatrix`.

Parameters

dstMatrix	The destination matrix, of size ISIZE x N.
srcMatrix	The source matrix, of size ISIZE x N.

Performs the operation

dstMatrix[ i ][ j ] = srcMatrix[ i ][ j ]

◆ crossProduct()

template<typename DST_VECTOR , typename VECTOR_A , typename VECTOR_B >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::crossProduct	(	DST_VECTOR &&LVARRAY_RESTRICT_REF	dstVector,
		VECTOR_A const &LVARRAY_RESTRICT_REF	vectorA,
		VECTOR_B const &LVARRAY_RESTRICT_REF	vectorB
	)

inline

Compute the cross product of vectorA and vectorB and put it in dstVector.

Template Parameters

DST_VECTOR	The type of `dstVector`.
VECTOR_A	The type of `vectorA`.
VECTOR_B	The type of `vectorB`.

Parameters

dstVector	The vector to write the cross product to, of length 3.
vectorA	The first vector in the cross product, of length 3.
vectorB	THe second vector in the cross product, of length 3.

◆ denseToSymmetric()

template<std::ptrdiff_t M, typename DST_SYM_MATRIX , typename SRC_MATRIX >

LVARRAY_HOST_DEVICE constexpr void LvArray::tensorOps::denseToSymmetric	(	DST_SYM_MATRIX &&	dstSymMatrix,
		SRC_MATRIX const &	srcMatrix
	)

inline

Convert the upper triangular part of srcMatrix to a symmetric matrix.

Template Parameters

M	The size of `dstSymMatrix` and `srcMatrix`.
DST_SYM_MATRIX	The type of `dstSymMatrix`.
SRC_MATRIX	The type of `srcMatrix`.

Parameters

dstSymMatrix	The resulting MxM symmetric matrix.
srcMatrix	The MxM matrix to convert to a symmetric matrix.

◆ determinant()

template<std::ptrdiff_t M, typename MATRIX >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK auto LvArray::tensorOps::determinant ( MATRIX const & matrix )

inline

Returns: Return the determinant of the matrix matrix.

Template Parameters

M	The size of `matrix`.
MATRIX	The type of `matrix`.

Parameters

matrix The M x M matrix to get the determinant of.

◆ fill() [1/2]

template<std::ptrdiff_t ISIZE, typename VECTOR >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::fill	(	VECTOR &&	vector,
		std::remove_reference_t< decltype(vector[0]) > const	value
	)

inline

Set the entries of vector to value.

Template Parameters

ISIZE	The size of `vector`.
VECTOR	The type of `vector`.

Parameters

vector	The vector to set the entries of, of length M.
value	The value to set the entries to.

Performs the operation

vector[ i ] = value

◆ fill() [2/2]

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, typename MATRIX >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::fill	(	MATRIX &&	matrix,
		std::remove_reference_t< decltype(matrix[0][0]) > const	value
	)

inline

Set the entries of matrix to value.

Template Parameters

ISIZE	The size of the first dimension of `matrix`.
JSIZE	The size of the second dimension of `matrix`.
MATRIX	The type of `matrix`.

Parameters

matrix	The matrix to set the entries of, of size ISIZE x N.
value	The value to set the entries to.

Performs the operation

matrix[ i ][ j ] = value

◆ hadamardProduct()

template<std::ptrdiff_t ISIZE, typename DST_VECTOR , typename VECTOR_A , typename VECTOR_B >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::hadamardProduct	(	DST_VECTOR &&LVARRAY_RESTRICT_REF	dstVector,
		VECTOR_A const &LVARRAY_RESTRICT_REF	vectorA,
		VECTOR_B const &LVARRAY_RESTRICT_REF	vectorB
	)

inline

Multiply the elements of vectorA and vectorB putting the result into dstVector.

Template Parameters

ISIZE	The length of `dstVector` and `srcVector`.
DST_VECTOR	The type of `dstVector`.
SRC_VECTOR	The type of `srcVector`.

Parameters

dstVector	The destination vector, of length M.
vectorA	The first source vector, of length M.
vectorB	The second source vector, of length M.

Performs the operation

dstVector[ i ] = vectorA[ i ] * vectorB[ i ]

◆ invert() [1/2]

template<std::ptrdiff_t M, typename DST_MATRIX , typename SRC_MATRIX >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK auto LvArray::tensorOps::invert	(	DST_MATRIX &&LVARRAY_RESTRICT_REF	dstMatrix,
		SRC_MATRIX const &LVARRAY_RESTRICT_REF	srcMatrix
	)

inline

Invert the source matrix srcMatrix and store the result in dstMatrix.

Template Parameters

M	The size of the matrices `dstMatrix` and `srcMatrix`.
DST_MATRIX	The type of `dstMatrix`.
SRC_MATRIX	The type of `srcMatrix`.

Parameters

dstMatrix	The M x M matrix to write the inverse to.
srcMatrix	The M x M matrix to take the inverse of.

Returns: The determinant.

Note: srcMatrix can contain integers but dstMatrix must contain floating point values.

◆ invert() [2/2]

template<std::ptrdiff_t M, typename MATRIX >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK auto LvArray::tensorOps::invert ( MATRIX && matrix )

inline

Invert the matrix matrix overwritting it.

Template Parameters

M	The size of the matrix `matrix`.
MATRIX	The type of `matrix`.

Parameters

matrix The M x M matrix to take the inverse of and overwrite.

Returns: The determinant.

Note: matrix must contain floating point values.

◆ l2Norm()

template<std::ptrdiff_t ISIZE, typename VECTOR >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK auto LvArray::tensorOps::l2Norm ( VECTOR const & vector )

inline

Returns: The L2 norm of vector.

Template Parameters

ISIZE	The length of `vector`.
VECTOR	The type of `vector`.

Parameters

vector The vector to get the L2 norm of, of length M.

