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Intel® oneAPI Math Kernel Library LAPACK Examples

ID 766877
Date 12/20/2021
Public

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DSYEVR Example Program in C

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/*
   DSYEVR Example.
   ==============

   Program computes the smallest eigenvalues and the corresponding
   eigenvectors of a real symmetric matrix A using the Relatively Robust
   Representations, where A is:

     0.67  -0.20   0.19  -1.06   0.46
    -0.20   3.82  -0.13   1.06  -0.48
     0.19  -0.13   3.27   0.11   1.10
    -1.06   1.06   0.11   5.86  -0.98
     0.46  -0.48   1.10  -0.98   3.54

   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.
   ========================

 DSYEVR Example Program Results

 The total number of eigenvalues found: 3

 Selected eigenvalues
   0.43   2.14   3.37

 Selected eigenvectors (stored columnwise)
  -0.98  -0.01  -0.08
   0.01   0.02  -0.93
   0.04  -0.69  -0.07
  -0.18   0.19   0.31
   0.07   0.69  -0.13
*/
#include <stdlib.h>
#include <stdio.h>

/* DSYEVR prototype */
extern void dsyevr( char* jobz, char* range, char* uplo, int* n, double* a,
                int* lda, double* vl, double* vu, int* il, int* iu, double* abstol,
                int* m, double* w, double* z, int* ldz, int* isuppz, double* work,
                int* lwork, int* iwork, int* liwork, int* info );
/* Auxiliary routines prototypes */
extern void print_matrix( char* desc, int m, int n, double* 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, liwork;
        double abstol, vl, vu;
        int iwkopt;
        int* iwork;
        double wkopt;
        double* work;
        /* Local arrays */
        int isuppz[N];
        double w[N], z[LDZ*NSELECT];
        double a[LDA*N] = {
            0.67,  0.00,  0.00,  0.00,  0.00,
           -0.20,  3.82,  0.00,  0.00,  0.00,
            0.19, -0.13,  3.27,  0.00,  0.00,
           -1.06,  1.06,  0.11,  5.86,  0.00,
            0.46, -0.48,  1.10, -0.98,  3.54
        };
        /* Executable statements */
        printf( " DSYEVR 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;
        liwork = -1;
        dsyevr( "Vectors", "Indices", "Upper", &n, a, &lda, &vl, &vu, &il, &iu,
                        &abstol, &m, w, z, &ldz, isuppz, &wkopt, &lwork, &iwkopt, &liwork,
                        &info );
        lwork = (int)wkopt;
        work = (double*)malloc( lwork*sizeof(double) );
        liwork = iwkopt;
        iwork = (int*)malloc( liwork*sizeof(int) );
        /* Solve eigenproblem */
        dsyevr( "Vectors", "Indices", "Upper", &n, a, &lda, &vl, &vu, &il, &iu,
                        &abstol, &m, w, z, &ldz, isuppz, work, &lwork, iwork, &liwork,
                        &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*)iwork );
        free( (void*)work );
        exit( 0 );
} /* End of DSYEVR 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" );
        }
}