Question

所以我试图从文本文件中读取矩阵 A ，这是正确的。用户输入矢量B.然后我想执行高斯消元（Ax = b）来得到解向量x。我得到的x的值是-1。＃IND我不明白为什么......我猜测SystemSolution中出了什么问题？

 #include <iostream>
#include <vector>
#include <iomanip>
#include <fstream>
#include <string>
#include <sstream>

using namespace std;

//this program does gaussian elimination for a matrix Ax=b

vector<double> SystemSolution(vector<vector<double>> A, vector<double> b)
{

    //Determine and test size of a matrix
    int n = A.size();
    for (int i = 0; i < n; i++)
        if (n != A[i].size())
            throw "Error! Number of rows and columns of matrix must be equal!";

    vector<double> x(b.size());
    //x is the vector of solutions


    for (int i = 0; i < n - 1; i++)
    {
        for (int j = i + 1; j < n; j++)
        {
            //Finding pivot
            double pivot = A[i][i];
            int index = i;
            for (int k = i + 1; k < n; k++)
            {
                if (pivot > abs(A[k][i]))
                {
                    index = k;
                    pivot = A[k][i];
                }
            }

            //Row exchange
            for (int k = 0; k < n; k++)
            {
                double tmp = A[i][k];
                A[i][k] = A[index][k];
                A[index][k] = tmp;
            }

            //Elimination
            double coefficient = -(A[j][i] / A[i][i]);
            for (int k = i; k < n; k++)
            {
                A[j][k] += coefficient*A[i][k];
            }

            b[j] += coefficient*b[i];
        }
    }

    //Back-substitution
    x[n - 1] = b[n - 1] / A[n - 1][n - 1];
    for (int i = n - 2; i >= 0; i--)
    {
        double sum = 0;
        for (int j = i; j < n; j++)
        {
            sum += x[j] * A[i][j];
        }
        x[i] = (b[i] - sum) / A[i][i];
    }

    return x;
}



void PrintVector(const vector<double> &b)
{
    for (int i = 0; i < b.size(); i++)
        cout << setiosflags(ios::showpoint | ios::fixed | ios::right)
        << setprecision(4)
        << setw(8) << b[i] << endl;
}

void PrintMatrix(const vector<vector<double> > &A)
{
    for (int i = 0; i < A.size(); i++)
    {
        for (int j = 0; j < A[i].size(); j++)
            cout << setiosflags(ios::showpoint | ios::fixed | ios::right)
            << setprecision(4)
            << setw(8) << A[i][j];
        cout << endl;
    }
}
int main()
{
    int n;
    cout << "Please enter the number of rows/columns:";

    cin >> n;

    ifstream matrixFile;

    matrixFile.open("matrix.txt");

    if (matrixFile.is_open()){

        //matrix A values
        vector<vector<double>> A(n, vector<double>(n));
        vector<double> b(n);
        string line;
        int col = 0;
        int row = 0;

        while (getline(matrixFile, line)){

            istringstream stream(line);

            int x;
            col = 0; //reset 

            while (stream >> x){
                A[row][col] = x;
                col++;
            }

            row++;

        }





        cout << "Please enter vector b:"<<endl;
        //vector b values
        for (int i = 0; i < row; i++)
        {
            cout << "b[" << i + 1 << "]= ";
            cin >> b[i];    
        }



        vector<double> x = SystemSolution(A, b);
        cout << "- SOLUTIONS -" << endl;
        cout << "Matrix:" << endl;
        PrintMatrix(A);
        cout << "\nVector x:" << endl;
        PrintVector(x);

    }
    else{
        cout << "File failed to open!";
    }
    matrixFile.close();

    return 0;
}

Answer 1

您的代码中可能会有一些除以零的部分：

double coefficient = -(A[j][i] / A[i][i]);
/* .. */
x[n - 1] = b[n - 1] / A[n - 1][n - 1];
/* .. */
x[i] = (b[i] - sum) / A[i][i];

在这里查看高斯消除： Square Matrix Inversion in C

审核并调试你的。

从txt文件中读取矩阵做高斯消元（C ++）

1 个答案: