Matrix-Vector Operations

Efficient products between matrices and vectors. More...

Functions
template<typename T_Scalar>
void	cla3p::ops::mult (T_Scalar alpha, op_t opA, const dns::XxMatrix< T_Scalar > &A, const dns::XxVector< T_Scalar > &x, T_Scalar beta, dns::XxVector< T_Scalar > &y)
	Updates a vector with a matrix-vector product.
template<typename T_Scalar>
void	cla3p::ops::trimult (op_t opA, const dns::XxMatrix< T_Scalar > &A, dns::XxVector< T_Scalar > &x)
	Replaces a vector with a triangular matrix-vector product.
template<typename T_Scalar>
void	cla3p::ops::trisol (op_t opA, const dns::XxMatrix< T_Scalar > &A, dns::XxVector< T_Scalar > &b)
	Replaces a vector with the 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::XxVector< T_Scalar > &x, T_Scalar beta, dns::XxVector< T_Scalar > &y)
	Updates a vector with a matrix-vector 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::XxVector< T_Scalar > &x, T_Scalar beta, dns::XxVector< T_Scalar > &y)
	Updates a vector with a matrix-vector product.

Detailed Description

Efficient products between matrices and vectors.

Function Documentation

mult() [1/3]

template<typename T_Scalar>

void cla3p::ops::mult	(	T_Scalar	alpha,
		op_t	opA,
		const dns::XxMatrix< T_Scalar > &	A,
		const dns::XxVector< T_Scalar > &	x,
		T_Scalar	beta,
		dns::XxVector< T_Scalar > &	y )

Updates a vector with a matrix-vector product.

Performs the operation \( y = \beta \cdot y + \alpha \cdot op_A(A) \cdot x \).

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. If A is symmetric or hermitian, opA is ignored.
[in]	A	The input matrix.
[in]	x	The input vector.
[in]	beta	The scaling coefficient for y.
[in,out]	y	The vector to be updated.

trimult()

template<typename T_Scalar>

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

Replaces a vector with a triangular matrix-vector product.

Performs the operation \( x = op_A(A) \cdot x \).

Template Parameters

T_Scalar

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

Parameters

[in]	opA	The operation to be performed for matrix A.
[in]	A	The input triangular matrix.
[in,out]	x	The vector to be replaced.

trisol()

template<typename T_Scalar>

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

Replaces a vector with the solution of a triangular system.

Solves the system \( op_A(A) \cdot x = b \).

Template Parameters

T_Scalar

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

Parameters

[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.

mult() [2/3]

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::XxVector< T_Scalar > &	x,
		T_Scalar	beta,
		dns::XxVector< T_Scalar > &	y )

Updates a vector with a matrix-vector product.

Performs the operation \( y = \beta \cdot y + \alpha \cdot op_A(A) \cdot x \).

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. If A is symmetric or hermitian, opA is ignored.
[in]	A	The input matrix.
[in]	x	The input vector.
[in]	beta	The scaling coefficient for y.
[in,out]	y	The vector to be updated.

mult() [3/3]

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::XxVector< T_Scalar > &	x,
		T_Scalar	beta,
		dns::XxVector< T_Scalar > &	y )

Updates a vector with a matrix-vector product.

Performs the operation \( y = \beta \cdot y + \alpha \cdot op_A(A) \cdot x \).

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. If A is symmetric or hermitian, opA is ignored.
[in]	A	The input matrix.
[in]	x	The input vector.
[in]	beta	The scaling coefficient for y.
[in,out]	y	The vector to be updated.