This class contains a collection of BLAS and LAPACK linear algebra operations for GEOSX array1d and array2d. More...

#include <BlasLapackLA.hpp>

Public Types
enum	RandomNumberDistribution : integer { RandomNumberDistribution::UNIFORM_01 = 1, RandomNumberDistribution::UNIFORM_m1p1 = 2, RandomNumberDistribution::NORMAL_01 = 3 }
	This enum class specifies the type of distribution for generating random real numbers. More...

template<typename T >
using	Vec = arraySlice1d< T >
	Alias for 1d slice representing a vector.

template<typename T >
using	MatRowMajor = arraySlice2d< T, MatrixLayout::ROW_MAJOR >
	Alias for 2d slice representing a row-major dense matrix.

template<typename T >
using	MatColMajor = arraySlice2d< T, MatrixLayout::COL_MAJOR >
	Alias for 2d slice representing a column-major dense matrix.

Static Public Member Functions
static real64	vectorNorm1 (Vec< real64 const > const &X)
	Returns the 1-norm of the vector. More...

static real64	vectorNorm2 (Vec< real64 const > const &X)
	Returns the two norm of the vector. More...

static real64	vectorNormInf (Vec< real64 const > const &X)
	Returns the infinity-norm of the vector. More...

static real64	determinant (MatRowMajor< real64 const > const &A)
	Returns the determinant of a square matrix. More...

static real64	determinant (MatColMajor< real64 const > const &A)
	Returns the determinant of a square matrix. More...

static real64	matrixNormInf (MatRowMajor< real64 const > const &A)
	Returns the infinity norm of the matrix. More...

static real64	matrixNormInf (MatColMajor< real64 const > const &A)
	Returns the infinity norm of the matrix. More...

static real64	matrixNorm1 (MatRowMajor< real64 const > const &A)
	Returns the one norm of the matrix. More...

static real64	matrixNorm1 (MatColMajor< real64 const > const &A)
	Returns the one norm of the matrix. More...

static real64	matrixNormFrobenius (MatRowMajor< real64 const > const &A)
	Returns the Frobenius norm of the matrix. More...

static real64	matrixNormFrobenius (MatColMajor< real64 const > const &A)
	Returns the Frobenius norm of the matrix. More...

static void	vectorVectorAdd (Vec< real64 const > const &X, Vec< real64 > const &Y, real64 const alpha=1.)
	Vector-Vector sum; `Y` = `alpha*X +` `Y`. More...

static void	matrixMatrixAdd (MatRowMajor< real64 const > const &A, MatRowMajor< real64 > const &B, real64 const alpha=1.)
	Matrix-Matrix sum; `B` = `alpha*A +` `B`. More...

static void	matrixMatrixAdd (MatColMajor< real64 const > const &A, MatColMajor< real64 > const &B, real64 const alpha=1.)
	Matrix-Matrix sum; `B` = `alpha*A +` `B`. More...

static void	vectorScale (real64 const alpha, Vec< real64 > const &X)
	In-place scalar-vector product; `X` = `alpha*X.` More...

static void	matrixScale (real64 const alpha, MatRowMajor< real64 > const &A)
	In-place scalar-matrix product; `A` = `alpha*A.` More...

static void	matrixScale (real64 const alpha, MatColMajor< real64 > const &A)
	In-place scalar-matrix product; `A` = `alpha*A.` More...

static real64	vectorDot (Vec< real64 const > const &X, Vec< real64 const > const &Y)
	Returns the dot product of two vectors. More...

static void	matrixVectorMultiply (MatRowMajor< real64 const > const &A, Vec< real64 const > const &X, Vec< real64 > const &Y, real64 const alpha=1.0, real64 const beta=0.0)
	Matrix-Vector product; `Y` = `alphaAX + beta*Y.` More...

static void	matrixTVectorMultiply (MatRowMajor< real64 const > const &A, Vec< real64 const > const &X, Vec< real64 > const &Y, real64 const alpha=1.0, real64 const beta=0.0)
	transpose(Matrix)-Vector product; `Y` = `alphatranspose(A)X + beta*Y.` More...

