Program f08kufe
! F08KUF Example Program Text
! Mark 30.1 Release. NAG Copyright 2024.
! .. Use Statements ..
Use nag_library, Only: f06tff, f06thf, nag_wp, x04dbf, zgebrd, zgelqf, &
zgeqrf, zunglq, zungqr, zunmbr
! .. Implicit None Statement ..
Implicit None
! .. Parameters ..
Complex (Kind=nag_wp), Parameter :: zero = (0.0E0_nag_wp,0.0E0_nag_wp)
Integer, Parameter :: nin = 5, nout = 6
! .. Local Scalars ..
Integer :: i, ic, ifail, info, lda, ldph, ldu, &
lwork, m, n
! .. Local Arrays ..
Complex (Kind=nag_wp), Allocatable :: a(:,:), ph(:,:), tau(:), taup(:), &
tauq(:), u(:,:), work(:)
Real (Kind=nag_wp), Allocatable :: d(:), e(:)
Character (1) :: clabs(1), rlabs(1)
! .. Executable Statements ..
Write (nout,*) 'F08KUF Example Program Results'
! Skip heading in data file
Read (nin,*)
Do ic = 1, 2
Read (nin,*) m, n
lda = m
ldph = n
ldu = m
lwork = 64*(m+n)
Allocate (a(lda,n),ph(ldph,n),tau(n),taup(n),tauq(n),u(ldu,n), &
work(lwork),d(n),e(n-1))
! Read A from data file
Read (nin,*)(a(i,1:n),i=1,m)
If (m>=n) Then
! Compute the QR factorization of A
! The NAG name equivalent of zgeqrf is f08asf
Call zgeqrf(m,n,a,lda,tau,work,lwork,info)
! Copy A to U
Call f06tff('Lower',m,n,a,lda,u,ldu)
! Form Q explicitly, storing the result in U
! The NAG name equivalent of zungqr is f08atf
Call zungqr(m,n,n,u,ldu,tau,work,lwork,info)
! Copy R to PH (used as workspace)
Call f06tff('Upper',n,n,a,lda,ph,ldph)
! Set the strictly lower triangular part of R to zero
Call f06thf('Lower',n-1,n-1,zero,zero,ph(2,1),ldph)
! Bidiagonalize R
! The NAG name equivalent of zgebrd is f08ksf
Call zgebrd(n,n,ph,ldph,d,e,tauq,taup,work,lwork,info)
! Update Q, storing the result in U
! The NAG name equivalent of zunmbr is f08kuf
Call zunmbr('Q','Right','No transpose',m,n,n,ph,ldph,tauq,u,ldu, &
work,lwork,info)
! Print bidiagonal form and matrix Q
Write (nout,*)
Write (nout,*) 'Example 1: bidiagonal matrix B'
Write (nout,*) 'Diagonal'
Write (nout,99999) d(1:n)
Write (nout,*) 'Superdiagonal'
Write (nout,99999) e(1:n-1)
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,n,u,ldu,'Bracketed','F7.4', &
'Example 1: matrix Q','Integer',rlabs,'Integer',clabs,80,0,ifail)
Else
! Compute the LQ factorization of A
! The NAG name equivalent of zgelqf is f08avf
Call zgelqf(m,n,a,lda,tau,work,lwork,info)
! Copy A to PH
Call f06tff('Upper',m,n,a,lda,ph,ldph)
! Form Q explicitly, storing the result in PH
! The NAG name equivalent of zunglq is f08awf
Call zunglq(n,n,m,ph,ldph,tau,work,lwork,info)
! Copy L to U (used as workspace)
Call f06tff('Lower',m,m,a,lda,u,ldu)
! Set the strictly upper triangular part of L to zero
Call f06thf('Upper',m-1,m-1,zero,zero,u(1,2),ldu)
! Bidiagonalize L
! The NAG name equivalent of zgebrd is f08ksf
Call zgebrd(m,m,u,ldu,d,e,tauq,taup,work,lwork,info)
! Update P**H, storing the result in PH
! The NAG name equivalent of zunmbr is f08kuf
Call zunmbr('P','Left','Conjugate transpose',m,n,m,u,ldu,taup,ph, &
ldph,work,lwork,info)
! Print bidiagonal form and matrix P**H
Write (nout,*)
Write (nout,*) 'Example 2: bidiagonal matrix B'
Write (nout,*) 'Diagonal'
Write (nout,99999) d(1:m)
Write (nout,*) 'Superdiagonal'
Write (nout,99999) e(1:m-1)
Write (nout,*)
Flush (nout)
ifail = 0
Call x04dbf('General',' ',m,n,ph,ldph,'Bracketed','F7.4', &
'Example 2: matrix P**H','Integer',rlabs,'Integer',clabs,80,0, &
ifail)
End If
Deallocate (a,ph,tau,taup,tauq,u,work,d,e)
End Do
99999 Format (3X,(8F8.4))
End Program f08kufe