forked from TASC/HLRS-OpenMP-GPU-2024
289 lines
8.3 KiB
C
289 lines
8.3 KiB
C
#include <stdio.h>
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#include <stdlib.h>
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#include <string.h>
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#include <unistd.h>
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#include <errno.h>
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#include <assert.h>
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#include <sys/time.h>
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#include <sys/times.h>
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#include <math.h>
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#include <mkl.h>
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#include "omp.h"
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#if !defined(_OPENMP)
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int omp_get_max_threads() { return 1; }
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int omp_get_num_threads() { return 1; }
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#endif
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void cholesky(int ts, int nt, double* Ah[nt][nt])
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{
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#ifdef VERBOSE
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printf("> Computing Cholesky Factorization: indirect blocked matrix...\n");
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#endif
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for (int k = 0; k < nt; k++) {
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// Diagonal Block factorization: using LAPACK
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LAPACKE_dpotrf(LAPACK_COL_MAJOR, 'L', ts, Ah[k][k], ts);
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// Triangular systems
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for (int i = k + 1; i < nt; i++) {
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cblas_dtrsm(CblasColMajor, CblasRight, CblasLower, CblasTrans, CblasNonUnit, ts, ts, 1.0, Ah[k][k], ts, Ah[k][i], ts);
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}
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// Update trailing matrix
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for (int i = k + 1; i < nt; i++) {
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for (int j = k + 1; j < i; j++) {
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cblas_dgemm(CblasColMajor, CblasNoTrans, CblasTrans, ts, ts, ts, -1.0, Ah[k][i], ts, Ah[k][j], ts, 1.0, Ah[j][i], ts);
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}
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cblas_dsyrk(CblasColMajor, CblasLower, CblasNoTrans, ts, ts, -1.0, Ah[k][i], ts, 1.0, Ah[i][i], ts);
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}
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}
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#ifdef VERBOSE
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printf("> ...end of Cholesky Factorization.\n");
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#endif
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}
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float get_time()
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{
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static double gtod_ref_time_sec = 0.0;
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struct timeval tv;
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gettimeofday(&tv, NULL);
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// If this is the first invocation of through dclock(), then initialize the
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// "reference time" global variable to the seconds field of the tv struct.
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if (gtod_ref_time_sec == 0.0) gtod_ref_time_sec = (double) tv.tv_sec;
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// Normalize the seconds field of the tv struct so that it is relative to the
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// "reference time" that was recorded during the first invocation of dclock().
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const double norm_sec = (double) tv.tv_sec - gtod_ref_time_sec;
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// Compute the number of seconds since the reference time.
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const double t = norm_sec + tv.tv_usec * 1.0e-6;
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return (float) t;
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}
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// Robust Check the factorization of the matrix A2
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// Using directly Fortran services: dlacpy_, dtrmm, dlange_
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static int check_factorization(int N, double *A1, double *A2, int LDA, char uplo, double eps)
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{
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#ifdef VERBOSE
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printf("> Checking the Cholesky Factorization... \n");
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#endif
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char NORM = 'I', ALL = 'A', UP = 'U', LO = 'L', TR = 'T', NU = 'N', RI = 'R';
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double *Residual = (double *) malloc(N*N*sizeof(double));
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double *L1 = (double *) malloc(N*N*sizeof(double));
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double *L2 = (double *) malloc(N*N*sizeof(double));
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double *work = (double *) malloc(N*sizeof(double));
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memset((void*)L1, 0, N*N*sizeof(double));
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memset((void*)L2, 0, N*N*sizeof(double));
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double alpha= 1.0;
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dlacpy_(&ALL, &N, &N, A1, &LDA, Residual, &N);
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/* Dealing with L'L or U'U */
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if (uplo == 'U'){
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dlacpy_(&UP, &N, &N, A2, &LDA, L1, &N);
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dlacpy_(&UP, &N, &N, A2, &LDA, L2, &N);
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dtrmm(&LO, &uplo, &TR, &NU, &N, &N, &alpha, L1, &N, L2, &N);
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} else{
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dlacpy_(&LO, &N, &N, A2, &LDA, L1, &N);
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dlacpy_(&LO, &N, &N, A2, &LDA, L2, &N);
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dtrmm(&RI, &LO, &TR, &NU, &N, &N, &alpha, L1, &N, L2, &N);
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}
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/* Compute the Residual || A -L'L|| */
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for (int i = 0; i < N; i++)
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for (int j = 0; j < N; j++)
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Residual[j*N+i] = L2[j*N+i] - Residual[j*N+i];
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double Rnorm = dlange_(&NORM, &N, &N, Residual, &N, work);
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double Anorm = dlange_(&NORM, &N, &N, A1, &N, work);
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#ifdef VERBOSE
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printf("> - ||L'L-A||_oo/(||A||_oo.N.eps) = %e \n",Rnorm / (Anorm*N*eps));
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#endif
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const int info_factorization = isnan(Rnorm/(Anorm*N*eps)) || isinf(Rnorm/(Anorm*N*eps)) || (Rnorm/(Anorm*N*eps) > 60.0);
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#ifdef VERBOSE
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if ( info_factorization) printf("> - Factorization is suspicious!\n");
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else printf("> - Factorization is CORRECT!\n");
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#endif
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free(Residual); free(L1); free(L2); free(work);
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return info_factorization;
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}
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void initialize_matrix(const int n, const int ts, double *matrix)
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{
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#ifdef VERBOSE
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printf("> Initializing matrix with random values...\n");
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#endif
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int ISEED[4] = {0,0,0,1};
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int intONE=1;
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for (int i = 0; i < n*n; i+=n) {
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dlarnv_(&intONE, &ISEED[0], &n, &matrix[i]);
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}
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for (int i=0; i<n; i++) {
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for (int j=0; j<n; j++) {
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matrix[j*n+i] = matrix[j*n+i] + matrix[i*n+j];
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matrix[i*n+j] = matrix[j*n+i];
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}
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}
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// Diagonal values