static void	matrixMatrixMultiply (MatRowMajor< real64 const > const &A, MatRowMajor< real64 const > const &B, MatRowMajor< real64 > const &C, real64 const alpha=1.0, real64 const beta=0.0)
	Matrix-Matrix product; `C` = `alphaAB + beta*C.` More...

static void	matrixTMatrixMultiply (MatRowMajor< real64 const > const &A, MatRowMajor< real64 const > const &B, MatRowMajor< real64 > const &C, real64 const alpha=1.0, real64 const beta=0.0)
	transpose(Matrix)-Matrix product; `C` = `alphatranspose(A)B + beta*C.` More...

static void	matrixMatrixTMultiply (MatRowMajor< real64 const > const &A, MatRowMajor< real64 const > const &B, MatRowMajor< real64 > const &C, real64 const alpha=1.0, real64 const beta=0.0)
	Matrix-transpose(Matrix) product; `C` = `alphaAtranspose(B) + beta*C.` More...

static void	matrixTMatrixTMultiply (MatRowMajor< real64 const > const &A, MatRowMajor< real64 const > const &B, MatRowMajor< real64 > const &C, real64 const alpha=1.0, real64 const beta=0.0)
	transpose(Matrix)-transpose(Matrix) product; `C` = `alphatranspose(A)transpose(B) + beta*C.` More...

static void	matrixInverse (MatRowMajor< real64 const > const &A, MatRowMajor< real64 > const &Ainv, real64 &detA)
	Computes the inverse matrix; `Ainv` = `inverse(A)`. More...

static void	matrixInverse (MatColMajor< real64 const > const &A, MatColMajor< real64 > const &Ainv, real64 &detA)
	Computes the inverse matrix; `Ainv` = `inverse(A)`. More...

static void	matrixInverse (MatRowMajor< real64 const > const &A, MatRowMajor< real64 > const &Ainv)
	Computes the inverse matrix; `Ainv` = `inverse(A)`. More...

static void	matrixInverse (MatColMajor< real64 const > const &A, MatColMajor< real64 > const &Ainv)
	Computes the inverse matrix; `Ainv` = `inverse(A)`. More...

static void	vectorCopy (Vec< real64 const > const &X, Vec< real64 > const &Y)
	Vector copy; `Y` = `X`. More...

static void	matrixCopy (MatRowMajor< real64 const > const &A, MatRowMajor< real64 > const &B)
	Matrix copy; `B` = `A`. More...

static void	matrixCopy (MatColMajor< real64 const > const &A, MatColMajor< real64 > const &B)
	Matrix copy; `B` = `A`. More...

static void	setRandomNumberGeneratorSeed (arraySlice1d< int const > const &seed)
	Set the random number generator seed. More...

static void	getRandomNumberGeneratorSeed (arraySlice1d< int > const &seed)
	Get the random number generator seed. More...

static void	vectorRand (Vec< real64 > const &X, RandomNumberDistribution const &idist=RandomNumberDistribution::UNIFORM_01)
	Sets vector entries to random real numbers. More...

static void	matrixRand (MatRowMajor< real64 > const &A, RandomNumberDistribution const &idist=RandomNumberDistribution::UNIFORM_01)
	Sets matrix entries to random real numbers. More...

static void	matrixRand (MatColMajor< real64 > const &A, RandomNumberDistribution const &idist=RandomNumberDistribution::UNIFORM_01)
	Sets matrix entries to random real numbers. More...

static void	matrixSVD (MatRowMajor< real64 const > const &A, MatRowMajor< real64 > const &U, Vec< real64 > const &S, MatRowMajor< real64 > const &VT)
	Computes the singular value decomposition of A. More...

static void	matrixSVD (MatColMajor< real64 const > const &A, MatColMajor< real64 > const &U, Vec< real64 > const &S, MatColMajor< real64 > const &VT)
	Computes the singular value decomposition of A. More...

static void	matrixEigenvalues (MatRowMajor< real64 const > const &A, Vec< std::complex< real64 > > const &lambda)
	Computes the eigenvalues of A. More...

static void	matrixEigenvalues (MatColMajor< real64 const > const &A, Vec< std::complex< real64 > > const &lambda)
	Computes the eigenvalues of A. More...

