计算方法实验2（补充）：列主元消元法解线性方程组

C++源代码

#include<bits/stdc++.h>
using namespace std;// 列主元消去法求解线性方程组
vector<long double> Column_Elimination(vector<vector<long double>> A, vector<long double> b);int main()
{vector<vector<long double>> A(3, vector<long double>(3, 0));A[0][0] = 2, A[0][1] = 4, A[0][2] = -3;A[1][0] = 4, A[1][1] = -3, A[1][2] = 1;A[2][0] = 1, A[2][1] = 3, A[2][2] = -2;vector<long double> b(3, 1);vector<long double> X = Column_Elimination(A, b);for(int i = 0; i < 3; i++)cout << X[i] << " ";return 0;
}// 列主元消去法求解线性方程组
vector<long double> Column_Elimination(vector<vector<long double>> A, vector<long double> b)
{int n = A.size();vector<long double> x(n, 0);vector<vector<long double>> matrix(n, vector<long double>(n + 1, 0));for(int i = 0; i < n; i++){matrix[i][n] = b[i];for(int j = 0; j < n; j++)matrix[i][j] = A[i][j];}for(int col = 0; col < n; col++)//找到列主元{long double maxnum = abs(matrix[col][col]);int maxrow = col;for(int row = col + 1; row < n; row++){if(abs(matrix[row][col]) > maxnum){maxnum = abs(matrix[row][col]);maxrow = row;}}swap(matrix[col], matrix[maxrow]);for(int row = col + 1; row < n; row++){long double res = matrix[row][col] / matrix[col][col];for(int loc = col; loc <= n; loc++)matrix[row][loc] -= matrix[col][loc] * res; }}for(int row = n - 1; row >= 0; row--)//回代{for(int col = row + 1; col < n; col++){matrix[row][n] -= matrix[col][n] * matrix[row][col] / matrix[col][col];matrix[row][col] = 0;}matrix[row][n] /= matrix[row][row];matrix[row][row] = 1;}for(int i = 0; i < n; i++)x[i] = matrix[i][n];return x;
}

补充:python解线性方程组

import numpy as npA = np.array([[2, 4, -3], [4, -3, 1], [1, 3, -2]])
b = np.array([1, 1, 1])x = np.linalg.solve(A, b)print(x)