◆ l2NormSquared()

template<std::ptrdiff_t ISIZE, typename VECTOR >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK auto LvArray::tensorOps::l2NormSquared ( VECTOR const & vector )

inline

Returns: The L2 norm squared of vector.

Template Parameters

ISIZE	The length of `vector`.
VECTOR	The type of `vector`.

Parameters

vector The vector to get the L2 norm squared of, of length M.

◆ maxAbsoluteEntry()

template<std::ptrdiff_t ISIZE, typename VECTOR >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK auto LvArray::tensorOps::maxAbsoluteEntry ( VECTOR && vector )

inline

Returns: Return the largest absolute entry of vector.

Template Parameters

ISIZE	The size of `vector`.
VECTOR	The type of `vector`.

Parameters

vector The vector to get the maximum entry of, of length M.

◆ normalize()

template<std::ptrdiff_t ISIZE, typename VECTOR >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK auto LvArray::tensorOps::normalize ( VECTOR && vector )

inline

Scale vector to a unit vector.

Template Parameters

ISIZE	The length of `vector`.
VECTOR	The type of `vector`.

Parameters

vector The vector normalize, of length M.

Returns: The previous L2 norm of vector.

◆ Ri_add_AijBj()

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, typename DST_VECTOR , typename MATRIX_A , typename VECTOR_B >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::Ri_add_AijBj	(	DST_VECTOR &&LVARRAY_RESTRICT_REF	dstVector,
		MATRIX_A const &LVARRAY_RESTRICT_REF	matrixA,
		VECTOR_B const &LVARRAY_RESTRICT_REF	vectorB
	)

inline

Perform the matrix vector multiplication of matrixA and vectorB adding the result to dstVector.

Template Parameters

ISIZE	The length of `dstVector` and the size of the first dimension of `matrixA`.
JSIZE	The size of the second dimension of `matrixA` and the length of `vectorBB`.
DST_VECTOR	The type of `dstVector`.
MATRIX_A	The type of `matrixA`.
VECTOR_B	The type of `vectorB`.

Parameters

dstVector	The vector to add the result to, of length M.
matrixA	The matrix to multiply `vectorB` by, of size ISIZE x N.
vectorB	The vector multiplied by `matrixA`, of length N.

Performs the operations

dstVector[ i ] += matrixA[ i ][ j ] * vectorB[ j ]

◆ Ri_add_AjiBj()

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, typename DST_VECTOR , typename MATRIX_A , typename VECTOR_B >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::Ri_add_AjiBj	(	DST_VECTOR &&LVARRAY_RESTRICT_REF	dstVector,
		MATRIX_A const &LVARRAY_RESTRICT_REF	matrixA,
		VECTOR_B const &LVARRAY_RESTRICT_REF	vectorB
	)

inline

Perform the matrix vector multiplication of the transpose of matrixA and vectorB adding the result to dstVector.

Template Parameters

ISIZE	The length of `dstVector` and the size of the second dimension of `matrixA`.
JSIZE	The size of the first dimension of `matrixA` and the length of `vectorB`.
DST_VECTOR	The type of `dstVector`.
MATRIX_A	The type of `matrixA`.
VECTOR_B	The type of `vectorB`.

Parameters

dstVector	The vector to add the result to, of length M.
matrixA	The matrix to multiply `vectorB` by, of size JSIZE x M.
vectorB	The vector multiplied by `matrixA`, of length N.

Performs the operations

dstVector[ i ] += matrixA[ j ][ i ] * vectorB[ j ]

◆ Ri_add_symAijBj()

template<std::ptrdiff_t M, typename DST_VECTOR , typename SYM_MATRIX_A , typename VECTOR_B >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::Ri_add_symAijBj	(	DST_VECTOR &&LVARRAY_RESTRICT_REF	dstVector,
		SYM_MATRIX_A const &LVARRAY_RESTRICT_REF	symMatrixA,
		VECTOR_B const &LVARRAY_RESTRICT_REF	vectorB
	)

inline

Multiply the vector vectorB by the symmetric matrix symMatrixA and add the result to dstVector.

Template Parameters

M	The size of `dstVector`, `symMatrixA`, and `vectorB`.
DST_VECTOR	The type of `dstVector`.
SYM_MATRIX_A	The type of `symMatrixA`.
VECTOR_B	The type of `vectorB`.

Parameters

dstVector	The vector of length M to add the result to.
symMatrixA	The M x M symmetric matrix to multiply `vectorB` by.
vectorB	The vector of length M to be multiplied by `symMatrixA`.

Performs the operation

dstVector[ i ] += symMatrixA[ i ][ j ] * vectorB[ j ]

◆ Ri_eq_AijBj()

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, typename DST_VECTOR , typename MATRIX_A , typename VECTOR_B >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::Ri_eq_AijBj	(	DST_VECTOR &&LVARRAY_RESTRICT_REF	dstVector,
		MATRIX_A const &LVARRAY_RESTRICT_REF	matrixA,
		VECTOR_B const &LVARRAY_RESTRICT_REF	vectorB
	)

inline

Perform the matrix vector multiplication of matrixA and vectorB writing the result to dstVector.

Template Parameters

ISIZE	The length of `dstVector` and the size of the first dimension of `matrixA`.
JSIZE	The size of the second dimension of `matrixA` and the length of `vectorBB`.
DST_VECTOR	The type of `dstVector`.
MATRIX_A	The type of `matrixA`.
VECTOR_B	The type of `vectorB`.

Parameters

dstVector	The vector to write the result to, of length M.
matrixA	The matrix to multiply `vectorB` by, of size ISIZE x N.
vectorB	The vector multiplied by `matrixA`, of length N.

