Householder

Implements the householder matrix, the householder vector and some operations with them like as premultiply a householder matrix with other matrix. More...

Defines
#define	_OPENMP_HOUSEHOLDER_DIMENSION   1e2
	Minimum value for using openmp in Householder.
Functions
void *	householder_vector (size_t n, double *const x, double *const v)
	Derive the householder vector.
void *	householder_matrix (size_t m, double **const A, double *const v, size_t idx)
	Derive the householder vector using a matrix.
void *	premult_matrix (size_t m, size_t n, double **const A, double **const QR, double *const v, double *const w, size_t idx)
	Compute where and are respectively m-by-n and n-by-n matrixs.
void	premult_vector (size_t n, double *const v, double *const b)
	Compute where and are respectively n-by-1 and n-by-n matrixs.
void	postmult (size_t m, size_t n, double **const A, double *const v, double *const w)
	Compute where and are respectively m-by-n and n-by-n matrixs.

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Detailed Description

Implements the householder matrix, the householder vector and some operations with them like as premultiply a householder matrix with other matrix.

The householder matrix with householder vector is

And the householder vector of a vector is .

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Define Documentation

#define _OPENMP_HOUSEHOLDER_DIMENSION   1e2

Minimum value for using openmp in Householder.

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Function Documentation

void * householder_matrix	(	size_t	m,
		double **const	A,
		double *const	v,
		size_t	idx
	)

Derive the householder vector using a matrix.

Parameters:

[in]	m	Dimension of vector
[in]	A	Matrix m-by-n
[in]	idx	Index of matrix where is started to compute the vector householder
[out]	v	Householder vector

Return values:

NULL	If the vector's elements of v[idx:] are all 0
1	Otherwise

Precondition:

The dimension is > 0 and idx is < than number of columns of A

Postcondition:

v[idx:] has been modified

References print_vector().

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void * householder_vector	(	size_t	n,
		double *const	x,
		double *const	v
	)

Derive the householder vector.

Parameters:

[in]	n	Dimension of vector
[in]	x	Input vector
[out]	v	Householder vector

Return values:

NULL	If the vector's elements of x are all 0
1	Otherwise

Precondition:

The dimension is not zero

Note:

The vector pointers x and v can be the same

References euclidian_norm().

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void postmult	(	size_t	m,
		size_t	n,
		double **const	A,
		double *const	v,
		double *const	w
	)

Compute where and are respectively m-by-n and n-by-n matrixs.

Parameters:

[in]	m	Rows
[in]	n	Columns
[in,out]	A	Matrix m-by-n where will be saved the result
[in]	v	Householder vector of dimension n
[in]	w	Auxiliar vector of dimension m

References inner_product().

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void premult_matrix	(	size_t	m,
		size_t	n,
		double **const	A,
		double **const	QR,
		double *const	v,
		double *const	w,
		size_t	idx
	)

Compute where and are respectively m-by-n and n-by-n matrixs.

Parameters:

[in]	m	Rows
[in]	n	Columns
[in]	A	Matrix m-by-n
[in]	v	Householder vector of dimension m
[in]	w	Auxiliar vector of dimension n
[in]	idx	Index of vectors where is started to compute
[out]	QR	Matrix m-by-n where will be saved the result

Precondition:

n <= m and idx < m

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void premult_vector	(	size_t	n,
		double *const	v,
		double *const	b
	)

Compute where and are respectively n-by-1 and n-by-n matrixs.

Parameters:

[in]	m	Rows
[in]	n	Columns
[in]	v	Householder vector of dimension n
[in,out]	b	Vector n-dimensional where will be saved the result