SMatrixAlgebraModule

A module for performing linear algebra using sparse matrices.

Uses

Interfaces

ScaleMatrix IncrementMatrix DotMatrix PairwiseMultiplyMatrix MatrixMultiply MatrixColumnNorm MatrixNorm MatrixGrandSum

Interfaces

public interface ScaleMatrix

private subroutine ScaleMatrix_lsr(matA, constant)

Will scale a sparse matrix by a constant.

Arguments

Type	Intent	Optional	Attributes		Name
type(Matrix_lsr),	intent(inout)			::	matA	Matrix A.
real(kind=NTREAL),	intent(in)			::	constant	Constant scale factor.

private subroutine ScaleMatrix_lsc(matA, constant)

Will scale a sparse matrix by a constant.

Arguments

Type	Intent	Optional	Attributes		Name
type(Matrix_lsc),	intent(inout)			::	matA	Matrix A.
real(kind=NTREAL),	intent(in)			::	constant	Constant scale factor.

private subroutine ScaleMatrix_lsc_c(matA, constant)

Will scale a sparse matrix by a constant. Will scale a sparse matrix by a constant.

Arguments

Type	Intent	Optional	Attributes		Name
type(Matrix_lsc),	intent(inout)			::	matA	Matrix A.
complex(kind=NTCOMPLEX),	intent(in)			::	constant	Constant scale factor.

public interface IncrementMatrix

private subroutine IncrementMatrix_lsr(matA, matB, alpha_in, threshold_in)

Matrix B = alpha*Matrix A + Matrix B (AXPY). This will utilize the sparse vector addition routine.

Arguments

Type	Intent	Optional		Name
type(Matrix_lsr),	intent(in)		::	matA	Matrix A.
type(Matrix_lsr),	intent(inout)		::	matB	Matrix B.
real(kind=NTREAL),	intent(in),	optional	::	alpha_in	Multiplier (default=1.0).
real(kind=NTREAL),	intent(in),	optional	::	threshold_in	For flushing values to zero (default=0).

private subroutine IncrementMatrix_lsc(matA, matB, alpha_in, threshold_in)

Matrix B = alpha*Matrix A + Matrix B (AXPY). This will utilize the sparse vector addition routine.

Arguments

Type	Intent	Optional		Name
type(Matrix_lsc),	intent(in)		::	matA	Matrix A.
type(Matrix_lsc),	intent(inout)		::	matB	Matrix B.
real(kind=NTREAL),	intent(in),	optional	::	alpha_in	Multiplier (default=1.0).
real(kind=NTREAL),	intent(in),	optional	::	threshold_in	For flushing values to zero (default=0).

public interface DotMatrix

private subroutine DotMatrix_lsr(matA, matB, product)

Product = sum(MatA[ij]*MatB[ij])

Arguments

Type	Intent		Name
type(Matrix_lsr),	intent(in)	::	matA	Matrix A.
type(Matrix_lsr),	intent(in)	::	matB	Matrix B.
real(kind=NTREAL),	intent(out)	::	product	Dot product.

private subroutine DotMatrix_lsc(matA, matB, product)

Arguments

Type	Intent		Name
type(Matrix_lsc),	intent(in)	::	matA	Matrix A.
type(Matrix_lsc),	intent(in)	::	matB	Matrix B.
complex(kind=NTCOMPLEX),	intent(out)	::	product	Dot product.

public interface PairwiseMultiplyMatrix

private subroutine PairwiseMultiplyMatrix_lsr(matA, matB, matC)

Pairwise Multiply two matrices. This will utilize the sparse vector pairwise multiply routine.

Arguments

Type	Intent		Name
type(Matrix_lsr),	intent(in)	::	matA	Matrix A.
type(Matrix_lsr),	intent(in)	::	matB	Matrix B.
type(Matrix_lsr),	intent(inout)	::	matC	matC = MatA mult MatB.

private subroutine PairwiseMultiplyMatrix_lsc(matA, matB, matC)

Pairwise Multiply two matrices. This will utilize the sparse vector pairwise routine.

Arguments

Type	Intent		Name
type(Matrix_lsc),	intent(in)	::	matA	Matrix A.
type(Matrix_lsc),	intent(in)	::	matB	Matrix B.
type(Matrix_lsc),	intent(inout)	::	matC	matC = MatA mult MatB.

public interface MatrixMultiply

private subroutine GemmMatrix_lsr(matA, matB, matC, IsATransposed_in, IsBTransposed_in, alpha_in, beta_in, threshold_in, blocked_memory_pool_in)

Multiply two matrices together, and add to the third. C := alphamatAop( matB ) + beta*matC

Arguments

Type	Intent	Optional	Attributes		Name
type(Matrix_lsr),	intent(in)			::	matA	Matrix A.
type(Matrix_lsr),	intent(in)			::	matB	Matrix B.
type(Matrix_lsr),	intent(inout)			::	matC	matC = alphamatAop( matB ) + beta*matC.
logical,	intent(in),	optional		::	IsATransposed_in	True if A is already transposed.
logical,	intent(in),	optional		::	IsBTransposed_in	True if B is already transposed.
real(kind=NTREAL),	intent(in),	optional		::	alpha_in	Scales the multiplication.
real(kind=NTREAL),	intent(in),	optional		::	beta_in	Scales matrix we sum on to.
real(kind=NTREAL),	intent(in),	optional		::	threshold_in	For flushing values to zero. Default value is 0.0.
type(MatrixMemoryPool_lr),	intent(inout),	optional	TARGET	::	blocked_memory_pool_in	An optional memory pool for doing the calculation.