Performs the operations

dstVector[ i ] = matrixA[ i ][ j ] * vectorB[ j ]

◆ Ri_eq_AjiBj()

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, typename DST_VECTOR , typename MATRIX_A , typename VECTOR_B >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::Ri_eq_AjiBj	(	DST_VECTOR &&LVARRAY_RESTRICT_REF	dstVector,
		MATRIX_A const &LVARRAY_RESTRICT_REF	matrixA,
		VECTOR_B const &LVARRAY_RESTRICT_REF	vectorB
	)

inline

Perform the matrix vector multiplication of the transpose of matrixA and vectorB writing the result to dstVector.

Template Parameters

ISIZE	The length of `dstVector` and the size of the second dimension of `matrixA`.
JSIZE	The size of the first dimension of `matrixA` and the length of `vectorB`.
DST_VECTOR	The type of `dstVector`.
MATRIX_A	The type of `matrixA`.
VECTOR_B	The type of `vectorB`.

Parameters

dstVector	The vector to write the result to, of length M.
matrixA	The matrix to multiply `vectorB` by, of size JSIZE x M.
vectorB	The vector multiplied by `matrixA`, of length N.

Performs the operations

dstVector[ i ] = matrixA[ j ][ i ] * vectorB[ j ]

◆ Ri_eq_symAijBj()

template<std::ptrdiff_t M, typename DST_VECTOR , typename SYM_MATRIX_A , typename VECTOR_B >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::Ri_eq_symAijBj	(	DST_VECTOR &&LVARRAY_RESTRICT_REF	dstVector,
		SYM_MATRIX_A const &LVARRAY_RESTRICT_REF	symMatrixA,
		VECTOR_B const &LVARRAY_RESTRICT_REF	vectorB
	)

inline

Multiply the vector vectorB by the symmetric matrix symMatrixA and store the result in dstVector.

Template Parameters

M	The size of `dstVector`, `symMatrixA`, and `vectorB`.
DST_VECTOR	The type of `dstVector`.
SYM_MATRIX_A	The type of `symMatrixA`.
VECTOR_B	The type of `vectorB`.

Parameters

dstVector	The vector of length M to write the result to.
symMatrixA	The M x M symmetric matrix to multiply `vectorB` by.
vectorB	The vector of length M to be multiplied by `symMatrixA`.

Performs the operation

dstVector[ i ] = symMatrixA[ i ][ j ] * vectorB[ j ]

◆ Rij_add_AiBj()

template<std::ptrdiff_t JSIZE, std::ptrdiff_t ISIZE, typename DST_MATRIX , typename VECTOR_A , typename VECTOR_B >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::Rij_add_AiBj	(	DST_MATRIX &&LVARRAY_RESTRICT_REF	dstMatrix,
		VECTOR_A const &LVARRAY_RESTRICT_REF	vectorA,
		VECTOR_B const &LVARRAY_RESTRICT_REF	vectorB
	)

inline

Perform the outer product of vectorA and vectorB adding the result to dstMatrix.

Template Parameters

ISIZE	The size of the first dimension of `dstMatrix` and the length of `vectorA`.
JSIZE	The size of the second dimension of `dstMatrix` and the length of `vectorB`.
DST_MATRIX	The type of `dstMatrix`.
VECTOR_A	The type of `vectorA`.
VECTOR_B	The type of `vectorB`.

Parameters

dstMatrix	The matrix the result is added to, of size ISIZE x N.
vectorA	The first vector in the outer product, of length M.
vectorB	The second vector in the outer product, of length N.

Performs the operations

dstMatrix[ i ][ j ] += vectorA[ i ] * vectorB[ j ]

◆ Rij_add_AikAjk()

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, typename DST_MATRIX , typename MATRIX_A >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::Rij_add_AikAjk	(	DST_MATRIX &&LVARRAY_RESTRICT_REF	dstMatrix,
		MATRIX_A const &LVARRAY_RESTRICT_REF	matrixA
	)

inline

Multiply matrixA with the transpose of itself and put the result into dstMatrix.

Template Parameters

ISIZE	The size of the first dimension of `matrixA` and both dimensions of `dstMatrix`.
JSIZE	The size of the second dimension of matrixA.
DST_MATRIX	The type of `dstMatrix`.
MATRIX_A	The type of `matrixA`.

Parameters

dstMatrix	The matrix the result is written to, of size ISIZE x M.
matrixA	The matrix in the multiplication, of size ISIZE x N.

Performs the operation

dstMatrix[ i ][ j ] += matrixA[ i ][ k ] * matrixA[ j ][ k ]

◆ Rij_add_AikBjk()

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, std::ptrdiff_t KSIZE, typename DST_MATRIX , typename MATRIX_A , typename MATRIX_B >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::Rij_add_AikBjk	(	DST_MATRIX &&LVARRAY_RESTRICT_REF	dstMatrix,
		MATRIX_A const &LVARRAY_RESTRICT_REF	matrixA,
		MATRIX_B const &LVARRAY_RESTRICT_REF	matrixB
	)

inline

Multiply matrixA with the transpose of matrixB and put the result into dstMatrix.

Template Parameters

ISIZE	The size of the first dimension of `dstMatrix` and `matrixA`.
JSIZE	The size of the second dimension of `dstMatrix` and the first dimension of `matrixB`.
KSIZE	The size of the second dimension of `matrixA` and `matrixB`.
DST_MATRIX	The type of `dstMatrix`.
MATRIX_A	The type of `matrixA`.
MATRIX_B	The type of `matrixB`.

Parameters

dstMatrix	The matrix the result is written to, of size ISIZE x N.
matrixA	The left matrix in the multiplication, of size ISIZE x P.
matrixB	The right matrix in the multiplication, of size JSIZE x P.

