Developer Reference

## Intel® oneAPI Math Kernel Library LAPACK Examples

ID 766877
Date 3/31/2023
Public

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## LAPACKE_sgelsd Example Program in C for Row Major Data Layout

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/*
LAPACKE_sgelsd 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.
========================

LAPACKE_sgelsd (row-major, high-level) 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>
#include "mkl_lapacke.h"

/* Auxiliary routines prototypes */
extern void print_matrix( char* desc, MKL_INT m, MKL_INT n, float* a, MKL_INT lda );

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

/* Main program */
int main() {
/* Locals */
MKL_INT m = M, n = N, nrhs = NRHS, lda = LDA, ldb = LDB, info, rank;
/* Negative rcond means using default (machine precision) value */
float rcond = -1.0;
/* Local arrays */
float s[M];
float a[LDA*M] = {
0.12f, -8.19f, 7.69f, -2.26f, -4.71f,
-6.91f,  2.22f, -5.12f, -9.08f,  9.96f,
-3.33f, -8.94f, -6.72f, -4.40f, -9.98f,
3.97f,  3.33f, -2.74f, -7.92f, -3.20f
};
float b[LDB*N] = {
7.30f,  0.47f, -6.28f,
1.33f,  6.58f, -3.42f,
2.68f, -1.71f, 3.46f,
-9.62f, -0.79f, 0.41f,
0.00f,  0.00f, 0.00f
};
/* Executable statements */
printf( "LAPACKE_sgelsd (row-major, high-level) Example Program Results\n" );
/* Solve the equations A*X = B */
info = LAPACKE_sgelsd( LAPACK_ROW_MAJOR, m, n, nrhs, a, lda, b, ldb,
s, rcond, &rank );
/* 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 );
exit( 0 );
} /* End of LAPACKE_sgelsd Example */

/* Auxiliary routine: printing a matrix */
void print_matrix( char* desc, MKL_INT m, MKL_INT n, float* a, MKL_INT lda ) {
MKL_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*lda+j] );
printf( "\n" );
}
}