561 lines
11 KiB
C
561 lines
11 KiB
C
#include "solve.h"
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#include "matrix.h"
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#include <math.h>
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double t1_solve(const double * restrict A, double * restrict x_0, double * restrict x, int n, int m)
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{
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for (int i = 0; i < m; ++i)
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{
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double * swap_temp;
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matvec_mul(n, A, x_0, x);
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swap_temp = x;
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x = x_0;
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x_0 = swap_temp;
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}
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if (m % 2 == 0)
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{
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for (int i = 0; i < n; i++)
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{
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double temp = x[i];
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x[i] = x_0[i];
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x_0[i] = temp;
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}
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} else
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{
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double * swap_temp = x;
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x = x_0;
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x_0 = swap_temp;
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}
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return t1_get_eigenvalue_approx(A, x, x_0, n);
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}
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double t1_get_eigenvalue_approx(const double * restrict A, double * restrict x_k, double * restrict x, int n)
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{
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double dot_Ax_x = 0;
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double dot_x_x = 0;
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double rayleigh_quotient = 0;
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#pragma omp parallel for reduction(+:dot_Ax_x, dot_x_x)
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for (int i = 0; i < n; i++)
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{
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double x_i = x_k[i];
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double sum = 0;
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#pragma omp simd reduction(+:sum)
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for (int j = 0; j < n; j++)
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sum += A[i * n + j] * x_k[j];
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x[i] = sum;
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dot_Ax_x += sum * x_i;
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dot_x_x += x_i * x_i;
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}
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rayleigh_quotient = dot_Ax_x / dot_x_x;
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return rayleigh_quotient;
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}
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double t1_get_residual_norm(double * restrict x_k, double * restrict x, int n, double r1)
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{
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double norm_r1x_1 = 0;
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double residual_norm_1 = 0;
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double relative_residual = 0;
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#pragma omp parallel for reduction(+:residual_norm_1, norm_r1x_1)
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for (int i = 0; i < n; ++i)
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{
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double rx = r1 * x_k[i];
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residual_norm_1 += fabs(x[i] - rx);
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norm_r1x_1 += fabs(rx);
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}
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relative_residual = residual_norm_1 / norm_r1x_1;
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return relative_residual;
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}
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void t2_solve(const double * restrict A, double * restrict x_0, const double * restrict b, double * restrict x, int n, int m, double t)
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{
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for (int k = 0; k < m; ++k)
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{
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double * swap_temp;
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matvec_mul(n, A, x_0, x);
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#pragma omp simd
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for (int i = 0; i < n; ++i)
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x[i] = (b[i] - x[i]) * t + x_0[i];
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swap_temp = x;
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x = x_0;
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x_0 = swap_temp;
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}
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if (m % 2 == 0) // Проверил 100 раз
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for (int i = 0; i < n; i++)
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{
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double temp = x[i];
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x[i] = x_0[i];
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x_0[i] = temp;
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}
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else
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{
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double * swap_temp = x;
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x = x_0;
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x_0 = swap_temp;
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}
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}
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void t3_solve(const double * restrict A, double * restrict x_0, const double * restrict b, double * restrict x, double * restrict r, int n, int m)
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{
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for (int k = 0; k < m; ++k)
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{
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double *swap_temp = 0;
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double t = 0;
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double dot_r_r = 0, dot_Ar_r = 0;
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#pragma omp parallel for
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for (int i = 0; i < n; ++i)
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{
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double sum = 0;
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#pragma omp simd reduction(+:sum)
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for (int j = 0; j < n; ++j)
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sum += A[i*n + j] * x_0[j];
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r[i] = sum - b[i];
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}
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#pragma omp parallel for reduction(+:dot_r_r, dot_Ar_r)
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for (int i = 0; i < n; ++i)
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{
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double ri = r[i];
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double sum = 0;
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#pragma omp simd reduction(+:sum)
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for (int j = 0; j < n; ++j)
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sum += A[i*n + j] * r[j];
