NAG Library Manual, Mark 28.4
Interfaces:  FL   CL   CPP   AD 

NAG FL Interface Introduction
Example description
    Program f08vufe

!     F08VUF Example Program Text

!     Mark 28.4 Release. NAG Copyright 2022.

!     .. Use Statements ..
      Use nag_library, Only: f06uaf, nag_wp, x02ajf, x04dbf, zggsvp3, ztgsja
!     .. Implicit None Statement ..
      Implicit None
!     .. Parameters ..
      Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
      Real (Kind=nag_wp)               :: eps, tola, tolb
      Integer                          :: i, ifail, info, irank, j, k, l, lda, &
                                          ldb, ldq, ldu, ldv, lwork, m, n,     &
                                          ncycle, p
!     .. Local Arrays ..
      Complex (Kind=nag_wp), Allocatable :: a(:,:), b(:,:), q(:,:), tau(:),    &
                                          u(:,:), v(:,:), work(:)
      Complex (Kind=nag_wp)            :: wdum(1)
      Real (Kind=nag_wp), Allocatable  :: alpha(:), beta(:), rwork(:)
      Integer, Allocatable             :: iwork(:)
      Character (1)                    :: clabs(1), rlabs(1)
!     .. Intrinsic Procedures ..
      Intrinsic                        :: max, nint, real
!     .. Executable Statements ..
      Write (nout,*) 'F08VUF Example Program Results'
      Write (nout,*)
      Flush (nout)
!     Skip heading in data file
      Read (nin,*)
      Read (nin,*) m, n, p
      lda = m
      ldb = p
      ldq = n
      ldu = m
      ldv = p
      Allocate (a(lda,n),alpha(n),b(ldb,n),beta(n),q(ldq,n),tau(n),u(ldu,m),   &

!     Perform workspace query to get optimal size of work
!     The NAG name equivalent of zggsvp3 is f08vuf
      lwork = -1
      Call zggsvp3('U','V','Q',m,p,n,a,lda,b,ldb,tola,tolb,k,l,u,ldu,v,ldv,q,  &
      lwork = nint(real(wdum(1)))
      Allocate (work(lwork))

!     Read the m by n matrix A and p by n matrix B from data file

      Read (nin,*)(a(i,1:n),i=1,m)
      Read (nin,*)(b(i,1:n),i=1,p)

!     Compute tola and tolb as
!         tola = max(m,n)*norm(A)*macheps
!         tolb = max(p,n)*norm(B)*macheps

      eps = x02ajf()
      tola = real(max(m,n),kind=nag_wp)*f06uaf('One-norm',m,n,a,lda,rwork)*eps
      tolb = real(max(p,n),kind=nag_wp)*f06uaf('One-norm',p,n,b,ldb,rwork)*eps

!     Compute the factorization of (A, B)
!         (A = U*S*(Q**H), B = V*T*(Q**H))

!     The NAG name equivalent of zggsvp3 is f08vuf
      Call zggsvp3('U','V','Q',m,p,n,a,lda,b,ldb,tola,tolb,k,l,u,ldu,v,ldv,q,  &

!     Compute the generalized singular value decomposition of (A, B)
!         (A = U*D1*(0 R)*(Q**H), B = V*D2*(0 R)*(Q**H))

      Deallocate (work)
      Allocate (work(2*n))

!     The NAG name equivalent of ztgsja is f08ysf
      Call ztgsja('U','V','Q',m,p,n,k,l,a,lda,b,ldb,tola,tolb,alpha,beta,u,    &

!     Print solution

      irank = k + l
      Write (nout,*) 'Number of infinite generalized singular values (k)'
      Write (nout,99999) k
      Write (nout,*) 'Number of finite generalized singular values (l)'
      Write (nout,99999) l
      Write (nout,*) 'Effective Numerical rank of (A; B) (k+l)'
      Write (nout,99999) irank
      Write (nout,*)
      Write (nout,*) 'Finite generalized singular values'
      Write (nout,99998)(alpha(j)/beta(j),j=k+1,irank)
      Write (nout,*)
      Flush (nout)

!     ifail: behaviour on error exit
!            =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
      ifail = 0
      Call x04dbf('General',' ',m,m,u,ldu,'Bracketed','1P,E12.4',              &
        'Unitary matrix U','Integer',rlabs,'Integer',clabs,80,0,ifail)

      Write (nout,*)
      Flush (nout)

      Call x04dbf('General',' ',p,p,v,ldv,'Bracketed','1P,E12.4',              &
        'Unitary matrix V','Integer',rlabs,'Integer',clabs,80,0,ifail)

      Write (nout,*)
      Flush (nout)

      Call x04dbf('General',' ',n,n,q,ldq,'Bracketed','1P,E12.4',              &
        'Unitary matrix Q','Integer',rlabs,'Integer',clabs,80,0,ifail)

      Write (nout,*)
      Flush (nout)

      Call x04dbf('Upper triangular','Non-unit',irank,irank,a(1,n-irank+1),    &
        lda,'Bracketed','1P,E12.4','Nonsingular upper triangular matrix R',    &

      Write (nout,*)
      Write (nout,*) 'Number of cycles of the Kogbetliantz method'
      Write (nout,99999) ncycle

99999 Format (1X,I5)
99998 Format (3X,8(1P,E12.4))
    End Program f08vufe