Detailed Description

This class contains a collection of BLAS and LAPACK linear algebra operations for GEOSX array1d and array2d.

Definition at line 34 of file BlasLapackLA.hpp.

Member Enumeration Documentation

◆ RandomNumberDistribution

enum geosx::BlasLapackLA::RandomNumberDistribution : integer

strong

This enum class specifies the type of distribution for generating random real numbers.

Enumerator
UNIFORM_01	uniform distribution (0,1)
UNIFORM_m1p1	uniform distribution (-1,1)
NORMAL_01	normal distribution (0,1)

Definition at line 52 of file BlasLapackLA.hpp.

Member Function Documentation

◆ determinant() [1/2]

static real64 geosx::BlasLapackLA::determinant ( MatRowMajor< real64 const > const & A )

static

Returns the determinant of a square matrix.

Parameters

[in] A GEOSX array2d.

Returns: the matrix determinant.

Note: This function is hardcoded for square matrices up to order four. For dimensions larger than four, the determinant is computed using LAPACK's function DGETRF. To avoid matrix transposition/copy due to the row major ordering used in GEOSX for array2d, the determinant is computed for the transpose matrix, i.e. assuming column major ordering, for best performance.

◆ determinant() [2/2]

static real64 geosx::BlasLapackLA::determinant ( MatColMajor< real64 const > const & A )

static

Returns the determinant of a square matrix.

Parameters

[in] A GEOSX array2d.

Returns: the matrix determinant.

Note: This function is hardcoded for square matrices up to order four. For dimensions larger than four, the determinant is computed using LAPACK's function DGETRF. To avoid matrix transposition/copy due to the row major ordering used in GEOSX for array2d, the determinant is computed for the transpose matrix, i.e. assuming column major ordering, for best performance.

◆ getRandomNumberGeneratorSeed()

static void geosx::BlasLapackLA::getRandomNumberGeneratorSeed ( arraySlice1d< int > const & seed )

static

Get the random number generator seed.

Parameters

[out] seed GEOSX array1d, dimension (4).

◆ matrixCopy() [1/2]

static void geosx::BlasLapackLA::matrixCopy	(	MatRowMajor< real64 const > const &	A,
		MatRowMajor< real64 > const &	B
	)

static

Matrix copy; B = A.

Parameters

[in]	A	GEOSX array2d.
[out]	B	GEOSX array2d.

Warning: Assumes that A and B have the same size.

◆ matrixCopy() [2/2]

static void geosx::BlasLapackLA::matrixCopy	(	MatColMajor< real64 const > const &	A,
		MatColMajor< real64 > const &	B
	)

static

Matrix copy; B = A.

Parameters

[in]	A	GEOSX array2d.
[out]	B	GEOSX array2d.

Warning: Assumes that A and B have the same size.

◆ matrixEigenvalues() [1/2]

static void geosx::BlasLapackLA::matrixEigenvalues	(	MatRowMajor< real64 const > const &	A,
		Vec< std::complex< real64 > > const &	lambda
	)

static

Computes the eigenvalues of A.

If size(A) = (N,N), this function expects: size(lambda) = N On exit, lambda contains the eigenvalues of A

Parameters

[in]	A	GEOSX array2d.
[out]	lambda	GEOSX array1d.

◆ matrixEigenvalues() [2/2]

static void geosx::BlasLapackLA::matrixEigenvalues	(	MatColMajor< real64 const > const &	A,
		Vec< std::complex< real64 > > const &	lambda
	)

static

Computes the eigenvalues of A.

If size(A) = (N,N), this function expects: size(lambda) = N On exit, lambda contains the eigenvalues of A

Parameters

[in]	A	GEOSX array2d.
[out]	lambda	GEOSX array1d.

◆ matrixInverse() [1/4]

static void geosx::BlasLapackLA::matrixInverse	(	MatRowMajor< real64 const > const &	A,
		MatRowMajor< real64 > const &	Ainv,
		real64 &	detA
	)

static

Computes the inverse matrix; Ainv = inverse(A).

Computes the inverse of the square matrix A and stores it in Ainv, and also returns the determinant of A.

