* F08XBF Example Program Text * Mark 21 Release. NAG Copyright 2004. * .. Parameters .. INTEGER NIN, NOUT PARAMETER (NIN=5,NOUT=6) INTEGER NB, NMAX PARAMETER (NB=64,NMAX=10) INTEGER LDA, LDB, LDVSL, LDVSR, LIWORK, LWORK PARAMETER (LDA=NMAX,LDB=NMAX,LDVSL=NMAX,LDVSR=NMAX, + LIWORK=NMAX+6,LWORK=8*(NMAX+1) + +16+NMAX*NB+NMAX*NMAX/2) * .. Local Scalars .. DOUBLE PRECISION ABNORM, ANORM, BNORM, EPS, TOL INTEGER I, IFAIL, INFO, J, LWKOPT, N, SDIM * .. Local Arrays .. DOUBLE PRECISION A(LDA,NMAX), ALPHAI(NMAX), ALPHAR(NMAX), + B(LDB,NMAX), BETA(NMAX), RCONDE(2), RCONDV(2), + VSL(LDVSL,NMAX), VSR(LDVSR,NMAX), WORK(LWORK) INTEGER IWORK(LIWORK) LOGICAL BWORK(NMAX) * .. External Functions .. DOUBLE PRECISION F06BNF, F06RAF, X02AJF LOGICAL DELCTG EXTERNAL F06BNF, F06RAF, X02AJF, DELCTG * .. External Subroutines .. EXTERNAL DGGESX, X04CAF * .. Executable Statements .. WRITE (NOUT,*) 'F08XBF Example Program Results' WRITE (NOUT,*) * Skip heading in data file READ (NIN,*) READ (NIN,*) N IF (N.LE.NMAX) THEN * * Read in the matrices A and B * READ (NIN,*) ((A(I,J),J=1,N),I=1,N) READ (NIN,*) ((B(I,J),J=1,N),I=1,N) * * Find the Frobenius norms of A and B * ANORM = F06RAF('Frobenius',N,N,A,LDA,WORK) BNORM = F06RAF('Frobenius',N,N,B,LDB,WORK) * * Find the generalized Schur form * CALL DGGESX('Vectors (left)','Vectors (right)','Sort',DELCTG, + 'Both reciprocal condition numbers',N,A,LDA,B,LDB, + SDIM,ALPHAR,ALPHAI,BETA,VSL,LDVSL,VSR,LDVSR,RCONDE, + RCONDV,WORK,LWORK,IWORK,LIWORK,BWORK,INFO) * IF (INFO.GT.0 .AND. INFO.NE.(N+2)) THEN WRITE (NOUT,99999) 'Failure in DGGESX. INFO =', INFO ELSE WRITE (NOUT,99999) + 'Number of eigenvalues for which DELCTG is true = ', SDIM, + '(dimension of deflating subspaces)' WRITE (NOUT,*) IF (INFO.EQ.(N+2)) THEN WRITE (NOUT,99998) '***Note that rounding errors mean ', + 'that leading eigenvalues in the generalized', + 'Schur form no longer satisfy DELCTG = .TRUE.' WRITE (NOUT,*) END IF * * Print out the factors of the generalized Schur factorization * IFAIL = 0 CALL X04CAF('General',' ',N,N,A,LDA, + 'Generalized Schur matrix S',IFAIL) * WRITE (NOUT,*) CALL X04CAF('General',' ',N,N,B,LDB, + 'Generalized Schur matrix T',IFAIL) * WRITE (NOUT,*) CALL X04CAF('General',' ',N,N,VSL,LDVSL, + 'Matrix of left generalized Schur vectors', + IFAIL) * WRITE (NOUT,*) CALL X04CAF('General',' ',N,N,VSR,LDVSR, + 'Matrix of right generalized Schur vectors', + IFAIL) * * Print out the reciprocal condition numbers * WRITE (NOUT,*) WRITE (NOUT,99997) + 'Reciprocals of left and right projection norms onto', + 'the deflating subspaces for the selected eigenvalues', + 'RCONDE(1) = ', RCONDE(1), ', RCONDE(2) = ', RCONDE(2) WRITE (NOUT,*) WRITE (NOUT,99997) + 'Reciprocal condition numbers for the left and right', + 'deflating subspaces', 'RCONDV(1) = ', RCONDV(1), + ', RCONDV(2) = ', RCONDV(2) * * Compute the machine precision and sqrt(ANORM**2+BNORM**2) * EPS = X02AJF() ABNORM = F06BNF(ANORM,BNORM) TOL = EPS*ABNORM * * Print out the approximate asymptotic error bound on the * average absolute error of the selected eigenvalues given by * * eps*norm((A, B))/PL, where PL = RCONDE(1) * WRITE (NOUT,*) WRITE (NOUT,99996) + 'Approximate asymptotic error bound for selected ', + 'eigenvalues = ', TOL/RCONDE(1) * * Print out an approximate asymptotic bound on the maximum * angular error in the computed deflating subspaces given by * * eps*norm((A, B))/DIF(2), where DIF(2) = RCONDV(2) * WRITE (NOUT,99996) + 'Approximate asymptotic error bound for the deflating ', + 'subspaces = ', TOL/RCONDV(2) * LWKOPT = WORK(1) IF (LWORK.LT.LWKOPT) THEN WRITE (NOUT,*) WRITE (NOUT,99995) 'Optimum workspace required = ', + LWKOPT, 'Workspace provided = ', LWORK END IF END IF ELSE WRITE (NOUT,*) WRITE (NOUT,*) 'NMAX too small' END IF STOP * 99999 FORMAT (1X,A,I4,/1X,A) 99998 FORMAT (1X,2A,/1X,A) 99997 FORMAT (1X,A,/1X,A,/1X,2(A,1P,E8.1)) 99996 FORMAT (1X,2A,1P,E8.1) 99995 FORMAT (1X,A,I5,/1X,A,I5) END LOGICAL FUNCTION DELCTG(AR,AI,B) * .. Scalar Arguments .. * * Logical function DELCTG for use with DGGESX (F08XBF) * * Returns the value .TRUE. if the imaginary part of the eigenvalue * (AR + AI*i)/B is zero, i.e. the eigenvalue is real * DOUBLE PRECISION AI, AR, B * .. Local Scalars .. LOGICAL D * .. Executable Statements .. IF (AI.EQ.0.0D0) THEN D = .TRUE. ELSE D = .FALSE. END IF * DELCTG = D * RETURN END