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Intel® oneAPI Math Kernel Library LAPACK Examples

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

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

 LAPACKE_zheevx (row-major, high-level) 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>
#include "mkl_lapacke.h"

/* Auxiliary routines prototypes */
extern void print_matrix( char* desc, MKL_INT m, MKL_INT n, MKL_Complex16* a, MKL_INT lda );
extern void print_rmatrix( char* desc, MKL_INT m, MKL_INT n, double* a, MKL_INT lda );

/* Parameters */
#define N 4
#define LDA N
#define LDZ N

/* Main program */
int main() {
        /* Locals */
        MKL_INT n = N, lda = LDA, ldz = LDZ, il, iu, m, info;
        double abstol, vl, vu;
        /* Local arrays */
        MKL_INT ifail[N];
        double w[N];
        MKL_Complex16 z[LDZ*N];
        MKL_Complex16 a[LDA*N] = {
           { 6.51,  0.00}, { 0.00,  0.00}, { 0.00,  0.00}, { 0.00,  0.00},
           {-5.92, -9.53}, {-1.73,  0.00}, { 0.00,  0.00}, { 0.00,  0.00},
           {-2.46, -2.91}, { 6.50, -2.09}, { 6.90,  0.00}, { 0.00,  0.00},
           { 8.84, -3.21}, { 1.32, -8.81}, {-0.59, -2.47}, {-2.85,  0.00}
        };
        /* Executable statements */
        printf( "LAPACKE_zheevx (row-major, high-level) 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;
        /* Solve eigenproblem */
        info = LAPACKE_zheevx( LAPACK_ROW_MAJOR, 'V', 'V', 'L', n, a, lda,
                        vl, vu, il, iu, abstol, &m, w, z, ldz, ifail );
        /* 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 );
        exit( 0 );
} /* End of LAPACKE_zheevx Example */

/* Auxiliary routine: printing a matrix */
void print_matrix( char* desc, MKL_INT m, MKL_INT n, MKL_Complex16* 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,%6.2f)", a[i*lda+j].real, a[i*lda+j].imag );
                printf( "\n" );
        }
}

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