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Intel® oneAPI Math Kernel Library LAPACK Examples

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

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/*
   SSYEVX Example.
   ==============

   Program computes the smallest eigenvalues and the corresponding
   eigenvectors of a real symmetric matrix A:

     6.29  -0.39   0.61   1.18  -0.08
    -0.39   7.19   0.81   1.19  -0.08
     0.61   0.81   5.48  -3.13   0.22
     1.18   1.19  -3.13   3.79  -0.26
    -0.08  -0.08   0.22  -0.26   0.83

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

   The routine computes selected eigenvalues and, optionally, eigenvectors of
   an n-by-n real symmetric 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.
   ========================

 SSYEVX Example Program Results

 The total number of eigenvalues found: 3

 Selected eigenvalues
   0.71   0.82   6.58

 Selected eigenvectors (stored columnwise)
   0.22   0.09  -0.95
   0.21   0.08  -0.04
  -0.52  -0.22  -0.29
  -0.73  -0.21  -0.09
  -0.32   0.94   0.01
*/
#include <stdlib.h>
#include <stdio.h>

/* SSYEVX prototype */
extern void ssyevx( char* jobz, char* range, char* uplo, int* n, float* a,
                int* lda, float* vl, float* vu, int* il, int* iu, float* abstol,
                int* m, float* w, float* z, int* ldz, float* work, int* lwork,
      int* iwork, int* ifail, int* info );
/* Auxiliary routines prototypes */
extern void print_matrix( char* desc, int m, int n, float* a, int lda );

/* Parameters */
#define N 5
#define NSELECT 3
#define LDA N
#define LDZ N

/* Main program */
int main() {
        /* Locals */
        int n = N, il, iu, m, lda = LDA, ldz = LDZ, info, lwork;
        float abstol, vl, vu;
        float wkopt;
        float* work;
        /* Local arrays */
   /* iwork dimension should be at least 5*n */
        int iwork[5*N], ifail[N];
        float w[N], z[LDZ*NSELECT];
        float a[LDA*N] = {
            6.29f,  0.00f,  0.00f,  0.00f,  0.00f,
           -0.39f,  7.19f,  0.00f,  0.00f,  0.00f,
            0.61f,  0.81f,  5.48f,  0.00f,  0.00f,
            1.18f,  1.19f, -3.13f,  3.79f,  0.00f,
           -0.08f, -0.08f,  0.22f, -0.26f,  0.83f
        };
        /* Executable statements */
        printf( " SSYEVX Example Program Results\n" );
        /* Negative abstol means using the default value */
        abstol = -1.0;
        /* Set il, iu to compute NSELECT smallest eigenvalues */
        il = 1;
        iu = NSELECT;
        /* Query and allocate the optimal workspace */
        lwork = -1;
        ssyevx( "Vectors", "Indices", "Upper", &n, a, &lda, &vl, &vu, &il, &iu,
                        &abstol, &m, w, z, &ldz, &wkopt, &lwork, iwork, ifail, &info );
        lwork = (int)wkopt;
        work = (float*)malloc( lwork*sizeof(float) );
        /* Solve eigenproblem */
        ssyevx( "Vectors", "Indices", "Upper", &n, a, &lda, &vl, &vu, &il, &iu,
                        &abstol, &m, w, z, &ldz, work, &lwork, 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_matrix( "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 SSYEVX Example */

/* Auxiliary routine: printing a matrix */
void print_matrix( char* desc, int m, int n, float* 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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