starpu-max/examples/lu/lu_example.c

/*
 * StarPU
 * Copyright (C) INRIA 2008-2009 (see AUTHORS file)
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU Lesser General Public License as published by
 * the Free Software Foundation; either version 2.1 of the License, or (at
 * your option) any later version.
 *
 * This program is distributed in the hope that it will be useful, but
 * WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
 *
 * See the GNU Lesser General Public License in COPYING.LGPL for more details.
 */

#include <stdlib.h>
#include <stdio.h>
#include <string.h>
#include <time.h>
#include <math.h>
#include <starpu.h>

#include "xlu.h"
#include "xlu_kernels.h"

static unsigned long size = 16384;
static unsigned nblocks = 16;
static unsigned check = 0;
static unsigned pivot = 0;
static unsigned no_stride = 0;

TYPE *A, *A_saved;

/* in case we use non-strided blocks */
TYPE **A_blocks;

static void parse_args(int argc, char **argv)
{
	int i;
	for (i = 1; i < argc; i++) {
		if (strcmp(argv[i], "-size") == 0) {
			char *argptr;
			size = strtol(argv[++i], &argptr, 10);
		}

		if (strcmp(argv[i], "-nblocks") == 0) {
			char *argptr;
			nblocks = strtol(argv[++i], &argptr, 10);
		}

		if (strcmp(argv[i], "-check") == 0) {
			check = 1;
		}

		if (strcmp(argv[i], "-piv") == 0) {
			pivot = 1;
		}

		if (strcmp(argv[i], "-no-stride") == 0) {
			no_stride = 1;
		}

	}
}

static void display_matrix(TYPE *m, unsigned n, unsigned ld, char *str)
{
#if 0
	fprintf(stderr, "***********\n");
	fprintf(stderr, "Display matrix %s\n", str);
	unsigned i,j;
	for (j = 0; j < n; j++)
	{
		for (i = 0; i < n; i++)
		{
			fprintf(stderr, "%2.2f\t", m[i+j*ld]);
		}
		fprintf(stderr, "\n");
	}
	fprintf(stderr, "***********\n");
#endif
}

void copy_blocks_into_matrix(void)
{
	unsigned blocksize = (size/nblocks);

	unsigned i, j;
	unsigned bi, bj;
	for (bj = 0; bj < nblocks; bj++)
	for (bi = 0; bi < nblocks; bi++)
	{
		for (j = 0; j < blocksize; j++)
		for (i = 0; i < blocksize; i++)
		{
			A[(i+bi*blocksize) + (j + bj*blocksize)*size] =
				A_blocks[bi+nblocks*bj][i + j * blocksize];
		}

		//free(A_blocks[bi+nblocks*bj]);
	}
}



void copy_matrix_into_blocks(void)
{
	unsigned blocksize = (size/nblocks);

	unsigned i, j;
	unsigned bi, bj;
	for (bj = 0; bj < nblocks; bj++)
	for (bi = 0; bi < nblocks; bi++)
	{
		starpu_malloc_pinned_if_possible((void **)&A_blocks[bi+nblocks*bj], (size_t)blocksize*blocksize*sizeof(TYPE));

		for (j = 0; j < blocksize; j++)
		for (i = 0; i < blocksize; i++)
		{
			A_blocks[bi+nblocks*bj][i + j * blocksize] =
			A[(i+bi*blocksize) + (j + bj*blocksize)*size];
		}
	}
}

static void init_matrix(void)
{
	/* allocate matrix */
	starpu_malloc_pinned_if_possible((void **)&A, (size_t)size*size*sizeof(TYPE));
	STARPU_ASSERT(A);

	starpu_srand48((long int)time(NULL));
	//starpu_srand48(0);

	/* initialize matrix content */
	unsigned long i,j;
	for (j = 0; j < size; j++)
	{
		for (i = 0; i < size; i++)
		{
			A[i + j*size] = (TYPE)starpu_drand48();
		}
	}

}

static void save_matrix(void)
{
	A_saved = malloc((size_t)size*size*sizeof(TYPE));
	STARPU_ASSERT(A_saved);

	memcpy(A_saved, A, (size_t)size*size*sizeof(TYPE));
}

static double frobenius_norm(TYPE *v, unsigned n)
{
	double sum2 = 0.0;