Parameters

[in]	A	GEOSX array2d.
[out]	Ainv	GEOSX array2d.
[out]	detA	Determinant of matrix `A`.

Warning: Assumes Ainv already has the same size as A.

Note: This function is hardcoded for matrices up to order three. For dimensions larger than three, the function calls LAPACK functions DGETRF and DGETRI. Because of the row major ordering used by GEOSX array2d, the inverse of A is practically computed as the transpose matrix of the transpose matrix inverse using lapack operation based on column-major ordering. This removes the need for any copy/transposition that would be required operating with the row-major layout.

◆ matrixInverse() [2/4]

static void geosx::BlasLapackLA::matrixInverse	(	MatColMajor< real64 const > const &	A,
		MatColMajor< real64 > const &	Ainv,
		real64 &	detA
	)

static

Computes the inverse matrix; Ainv = inverse(A).

Computes the inverse of the square matrix A and stores it in Ainv, and also returns the determinant of A.

Parameters

[in]	A	GEOSX array2d.
[out]	Ainv	GEOSX array2d.
[out]	detA	Determinant of matrix `A`.

Warning: Assumes Ainv already has the same size as A.

Note: This function is hardcoded for matrices up to order three. For dimensions larger than three, the function calls LAPACK functions DGETRF and DGETRI. Because of the row major ordering used by GEOSX array2d, the inverse of A is practically computed as the transpose matrix of the transpose matrix inverse using lapack operation based on column-major ordering. This removes the need for any copy/transposition that would be required operating with the row-major layout.

◆ matrixInverse() [3/4]

static void geosx::BlasLapackLA::matrixInverse	(	MatRowMajor< real64 const > const &	A,
		MatRowMajor< real64 > const &	Ainv
	)

static

Computes the inverse matrix; Ainv = inverse(A).

Computes the inverse of the square matrix A and stores it in Ainv.

Parameters

[in]	A	GEOSX array2d.
[out]	Ainv	GEOSX array2d.

Warning: Assumes Ainv already has the same size as A.

Note: This function is hardcoded for matrices up to order three. For dimensions larger than three, the function calls LAPACK functions DGETRF and DGETRI. Because of the row major ordering used by GEOSX array2d, the inverse of A is practically computed as the transpose matrix of the transpose matrix inverse using lapack operation based on column-major ordering. This removes the need for any copy/transposition that would be required operating with the row-major layout.

◆ matrixInverse() [4/4]

static void geosx::BlasLapackLA::matrixInverse	(	MatColMajor< real64 const > const &	A,
		MatColMajor< real64 > const &	Ainv
	)

static

Computes the inverse matrix; Ainv = inverse(A).

Computes the inverse of the square matrix A and stores it in Ainv.

Parameters

[in]	A	GEOSX array2d.
[out]	Ainv	GEOSX array2d.

Warning: Assumes Ainv already has the same size as A.

Note: This function is hardcoded for matrices up to order three. For dimensions larger than three, the function calls LAPACK functions DGETRF and DGETRI. Because of the row major ordering used by GEOSX array2d, the inverse of A is practically computed as the transpose matrix of the transpose matrix inverse using lapack operation based on column-major ordering. This removes the need for any copy/transposition that would be required operating with the row-major layout.

◆ matrixMatrixAdd() [1/2]

static void geosx::BlasLapackLA::matrixMatrixAdd	(	MatRowMajor< real64 const > const &	A,
		MatRowMajor< real64 > const &	B,
		real64 const	alpha = `1.`
	)

static

Matrix-Matrix sum; B = alpha*A + B.

Computes (alpha*A + B) and overwrites the result on p B, with optional scaling.

Parameters

[in]	A	GEOSX array2d.
[in,out]	B	GEOSX array2d.
[in]	alpha	Optional scalar to multiply with `A`.

Warning: Assumes that A and B have the same size.

◆ matrixMatrixAdd() [2/2]

static void geosx::BlasLapackLA::matrixMatrixAdd	(	MatColMajor< real64 const > const &	A,
		MatColMajor< real64 > const &	B,
		real64 const	alpha = `1.`
	)

static

Matrix-Matrix sum; B = alpha*A + B.

Computes (alpha*A + B) and overwrites the result on p B, with optional scaling.

