Program f08qgfe
! F08QGF Example Program Text
! Mark 28.5 Release. NAG Copyright 2022.
! .. Use Statements ..
Use nag_library, Only: dgemm, dlange => f06raf, dtrsen, 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, s, sep
Integer :: i, ifail, info, lda, ldc, ldq, ldt, &
liwork, lwork, m, n
! .. Local Arrays ..
Real (Kind=nag_wp), Allocatable :: a(:,:), c(:,:), q(:,:), t(:,:), &
wi(:), work(:), wr(:)
Integer, Allocatable :: iwork(:)
Logical, Allocatable :: select(:)
! .. Executable Statements ..
Write (nout,*) 'F08QGF Example Program Results'
Write (nout,*)
Flush (nout)
! Skip heading in data file
Read (nin,*)
Read (nin,*) n
lda = n
ldc = n
ldq = n
ldt = n
liwork = (n*n)/4
lwork = (n*n)/2
Allocate (a(lda,n),c(ldc,n),q(ldq,n),t(ldt,n),wi(n),work(lwork),wr(n), &
iwork(liwork),select(n))
! Read T, Q and the logical array SELECT from data file
Read (nin,*)(t(i,1:n),i=1,n)
Read (nin,*)(q(i,1:n),i=1,n)
Read (nin,*) select(1:n)
! Compute Q * T * Q**T to find A
! The NAG name equivalent of dgemm is f06yaf
alpha = 1._nag_wp
beta = 0._nag_wp
Call dgemm('N','N',n,n,n,alpha,q,ldq,t,ldt,beta,c,ldc)
Call dgemm('N','T',n,n,n,alpha,c,ldc,q,ldq,beta,a,lda)
! Print Matrix A, as computed from Q * T * Q**T
! ifail: behaviour on error exit
! =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 0
Call x04caf('General',' ',n,n,a,lda,'Matrix A computed from Q*T*Q^T', &
ifail)
Write (nout,*)
Flush (nout)
! Reorder the Schur factor T and update the matrix Q to obtain TT and QT
! The NAG name equivalent of dtrsen is f08qgf
Call dtrsen('Both','Vectors',select,n,t,ldt,q,ldq,wr,wi,m,s,sep,work, &
lwork,iwork,liwork,info)
! Compute (Q * T * Q^T) - (QT * TT * QT^T) and store in A,
! i.e. the difference between reconstructed A using Schur and reordered
! Schur decompositions.
alpha = 1._nag_wp
beta = 0._nag_wp
Call dgemm('N','N',n,n,n,alpha,q,ldq,t,ldt,beta,c,ldc)
alpha = -1._nag_wp
beta = 1._nag_wp
Call dgemm('N','T',n,n,n,alpha,c,ldc,q,ldq,beta,a,lda)
! Find norm of difference matrix and print warning if it is too large
! f06raf is the NAG name equivalent of the LAPACK auxiliary dlange
norm = dlange('O',lda,n,a,lda,work)
If (norm>x02ajf()**0.8_nag_wp) Then
Write (nout,*) 'Norm of A - (QT * TT * QT^T) is much greater than 0.'
Write (nout,*) 'Schur factorization has failed.'
Else
! Print Result
Write (nout,99999) 'Condition number estimate', &
' of the selected cluster of eigenvalues = ', 1.0_nag_wp/s
Write (nout,*)
Write (nout,99999) 'Condition number estimate of the spec', &
'ified invariant subspace = ', 1.0_nag_wp/sep
End If
99999 Format (1X,A,A,1P,E10.2)
End Program f08qgfe