! F08PAF Example Program Text
! Mark 29.2 Release. NAG Copyright 2023.
Module f08pafe_mod
! F08PAF Example Program Module:
! Parameters and User-defined Routines
! .. Use Statements ..
Use nag_library, Only: nag_wp
! .. Implicit None Statement ..
Implicit None
! .. Accessibility Statements ..
Private
Public :: select
! .. Parameters ..
Integer, Parameter, Public :: nb = 64, nin = 5, nout = 6
Contains
Function select(wr,wi)
! Logical function select for use with DGEES (F08PAF)
! Returns the value .TRUE. if the eigenvalue is real and positive
! .. Function Return Value ..
Logical :: select
! .. Scalar Arguments ..
Real (Kind=nag_wp), Intent (In) :: wi, wr
! .. Executable Statements ..
select = (wr>0._nag_wp .And. wi==0._nag_wp)
Return
End Function select
End Module f08pafe_mod
Program f08pafe
! F08PAF Example Main Program
! .. Use Statements ..
Use f08pafe_mod, Only: nb, nin, nout, select
Use nag_library, Only: dgees, dgemm, dlange => f06raf, nag_wp, x02ajf, &
x04caf
! .. Implicit None Statement ..
Implicit None
! .. Local Scalars ..
Real (Kind=nag_wp) :: alpha, beta, norm
Integer :: i, ifail, info, lda, ldc, ldd, ldvs, &
lwork, n, sdim
! .. Local Arrays ..
Real (Kind=nag_wp), Allocatable :: a(:,:), c(:,:), d(:,:), vs(:,:), &
wi(:), work(:), wr(:)
Real (Kind=nag_wp) :: dummy(1), rwork(1)
Logical, Allocatable :: bwork(:)
! .. Intrinsic Procedures ..
Intrinsic :: max, nint
! .. Executable Statements ..
Write (nout,*) 'F08PAF Example Program Results'
Write (nout,*)
Flush (nout)
! Skip heading in data file
Read (nin,*)
Read (nin,*) n
lda = n
ldc = n
ldd = n
ldvs = n
Allocate (a(lda,n),c(ldc,n),d(ldd,n),vs(ldvs,n),wi(n),wr(n),bwork(n))
! Use routine workspace query to get optimal workspace.
lwork = -1
! The NAG name equivalent of dgees is f08paf
Call dgees('Vectors (Schur)','Sort',select,n,a,lda,sdim,wr,wi,vs,ldvs, &
dummy,lwork,bwork,info)
! Make sure that there is enough workspace for block size nb.
lwork = max((nb+2)*n,nint(dummy(1)))
Allocate (work(lwork))
! Read in the matrix A
Read (nin,*)(a(i,1:n),i=1,n)
! Copy A into D
d(1:n,1:n) = a(1:n,1:n)
! Print matrix A
! ifail: behaviour on error exit
! =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 0
Call x04caf('General',' ',n,n,a,lda,'Matrix A',ifail)
Write (nout,*)
Flush (nout)
! Find the Schur factorization of A
! The NAG name equivalent of dgees is f08paf
Call dgees('Vectors (Schur)','Sort',select,n,a,lda,sdim,wr,wi,vs,ldvs, &
work,lwork,bwork,info)
If (info==0 .Or. info==(n+2)) Then
! Compute A - Z*T*Z^T from the factorization of A and store in matrix D
! The NAG name equivalent of dgemm is f06yaf
alpha = 1.0_nag_wp
beta = 0.0_nag_wp
Call dgemm('N','N',n,n,n,alpha,vs,ldvs,a,lda,beta,c,ldc)
alpha = -1.0_nag_wp
beta = 1.0_nag_wp
Call dgemm('N','T',n,n,n,alpha,c,ldc,vs,ldvs,beta,d,ldd)
! Find norm of matrix D and print warning if it is too large
! f06raf is the NAG name equivalent of the LAPACK auxiliary dlange
norm = dlange('O',ldd,n,d,ldd,rwork)
If (norm>x02ajf()**0.8_nag_wp) Then
Write (nout,*) 'Norm of A-(Z*T*Z^T) is much greater than 0.'
Write (nout,*) 'Schur factorization has failed.'
Else
! Print solution
Write (nout,99999) &
'Number of eigenvalues for which SELECT is true = ', sdim, &
'(dimension of invariant subspace)'
Write (nout,*)
! Print eigenvalues.
Write (nout,*) 'Selected eigenvalues'
Write (nout,99997)(' (',wr(i),',',wi(i),')',i=1,sdim)
Write (nout,*)
If (info==(n+2)) Then
Write (nout,99996) '***Note that rounding errors mean ', &
'that leading eigenvalues in the Schur form', &
'no longer satisfy SELECT = .TRUE.'
Write (nout,*)
End If
End If
Else
Write (nout,99998) 'Failure in DGEES. INFO = ', info
End If
99999 Format (1X,A,I4,/,1X,A)
99998 Format (1X,A,I4)
99997 Format (1X,A,F8.4,A,F8.4,A)
99996 Format (1X,2A,/,1X,A)
End Program f08pafe