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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

ZHEEVX Example Program in C

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/*
   ZHEEVX Example.
   ==============

   Program computes eigenvalues specified by a selected range of values
   and corresponding eigenvectors of a complex Hermitian matrix A:

   (  6.51,  0.00) ( -5.92,  9.53) ( -2.46,  2.91) (  8.84,  3.21)
   ( -5.92, -9.53) ( -1.73,  0.00) (  6.50,  2.09) (  1.32,  8.81)
   ( -2.46, -2.91) (  6.50, -2.09) (  6.90,  0.00) ( -0.59,  2.47)
   (  8.84, -3.21) (  1.32, -8.81) ( -0.59, -2.47) ( -2.85,  0.00)

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

   The routine computes selected eigenvalues and, optionally, eigenvectors of
   an n-by-n complex Hermitian matrix A. The eigenvector v(j) of A satisfies

   A*v(j) = lambda(j)*v(j)

   where lambda(j) is its eigenvalue. The computed eigenvectors are
   orthonormal.
   Eigenvalues and eigenvectors can be selected by specifying either a range
   of values or a range of indices for the desired eigenvalues.

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

 ZHEEVX Example Program Results

 The total number of eigenvalues found: 3

 Selected eigenvalues
   0.09   9.53  18.75

 Selected eigenvectors (stored columnwise)
 (  0.18,  0.00) ( -0.54,  0.00) (  0.67,  0.00)
 ( -0.40, -0.31) ( -0.21, -0.17) ( -0.30, -0.43)
 (  0.60,  0.40) ( -0.35, -0.28) ( -0.39, -0.34)
 ( -0.34,  0.26) ( -0.57,  0.35) (  0.05,  0.05)
*/
#include <stdlib.h>
#include <stdio.h>

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

/* ZHEEVX prototype */
extern void zheevx( char* jobz, char* range, char* uplo, int* n, dcomplex* a,
                int* lda, double* vl, double* vu, int* il, int* iu, double* abstol,
                int* m, double* w, dcomplex* z, int* ldz, dcomplex* work, int* lwork,
                double* rwork, int* iwork, int* ifail, 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 N 4
#define LDA N
#define LDZ N

/* Main program */
int main() {
        /* Locals */
        int n = N, lda = LDA, ldz = LDZ, il, iu, m, info, lwork;
        double abstol, vl, vu;
        dcomplex wkopt;
        dcomplex* work;
        /* Local arrays */
        /* iwork dimension should be at least 5*n */
        int iwork[5*N], ifail[N];
        /* rwork dimension should be at least 7*n */
        double w[N], rwork[7*N];
        dcomplex z[LDZ*N];
        dcomplex a[LDA*N] = {
           { 6.51,  0.00}, {-5.92, -9.53}, {-2.46, -2.91}, { 8.84, -3.21},
           { 0.00,  0.00}, {-1.73,  0.00}, { 6.50, -2.09}, { 1.32, -8.81},
           { 0.00,  0.00}, { 0.00,  0.00}, { 6.90,  0.00}, {-0.59, -2.47},
           { 0.00,  0.00}, { 0.00,  0.00}, { 0.00,  0.00}, {-2.85,  0.00}
        };
        /* Executable statements */
        printf( " ZHEEVX Example Program Results\n" );
        /* Negative abstol means using the default value */
        abstol = -1.0;
        /* Set VL, VU to compute eigenvalues in half-open (VL,VU] interval */
        vl = 0.0;
        vu = 100.0;
        /* Query and allocate the optimal workspace */
        lwork = -1;
        zheevx( "Vectors", "Values", "Lower", &n, a, &lda, &vl, &vu, &il, &iu,
                        &abstol, &m, w, z, &ldz, &wkopt, &lwork, rwork, iwork, ifail, &info );
        lwork = (int)wkopt.re;
        work = (dcomplex*)malloc( lwork*sizeof(dcomplex) );
        /* Solve eigenproblem */
        zheevx( "Vectors", "Values", "Lower", &n, a, &lda, &vl, &vu, &il, &iu,
                        &abstol, &m, w, z, &ldz, work, &lwork, rwork, iwork, ifail, &info );
        /* Check for convergence */
        if( info > 0 ) {
                printf( "The algorithm failed to compute eigenvalues.\n" );
                exit( 1 );
        }
        /* Print the number of eigenvalues found */
        printf( "\n The total number of eigenvalues found:%2i\n", m );
        /* Print eigenvalues */
        print_rmatrix( "Selected eigenvalues", 1, m, w, 1 );
        /* Print eigenvectors */
        print_matrix( "Selected eigenvectors (stored columnwise)", n, m, z, ldz );
        /* Free workspace */
        free( (void*)work );
        exit( 0 );
} /* End of ZHEEVX 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" );
        }
}
Parent topic: ZHEEVX Example
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