gep_dm_full_chain.c

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

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

int main(int argc, char **argv)
{
    const int n = 3000; // matrix dimension
    const int root = 0; // root rank

    // initialize MPI

    int thread_support;
    MPI_Init_thread(
        &argc, (char ***)&argv, MPI_THREAD_MULTIPLE, &thread_support);

    int world_rank;
    MPI_Comm_rank(MPI_COMM_WORLD, &world_rank);

    // the root node initializes the matrices locally

    int ldA = 0, ldB = 0, ldQ = 0, ldZ = 0, ldC = 0, ldD = 0;
    double *A = NULL, *B = NULL, *Q = NULL, *Z = NULL, *C = NULL, *D = NULL;
    if (world_rank == root) {
        srand((unsigned) time(NULL));

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

        ldA = ((n/8)+1)*8, ldC = ((n/8)+1)*8;
        A = malloc(n*ldA*sizeof(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 a full random matrix B and a copy D

        ldB = ((n/8)+1)*8, ldD = ((n/8)+1)*8;
        B = malloc(n*ldB*sizeof(double));
        D = malloc(n*ldD*sizeof(double));
        for (int j = 0; j < n; j++)
            for (int i = 0; i < n; i++)
                B[j*ldB+i] = D[j*ldD+i] = 2.0*rand()/RAND_MAX - 1.0;

        // generate an identity matrix Q

        ldQ = ((n/8)+1)*8;
        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;

        // generate an identity matrix Z

        ldZ = ((n/8)+1)*8;
        Z = malloc(n*ldZ*sizeof(double));
        for (int j = 0; j < n; j++)
            for (int i = 0; i < n; i++)
                Z[j*ldZ+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));
    double *beta = 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_FAST_DM flag indicates that the library should
    // initialize itself for distributed memory computations and keep StarPU
    // worker threads and StarPU-MPI communication thread awake between
    // interface function calls.

    starneig_node_init(-1, -1, STARNEIG_FAST_DM);

    // create a two-dimensional block cyclic distribution with column-major
    // ordering

    starneig_distr_t distr = starneig_distr_init_mesh(
        -1, -1, STARNEIG_ORDER_COL_MAJOR);

    // Convert the local matrix A to a distributed matrix lA that is owned by
    // the root node. This is done in-place, i.e., the matrices A and lA point
    // to the same data.

    starneig_distr_matrix_t lA = starneig_distr_matrix_create_local(
        n, n, STARNEIG_REAL_DOUBLE, root, A, ldA);

    // create a distributed matrix dA using the earlier created data
    // distribution and default distributed block size

    starneig_distr_matrix_t dA =
        starneig_distr_matrix_create(n, n, -1, -1, STARNEIG_REAL_DOUBLE, distr);

    // copy the local matrix lA to the distributed matrix dA (scatter)

    starneig_distr_matrix_copy(lA, dA);

    // scatter the matrix B

    starneig_distr_matrix_t lB = starneig_distr_matrix_create_local(
        n, n, STARNEIG_REAL_DOUBLE, root, B, ldB);
    starneig_distr_matrix_t dB =
        starneig_distr_matrix_create(n, n, -1, -1, STARNEIG_REAL_DOUBLE, distr);
    starneig_distr_matrix_copy(lB, dB);

    // scatter the matrix Q

    starneig_distr_matrix_t lQ = starneig_distr_matrix_create_local(
        n, n, STARNEIG_REAL_DOUBLE, root, Q, ldQ);
    starneig_distr_matrix_t dQ =
        starneig_distr_matrix_create(n, n, -1, -1, STARNEIG_REAL_DOUBLE, distr);
    starneig_distr_matrix_copy(lQ, dQ);

    // scatter the matrix Z

    starneig_distr_matrix_t lZ = starneig_distr_matrix_create_local(
        n, n, STARNEIG_REAL_DOUBLE, root, Z, ldZ);
    starneig_distr_matrix_t dZ =
        starneig_distr_matrix_create(n, n, -1, -1, STARNEIG_REAL_DOUBLE, distr);
    starneig_distr_matrix_copy(lZ, dZ);

    // reduce the dense-dense matrix pencil (A,B) to Hessenberg-triangular form

    printf("Hessenberg-triangular reduction...\n");
    starneig_GEP_DM_HessenbergTriangular(dA, dB, dQ, dZ);

    // reduce the Hessenberg-triangular matrix pencil (A,B) to generalized Schur
    // form

    printf("Schur reduction...\n");
    starneig_GEP_DM_Schur(dA, dB, dQ, dZ, real, imag, beta);

    // select eigenvalues that have positive a real part

    int num_selected;
    starneig_GEP_DM_Select(dA, dB, &predicate, NULL, select, &num_selected);
    printf("Selected %d eigenvalues out of %d.\n", num_selected, n);

    // reorder selected eigenvalues to the upper left corner of the generalized
    // Schur form (A,B)

    printf("Reordering...\n");
    starneig_GEP_DM_ReorderSchur(select, dA, dB, dQ, dZ, real, imag, beta);

    // copy the distributed matrix dA back to the local matrix lA (gather)

    starneig_distr_matrix_copy(dA, lA);

    // free the distributed matrix lA (matrix A is not freed)

    starneig_distr_matrix_destroy(lA);

    // free the distributed matrix dA (all local resources are freed)

    starneig_distr_matrix_destroy(dA);

    // gather the matrix B

    starneig_distr_matrix_copy(dB, lB);
    starneig_distr_matrix_destroy(lB);
    starneig_distr_matrix_destroy(dB);

    // gather the matrix Q

    starneig_distr_matrix_copy(dQ, lQ);
    starneig_distr_matrix_destroy(lQ);
    starneig_distr_matrix_destroy(dQ);

    // gather the matrix Z

    starneig_distr_matrix_copy(dZ, lZ);
    starneig_distr_matrix_destroy(lZ);
    starneig_distr_matrix_destroy(dZ);

    // free the data distribution

    starneig_distr_destroy(distr);

    // de-initialize the StarNEig library

    starneig_node_finalize();

    // de-initialize MPI

    MPI_Finalize();

    if (world_rank == root) {

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

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

        // check residual || Q B Z^T - D ||_F / || D ||_F

        check_residual(n, ldQ, ldB, ldZ, ldD, Q, B, Z, D);

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

        check_orthogonality(n, ldQ, Q);

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

        check_orthogonality(n, ldZ, Z);
    }

    // cleanup

    free(A);
    free(C);
    free(B);
    free(D);
    free(Q);
    free(Z);

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

    return 0;
}