Program f08ntfe ! F08NTF Example Program Text ! Mark 24 Release. NAG Copyright 2012. ! .. Use Statements .. Use nag_library, Only: nag_wp, x02ajf, x04dbf, zgehrd, zgemm, zhseqr, & zlange => f06uaf, zunghr ! .. Implicit None Statement .. Implicit None ! .. Parameters .. Integer, Parameter :: nin = 5, nout = 6 ! .. Local Scalars .. Complex (Kind=nag_wp) :: alpha, beta Real (Kind=nag_wp) :: norm Integer :: i, ifail, info, lda, ldc, ldd, ldz, & lwork, n ! .. Local Arrays .. Complex (Kind=nag_wp), Allocatable :: a(:,:), c(:,:), d(:,:), tau(:), & w(:), work(:), z(:,:) Real (Kind=nag_wp), Allocatable :: rwork(:) Character (1) :: clabs(1), rlabs(1) ! .. Intrinsic Procedures .. Intrinsic :: cmplx ! .. Executable Statements .. Write (nout,*) 'F08NTF Example Program Results' Write (nout,*) Flush (nout) ! Skip heading in data file Read (nin,*) Read (nin,*) n lda = n ldc = n ldd = n ldz = n lwork = 64*(n-1) Allocate (a(lda,n),c(ldc,n),d(ldd,n),rwork(lda),tau(n),w(n),work(lwork), & z(ldz,n)) ! Read A from data file Read (nin,*)(a(i,1:n),i=1,n) ! Store A in D d(1:ldd,1:n) = a(1:lda,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 x04dbf('General',' ',n,n,a,lda,'Bracketed','F7.4','Matrix A', & 'Integer',rlabs,'Integer',clabs,80,0,ifail) Write (nout,*) Flush (nout) ! Reduce A to upper Hessenberg form H = (Q**H)*A*Q ! The NAG name equivalent of zgehrd is f08nsf Call zgehrd(n,1,n,a,lda,tau,work,lwork,info) ! Copy A into Z z(1:n,1:n) = a(1:n,1:n) ! Form Q explicitly, storing the result in Z ! The NAG name equivalent of zunghr is f08ntf Call zunghr(n,1,n,z,ldz,tau,work,lwork,info) ! Calculate the Schur factorization of H = Y*T*(Y**H) and form ! Q*Y explicitly, storing the result in Z ! Note that A = Z*T*(Z**H), where Z = Q*Y ! The NAG name equivalent of zhseqr is f08psf Call zhseqr('Schur form','Vectors',n,1,n,a,lda,w,z,ldz,work,lwork,info) ! Compute A - Z*T*Z^H from Schur factorization of A, and store in matrix D ! The NAG name equivelent of zgemm is f06zaf alpha = cmplx(1,kind=nag_wp) beta = cmplx(0,kind=nag_wp) Call zgemm('N','N',n,n,n,alpha,z,ldz,a,lda,beta,c,ldc) alpha = cmplx(-1,kind=nag_wp) beta = cmplx(1,kind=nag_wp) Call zgemm('N','C',n,n,n,alpha,c,ldc,z,ldz,beta,d,ldd) ! Find norm of matrix D and print warning if it is too large ! f06uaf is the NAG name equivalent of the LAPACK auxiliary zlange norm = zlange('O',ldd,n,d,ldd,rwork) If (norm>x02ajf()**0.8_nag_wp) Then Write (nout,*) 'Norm of A-(Z*T*Z^H) is much greater than 0.' Write (nout,*) 'Schur factorization has failed.' Else ! Print eigenvalues. Write (nout,*) 'Eigenvalues' Write (nout,99999)(w(i),i=1,n) End If 99999 Format ((3X,4(' (',F7.4,',',F7.4,')':))) End Program f08ntfe