Home Man
Search
Today's Posts
Register

Linux & Unix Commands - Search Man Pages

RedHat 9 (Linux i386) - man page for dgges (redhat section l)

DGGES(l)					)					 DGGES(l)

NAME
       DGGES - compute for a pair of N-by-N real nonsymmetric matrices (A,B),

SYNOPSIS
       SUBROUTINE DGGES( JOBVSL,  JOBVSR,  SORT, DELCTG, N, A, LDA, B, LDB, SDIM, ALPHAR, ALPHAI,
			 BETA, VSL, LDVSL, VSR, LDVSR, WORK, LWORK, BWORK, INFO )

	   CHARACTER	 JOBVSL, JOBVSR, SORT

	   INTEGER	 INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N, SDIM

	   LOGICAL	 BWORK( * )

	   DOUBLE	 PRECISION A( LDA, * ), ALPHAI( * ), ALPHAR( * ), B( LDB, * ), BETA( * ),
			 VSL( LDVSL, * ), VSR( LDVSR, * ), WORK( * )

	   LOGICAL	 DELCTG

	   EXTERNAL	 DELCTG

PURPOSE
       DGGES  computes for a pair of N-by-N real nonsymmetric matrices (A,B), the generalized ei-
       genvalues, the generalized real Schur form (S,T), optionally, the left and/or right matri-
       ces of Schur vectors (VSL and VSR). This gives the generalized Schur factorization

		(A,B) = ( (VSL)*S*(VSR)**T, (VSL)*T*(VSR)**T )

       Optionally,  it	also  orders  the  eigenvalues	so that a selected cluster of eigenvalues
       appears in the leading diagonal blocks of the upper  quasi-triangular  matrix  S  and  the
       upper  triangular  matrix  T.The  leading  columns of VSL and VSR then form an orthonormal
       basis for the corresponding left and right eigenspaces (deflating subspaces).

       (If only the generalized eigenvalues are needed, use the driver DGGEV  instead,	which  is
       faster.)

       A  generalized eigenvalue for a pair of matrices (A,B) is a scalar w or a ratio alpha/beta
       = w, such that  A - w*B is singular.  It is usually represented as the pair  (alpha,beta),
       as there is a reasonable interpretation for beta=0 or both being zero.

       A  pair	of matrices (S,T) is in generalized real Schur form if T is upper triangular with
       non-negative diagonal and S is block upper  triangular  with  1-by-1  and  2-by-2  blocks.
       1-by-1 blocks correspond to real generalized eigenvalues, while 2-by-2 blocks of S will be
       "standardized" by making the corresponding elements of T have the form:
	       [  a  0	]
	       [  0  b	]

       and the pair of corresponding 2-by-2 blocks in S and T will have a complex conjugate  pair
       of generalized eigenvalues.

ARGUMENTS
       JOBVSL  (input) CHARACTER*1
	       = 'N':  do not compute the left Schur vectors;
	       = 'V':  compute the left Schur vectors.

       JOBVSR  (input) CHARACTER*1
	       = 'N':  do not compute the right Schur vectors;
	       = 'V':  compute the right Schur vectors.

       SORT    (input) CHARACTER*1
	       Specifies  whether or not to order the eigenvalues on the diagonal of the general-
	       ized Schur form.  = 'N':  Eigenvalues are not ordered;
	       = 'S':  Eigenvalues are ordered (see DELZTG);

       DELZTG  (input) LOGICAL FUNCTION of three DOUBLE PRECISION arguments
	       DELZTG must be declared EXTERNAL in the calling subroutine.  If SORT = 'N', DELZTG
	       is not referenced.  If SORT = 'S', DELZTG is used to select eigenvalues to sort to
	       the top left of the Schur form.	An  eigenvalue	(ALPHAR(j)+ALPHAI(j))/BETA(j)  is
	       selected  if  DELZTG(ALPHAR(j),ALPHAI(j),BETA(j)) is true; i.e. if either one of a
	       complex conjugate pair of eigenvalues is selected, then both  complex  eigenvalues
	       are selected.

	       Note that in the ill-conditioned case, a selected complex eigenvalue may no longer
	       satisfy DELZTG(ALPHAR(j),ALPHAI(j), BETA(j)) = .TRUE. after ordering. INFO  is  to
	       be set to N+2 in this case.

