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279 lines
9 KiB
C
279 lines
9 KiB
C
/*
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* BSD 2-Clause License
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*
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* Copyright (c) 2020, Alessandro Capotondi
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions are met:
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*
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* * Redistributions of source code must retain the above copyright notice, this
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* list of conditions and the following disclaimer.
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*
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* * Redistributions in binary form must reproduce the above copyright notice,
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* this list of conditions and the following disclaimer in the documentation
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* and/or other materials provided with the distribution.
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
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* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
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* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
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* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*/
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/**
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* @file jacobi.c
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* @author Alessandro Capotondi
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* @date 27 Mar 2020
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* @brief This code solves the steady state heat equation on a rectangular region.
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* This code solves the steady state heat equation on a rectangular region.
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* The sequential version of this program needs approximately
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* 18/epsilon iterations to complete.
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* The physical region, and the boundary conditions, are suggested
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* by this diagram;
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* W = 0
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* +------------------+
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* | |
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* W = 100 | | W = 100
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* | |
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* +------------------+
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* W = 100
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* The region is covered with a grid of M by N nodes, and an N by N
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* array W is used to record the temperature. The correspondence between
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* array indices and locations in the region is suggested by giving the
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* indices of the four corners:
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* I = 0
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* [0][0]-------------[0][N-1]
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* | |
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* J = 0 | | J = N-1
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* | |
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* [M-1][0]-----------[M-1][N-1]
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* I = M-1
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* The steady state solution to the discrete heat equation satisfies the
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* following condition at an interior grid point:
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* W[Central] = (1/4) * ( W[North] + W[South] + W[East] + W[West] )
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* where "Central" is the index of the grid point, "North" is the index
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* of its immediate neighbor to the "north", and so on.
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*
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* Given an approximate solution of the steady state heat equation, a
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* "better" solution is given by replacing each interior point by the
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* average of its 4 neighbors - in other words, by using the condition
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* as an ASSIGNMENT statement:
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* W[Central] <= (1/4) * ( W[North] + W[South] + W[East] + W[West] )
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* If this process is repeated often enough, the difference between successive
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* estimates of the solution will go to zero.
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* This program carries out such an iteration, using a tolerance specified by
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* the user, and writes the final estimate of the solution to a file that can
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* be used for graphic processing.
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* icensing:
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* This code is distributed under the GNU LGPL license.
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* odified:
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* 18 October 2011
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* uthor:
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* Original C version by Michael Quinn.
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* This C version by John Burkardt.
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* eference:
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* Michael Quinn,
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* Parallel Programming in C with MPI and OpenMP,
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* McGraw-Hill, 2004,
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* ISBN13: 978-0071232654,
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* LC: QA76.73.C15.Q55.
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* ocal parameters:
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* Local, double DIFF, the norm of the change in the solution from one iteration
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* to the next.
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* Local, double MEAN, the average of the boundary values, used to initialize
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* the values of the solution in the interior.
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* Local, double U[M][N], the solution at the previous iteration.
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* Local, double W[M][N], the solution computed at the latest iteration.
