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main.c
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main.c
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#include <math.h>
#include <stdlib.h>
#include <stdio.h>
#include <string.h>
#include "mpi.h"
#include "global.h"
int tag = 99;
int exit_tag = 10;
typedef struct _range {
int begin;
int end;
} range;
void print_vector(double *x, int n)
{
for (int i = 0; i < n; i++)
printf("%f\n", x[i]);
}
double mul_matrix_row_ind(matrix *m, double *vector, int row_ind)
{
int cur_row_start = m->row_start_ind[row_ind];
int cur_row_end = row_ind < m->n-1 ? m->row_start_ind[row_ind+1] : m->nelements;
double result = 0.0;
for (int i = cur_row_start; i < cur_row_end; i++)
result += m->vals[i]*vector[m->col_ind[i]];
return result;
}
void mul_matrix_row(matrix *m, double *vector, double *out, int start_row, int end_row)
{
for (int i = start_row; i < end_row; i++)
out[i] = mul_matrix_row_ind(m, vector, i);
}
void forward_subst(matrix *m, double *x, double *b)
{
int el_ind = 0;
int col = 0;
x[0] = b[0]/m->vals[el_ind];
for (int i = 1; i < m->n; i++)
{
el_ind = m->row_start_ind[i];
col = m->col_ind[el_ind];
double accumulated = 0.0;
while (col < i)
{
accumulated += m->vals[el_ind]*x[col];
el_ind++;
col = m->col_ind[el_ind];
}
x[i] = (b[i]-accumulated)/m->vals[el_ind];
}
}
int find_diag_el_ind(matrix *a, int row)
{
int el_ind = a->row_start_ind[row];
while (a->col_ind[el_ind] < row)
el_ind++;
return el_ind;
}
matrix get_iterative_lower_matrix(matrix *a, double w)
{
matrix it_matrix;
matrix am = *a;
it_matrix.vals = malloc(am.nelements*sizeof(double));
it_matrix.col_ind = malloc(am.nelements*sizeof(int));
it_matrix.row_start_ind = malloc(am.n*sizeof(int));
it_matrix.n = am.n;
int it_el_ind = 0;
for (int i = 0; i < am.n; i++)
{
int diag_el_ind = find_diag_el_ind(a, i);
double diag_el_value = am.vals[diag_el_ind];
it_matrix.row_start_ind[i] = it_el_ind;
for (int j = am.row_start_ind[i]; j < diag_el_ind; j++)
{
it_matrix.vals[it_el_ind] = w*am.vals[j]/diag_el_value;
it_matrix.col_ind[it_el_ind] = am.col_ind[j];
it_el_ind++;
}
it_matrix.vals[it_el_ind] = 1;
it_matrix.col_ind[it_el_ind] = i;
it_el_ind++;
}
it_matrix.nelements = it_el_ind;
return it_matrix;
}
matrix get_iterative_upper_matrix(matrix *a, double w)
{
matrix *it_matrix_upper = malloc(sizeof(*it_matrix_upper));
matrix it_matrix = *it_matrix_upper;
matrix am = *a;
it_matrix.col_ind = malloc(am.nelements*sizeof(int));
it_matrix.row_start_ind = malloc(am.n*sizeof(int));
it_matrix.vals = malloc(am.nelements*sizeof(double));
it_matrix.n = am.n;
int it_el_ind = 0;
for (int i = 0; i < am.n-1; i++)
{
int diag_el_ind = find_diag_el_ind(a, i);
double diag_el_value = am.vals[diag_el_ind];
it_matrix.row_start_ind[i] = it_el_ind;
it_matrix.vals[it_el_ind] = 1-w;
it_matrix.col_ind[it_el_ind] = i;
it_el_ind++;
for (int j = diag_el_ind+1; j < am.row_start_ind[i+1]; j++)
{
it_matrix.vals[it_el_ind] = -w*am.vals[j]/diag_el_value;
it_matrix.col_ind[it_el_ind] = am.col_ind[j];
it_el_ind++;
}
}
it_matrix.vals[it_el_ind] = 1-w;
it_matrix.col_ind[it_el_ind] = am.n-1;
it_matrix.nelements = it_el_ind+1;
it_matrix.row_start_ind[am.n-1] = it_el_ind;
return it_matrix;
}
double* get_iterative_vector(matrix *a, double w, double *b)
{
double *it_vec = malloc(a->n*sizeof(double));
for (int i = 0; i < a->n; i++)
{
int diag_el_ind = find_diag_el_ind(a, i);
double diag_el_val = a->vals[diag_el_ind];
it_vec[i] = w*b[i]/diag_el_val;
}
return it_vec;
}
void add_vector(double *x, double *b, int n)
{
for (int i = 0; i < n; i++)
x[i] += b[i];
}
void solve(matrix *a, double *x, double *b)
{
double w = 1.0;
int steps = 1000;
double *it_vec = get_iterative_vector(a, w, b);
matrix upper = get_iterative_upper_matrix(a, w);
matrix lower = get_iterative_lower_matrix(a, w);
double *z = malloc(a->n*sizeof(*z));
for (int i = 0; i < steps; i++)
{
mul_matrix_row(&upper, x, z, 0, a->n);
add_vector(z, it_vec, a->n);
forward_subst(&lower, x, z);
}
}
range compute_range(int nrows, int nchild, int child_id)
{
range r;
int rows_per_child = nrows / nchild;
int rest = nrows % nchild;