       N       (input) INTEGER
	       The order of the matrices A, B, VSL, and VSR.  N >= 0.

       A       (input/output) DOUBLE PRECISION array, dimension (LDA, N)
	       On  entry,  the first of the pair of matrices.  On exit, A has been overwritten by
	       its generalized Schur form S.

       LDA     (input) INTEGER
	       The leading dimension of A.  LDA >= max(1,N).

       B       (input/output) DOUBLE PRECISION array, dimension (LDB, N)
	       On entry, the second of the pair of matrices.  On exit, B has been overwritten  by
	       its generalized Schur form T.

       LDB     (input) INTEGER
	       The leading dimension of B.  LDB >= max(1,N).

       SDIM    (output) INTEGER
	       If SORT = 'N', SDIM = 0.  If SORT = 'S', SDIM = number of eigenvalues (after sort-
	       ing) for which DELZTG is true.  (Complex conjugate pairs for which DELZTG is  true
	       for either eigenvalue count as 2.)

       ALPHAR  (output) DOUBLE PRECISION array, dimension (N)
	       ALPHAI	(output)  DOUBLE  PRECISION  array, dimension (N) BETA	  (output) DOUBLE
	       PRECISION  array,  dimension  (N)  On  exit,  (ALPHAR(j)  +  ALPHAI(j)*i)/BETA(j),
	       j=1,...,N,  will  be  the  generalized  eigenvalues.  ALPHAR(j) + ALPHAI(j)*i, and
	       BETA(j),j=1,...,N are the diagonals of the complex Schur  form  (S,T)  that  would
	       result  if the 2-by-2 diagonal blocks of the real Schur form of (A,B) were further
	       reduced to triangular form  using  2-by-2  complex  unitary  transformations.   If
	       ALPHAI(j)  is  zero,  then the j-th eigenvalue is real; if positive, then the j-th
	       and (j+1)-st eigenvalues are a complex conjugate pair, with ALPHAI(j+1) negative.

	       Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j) may	easily	over-  or
	       underflow, and BETA(j) may even be zero.  Thus, the user should avoid naively com-
	       puting the ratio.  However, ALPHAR and ALPHAI will be always less than and usually
	       comparable with norm(A) in magnitude, and BETA always less than and usually compa-
	       rable with norm(B).

       VSL     (output) DOUBLE PRECISION array, dimension (LDVSL,N)
	       If JOBVSL = 'V', VSL will contain the left Schur vectors.  Not referenced if  JOB-
	       VSL = 'N'.

       LDVSL   (input) INTEGER
	       The  leading dimension of the matrix VSL. LDVSL >=1, and if JOBVSL = 'V', LDVSL >=
	       N.

       VSR     (output) DOUBLE PRECISION array, dimension (LDVSR,N)
	       If JOBVSR = 'V', VSR will contain the right Schur vectors.  Not referenced if JOB-
	       VSR = 'N'.

       LDVSR   (input) INTEGER
	       The leading dimension of the matrix VSR. LDVSR >= 1, and if JOBVSR = 'V', LDVSR >=
	       N.

       WORK    (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
	       On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

       LWORK   (input) INTEGER
	       The dimension of the array WORK.  LWORK >= 8*N+16.

	       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.

       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.
	       = 1,...,N: The QZ iteration failed.  (A,B) are not in Schur form,  but  ALPHAR(j),
	       ALPHAI(j),  and	BETA(j)  should be correct for j=INFO+1,...,N.	> N:  =N+1: other
	       than QZ iteration failed in DHGEQZ.
	       =N+2: after reordering, roundoff changed values of  some  complex  eigenvalues  so
	       that  leading  eigenvalues  in  the  Generalized  Schur	form  no  longer  satisfy
	       DELZTG=.TRUE.  This could also be caused due to scaling.  =N+3: reordering  failed
	       in DTGSEN.

LAPACK version 3.0			   15 June 2000 				 DGGES(l)


All times are GMT -4. The time now is 09:18 PM.

Unix & Linux Forums Content Copyrightę1993-2018. All Rights Reserved.
UNIX.COM Login
Username:
Password:  
Show Password