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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;}
    
   

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