Program f08qufe

!     F08QUF Example Program Text

!     Mark 27.3 Release. NAG Copyright 2021.

!     .. Use Statements ..
      Use nag_library, Only: nag_wp, x02ajf, x04dbf, zgemm, zlange => f06uaf,  &
                             ztrsen
!     .. Implicit None Statement ..
      Implicit None
!     .. Parameters ..
      Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
      Complex (Kind=nag_wp)            :: alpha, beta
      Real (Kind=nag_wp)               :: norm, s, sep
      Integer                          :: i, ifail, info, lda, ldc, ldq, ldt,  &
                                          lwork, m, n
!     .. Local Arrays ..
      Complex (Kind=nag_wp), Allocatable :: a(:,:), c(:,:), q(:,:), t(:,:),    &
                                          w(:), work(:)
      Real (Kind=nag_wp)               :: rwork(1)
      Logical, Allocatable             :: select(:)
      Character (1)                    :: clabs(1), rlabs(1)
!     .. Intrinsic Procedures ..
      Intrinsic                        :: cmplx
!     .. Executable Statements ..
      Write (nout,*) 'F08QUF Example Program Results'
      Write (nout,*)
      Flush (nout)
!     Skip heading in data file
      Read (nin,*)
      Read (nin,*) n
      ldc = n
      lda = n
      ldq = n
      ldt = n
      lwork = (n*n)/2
      Allocate (a(lda,n),c(ldc,n),q(ldq,n),t(ldt,n),w(n),work(lwork),          &
        select(n))

!     Read T, Q and the logical array SELECT from data file

      Read (nin,*)(t(i,1:n),i=1,n)
      Read (nin,*)
      Read (nin,*)(q(i,1:n),i=1,n)
      Read (nin,*)
      Read (nin,*) select(1:n)

!     Compute Q * T * Q**T to find  A
!     The NAG name equivalent of zgemm is f06zaf
      alpha = cmplx(1,kind=nag_wp)
      beta = cmplx(0,kind=nag_wp)
      Call zgemm('N','N',n,n,n,alpha,q,ldq,t,ldt,beta,c,ldc)
      Call zgemm('N','C',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 x04dbf('General',' ',n,n,a,lda,'Bracketed','F7.4',                  &
        'Matrix A created from Q*T*Q^T','Integer',rlabs,'Integer',clabs,80,0,  &
        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 ztrsen is f08quf
      Call ztrsen('Both','Vectors',select,n,t,ldt,q,ldq,w,m,s,sep,work,lwork,  &
        info)

!     Compute (Q * T * Q^H) - (QT * TT * QT^H) and store in A,
!     i.e. the difference between reconstructed A using Schur and reordered
!          Schur decompositions.
      alpha = cmplx(1,kind=nag_wp)
      beta = cmplx(0,kind=nag_wp)
      Call zgemm('N','N',n,n,n,alpha,q,ldq,t,ldt,beta,c,ldc)
      alpha = cmplx(-1,kind=nag_wp)
      beta = cmplx(1,kind=nag_wp)
      Call zgemm('N','C',n,n,n,alpha,c,ldc,q,ldq,beta,a,lda)

!     Find norm of difference matrix and print warning if it is too large
!     f06uaf is the NAG name equivalent of the LAPACK auxiliary zlange
      norm = zlange('O',lda,n,a,lda,rwork)
      If (norm>x02ajf()**0.5_nag_wp) Then
        Write (nout,*) 'Norm of A - (QT * TT * QT^H) is much greater than 0.'
        Write (nout,*) 'Schur factorization has failed.'
      Else
!       Print condition estimates
        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 specified ',      &
          'invariant subspace    = ', 1.0_nag_wp/sep
      End If

99999 Format (1X,A,A,1P,E10.2)
    End Program f08qufe