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Cholesky decomposition/Разложение Холецкого на C++
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| #include <iostream> | |
| #include <cmath> | |
| using namespace std; | |
| void FillMatrix(double **matrix, const int size){ | |
| for (int i=0; i<size; i++){ | |
| for (int j=0; j<size; j++){ | |
| cout << "a[" << i+1 << "][" << j+1 << "] = "; | |
| cin >> matrix[i][j]; | |
| } | |
| } | |
| } | |
| void PrintMatrix(double **matrix, const int size){ | |
| for (int i=0; i<size; i++){ | |
| for (int j=0; j<size; j++){ | |
| cout << matrix[i][j] << "\t"; | |
| } | |
| cout << endl; | |
| } | |
| } | |
| void clearMemory(double** matrix, int size){ | |
| for (int i = 0; i < size; i++) { | |
| delete[] matrix[i]; | |
| } | |
| delete [] matrix; | |
| } | |
| void Transpose(double **matrix, double **transposed, const int size){ | |
| for (int i=0; i<size; i++){ | |
| for (int j=0; j<size; j++){ | |
| transposed[i][j] = matrix[j][i]; | |
| } | |
| } | |
| } | |
| int main(){ | |
| int size = 3; | |
| double **A = new double *[size]; | |
| for (int i = 0; i < size; i++) { | |
| A[i] = new double [size]; | |
| } | |
| double **Transposed = new double *[size]; | |
| for (int i = 0; i < size; i++) { | |
| Transposed[i] = new double [size]; | |
| } | |
| double **L = new double *[size]; | |
| for (int i = 0; i < size; i++) { | |
| L[i] = new double [size]; | |
| } | |
| //FillMatrix(A, size); | |
| A[0][0] =4; A[0][1] =12; A[0][2] =-16; | |
| A[1][0] =12; A[1][1] =37; A[1][2] =-43; | |
| A[2][0] =-16; A[2][1] =-43; A[2][2] =98; | |
| Transpose(A, Transposed, size); | |
| cout << "A =" << endl; | |
| PrintMatrix(A, size); | |
| for (int i=0; i<size; i++){ | |
| for (int j=0; j<size; j++){ | |
| if (Transposed[i][j] != A[i][j]){ | |
| cout << "Матрица не является симметричной." << endl; | |
| exit(0); | |
| } | |
| } | |
| } | |
| for (int i = 0; i < size; i++) { | |
| for (int j = 0; j <= i; j++) { | |
| double sum = 0; | |
| for (int k = 0; k < j; k++) { | |
| sum += L[i][k] * L[j][k]; | |
| } | |
| if (i == j) { | |
| L[i][j] = sqrt(A[i][i] - sum); | |
| if ((L[i][i] <= 0) || isnan(L[i][i])) { | |
| cout << "Матрица не положительно определенная." << endl; | |
| exit(0); | |
| } | |
| } | |
| else { | |
| L[i][j] = (1.0 / L[j][j] * (A[i][j] - sum)); | |
| } | |
| } | |
| } | |
| cout << endl << "L =" << endl; | |
| PrintMatrix(L, size); | |
| clearMemory(A,size); | |
| clearMemory(Transposed, size); | |
| clearMemory(L, size); | |
| return 0; | |
| } |
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