Parameters

[in]	A	GEOSX array2d.
[in,out]	B	GEOSX array2d.
[in]	alpha	Optional scalar to multiply with `A`.

Warning: Assumes that A and B have the same size.

◆ matrixMatrixMultiply()

static void geosx::BlasLapackLA::matrixMatrixMultiply	(	MatRowMajor< real64 const > const &	A,
		MatRowMajor< real64 const > const &	B,
		MatRowMajor< real64 > const &	C,
		real64 const	alpha = `1.0`,
		real64 const	beta = `0.0`
	)

static

Matrix-Matrix product; C = alpha*A*B + beta*C.

Computes matrix-matrix product with optional scaling and accumulation.

Parameters

[in]	A	GEOSX array2d.
[in]	B	GEOSX array2d.
[in,out]	C	GEOSX array1d.
[in]	alpha	Optional scalar to multiply with `A*B.`
[in]	beta	Optional parameter to control the accumulation.

Warning: Assumes that A and B have compatible sizes and that C already has the right size.

◆ matrixMatrixTMultiply()

static void geosx::BlasLapackLA::matrixMatrixTMultiply	(	MatRowMajor< real64 const > const &	A,
		MatRowMajor< real64 const > const &	B,
		MatRowMajor< real64 > const &	C,
		real64 const	alpha = `1.0`,
		real64 const	beta = `0.0`
	)

static

Matrix-transpose(Matrix) product; C = alpha*A*transpose(B) + beta*C.

Computes matrix-transpose(matrix) product with optional scaling and accumulation.

Parameters

[in]	A	GEOSX array2d.
[in]	B	GEOSX array2d.
[in,out]	C	GEOSX array1d.
[in]	alpha	Optional scalar to multiply with `A*transpose`(B).
[in]	beta	Optional parameter to control the accumulation.

Warning: Assumes that A and transpose(B) have compatible sizes and that C already has the right size.

◆ matrixNorm1() [1/2]

static real64 geosx::BlasLapackLA::matrixNorm1 ( MatRowMajor< real64 const > const & A )

static

Returns the one norm of the matrix.

Parameters

[in] A GEOSX array2d.

Returns: the matrix 1-norm.

Note: Row major ordering is used for GEOSX array2d. Since LAPACK native routines are using a column major ordering (Fortran), the one norm is computed as the infinity norm of the transpose matrix, i.e. assuming column major ordering, for best performance.

◆ matrixNorm1() [2/2]

static real64 geosx::BlasLapackLA::matrixNorm1 ( MatColMajor< real64 const > const & A )

static

Returns the one norm of the matrix.

Parameters

[in] A GEOSX array2d.

Returns: the matrix 1-norm.

Note: Row major ordering is used for GEOSX array2d. Since LAPACK native routines are using a column major ordering (Fortran), the one norm is computed as the infinity norm of the transpose matrix, i.e. assuming column major ordering, for best performance.

◆ matrixNormFrobenius() [1/2]

static real64 geosx::BlasLapackLA::matrixNormFrobenius ( MatRowMajor< real64 const > const & A )

static

Returns the Frobenius norm of the matrix.

Parameters

[in] A GEOSX array2d.

Returns: the Frobenius norm of the matrix.

Note: Row major ordering is used for GEOSX array2d. Since LAPACK native routines are using a column major ordering (Fortran), the one norm is computed for the transpose matrix, i.e. assuming column major ordering, for best performance.

◆ matrixNormFrobenius() [2/2]

static real64 geosx::BlasLapackLA::matrixNormFrobenius ( MatColMajor< real64 const > const & A )

static

Returns the Frobenius norm of the matrix.

Parameters

[in] A GEOSX array2d.

Returns: the Frobenius norm of the matrix.

Note: Row major ordering is used for GEOSX array2d. Since LAPACK native routines are using a column major ordering (Fortran), the one norm is computed for the transpose matrix, i.e. assuming column major ordering, for best performance.

◆ matrixNormInf() [1/2]

static real64 geosx::BlasLapackLA::matrixNormInf ( MatRowMajor< real64 const > const & A )

static

Returns the infinity norm of the matrix.

Parameters

[in] A GEOSX array2d.

