Matrix-Matrix Operations

High-performance matrix multiplications (GEMM). More...

Functions
template<typename T_Scalar>
void	cla3p::ops::mult (T_Scalar alpha, op_t opA, const dns::XxMatrix< T_Scalar > &A, op_t opB, const dns::XxMatrix< T_Scalar > &B, T_Scalar beta, dns::XxMatrix< T_Scalar > &C)
	Updates a general matrix with a matrix-matrix product.
template<typename T_Scalar>
void	cla3p::ops::trimult (T_Scalar alpha, op_t opA, const dns::XxMatrix< T_Scalar > &A, dns::XxMatrix< T_Scalar > &B)
	Replaces a matrix with a scaled triangular matrix-matrix product.
template<typename T_Scalar>
void	cla3p::ops::trimult (T_Scalar alpha, dns::XxMatrix< T_Scalar > &B, op_t opA, const dns::XxMatrix< T_Scalar > &A)
	Replaces a matrix with a scaled triangular matrix-matrix product.
template<typename T_Scalar>
void	cla3p::ops::trisol (T_Scalar alpha, op_t opA, const dns::XxMatrix< T_Scalar > &A, dns::XxMatrix< T_Scalar > &B)
	Replaces a matrix with the scaled solution of a triangular system.
template<typename T_Scalar>
void	cla3p::ops::trisol (T_Scalar alpha, dns::XxMatrix< T_Scalar > &B, op_t opA, const dns::XxMatrix< T_Scalar > &A)
	Replaces a matrix with the scaled solution of a triangular system.
template<typename T_Int, typename T_Scalar>
void	cla3p::ops::mult (T_Scalar alpha, op_t opA, const csr::XxMatrix< T_Int, T_Scalar > &A, const dns::XxMatrix< T_Scalar > &B, T_Scalar beta, dns::XxMatrix< T_Scalar > &C)
	Updates a general dense matrix with a sparse-dense matrix-matrix product.
template<typename T_Int, typename T_Scalar>
void	cla3p::ops::mult (T_Scalar alpha, op_t opA, const csc::XxMatrix< T_Int, T_Scalar > &A, const dns::XxMatrix< T_Scalar > &B, T_Scalar beta, dns::XxMatrix< T_Scalar > &C)
	Updates a general dense matrix with a sparse-dense matrix-matrix product.
template<typename T_Int, typename T_Scalar>
void	cla3p::ops::mult (T_Scalar alpha, op_t opA, const csr::XxMatrix< T_Int, T_Scalar > &A, op_t opB, const csr::XxMatrix< T_Int, T_Scalar > &B, T_Scalar beta, dns::XxMatrix< T_Scalar > &C)
	Updates a dense matrix with a sparse-sparse matrix-matrix product.
template<typename T_Int, typename T_Scalar>
void	cla3p::ops::mult (T_Scalar alpha, op_t opA, const csc::XxMatrix< T_Int, T_Scalar > &A, op_t opB, const csc::XxMatrix< T_Int, T_Scalar > &B, T_Scalar beta, dns::XxMatrix< T_Scalar > &C)
	Updates a dense matrix with a sparse-sparse matrix-matrix product.
template<typename T_Int, typename T_Scalar>
csr::XxMatrix< T_Int, T_Scalar >	cla3p::ops::mult (T_Scalar alpha, op_t opA, const csr::XxMatrix< T_Int, T_Scalar > &A, op_t opB, const csr::XxMatrix< T_Int, T_Scalar > &B)
	Creates a general sparse matrix from a sparse-sparse matrix-matrix product.
template<typename T_Int, typename T_Scalar>
csc::XxMatrix< T_Int, T_Scalar >	cla3p::ops::mult (T_Scalar alpha, op_t opA, const csc::XxMatrix< T_Int, T_Scalar > &A, op_t opB, const csc::XxMatrix< T_Int, T_Scalar > &B)
	Creates a general sparse matrix from a sparse-sparse matrix-matrix product.

Detailed Description

High-performance matrix multiplications (GEMM).

Function Documentation

mult() [1/7]

template<typename T_Scalar>

void cla3p::ops::mult	(	T_Scalar	alpha,
		op_t	opA,
		const dns::XxMatrix< T_Scalar > &	A,
		op_t	opB,
		const dns::XxMatrix< T_Scalar > &	B,
		T_Scalar	beta,
		dns::XxMatrix< T_Scalar > &	C )

Updates a general matrix with a matrix-matrix product.

Performs the operation \( C = \beta \cdot C + \alpha \cdot op_A(A) \cdot op_B(B) \). C can be General/Symmetric/Hermitian. If C is Symmetric/Hermitian, it is assumed that the outcome of the operation \( op_A(A) \cdot op_B(B) \) is also Symmetric/Hermitian and only the corresponding part (upper/lower) will be calculated. Valid combinations are the following:

A	B	opA	opB	C
General	General	unconstrained	unconstrained	General/Symmetric/Hermitian
Symmetric	General	ignored	must be set to N	General
Hermitian	General	ignored	must be set to N	General
Triangular	General	unconstrained	must be set to N	General
General	Symmetric	must be set to N	ignored	General
General	Hermitian	must be set to N	ignored	General
General	Triangular	must be set to N	unconstrained	General

Template Parameters

T_Scalar

The scalar type (e.g., float, double, complex).