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dot_Ar_r += sum * ri;
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dot_r_r += ri * ri;
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}
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t = dot_r_r / dot_Ar_r;
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#pragma omp simd
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for (int i = 0; i < n; ++i)
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x[i] = x_0[i] - r[i]*t;
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swap_temp = x;
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x = x_0;
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x_0 = swap_temp;
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}
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if (m % 2 == 0) // Проверил 100 раз
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#pragma omp simd
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for (int i = 0; i < n; i++)
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{
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double temp = x[i];
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x[i] = x_0[i];
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x_0[i] = temp;
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}
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else
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{
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double * swap_temp = x;
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x = x_0;
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x_0 = swap_temp;
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}
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}
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void t4_solve(const double * restrict A, double * restrict x_0, const double * restrict b, double * restrict x, double * restrict r, int n, int m)
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{
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for (int k = 0; k < m; ++k)
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{
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double *swap_temp = 0;
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double t = 0;
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double dot_Ar_r = 0, dot_Ar_Ar = 0;
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#pragma omp parallel for
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for (int i = 0; i < n; ++i)
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{
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double sum = 0;
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#pragma omp simd reduction(+:sum)
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for (int j = 0; j < n; ++j)
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sum += A[i*n + j] * x_0[j];
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r[i] = sum - b[i];
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}
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#pragma omp parallel for reduction(+:dot_Ar_r, dot_Ar_Ar)
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for (int i = 0; i < n; ++i)
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{
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double ri = r[i];
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double sum = 0;
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#pragma omp simd reduction(+:sum)
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for (int j = 0; j < n; ++j)
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sum += A[i*n + j] * r[j];
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dot_Ar_r += sum * ri;
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dot_Ar_Ar += sum * sum;
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}
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t = dot_Ar_r / dot_Ar_Ar;
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#pragma omp simd
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for (int i = 0; i < n; ++i)
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x[i] = x_0[i] - r[i]*t;
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swap_temp = x;
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x = x_0;
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x_0 = swap_temp;
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}
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if (m % 2 == 0) // Проверил 100 раз
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#pragma omp simd
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for (int i = 0; i < n; i++)
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{
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double temp = x[i];
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x[i] = x_0[i];
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x_0[i] = temp;
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}
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else
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{
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double * swap_temp = x;
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x = x_0;
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x_0 = swap_temp;
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}
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}
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void t5_solve(const double * restrict A, double * restrict x_0, const double * restrict b, double * restrict x, double * restrict r, int n, int m)
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{
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for (int k = 0; k < m; ++k)
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{
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double *swap_temp = 0;
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double t = 0;
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double dot_Dr_r = 0, dot_ADr_Dr = 0;
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#pragma omp parallel for
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for (int i = 0; i < n; ++i)
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{
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double sum = 0;
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#pragma omp simd reduction(+:sum)
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for (int j = 0; j < n; ++j)
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sum += A[i*n + j] * x_0[j];
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r[i] = sum - b[i];
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}
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#pragma omp parallel for reduction(+:dot_Dr_r)
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for (int i = 0; i < n; ++i)
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{
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double d_ri = r[i] / A[i*n +i];
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dot_Dr_r += d_ri * r[i];
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r[i] = d_ri;
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}
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#pragma omp parallel for reduction(+:dot_ADr_Dr)
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for (int i = 0; i < n; ++i)
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{
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double sum = 0;
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#pragma omp simd reduction(+:sum)
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for (int j = 0; j < n; ++j)
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sum += A[i*n + j] * r[j];
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dot_ADr_Dr += sum * r[i];
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}
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t = dot_Dr_r / dot_ADr_Dr;
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#pragma omp simd
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for (int i = 0; i < n; ++i)
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x[i] = x_0[i] - r[i]*t;
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swap_temp = x;
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x = x_0;
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x_0 = swap_temp;
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}
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if (m % 2 == 0) // Проверил 100 раз
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#pragma omp simd
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for (int i = 0; i < n; i++)
