sep_sm_full_chain.c

#include "validate.h"
#include <stdlib.h>
#include <stdio.h>
#include <time.h>
#include <starneig/starneig.h>

// a predicate function that selects all eigenvalues that have positive a real
// part
static int predicate(double real, double imag, void *arg)
{
    if (0.0 < real)
        return 1;
    return 0;
}

int main()
{
    const int n = 3000; // matrix dimension

    srand((unsigned) time(NULL));

    // generate a full random matrix A and a copy C

    int ldA = ((n/8)+1)*8, ldC = ((n/8)+1)*8;
    double *A = malloc(n*ldA*sizeof(double));
    double *C = malloc(n*ldC*sizeof(double));
    for (int j = 0; j < n; j++)
        for (int i = 0; i < n; i++)
            A[j*ldA+i] = C[j*ldC+i] = 2.0*rand()/RAND_MAX - 1.0;

    // generate an identity matrix Q

    int ldQ = ((n/8)+1)*8;
    double *Q = malloc(n*ldA*sizeof(double));
    for (int j = 0; j < n; j++)
        for (int i = 0; i < n; i++)
            Q[j*ldQ+i] = i == j ? 1.0 : 0.0;

    // allocate space for the eigenvalues and the eigenvalue selection vector

    double *real = malloc(n*sizeof(double));
    double *imag = malloc(n*sizeof(double));
    int *select = malloc(n*sizeof(int));

    // Initialize the StarNEig library using a default number of CPU cores and
    // GPUs. The STARNEIG_HINT_SM flag indicates that the library should
    // initialize itself for shared memory computations.

    starneig_node_init(-1, -1, STARNEIG_HINT_SM);

    // reduce the full matrix matrix A to upper Hessenberg form

    printf("Hessenberg reduction...\n");
    starneig_SEP_SM_Hessenberg(n, A, ldA, Q, ldQ);

    // reduce the upper Hessenberg matrix A to Schur form

    printf("Schur reduction...\n");
    starneig_SEP_SM_Schur(n, A, ldA, Q, ldQ, real, imag);

    // select eigenvalues that have positive a real part

    int num_selected;
    starneig_SEP_SM_Select(n, A, ldA, &predicate, NULL, select, &num_selected);
    printf("Selected %d eigenvalues out of %d.\n", num_selected, n);

    // reorder the selected eigenvalues to the upper left corner of the matrix A

    printf("Reordering...\n");
    starneig_SEP_SM_ReorderSchur(n, select, A, ldA, Q, ldQ, real, imag);

    // de-initialize the StarNEig library

    starneig_node_finalize();

    // check residual || Q A Q^T - C ||_F / || C ||_F

    check_residual(n, ldQ, ldA, ldQ, ldC, Q, A, Q, C);

    // check residual || Q Q^T - I ||_F / || I ||_F

    check_orthogonality(n, ldQ, Q);

    // cleanup

    free(A);
    free(C);
    free(Q);

    free(real);
    free(imag);
    free(select);

    return 0;
}