Developer Reference

## Intel® oneAPI Math Kernel Library LAPACK Examples

ID 766877
Date 12/20/2021
Public

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## DGELSD Example Program in C

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/*
DGELSD Example.
==============

Program computes the minimum norm-solution to a real linear least squares
problem using the singular value decomposition of A,
where A is the coefficient matrix:

0.12  -8.19   7.69  -2.26  -4.71
-6.91   2.22  -5.12  -9.08   9.96
-3.33  -8.94  -6.72  -4.40  -9.98
3.97   3.33  -2.74  -7.92  -3.20

and B is the right-hand side matrix:

7.30   0.47  -6.28
1.33   6.58  -3.42
2.68  -1.71   3.46
-9.62  -0.79   0.41

Description.
============

The routine computes the minimum-norm solution to a real linear least
squares problem: minimize ||b - A*x|| using the singular value
decomposition (SVD) of A. A is an m-by-n matrix which may be rank-deficient.

Several right hand side vectors b and solution vectors x can be handled
in a single call; they are stored as the columns of the m-by-nrhs right
hand side matrix B and the n-by-nrhs solution matrix X.

The effective rank of A is determined by treating as zero those singular
values which are less than rcond times the largest singular value.

Example Program Results.
========================

DGELSD Example Program Results

Minimum norm solution
-0.69  -0.24   0.06
-0.80  -0.08   0.21
0.38   0.12  -0.65
0.29  -0.24   0.42
0.29   0.35  -0.30

Effective rank =      4

Singular values
18.66  15.99  10.01   8.51
*/
#include <stdlib.h>
#include <stdio.h>

/* DGELSD prototype */
extern void dgelsd( int* m, int* n, int* nrhs, double* a, int* lda,
double* b, int* ldb, double* s, double* rcond, int* rank,
double* work, int* lwork, int* iwork, int* info );
/* Auxiliary routines prototypes */
extern void print_matrix( char* desc, int m, int n, double* a, int lda );

/* Parameters */
#define M 4
#define N 5
#define NRHS 3
#define LDA M
#define LDB N

/* Main program */
int main() {
/* Locals */
int m = M, n = N, nrhs = NRHS, lda = LDA, ldb = LDB, info, lwork, rank;
/* Negative rcond means using default (machine precision) value */
double rcond = -1.0;
double wkopt;
double* work;
/* Local arrays */
/* iwork dimension should be at least 3*min(m,n)*nlvl + 11*min(m,n),
where nlvl = max( 0, int( log_2( min(m,n)/(smlsiz+1) ) )+1 )
and smlsiz = 25 */
int iwork[3*M*0+11*M];
double s[M];
double a[LDA*N] = {
0.12, -6.91, -3.33,  3.97,
-8.19,  2.22, -8.94,  3.33,
7.69, -5.12, -6.72, -2.74,
-2.26, -9.08, -4.40, -7.92,
-4.71,  9.96, -9.98, -3.20
};
double b[LDB*NRHS] = {
7.30,  1.33,  2.68, -9.62,  0.00,
0.47,  6.58, -1.71, -0.79,  0.00,
-6.28, -3.42,  3.46,  0.41,  0.00
};
/* Executable statements */
printf( " DGELSD Example Program Results\n" );
/* Query and allocate the optimal workspace */
lwork = -1;
dgelsd( &m, &n, &nrhs, a, &lda, b, &ldb, s, &rcond, &rank, &wkopt, &lwork,
iwork, &info );
lwork = (int)wkopt;
work = (double*)malloc( lwork*sizeof(double) );
/* Solve the equations A*X = B */
dgelsd( &m, &n, &nrhs, a, &lda, b, &ldb, s, &rcond, &rank, work, &lwork,
iwork, &info );
/* Check for convergence */
if( info > 0 ) {
printf( "The algorithm computing SVD failed to converge;\n" );
printf( "the least squares solution could not be computed.\n" );
exit( 1 );
}
/* Print minimum norm solution */
print_matrix( "Minimum norm solution", n, nrhs, b, ldb );
/* Print effective rank */
printf( "\n Effective rank = %6i\n", rank );
/* Print singular values */
print_matrix( "Singular values", 1, m, s, 1 );
/* Free workspace */
free( (void*)work );
exit( 0 );
} /* End of DGELSD Example */

/* Auxiliary routine: printing a matrix */
void print_matrix( char* desc, int m, int n, double* a, int lda ) {
int i, j;
printf( "\n %s\n", desc );
for( i = 0; i < m; i++ ) {
for( j = 0; j < n; j++ ) printf( " %6.2f", a[i+j*lda] );
printf( "\n" );
}
}