Performs the operation

dstMatrix[ i ][ j ] += matrixA[ i ][ k ] * matrixB[ j ][ k ]

◆ Rij_add_AikBkj()

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, std::ptrdiff_t KSIZE, typename DST_MATRIX , typename MATRIX_A , typename MATRIX_B >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::Rij_add_AikBkj	(	DST_MATRIX &&LVARRAY_RESTRICT_REF	dstMatrix,
		MATRIX_A const &LVARRAY_RESTRICT_REF	matrixA,
		MATRIX_B const &LVARRAY_RESTRICT_REF	matrixB
	)

inline

Multiply matrixA with matrixB and add the result to dstMatrix.

Template Parameters

ISIZE	The size of the first dimension of `dstMatrix` and `matrixA`.
JSIZE	The size of the second dimension of `dstMatrix` and `matrixB`.
KSIZE	The size of the second dimension of `matrixA` and first dimension of `matrixB`.
DST_MATRIX	The type of `dstMatrix`.
MATRIX_A	The type of `matrixA`.
MATRIX_B	The type of `matrixB`.

Parameters

dstMatrix	The matrix the result is added to, of size ISIZE x N.
matrixA	The left matrix in the multiplication, of size ISIZE x P.
matrixB	The right matrix in the multiplication, of size KSIZE x N.

Performs the operation

dstMatrix[ i ][ j ] += matrixA[ i ][ k ] * matrixB[ k ][ j ]

◆ Rij_add_AkiBkj()

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, std::ptrdiff_t KSIZE, typename DST_MATRIX , typename MATRIX_A , typename MATRIX_B >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::Rij_add_AkiBkj	(	DST_MATRIX &&LVARRAY_RESTRICT_REF	dstMatrix,
		MATRIX_A const &LVARRAY_RESTRICT_REF	matrixA,
		MATRIX_B const &LVARRAY_RESTRICT_REF	matrixB
	)

inline

Multiply the transpose of matrixA with matrixB and add the result into dstMatrix.

Template Parameters

ISIZE	The size of the first dimension of `dstMatrix` and the second dimension of `matrixA`.
JSIZE	The size of the second dimension of `dstMatrix` and `matrixB`.
KSIZE	The size of the first dimension of `matrixA` and `matrixB`.
DST_MATRIX	The type of `dstMatrix`.
MATRIX_A	The type of `matrixA`.
MATRIX_B	The type of `matrixB`.

Parameters

dstMatrix	The matrix the result is written to, of size ISIZE x N.
matrixA	The left matrix in the multiplication, of size KSIZE x M.
matrixB	The right matrix in the multiplication, of size KSIZE x N.

Performs the operation

dstMatrix[ i ][ j ] += matrixA[ k ][ i ] * matrixB[ k ][ j ]

◆ Rij_eq_AiBj()

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, typename DST_MATRIX , typename VECTOR_A , typename VECTOR_B >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::Rij_eq_AiBj	(	DST_MATRIX &&LVARRAY_RESTRICT_REF	dstMatrix,
		VECTOR_A const &LVARRAY_RESTRICT_REF	vectorA,
		VECTOR_B const &LVARRAY_RESTRICT_REF	vectorB
	)

inline

Perform the outer product of vectorA and vectorB writing the result to dstMatrix.

Template Parameters

ISIZE	The size of the first dimension of `dstMatrix` and the length of `vectorA`.
JSIZE	The size of the second dimension of `dstMatrix` and the length of `vectorB`.
DST_MATRIX	The type of `dstMatrix`.
VECTOR_A	The type of `vectorA`.
VECTOR_B	The type of `vectorB`.

Parameters

dstMatrix	The matrix the result is written to, of size ISIZE x N.
vectorA	The first vector in the outer product, of length M.
vectorB	The second vector in the outer product, of length N.

Performs the operations

dstMatrix[ i ][ j ] = vectorA[ i ] * vectorB[ j ]

◆ Rij_eq_AikBjk()

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, std::ptrdiff_t KSIZE, typename DST_MATRIX , typename MATRIX_A , typename MATRIX_B >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::Rij_eq_AikBjk	(	DST_MATRIX &&LVARRAY_RESTRICT_REF	dstMatrix,
		MATRIX_A const &LVARRAY_RESTRICT_REF	matrixA,
		MATRIX_B const &LVARRAY_RESTRICT_REF	matrixB
	)

inline

Multiply matrixA with the transpose of matrixB and put the result into dstMatrix.

Template Parameters

ISIZE	The size of the first dimension of `dstMatrix` and `matrixA`.
JSIZE	The size of the second dimension of `dstMatrix` and the first dimension of `matrixB`.
KSIZE	The size of the second dimension of `matrixA` and `matrixB`.
DST_MATRIX	The type of `dstMatrix`.
MATRIX_A	The type of `matrixA`.
MATRIX_B	The type of `matrixB`.

Parameters

dstMatrix	The matrix the result is written to, of size ISIZE x N.
matrixA	The left matrix in the multiplication, of size ISIZE x P.
matrixB	The right matrix in the multiplication, of size JSIZE x P.

Performs the operation

dstMatrix[ i ][ j ] = matrixA[ i ][ k ] * matrixB[ j ][ k ]

◆ Rij_eq_AikBkj()

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, std::ptrdiff_t KSIZE, typename DST_MATRIX , typename MATRIX_A , typename MATRIX_B >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::Rij_eq_AikBkj	(	DST_MATRIX &&LVARRAY_RESTRICT_REF	dstMatrix,
		MATRIX_A const &LVARRAY_RESTRICT_REF	matrixA,
		MATRIX_B const &LVARRAY_RESTRICT_REF	matrixB
	)

inline

Multiply matrixA with matrixB and put the result into dstMatrix.

Template Parameters

ISIZE	The size of the first dimension of `dstMatrix` and `matrixA`.
JSIZE	The size of the second dimension of `dstMatrix` and `matrixB`.
KSIZE	The size of the second dimension of `matrixA` and first dimension of `matrixB`.
DST_MATRIX	The type of `dstMatrix`.
MATRIX_A	The type of `matrixA`.
MATRIX_B	The type of `matrixB`.

