Inner/Outer product Operations

Dot products and rank-1 updates. More...

Functions
template<typename T_Scalar>
T_Scalar	cla3p::ops::dot (const dns::XxVector< T_Scalar > &x, const dns::XxVector< T_Scalar > &y)
	Calculate vector dot product.
template<typename T_Scalar>
T_Scalar	cla3p::ops::dotc (const dns::XxVector< T_Scalar > &x, const dns::XxVector< T_Scalar > &y)
	Calculate vector conjugate dot product.
template<typename T_Scalar>
void	cla3p::ops::outer (T_Scalar alpha, const dns::XxVector< T_Scalar > &x, const dns::XxVector< T_Scalar > &y, dns::XxMatrix< T_Scalar > &A)
	Update a matrix with a vector outer product.
template<typename T_Scalar>
void	cla3p::ops::outerc (T_Scalar alpha, const dns::XxVector< T_Scalar > &x, const dns::XxVector< T_Scalar > &y, dns::XxMatrix< T_Scalar > &A)
	Update a matrix with a conjugate vector outer product.

Detailed Description

Dot products and rank-1 updates.

Function Documentation

dot()

template<typename T_Scalar>

T_Scalar cla3p::ops::dot	(	const dns::XxVector< T_Scalar > &	x,
		const dns::XxVector< T_Scalar > &	y )

Calculate vector dot product.

Performs the operation \( x^T \cdot y \).

Template Parameters

T_Scalar

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

Parameters

[in]	x	The input vector.
[in]	y	The input vector.

Returns

The dot product value.

Examples

ex01k_dense_vector_algebra_dot.cpp.

dotc()

template<typename T_Scalar>

T_Scalar cla3p::ops::dotc	(	const dns::XxVector< T_Scalar > &	x,
		const dns::XxVector< T_Scalar > &	y )

Calculate vector conjugate dot product.

Performs the operation \( x^H \cdot y \).

Template Parameters

T_Scalar

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

Parameters

[in]	x	The input vector.
[in]	y	The input vector.

Returns

The conjugate dot product value.

outer()

template<typename T_Scalar>

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

Update a matrix with a vector outer product.

Performs the operation \( A = A + \alpha \cdot x y^T \). A can be General/Symmetric/Hermitian. If A is Symmetric/Hermitian, it is assumed that the outcome of the operation \( x y^T \) is also Symmetric/Hermitian and only the corresponding part (upper/lower) will be calculated.

Template Parameters

T_Scalar

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

Parameters

[in]	alpha	The update coefficient.
[in]	x	The input vector.
[in]	y	The input vector.
[in,out]	A	The matrix to be updated.

outerc()

template<typename T_Scalar>

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

Update a matrix with a conjugate vector outer product.

Performs the operation \( A = A + \alpha \cdot x y^H \). A can be General/Symmetric/Hermitian. If A is Symmetric/Hermitian, it is assumed that the outcome of the operation \( x y^H \) is also Symmetric/Hermitian and only the corresponding part (upper/lower) will be calculated.

Template Parameters

T_Scalar

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

Parameters

[in]	alpha	The update coefficient.
[in]	x	The input vector.
[in]	y	The input vector.
[in,out]	A	The matrix to be updated.