	/* compute sqrt(Sum(|x|^2)) */

	unsigned i,j;
	for (j = 0; j < n; j++)
	for (i = 0; i < n; i++)
	{
		double a = fabsl((double)v[i+n*j]);
		sum2 += a*a;
	}

	return sqrt(sum2);
}

static pivot_saved_matrix(unsigned *ipiv)
{
	unsigned k;
	for (k = 0; k < size; k++)
	{
		if (k != ipiv[k])
		{
	//		fprintf(stderr, "SWAP %d and %d\n", k, ipiv[k]);
			CPU_SWAP(size, &A_saved[k*size], 1, &A_saved[ipiv[k]*size], 1);
		}
	}
}

static void check_result(void)
{
	unsigned i,j;
	TYPE *L, *U;

	L = malloc((size_t)size*size*sizeof(TYPE));
	U = malloc((size_t)size*size*sizeof(TYPE));

	memset(L, 0, size*size*sizeof(TYPE));
	memset(U, 0, size*size*sizeof(TYPE));

	/* only keep the lower part */
	for (j = 0; j < size; j++)
	{
		for (i = 0; i < j; i++)
		{
			L[j+i*size] = A[j+i*size];
		}

		/* diag i = j */
		L[j+j*size] = A[j+j*size];
		U[j+j*size] = 1.0;

		for (i = j+1; i < size; i++)
		{
			U[j+i*size] = A[j+i*size];
		}
	}

	display_matrix(L, size, size, "L");
	display_matrix(U, size, size, "U");

	/* now A_err = L, compute L*U */
	CPU_TRMM("R", "U", "N", "U", size, size, 1.0f, U, size, L, size);

	display_matrix(A_saved, size, size, "P A_saved");
	display_matrix(L, size, size, "LU");

	/* compute "LU - A" in L*/
	CPU_AXPY(size*size, -1.0, A_saved, 1, L, 1);
	display_matrix(L, size, size, "Residuals");
	
	TYPE err = CPU_ASUM(size*size, L, 1);
	int max = CPU_IAMAX(size*size, L, 1);

	fprintf(stderr, "Avg error : %e\n", err/(size*size));
	fprintf(stderr, "Max error : %e\n", L[max]);

	double residual = frobenius_norm(L, size);
	double matnorm = frobenius_norm(A_saved, size);

	fprintf(stderr, "||%sA-LU|| / (||A||*N) : %e\n", pivot?"P":"", residual/(matnorm*size));

	if (residual/(matnorm*size) > 1e-5)
		exit(-1);
}

int main(int argc, char **argv)
{
	parse_args(argc, argv);

	starpu_init(NULL);

	starpu_helper_init_cublas();

	init_matrix();

	unsigned *ipiv;
	if (check)
		save_matrix();

	display_matrix(A, size, size, "A");

	/* Factorize the matrix (in place) */
	if (pivot)
	{
 		ipiv = malloc(size*sizeof(unsigned));
		if (no_stride)
		{
			/* in case the LU decomposition uses non-strided blocks, we _copy_ the matrix into smaller blocks */
			A_blocks = malloc(nblocks*nblocks*sizeof(TYPE **));
			copy_matrix_into_blocks();

			STARPU_LU(lu_decomposition_pivot_no_stride)(A_blocks, ipiv, size, size, nblocks);

			copy_blocks_into_matrix();
			free(A_blocks);
		}
		else 
		{
			struct timeval start;
			struct timeval end;

			gettimeofday(&start, NULL);

			STARPU_LU(lu_decomposition_pivot)(A, ipiv, size, size, nblocks);
	
			gettimeofday(&end, NULL);

			double timing = (double)((end.tv_sec - start.tv_sec)*1000000 + (end.tv_usec - start.tv_usec));
			
			unsigned n = size;
			double flop = (2.0f*n*n*n)/3.0f;
			fprintf(stderr, "Synthetic GFlops (TOTAL) : \n");
			fprintf(stdout, "%d	%6.2f\n", n, (flop/timing/1000.0f));
		}
	}
	else
	{
		STARPU_LU(lu_decomposition)(A, size, size, nblocks);
	}

	if (check)
	{
		if (pivot)
			pivot_saved_matrix(ipiv);

		check_result();
	}

	starpu_helper_shutdown_cublas();

	starpu_shutdown();

	return 0;
}