r.begin = child_id * rows_per_child +
(child_id < rest ? child_id : rest);
r.end = r.begin + rows_per_child + (child_id < rest ? 1 : 0);
return r;
}
void send_matrix(matrix send, int child_id)
{
MPI_Send(&send.n, 1, MPI_INT, child_id, tag, MPI_COMM_WORLD);
MPI_Send(&send.nelements, 1, MPI_INT, child_id, tag, MPI_COMM_WORLD);
MPI_Send(send.vals, send.nelements, MPI_DOUBLE, child_id, tag, MPI_COMM_WORLD);
MPI_Send(send.col_ind, send.nelements, MPI_INT, child_id, tag, MPI_COMM_WORLD);
MPI_Send(send.row_start_ind, send.n, MPI_INT, child_id, tag, MPI_COMM_WORLD);
}
void send_values(double *v, int n, int child_id)
{
MPI_Send(&n, 1, MPI_INT, child_id, tag, MPI_COMM_WORLD);
MPI_Send(v, n, MPI_DOUBLE, child_id, tag, MPI_COMM_WORLD);
}
int receive_vector (values v)
{
MPI_Status status;
MPI_Recv(&v.n, 1, MPI_INT, 0, MPI_ANY_TAG, MPI_COMM_WORLD, &status );
if (status.MPI_TAG == exit_tag)
return exit_tag;
MPI_Recv(v.v, v.n, MPI_DOUBLE, 0, MPI_ANY_TAG, MPI_COMM_WORLD, &status );
return status.MPI_TAG;
}
void wait_for_results(double *z, int n, int nproc, int child_id)
{
MPI_Status status;
range r = compute_range(n, nproc, child_id);
MPI_Recv(z+r.begin, r.end-r.begin, MPI_DOUBLE, child_id, tag, MPI_COMM_WORLD, &status);
}
void terminate_children (int nproc)
{
// MPI_Abort(MPI_COMM_WORLD, 0);
for (int i = 1; i < nproc; i++)
MPI_Send(NULL, 0, MPI_DOUBLE, i, exit_tag, MPI_COMM_WORLD);
}
void solve_parallel(matrix *a, double *x, double *b, int nproc, int steps)
{
double w = 1.0;
double *it_vec = get_iterative_vector(a, w, b);
matrix upper = get_iterative_upper_matrix(a, w);
matrix lower = get_iterative_lower_matrix(a, w);
double *z = malloc(a->n*sizeof(*z));
for (int i = 1; i < nproc; i++)
send_matrix(upper, i);
for (int s = 0; s < steps; s++)
{
for (int i = 1; i < nproc; i++)
send_values(x, a->n, i);
range r = compute_range(a->n, nproc, 0);
mul_matrix_row(&upper, x, z, r.begin, r.end);
for (int i = 1; i < nproc; i++)
wait_for_results(z, a->n, nproc, i);
add_vector(z, it_vec, a->n);
forward_subst(&lower, x, z);
}
terminate_children(nproc);
}
matrix receive_matrix()
{
matrix rec;
MPI_Status status;
MPI_Recv(&rec.n, 1, MPI_INT, 0, tag, MPI_COMM_WORLD, &status );
MPI_Recv(&rec.nelements, 1, MPI_INT, 0, tag, MPI_COMM_WORLD, &status );
rec.vals = malloc(rec.nelements*sizeof(double));
rec.col_ind = malloc(rec.nelements*sizeof(int));
rec.row_start_ind = malloc(rec.n*sizeof(int));
MPI_Recv(rec.vals, rec.nelements, MPI_DOUBLE, 0, tag, MPI_COMM_WORLD, &status );
MPI_Recv(rec.col_ind, rec.nelements, MPI_INT, 0, tag, MPI_COMM_WORLD, &status );
MPI_Recv(rec.row_start_ind, rec.n, MPI_INT, 0, tag, MPI_COMM_WORLD, &status );
return rec;
}
double* initialize_x(int n, double initial_value)
{
double *x = malloc(n*sizeof(double));
for (int i = 0; i < n; i++)
x[i] = initial_value;
return x;
}
int main(int argc, char *argv[])
{
#ifndef DEBUG
int nproc;
int rank;
MPI_Init(&argc, &argv);
MPI_Comm_size(MPI_COMM_WORLD, &nproc);
MPI_Comm_rank(MPI_COMM_WORLD, &rank);
if (rank == 0)
{
FILE *fm = argc > 1 ? fopen(argv[1], "r") : fopen("matrixA.dat", "r");
FILE *fv = argc > 2 ? fopen(argv[2], "r") : fopen("vectorB.dat", "r");
int steps = argc > 3 ? atof(argv[3]) : 1;
matrix a = create_matrix_from_file(fm);
values b = create_vector_from_file(fv);
double *x = initialize_x(a.n, 0.0);
solve_parallel(&a, x, b.v, nproc, steps);
print_vector(x, a.n);
}
else
{
matrix m = receive_matrix();
double *z = malloc(m.n*sizeof(*z));
values v;
v.n = m.n;
v.v = malloc(v.n*sizeof(*v.v));
while (1) {
if (receive_vector(v) == exit_tag)
break;
range r = compute_range(v.n, nproc, rank);
mul_matrix_row(&m, v.v, z, r.begin, r.end);
MPI_Send(z+r.begin, r.end-r.begin, MPI_DOUBLE, 0, tag, MPI_COMM_WORLD);
}
}
MPI_Finalize();
#endif
#ifdef DEBUG
// test();
FILE *fm = argc > 1 ? fopen(argv[1], "r") : fopen("matrixA.dat", "r");
FILE *fv = argc > 2 ? fopen(argv[2], "r") : fopen("vectorB.dat", "r");
matrix m = create_matrix_from_file(fm);
values vector = create_vector_from_file(fv);
double *x = initialize_x(m.n, 0.0);
solve(&m, x, vector.v);
print_vector(x, m.n);
#endif
return 0;
}