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Cholesky decomposition. Find more at https://yegorsh-public.notion.site/Cholesky-decomposition-01f53b0b091641ba896ddfc3beb9660c
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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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