Add/Update Operations

Operations for summing or updating existing containers. More...

Functions
template<typename T_Scalar>
dns::XxVector< T_Scalar >	cla3p::ops::add (T_Scalar alpha, const dns::XxVector< T_Scalar > &x, T_Scalar beta, const dns::XxVector< T_Scalar > &y)
	Adds two compatible scaled dense vectors.
template<typename T_Scalar>
dns::XxMatrix< T_Scalar >	cla3p::ops::add (T_Scalar alpha, const dns::XxMatrix< T_Scalar > &A, T_Scalar beta, const dns::XxMatrix< T_Scalar > &B)
	Adds two compatible scaled dense matrices.
template<typename T_Int, typename T_Scalar>
csr::XxMatrix< T_Int, T_Scalar >	cla3p::ops::add (T_Scalar alpha, const csr::XxMatrix< T_Int, T_Scalar > &A, T_Scalar beta, const csr::XxMatrix< T_Int, T_Scalar > &B)
	Adds two compatible sparse matrices.
template<typename T_Int, typename T_Scalar>
csc::XxMatrix< T_Int, T_Scalar >	cla3p::ops::add (T_Scalar alpha, const csc::XxMatrix< T_Int, T_Scalar > &A, T_Scalar beta, const csc::XxMatrix< T_Int, T_Scalar > &B)
	Adds two compatible sparse matrices.
template<typename T_Matrix>
lra::XxMatrix< T_Matrix >	cla3p::ops::add (typename T_Matrix::value_type alpha, const lra::XxMatrix< T_Matrix > &A, typename T_Matrix::value_type beta, const lra::XxMatrix< T_Matrix > &B, const lra::RankModerator< T_Matrix > &rmod)
	Adds two compatible low-rank matrices.
template<typename T_Scalar>
void	cla3p::ops::update (T_Scalar alpha, const dns::XxVector< T_Scalar > &x, dns::XxVector< T_Scalar > &y)
	Update a dense vector with a compatible scaled dense vector.
template<typename T_Scalar>
void	cla3p::ops::update (T_Scalar alpha, const dns::XxMatrix< T_Scalar > &A, dns::XxMatrix< T_Scalar > &B)
	Update a dense matrix with a compatible scaled dense matrix.
template<typename T_Int, typename T_Scalar>
void	cla3p::ops::update (T_Scalar alpha, const csr::XxMatrix< T_Int, T_Scalar > &A, csr::XxMatrix< T_Int, T_Scalar > &B)
	Update a sparse matrix with a compatible scaled sparse matrix.
template<typename T_Int, typename T_Scalar>
void	cla3p::ops::update (T_Scalar alpha, const csc::XxMatrix< T_Int, T_Scalar > &A, csc::XxMatrix< T_Int, T_Scalar > &B)
	Update a sparse matrix with a compatible scaled sparse matrix.

Detailed Description

Operations for summing or updating existing containers.

Function Documentation

add() [1/5]

template<typename T_Scalar>

dns::XxVector< T_Scalar > cla3p::ops::add	(	T_Scalar	alpha,
		const dns::XxVector< T_Scalar > &	x,
		T_Scalar	beta,
		const dns::XxVector< T_Scalar > &	y )

Adds two compatible scaled dense vectors.

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

Template Parameters

T_Scalar

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

Parameters

[in]	alpha	The scaling coefficient for x.
[in]	x	The first input dense vector.
[in]	beta	The scaling coefficient for y.
[in]	y	The second input dense vector.

Returns

The result of the operation \( \alpha \cdot x + \beta \cdot y \).

Examples

ex01j_dense_vector_algebra_add.cpp, ex02l_dense_matrix_algebra_add.cpp, and ex06l_sparse_matrix_algebra_add.cpp.

add() [2/5]

template<typename T_Scalar>

dns::XxMatrix< T_Scalar > cla3p::ops::add	(	T_Scalar	alpha,
		const dns::XxMatrix< T_Scalar > &	A,
		T_Scalar	beta,
		const dns::XxMatrix< T_Scalar > &	B )

Adds two compatible scaled dense matrices.

Performs the operation \( \alpha \cdot A + \beta \cdot B \).

Template Parameters

T_Scalar

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

Parameters

[in]	alpha	The scaling coefficient for A.
[in]	A	The first input dense matrix.
[in]	beta	The scaling coefficient for B.
[in]	B	The second input dense matrix.