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{
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double temp = x[i];
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x[i] = x_0[i];
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x_0[i] = temp;
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}
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else
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{
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double * swap_temp = x;
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x = x_0;
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x_0 = swap_temp;
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}
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}
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void t6_solve(const double * restrict A, double * restrict x_0, const double * restrict b, double * restrict x, double * restrict r, int n, int m)
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{
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for (int k = 0; k < m; ++k)
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{
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double *swap_temp = 0;
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double t = 0;
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double dot_ADr_r = 0, dot_ADr_ADr = 0;
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#pragma omp parallel for
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for (int i = 0; i < n; ++i)
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{
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double sum = 0;
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#pragma omp simd reduction(+:sum)
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for (int j = 0; j < n; ++j)
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sum += A[i*n + j] * x_0[j];
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r[i] = (sum - b[i]) / A[i*n + i];
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}
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#pragma omp parallel for reduction(+:dot_ADr_r, dot_ADr_ADr)
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for (int i = 0; i < n; ++i)
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{
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double sum = 0;
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#pragma omp simd reduction(+:sum)
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for (int j = 0; j < n; ++j)
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sum += A[i*n + j] * r[j];
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dot_ADr_r += sum * r[i] * A[i*n + i];
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dot_ADr_ADr += sum * sum;
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}
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t = dot_ADr_r / dot_ADr_ADr;
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#pragma omp simd
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for (int i = 0; i < n; ++i)
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x[i] = x_0[i] - (r[i]*t);
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swap_temp = x;
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x = x_0;
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x_0 = swap_temp;
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}
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if (m % 2 == 0) // Проверил 100 раз
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#pragma omp simd
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for (int i = 0; i < n; i++)
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{
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double temp = x[i];
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x[i] = x_0[i];
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x_0[i] = temp;
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}
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else
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{
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double * swap_temp = x;
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x = x_0;
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x_0 = swap_temp;
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}
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}
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void t7_solve(const double * restrict A, double * restrict x_0, const double * restrict b, double * restrict x, double * restrict r, int n, int m, double t)
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{
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(void)r;
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for (int k = 0; k < m; ++k)
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{
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double * swap_temp;
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#pragma omp parallel for
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for (int i = 0; i < n; ++i)
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{
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double sum = 0;
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#pragma omp simd reduction(+:sum)
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for (int j = 0; j < n; ++j)
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sum += A[i*n + j] * x_0[j];
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x[i] = x_0[i] + ((b[i] - sum) / A[i*n + i]) * t;
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}
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swap_temp = x;
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x = x_0;
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x_0 = swap_temp;
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}
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if (m % 2 == 0) // Проверил 100 раз
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for (int i = 0; i < n; i++)
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{
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double temp = x[i];
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x[i] = x_0[i];
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x_0[i] = temp;
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}
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else
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{
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double * swap_temp = x;
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x = x_0;
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x_0 = swap_temp;
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}
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}
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void t8_solve(const double * restrict A, double * restrict x_0, const double * restrict b, double * restrict x, double * restrict r, double * restrict w, int n, int m, double t)
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{
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(void)r;
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(void)w;
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for (int k = 0; k < m; ++k)
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{
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double * swap_temp;
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for (int i = 0; i < n; ++i)
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{
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double sum_x = 0;
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double sum_r = 0;
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double temp = 0;
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double aii = A[i*n + i];
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#pragma omp simd reduction(+:sum_x, sum_r)
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for (int j = 0; j < i; ++j)
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{
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double aij = A[i*n + j];
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double rj = aij * x_0[j];
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sum_x += rj - aij * x[j];
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sum_r += rj;
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}
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temp = aii * x_0[i];
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sum_x += temp;
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sum_r += temp;
