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Intel® oneAPI Math Kernel Library LAPACK Examples

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ID 766877
Date 10/31/2024
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Document Table of Contents
Document Table of Contents x
Intel® oneAPI Math Kernel Library LAPACK Examples
Intel® oneAPI Math Kernel Library LAPACK Examples x
Legal Information Intel® oneAPI Math Kernel Library LAPACK Examples LAPACK Examples LAPACK Routines: Linear Equations Least Squares and Eigenvalue Problems
Intel® oneAPI Math Kernel Library LAPACK Examples x
What's New Notational Conventions C Interface Conventions Compiling and Running Examples Compiling and Building Fortran Examples Compiling and Building C Examples Getting Help and Support
LAPACK Routines: Linear Equations x
?gesv function ?posv function ?sysv function ?hesv function
?gesv function x
CGESV Example DGESV Example SGESV Example ZGESV Example
CGESV Example x
CGESV Example Program in Fortran CGESV Example Program in C LAPACKE_cgesv Example Program in C for Row Major Data Layout LAPACKE_cgesv Example Program in C for Column Major Data Layout
DGESV Example x
DGESV Example Program in Fortran DGESV Example Program in C LAPACK_dgesv Example Program in C for Row Major Data Layout LAPACKE_dgesv Example Program in C for Column Major Data Layout
SGESV Example x
SGESV Example Program in Fortran SGESV Example Program in C LAPACK_sgesv Example Program in C for Row Major Data Layout LAPACK_sgesv Example Program in C for Column Major Data Layout
ZGESV Example x
ZGESV Example Program in Fortran ZGESV Example Program in C LAPACKE_zgesv Example Program in C for Row Major Data Layout LAPACKE_zgesv Example Program in C for Column Major Data Layout
?posv function x
CPOSV Example DPOSV Example SPOSV Example ZPOSV Example
CPOSV Example x
CPOSV Example Program in Fortran CPOSV Example Program in C LAPACKE_cposv Example Program in C for Row Major Data Layout LAPACK_cposv Example Program in C for Column Major Data Layout
DPOSV Example x
DPOSV Example Program in Fortran DPOSV Example Program in C LAPACKE_dposv Example Program in C for Row Major Data Layout LAPACK_dposv Example Program in C for Column Major Data Layout
SPOSV Example x
SPOSV Example Program in Fortran SPOSV Example Program in C LAPACK_sposv Example Program in C for Row Major Data Layout LAPACKE_sposv Example Program in C for Column Major Data Layout
ZPOSV Example x
ZPOSV Example Program in Fortran ZPOSV Example Program in C LAPACKE_zposv Example Program in C for Row Major Data Layout LAPACK_zposv Example Program in C for Column Major Data Layout
?sysv function x
CSYSV Example DSYSV Example SSYSV Example ZSYSV Example
CSYSV Example x
CSYSV Example Program in Fortran CSYSV Example Program in C LAPACKE_csysv Example Program in C for Row Major Data Layout LAPACKE_csysv Example Program in C for Column Major Data Layout
DSYSV Example x
DSYSV Example Program in Fortran DSYSV Example Program in C LAPACKE_dsysv Example Program in C for Row Major Data Layout LAPACKE_dsysv Example Program in C for Column Major Data Layout
SSYSV Example x
SSYSV Example Program in Fortran SYSV Example Program in C LAPACKE_ssysv Example Program in C for Row Major Data Layout LAPACKE_ssysv Example Program in C for Column Major Data Layout
ZSYSV Example x
ZSYSV Example Program in Fortran ZSYSV Example Program in C LAPACKE_zsysv Example Program in C for Row Major Data Layout LAPACKE_zsysv Example Program in C for Column Major Data Layout
?hesv function x
CHESV Example ZHESV Example
CHESV Example x
CHESV Example Program in Fortran CHESV Example Program in C LAPACKE_chesv Example Program in C for Row Major Data Layout LAPACKE_chesv Example Program in C for Column Major Data Layout
ZHESV Example x
ZHESV Example Program in Fortran ZHESV Example Program in C LAPACKE_zhesv Example Program in C for Row Major Data Layout LAPACKE_zhesv Example Program in C for Column Major Data Layout
Least Squares and Eigenvalue Problems x
Linear Least Squares (LLS) Problems Symmetric Eigenproblems Nonsymmetric Eigenproblems Singular Value Decomposition
Linear Least Squares (LLS) Problems x
?gels function ?gelsd function
?gels function x
