void zrhqr(float a[], int m, float rtr[], float rti[])
{
void balanc(float **a, int n);
void hqr(float **a, int n, float wr[], float wi[]);
int j,k;
float **hess,xr,xi;
hess=matrix(1,MAXM,1,MAXM);
if (m > MAXM || a[m] == 0.0) nrerror("bad args in zrhqr");
for (k=1;k<=m;k++) {
hess[1][k] = -a[m-k]/a[m];
for (j=2;j<=m;j++) hess[j][k]=0.0;
if (k != m) hess[k+1][k]=1.0;
}
balanc(hess,m);
hqr(hess,m,rtr,rti);
for (j=2;j<=m;j++) {
xr=rtr[j];
xi=rti[j];
for (k=j-1;k>=1;k--) {
if (rtr[k] <= xr) break;
rtr[k+1]=rtr[k];
rti[k+1]=rti[k];
}
rtr[k+1]=xr;
rti[k+1]=xi;
}
free_matrix(hess,1,MAXM,1,MAXM);
}
int main(void)
{
int i,j;
static float c[NP][NP]=
{1.0,2.0,0.0,0.0,0.0,
-2.0,3.0,0.0,0.0,0.0,
3.0,4.0,50.0,0.0,0.0,
-4.0,5.0,-60.0,7.0,0.0,
-5.0,6.0,-70.0,8.0,-9.0};
float *wr,*wi,**a;
wr=vector(1,NP);
wi=vector(1,NP);
a=convert_matrix(&c[0][0],1,NP,1,NP);
printf("matrix:\n");
for (i=1;i<=NP;i++) {
for (j=1;j<=NP;j++) printf("%12.2f",a[i][j]);
printf("\n");
}
balanc(a,NP);
elmhes(a,NP);
hqr(a,NP,wr,wi);
printf("eigenvalues:\n");
printf("%11s %16s \n","real","imag.");
for (i=1;i<=NP;i++) printf("%15f %14f\n",wr[i],wi[i]);
free_convert_matrix(a,1,NP,1,NP);
free_vector(wi,1,NP);
free_vector(wr,1,NP);
return 0;
}
int main(void)
{
int i,j;
float *c,*r,**a;
c=vector(1,NP);
r=vector(1,NP);
a=matrix(1,NP,1,NP);
for (i=1;i<=NP;i++)
for (j=1;j<=NP;j++)
a[i][j] = (((i & 1) && !(j & 1)) ? 100.0 : 1.0);
/* Write norms */
for (i=1;i<=NP;i++) {
r[i]=c[i]=0.0;
for (j=1;j<=NP;j++) {
r[i] += fabs(a[i][j]);
c[i] += fabs(a[j][i]);
}
}
printf("rows:\n");
for (i=1;i<=NP;i++) printf("%12.2f",r[i]);
printf("\ncolumns:\n");
for (i=1;i<=NP;i++) printf("%12.2f",c[i]);
printf("\n\n***** Balancing matrix *****\n\n");
balanc(a,NP);
/* Write norms */
for (i=1;i<=NP;i++) {
r[i]=c[i]=0.0;
for (j=1;j<=NP;j++) {
r[i] += fabs(a[i][j]);
c[i] += fabs(a[j][i]);
}
}
printf("rows:\n");
for (i=1;i<=NP;i++) printf("%12.2f",r[i]);
printf("\ncolumns:\n");
for (i=1;i<=NP;i++) printf("%12.2f",c[i]);
printf("\n");
free_matrix(a,1,NP,1,NP);
free_vector(r,1,NP);
free_vector(c,1,NP);
return 0;
}
