IntelĀ® oneAPI Math Kernel Library LAPACK Examples

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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" );
        }
}