! F08PPF Example Program Text ! Mark 24 Release. NAG Copyright 2012. Module f08ppfe_mod ! F08PPF Example Program Module: ! Parameters and User-defined Routines ! .. Use Statements .. Use nag_library, Only: nag_wp ! .. Implicit None Statement .. Implicit None ! .. Parameters .. Integer, Parameter :: nb = 64, nin = 5, nout = 6 Contains Function select(w) ! Logical function select for use with ZGEESX (F08PPF) ! Returns the value .TRUE. if the real part of the eigenvalue ! w is positive. ! .. Function Return Value .. Logical :: select ! .. Scalar Arguments .. Complex (Kind=nag_wp), Intent (In) :: w ! .. Local Scalars .. Logical :: d ! .. Intrinsic Procedures .. Intrinsic :: real ! .. Executable Statements .. If (real(w)>0.0_nag_wp) Then d = .True. Else d = .False. End If select = d Return End Function select End Module f08ppfe_mod Program f08ppfe ! F08PPF Example Main Program ! .. Use Statements .. Use nag_library, Only: f06uaf, nag_wp, x02ajf, zgeesx Use f08ppfe_mod, Only: nb, nin, nout, select ! .. Implicit None Statement .. Implicit None ! .. Local Scalars .. Real (Kind=nag_wp) :: anorm, eps, rconde, rcondv, tol Integer :: i, info, lda, ldvs, lwork, n, sdim ! .. Local Arrays .. Complex (Kind=nag_wp), Allocatable :: a(:,:), vs(:,:), w(:), work(:) Complex (Kind=nag_wp) :: dummy(1) Real (Kind=nag_wp), Allocatable :: rwork(:) Logical, Allocatable :: bwork(:) ! .. Intrinsic Procedures .. Intrinsic :: max, nint, real ! .. Executable Statements .. Write (nout,*) 'F08PPF Example Program Results' Write (nout,*) Flush (nout) ! Skip heading in data file Read (nin,*) Read (nin,*) n lda = n ldvs = n Allocate (a(lda,n),vs(ldvs,n),w(n),rwork(n),bwork(n)) ! Use routine workspace query to get optimal workspace. lwork = -1 ! The NAG name equivalent of zgeesx is f08ppf Call zgeesx('Vectors (Schur)','Sort',select, & 'Both reciprocal condition numbers',n,a,lda,sdim,w,vs,ldvs,rconde, & rcondv,dummy,lwork,rwork,bwork,info) ! Make sure that there is enough workspace for blocksize nb. lwork = max(n*(nb+1+n/2),nint(real(dummy(1)))) Allocate (work(lwork)) ! Read in the matrix A Read (nin,*)(a(i,1:n),i=1,n) ! Find the Frobenius norms of A anorm = f06uaf('Frobenius',n,n,a,lda,rwork) ! Find the Schur factorization of A ! The NAG name equivalent of zgeesx is f08ppf Call zgeesx('Vectors (Schur)','Sort',select, & 'Both reciprocal condition numbers',n,a,lda,sdim,w,vs,ldvs,rconde, & rcondv,work,lwork,rwork,bwork,info) If (info==0 .Or. info==(n+2)) Then Write (nout,*) 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,99998)(i,w(i),i=1,sdim) Write (nout,*) If (info==(n+2)) Then Write (nout,99998) '***Note that rounding errors mean ', & 'that leading eigenvalues in the Schur form', & 'no longer satisfy SELECT = .TRUE.' Write (nout,*) End If Flush (nout) ! Print out the reciprocal condition numbers Write (nout,99997) 'Reciprocal of projection norm onto the invariant', & 'subspace for the selected eigenvalues', 'RCONDE = ', rconde Write (nout,*) Write (nout,99996) & 'Reciprocal condition number for the invariant subspace', & 'RCONDV = ', rcondv ! Compute the machine precision eps = x02ajf() tol = eps*anorm ! Print out the approximate asymptotic error bound on the ! average absolute error of the selected eigenvalues given by ! eps*norm(A)/RCONDE Write (nout,*) Write (nout,99995) 'Approximate asymptotic error bound for selected ', & 'eigenvalues = ', tol/rconde ! Print out an approximate asymptotic bound on the maximum ! angular error in the computed invariant subspace given by ! eps*norm(A)/RCONDV Write (nout,99995) & 'Approximate asymptotic error bound for the invariant ', & 'subspace = ', tol/rcondv Else Write (nout,99994) 'Failure in ZGEESX. INFO =', info End If 99999 Format (1X,A,I4/1X,A) 99998 Format (1X,I4,2X,' (',F7.4,',',F7.4,')':) 99997 Format (1X,A/1X,A/1X,A,1P,E8.1) 99996 Format (1X,A/1X,A,1P,E8.1) 99995 Format (1X,2A,1P,E8.1) 99994 Format (1X,A,I4) End Program f08ppfe