example3_4.java

清华大学2002年出版的《科学与工程数值计算算法Java》配套源码

import corejava.*;
public class Example3_4
{
public static double  GaussSolve(double[][] a,double[][] b,double[][] c,int n,int m)
  { int i,j,k,row,colunm;
    double temp,max,d=1;
    int[] p=new int[n];
    for(i=0;i<n;i++)p[i]=i;
      for(i=0;i<n-1;i++)
      { //找主元
		row=i;colunm=i;
        max=Math.abs(a[i][i]);
	    for(j=i;j<n;j++)
         for(k=i;k<n;k++)
          {temp=Math.abs(a[j][k]);
           if(temp>max){max=temp;row=j;colunm=k;}
	      }
	    if (max==0){return 0;}
	    //第row行、第i行互换
	    if(row!=i)
	    { for(k=i;k<n;k++)
	      {temp=a[i][k];a[i][k]=a[row][k];a[row][k]=temp;}
	      for(k=0;k<m;k++)
	      {temp=b[i][k];b[i][k]=b[row][k];b[row][k]=temp;}
	    }
	    //第column列、第i列互换
	    if(colunm!=i)
	    { for(j=0;j<n;j++)
	      {temp=a[j][colunm];a[j][colunm]=a[j][i];a[j][i]=temp;}
	      k=p[i];p[i]=p[colunm];p[colunm]=k;
	      }
	    d*=a[i][i];
	    //第i行归一化
	     for(k=i+1;k<n;k++)a[i][k]/=a[i][i];
	     for(k=0;k<m;k++)b[i][k]/=a[i][i];
	     a[i][i]=1;
	    //消元
	    for(j=i+1;j<n;j++)
	     { for(k=i+1;k<n;k++)a[j][k]-=a[j][i]*a[i][k];
		   for(k=0;k<m;k++)b[j][k]-=a[j][i]*b[i][k];
		   a[j][i]=0;
	     }
	   }
       d*=a[n-1][n-1];
       //回代
       for(k=0;k<m;k++)
       {b[n-1][k]/=a[n-1][n-1];
        for(i=n-2;i>=0;i--)
          for(j=i+1;j<n;j++)
           b[i][k]-=a[i][j]*b[j][k];
       }

       //调整次序
       for(i=0;i<n;i++)
         for(j=0;j<m;j++)
         c[p[i]][j]=b[i][j];

       return d;
  }

 public static boolean GaussComplex(double[][] a,double[][] b,double[] c,double[] d, int n)
  { double[][] e=new double[2*n][2*n];
    double[][] x=new double[2*n][1];
    double[][] y=new double[2*n][1];
    double t;
    int i,j;
    for(i=0;i<n;i++)
      for(j=0;j<n;j++)
      {e[i][j]=a[i][j];
       e[n+i][n+j]=a[i][j];
       e[i][n+j]=-b[i][j];
       e[n+i][j]=b[i][j];
       x[i][0]=c[i];
       x[n+i][0]=d[i];
	  }
	t=GaussSolve(e,x,y,2*n,1);
	if (t==0)return false;
	for(i=0;i<n;i++)
	{c[i]=y[i][0];d[i]=y[n+i][0];}
	return true;
 }

public static void main(String[] args)
{double[][] a ={{1,3,2,13},{7,2,1,-2},{9,15,3,-2},{-2,-2,11,5}};
 double[][] b ={{3,-2,1,6},{-2,7,5,8},{9,-3,15,1},{-2,-2,7,6}};
 double[] c={2,7,3,9};
 double[] d={1,2,-2,3};
 int i,j;
 if (GaussComplex(a,b,c,d,4))
   { for(i=0;i<4;i++)
      {Format.printf("x%d=",i+1);
       Format.printf("%f",c[i]);
       if(d[i]<=0)Format.printf("%fI\n",d[i]);
       else Format.printf("+%fI\n",d[i]);
	  }
   }
else
 {System.out.print("系数矩阵奇异\n");}
}
}