CGELS Example DGELS Example SGELS Example ZGELS Example
CGELS Example x
CGELS Example Program in Fortran CGELS Example Program in C LAPACKE_cgels Example Program in C for Row Major Data Layout LAPACKE_cgels Example Program in C for Column Major Data Layout
DGELS Example x
DGELS Example Program in Fortran DGELS Example Program in C LAPACKE_dgels Example Program in C for Row Major Data Layout LAPACKE_dgels Example Program in C for Column Major Data Layout
SGELS Example x
SGELS Example Program in Fortran SGELS Example Program in C LAPACKE_sgels Example Program in C for Row Major Data Layout LAPACKE_sgels Example Program in C for Column Major Data Layout
ZGELS Example x
ZGELS Example Program in Fortran ZGELS Example Program in C LAPACKE_zgels Example Program in C for Row Major Data Layout LAPACKE_zgels Example Program in C for Column Major Data Layout
?gelsd function x
CGELSD Example DGELSD Example SGELSD Example ZGELSD Example
CGELSD Example x
CGELSD Example Program in Fortran CGELSD Example Program in C LAPACKE_cgelsd Example Program in C for Row Major Data Layout LAPACKE_cgelsd Example Program in C for Column Major Data Layout
DGELSD Example x
DGELSD Example Program in Fortran DGELSD Example Program in C LAPACKE_dgelsd Example Program in C for Row Major Data Layout LAPACKE_dgelsd Example Program in C for Column Major Data Layout
SGELSD Example x
SGELSD Example Program in Fortran SGELSD Example Program in C LAPACKE_sgelsd Example Program in C for Row Major Data Layout LAPACKE_sgelsd Example Program in C for Column Major Data Layout
ZGELSD Example x
ZGELSD Example Program in Fortran ZGELSD Example Program in C LAPACKE_zgelsd Example Program in C for Row Major Data Layout LAPACKE_zgelsd Example Program in C for Column Major Data Layout
Symmetric Eigenproblems x
?syev function ?heev function ?syevd function ?heevd function ?syevx function ?heevx function ?syevr function ?heevr function
?syev function x
DSYEV Example SSYEV Example
DSYEV Example x
DSYEV Example Program in Fortran DSYEV Example Program in C LAPACKE_dsyev Example Program in C for Row Major Data Layout LAPACKE_dsyev Example Program in C for Column Major Data Layout
SSYEV Example x
SSYEV Example Program in Fortran SSYEV Example Program in C LAPACKE_ssyev Example Program in C for Row Major Data Layout LAPACKE_ssyev Example Program in C for Column Major Data Layout
?heev function x
CHEEV Example ZHEEV Example
CHEEV Example x
CHEEV Example Program in Fortran CHEEV Example Program in C LAPACKE_cheev Example Program in C for Row Major Data Layout LAPACKE_cheev Example Program in C for Column Major Data Layout
ZHEEV Example x
ZHEEV Example Program in Fortran ZHEEV Example Program in C LAPACKE_zheev Example Program in C for Row Major Data Layout LAPACKE_zheev Example Program in C for Column Major Data Layout
?syevd function x
DSYEVD Example SSYEVD Example
DSYEVD Example x
DSYEVD Example Program in Fortran DSYEVD Example Program in C LAPACKE_dsyevd Example Program in C for Row Major Data Layout LAPACKE_dsyevd Example Program in C for Column Major Data Layout
SSYEVD Example x
SSYEVD Example Program in Fortran SSYEVD Example Program in C LAPACKE_ssyevd Example Program in C for Row Major Data Layout LAPACKE_ssyevd Example Program in C for Column Major Data Layout
?heevd function x
CHEEVD Example ZHEEVD Example
CHEEVD Example x
CHEEVD Example Program in Fortran CHEEVD Example Program in C LAPACKE_cheevd Example Program in C for Row Major Data Layout LAPACKE_cheevd Example Program in C for Column Major Data Layout
ZHEEVD Example x
ZHEEVD Example Program in Fortran ZHEEVD Example Program in C LAPACKE_zheevd Example Program in C for Row Major Data Layout LAPACKE_zheevd Example Program in C for Column Major Data Layout
?syevx function x
DSYEVX Example SSYEVX Example
DSYEVX Example x
DSYEVX Example Program in Fortran DSYEVX Example Program in C LAPACKE_dsyevx Example Program in C for Row Major Data Layout LAPACKE_dsyevx Example Program in C for Column Major Data Layout
SSYEVX Example x
SSYEVX Example Program in Fortran SSYEVX Example Program in C LAPACKE_ssyevx Example Program in C for Row Major Data Layout LAPACKE_ssyevx Example Program in C for Column Major Data Layout
?heevx function x