Returns: the matrix inf-norm.

Note: Row major ordering is used for GEOSX array2d. Since LAPACK native routines are using a column major ordering (Fortran), the infinity norm is computed as the one norm of the transpose matrix, i.e. assuming column major ordering, for best performance.

◆ matrixNormInf() [2/2]

static real64 geosx::BlasLapackLA::matrixNormInf ( MatColMajor< real64 const > const & A )

static

Returns the infinity norm of the matrix.

Parameters

[in] A GEOSX array2d.

Returns: the matrix inf-norm.

Note: Row major ordering is used for GEOSX array2d. Since LAPACK native routines are using a column major ordering (Fortran), the infinity norm is computed as the one norm of the transpose matrix, i.e. assuming column major ordering, for best performance.

◆ matrixRand() [1/2]

static void geosx::BlasLapackLA::matrixRand	(	MatRowMajor< real64 > const &	A,
		RandomNumberDistribution const &	idist = `RandomNumberDistribution::UNIFORM_01`
	)

static

Sets matrix entries to random real numbers.

Sets matrix entries to random real numbers from a uniform or normal distribution without specifying the seed of the random number generator.

Parameters

[out]	A	GEOSX array1d.
[in]	idist	Optional RandomNumberDistribution enum value specifying the distribution of the random numbers.

◆ matrixRand() [2/2]

static void geosx::BlasLapackLA::matrixRand	(	MatColMajor< real64 > const &	A,
		RandomNumberDistribution const &	idist = `RandomNumberDistribution::UNIFORM_01`
	)

static

Sets matrix entries to random real numbers.

Sets matrix entries to random real numbers from a uniform or normal distribution without specifying the seed of the random number generator.

Parameters

[out]	A	GEOSX array1d.
[in]	idist	Optional RandomNumberDistribution enum value specifying the distribution of the random numbers.

◆ matrixScale() [1/2]

static void geosx::BlasLapackLA::matrixScale	(	real64 const	alpha,
		MatRowMajor< real64 > const &	A
	)

static

In-place scalar-matrix product; A = alpha*A.

Parameters

[in]	alpha	Scalar to multiply with `A`.
[in,out]	A	GEOSX array2d.

◆ matrixScale() [2/2]

static void geosx::BlasLapackLA::matrixScale	(	real64 const	alpha,
		MatColMajor< real64 > const &	A
	)

static

In-place scalar-matrix product; A = alpha*A.

Parameters

[in]	alpha	Scalar to multiply with `A`.
[in,out]	A	GEOSX array2d.

◆ matrixSVD() [1/2]

static void geosx::BlasLapackLA::matrixSVD	(	MatRowMajor< real64 const > const &	A,
		MatRowMajor< real64 > const &	U,
		Vec< real64 > const &	S,
		MatRowMajor< real64 > const &	VT
	)

static

Computes the singular value decomposition of A.

If size(A) = (M,N), this function expects: size(U) = (M,min(M,N)), size(VT) = (min(M,N),N), and size(S) = min(M,N) On exit, S contains the singular values of A and U contains an orthonormal basis of range(A)

Parameters

[in]	A	GEOSX array2d.
[out]	U	GEOSX array2d.
[out]	S	GEOSX array1d.
[out]	VT	GEOSX array2d.

◆ matrixSVD() [2/2]

static void geosx::BlasLapackLA::matrixSVD	(	MatColMajor< real64 const > const &	A,
		MatColMajor< real64 > const &	U,
		Vec< real64 > const &	S,
		MatColMajor< real64 > const &	VT
	)

static

Computes the singular value decomposition of A.

If size(A) = (M,N), this function expects: size(U) = (M,min(M,N)), size(VT) = (min(M,N),N), and size(S) = min(M,N) On exit, S contains the singular values of A and U contains an orthonormal basis of range(A)

Parameters

[in]	A	GEOSX array2d.
[out]	U	GEOSX array2d.
[out]	S	GEOSX array1d.
[out]	VT	GEOSX array2d.