Parameters

[in]	alpha	The scaling coefficient.
[in]	opA	The operation to be performed for matrix A.
[in]	A	The input matrix.
[in]	opB	The operation to be performed for matrix B.
[in]	B	The input matrix.
[in]	beta	The scaling coefficient for C.
[in,out]	C	The matrix to be updated.

Examples

ex02m_dense_matrix_algebra_vmult.cpp, ex02n_dense_matrix_algebra_mmult.cpp, ex02o_dense_matrix_algebra_mtmult.cpp, ex06m_sparse_matrix_algebra_vmult.cpp, and ex06n_sparse_matrix_algebra_mmult.cpp.

trimult() [1/2]

template<typename T_Scalar>

void cla3p::ops::trimult	(	T_Scalar	alpha,
		op_t	opA,
		const dns::XxMatrix< T_Scalar > &	A,
		dns::XxMatrix< T_Scalar > &	B )

Replaces a matrix with a scaled triangular matrix-matrix product.

Performs the operation \( B = \alpha \cdot op_A(A) \cdot B \).

Template Parameters

T_Scalar

The scalar type (e.g., float, double, complex).

Parameters

[in]	alpha	The scaling coefficient.
[in]	opA	The operation to be performed for matrix A.
[in]	A	The input triangular matrix.
[in,out]	B	The matrix to be replaced.

trimult() [2/2]

template<typename T_Scalar>

void cla3p::ops::trimult	(	T_Scalar	alpha,
		dns::XxMatrix< T_Scalar > &	B,
		op_t	opA,
		const dns::XxMatrix< T_Scalar > &	A )

Replaces a matrix with a scaled triangular matrix-matrix product.

Performs the operation \( B = \alpha \cdot B \cdot op_A(A) \).

Template Parameters

T_Scalar

The scalar type (e.g., float, double, complex).

Parameters

[in]	alpha	The scaling coefficient.
[in,out]	B	The matrix to be replaced.
[in]	opA	The operation to be performed for matrix A.
[in]	A	The input triangular matrix.

trisol() [1/2]

template<typename T_Scalar>

void cla3p::ops::trisol	(	T_Scalar	alpha,
		op_t	opA,
		const dns::XxMatrix< T_Scalar > &	A,
		dns::XxMatrix< T_Scalar > &	B )

Replaces a matrix with the scaled solution of a triangular system.

Solves the system \( op_A(A) \cdot X = \alpha \cdot B \).

Template Parameters

T_Scalar

The scalar type (e.g., float, double, complex).

Parameters

[in]	alpha	The scaling coefficient.
[in]	opA	The operation to be performed for matrix A.
[in]	A	The input triangular matrix.
[in,out]	B	On entry, the rhs, on exit the system solution X.

trisol() [2/2]

template<typename T_Scalar>

void cla3p::ops::trisol	(	T_Scalar	alpha,
		dns::XxMatrix< T_Scalar > &	B,
		op_t	opA,
		const dns::XxMatrix< T_Scalar > &	A )

Replaces a matrix with the scaled solution of a triangular system.

Solves the system \( X \cdot op_A(A) = \alpha \cdot B \).

Template Parameters

T_Scalar

The scalar type (e.g., float, double, complex).

Parameters

[in]	alpha	The scaling coefficient.
[in,out]	B	On entry, the rhs, on exit the system solution X.
[in]	opA	The operation to be performed for matrix A.
[in]	A	The input triangular matrix.

mult() [2/7]

template<typename T_Int, typename T_Scalar>

void cla3p::ops::mult	(	T_Scalar	alpha,
		op_t	opA,
		const csr::XxMatrix< T_Int, T_Scalar > &	A,
		const dns::XxMatrix< T_Scalar > &	B,
		T_Scalar	beta,
		dns::XxMatrix< T_Scalar > &	C )

Updates a general dense matrix with a sparse-dense matrix-matrix product.

Performs the operation \( C = \beta \cdot C + \alpha \cdot op_A(A) \cdot B \). Valid combinations are the following:

A	B	opA	C
General	General	unconstrained	General
Symmetric	General	ignored	General
Hermitian	General	ignored	General

Template Parameters

T_Int	The integer type for indexing.
T_Scalar	The scalar type (e.g., float, double, complex).

Parameters

[in]	alpha	The scaling coefficient.
[in]	opA	The operation to be performed for matrix A.
[in]	A	The input sparse matrix.
[in]	B	The input dense matrix.
[in]	beta	The scaling coefficient for C.
[in,out]	C	The dense matrix to be updated.

mult() [3/7]

template<typename T_Int, typename T_Scalar>

void cla3p::ops::mult	(	T_Scalar	alpha,
		op_t	opA,
		const csc::XxMatrix< T_Int, T_Scalar > &	A,
		const dns::XxMatrix< T_Scalar > &	B,
		T_Scalar	beta,
		dns::XxMatrix< T_Scalar > &	C )

Updates a general dense matrix with a sparse-dense matrix-matrix product.