CHEEVX Example ZHEEVX Example
CHEEVX Example x
CHEEVX Example Program in Fortran CHEEVX Example Program in C LAPACKE_cheevx Example Program in C for Row Major Data Layout LAPACKE_cheevx Example Program in C for Column Major Data Layout
ZHEEVX Example x
ZHEEVX Example Program in Fortran ZHEEVX Example Program in C LAPACKE_zheevx Example Program in C for Row Major Data Layout LAPACKE_zheevx Example Program in C for Column Major Data Layout
?syevr function x
DSYEVR Example SSYEVR Example
DSYEVR Example x
DSYEVR Example Program in Fortran DSYEVR Example Program in C LAPACKE_dsyevr Example Program in C for Row Major Data Layout LAPACKE_dsyevr Example Program in C for Column Major Data Layout
SSYEVR Example x
SSYEVR Example Program in Fortran SSYEVR Example Program in C LAPACKE_ssyevr Example Program in C for Row Major Data Layout LAPACKE_ssyevr Example Program in C for Column Major Data Layout
?heevr function x
CHEEVR Example ZHEEVR Example
CHEEVR Example x
CHEEVR Example Program in Fortran CHEEVR Example Program in C LAPACKE_cheevr Example Program in C for Row Major Data Layout LAPACKE_cheevr Example Program in C for Column Major Data Layout
ZHEEVR Example x
ZHEEVR Example Program in Fortran ZHEEVR Example Program in C LAPACKE_zheevr Example Program in C for Row Major Data Layout LAPACKE_zheevr Example Program in C for Column Major Data Layout
Nonsymmetric Eigenproblems x
?geev function
?geev function x
CGEEV Example DGEEV Example SGEEV Example ZGEEV Example
CGEEV Example x
CGEEV Example Program in Fortran CGEEV Example Program in C LAPACKE_cgeev Example Program in C for Row Major Data Layout LAPACKE_cgeev Example Program in C for Column Major Data Layout
DGEEV Example x
DGEEV Example Program in Fortran DGEEV Example Program in C LAPACKE_dgeev Example Program in C for Row Major Data Layout LAPACKE_dgeev Example Program in C for Column Major Data Layout
SGEEV Example x
SGEEV Example Program in Fortran SGEEV Example Program in C LAPACKE_sgeev Example Program in C for Row Major Data Layout LAPACKE_sgeev Example Program in C for Column Major Data Layout
ZGEEV Example x
ZGEEV Example Program in Fortran ZGEEV Example Program in C LAPACKE_zgeev Example Program in C for Row Major Data Layout LAPACKE_zgeev Example Program in C for Column Major Data Layout
Singular Value Decomposition x
?gesvd function ?gesdd function
?gesvd function x
CGESVD Example DGESVD Example SGESVD Example ZGESVD Example
CGESVD Example x
CGESVD Example Program in Fortran CGESVD Example Program in C LAPACKE_cgesvd Example Program in C for Row Major Data Layout LAPACKE_cgesvd Example Program in C for Column Major Data Layout
DGESVD Example x
DGESVD Example Program in Fortran DGESVD Example Program in C LAPACKE_dgesvd Example Program in C for Row Major Data Layout LAPACKE_dgesvd Example Program in C for Column Major Data Layout
SGESVD Example x
SGESVD Example Program in Fortran SGESVD Example Program in C LAPACKE_sgesvd Example Program in C for Row Major Data Layout LAPACKE_sgesvd Example Program in C for Column Major Data Layout
ZGESVD Example x
ZGESVD Example Program in Fortran ZGESVD Example Program in C LAPACKE_zgesvd Example Program in C for Row Major Data Layout LAPACKE_zgesvd Example Program in C for Column Major Data Layout
?gesdd function x
CGESDD Example DGESDD Example SGESDD Example ZGESDD Example
CGESDD Example x
CGESDD Example Program in Fortran CGESDD Example Program in C LAPACKE_cgesdd Example Program in C for Row Major Data Layout LAPACKE_cgesdd Example Program in C for Column Major Data Layout
DGESDD Example x
DGESDD Example Program in Fortran DGESDD Example Program in C LAPACKE_dgesdd Example Program in C for Row Major Data Layout LAPACKE_dgesdd Example Program in C for Column Major Data Layout
SGESDD Example x
SGESDD Example Program in Fortran SGESDD Example Program in C LAPACKE_sgesdd Example Program in C for Row Major Data Layout LAPACKE_sgesdd Example Program in C for Column Major Data Layout
ZGESDD Example x
ZGESDD Example Program in Fortran ZGESDD Example Program in C LAPACKE_zgesdd Example Program in C for Row Major Data Layout LAPACKE_zgesdd Example Program in C for Column Major Data Layout
Intel® oneAPI Math Kernel Library LAPACK Examples

