sor.cpp

SOR解n维线性方程组 用vc语言完成SOR解n维线性方程组

// SOR.cpp : Defines the entry point for the console application.
//

#include "stdafx.h"

#include<stdio.h>
#include<stdlib.h>
#include<math.h>
#include<conio.h>
#define A(x,y) A[(u+1)*(x)+y]
#define PRECISION 0.0001
int i,j,u;
float max(int u,float *x,float *y)
{float max;
 int k=0;
 for(i=0;i<u;++i)
  {max=fabs(x[k]-y[k]);
   if(fabs(x[i]-y[i])>max)
   k=i;
  }
 return max;
}
float max1(int u,float *A,float *x)
{float max,*sum;
 int k=0;
 sum=(float *)malloc(u*sizeof(float));
 for(i=0;i<u;++i)
 sum[i]=0;
 for(i=0;i<u;++i)
 {
  for(j=0;j<u;++j)
  sum[i]+=A(i,j)*x[j];
  sum[i]=fabs((A(i,u)-sum[i])/A(i,i));
 }
  for(i=0;i<u;++i)
  {max=sum[k];
   if(sum[i]>max)
   k=i;
  }
 return max;
}
void SOR(int u,float *A,float *x)
{int k;
 float w,sum;
 printf("\nPlease input the relax VAR:w="); //松弛变量w
 scanf("%f",&w);
 for(k=1;max1(u,A,x)>PRECISION;++k)
  for(i=0;i<u;++i)
  {sum=0;
   for(j=0;j<u;++j)
   sum+=A(i,j)*x[j];
   x[i]+=w*(A(i,u)-sum)/A(i,i);
  }
 printf("The SOR times :%d\n",k);
 printf("The SOR solution:");
 for(i=0;i<u;++i)
 printf("x[%d]=%f ",i+1,x[i]);
}





int main(int argc, char* argv[])
{
	char c;
 float *A,*x,*x_;
 printf("\nPlease input the number of lines:");
 scanf("%d",&u);
 A=(float *)calloc(u*(u+1),sizeof(float));
 x=(float *)malloc(u*sizeof(float));
 x_=(float *)malloc(u*sizeof(float));
 printf("Please input the matrix A(%d*%d):\n",u,u);//n*n矩阵（线形方程组的增广矩阵）

  for(i=1;i<=u;++i)
{printf("\nPlease input line %d:",i);
  for(j=1;j<=u;++j)
  scanf("%f",&A(i-1,j-1));}
 printf("Please input the origin %d dimensions vector x0=",u);
 for(i=0;i<u;++i)
 scanf("%f",&x[i]);
SOR(u,A,x);
printf("\nPlease press enter key to quit !");
getch();
	return 0;
}