! F08PAF Example Program Text ! Mark 24 Release. NAG Copyright 2012. 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 ! .. Parameters .. Integer, Parameter :: 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 ! .. Function Return Value .. Logical :: select ! .. Scalar Arguments .. Real (Kind=nag_wp), Intent (In) :: wi, wr ! .. Local Scalars .. Logical :: d ! .. Executable Statements .. If (wi==0.0_nag_wp) Then d = .True. Else d = .False. End If select = d Return End Function select End Module f08pafe_mod Program f08pafe ! F08PAF Example Main Program ! .. Use Statements .. Use nag_library, Only: dgees, dgemm, dlange => f06raf, nag_wp, x02ajf, & x04caf Use f08pafe_mod, Only: nb, nin, nout, select ! .. 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 blocksize nb. lwork = max((nb+2)*n,nint(dummy(1))) Allocate (work(lwork)) ! Read the matrix A from data file 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 ! 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^H from the factorization of A and store in matrix D ! The NAG name equivelent 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 eigenvalues. Write (nout,*) 'Eigenvalues' Write (nout,99998)(' (',wr(i),',',wi(i),')',i=1,n) End If Else Write (nout,99999) 'Failure in DGEES. INFO = ', info End If 99999 Format (1X,A,I4) 99998 Format (1X,A,F8.4,A,F8.4,A) End Program f08pafe