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for (int i = 0; i < n; i++) {
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matrix[i*n+i] += (double) n;
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}
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}
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void gather_block(const int N, const int ts, double *Alin, double *A)
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{
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for (int i = 0; i < ts; i++)
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for (int j = 0; j < ts; j++) {
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A[i*ts + j] = Alin[i*N + j];
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}
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}
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void scatter_block(const int N, const int ts, double *A, double *Alin)
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{
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for (int i = 0; i < ts; i++)
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for (int j = 0; j < ts; j++) {
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Alin[i*N + j] = A[i*ts + j];
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}
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}
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void convert_to_blocks(const int ts, const int DIM, const int N, double Alin[N][N], double *A[DIM][DIM])
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{
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#ifdef VERBOSE
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printf("> Converting linear matrix to blocks...\n");
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#endif
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for (int i = 0; i < DIM; i++)
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for (int j = 0; j < DIM; j++) {
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gather_block ( N, ts, &Alin[i*ts][j*ts], A[i][j]);
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}
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}
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void convert_to_linear(const int ts, const int DIM, const int N, double *A[DIM][DIM], double Alin[N][N])
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{
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#ifdef VERBOSE
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printf("> Converting blocked matrix to linear...\n");
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#endif
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for (int i = 0; i < DIM; i++)
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for (int j = 0; j < DIM; j++) {
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scatter_block ( N, ts, A[i][j], (double *) &Alin[i*ts][j*ts]);
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}
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}
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int main(int argc, char* argv[])
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{
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char *result[3] = {"n/a","pass","FAIL"};
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const double eps = pow(2.0, -53);
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// If number of arguments is not 4, print help
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if ( argc != 4) {
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printf( "%s: matrix_size block_size check[0|1]?\n", argv[0] );
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exit( -1 );
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}
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const int n = atoi(argv[1]); // matrix size
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const int ts = atoi(argv[2]); // tile size
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int check = atoi(argv[3]); // check result?
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// Compute number of tiles
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const int nt = n / ts;
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assert((nt*ts) == n); // tile size should divide size
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// Allocate matrix
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double * const matrix = (double *) malloc(n * n * sizeof(double));
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assert(matrix != NULL);
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// Initialize matrix
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initialize_matrix(n, ts, matrix);
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// Allocate original matrix, and duplicate it, for debugging purposes
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double * const original_matrix = (double *) malloc(n * n * sizeof(double));
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assert(original_matrix != NULL);
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// Save a copy of the original matrix
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for (int i = 0; i < n * n; i++ ) {
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original_matrix[i] = matrix[i];
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}
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// Set version description: Indirect blocked matrix
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const char *version = "I-Blocked matrix";
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// Allocate blocked matrix
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double *Ah[nt][nt];
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for (int i = 0; i < nt; i++) {
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for (int j = 0; j < nt; j++) {
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Ah[i][j] = malloc(ts * ts * sizeof(double));
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assert(Ah[i][j] != NULL);
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}
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}
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// ---------------------------------------
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// Convert, compute (time), and re-convert
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// ---------------------------------------
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convert_to_blocks(ts, nt, n, (double(*)[n]) matrix, Ah);
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const float tref = get_time();
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cholesky(ts, nt, (double* (*)[nt]) Ah);
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const float time = get_time() - tref;
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convert_to_linear(ts, nt, n, Ah, (double (*)[n]) matrix);
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// Free blocked matrix
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for (int i = 0; i < nt; i++) {
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for (int j = 0; j < nt; j++) {
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assert(Ah[i][j] != NULL);
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free(Ah[i][j]);
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}
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}
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// Check result, if requested
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if ( check ) {
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const char uplo = 'L';
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if ( check_factorization( n, original_matrix, matrix, n, uplo, eps) ) check++;
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}
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// Free original matrix, not needed anymore
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free(original_matrix);
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// Compute GFLOPs (Not verified)
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float gflops = (((1.0 / 3.0) * n * n * n) / ((time) * 1.0e+9));
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// Print results
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#ifdef VERBOSE
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printf( "\n" );
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printf( "============ CHOLESKY RESULTS ============\n" );
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printf( " test %s\n", argv[0]);
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printf( " version %s\n", version);
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printf( " matrix size: %dx%d\n", n, n);
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printf( " tile size: %dx%d\n", ts, ts);
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printf( " number of threads: %d\n", omp_get_max_threads());
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printf( " time (s): %f\n", time);
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printf( " performance (gflops): %f\n", gflops);
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printf( " check: %s\n", result[check]);
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printf( "==========================================\n" );
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#else
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printf("test, %s, version, %s, n, %d, ts, %d, num_threads, %d, gflops, %f, time, %f, check, %s\n", argv[0], version, n, ts, omp_get_max_threads(), gflops, time, result[check]);
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#endif
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// Free matrix
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free(matrix);
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return 0;
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}
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