矩阵sum_矩阵LU分解的MATLAB与C++实现

MATLAB实现：

% 矩阵LU分解
function [L,U] = lu_decomposition(A)
    n = size(A,1);
    L = eye(n);
    U = A;
    for i=1:n-1
        if abs(U(i,i)) < eps
            error('Zero pivot encountered');
        end
        for j=i+1:n
            L(j,i) = U(j,i) / U(i,i);
            U(j,:) = U(j,:) - L(j,i)*U(i,:);
        end
    end
end

% 矩阵求和
function S = matrix_sum(A)
    S = sum(sum(A));
end

% 测试
A = [1 2 3; 4 5 6; 7 8 9];
[L,U] = lu_decomposition(A);
S = matrix_sum(A);
disp('A=');
disp(A);
disp('L=');
disp(L);
disp('U=');
disp(U);
disp('sum(A)=');
disp(S);

C++实现：

#include <iostream>
#include <vector>
using namespace std;

// 矩阵LU分解
void lu_decomposition(vector<vector<double>>& A, vector<vector<double>>& L, vector<vector<double>>& U)
{
    int n = A.size();
    L = vector<vector<double>>(n, vector<double>(n, 0));
    U = A;
    for(int i=0;i<n-1;i++)
    {
        if(abs(U[i][i]) < 1e-6)
        {
            throw "Zero pivot encountered";
        }
        for(int j=i+1;j<n;j++)
        {
            L[j][i] = U[j][i] / U[i][i];
            for(int k=i;k<n;k++)
            {
                U[j][k] -= L[j][i] * U[i][k];
            }
        }
    }
    for(int i=0;i<n;i++)
    {
        L[i][i] = 1;
    }
}

// 矩阵求和
double matrix_sum(vector<vector<double>>& A)
{
    double S = 0;
    for(int i=0;i<A.size();i++)
    {
        for(int j=0;j<A[0].size();j++)
        {
            S += A[i][j];
        }
    }
    return S;
}

// 测试
int main()
{
    vector<vector<double>> A{{1,2,3},{4,5,6},{7,8,9}};
    vector<vector<double>> L,U;
    lu_decomposition(A,L,U);
    double S = matrix_sum(A);
    cout << "A=" << endl;
    for(auto row:A)
    {
        for(auto ele:row)
        {
            cout << ele << " ";
        }
        cout << endl;
    }
    cout << "L=" << endl;
    for(auto row:L)
    {
        for(auto ele:row)
        {
            cout << ele << " ";
        }
        cout << endl;
    }
    cout << "U=" << endl;
    for(auto row:U)
    {
        for(auto ele:row)
        {
            cout << ele << " ";
        }
        cout << endl;
    }
    cout << "sum(A)=" << S << endl;
    return 0;
}