Program f08qufe ! F08QUF Example Program Text ! Mark 24 Release. NAG Copyright 2012. ! .. Use Statements .. Use nag_library, Only: nag_wp, x02ajf, x04dbf, zgemm, zlange => f06uaf, & ztrsen ! .. 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, s, sep Integer :: i, ifail, info, lda, ldc, ldq, ldt, & lwork, m, n ! .. Local Arrays .. Complex (Kind=nag_wp), Allocatable :: a(:,:), c(:,:), q(:,:), t(:,:), & w(:), work(:) Real (Kind=nag_wp) :: rwork(1) Logical, Allocatable :: select(:) Character (1) :: clabs(1), rlabs(1) ! .. Intrinsic Procedures .. Intrinsic :: cmplx ! .. Executable Statements .. Write (nout,*) 'F08QUF Example Program Results' Write (nout,*) Flush (nout) ! Skip heading in data file Read (nin,*) Read (nin,*) n ldc = n lda = n ldq = n ldt = n lwork = (n*n)/2 Allocate (a(lda,n),c(ldc,n),q(ldq,n),t(ldt,n),w(n),work(lwork), & select(n)) ! Read T, Q and the logical array SELECT from data file Read (nin,*)(t(i,1:n),i=1,n) Read (nin,*) Read (nin,*)(q(i,1:n),i=1,n) Read (nin,*) Read (nin,*) select(1:n) ! Compute Q * T * Q**T to find A ! 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,q,ldq,t,ldt,beta,c,ldc) Call zgemm('N','C',n,n,n,alpha,c,ldc,q,ldq,beta,a,lda) ! Print Matrix A, as computed from Q * T * Q**T ! 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 created from Q*T*Q^T','Integer',rlabs,'Integer',clabs,80,0, & ifail) Write (nout,*) Flush (nout) ! Reorder the Schur factor T and update the matrix Q to obtain TT and QT ! The NAG name equivalent of ztrsen is f08quf Call ztrsen('Both','Vectors',select,n,t,ldt,q,ldq,w,m,s,sep,work,lwork, & info) ! Compute (Q * T * Q^H) - (QT * TT * QT^H) and store in A, ! i.e. the difference between reconstructed A using Schur and reordered ! Schur decompositions. alpha = cmplx(1,kind=nag_wp) beta = cmplx(0,kind=nag_wp) Call zgemm('N','N',n,n,n,alpha,q,ldq,t,ldt,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,q,ldq,beta,a,lda) ! Find norm of difference matrix and print warning if it is too large ! f06uaf is the NAG name equivalent of the LAPACK auxiliary zlange norm = zlange('O',lda,n,a,lda,rwork) If (norm>x02ajf()**0.8_nag_wp) Then Write (nout,*) 'Norm of A - (QT * TT * QT^H) is much greater than 0.' Write (nout,*) 'Schur factorization has failed.' Else ! Print condition estimates Write (nout,99999) 'Condition number estimate', & ' of the selected cluster of eigenvalues = ', 1.0_nag_wp/s Write (nout,*) Write (nout,99999) 'Condition number estimate of the specified ', & 'invariant subspace = ', 1.0_nag_wp/sep End If 99999 Format (1X,A,A,1P,E10.2) End Program f08qufe