// 程序7.2 Gauss 消元法 — 列选主元
#include <stdio.h>
#include <stdlib.h>
#include <conio.h>
#include <math.h>
#define MAX_n 100
#define PRECISION 0.0000001
void MatrixInput(float A[][MAX_n],int m,int n)
{
int i,j;float ftmp;
printf("\n===Begin input Matrix elements===\n");
for(i=1;i<=m;++i)
{
printf("Input_Line %d : ",i);
for(j=1;j<=n;++j)
{scanf("%f",&ftmp);A[i][j]=ftmp;}
}
}
void MatrixOneColumnOutput(float A[][MAX_n],int n,int k)
{
int i;
for(i=1;i<=n;++i)
printf("\nx[%d]=%f",i,A[i][k]);
}
int UpTriangle(float U[][MAX_n],int n)
{
int i,j;
for(i=n;i>0;--i)
{
if(fabs(U[i][i])<PRECISION)return 1;
for(j=i+1;j<=n;++j)
U[i][n+1]-=U[i][j]*U[j][n+1];
U[i][n+1]/=U[i][i];
}
return 0;
}
void Swap(float *a,float *b)
{
float ftmp;
ftmp=*a;
*a=*b;
*b=ftmp;
}
int GaussElimination_column_select(float A[][MAX_n],int n)
{
int i,j,k;
float fTmp;
for(i=1;i<n;++i)
{
//-------------------------------------------
for(k=i,j=i+1;j<=n;++j)
if(fabs(A[j][i])>fabs(A[k][i])) k=j;
for(j=i;j<=n+1;++j)
Swap(&A[i][j],&A[k][j]);
//-------------------------------------------
if(fabs(A[i][i])<PRECISION)return 1;
for(j=i+1;j<=n;++j)
for(k=i+1;k<=n+1;++k)
A[j][k]-=A[i][k]*A[j][i]/A[i][i];
}
UpTriangle(A,n);
return 0;
}
void main()
{
int n;
float A[MAX_n][MAX_n];
printf("\nInput n=");
scanf("%d",&n);
if(n>=MAX_n-1)
{
printf("\n\007n must <%d!",MAX_n);
exit(0);
}
MatrixInput(A,n,n+1);
if(GaussElimination_column_select(A,n))
printf("\nGauss Failed!");
else
{
printf("\nOutput Solution:");
MatrixOneColumnOutput(A,n,n+1);
}
printf("\n\n\007Press any key to quit!\n");
getch();
}
/*
运行实例:(注意,输入为方程组的增广矩阵)
Input n=4
===Begin input Matrix elements===
Input_Line 1 : 0.4096 0.1234 0.3678 0.2943 0.4043
Input_Line 2 : 0.2246 0.3872 0.4015 0.1129 0.155
Input_Line 3 : 0.3645 0.192 0.3781 0.0643 0.424
Input_Line 4 : 0.1784 0.4002 0.2786 0.3927 -0.2557
Output Sulution:
x[1]=-0.181918
x[2]=-1.663031
x[3]=2.217229
x[4]=-0.446704
Press any key to quit!
*/