/* 高斯列主元消去法解線代數方程組 */

#include "math.h"

#include "stdio.h"

#include "stdlib.h"

void max_ele(double af[][21],int n,int k)  /* 選主元 */

  {double max1,t;

   int i,j;

   max1=af[k][k]; i=k;

   for (j=k+1;j<=n;j++)

     if(fabs(af[j][k])>fabs(max1)) i=j;

   if(i>k)

     for (j=k;j<=n+1;j++)

       {t=af[i][j],af[i][j]=af[k][j],af[k][j]=t;}

  }

int gauss(double a[][20],double f[],double x[],int n)

/* Guass 消去法,引入af[20[21],x[]是為了不改變矩陣a[][],f[]

   及簡化程序  */

 {int i,j,k;

  double af[20][21],del,t;

  for(i=1;i<=n;i++)

    { for(j=1;j<=n;j++)  af[i][j]=a[i][j];

      af[i][n+1]=f[i];

    }

  for (k=1;k<n;k++)

    { max_ele(af,n,k);

      del=af[k][k];

      if (fabs(del)<1e-7)

       {printf("Single! press any key return...\n");

        getchar();

        return 0;}

      for (j=k;j<=n+1;j++)  af[k][j]/=del;

      for (i=k+1;i<=n;i++)

       { t=af[i][k];

         for (j=k;j<=n+1;j++)

           af[i][j]-=af[k][j]*t;

       }

     }

  del=af[n][n];

  for (j=n;j<=n+1;j++) af[n][j]/=del;

  for (j=1;j<=n;j++) x[j]=af[j][n+1];

  for (i=n-1;i>0;i--)

    for (j=n;j>i;j--)  x[i]-=x[j]*af[i][j];

  return 1;

 }

main()

 { double a[20][20], f[20],x[20];

   int i,j,n;

   printf("Input n(<20)");

   scanf("%d",&n);

   /* 隨機生成系數矩陣及右端項,進行檢驗 */

   for (i=1;i<=n;i++)

      for (j=1;j<=n;j++) a[i][j]=(float)rand()/100.0;

   for (i=1;i<=n;i++)

     { for (j=1;j<=n;j++) printf("%8.4f ",a[i][j]);

       printf("\n");}

   for (i=1;i<=n;i++)

     { f[i]=0;

       for (j=1;j<=n;j++) f[i]+=a[i][j];

      }

   gauss(a,f,x,n);

   for (i=1;i<=n;i++)  printf("%lf ",x[i]);

   printf("\n");

 }