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Intel® oneAPI Math Kernel Library LAPACK Examples

ID 766877
Date 12/20/2021
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LAPACKE_dgels Example Program in C for Row Major Data Layout

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/*
   LAPACKE_dgels Example.
   ======================

   Program computes the least squares solution to the overdetermined linear
   system A*X = B with full rank matrix A using QR factorization,
   where A is the coefficient matrix:

     1.44  -7.84  -4.39   4.53
    -9.96  -0.28  -3.24   3.83
    -7.55   3.24   6.27  -6.64
     8.34   8.09   5.28   2.06
     7.08   2.52   0.74  -2.47
    -5.45  -5.70  -1.19   4.70

   and B is the right-hand side matrix:

     8.58   9.35
     8.26  -4.43
     8.48  -0.70
    -5.28  -0.26
     5.72  -7.36
     8.93  -2.52

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

   The routine solves overdetermined or underdetermined real linear systems
   involving an m-by-n matrix A, or its transpose, using a QR or LQ
   factorization of A. It is assumed that A has full rank.

   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.

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

 LAPACKE_dgels (row-major, high-level) Example Program Results

 Solution
  -0.45   0.25
  -0.85  -0.90
   0.71   0.63
   0.13   0.14

 Residual sum of squares for the solution
 195.36 107.06

 Details of QR factorization
 -17.54  -4.76  -1.96   0.42
  -0.52  12.40   7.88  -5.84
  -0.40  -0.14  -5.75   4.11
   0.44  -0.66  -0.20  -7.78
   0.37  -0.26  -0.17  -0.15
  -0.29   0.46   0.41   0.24
*/
#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, double* a, MKL_INT lda );
extern void print_vector_norm( char* desc, MKL_INT m, MKL_INT n, double* a, MKL_INT lda );

/* Parameters */
#define M 6
#define N 4
#define NRHS 2
#define LDA N
#define LDB NRHS

/* Main program */
int main() {
        /* Locals */
        MKL_INT m = M, n = N, nrhs = NRHS, lda = LDA, ldb = LDB, info;
        /* Local arrays */
        double a[LDA*M] = {
            1.44, -7.84, -4.39,  4.53,
           -9.96, -0.28, -3.24,  3.83,
           -7.55, 3.24, 6.27, -6.64,
            8.34, 8.09, 5.28,  2.06,
            7.08, 2.52, 0.74, -2.47,
           -5.45, -5.70, -1.19,  4.70
        };
        double b[LDB*M] = {
            8.58, 9.35,
            8.26, -4.43,
            8.48, -0.70,
           -5.28, -0.26,
            5.72, -7.36,
            8.93, -2.52
        };
        /* Executable statements */
        printf( "LAPACKE_dgels (row-major, high-level) Example Program Results\n" );
        /* Solve the equations A*X = B */
        info = LAPACKE_dgels( LAPACK_ROW_MAJOR, 'N', m, n, nrhs, a, lda,
                        b, ldb );
        /* Check for the full rank */
        if( info > 0 ) {
                printf( "The diagonal element %i of the triangular factor ", info );
                printf( "of A is zero, so that A does not have full rank;\n" );
                printf( "the least squares solution could not be computed.\n" );
                exit( 1 );
        }
        /* Print least squares solution */
        print_matrix( "Least squares solution", n, nrhs, b, ldb );
        /* Print residual sum of squares for the solution */
        print_vector_norm( "Residual sum of squares for the solution", m-n, nrhs,
                        &b[n*ldb], ldb );
        /* Print details of QR factorization */
        print_matrix( "Details of QR factorization", m, n, a, lda );
        exit( 0 );
} /* End of LAPACKE_dgels Example */

/* Auxiliary routine: printing a matrix */
void print_matrix( char* desc, MKL_INT m, MKL_INT n, double* 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" );
        }
}

/* Auxiliary routine: printing norms of matrix columns */
void print_vector_norm( char* desc, MKL_INT m, MKL_INT n, double* a, MKL_INT lda ) {
        MKL_INT i, j;
        double norm;
        printf( "\n %s\n", desc );
        for( j = 0; j < n; j++ ) {
                norm = 0.0;
                for( i = 0; i < m; i++ ) norm += a[i*lda+j] * a[i*lda+j];
                printf( " %6.2f", norm );
        }
        printf( "\n" );
}