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#include <stdio.h>
#include <stdlib.h>
#include <math.h>
float f (float x,float y,float z)
{ return (x*x+y*y+z*z-9);}
float g (float x,float y,float z)
{ return (x*x+y*y-3*x);}
float h (float x,float y,float z)
{ return (y+z-2);}
float df_1(float x,float y,float z)
{ return (2*x);}
float df_2(float x,float y,float z)
{ return (2*y);}
float df_3(float x,float y,float z)
{ return (2*z);}
float dg_1(float x,float y,float z)
{ return (2*x-3);}
float dg_2(float x,float y,float z)
{ return (2*y);}
float dg_3(float x,float y,float z)
{ return (0);}
float dh_1(float x,float y,float z)
{ return (0);}
float dh_2(float x,float y,float z)
{ return (1);}
float dh_3(float x,float y,float z)
{ return (1);}
int main()
{
float x0,y0,z0,x[19],x1[19],x2[19],a[19][19], b[19],p,s,eps=0.001;
int i,j,k,iter=1,n=3;
printf("donner la valeur de x0 ");
scanf("%f",&x0);
printf("donner la valeur de y0 ");
scanf("%f",&y0);
printf("donner la valeur de z0 ");
scanf("%f",&z0);
do
{
a[0][0]= df_1( x0,y0,z0);
a[0][1]= df_2( x0,y0,z0);
a[0][2]= df_3( x0,y0,z0);
b[0]= (df_1( x0,y0,z0))*x0+(df_2( x0,y0,z0))*y0+(df_3( x0,y0,z0))*z0-f ( x0,y0,z0);
a[1][0]= dg_1( x0,y0,z0);
a[1][1]= dg_2( x0,y0,z0);
a[1][2]= dg_3( x0,y0,z0);
b[1]= (dg_1( x0,y0,z0))*x0+(dg_2( x0,y0,z0))*y0+(dg_3( x0,y0,z0))*z0-g ( x0,y0,z0);
a[2][0]= dh_1( x0,y0,z0);
a[2][1]= dh_2( x0,y0,z0);
a[2][2]= dh_3( x0,y0,z0);
b[2]= (dh_1( x0,y0,z0))*x0+(dh_2( x0,y0,z0))*y0+(dh_3( x0,y0,z0))*z0-h ( x0,y0,z0);
printf("%f",a[2][2]);
for(k=0;k<n-1;k++)
{
if (a[k][k]==0)
{
printf("\n\n * Un pivot nul ! => methode de Gauss non applicable\n\n");
system("PAUSE");main();
}
//réduction
for(i=k+1;i<n;i++)
{
p=a[i][k]/a[k][k];
for (j=k;j<n;j++) a[i][j]=a[i][j]-p*a[k][j];
b[i]=b[i]-p*b[k];
}
}
//Résolution
for(i=n-1;i>=0;i--)
{
s=0;
for(j=i+1;j<n;j++)s=s+a[i][j]*x[j];
x[i]=(b[i]-s)/a[i][i];
}
for(i=0;i<n;i++)
{
for (j=0;j<n;j++) if (fabs(a[i][j])<eps) a[i][j]=0;
if (fabs(b[i])<eps) b[i]=0;
}
printf("\n-------------- Gauss -------------\n");
printf("\n * La matrice reduite :");
printf("\n\n");
for (i=0;i<n;i++)
{
printf(" [");
for (j=0;j<n;j++)
{
printf(" %.4f ",a[i][j]);
}
printf("] [ %.4f ]",b[i]);
printf("\n");
}
printf("\n * La resolution donne :\n\n");
for (i=0;i<n;i++) printf(" X_%d = %f ;\n",i+1,x[i]);
iter++;
x0=x[0];
y0=x[1];
z0=x[2];
}while( (fabs(x[0]-x0)<eps) && (fabs(x[1]-y0)<eps) && (fabs(x[2]-z0)<eps) ) ;
printf("le nombre d'iterations est %d\n",iter);
system("PAUSE");
} |