Singular Value Decomposition

Data Structures
struct	mirml_nr_svd_t_
	Structure for Singular Value Decomposition (SVD) of matrices: A=U*W*V^T. More...

Typedefs
typedef struct mirml_nr_svd_t_	mirml_nr_svd_t
	Structure for Singular Value Decomposition (SVD) of matrices: A=U*W*V^T.

Functions
mirkl_error_t *	mirml_nr_svd_init (mirml_nr_svd_t **svd)
	Allocation and initialization of SVD structure.
mirkl_error_t *	mirml_nr_svd_decompose (mirml_matrix_t *a, mirkl_size_t i0, mirkl_size_t j0, mirkl_size_t cm, mirkl_size_t cn, mirml_nr_svd_t *svd)
	SVD decomposition. More...
mirkl_error_t *	mirml_nr_svd_reorder (mirml_nr_svd_t *svd)
	Sorting of singular values and matrices U and V after succesful mirml_nr_svd_decompose.
void	mirml_nr_svd_free (mirml_nr_svd_t *svd)
	Deallocates SVD structure and its content. More...
mirkl_error_t *	mirml_nr_svd_invert (mirml_nr_svd_t *svd, mirml_matrix_t **out_m)
	Calculation of inverted matrix with help of SVD decomposition. More...
mirkl_error_t *	mirml_nr_svd_vsolve (mirml_nr_svd_t *svd, mirml_vector_t *b, mirml_vector_t **x)
	Solves A*x=b for a vector x using the pseudoinverse of A as obtained by SVD. More...
mirkl_error_t *	mirml_nr_svd_msolve (mirml_nr_svd_t *svd, mirml_matrix_t *b, mirml_matrix_t **x)
	Solves m sets of n equations A*X=B using the pseudoinverse of A. More...
mirkl_error_t *	mirml_nr_svd_range (mirml_nr_svd_t *svd, mirml_matrix_t **rnge)
	Give an orthonormal basis for the range of SVD'ed matrix as the columns of a returned matrix. More...
mirkl_error_t *	mirml_nr_svd_nullspace (mirml_nr_svd_t *svd, mirml_matrix_t **nullsp)
	Give an orthonormal basis for the nullspace of SVD'ed matrix as the columns of a returned matrix. More...

Detailed Description

Function Documentation

mirml_nr_svd_decompose()

mirkl_error_t * mirml_nr_svd_decompose	(	mirml_matrix_t *	a,
		mirkl_size_t	i0,
		mirkl_size_t	j0,
		mirkl_size_t	cm,
		mirkl_size_t	cn,
		mirml_nr_svd_t *	svd
	)

SVD decomposition.

Parameters

[in]	a	Matrix to be decomposed.
[in]	i0	Starting row index, from which the input matrix should be processed.
[in]	j0	Starting column index, from which the input matrix should be processed.
[in]	cm	Custom number of rows in input matrix to be processed. All rows of input matrix starting from index i0 will be processed if cm is 0.
[in]	cn	Custom number of columns in input matrix to be processed. All columns of input matrix starting from index j0 will be processed if cn is 0.
[in,out]	svd	Preallocated and initialized structure with results of SVD decomposition on output.

Note

The allocated structure must be freed with the mirml_nr_svd_free.

i0, j0, cm, cn are all zero in simplest case when the whole input matrix should be decomposed.

mirml_nr_svd_free()

void mirml_nr_svd_free

(

mirml_nr_svd_t *

svd

)

Deallocates SVD structure and its content.

Note

The pointer svd after the call is not valid anymore.

mirml_nr_svd_invert()

mirkl_error_t * mirml_nr_svd_invert	(	mirml_nr_svd_t *	svd,
		mirml_matrix_t **	out_m
	)

Calculation of inverted matrix with help of SVD decomposition.

Parameters

[in]	svd	Structure of SVD.
[in,out]	out_m	Inverted matrix on output. Can be preallocated, otherwise it is allocated inside the function.

Note

This function must be called after the mirml_nr_svd_decompose function.

Warning

It is user's responsibility to free the output matrix.

mirml_nr_svd_msolve()

mirkl_error_t * mirml_nr_svd_msolve	(	mirml_nr_svd_t *	svd,
		mirml_matrix_t *	b,
		mirml_matrix_t **	x
	)

Solves m sets of n equations A*X=B using the pseudoinverse of A.

Parameters

[in]	svd	Structure of SVD.
[in]	b	right-hand sides as b[0..n-1][0..m-1].
[in,out]	x	Returned solutions as x[0..n-1][0..m-1]. This matrix can be preallocated, otherwise it is allocated inside the function.

Note

This function must be called after the mirml_nr_svd_decompose function.

Warning

It is user's responsibility to free the output matrix.

mirml_nr_svd_nullspace()

mirkl_error_t * mirml_nr_svd_nullspace	(	mirml_nr_svd_t *	svd,
		mirml_matrix_t **	nullsp
	)

Give an orthonormal basis for the nullspace of SVD'ed matrix as the columns of a returned matrix.

Parameters

[in]	svd	Structure of SVD.
[in,out]	nullsp	Returned range matrix. It can be preallocated, otherwise it is allocated inside the function.

Note

This function must be called after the mirml_nr_svd_decompose function.

Warning

It is user's responsibility to free the output matrix.

mirml_nr_svd_range()

mirkl_error_t * mirml_nr_svd_range	(	mirml_nr_svd_t *	svd,
		mirml_matrix_t **	rnge
	)

Give an orthonormal basis for the range of SVD'ed matrix as the columns of a returned matrix.

Parameters

[in]	svd	Structure of SVD.
[in,out]	rnge	Returned range matrix. It can be preallocated, otherwise it is allocated inside the function.

Note

This function must be called after the mirml_nr_svd_decompose function.

Warning

It is user's responsibility to free the output matrix.

mirml_nr_svd_vsolve()

mirkl_error_t * mirml_nr_svd_vsolve	(	mirml_nr_svd_t *	svd,
		mirml_vector_t *	b,
		mirml_vector_t **	x
	)

Solves A*x=b for a vector x using the pseudoinverse of A as obtained by SVD.

Parameters

[in]	svd	Structure of SVD.
[in]	b	Right-hand-side vector.
[in,out]	x	Left-hand-side vector of unknowns to be determined. Can be preallocated, otherwise it is allocated inside the function.

Note

This function must be called after the mirml_nr_svd_decompose function.

Warning

It is user's responsibility to free the output vector.