Parameters

dstMatrix	The matrix the result is written to, of size ISIZE x N.
matrixA	The left matrix in the multiplication, of size ISIZE x P.
matrixB	The right matrix in the multiplication, of size KSIZE x N.

Performs the operation

dstMatrix[ i ][ j ] = matrixA[ i ][ k ] * matrixB[ k ][ j ]

◆ Rij_eq_AikSymBklAjl()

template<std::ptrdiff_t M, typename DST_SYM_MATRIX , typename MATRIX_A , typename SYM_MATRIX_B >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::Rij_eq_AikSymBklAjl	(	DST_SYM_MATRIX &&LVARRAY_RESTRICT_REF	dstSymMatrix,
		MATRIX_A const &LVARRAY_RESTRICT_REF	matrixA,
		SYM_MATRIX_B const &LVARRAY_RESTRICT_REF	symMatrixB
	)

inline

Multiply the transpose of matrix matrixA by the symmetric matrix symMatrixB then by matrixA and store the result in dstSymMatrix.

Template Parameters

M	The size of `dstSymMatrix`, `matrixA` and `symMatrixB`.
DST_SYM_MATRIX	The type of `dstSymMatrix`.
MATRIX_A	The type of `matrixA`.
SYM_MATRIX_B	The type of `symMatrixB`.

Parameters

dstSymMatrix	The M x M symmetric matrix to write the result to.
matrixA	The M x M matrix to pre and post multiply `symMatrixB` by.
symMatrixB	The M x M symmetric matrix that gets pre multiplied by `matrixA` and post postmultiplied by the transpose of `matrixA`.

Performs the operation

dstSymMatrix[ i ][ j ] = matrixA[ i ][ k ] * symMatrixB[ k ][ l ] * matrixA[ j ][ l ]

◆ Rij_eq_AkiAkj()

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, typename DST_MATRIX , typename MATRIX_A >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::Rij_eq_AkiAkj	(	DST_MATRIX &&LVARRAY_RESTRICT_REF	dstMatrix,
		MATRIX_A const &LVARRAY_RESTRICT_REF	matrixA
	)

inline

Multiply the transpose of matrixA with matrixA and put the result into dstMatrix.

Template Parameters

ISIZE	The size of both dimensions of `dstMatrix` and the second dimension of `matrixA`.
JSIZE	The size of the first dimension of `matrixA`.
DST_MATRIX	The type of `dstMatrix`.
MATRIX_A	The type of `matrixA`.

Parameters

dstMatrix	The matrix the result is written to, of size ISIZE x ISIZE.
matrixA	The left matrix in the multiplication, of size JSIZE x ISIZE.

Performs the operation

dstMatrix[ i ][ j ] = matrixA[ k ][ i ] * matrixA[ k ][ j ]

◆ Rij_eq_AkiBkj()

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, std::ptrdiff_t KSIZE, typename DST_MATRIX , typename MATRIX_A , typename MATRIX_B >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::Rij_eq_AkiBkj	(	DST_MATRIX &&LVARRAY_RESTRICT_REF	dstMatrix,
		MATRIX_A const &LVARRAY_RESTRICT_REF	matrixA,
		MATRIX_B const &LVARRAY_RESTRICT_REF	matrixB
	)

inline

Multiply the transpose of matrixA with matrixB and put the result into dstMatrix.

Template Parameters

ISIZE	The size of the first dimension of `dstMatrix` and the second dimension of `matrixA`.
JSIZE	The size of the second dimension of `dstMatrix` and `matrixB`.
KSIZE	The size of the first dimension of `matrixA` and `matrixB`.
DST_MATRIX	The type of `dstMatrix`.
MATRIX_A	The type of `matrixA`.
MATRIX_B	The type of `matrixB`.

Parameters

dstMatrix	The matrix the result is written to, of size ISIZE x N.
matrixA	The left matrix in the multiplication, of size KSIZE x M.
matrixB	The right matrix in the multiplication, of size KSIZE x N.

Performs the operation

dstMatrix[ i ][ j ] = matrixA[ k ][ i ] * matrixB[ k ][ j ]

◆ Rij_eq_symAikBjk()

template<std::ptrdiff_t M, typename DST_MATRIX , typename SYM_MATRIX_A , typename MATRIX_B >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::Rij_eq_symAikBjk	(	DST_MATRIX &&LVARRAY_RESTRICT_REF	dstMatrix,
		SYM_MATRIX_A const &LVARRAY_RESTRICT_REF	symMatrixA,
		MATRIX_B const &LVARRAY_RESTRICT_REF	matrixB
	)

inline

Multiply the transpose of matrix matrixB by the symmetric matrix symMatrixA and store the result in dstMatrix.

Template Parameters

M	The size of `dstMatrix`, `symMatrixA` and `matrixB`.
DST_MATRIX	The type of `dstMatrix`.
SYM_MATRIX_A	The type of `symMatrixA`.
MATRIX_B	The type of `matrixB`.

Parameters

dstMatrix	The M x M matrix to write the result to.
symMatrixA	The M x M symmetric matrix to multiply `matrixB` by.
matrixB	The M x M matrix to be multiplied by `matrixB`.

Performs the operation

dstMatrix[ i ][ j ] = symMatrixA[ i ][ k ] * matrixB[ j ][ k ]

◆ scale() [1/2]

template<std::ptrdiff_t ISIZE, typename VECTOR >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::scale	(	VECTOR &&	vector,
		std::remove_reference_t< decltype(vector[0]) > const	scale
	)

inline

Multiply the entries of vector by scale.

Template Parameters

ISIZE	The size of `vector`.
VECTOR	The type of `vector`.

