svdcmp_lapack.c File Reference

#include "mbs_matrix.h"
#include "mbs_lapack.h"
#include "mbs_message.h"
#include "mbs_1D_array.h"
#include "mbs_errors_names.h"

Macros
#define	MSG_ERR   ">> SVD_LPK>> "
#define	MSG_PRE   " >> "

Functions
int	mbs_over_under_determined (double **A, double *b, int x, int y)
	Solve a linear system of equations, A*x=b, using dgelss lapack function. More...
int	mbs_svdDcmp_0 (double **A, int x, int y, double **U, double **S, double **VT)
	Realize the singular value decomposition. More...

Macro Definition Documentation

MSG_ERR

#define MSG_ERR   ">> SVD_LPK>> "

MSG_PRE

#define MSG_PRE   " >> "

Function Documentation

mbs_over_under_determined()

int mbs_over_under_determined	(	double **	A,
		double *	b,
		int	x,
		int	y
	)

Solve a linear system of equations, A*x=b, using dgelss lapack function.

This function mainly transfers the MBsysC arrays with index starting at 1 (see get_dmat_1() and get_dvec_1()) to Lapack-compatible arrays (index starting at 0, col. major memory).

The following explanations come from the Lapack documentation. This function solves overdetermined or underdetermined systems.

For overdetermined system it minimizes 2-norm(| b - A*x |).

For underdetermined system it minimizes 2-norm(| x |).

Parameters

[in,out]	A	main matrix of size [x,y] with first line and row unused using row major memory.
[in,out]	b	As input it contains the vector b of size [y] with index starting at 1. As output it contains the solution vector x.

For overdetermined system, the residual sum-of-squares for the solution is the sum of the elements from b[x+1] to b[y+1].

Parameters

[in]	x	the number of row of A, which is the number of equations.
[in]	y	the number of col. of A, which is the number of unknowns.

Returns

error status, < 0 in case of failure.

mbs_svdDcmp_0()

int mbs_svdDcmp_0	(	double **	A,
		int	x,
		int	y,
		double **	U,
		double **	S,
		double **	VT
	)

Realize the singular value decomposition.

A = U * S * transpose(V)

Parameters

[in]	A	: the rectangular matrix
[in]	x	: the number of row of A
[in]	y	: the number of row of A
[in]	U	: the x-by-x orthogonal matrix U;
[in]	S	: the x-by-y matrix which is zero except for its min(x,y) diagonal elements
[in]	VT	: the y-by-y orthogonal matrix V**T.