DGELS Example Program in C

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

 DGELS 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>

/* DGELS prototype */
extern void dgels( char* trans, int* m, int* n, int* nrhs, double* a, int* lda,
                double* b, int* ldb, double* work, int* lwork, int* info );
/* Auxiliary routines prototypes */
extern void print_matrix( char* desc, int m, int n, double* a, int lda );
extern void print_vector_norm( char* desc, int m, int n, double* a, int lda );

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

/* Main program */
int main() {
        /* Locals */
        int m = M, n = N, nrhs = NRHS, lda = LDA, ldb = LDB, info, lwork;
        double wkopt;
        double* work;
        /* Local arrays */
        double a[LDA*N] = {
            1.44, -9.96, -7.55,  8.34,  7.08, -5.45,
           -7.84, -0.28,  3.24,  8.09,  2.52, -5.70,
           -4.39, -3.24,  6.27,  5.28,  0.74, -1.19,
            4.53,  3.83, -6.64,  2.06, -2.47,  4.70
        };
        double b[LDB*NRHS] = {
            8.58,  8.26,  8.48, -5.28,  5.72,  8.93,
            9.35, -4.43, -0.70, -0.26, -7.36, -2.52
        };
        /* Executable statements */
        printf( " DGELS Example Program Results\n" );
        /* Query and allocate the optimal workspace */
        lwork = -1;
        dgels( "No transpose", &m, &n, &nrhs, a, &lda, b, &ldb, &wkopt, &lwork,
                        &info );
        lwork = (int)wkopt;
        work = (double*)malloc( lwork*sizeof(double) );
        /* Solve the equations A*X = B */
        dgels( "No transpose", &m, &n, &nrhs, a, &lda, b, &ldb, work, &lwork,
                        &info );
        /* 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 );
        /* Print details of QR factorization */
        print_matrix( "Details of QR factorization", m, n, a, lda );
        /* Free workspace */
        free( (void*)work );
        exit( 0 );
} /* End of DGELS 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" );
        }
}

/* Auxiliary routine: printing norms of matrix columns */
void print_vector_norm( char* desc, int m, int n, double* a, int lda ) {
        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+j*lda] * a[i+j*lda];
                printf( " %6.2f", norm );
        }
        printf( "\n" );
}
Parent topic: DGELS Example
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