Parameters

vector	The vector to scale, of length M.
scale	The value to scale the entries of `vector` by.

Performs the operation

vector[ i ] *= scale

◆ scale() [2/2]

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, typename MATRIX >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::scale	(	MATRIX &&	matrix,
		std::remove_reference_t< decltype(matrix[0][0]) > const	scale
	)

inline

Multiply the entries of matrix by scale.

Template Parameters

ISIZE	The size of the first dimension of `matrix`.
JSIZE	The size of the second dimension of `matrix`.
MATRIX	The type of `matrix`.

Parameters

matrix	The matrix to scale, of size ISIZE x N.
scale	The value scale the entries of `vector` by.

Performs the operations

matrix[ i ][ j ] *= scale

◆ scaledAdd() [1/2]

template<std::ptrdiff_t ISIZE, typename DST_VECTOR , typename SRC_VECTOR >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::scaledAdd	(	DST_VECTOR &&LVARRAY_RESTRICT_REF	dstVector,
		SRC_VECTOR const &LVARRAY_RESTRICT_REF	srcVector,
		std::remove_reference_t< decltype(srcVector[0]) > const	scale
	)

inline

Add srcVector scaled by scale to dstVector.

Template Parameters

ISIZE	The length of `dstVector` and `srcVector`.
DST_VECTOR	The type of `dstVector`.
SRC_VECTOR	The type of `srcVector`.

Parameters

dstVector	The destination vector, of length M.
srcVector	The source vector, of length M.
scale	The value to scale the entries of `srcVector` by.

Performs the operation

dstVector[ i ] += scale * srcVector[ i ]

◆ scaledAdd() [2/2]

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, typename DST_MATRIX , typename SRC_MATRIX >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::scaledAdd	(	DST_MATRIX &&LVARRAY_RESTRICT_REF	dstMatrix,
		SRC_MATRIX const &LVARRAY_RESTRICT_REF	srcMatrix,
		std::remove_reference_t< decltype(srcMatrix[0][0]) > const	scale
	)

inline

Add srcMatrix scaled by scale to dstMatrix.

Template Parameters

ISIZE	The size of the first dimension of `dstMatrix` and `srcMatrix`.
JSIZE	The size of the second dimension of `dstMatrix` and `srcMatrix`.
DST_MATRIX	The type of `dstMatrix`.
SRC_MATRIX	The type of `srcMatrix`.

Parameters

dstMatrix	The destination matrix, of size ISIZE x N.
srcMatrix	The source matrix, of size ISIZE x N.
scale	The value to scale the entries of `srcMatrix` by.

Performs the operation

dstMatrix[ i ][ j ] += srcMatrix[ i ][ j ]

◆ scaledCopy() [1/2]

template<std::ptrdiff_t ISIZE, typename DST_VECTOR , typename SRC_VECTOR >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::scaledCopy	(	DST_VECTOR &&LVARRAY_RESTRICT_REF	dstVector,
		SRC_VECTOR const &LVARRAY_RESTRICT_REF	srcVector,
		std::remove_reference_t< decltype(srcVector[0]) > const	scale
	)

inline

Copy srcVector scaled by scale into dstVector.

Template Parameters

ISIZE	The length of `dstVector` and `srcVector`.
DST_VECTOR	The type of `dstVector`.
SRC_VECTOR	The type of `srcVector`.

Parameters

dstVector	The destination vector, of length M.
srcVector	The source vector, of length M.
scale	The value to scale `srcVector` by.

Performs the operations

dstVector[ i ] = scale * srcVector[ i ]

◆ scaledCopy() [2/2]

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, typename DST_MATRIX , typename SRC_MATRIX >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::scaledCopy	(	DST_MATRIX &&LVARRAY_RESTRICT_REF	dstMatrix,
		SRC_MATRIX const &LVARRAY_RESTRICT_REF	srcMatrix,
		std::remove_reference_t< decltype(srcMatrix[0][0]) > const	scale
	)

inline

Copy srcMatrix scaled by scale into dstMatrix.

Template Parameters

ISIZE	The size of the first dimension of `dstMatrix` and `srcMatrix`.
JSIZE	The size of the second dimension of `dstMatrix` and `srcMatrix`.
DST_MATRIX	The type of `dstMatrix`.
SRC_MATRIX	The type of `srcMatrix`.

Parameters

dstMatrix	The destination matrix, of size ISIZE x N.
srcMatrix	The source matrix, of size ISIZE x N.
scale	The value to scale `srcMatrix` by.

Performs the operation

dstMatrix[ i ][ j ] = scale * srcMatrix[ i ][ j ]

◆ subtract()

template<std::ptrdiff_t ISIZE, typename DST_VECTOR , typename SRC_VECTOR >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::subtract	(	DST_VECTOR &&LVARRAY_RESTRICT_REF	dstVector,
		SRC_VECTOR const &LVARRAY_RESTRICT_REF	srcVector
	)

inline

Subtract srcVector from dstVector.

Template Parameters

ISIZE	The length of `dstVector` and `srcVector`.
DST_VECTOR	The type of `dstVector`.
SRC_VECTOR	The type of `srcVector`.

Parameters

dstVector	The destination vector, of length M.
srcVector	The source vector, of length M.

Performs the operation

dstVector[ i ] -= srcVector[ i ]

◆ symAddIdentity()

template<std::ptrdiff_t ISIZE, typename SYM_MATRIX >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::symAddIdentity	(	SYM_MATRIX &&	symMatrix,
		std::remove_reference_t< decltype(symMatrix[0]) > const	scale
	)

inline

Add scale times the identity matrix to symMatrix.

Template Parameters

ISIZE	The size of `symMatrix`.
SYM_MATRIX	The type of `symMatrix`.

Parameters

symMatrix	The ISIZE x ISIZE symmetric matrix to add the identity matrix to.
scale	The amount to scale the identity matrix by.

