Program f08tafe
! F08TAF Example Program Text
! Mark 28.6 Release. NAG Copyright 2022.
! .. Use Statements ..
Use nag_library, Only: dspgv, dtpcon, f06rdf, nag_wp, x02ajf
! .. Implicit None Statement ..
Implicit None
! .. Parameters ..
Integer, Parameter :: nin = 5, nout = 6
Character (1), Parameter :: uplo = 'U'
! .. Local Scalars ..
Real (Kind=nag_wp) :: anorm, bnorm, eps, rcond, rcondb, &
t1, t2
Integer :: i, info, j, n
! .. Local Arrays ..
Real (Kind=nag_wp), Allocatable :: ap(:), bp(:), eerbnd(:), w(:), &
work(:)
Real (Kind=nag_wp) :: dummy(1,1)
Integer, Allocatable :: iwork(:)
! .. Intrinsic Procedures ..
Intrinsic :: abs
! .. Executable Statements ..
Write (nout,*) 'F08TAF Example Program Results'
Write (nout,*)
! Skip heading in data file
Read (nin,*)
Read (nin,*) n
Allocate (ap((n*(n+1))/2),bp((n*(n+1))/2),eerbnd(n),w(n),work(3*n),iwork &
(n))
! Read the upper or lower triangular parts of the matrices A and
! B from data file
If (uplo=='U') Then
Read (nin,*)((ap(i+(j*(j-1))/2),j=i,n),i=1,n)
Read (nin,*)((bp(i+(j*(j-1))/2),j=i,n),i=1,n)
Else If (uplo=='L') Then
Read (nin,*)((ap(i+((2*n-j)*(j-1))/2),j=1,i),i=1,n)
Read (nin,*)((bp(i+((2*n-j)*(j-1))/2),j=1,i),i=1,n)
End If
! Compute the one-norms of the symmetric matrices A and B
anorm = f06rdf('One norm',uplo,n,ap,work)
bnorm = f06rdf('One norm',uplo,n,bp,work)
! Solve the generalized symmetric eigenvalue problem
! A*x = lambda*B*x (itype = 1)
! The NAG name equivalent of dspgv is f08taf
Call dspgv(1,'No vectors',uplo,n,ap,bp,w,dummy,1,work,info)
If (info==0) Then
! Print solution
Write (nout,*) 'Eigenvalues'
Write (nout,99999) w(1:n)
! Call DTPCON (F07UGF) to estimate the reciprocal condition
! number of the Cholesky factor of B. Note that:
! cond(B) = 1/rcond**2
Call dtpcon('One norm',uplo,'Non-unit',n,bp,rcond,work,iwork,info)
! Print the reciprocal condition number of B
rcondb = rcond**2
Write (nout,*)
Write (nout,*) 'Estimate of reciprocal condition number for B'
Write (nout,99998) rcondb
! Get the machine precision, eps, and if rcondb is not less
! than eps**2, compute error estimates for the eigenvalues
eps = x02ajf()
If (rcond>=eps) Then
t1 = eps/rcondb
t2 = anorm/bnorm
Do i = 1, n
eerbnd(i) = t1*(t2+abs(w(i)))
End Do
! Print the approximate error bounds for the eigenvalues
Write (nout,*)
Write (nout,*) 'Error estimates for the eigenvalues'
Write (nout,99998) eerbnd(1:n)
Else
Write (nout,*)
Write (nout,*) 'B is very ill-conditioned, error ', &
'estimates have not been computed'
End If
Else If (info>n .And. info<=2*n) Then
i = info - n
Write (nout,99997) 'The leading minor of order ', i, &
' of B is not positive definite'
Else
Write (nout,99996) 'Failure in DSPGV. INFO =', info
End If
99999 Format (3X,(6F11.4))
99998 Format (4X,1P,6E11.1)
99997 Format (1X,A,I4,A)
99996 Format (1X,A,I4)
End Program f08tafe