👤
Home Man
Search
Today's Posts
Register

Linux & Unix Commands - Search Man Pages
Man Page or Keyword Search:
Select Section of Man Page:
Select Man Page Repository:

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

DGEGS(l)					)					 DGEGS(l)

NAME
       DGEGS - routine is deprecated and has been replaced by routine DGGES

SYNOPSIS
       SUBROUTINE DGEGS( JOBVSL,  JOBVSR,  N,  A,  LDA, B, LDB, ALPHAR, ALPHAI, BETA, VSL, LDVSL,
			 VSR, LDVSR, WORK, LWORK, INFO )

	   CHARACTER	 JOBVSL, JOBVSR

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

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

PURPOSE
       This  routine  is deprecated and has been replaced by routine DGGES.  DGEGS computes for a
       pair of N-by-N real nonsymmetric matrices A, B: the generalized	eigenvalues  (alphar  +/-
       alphai*i,  beta),  the real Schur form (A, B), and optionally left and/or right Schur vec-
       tors (VSL and VSR).

       (If only the generalized eigenvalues are needed, use the driver DGEGV instead.)

       A generalized eigenvalue for a pair of matrices (A,B) is, roughly speaking, 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, and even	for  both
       being  zero.  A good beginning reference is the book, "Matrix Computations", by G. Golub &
       C. van Loan (Johns Hopkins U. Press)

       The (generalized) Schur form of a pair of matrices  is  the  result  of	multiplying  both
       matrices  on the left by one orthogonal matrix and both on the right by another orthogonal
       matrix, these two orthogonal matrices being chosen so as to bring  the  pair  of  matrices
       into (real) Schur form.

       A  pair	of  matrices A, B is in generalized real Schur form if B is upper triangular with
       non-negative diagonal and A 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 A will be
       "standardized" by making the corresponding elements of B have the form:
	       [  a  0	]
	       [  0  b	]

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

       The  left  and right Schur vectors are the columns of VSL and VSR, respectively, where VSL
       and VSR are the orthogonal matrices which reduce A and B to Schur form:

       Schur form of (A,B) = ( (VSL)**T A (VSR), (VSL)**T B (VSR) )

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.

       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  whose  generalized  eigenvalues  and
	       (optionally)  Schur  vectors  are  to be computed.  On exit, the generalized Schur
	       form of A.  Note: to avoid overflow, the Frobenius norm of the matrix A should  be
	       less than the overflow threshold.

       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 whose generalized eigenvalues and
	       (optionally) Schur vectors are to be computed.  On  exit,  the  generalized  Schur
	       form  of B.  Note: to avoid overflow, the Frobenius norm of the matrix B should be
	       less than the overflow threshold.

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

       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,
	       j=1,...,N   and	 BETA(j),j=1,...,N   are  the diagonals of the complex Schur form
	       (A,B) 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 trans-
	       formations.  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 alpha/beta.  However, ALPHAR and ALPHAI will be always less  than
	       and  usually  comparable  with norm(A) in magnitude, and BETA always less than and
	       usually comparable with norm(B).

       VSL     (output) DOUBLE PRECISION array, dimension (LDVSL,N)
	       If JOBVSL = 'V', VSL will contain the left Schur vectors.  (See "Purpose", above.)
	       Not referenced if JOBVSL = '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.	 (See  "Purpose",
	       above.)	Not referenced if JOBVSR = '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	>=  max(1,4*N).   For  good  performance,
	       LWORK  must  generally  be  larger.   To  compute the optimal value of LWORK, call
	       ILAENV to get blocksizes (for DGEQRF, DORMQR, and DORGQR.)  Then compute:  NB   --
	       MAX  of	the blocksizes for DGEQRF, DORMQR, and DORGQR The optimal LWORK is  2*N +
	       N*(NB+1).

	       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.

       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:  errors that
	       usually indicate LAPACK problems:
	       =N+1: error return from DGGBAL
	       =N+2: error return from DGEQRF
	       =N+3: error return from DORMQR
	       =N+4: error return from DORGQR
	       =N+5: error return from DGGHRD
	       =N+6: error return from DHGEQZ (other than failed iteration)  =N+7:  error  return
	       from DGGBAK (computing VSL)
	       =N+8: error return from DGGBAK (computing VSR)
	       =N+9: error return from DLASCL (various places)

LAPACK version 3.0			   15 June 2000 				 DGEGS(l)


All times are GMT -4. The time now is 11:09 PM.

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





Not a Forum Member?
Forgot Password?