Program f08xefe ! F08XEF Example Program Text ! Mark 24 Release. NAG Copyright 2012. ! .. Use Statements .. Use nag_library, Only: dgeqrf, dggbal, dgghrd, dhgeqz, dormqr, nag_wp, & x04caf ! .. Implicit None Statement .. Implicit None ! .. Parameters .. Integer, Parameter :: nin = 5, nout = 6 ! .. Local Scalars .. Integer :: i, ifail, ihi, ilo, info, irows, & jwork, lda, ldb, ldq, ldz, lwork, n Character (1) :: compq, compz, job ! .. Local Arrays .. Real (Kind=nag_wp), Allocatable :: a(:,:), alphai(:), alphar(:), & b(:,:), beta(:), lscale(:), q(:,:), & rscale(:), tau(:), work(:), z(:,:) ! .. Intrinsic Procedures .. Intrinsic :: nint ! .. Executable Statements .. Write (nout,*) 'F08XEF Example Program Results' Flush (nout) ! Skip heading in data file Read (nin,*) Read (nin,*) n ldq = 1 ldz = 1 lda = n ldb = n lwork = 6*n Allocate (alphai(n),alphar(n),beta(n),a(lda,n),lscale(n),q(ldq,ldq), & rscale(n),b(ldb,n),tau(n),work(lwork),z(ldz,ldz)) ! READ matrix A from data file Read (nin,*)(a(i,1:n),i=1,n) ! READ matrix B from data file Read (nin,*)(b(i,1:n),i=1,n) ! Balance matrix pair (A,B) job = 'B' ! The NAG name equivalent of dggbal is f08whf Call dggbal(job,n,a,lda,b,ldb,ilo,ihi,lscale,rscale,work,info) ! Matrix A after balancing ! 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 after balancing',ifail) Write (nout,*) Flush (nout) ! Matrix B after balancing ifail = 0 Call x04caf('General',' ',n,n,b,ldb,'Matrix B after balancing',ifail) Write (nout,*) Flush (nout) ! Reduce B to triangular form using QR irows = ihi + 1 - ilo ! The NAG name equivalent of dgeqrf is f08aef Call dgeqrf(irows,irows,b(ilo,ilo),ldb,tau,work,lwork,info) ! Apply the orthogonal transformation to matrix A ! The NAG name equivalent of dormqr is f08agf Call dormqr('L','T',irows,irows,irows,b(ilo,ilo),ldb,tau,a(ilo,ilo),lda, & work,lwork,info) ! Compute the generalized Hessenberg form of (A,B) -> (H,T) compq = 'N' compz = 'N' ! The NAG name equivalent of dgghrd is f08wef Call dgghrd(compq,compz,irows,1,irows,a(ilo,ilo),lda,b(ilo,ilo),ldb,q, & ldq,z,ldz,info) ! Matrix A (H) in generalized Hessenberg form. ifail = 0 Call x04caf('General',' ',n,n,a,lda,'Matrix A in Hessenberg form',ifail) Write (nout,*) Flush (nout) ! Matrix B (T) in generalized Hessenberg form. ifail = 0 Call x04caf('General',' ',n,n,b,ldb,'Matrix B is triangular',ifail) ! Routine DHGEQZ ! Workspace query: jwork = -1 jwork = -1 job = 'E' ! The NAG name equivalent of dhgeqz is f08xef Call dhgeqz(job,compq,compz,n,ilo,ihi,a,lda,b,ldb,alphar,alphai,beta,q, & ldq,z,ldz,work,jwork,info) Write (nout,*) Write (nout,99999) nint(work(1)) Write (nout,99998) lwork Write (nout,*) ! Compute the generalized Schur form ! if the workspace lwork is adequate If (nint(work(1))<=lwork) Then ! The NAG name equivalent of dhgeqz is f08xef Call dhgeqz(job,compq,compz,n,ilo,ihi,a,lda,b,ldb,alphar,alphai,beta, & q,ldq,z,ldz,work,lwork,info) ! Print the generalized eigenvalues Write (nout,99997) Do i = 1, n If (beta(i)/=0.0E0_nag_wp) Then Write (nout,99996) i, '(', alphar(i)/beta(i), ',', & alphai(i)/beta(i), ')' Else Write (nout,99994) i End If End Do Else Write (nout,99995) End If 99999 Format (1X,'Minimal required LWORK = ',I6) 99998 Format (1X,'Actual value of LWORK = ',I6) 99997 Format (1X,'Generalized eigenvalues') 99996 Format (1X,I4,5X,A,F7.3,A,F7.3,A) 99995 Format (1X,'Insufficient workspace allocated for call to F08XEF/DHGEQZ') 99994 Format (1X,I4,'Eigenvalue is infinite') End Program f08xefe