Program f08vqfe
! F08VQF Example Program Text
! Mark 29.2 Release. NAG Copyright 2023.
! .. Use Statements ..
Use nag_library, Only: nag_wp, x02ajf, x04dbf, zggsvd3, ztrcon
! .. Implicit None Statement ..
Implicit None
! .. Parameters ..
Integer, Parameter :: nin = 5, nout = 6
! .. Local Scalars ..
Real (Kind=nag_wp) :: eps, rcond, serrbd
Integer :: i, ifail, info, irank, j, k, l, lda, &
ldb, ldq, ldu, ldv, lwork, m, n, p
! .. Local Arrays ..
Complex (Kind=nag_wp), Allocatable :: a(:,:), b(:,:), q(:,:), 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 :: nint, real
! .. Executable Statements ..
Write (nout,*) 'F08VQF 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),b(ldb,n),q(ldq,n),u(ldu,m),v(ldv,p),alpha(n),beta(n), &
rwork(2*n),iwork(n))
! Perform workspace query to get optimal size of work
! The NAG name equivalent of zggsvd3 is f08vqf
lwork = -1
Call zggsvd3('U','V','Q',m,n,p,k,l,a,lda,b,ldb,alpha,beta,u,ldu,v,ldv,q, &
ldq,wdum,lwork,rwork,iwork,info)
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 the generalized singular value decomposition of (A, B)
! (A = U*D1*(0 R)*(Q**H), B = V*D2*(0 R)*(Q**H), m.ge.n)
! The NAG name equivalent of zggsvd3 is f08vqf
Call zggsvd3('U','V','Q',m,n,p,k,l,a,lda,b,ldb,alpha,beta,u,ldu,v,ldv,q, &
ldq,work,lwork,rwork,iwork,info)
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,*) '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 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', &
'Integer',rlabs,'Integer',clabs,80,0,ifail)
! Call ZTRCON (F07TUF) to estimate the reciprocal condition
! number of R
Call ztrcon('Infinity-norm','Upper','Non-unit',irank,a(1,n-irank+1), &
lda,rcond,work,rwork,info)
Write (nout,*)
Write (nout,*) 'Estimate of reciprocal condition number for R'
Write (nout,99997) rcond
Write (nout,*)
! So long as irank = n, get the machine precision, eps, and
! compute the approximate error bound for the computed
! generalized singular values
If (irank==n) Then
eps = x02ajf()
serrbd = eps/rcond
Write (nout,*) 'Error estimate for the generalized singular values'
Write (nout,99997) serrbd
Else
Write (nout,*) '(A**T B**T)**T is not of full rank'
End If
Else
Write (nout,99996) 'Failure in ZGGSVD3. INFO =', info
End If
99999 Format (1X,I5)
99998 Format (4X,8(1P,E13.4))
99997 Format (3X,1P,E11.1)
99996 Format (1X,A,I4)
End Program f08vqfe