高斯列主元消去法_解线性方程组的直接解法

高斯列主元消去法_解线性方程组的直接解法

标签：计算方法实验

#include 
#include 

const int maxn = 15;
double a[maxn][maxn], b[maxn];

int main()
{
    int n;

    freopen("gauss.txt", "r", stdin);  //读入数据
    scanf("%d", &n);
    for(int i = 1; i <= n; i++)
    {
        for(int j = 1; j <= n; j++)  scanf("%lf", &a[i][j]);
        scanf("%lf", &b[i]);
    }
    /*打印数据文件
    for(int i = 1; i <= n; i++)
    {
        for(int j = 1; j <= n; j++)  printf("%10f", a[i][j]);
        printf("%10f\n", b[i]);
    }
    printf("\n");
    */

    for(int k = 1; k <= n - 1; k++)  //n - 1列
    {
        int column = k;
        double mainelement = a[k][k];

        for(int i = k; i <= n; i++)  //找主元素
            if(fabs(a[i][k]) > mainelement)
            {
                mainelement = fabs(a[i][k]);
                column = i;
            }
        for(int j = k; j <= n; j++)  //交换两行
        {
            double atemp = a[k][j];
            a[k][j] = a[column][j];
            a[column][j] = atemp;
        }
        double btemp = b[k];
        b[k] = b[column];
        b[column] = btemp;

        for(int i = k + 1; i <= n; i++)  //消元过程
        {
            double Mik = a[i][k] / a[k][k];
            for(int j = k; j <= n; j++)  a[i][j] -= Mik * a[k][j];
            b[i] -= Mik * b[k];
        }
    }

    for(int i = 1; i <= n; i++)  //经列主元高斯消去法得到的上三角阵(最后一列为常系数)
    {
        for(int j = 1; j <= n; j++)  printf("%10f", a[i][j]);
        printf("%10f\n", b[i]);
    }
    printf("\n");

    b[n] /= a[n][n];  //回代过程
    for(int i = n - 1; i >= 1; i--)
    {
        double sum = 0;

        for(int j = i + 1; j <= n; j++)  sum += a[i][j] * b[j];
        b[i] = (b[i] - sum) / a[i][i];
    }
    for(int i = 1; i <= n; i++)  printf("x%d = %10f\n", i, b[i]);  //小优化b[]->x[]

    return 0;
}

数据文件

实验结果