◆ matrixTMatrixMultiply()

static void geosx::BlasLapackLA::matrixTMatrixMultiply	(	MatRowMajor< real64 const > const &	A,
		MatRowMajor< real64 const > const &	B,
		MatRowMajor< real64 > const &	C,
		real64 const	alpha = `1.0`,
		real64 const	beta = `0.0`
	)

static

transpose(Matrix)-Matrix product; C = alpha*transpose(A)*B + beta*C.

Computes transpose(matrix)-matrix product with optional scaling and accumulation.

Parameters

[in]	A	GEOSX array2d.
[in]	B	GEOSX array2d.
[in,out]	C	GEOSX array2d.
[in]	alpha	Optional scalar to multiply with `transpose(A)*B.`
[in]	beta	Optional parameter to control the accumulation.

Warning: Assumes that transpose(A) and B have compatible sizes and that C already has the right size.

◆ matrixTMatrixTMultiply()

static void geosx::BlasLapackLA::matrixTMatrixTMultiply	(	MatRowMajor< real64 const > const &	A,
		MatRowMajor< real64 const > const &	B,
		MatRowMajor< real64 > const &	C,
		real64 const	alpha = `1.0`,
		real64 const	beta = `0.0`
	)

static

transpose(Matrix)-transpose(Matrix) product; C = alpha*transpose(A)*transpose(B) + beta*C.

Computes transpose(matrix)-transpose(matrix) product with optional scaling and accumulation.

Parameters

[in]	A	GEOSX array2d.
[in]	B	GEOSX array2d.
[in,out]	C	GEOSX array1d.
[in]	alpha	Optional scalar to multiply with `tranpose(A)*transpose`(B).
[in]	beta	Optional parameter to control the accumulation.

Warning: Assumes that tranpose(A) and transpose(B) have compatible sizes and that C already has the right size.

◆ matrixTVectorMultiply()

static void geosx::BlasLapackLA::matrixTVectorMultiply	(	MatRowMajor< real64 const > const &	A,
		Vec< real64 const > const &	X,
		Vec< real64 > const &	Y,
		real64 const	alpha = `1.0`,
		real64 const	beta = `0.0`
	)

static

transpose(Matrix)-Vector product; Y = alpha*transpose(A)*X + beta*Y.

Computes transpose(matrix)-vector product with optional scaling and accumulation.

Parameters

[in]	A	GEOSX array2d.
[in]	X	GEOSX array1d.
[in,out]	Y	GEOSX array1d.
[in]	alpha	Optional scalar to multiply with `transpose(A)*X.`
[in]	beta	Optional parameter to control the accumulation.

Warning: Assumes that X and Y have compatible sizes with transpose(A).

◆ matrixVectorMultiply()

static void geosx::BlasLapackLA::matrixVectorMultiply	(	MatRowMajor< real64 const > const &	A,
		Vec< real64 const > const &	X,
		Vec< real64 > const &	Y,
		real64 const	alpha = `1.0`,
		real64 const	beta = `0.0`
	)

static

Matrix-Vector product; Y = alpha*A*X + beta*Y.

Computes matrix-vector product with optional scaling and accumulation.

Parameters

[in]	A	GEOSX array2d.
[in]	X	GEOSX array1d.
[in,out]	Y	GEOSX array1d.
[in]	alpha	Optional scalar to multiply with `A*X.`
[in]	beta	Optional parameter to control the accumulation.

Warning: Assumes that X and Y have compatible sizes with A.

◆ setRandomNumberGeneratorSeed()

static void geosx::BlasLapackLA::setRandomNumberGeneratorSeed ( arraySlice1d< int const > const & seed )

static

Set the random number generator seed.

Parameters

[in] seed GEOSX array1d, dimension (4). The elements must be between 0 and 4095, and seed(4) must be odd.

◆ vectorCopy()

static void geosx::BlasLapackLA::vectorCopy	(	Vec< real64 const > const &	X,
		Vec< real64 > const &	Y
	)

static

Vector copy; Y = X.

Parameters

[in]	X	GEOSX array1d.
[out]	Y	GEOSX array1d.

Warning: Assumes that X and Y have the same size.

◆ vectorDot()

static real64 geosx::BlasLapackLA::vectorDot	(	Vec< real64 const > const &	X,
		Vec< real64 const > const &	Y
	)

static

Returns the dot product of two vectors.

Parameters

[in]	X	GEOSX array1d.
[in]	Y	GEOSX array1d.

Returns: the dot product of the two vectors.

◆ vectorNorm1()

static real64 geosx::BlasLapackLA::vectorNorm1 ( Vec< real64 const > const & X )

static

Returns the 1-norm of the vector.

Parameters

[in] X GEOSX array1d.

Returns: the vector 1-norm.

◆ vectorNorm2()

static real64 geosx::BlasLapackLA::vectorNorm2 ( Vec< real64 const > const & X )

static

Returns the two norm of the vector.

Parameters

[in] X GEOSX array1d.

Returns: the vector 2-norm.

◆ vectorNormInf()

static real64 geosx::BlasLapackLA::vectorNormInf ( Vec< real64 const > const & X )

static

Returns the infinity-norm of the vector.

Parameters

[in] X GEOSX array1d.

Returns: the vector inf-norm.

◆ vectorRand()

static void geosx::BlasLapackLA::vectorRand	(	Vec< real64 > const &	X,
		RandomNumberDistribution const &	idist = `RandomNumberDistribution::UNIFORM_01`
	)

static

Sets vector entries to random real numbers.

Sets vector entries to random real numbers from a uniform or normal distribution without specifying the seed of the random number generator.

Parameters

[out]	X	GEOSX array1d.
[in]	idist	Optional RandomNumberDistribution enum value specifying the distribution of the random numbers.

◆ vectorScale()

static void geosx::BlasLapackLA::vectorScale	(	real64 const	alpha,
		Vec< real64 > const &	X
	)

static

In-place scalar-vector product; X = alpha*X.

Parameters

[in]	alpha	Scalar to multiply with `X`.
[in,out]	X	GEOSX array1d.

◆ vectorVectorAdd()

static void geosx::BlasLapackLA::vectorVectorAdd	(	Vec< real64 const > const &	X,
		Vec< real64 > const &	Y,
		real64 const	alpha = `1.`
	)

static

Vector-Vector sum; Y = alpha*X + Y.

Computes (alpha*X + Y) and overwrites the result on Y, with optional scaling.

Parameters

[in]	X	GEOSX array1d.
[in,out]	Y	GEOSX array1d.
[in]	alpha	Optional scalar to multiply with `X`.

Warning: Assumes that X and Y have the same size.

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

coreComponents/linearAlgebra/interfaces/dense/BlasLapackLA.hpp

Public Types

Static Public Member Functions

Detailed Description

Member Enumeration Documentation

◆ RandomNumberDistribution

Member Function Documentation

◆ determinant() [1/2]

◆ determinant() [2/2]

◆ getRandomNumberGeneratorSeed()

◆ matrixCopy() [1/2]

◆ matrixCopy() [2/2]

◆ matrixEigenvalues() [1/2]

◆ matrixEigenvalues() [2/2]

◆ matrixInverse() [1/4]

◆ matrixInverse() [2/4]

◆ matrixInverse() [3/4]

◆ matrixInverse() [4/4]

◆ matrixMatrixAdd() [1/2]

◆ matrixMatrixAdd() [2/2]

◆ matrixMatrixMultiply()

◆ matrixMatrixTMultiply()

◆ matrixNorm1() [1/2]

◆ matrixNorm1() [2/2]

◆ matrixNormFrobenius() [1/2]

◆ matrixNormFrobenius() [2/2]

◆ matrixNormInf() [1/2]

◆ matrixNormInf() [2/2]

◆ matrixRand() [1/2]

◆ matrixRand() [2/2]

◆ matrixScale() [1/2]

◆ matrixScale() [2/2]

◆ matrixSVD() [1/2]

◆ matrixSVD() [2/2]

◆ matrixTMatrixMultiply()

◆ matrixTMatrixTMultiply()

◆ matrixTVectorMultiply()

◆ matrixVectorMultiply()

◆ setRandomNumberGeneratorSeed()

◆ vectorCopy()

◆ vectorDot()

◆ vectorNorm1()

◆ vectorNorm2()

◆ vectorNormInf()

◆ vectorRand()

◆ vectorScale()

◆ vectorVectorAdd()