Performs the operations

matrix[ i ][ i ] += scale

◆ symDeterminant()

template<std::ptrdiff_t M, typename SYM_MATRIX >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK auto LvArray::tensorOps::symDeterminant ( SYM_MATRIX const & symMatrix )

inline

Returns: Return the determinant of the symmetric matrix symMatrix.

Template Parameters

SYM_MATRIX The type of symMatrix.

Parameters

symMatrix The M x M symmetric matrix to get the determinant of.

◆ symEigenvalues()

template<std::ptrdiff_t M, typename DST_VECTOR , typename SYM_MATRIX >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::symEigenvalues	(	DST_VECTOR &&LVARRAY_RESTRICT_REF	eigenvalues,
		SYM_MATRIX const &LVARRAY_RESTRICT_REF	symMatrix
	)

inline

Compute the eigenvalues of the symmetric matrix symMatrix.

Template Parameters

DST_VECTOR	The type of `eigenvalues`.
SYM_MATRIX	The type of `symMatrix`.

Parameters

eigenvalues	The vector of length M to write the eigenvalues to.
symMatrix	The MxM symmetric matrix to compute the eigenvalues of.

Computes the eigenvalues by directly solving the characteristic equation, they are returned sorted in ascending order.

Note: The 3x3 matrices eigenvalues are computed to within the following relative tolerance: double precision: 3e-8 single precision: 5e-4 However for matrices with well spaced eigenvalues the precision is many orders greater.; symMatrix can contain integers but eigenvalues must contain floating point numbers.

◆ symEigenvectors()

template<std::ptrdiff_t M, typename DST_VECTOR , typename DST_MATRIX , typename SYM_MATRIX >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::symEigenvectors	(	DST_VECTOR &&LVARRAY_RESTRICT_REF	eigenvalues,
		DST_MATRIX &&LVARRAY_RESTRICT_REF	eigenvectors,
		SYM_MATRIX const &LVARRAY_RESTRICT_REF	symMatrix
	)

inline

Compute the eigenvalues and eigenvectors of the symmetric matrix symMatrix.

Template Parameters

DST_VECTOR	The type of `eigenvalues`.
DST_MATRIX	The type of `eigenvectors`
SYM_MATRIX	The type of `symMatrix`.

Parameters

eigenvalues	The vector of length M to write the eigenvalues to.
eigenvectors	The MxM matrix to write the eigenvectors to.
symMatrix	The MxM symmetric matrix to compute the eigenvalues of.

Computes the eigenvalues by directly solving the characteristic equation, they are returned sorted in ascending order. The row

eigenvectors[ i ]

contains the eigenvector corresponding to

eigenvalues[ i ]

.

Note: For 3x3 matrices the eigenvalues are computed to within the following relative tolerance: double precision: 3e-8 single precision: 5e-4 However for matrices with well spaced eigenvalues the precision is many orders greater.; symMatrix can contain integers but eigenvalues must contain floating point numbers.

◆ symInvert() [1/2]

template<std::ptrdiff_t M, typename DST_SYM_MATRIX , typename SRC_SYM_MATRIX >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK auto LvArray::tensorOps::symInvert	(	DST_SYM_MATRIX &&LVARRAY_RESTRICT_REF	dstSymMatrix,
		SRC_SYM_MATRIX const &LVARRAY_RESTRICT_REF	srcSymMatrix
	)

inline

Invert the symmetric matrix srcSymMatrix and store the result in dstSymMatrix.

Template Parameters

M	The size of the symmetric matrices `dstSymMatrix` and `srcSymMatrix`.
DST_SYM_MATRIX	The type of `dstSymMatrix`.
SRC_SYM_MATRIX	The type of `srcSymMatrix`.

Parameters

dstSymMatrix	The M x M symmetric matrix to write the inverse to.
srcSymMatrix	The M x M symmetric matrix to take the inverse of.

Returns: The determinant.

Note: srcSymMatrix can contain integers but dstMatrix must contain floating point values.

◆ symInvert() [2/2]

template<std::ptrdiff_t M, typename SYM_MATRIX >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK auto LvArray::tensorOps::symInvert ( SYM_MATRIX && symMatrix )

inline

Invert the symmetric matrix symMatrix overwritting it.

Template Parameters

M	The size of the matrix `symMatrix`.
SYM_MATRIX	The type of `symMatrix`.

Parameters

symMatrix The M x M symmetric matrix to take the inverse of and overwrite.

Returns: The determinant.

Note: symMatrix must contain floating point values.

◆ symmetricToDense()

template<std::ptrdiff_t M, typename DST_MATRIX , typename SRC_SYM_MATRIX >

LVARRAY_HOST_DEVICE constexpr void LvArray::tensorOps::symmetricToDense	(	DST_MATRIX &&	dstMatrix,
		SRC_SYM_MATRIX const &	srcSymMatrix
	)

inline

Convert the srcSymMatrix into a dense matrix.

Template Parameters

M	The size of `dstMatrix` and `srcSymMatrix`.
DST_MATRIX	The type of `dstMatrix`.
SRC_SYM_MATRIX	The type of `srcSymMatrix`.

Parameters

dstMatrix	The resulting MxM matrix.
srcSymMatrix	The MxM symmetric matrix to convert.

◆ symRij_eq_AiAj()

template<std::ptrdiff_t M, typename DST_SYM_MATRIX , typename VECTOR_A >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::symRij_eq_AiAj	(	DST_SYM_MATRIX &&LVARRAY_RESTRICT_REF	dstMatrix,
		VECTOR_A const &LVARRAY_RESTRICT_REF	vectorA
	)

inline

Perform the outer product of vectorA with itself writing the result to dstMatrix.