Performs the operation \( C = \beta \cdot C + \alpha \cdot op_A(A) \cdot B \). Valid combinations are the following:

A	B	opA	C
General	General	unconstrained	General
Symmetric	General	ignored	General
Hermitian	General	ignored	General

Template Parameters

T_Int	The integer type for indexing.
T_Scalar	The scalar type (e.g., float, double, complex).

Parameters

[in]	alpha	The scaling coefficient.
[in]	opA	The operation to be performed for matrix A.
[in]	A	The input sparse matrix.
[in]	B	The input dense matrix.
[in]	beta	The scaling coefficient for C.
[in,out]	C	The dense matrix to be updated.

mult() [4/7]

template<typename T_Int, typename T_Scalar>

void cla3p::ops::mult	(	T_Scalar	alpha,
		op_t	opA,
		const csr::XxMatrix< T_Int, T_Scalar > &	A,
		op_t	opB,
		const csr::XxMatrix< T_Int, T_Scalar > &	B,
		T_Scalar	beta,
		dns::XxMatrix< T_Scalar > &	C )

Updates a dense matrix with a sparse-sparse matrix-matrix product.

Performs the operation \( C = \beta \cdot C + \alpha \cdot op_A(A) \cdot op_B(B) \). Valid combinations are the following:

A	B	opA	opB
General	General	unconstrained	unconstrained

Template Parameters

T_Int	The integer type for indexing.
T_Scalar	The scalar type (e.g., float, double, complex).

Parameters

[in]	alpha	The scaling coefficient.
[in]	opA	The operation to be performed for matrix A.
[in]	A	The input sparse matrix.
[in]	opB	The operation to be performed for matrix B.
[in]	B	The input dense matrix.
[in]	beta	The scaling coefficient for C.
[in,out]	C	The dense matrix to be updated.

mult() [5/7]

template<typename T_Int, typename T_Scalar>

void cla3p::ops::mult	(	T_Scalar	alpha,
		op_t	opA,
		const csc::XxMatrix< T_Int, T_Scalar > &	A,
		op_t	opB,
		const csc::XxMatrix< T_Int, T_Scalar > &	B,
		T_Scalar	beta,
		dns::XxMatrix< T_Scalar > &	C )

Updates a dense matrix with a sparse-sparse matrix-matrix product.

Performs the operation \( C = \beta \cdot C + \alpha \cdot op_A(A) \cdot op_B(B) \). Valid combinations are the following:

A	B	opA	opB
General	General	unconstrained	unconstrained

Template Parameters

T_Int	The integer type for indexing.
T_Scalar	The scalar type (e.g., float, double, complex).

Parameters

[in]	alpha	The scaling coefficient.
[in]	opA	The operation to be performed for matrix A.
[in]	A	The input sparse matrix.
[in]	opB	The operation to be performed for matrix B.
[in]	B	The input dense matrix.
[in]	beta	The scaling coefficient for C.
[in,out]	C	The dense matrix to be updated.

mult() [6/7]

template<typename T_Int, typename T_Scalar>

csr::XxMatrix< T_Int, T_Scalar > cla3p::ops::mult	(	T_Scalar	alpha,
		op_t	opA,
		const csr::XxMatrix< T_Int, T_Scalar > &	A,
		op_t	opB,
		const csr::XxMatrix< T_Int, T_Scalar > &	B )

Creates a general sparse matrix from a sparse-sparse matrix-matrix product.

Performs the operation \( \alpha \cdot op_A(A) \cdot op_B(B) \). Valid combinations are the following:

A	B	opA	opB
General	General	N or T	N or T

Template Parameters

T_Int	The integer type for indexing.
T_Scalar	The scalar type (e.g., float, double, complex).

Parameters

[in]	alpha	The scaling coefficient.
[in]	opA	The operation to be performed for matrix A.
[in]	A	The input sparse matrix.
[in]	opB	The operation to be performed for matrix B.
[in]	B	The input sparse matrix.

Returns

The matrix \( \alpha \cdot op_A(A) \cdot op_B(B) \).

mult() [7/7]

template<typename T_Int, typename T_Scalar>

csc::XxMatrix< T_Int, T_Scalar > cla3p::ops::mult	(	T_Scalar	alpha,
		op_t	opA,
		const csc::XxMatrix< T_Int, T_Scalar > &	A,
		op_t	opB,
		const csc::XxMatrix< T_Int, T_Scalar > &	B )

Creates a general sparse matrix from a sparse-sparse matrix-matrix product.

Performs the operation \( \alpha \cdot op_A(A) \cdot op_B(B) \). Valid combinations are the following:

A	B	opA	opB
General	General	N or T	N or T

Template Parameters

T_Int	The integer type for indexing.
T_Scalar	The scalar type (e.g., float, double, complex).

Parameters

[in]	alpha	The scaling coefficient.
[in]	opA	The operation to be performed for matrix A.
[in]	A	The input sparse matrix.
[in]	opB	The operation to be performed for matrix B.
[in]	B	The input sparse matrix.

Returns

The matrix \( \alpha \cdot op_A(A) \cdot op_B(B) \).