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#include <stdio.h>
#include <stdlib.h>
#include <omp.h>
#include <time.h>
double mul_vector_transpose_vector(double* v1, double* v2, int n) {
int i;
double result = 0;
#pragma omp parallel for reduction(+:result)
for (i = 0; i < n; i++) {
result += v1[i] * v2[i];
}
return result;
}
double* matrix_mul_vector(double** A, double* x, int n) {
int i, j;
double* result = (double*)malloc(n * sizeof(double));
#pragma omp parallel for
for (i = 0; i < n; i++) {
result[i] = mul_vector_transpose_vector(A[i], x, n);
}
return result;
}
double* negate_vector(double* g, int n) {
int i;
double* s = (double*)malloc(n * sizeof(double));
#pragma omp parallel for
for (i = 0; i < n; i++) {
s[i] = (-1) * g[i];
}
return s;
}
void copy_vector(double* v1, double* v2, int n) {
int i;
#pragma omp parallel for
for (i = 0; i < n; i++) {
v1[i] = v2[i];
}
}
double* scalar_mul_vector(double* s, double c, int n) {
int i;
double* result = (double*)malloc(n * sizeof(double));
#pragma omp parallel for
for (i = 0; i < n; i++) {
result[i] = c * s[i];
}
return result;
}
double* vector_add_vector(double* v1, double* v2, int n) {
int i;
double* result = (double*)malloc(n * sizeof(double));
#pragma omp parallel for
for (i = 0; i < n; i++) {
result[i] = v1[i] + v2[i];
}
return result;
}
double* vector_sub_vector(double* v1, double* v2, int n) {
int i;
double* result = (double*)malloc(n * sizeof(double));
#pragma omp parallel for
for (i = 0; i < n; i++) {
result[i] = v1[i] - v2[i];
}
return result;
}
int main() {
int n, i, j, t = 20;
printf("Enter the size of equation \n");
scanf_s("%d", &n);
double** A = (double**)malloc(n * sizeof(double*));
double* b = (double*)malloc(n * sizeof(double));
double* x = (double*)malloc(n * sizeof(double));
for (i = 0; i < n; i++) {
A[i] = (double*)malloc(n * sizeof(double));
}
printf("Enter the elements A \n");
for (i = 0; i < n; i++) {
for (j = 0; j < n; j++) {
scanf_s("%lf", &A[i][j]);
}
}
printf("Enter the elements of b \n");
for (i = 0; i < n; i++) {
scanf_s("%lf", &b[i]);
}
printf("Enter initial guess x \n");
for (i = 0; i < n; i++) {
scanf_s("%lf", &x[i]);
}
clock_t start, end;
start = clock();
double* Ax = matrix_mul_vector(A, x, n);
double* g = vector_sub_vector(Ax, b, n);
double* s = negate_vector(g, n);
double numerator = (-1) * mul_vector_transpose_vector(s, g, n);
double* tmp = matrix_mul_vector(A, s, n);
double denominator = mul_vector_transpose_vector(s, tmp, n);
double gamma = (numerator) / (denominator);
double* s1 = scalar_mul_vector(s, gamma, n);
x = vector_add_vector(x, s1, n);
while (t--) {
Ax = matrix_mul_vector(A, x, n);
double* gnew = vector_sub_vector(Ax, b, n);
numerator = mul_vector_transpose_vector(gnew, gnew, n);
denominator = mul_vector_transpose_vector(g, g, n);
double beta = (numerator) / (denominator);
s1 = scalar_mul_vector(s, beta, n);
double* neggnew = negate_vector(gnew, n);
s = vector_add_vector(s1, neggnew, n);
numerator = mul_vector_transpose_vector(s, neggnew, n);
tmp = matrix_mul_vector(A, s, n);
denominator = mul_vector_transpose_vector(s, tmp, n);
gamma = (numerator) / (denominator);
s1 = scalar_mul_vector(s, gamma, n);
x = vector_add_vector(x, s1, n);
copy_vector(g, gnew, n);
}
end = clock();
printf("Solution x = [");
for (i = 0; i < n - 1; i++) {
printf(" %lf,", x[i]);
}
printf(" %lf ]\n", x[n - 1]);
printf("Parallel execution time %f \n", (double)(end - start) / CLOCKS_PER_SEC);
return 0;
}
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