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authorjofret2009-04-28 07:17:00 +0000
committerjofret2009-04-28 07:17:00 +0000
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Moving lapack to right place
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- SUBROUTINE ZGEES( JOBVS, SORT, SELECT, N, A, LDA, SDIM, W, VS,
- $ LDVS, WORK, LWORK, RWORK, BWORK, INFO )
-*
-* -- LAPACK driver routine (version 3.1) --
-* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
-* November 2006
-*
-* .. Scalar Arguments ..
- CHARACTER JOBVS, SORT
- INTEGER INFO, LDA, LDVS, LWORK, N, SDIM
-* ..
-* .. Array Arguments ..
- LOGICAL BWORK( * )
- DOUBLE PRECISION RWORK( * )
- COMPLEX*16 A( LDA, * ), VS( LDVS, * ), W( * ), WORK( * )
-* ..
-* .. Function Arguments ..
- LOGICAL SELECT
- EXTERNAL SELECT
-* ..
-*
-* Purpose
-* =======
-*
-* ZGEES computes for an N-by-N complex nonsymmetric matrix A, the
-* eigenvalues, the Schur form T, and, optionally, the matrix of Schur
-* vectors Z. This gives the Schur factorization A = Z*T*(Z**H).
-*
-* Optionally, it also orders the eigenvalues on the diagonal of the
-* Schur form so that selected eigenvalues are at the top left.
-* The leading columns of Z then form an orthonormal basis for the
-* invariant subspace corresponding to the selected eigenvalues.
-*
-* A complex matrix is in Schur form if it is upper triangular.
-*
-* Arguments
-* =========
-*
-* JOBVS (input) CHARACTER*1
-* = 'N': Schur vectors are not computed;
-* = 'V': Schur vectors are computed.
-*
-* SORT (input) CHARACTER*1
-* Specifies whether or not to order the eigenvalues on the
-* diagonal of the Schur form.
-* = 'N': Eigenvalues are not ordered:
-* = 'S': Eigenvalues are ordered (see SELECT).
-*
-* SELECT (external procedure) LOGICAL FUNCTION of one COMPLEX*16 argument
-* SELECT must be declared EXTERNAL in the calling subroutine.
-* If SORT = 'S', SELECT is used to select eigenvalues to order
-* to the top left of the Schur form.
-* IF SORT = 'N', SELECT is not referenced.
-* The eigenvalue W(j) is selected if SELECT(W(j)) is true.
-*
-* N (input) INTEGER
-* The order of the matrix A. N >= 0.
-*
-* A (input/output) COMPLEX*16 array, dimension (LDA,N)
-* On entry, the N-by-N matrix A.
-* On exit, A has been overwritten by its Schur form T.
-*
-* LDA (input) INTEGER
-* The leading dimension of the array A. LDA >= max(1,N).
-*
-* SDIM (output) INTEGER
-* If SORT = 'N', SDIM = 0.
-* If SORT = 'S', SDIM = number of eigenvalues for which
-* SELECT is true.
-*
-* W (output) COMPLEX*16 array, dimension (N)
-* W contains the computed eigenvalues, in the same order that
-* they appear on the diagonal of the output Schur form T.
-*
-* VS (output) COMPLEX*16 array, dimension (LDVS,N)
-* If JOBVS = 'V', VS contains the unitary matrix Z of Schur
-* vectors.
-* If JOBVS = 'N', VS is not referenced.
-*
-* LDVS (input) INTEGER
-* The leading dimension of the array VS. LDVS >= 1; if
-* JOBVS = 'V', LDVS >= N.
-*
-* WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
-* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
-*
-* LWORK (input) INTEGER
-* The dimension of the array WORK. LWORK >= max(1,2*N).
-* For good performance, LWORK must generally be larger.
-*
-* If LWORK = -1, then a workspace query is assumed; the routine
-* only calculates the optimal size of the WORK array, returns
-* this value as the first entry of the WORK array, and no error
-* message related to LWORK is issued by XERBLA.
-*
-* RWORK (workspace) DOUBLE PRECISION array, dimension (N)
-*
-* BWORK (workspace) LOGICAL array, dimension (N)
-* Not referenced if SORT = 'N'.
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* < 0: if INFO = -i, the i-th argument had an illegal value.