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*
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*
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* @see https://en.wikipedia.org/wiki/Jacobi_method
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* @see http://algo.ing.unimo.it/people/andrea/Didattica/HPC/index.html
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*/
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#include <math.h>
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#include <stdio.h>
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#include <stdlib.h>
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#include <string.h>
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#include <sys/time.h>
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#include "utils.h"
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static int N;
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static int MAX_ITERATIONS;
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static int SEED;
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static double CONVERGENCE_THRESHOLD;
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static FILE *data;
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#define SEPARATOR "------------------------------------\n"
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// Return the current time in seconds since the Epoch
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double get_timestamp();
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// Parse command line arguments to set solver parameters
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void parse_arguments(int argc, char *argv[]);
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// Run the Jacobi solver
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// Returns the number of iterations performed
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int run(double *A, double *xtmp)
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{
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int iter = 0, iterations_print = 1;
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double err = 0.0;
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do
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{
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err = 0.0;
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#pragma omp parallel for reduction(max \
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: err) num_threads(NTHREADS)
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for (int i = 1; i < N - 1; i++)
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{
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for (int j = 1; j < N - 1; j++)
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{
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xtmp[i * N + j] = 0.25 * (A[(i - 1) * N + j] + A[(i + 1) * N + j] + A[i * N + j - 1] + A[i * N + j + 1]);
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err = fmax(err, fabs(xtmp[i * N + j] - A[i * N + j]));
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}
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}
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#pragma omp parallel for num_threads(NTHREADS)
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for (int i = 0; i < N; i++)
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{
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for (int j = 0; j < N; j++)
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{
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A[i * N + j] = xtmp[i * N + j];
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}
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}
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iter++;
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#ifdef DEBUG
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if (iter == iterations_print)
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{
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printf(" %8d %f\n", iter, err);
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iterations_print = 2 * iterations_print;
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}
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#endif
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} while (err > CONVERGENCE_THRESHOLD && iter < MAX_ITERATIONS);
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return iter;
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}
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int main(int argc, char *argv[])
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{
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parse_arguments(argc, argv);
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double *A = malloc(N * N * sizeof(double));
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double *xtmp = malloc(N * N * sizeof(double));
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printf(SEPARATOR);
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printf("Matrix size: %dx%d\n", N, N);
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printf("Maximum iterations: %d\n", MAX_ITERATIONS);
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printf("Convergence threshold: %lf\n", CONVERGENCE_THRESHOLD);
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printf(SEPARATOR);
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for (int ii = 0; ii < N; ii++)
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{
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for (int jj = 0; jj < N; jj++)
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{
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double f;
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fread(&f, sizeof(double), 1, data);
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A[ii * N + jj] = f;
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}
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}
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// Run Jacobi solver
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start_timer();
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int itr = run(A, xtmp);
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stop_timer();
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printf("Iterations = %d\n", itr);
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printf("Solver runtime = %lf ms\n", elapsed_ns() / 1E6);
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if (itr == MAX_ITERATIONS)
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printf("WARNING: solution did not converge\n");
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printf(SEPARATOR);
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free(A);
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free(xtmp);
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fclose(data);
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return 0;
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}
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int parse_int(const char *str)
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{
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char *next;
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int value = strtoul(str, &next, 10);
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return strlen(next) ? -1 : value;
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}
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double parse_double(const char *str)
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{
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char *next;
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double value = strtod(str, &next);
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return strlen(next) ? -1 : value;
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}
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void parse_arguments(int argc, char *argv[])
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{
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// Set default values
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N = 500;
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MAX_ITERATIONS = 2000;
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CONVERGENCE_THRESHOLD = 0.001;
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SEED = 0;
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for (int i = 1; i < argc; i++)
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{
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if (!strcmp(argv[i], "--convergence") || !strcmp(argv[i], "-c"))
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{
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if (++i >= argc || (CONVERGENCE_THRESHOLD = parse_double(argv[i])) < 0)
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{
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printf("Invalid convergence threshold\n");
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exit(1);
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}
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}
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else if (!strcmp(argv[i], "--iterations") || !strcmp(argv[i], "-i"))
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{
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if (++i >= argc || (MAX_ITERATIONS = parse_int(argv[i])) < 0)
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{
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printf("Invalid number of iterations\n");
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exit(1);
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}
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}
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else if (!strcmp(argv[i], "--norder") || !strcmp(argv[i], "-n"))
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{
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if (++i >= argc || (N = parse_int(argv[i])) < 0)
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{
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printf("Invalid matrix order\n");
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exit(1);
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}
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}
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else if (!strcmp(argv[i], "--help") || !strcmp(argv[i], "-h"))
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{
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printf("\n");
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printf("Usage: ./jacobi [OPTIONS]\n\n");
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printf("Options:\n");
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printf(" -h --help Print this message\n");
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printf(" -c --convergence C Set convergence threshold\n");
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printf(" -i --iterations I Set maximum number of iterations\n");
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printf(" -n --norder N Set maxtrix order (500 or 1000)\n");
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printf("\n");
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exit(0);
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}
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else
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{
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printf("Unrecognized argument '%s' (try '--help')\n", argv[i]);
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exit(1);
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}
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}
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if (N == 1000)
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data = fopen("data/jacobi-1000.bin", "rb");
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else if (N == 500)
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data = fopen("data/jacobi-500.bin", "rb");
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else
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{
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printf("Invalid matrix order\n");
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exit(1);
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}
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}
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