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#pragma omp simd reduction(+:sum_r)
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for (int j = i+1; j < n; ++j)
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sum_r += A[i*n + j] * x_0[j];
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x[i] = (sum_x + (b[i] - sum_r) * t) / aii;
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}
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swap_temp = x;
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x = x_0;
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x_0 = swap_temp;
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}
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if (m % 2 == 0) // Проверил 100 раз
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for (int i = 0; i < n; i++)
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{
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double temp = x[i];
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x[i] = x_0[i];
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x_0[i] = temp;
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}
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else
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{
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double * swap_temp = x;
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x = x_0;
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x_0 = swap_temp;
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}
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}
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void t9_solve(const double * restrict A, double * restrict x_0, const double * restrict b, double * restrict x, int n, int m, double t)
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{
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for (int k = 0; k < m; ++k)
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{
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double * swap_temp;
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for (int i = n-1; i >= 0; --i)
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{
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double sum_x = 0;
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double sum_r = 0;
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double temp = 0;
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double aii = A[i*n + i];
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#pragma omp simd reduction(+:sum_x, sum_r)
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for (int j = n-1; j > i; --j)
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{
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double aij = A[i*n + j];
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double rj = aij * x_0[j];
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sum_x += rj - aij * x[j];
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sum_r += rj;
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}
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temp = aii * x_0[i];
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sum_x += temp;
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sum_r += temp;
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#pragma omp simd reduction(+:sum_r)
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for (int j = i-1; j >= 0; --j)
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sum_r += A[i*n + j] * x_0[j];
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x[i] = (sum_x + (b[i] - sum_r) * t) / aii;
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}
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swap_temp = x;
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x = x_0;
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x_0 = swap_temp;
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}
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if (m % 2 == 0) // Проверил 100 раз
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for (int i = 0; i < n; i++)
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{
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double temp = x[i];
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x[i] = x_0[i];
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x_0[i] = temp;
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}
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else
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{
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double * swap_temp = x;
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x = x_0;
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x_0 = swap_temp;
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}
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}
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void t10_solve(const double * restrict A, double * restrict x_0, const double * restrict b, double * restrict x, double * restrict r, double * restrict w, int n, int m, double t)
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{
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for (int k = 0; k < m; ++k)
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{
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double *swap_temp = 0;
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#pragma omp parallel for
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for (int i = 0; i < n; ++i)
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{
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double sum = 0;
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#pragma omp simd reduction(+:sum)
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for (int j = 0; j < n; ++j)
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sum += A[i*n + j] * x_0[j];
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r[i] = (b[i] - sum) * t;
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}
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for (int i = 0; i < n; ++i)
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{
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double sum = r[i];
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double inai = 0;
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#pragma omp simd reduction(+:sum)
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for (int j = 0; j < i; ++j)
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sum -= A[i*n + j] * r[j];
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inai = 1./A[i*n + i];
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w[i] = inai;
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r[i] = sum * inai;
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}
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#pragma omp simd
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for (int i = 0; i < n; ++i)
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r[i] *= A[i*n + i];
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for (int i = n-1; i >= 0; --i)
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{
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double sum = r[i];
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#pragma omp simd reduction(+:sum)
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for (int j = n-1; j > i; --j)
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sum -= A[i*n + j] * r[j];
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r[i] = sum * w[i];
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}
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#pragma omp simd
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for (int i = 0; i < n; i++)
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x[i] = x_0[i] + r[i];
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swap_temp = x;
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x = x_0;
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|
x_0 = swap_temp;
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}
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if (m % 2 == 0) // Проверил 100 раз
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{
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|
#pragma omp simd
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for (int i = 0; i < n; i++)
|
|
{ double temp = x[i]; x[i] = x_0[i]; x_0[i] = temp; }
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} else
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|
{ double * swap_temp = x; x = x_0; x_0 = swap_temp; }
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|
}
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