Частина курсової

.cpp

#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;
}