f08scce.c

/* nag_lapackeig_dsygvd (f08scc) Example Program.
 *
 * Copyright 2025 Numerical Algorithms Group.
 *
 * Mark 31.1, 2025.
 */
#include<math.h>
#include<nag.h>
#include<stdio.h>
intmain(void){
/* Scalars */
doubleanorm,bnorm,eps,rcond,rcondb,t1,t2,t3;
Integeri,j,n,pda,pdb;
Integerexit_status=0;
/* Arrays */
double*a=0,*b=0,*eerbnd=0,*rcondz=0,*w=0,*zerbnd=0;
charnag_enum_arg[40];
/* Nag Types */
NagErrorfail;
Nag_OrderTypeorder;
Nag_UploTypeuplo;
#ifdef NAG_COLUMN_MAJOR
#define A(I, J) a[(J - 1) * pda + I - 1]
#define B(I, J) b[(J - 1) * pdb + I - 1]
order=Nag_ColMajor;
#else
#define A(I, J) a[(I - 1) * pda + J - 1]
#define B(I, J) b[(I - 1) * pdb + J - 1]
order=Nag_RowMajor;
#endif
INIT_FAIL(fail);
printf("nag_lapackeig_dsygvd (f08scc) Example Program Results\n\n");
/* Skip heading in data file */
scanf("%*[^\n]");
scanf("%"NAG_IFMT"%*[^\n]",&n);
if(n<0){
printf("Invalid n\n");
exit_status=1;
gotoEND;
;
}
scanf(" %39s%*[^\n]",nag_enum_arg);
/* nag_enum_name_to_value (x04nac).
 * Converts NAG enum member name to value
 */
uplo=(Nag_UploType)nag_enum_name_to_value(nag_enum_arg);
pda=n;
pdb=n;
/* Allocate memory */
if(!(a=NAG_ALLOC(n*n,double))||!(b=NAG_ALLOC(n*n,double))||
!(eerbnd=NAG_ALLOC(n,double))||!(rcondz=NAG_ALLOC(n,double))||
!(w=NAG_ALLOC(n,double))||!(zerbnd=NAG_ALLOC(n,double))){
printf("Allocation failure\n");
exit_status=-1;
gotoEND;
}
/* Read the triangular parts of the matrices A and B */
if(uplo==Nag_Upper){
for(i=1;i<=n;++i)
for(j=i;j<=n;++j)
scanf("%lf",&A(i,j));
scanf("%*[^\n]");
for(i=1;i<=n;++i)
for(j=i;j<=n;++j)
scanf("%lf",&B(i,j));
}else{
for(i=1;i<=n;++i)
for(j=1;j<=i;++j)
scanf("%lf",&A(i,j));
scanf("%*[^\n] ");
for(i=1;i<=n;++i)
for(j=1;j<=i;++j)
scanf("%lf",&B(i,j));
}
scanf("%*[^\n] ");
/* Compute the one-norms of the symmetric matrices A and B using
 * nag_blast_dsy_norm (f16rcc).
 */
nag_blast_dsy_norm(order,Nag_OneNorm,uplo,n,a,pda,&anorm,&fail);
nag_blast_dsy_norm(order,Nag_OneNorm,uplo,n,b,pdb,&bnorm,&fail);
if(fail.code!=NE_NOERROR){
printf("Error from nag_blast_dsy_norm (f16rcc).\n%s\n",fail.message);
exit_status=1;
gotoEND;
}
/* Solve the generalized symmetric eigenvalue problem A*B*x = lambda*x
 * using nag_lapackeig_dsygvd (f08scc).
 */
nag_lapackeig_dsygvd(order,2,Nag_DoBoth,uplo,n,a,pda,b,pdb,w,&fail);
if(fail.code!=NE_NOERROR){
printf("Error from nag_lapackeig_dsygvd (f08scc).\n%s\n",fail.message);
exit_status=1;
gotoEND;
}
/* Normalize the eigenvectors */
for(j=1;j<=n;j++)
for(i=n;i>=1;i--)
A(i,j)=A(i,j)/A(1,j);
/* Print eigensolution */
printf(" Eigenvalues\n ");
for(j=0;j<n;++j)
printf(" %10.4f%s",w[j],j%6==5?"\n":"");
printf("\n\n");
fflush(stdout);
nag_file_print_matrix_real_gen(order,Nag_GeneralMatrix,Nag_NonUnitDiag,n,
n,a,pda,"Eigenvectors",0,&fail);
if(fail.code!=NE_NOERROR){
printf("Error from nag_file_print_matrix_real_gen (x04cac).\n%s\n",
fail.message);
exit_status=1;
gotoEND;
}
/* Estimate the reciprocal condition number of the Cholesky factor of B.
 * nag_lapacklin_dtrcon (f07tgc)
 * Note that: cond(B) = 1.0/(rcond*rcond).
 */
nag_lapacklin_dtrcon(order,Nag_OneNorm,uplo,Nag_NonUnitDiag,n,b,pdb,
&rcond,&fail);
if(fail.code!=NE_NOERROR){
printf("Error from nag_lapacklin_dtrcon (f07tgc).\n%s\n",fail.message);
exit_status=1;
gotoEND;
}
/* Print the reciprocal condition number of B */
rcondb=rcond*rcond;
printf("\nEstimate of reciprocal condition number for B\n %11.1e\n",
rcondb);
/* Get the machine precision, using nag_machine_precision (x02ajc) */
eps=nag_machine_precision;
if(rcond<eps){
printf("\nB is very ill-conditioned, error estimates have not been"
" computed\n");
gotoEND;
}
/* Estimate reciprocal condition numbers for the eigenvectors of A - lambda*B
 * nag_lapackeig_ddisna (f08flc)
 */
nag_lapackeig_ddisna(Nag_EigVecs,n,n,w,rcondz,&fail);
if(fail.code!=NE_NOERROR){
printf("Error from nag_lapackeig_ddisna (f08flc).\n%s\n",fail.message);
exit_status=1;
gotoEND;
}
/* Compute the error estimates for the eigenvalues and eigenvectors. */
t1=1.0/rcond;
t2=eps*t1;
t3=anorm*bnorm;
for(i=0;i<n;++i){
eerbnd[i]=eps*(t3+fabs(w[i])/rcondb);
zerbnd[i]=t2*(t3/rcondz[i]+t1);
}
/* Print the approximate error bounds for the eigenvalues and vectors. */
printf("\nError estimates for the eigenvalues\n ");
for(i=0;i<n;++i)
printf(" %10.1e%s",eerbnd[i],i%6==5?"\n":"");
printf("\n\nError estimates for the eigenvectors\n ");
for(i=0;i<n;++i)
printf(" %10.1e%s",zerbnd[i],i%6==5?"\n":"");
printf("\n");
END:
NAG_FREE(a);
NAG_FREE(b);
NAG_FREE(eerbnd);
NAG_FREE(rcondz);
NAG_FREE(w);
NAG_FREE(zerbnd);
returnexit_status;
}