Returns

The result of the operation \( \alpha \cdot A + \beta \cdot B \).

add() [3/5]

template<typename T_Int, typename T_Scalar>

csr::XxMatrix< T_Int, T_Scalar > cla3p::ops::add	(	T_Scalar	alpha,
		const csr::XxMatrix< T_Int, T_Scalar > &	A,
		T_Scalar	beta,
		const csr::XxMatrix< T_Int, T_Scalar > &	B )

Adds two compatible sparse matrices.

Performs the operation \( \alpha \cdot A + \beta \cdot B \).

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 for A.
[in]	A	The first input sparse matrix.
[in]	beta	The scaling coefficient for B.
[in]	B	The second input sparse matrix.

Returns

The result of the operation \( \alpha \cdot A + \beta \cdot B \).

add() [4/5]

template<typename T_Int, typename T_Scalar>

csc::XxMatrix< T_Int, T_Scalar > cla3p::ops::add	(	T_Scalar	alpha,
		const csc::XxMatrix< T_Int, T_Scalar > &	A,
		T_Scalar	beta,
		const csc::XxMatrix< T_Int, T_Scalar > &	B )

Adds two compatible sparse matrices.

Performs the operation \( \alpha \cdot A + \beta \cdot B \).

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 for A.
[in]	A	The first input sparse matrix.
[in]	beta	The scaling coefficient for B.
[in]	B	The second input sparse matrix.

Returns

The result of the operation \( \alpha \cdot A + \beta \cdot B \).

add() [5/5]

template<typename T_Matrix>

lra::XxMatrix< T_Matrix > cla3p::ops::add	(	typename T_Matrix::value_type	alpha,
		const lra::XxMatrix< T_Matrix > &	A,
		typename T_Matrix::value_type	beta,
		const lra::XxMatrix< T_Matrix > &	B,
		const lra::RankModerator< T_Matrix > &	rmod )

Adds two compatible low-rank matrices.

Performs the operation \( \alpha \cdot A + \beta \cdot B \) with rank moderation.

Template Parameters

T_Matrix

The underlying matrix type.

Parameters

[in]	alpha	The scaling coefficient for A.
[in]	A	The first input low-rank matrix.
[in]	beta	The scaling coefficient for B.
[in]	B	The second input low-rank matrix.
[in]	rmod	The rank moderator that controls the rank cutoff.

Returns

The result of the operation \( \alpha \cdot A + \beta \cdot B \).

update() [1/4]

template<typename T_Scalar>

void cla3p::ops::update	(	T_Scalar	alpha,
		const dns::XxVector< T_Scalar > &	x,
		dns::XxVector< T_Scalar > &	y )

Update a dense vector with a compatible scaled dense vector.

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

Template Parameters

T_Scalar

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

Parameters

[in]	alpha	The scaling coefficient.
[in]	x	The input dense vector.
[in,out]	y	The dense vector to be updated.

Examples

ex01j_dense_vector_algebra_add.cpp, ex02l_dense_matrix_algebra_add.cpp, and ex06l_sparse_matrix_algebra_add.cpp.

update() [2/4]

template<typename T_Scalar>

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

Update a dense matrix with a compatible scaled dense matrix.

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

Template Parameters

T_Scalar

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

Parameters

[in]	alpha	The scaling coefficient.
[in]	A	The input dense matrix.
[in,out]	B	The dense matrix to be updated.

update() [3/4]

template<typename T_Int, typename T_Scalar>

void cla3p::ops::update	(	T_Scalar	alpha,
		const csr::XxMatrix< T_Int, T_Scalar > &	A,
		csr::XxMatrix< T_Int, T_Scalar > &	B )

Update a sparse matrix with a compatible scaled sparse matrix.

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

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]	A	The input sparse matrix.
[in,out]	B	The sparse matrix to be updated.

update() [4/4]

template<typename T_Int, typename T_Scalar>

void cla3p::ops::update	(	T_Scalar	alpha,
		const csc::XxMatrix< T_Int, T_Scalar > &	A,
		csc::XxMatrix< T_Int, T_Scalar > &	B )

Update a sparse matrix with a compatible scaled sparse matrix.

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

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]	A	The input sparse matrix.
[in,out]	B	The sparse matrix to be updated.