Program f08pefe
! F08PEF Example Program Text
! Mark 28.4 Release. NAG Copyright 2022.
! .. Use Statements ..
Use nag_library, Only: dgemm, dhseqr, dlange => f06raf, nag_wp, x02ajf, &
x04caf
! .. Implicit None Statement ..
Implicit None
! .. Parameters ..
Integer, Parameter :: nin = 5, nout = 6
! .. Local Scalars ..
Real (Kind=nag_wp) :: alpha, beta, norm
Integer :: i, ifail, info, ldc, ldd, ldh, ldz, &
lwork, n
! .. Local Arrays ..
Real (Kind=nag_wp), Allocatable :: c(:,:), d(:,:), h(:,:), wi(:), &
work(:), wr(:), z(:,:)
! .. Executable Statements ..
Write (nout,*) 'F08PEF Example Program Results'
Flush (nout)
! Skip heading in data file
Read (nin,*)
Read (nin,*) n
ldc = n
ldd = n
ldh = n
ldz = n
lwork = n
Allocate (c(ldc,n),d(ldd,n),h(ldh,n),wi(n),work(lwork),wr(n),z(ldz,n))
! Read H from data file
Read (nin,*)(h(i,1:n),i=1,n)
! Copy H into D
d(1:n,1:n) = h(1:n,1:n)
! Print Matrix H
! ifail: behaviour on error exit
! =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 0
Call x04caf('General',' ',n,n,h,ldh,'Matrix H',ifail)
! Calculate the eigenvalues and Schur factorization of H
! The NAG name equivalent of dhseqr is f08pef
Call dhseqr('Schur form','Initialize Z',n,1,n,h,ldh,wr,wi,z,ldz,work, &
lwork,info)
Write (nout,*)
If (info>0) Then
Write (nout,*) 'Failure to converge.'
Else
! Compute H - Z*T*Z^T from the factorization of A and store in matrix D
! The NAG name equivalent of dgemm is f06yaf
alpha = 1.0_nag_wp
beta = 0.0_nag_wp
Call dgemm('N','N',n,n,n,alpha,z,ldz,h,ldh,beta,c,ldc)
alpha = -1.0_nag_wp
beta = 1.0_nag_wp
Call dgemm('N','T',n,n,n,alpha,c,ldc,z,ldz,beta,d,ldd)
! Find norm of matrix D and print warning if it is too large
! f06raf is the NAG name equivalent of the LAPACK auxiliary dlange
norm = dlange('O',ldd,n,d,ldd,work)
If (norm>x02ajf()**0.8_nag_wp) Then
Write (nout,*) 'Norm of H-(Z*T*Z^T) is much greater than 0.'
Write (nout,*) 'Schur factorization has failed.'
Else
! Print eigenvalues
Write (nout,*) 'Eigenvalues'
Write (nout,99999)(' (',wr(i),',',wi(i),')',i=1,n)
End If
End If
99999 Format (1X,A,F8.4,A,F8.4,A)
End Program f08pefe