179 lines
3.6 KiB
C
179 lines
3.6 KiB
C
#include "solve.h"
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#include "io_status.h"
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#include <float.h>
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#include <math.h>
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#include "array_io.h"
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#include "matrix.h"
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#include <stdio.h>
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// c - changes in rows
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int t14_solve(int n, double * restrict A, double * restrict X, int * restrict c)
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{
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double norm = get_matrix_norm(n, A);
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// Проходимся по главным минорам
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for (int k = 0; k < n; ++k) {
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double maximum = -1.;
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int max_i = 0, max_j = 0;
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// Ищем максимальный элемент минора
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for (int i = k; i < n; ++i)
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for (int j = k; j < n; ++j)
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{
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double aij = fabs(A[i * n + j]);
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if (aij > maximum) {
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maximum = aij;
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max_i = i;
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max_j = j;
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}
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}
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// Если максимальный по модулю элемент равен нулю, значит матрица вырождена
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if (fabs(maximum) < DBL_EPSILON * norm)
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return SINGULAR;
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// Меняем строки местами, если максимум находится не в k строке
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if (max_i != k)
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{
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int kn = k*n;
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int in = max_i*n;
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for (int i = 0; i < k; ++i)
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{
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int kni = kn+i, ini = in+i;
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double swap = X[kni];
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X[kni] = X[ini];
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X[ini] = swap;
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}
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for (int i = k; i < n; ++i)
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{
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int kni = kn+i, ini = in+i;
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double swap = X[kni];
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X[kni] = X[ini];
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X[ini] = swap;
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swap = A[kni];
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A[kni] = A[ini];
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A[ini] = swap;
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}
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}
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// Меняем столбцы местами
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if (max_j != k)
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{
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int swap_temp = c[max_j];
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c[max_j] = c[k];
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c[k] = swap_temp;
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for (int in = 0; in < n*n; in+=n)
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{
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double swap = A[in + k];
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A[in + k] = A[in + max_j];
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A[in + max_j] = swap;
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}
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}
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gauss_inverse(n, k, A, X);
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}
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gauss_back_substitution(n, A, X);
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// Возвращаем строки назад
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for (int k = 0; k < n; ++k)
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{
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int pnt_cur = c[k];
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if (pnt_cur != k)
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{
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int pnt_nxt = 0;
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for (int j = 0; j < n; ++j)
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{
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int loc_cur = pnt_cur;
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double temp_cur = X[k*n + j];
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double temp_nxt = 0;
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do {
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temp_nxt = X[loc_cur*n + j];
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X[loc_cur*n + j] = temp_cur;
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temp_cur = temp_nxt;
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loc_cur = c[loc_cur];
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} while (loc_cur != k);
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X[k*n + j] = temp_cur;
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}
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do {
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pnt_nxt = c[pnt_cur];
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c[pnt_cur] = pnt_cur;
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pnt_cur = pnt_nxt;
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} while (pnt_nxt != k);
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c[k] = k;
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}
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}
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return 0;
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}
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void gauss_inverse(const int n, const int k, double * restrict A, double * restrict X)
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{
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const int kn = k*n;
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const int kk = kn + k;
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const double inv_akk = 1./A[kn + k];
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A[kn + k] = 1.;
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for (int ij = kn; ij <= kn+k; ++ij)
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{
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double xij = X[ij];
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if (fabs(xij) > DBL_EPSILON) X[ij] = xij*inv_akk;
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}
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for (int ij = kn + k+1; ij < kn+n; ++ij)
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{
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double aij = A[ij], xij = X[ij];
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if (fabs(aij) > DBL_EPSILON) A[ij] = aij*inv_akk;
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if (fabs(xij) > DBL_EPSILON) X[ij] = xij*inv_akk;
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}
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for (int i = k+1; i < n; ++i)
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{
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const int in = i*n;
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const double aik = A[in + k];
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A[in + k] = 0;
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X[in + k] -= X[kk] * aik;
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for (int j = 0; j < k; ++j)
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X[in + j] -= X[kn + j] * aik;
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for (int j = k+1; j < n; ++j)
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{
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A[in + j] -= A[kn + j] * aik;
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X[in + j] -= X[kn + j] * aik;
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}
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}
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}
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// Обратный ход метода Гаусса
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void gauss_back_substitution(const int n, double * restrict A, double * restrict X)
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{
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// Идём с последней строки и вычитаем её из последующих
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for (int k = n-1; k > 0; --k)
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{
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const int kn = k * n;
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for (int i = 0; i < k; ++i)
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{
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const int in = i*n;
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const double aik = A[in + k];
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A[in + k] = 0;
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for (int j = 0; j < n; ++j)
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X[in + j] -= X[kn + j] * aik;
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}
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}
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}
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