数值计算：高斯列主元消元法

这是一个解方程的程序。用的是高斯列主元消元法。

（在Visual C++.Net 2003 Windows Server 2003下调试成功）

目前没有检查是否有根。

// Gauss.cpp : 定义控制台应用程序的入口点。

//

//高斯列主元消元法

//2004-10-14

#include "stdafx.h"

#include "stdio.h"

#include "conio.h"

#include "math.h"

#define M 3 //The Size of Matrix

int _tmain(int argc, _TCHAR* argv[])

{


//Definitions


double A[M][M];


double b[M];


double m[M][M];


double x[M];


int i;


int j;


int k;


int r;


double Temp;


double Max;

//Input the Matrix A


printf("Please Input the Matrix A:\n");


for (i=0;i


{


for (j=0;j


{


scanf( "%lf",&A[i][j]);


}

}


//End Input


//Input the Matrix b


printf( "Please Input the Matrix b:\n");


for (i=0;i


{


scanf( "%lf",&b[i]);


}


//End Input





//Solve the Matrix A


for (k=0;k


{


//Choose the Main Item


Max=abs(A[k][k]);


for (i=k;i


{


if (abs(A[i][k]) >Max)


{


Max=abs(A[i][k]);


r=i;


}


}


//End Choose


//Change the Row r and Row k


for (i=0;i


{


Temp=A[k][i];


A[k][i]=A[r][i];


A[r][i]=Temp;


}


Temp=b[k];


b[k]=b[r];


b[r]=Temp;


//End Change


//Calculate m


for (i=k+1;i


{


m[i][k]=A[i][k]/A[k][k];


A[i][k]=m[i][k];


}


//End Calculate


//Calculate Others


for (i=k+1;i


{


for (j=k+1;j


{


A[i][j]=A[i][j]-m[i][k]*A[k][j];


}


b[i]=b[i]-m[i][k]*b[k];


A[i][k]=0;


}


//End Calculate


}


//End Solve


//Solve the Result


x[M-1]=b[M-1]/A[M-1][M-1];


for (i=M-2;i >=0;i--)


{


Temp=0;


for (j=i+1;j


{


Temp=Temp+A[i][j]*x[j];


}


x[i]=(b[i]-Temp)/A[i][i];


}


//End Solve


//Output the Result


printf( "\nThe Result Matrix is:");


for (i=0;i


{


printf( "X%d=%lf\t",i+1,x[i]);


}


//End Output


getch();


return 0;

}