private subroutine GemmMatrix_lsc(matA, matB, matC, IsATransposed_in, IsBTransposed_in, alpha_in, beta_in, threshold_in, blocked_memory_pool_in)

Multiply two matrices together, and add to the third. C := alphamatAop( matB ) + beta*matC

Arguments

Type	Intent	Optional	Attributes		Name
type(Matrix_lsc),	intent(in)			::	matA	Matrix A.
type(Matrix_lsc),	intent(in)			::	matB	Matrix B.
type(Matrix_lsc),	intent(inout)			::	matC	matC = alphamatAop( matB ) + beta*matC.
logical,	intent(in),	optional		::	IsATransposed_in	True if A is already transposed.
logical,	intent(in),	optional		::	IsBTransposed_in	True if B is already transposed.
real(kind=NTREAL),	intent(in),	optional		::	alpha_in	Scales the multiplication.
real(kind=NTREAL),	intent(in),	optional		::	beta_in	Scales matrix we sum on to.
real(kind=NTREAL),	intent(in),	optional		::	threshold_in	For flushing values to zero. Default value is 0.0.
type(MatrixMemoryPool_lc),	intent(inout),	optional	TARGET	::	blocked_memory_pool_in	An optional memory pool for doing the calculation.

public interface MatrixColumnNorm

private subroutine MatrixColumnNorm_lsr(this, norm_per_column)

Compute the norm of a sparse matrix along the columns.

Arguments

Type	Intent	Optional	Attributes		Name
type(Matrix_lsr),	intent(in)			::	this	The matrix to compute the norm of.
real(kind=NTREAL),	intent(out),		DIMENSION(this%columns)	::	norm_per_column	The norm value for each column in this matrix.

private subroutine MatrixColumnNorm_lsc(this, norm_per_column)

Compute the norm of a sparse matrix along the columns.

Arguments

Type	Intent	Optional	Attributes		Name
type(Matrix_lsc),	intent(in)			::	this	The matrix to compute the norm of.
real(kind=NTREAL),	intent(out),		DIMENSION(this%columns)	::	norm_per_column	The norm value for each column in this matrix.

public interface MatrixNorm

private pure function MatrixNorm_lsr(this) result(norm)

Compute the 1 norm of a sparse matrix.

Arguments

Type Intent Optional Attributes Name

type(Matrix_lsr), intent(in) :: this
The matrix to compute the norm of.

Return Value real(kind=NTREAL)

The norm of the matrix.
private pure function MatrixNorm_lsc(this) result(norm)

Compute the 1 norm of a sparse matrix.

Arguments

Type Intent Optional Attributes Name

type(Matrix_lsc), intent(in) :: this
The matrix to compute the norm of.

Return Value real(kind=NTREAL)

The norm of the matrix.

public interface MatrixGrandSum

private subroutine MatrixGrandSum_lsr(this, sum_value)

Sum the elements of a matrix

Arguments

Type	Intent	Optional	Attributes		Name
type(Matrix_lsr),	intent(in)			::	this	The matrix to sum
real(kind=NTREAL),	intent(out)			::	sum_value	The sum of the matrix elements

private subroutine MatrixGrandSum_lsc(this, sum_value)

Sum the elements of a matrix

Arguments

Type	Intent	Optional	Attributes		Name
type(Matrix_lsc),	intent(in)			::	this	The matrix to sum
complex(kind=NTCOMPLEX),	intent(out)			::	sum_value	The sum of the matrix elements

SMatrixAlgebraModule Module

Contents

Interfaces

Uses

Contents

Interfaces

Interfaces

public interface ScaleMatrix

private subroutine ScaleMatrix_lsr(matA, constant)

Arguments

private subroutine ScaleMatrix_lsc(matA, constant)

Arguments

private subroutine ScaleMatrix_lsc_c(matA, constant)

Arguments

public interface IncrementMatrix

private subroutine IncrementMatrix_lsr(matA, matB, alpha_in, threshold_in)

Arguments

private subroutine IncrementMatrix_lsc(matA, matB, alpha_in, threshold_in)

Arguments

public interface DotMatrix

private subroutine DotMatrix_lsr(matA, matB, product)

Arguments

private subroutine DotMatrix_lsc(matA, matB, product)

Arguments

public interface PairwiseMultiplyMatrix

private subroutine PairwiseMultiplyMatrix_lsr(matA, matB, matC)

Arguments

private subroutine PairwiseMultiplyMatrix_lsc(matA, matB, matC)

Arguments

public interface MatrixMultiply

private subroutine GemmMatrix_lsr(matA, matB, matC, IsATransposed_in, IsBTransposed_in, alpha_in, beta_in, threshold_in, blocked_memory_pool_in)

Arguments

private subroutine GemmMatrix_lsc(matA, matB, matC, IsATransposed_in, IsBTransposed_in, alpha_in, beta_in, threshold_in, blocked_memory_pool_in)

Arguments

public interface MatrixColumnNorm

private subroutine MatrixColumnNorm_lsr(this, norm_per_column)

Arguments

private subroutine MatrixColumnNorm_lsc(this, norm_per_column)

Arguments

public interface MatrixNorm

private pure function MatrixNorm_lsr(this) result(norm)

Arguments

Return Value real(kind=NTREAL)

private pure function MatrixNorm_lsc(this) result(norm)

Arguments

Return Value real(kind=NTREAL)

public interface MatrixGrandSum

private subroutine MatrixGrandSum_lsr(this, sum_value)

Arguments

private subroutine MatrixGrandSum_lsc(this, sum_value)

Arguments