void pade(double cof[], int n, float *resid)
{
void lubksb(float **a, int n, int *indx, float b[]);
void ludcmp(float **a, int n, int *indx, float *d);
void mprove(float **a, float **alud, int n, int indx[], float b[],
float x[]);
int j,k,*indx;
float d,rr,rrold,sum,**q,**qlu,*x,*y,*z;
indx=ivector(1,n);
q=matrix(1,n,1,n);
qlu=matrix(1,n,1,n);
x=vector(1,n);
y=vector(1,n);
z=vector(1,n);
for (j=1;j<=n;j++) {
y[j]=x[j]=cof[n+j];
for (k=1;k<=n;k++) {
q[j][k]=cof[j-k+n];
qlu[j][k]=q[j][k];
}
}
ludcmp(qlu,n,indx,&d);
lubksb(qlu,n,indx,x);
rr=BIG;
do {
rrold=rr;
for (j=1;j<=n;j++) z[j]=x[j];
mprove(q,qlu,n,indx,y,x);
for (rr=0.0,j=1;j<=n;j++)
rr += SQR(z[j]-x[j]);
} while (rr < rrold);
*resid=sqrt(rrold);
for (k=1;k<=n;k++) {
for (sum=cof[k],j=1;j<=k;j++) sum -= z[j]*cof[k-j];
y[k]=sum;
}
for (j=1;j<=n;j++) {
cof[j]=y[j];
cof[j+n] = -z[j];
}
free_vector(z,1,n);
free_vector(y,1,n);
free_vector(x,1,n);
free_matrix(qlu,1,n,1,n);
free_matrix(q,1,n,1,n);
free_ivector(indx,1,n);
}
int main(void)
{
int i,j,*indx;
long idum=(-13);
float d,*x,**a,**aa;
static float ainit[NP][NP]=
{1.0,2.0,3.0,4.0,5.0,
2.0,3.0,4.0,5.0,1.0,
1.0,1.0,1.0,1.0,1.0,
4.0,5.0,1.0,2.0,3.0,
5.0,1.0,2.0,3.0,4.0};
static float b[N+1]={0.0,1.0,1.0,1.0,1.0,1.0};
indx=ivector(1,N);
x=vector(1,N);
a=convert_matrix(&ainit[0][0],1,N,1,N);
aa=matrix(1,N,1,N);
for (i=1;i<=N;i++) {
x[i]=b[i];
for (j=1;j<=N;j++)
aa[i][j]=a[i][j];
}
ludcmp(aa,N,indx,&d);
lubksb(aa,N,indx,x);
printf("\nSolution vector for the equations:\n");
for (i=1;i<=N;i++) printf("%12.6f",x[i]);
printf("\n");
/* now phoney up x and let mprove fix it */
for (i=1;i<=N;i++) x[i] *= (1.0+0.2*ran3(&idum));
printf("\nSolution vector with noise added:\n");
for (i=1;i<=N;i++) printf("%12.6f",x[i]);
printf("\n");
mprove(a,aa,N,indx,b,x);
printf("\nSolution vector recovered by mprove:\n");
for (i=1;i<=N;i++) printf("%12.6f",x[i]);
printf("\n");
free_matrix(aa,1,N,1,N);
free_convert_matrix(a,1,N,1,N);
free_vector(x,1,N);
free_ivector(indx,1,N);
return 0;
}