Template Parameters

M	The size of both dimensions of `dstMatrix` and the length of `vectorA`.
DST_MATRIX	The type of `dstMatrix`.
VECTOR_A	The type of `vectorA`.

Parameters

dstMatrix	The matrix the result is written to, of size M x M.
vectorA	The first vector in the outer product, of length M.

Performs the operations

dstMatrix[ i ][ j ] = vectorA[ i ] * vectorA[ j ]

◆ symRij_eq_AiBj_plus_AjBi()

template<std::ptrdiff_t M, typename DST_SYM_MATRIX , typename VECTOR_A , typename VECTOR_B >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::symRij_eq_AiBj_plus_AjBi	(	DST_SYM_MATRIX &&LVARRAY_RESTRICT_REF	dstMatrix,
		VECTOR_A const &LVARRAY_RESTRICT_REF	vectorA,
		VECTOR_B const &LVARRAY_RESTRICT_REF	vectorB
	)

inline

Perform the unscaled symmetric outer product of vectorA and vectorB with itself writing the result to dstMatrix.

Template Parameters

M	The size of both dimensions of `dstMatrix` and the length of `vectorA`.
DST_MATRIX	The type of `dstMatrix`.
VECTOR_A	The type of `vectorA`.
VECTOR_B	The type of `vectorB`.

Parameters

dstMatrix	The matrix the result is written to, of size M x N.
vectorA	The first vector in the outer product, of length M.
vectorB	The second vector in the outer product, of length M.

Performs the operations

dstMatrix[ i ][ j ] = vectorA[ i ] * vectorB[ j ] + vectorA[ j ] * vectorB[ i ]

◆ symTrace()

template<std::ptrdiff_t ISIZE, typename SYM_MATRIX >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK auto LvArray::tensorOps::symTrace ( SYM_MATRIX const & symMatrix )

inline

Returns: The trace of symMatrix.

Template Parameters

ISIZE	The size of `symMatrix`.
SYM_MATRIX	The type of `symMatrix`.

Parameters

symMatrix The ISIZE x ISIZE symmetric matrix to get the trace of.

◆ trace()

template<std::ptrdiff_t ISIZE, typename MATRIX >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK auto LvArray::tensorOps::trace ( MATRIX const & matrix )

inline

Returns: The trace of matrix.

Template Parameters

ISIZE	The size of `matrix`.
MATRIX	The type of `matrix`.

Parameters

matrix The ISIZE x ISIZE matrix to get the trace of.

◆ transpose() [1/2]

template<std::ptrdiff_t ISIZE, std::ptrdiff_t JSIZE, typename DST_MATRIX , typename SRC_MATRIX >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::transpose	(	DST_MATRIX &&LVARRAY_RESTRICT_REF	dstMatrix,
		SRC_MATRIX const &LVARRAY_RESTRICT_REF	srcMatrix
	)

inline

Store the transpose of the NxM matrix srcMatrix in dstMatrix.

Template Parameters

ISIZE	The size of the first dimension of `dstMatrix` and the second dimension of `srcMatrix`.
JSIZE	The size of the second dimension of `dstMatrix` and the first dimension of `srcMatrix`.
DST_MATRIX	The type of `dstMatrix`.
SRC_MATRIX	The type of `srcMatrix`.

Parameters

dstMatrix	The MxN matrix where the transpose of `srcMatrix` is written.
srcMatrix	The NxM matrix to transpose.

◆ transpose() [2/2]

template<std::ptrdiff_t ISIZE, typename MATRIX >

LVARRAY_HOST_DEVICE CONSTEXPR_WITHOUT_BOUNDS_CHECK void LvArray::tensorOps::transpose ( MATRIX &&LVARRAY_RESTRICT_REF matrix )

inline

Transpose the MxM matrix matrix.

Template Parameters

ISIZE	The size of `matrix`.
MATRIX	The type of `matrix`.

Parameters

matrix The MxM matrix to transpose.

Functions

Variables

Detailed Description

Function Documentation

◆ add() [1/2]

◆ add() [2/2]

◆ addIdentity()

◆ addScalar()

◆ AiBi()

◆ copy() [1/2]

◆ copy() [2/2]

◆ crossProduct()

◆ denseToSymmetric()

◆ determinant()

◆ fill() [1/2]

◆ fill() [2/2]

◆ hadamardProduct()

◆ invert() [1/2]

◆ invert() [2/2]

◆ l2Norm()

◆ l2NormSquared()

◆ maxAbsoluteEntry()

◆ normalize()

◆ Ri_add_AijBj()

◆ Ri_add_AjiBj()

◆ Ri_add_symAijBj()

◆ Ri_eq_AijBj()

◆ Ri_eq_AjiBj()

◆ Ri_eq_symAijBj()

◆ Rij_add_AiBj()

◆ Rij_add_AikAjk()

◆ Rij_add_AikBjk()

◆ Rij_add_AikBkj()

◆ Rij_add_AkiBkj()

◆ Rij_eq_AiBj()

◆ Rij_eq_AikBjk()

◆ Rij_eq_AikBkj()

◆ Rij_eq_AikSymBklAjl()

◆ Rij_eq_AkiAkj()

◆ Rij_eq_AkiBkj()

◆ Rij_eq_symAikBjk()

◆ scale() [1/2]

◆ scale() [2/2]

◆ scaledAdd() [1/2]

◆ scaledAdd() [2/2]

◆ scaledCopy() [1/2]

◆ scaledCopy() [2/2]

◆ subtract()

◆ symAddIdentity()

◆ symDeterminant()

◆ symEigenvalues()

◆ symEigenvectors()

◆ symInvert() [1/2]

◆ symInvert() [2/2]

◆ symmetricToDense()

◆ symRij_eq_AiAj()

◆ symRij_eq_AiBj_plus_AjBi()

◆ symTrace()

◆ trace()

◆ transpose() [1/2]

◆ transpose() [2/2]