NAG Library Manual, Mark 28.7
Interfaces:  FL   CL   CPP   AD 

NAG FL Interface Introduction
Example description
    Program f08yefe

!     F08YEF Example Program Text

!     Mark 28.7 Release. NAG Copyright 2022.

!     .. Use Statements ..
      Use nag_library, Only: dggsvp, dtgsja, f06raf, nag_wp, x02ajf, x04cbf
!     .. 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, m, n, ncycle, p
!     .. Local Arrays ..
      Real (Kind=nag_wp), Allocatable  :: a(:,:), alpha(:), b(:,:), beta(:),   &
                                          q(:,:), tau(:), u(:,:), v(:,:),      &
      Integer, Allocatable             :: iwork(:)
      Character (1)                    :: clabs(1), rlabs(1)
!     .. Intrinsic Procedures ..
      Intrinsic                        :: max, real
!     .. Executable Statements ..
      Write (nout,*) 'F08YEF 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),   &

!     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)*f06raf('One-norm',m,n,a,lda,work)*eps
      tolb = real(max(p,n),kind=nag_wp)*f06raf('One-norm',p,n,b,ldb,work)*eps

!     Compute the factorization of (A, B)
!         (A = U1*S*(Q1**T), B = V1*T*(Q1**T))
!     The NAG name equivalent of dggsvp is f08vef
      Call dggsvp('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**T), B = V*D2*(0 R)*(Q**T))
!     The NAG name equivalent of dtgsja is f08yef
      Call dtgsja('U','V','Q',m,p,n,k,l,a,lda,b,ldb,tola,tolb,alpha,beta,u,    &

      If (info==0) Then

!       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**T B**T)**T (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 x04cbf('General',' ',m,m,u,ldu,'1P,E12.4','Orthogonal matrix U',  &

        Write (nout,*)
        Flush (nout)

        Call x04cbf('General',' ',p,p,v,ldv,'1P,E12.4','Orthogonal matrix V',  &

        Write (nout,*)
        Flush (nout)

        Call x04cbf('General',' ',n,n,q,ldq,'1P,E12.4','Orthogonal matrix Q',  &

        Write (nout,*)
        Flush (nout)

        Call x04cbf('Upper triangular','Non-unit',irank,irank,a(1,n-irank+1),  &
          lda,'1P,E12.4','Nonsingular upper triangular matrix R','Integer',    &

        Write (nout,*)
        Write (nout,*) 'Number of cycles of the Kogbetliantz method'
        Write (nout,99999) ncycle
        Write (nout,99997) 'Failure in DTGSJA. INFO =', info
      End If

99999 Format (1X,I5)
99998 Format (3X,8(1P,E12.4))
99997 Format (1X,A,I4)
    End Program f08yefe