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LU_decomposition.cpp

#include <iostream>
using namespace std;

void FillMatrix(double **matrix, const int size){
    for (int i=0; i<size; i++){
        for (int j=0; j<size; j++){
            matrix[i][j] = rand()%30;
        }
    }
}

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;
}

int main(){
    int size;
    cout << "Порядок матрицы = ";
    cin >> size;
    cout << endl;

    double **A = new double *[size];
    for (int i = 0; i < size; i++) {
        A[i] = new double [size];
    }

    FillMatrix(A,size);
    if (A[0][0] == 0){
        cout << "Невырожденная матрица A не имеет LU-разложения." << endl;
        exit(0);
    }

    double **Lower = new double *[size];
    for (int i = 0; i < size; i++) {
        Lower[i] = new double [size];
    }

    double **Upper = new double *[size];
    for (int i = 0; i < size; i++) {
        Upper[i] = new double [size];
    }

    for (int i=0; i<size; i++){
        for (int j=0; j<size; j++){
            Upper[i][j] = 0;
            Lower[i][j] = 0;
            Lower[i][i] = 1;
        }
    }

    for (int i=0; i<size; i++){
        for (int j=0; j<size; j++){
            if (i<=j){
                double Sum = 0;
                for (int k=0; k<=i-1; k++){
                    Sum += Lower[i][k] * Upper[k][j];
                }
                Upper[i][j] = A[i][j] - Sum;
            }
            else{
                double Sum = 0;
                for (int k=0; k<=j-1; k++){
                    Sum += Lower[i][k] * Upper[k][j];
                }
                Lower[i][j] = (A[i][j] - Sum) / Upper[j][j];
            }
        }
    }

    cout << "A = " << endl;
    PrintMatrix(A,size);
    cout << endl << "L = " << endl;
    PrintMatrix(Lower,size);
    cout << endl << "U = " << endl;
    PrintMatrix(Upper,size);

    clearMemory(A,size);
    clearMemory(Lower,size);
    clearMemory(Upper,size);

    return 0;
}