-* > 0: if INFO = i, and i is
-* <= N: the QR algorithm failed to compute all the
-* eigenvalues; elements 1:ILO-1 and i+1:N of W
-* contain those eigenvalues which have converged;
-* if JOBVS = 'V', VS contains the matrix which
-* reduces A to its partially converged Schur form.
-* = N+1: the eigenvalues could not be reordered because
-* some eigenvalues were too close to separate (the
-* problem is very ill-conditioned);
-* = N+2: after reordering, roundoff changed values of
-* some complex eigenvalues so that leading
-* eigenvalues in the Schur form no longer satisfy
-* SELECT = .TRUE.. This could also be caused by
-* underflow due to scaling.
-*
-* =====================================================================
-*
-* .. Parameters ..
- DOUBLE PRECISION ZERO, ONE
- PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
-* ..
-* .. Local Scalars ..
- LOGICAL LQUERY, SCALEA, WANTST, WANTVS
- INTEGER HSWORK, I, IBAL, ICOND, IERR, IEVAL, IHI, ILO,
- $ ITAU, IWRK, MAXWRK, MINWRK
- DOUBLE PRECISION ANRM, BIGNUM, CSCALE, EPS, S, SEP, SMLNUM
-* ..
-* .. Local Arrays ..
- DOUBLE PRECISION DUM( 1 )
-* ..
-* .. External Subroutines ..
- EXTERNAL DLABAD, XERBLA, ZCOPY, ZGEBAK, ZGEBAL, ZGEHRD,
- $ ZHSEQR, ZLACPY, ZLASCL, ZTRSEN, ZUNGHR
-* ..
-* .. External Functions ..
- LOGICAL LSAME
- INTEGER ILAENV
- DOUBLE PRECISION DLAMCH, ZLANGE
- EXTERNAL LSAME, ILAENV, DLAMCH, ZLANGE
-* ..
-* .. Intrinsic Functions ..
- INTRINSIC MAX, SQRT
-* ..
-* .. Executable Statements ..
-*
-* Test the input arguments
-*
- INFO = 0
- LQUERY = ( LWORK.EQ.-1 )
- WANTVS = LSAME( JOBVS, 'V' )
- WANTST = LSAME( SORT, 'S' )
- IF( ( .NOT.WANTVS ) .AND. ( .NOT.LSAME( JOBVS, 'N' ) ) ) THEN
- INFO = -1
- ELSE IF( ( .NOT.WANTST ) .AND. ( .NOT.LSAME( SORT, 'N' ) ) ) THEN
- INFO = -2
- ELSE IF( N.LT.0 ) THEN
- INFO = -4
- ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
- INFO = -6
- ELSE IF( LDVS.LT.1 .OR. ( WANTVS .AND. LDVS.LT.N ) ) THEN
- INFO = -10
- END IF
-*
-* Compute workspace
-* (Note: Comments in the code beginning "Workspace:" describe the
-* minimal amount of workspace needed at that point in the code,
-* as well as the preferred amount for good performance.
-* CWorkspace refers to complex workspace, and RWorkspace to real
-* workspace. NB refers to the optimal block size for the
-* immediately following subroutine, as returned by ILAENV.
-* HSWORK refers to the workspace preferred by ZHSEQR, as
-* calculated below. HSWORK is computed assuming ILO=1 and IHI=N,
-* the worst case.)
-*
- IF( INFO.EQ.0 ) THEN
- IF( N.EQ.0 ) THEN
- MINWRK = 1
- MAXWRK = 1
- ELSE
- MAXWRK = N + N*ILAENV( 1, 'ZGEHRD', ' ', N, 1, N, 0 )
- MINWRK = 2*N
-*
- CALL ZHSEQR( 'S', JOBVS, N, 1, N, A, LDA, W, VS, LDVS,
- $ WORK, -1, IEVAL )
- HSWORK = WORK( 1 )
-*
- IF( .NOT.WANTVS ) THEN
- MAXWRK = MAX( MAXWRK, HSWORK )
- ELSE
- MAXWRK = MAX( MAXWRK, N + ( N - 1 )*ILAENV( 1, 'ZUNGHR',
- $ ' ', N, 1, N, -1 ) )
- MAXWRK = MAX( MAXWRK, HSWORK )
- END IF
- END IF
- WORK( 1 ) = MAXWRK
-*
- IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
- INFO = -12
- END IF
- END IF
-*
- IF( INFO.NE.0 ) THEN
- CALL XERBLA( 'ZGEES ', -INFO )
- RETURN
- ELSE IF( LQUERY ) THEN
- RETURN
- END IF
-*
-* Quick return if possible
-*
- IF( N.EQ.0 ) THEN
- SDIM = 0
- RETURN
- END IF
-*
-* Get machine constants
-*
- EPS = DLAMCH( 'P' )
- SMLNUM = DLAMCH( 'S' )
- BIGNUM = ONE / SMLNUM
- CALL DLABAD( SMLNUM, BIGNUM )
- SMLNUM = SQRT( SMLNUM ) / EPS
- BIGNUM = ONE / SMLNUM
-*
-* Scale A if max element outside range [SMLNUM,BIGNUM]
-*
- ANRM = ZLANGE( 'M', N, N, A, LDA, DUM )
- SCALEA = .FALSE.
- IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
- SCALEA = .TRUE.
- CSCALE = SMLNUM
- ELSE IF( ANRM.GT.BIGNUM ) THEN
- SCALEA = .TRUE.
- CSCALE = BIGNUM
- END IF
- IF( SCALEA )
- $ CALL ZLASCL( 'G', 0, 0, ANRM, CSCALE, N, N, A, LDA, IERR )
-*
-* Permute the matrix to make it more nearly triangular
-* (CWorkspace: none)
-* (RWorkspace: need N)
-*
- IBAL = 1
- CALL ZGEBAL( 'P', N, A, LDA, ILO, IHI, RWORK( IBAL ), IERR )
-*
-* Reduce to upper Hessenberg form
-* (CWorkspace: need 2*N, prefer N+N*NB)
-* (RWorkspace: none)
-*
- ITAU = 1
- IWRK = N + ITAU
- CALL ZGEHRD( N, ILO, IHI, A, LDA, WORK( ITAU ), WORK( IWRK ),
- $ LWORK-IWRK+1, IERR )
-*
- IF( WANTVS ) THEN
-*
-* Copy Householder vectors to VS
-*
- CALL ZLACPY( 'L', N, N, A, LDA, VS, LDVS )
-*
-* Generate unitary matrix in VS
-* (CWorkspace: need 2*N-1, prefer N+(N-1)*NB)
-* (RWorkspace: none)
-*
- CALL ZUNGHR( N, ILO, IHI, VS, LDVS, WORK( ITAU ), WORK( IWRK ),
- $ LWORK-IWRK+1, IERR )
- END IF
-*
- SDIM = 0
-*
-* Perform QR iteration, accumulating Schur vectors in VS if desired
-* (CWorkspace: need 1, prefer HSWORK (see comments) )
-* (RWorkspace: none)
-*
- IWRK = ITAU
- CALL ZHSEQR( 'S', JOBVS, N, ILO, IHI, A, LDA, W, VS, LDVS,
- $ WORK( IWRK ), LWORK-IWRK+1, IEVAL )
- IF( IEVAL.GT.0 )
- $ INFO = IEVAL
-*
-* Sort eigenvalues if desired
-*
- IF( WANTST .AND. INFO.EQ.0 ) THEN
- IF( SCALEA )
- $ CALL ZLASCL( 'G', 0, 0, CSCALE, ANRM, N, 1, W, N, IERR )
- DO 10 I = 1, N
- BWORK( I ) = SELECT( W( I ) )
- 10 CONTINUE
-*
-* Reorder eigenvalues and transform Schur vectors
-* (CWorkspace: none)
-* (RWorkspace: none)
-*
- CALL ZTRSEN( 'N', JOBVS, BWORK, N, A, LDA, VS, LDVS, W, SDIM,
- $ S, SEP, WORK( IWRK ), LWORK-IWRK+1, ICOND )
- END IF
-*
- IF( WANTVS ) THEN
-*
-* Undo balancing
-* (CWorkspace: none)
-* (RWorkspace: need N)
-*
- CALL ZGEBAK( 'P', 'R', N, ILO, IHI, RWORK( IBAL ), N, VS, LDVS,
- $ IERR )
- END IF
-*
- IF( SCALEA ) THEN
-*
-* Undo scaling for the Schur form of A
-*
- CALL ZLASCL( 'U', 0, 0, CSCALE, ANRM, N, N, A, LDA, IERR )
- CALL ZCOPY( N, A, LDA+1, W, 1 )
- END IF
-*
- WORK( 1 ) = MAXWRK
- RETURN
-*
-* End of ZGEES
-*
- END