Program f08khfe
! F08KHF Example Program Text
! Mark 30.0 Release. NAG Copyright 2024.
! .. Use Statements ..
Use nag_library, Only: ddisna, dgejsv, nag_wp, x02ajf, x04caf
! .. Implicit None Statement ..
Implicit None
! .. Parameters ..
Integer, Parameter :: nb = 64, nin = 5, nout = 6
! .. Local Scalars ..
Real (Kind=nag_wp) :: eps, serrbd
Integer :: i, ifail, info, j, lda, ldu, ldv, &
lwork, m, n
! .. Local Arrays ..
Real (Kind=nag_wp), Allocatable :: a(:,:), rcondu(:), rcondv(:), s(:), &
u(:,:), v(:,:), work(:)
Integer, Allocatable :: iwork(:)
! .. Intrinsic Procedures ..
Intrinsic :: abs, max
! .. Executable Statements ..
Write (nout,*) 'F08KHF Example Program Results'
Write (nout,*)
Flush (nout)
! Skip heading in data file
Read (nin,*)
Read (nin,*) m, n
lda = m
ldu = m
ldv = n
lwork = max(3*n+n*n+m,3*n+n*n+n*nb,7)
Allocate (a(lda,n),rcondu(m),rcondv(m),s(n),u(ldu,n),v(ldv,n), &
work(lwork),iwork(m+3*n))
! Read the m by n matrix A from data file
Read (nin,*)((a(i,j),j=1,n),i=1,m)
! Compute the singular values and left and right singular vectors
! of A (A = U*S*V^T, m.ge.n)
! The NAG name equivalent of dgejsv is f08khf
Call dgejsv('E','U','V','R','N','N',m,n,a,lda,s,u,ldu,v,ldv,work,lwork, &
iwork,info)
If (info==0) Then
! Compute the approximate error bound for the computed singular values
! using the 2-norm, s(1) = norm(A), and machine precision, eps.
eps = x02ajf()
serrbd = eps*s(1)
! Print solution
If (abs(work(1)-work(2))<2.0_nag_wp*eps) Then
! No scaling required
Write (nout,'(1X,A)') 'Singular values'
Write (nout,99999)(s(j),j=1,n)
Else
Write (nout,'(/1X,A)') 'Scaled singular values'
Write (nout,99999)(s(j),j=1,n)
Write (nout,'(/1X,A)') 'For true singular values, multiply by a/b,'
Write (nout,99996) ' where a = ', work(1), ' and b = ', work(2)
End If
! ifail: behaviour on error exit
! =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
Write (nout,*)
Flush (nout)
ifail = 0
Call x04caf('General',' ',m,n,u,ldu,'Left singular vectors',ifail)
Write (nout,*)
Flush (nout)
ifail = 0
Call x04caf('General',' ',n,n,v,ldv,'Right singular vectors',ifail)
! Call DDISNA (F08FLF) to estimate reciprocal condition numbers for
! the singular vectors.
Call ddisna('Left',m,n,s,rcondu,info)
Call ddisna('Right',m,n,s,rcondv,info)
! Print the approximate error bounds for the singular values
! and vectors.
Write (nout,*)
Write (nout,'(/1X,A)') &
'Estimate of the condition number of column equilibrated A'
Write (nout,99998) work(3)
Write (nout,'(/1X,A)') 'Error estimate for the singular values'
Write (nout,99998) serrbd
Write (nout,'(/1X,A)') 'Error estimates for left singular vectors'
Write (nout,99998)(serrbd/rcondu(i),i=1,n)
Write (nout,'(/1X,A)') 'Error estimates for right singular vectors'
Write (nout,99998)(serrbd/rcondv(i),i=1,n)
Else
Write (nout,99997) 'Failure in DGEJSV. INFO =', info
End If
99999 Format (3X,8F8.4)
99998 Format (4X,1P,6E11.1)
99997 Format (1X,A,I4)
99996 Format (1X,2(A,1P,E13.5))
End Program f08khfe