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Частина курсової
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#include <iostream> | |
#include <vector> | |
#include <math.h> | |
#include <iomanip> | |
using namespace std; | |
//4 1 2 3 4 2 1 2 3 3 2 -1 2 4 3 2 1 | |
vector <vector<double>> matrix_inverse(vector <vector<double>> &matr, unsigned int n) { | |
vector <vector<double>> inv; | |
inv.reserve(n + 1); | |
for (int i = 1; i <= n; i++) { | |
inv[i].reserve(n + 1); | |
} | |
double d = matr[1][1] * matr[2][2] - matr[1][2] * matr[2][1]; | |
for (int i = 1; i <= n; i++) { | |
for (int j = 1; j <= n; j++) { | |
inv[i][j] = pow(-1, (i + j)) * matr[n - i + 1][n - j + 1] / d; | |
} | |
} | |
return inv; | |
} | |
vector <vector<double>> matrix_multiplication(vector <vector<double>> &matr, vector <vector<double>> &B, | |
unsigned int n) { | |
vector <vector<double>> C; | |
C.reserve(n + 1); | |
for (int i = 1; i <= n; i++) { | |
C[i].reserve(n + 1); | |
} | |
for (int i = 1; i <= n; i++) { | |
for (int j = 1; j <= n; j++) { | |
double s = 0; | |
for (int k = 1; k <= n; k++) { | |
s = s + matr[i][k] * B[k][j]; | |
} | |
C[i][j] = s; | |
} | |
} | |
return C; | |
} | |
int main() { | |
unsigned int n = 0; | |
cout << "Enter n:"; | |
cin >> n; | |
vector <vector<double>> A; | |
vector <vector<double>> A1; | |
vector <vector<double>> l11; | |
vector <vector<double>> l12; | |
vector <vector<double>> l21; | |
vector <vector<double>> l22; | |
A.resize(n + 1); | |
A1.resize(n + 1); | |
l11.resize(n + 1); | |
l12.resize(n + 1); | |
l21.resize(n + 1); | |
l22.resize(n + 1); | |
for (unsigned int i = 1; i <= n; i++) { | |
A[i].resize(n + 1); | |
A1[i].resize(n + 1); | |
l11[i].resize(n + 1); | |
l12[i].resize(n + 1); | |
l21[i].resize(n + 1); | |
l22[i].resize(n + 1); | |
} | |
cout << "Enter elements of matrix A:"; | |
for (unsigned int i = 1; i <= n; i++) { | |
for (int j = 1; j <= n; j++) { | |
cin >> A[i][j]; | |
} | |
} | |
for (int i = 1; i <= n; i++) { | |
for (int j = 1; j <= n; j++) { | |
if (i <= n / 2) { | |
if (j <= n / 2) | |
l11[i][j] = A[i][j]; | |
else | |
l12[i][j - n / 2] = A[i][j]; | |
} | |
else { | |
if (j <= n / 2) | |
l21[i - n / 2][j] = A[i][j]; | |
else | |
l22[i - n / 2][j - n / 2] = A[i][j]; | |
} | |
} | |
} | |
vector <vector<double>> l11_inversed = matrix_inverse(l11, n / 2); | |
vector <vector<double>> X = matrix_multiplication(l11_inversed, l12, n / 2); | |
vector <vector<double>> Y = matrix_multiplication(l21, l11_inversed, n / 2); | |
vector <vector<double>> Q = matrix_multiplication(Y, l12, n / 2); | |
for (int i = 1; i <= n / 2; i++) { | |
for (int j = 1; j <= n / 2; j++) { | |
Q[i][j] = l22[i][j] - Q[i][j]; | |
} | |
} | |
vector <vector<double>> Q_inversed = matrix_inverse(Q, n / 2); | |
vector <vector<double>> b11 = matrix_multiplication(Q_inversed, Y, n / 2); | |
b11 = matrix_multiplication(X, b11, n / 2); | |
vector <vector<double>> b12 = matrix_multiplication(X, Q_inversed, n / 2); | |
vector <vector<double>> b21 = matrix_multiplication(Q_inversed, Y, n / 2); | |
vector <vector<double>> b22 = Q_inversed; | |
for (int i = 1; i <= n / 2; i++) { | |
for (int j = 1; j <= n / 2; j++) { | |
b11[i][j] = l11_inversed[i][j] + b11[i][j]; | |
b12[i][j] = (-1) * b12[i][j]; | |
b21[i][j] = (-1) * b21[i][j]; | |
} | |
} | |
cout << "inverse matrix:" << endl; | |
for (int i = 1; i <= n; i++) { | |
for (int j = 1; j <= n; j++) { | |
if (i <= n / 2) { | |
if (j <= n / 2) | |
A1[i][j] = b11[i][j]; | |
else | |
A1[i][j] = b12[i][j - n / 2]; | |
} | |
else { | |
if (j <= n / 2) | |
A1[i][j] = b21[i - n / 2][j]; | |
else | |
A1[i][j] = Q_inversed[i - n / 2][j - n / 2]; | |
} | |
cout << setw(13) << A1[i][j]; | |
} | |
cout << endl; | |
} | |
return 0; | |
} |
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