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Intel® oneAPI Math Kernel Library LAPACK Examples

ID 766877
Date 12/20/2021
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ZGELSD Example Program in C

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/*
   ZGELSD Example.
   ==============

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

   (  4.55, -0.32) ( -4.36, -4.76) (  3.99, -6.84) (  8.03, -6.47)
   (  8.87, -3.11) (  0.02,  8.43) (  5.43, -9.30) (  2.28,  8.94)
   ( -0.74,  1.16) (  3.80, -6.12) ( -7.24,  0.72) (  2.21,  9.52)

   and B is the right-hand side matrix:

   ( -8.25,  7.98) (  2.91, -8.81)
   ( -5.04,  3.33) (  6.19,  0.19)
   (  7.98, -4.38) ( -5.96,  7.18)

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

   The routine computes the minimum-norm solution to a complex 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.
   ========================

 ZGELSD Example Program Results

 Minimum norm solution
 ( -0.08,  0.09) (  0.04,  0.16)
 ( -0.17,  0.10) (  0.17, -0.47)
 ( -0.92, -0.01) (  0.71, -0.41)
 ( -0.47, -0.26) (  0.69,  0.02)

 Effective rank =      3

 Singular values
  20.01  18.21   7.88
*/
#include <stdlib.h>
#include <stdio.h>

/* Complex datatype */
struct _dcomplex { double re, im; };
typedef struct _dcomplex dcomplex;

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

/* Parameters */
#define M 3
#define N 4
#define NRHS 2
#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;
        dcomplex wkopt;
        dcomplex* work;
        /* Local arrays */
        /* iwork dimension should be at least 3*min(m,n)*nlvl + 11*min(m,n),
                rwork dimension should be at least 10*min(m,n)+2*min(m,n)*smlsiz+
                +8*min(m,n)*nlvl+3*smlsiz*nrhs+(smlsiz+1)^2,
                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], rwork[10*M+2*M*25+8*M*0+3*25*NRHS+26*26];
        dcomplex a[LDA*N] = {
           { 4.55, -0.32}, { 8.87, -3.11}, {-0.74,  1.16},
           {-4.36, -4.76}, { 0.02,  8.43}, { 3.80, -6.12},
           { 3.99, -6.84}, { 5.43, -9.30}, {-7.24,  0.72},
           { 8.03, -6.47}, { 2.28,  8.94}, { 2.21,  9.52}
        };
        dcomplex b[LDB*NRHS] = {
           {-8.25,  7.98}, {-5.04,  3.33}, { 7.98, -4.38}, { 0.00,  0.00},
           { 2.91, -8.81}, { 6.19,  0.19}, {-5.96,  7.18}, { 0.00,  0.00}
        };
        /* Executable statements */
        printf( " ZGELSD Example Program Results\n" );
        /* Query and allocate the optimal workspace */
        lwork = -1;
        zgelsd( &m, &n, &nrhs, a, &lda, b, &ldb, s, &rcond, &rank, &wkopt, &lwork,
                        rwork, iwork, &info );
        lwork = (int)wkopt.re;
        work = (dcomplex*)malloc( lwork*sizeof(dcomplex) );
        /* Solve the equations A*X = B */
        zgelsd( &m, &n, &nrhs, a, &lda, b, &ldb, s, &rcond, &rank, work, &lwork,
                        rwork, 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_rmatrix( "Singular values", 1, m, s, 1 );
        /* Free workspace */
        free( (void*)work );
        exit( 0 );
} /* End of ZGELSD Example */

/* Auxiliary routine: printing a matrix */
void print_matrix( char* desc, int m, int n, dcomplex* 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,%6.2f)", a[i+j*lda].re, a[i+j*lda].im );
                printf( "\n" );
        }
}

/* Auxiliary routine: printing a real matrix */
void print_rmatrix( 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" );
        }
}

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