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dgegv.f(3)				      LAPACK				       dgegv.f(3)

NAME
       dgegv.f -

SYNOPSIS
   Functions/Subroutines
       subroutine dgegv (JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, VL, LDVL, VR,
	   LDVR, WORK, LWORK, INFO)
	    DGEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors
	   for GE matrices

Function/Subroutine Documentation
   subroutine dgegv (characterJOBVL, characterJOBVR, integerN, double precision, dimension( lda,
       * )A, integerLDA, double precision, dimension( ldb, * )B, integerLDB, double precision,
       dimension( * )ALPHAR, double precision, dimension( * )ALPHAI, double precision, dimension(
       * )BETA, double precision, dimension( ldvl, * )VL, integerLDVL, double precision,
       dimension( ldvr, * )VR, integerLDVR, double precision, dimension( * )WORK, integerLWORK,
       integerINFO)
	DGEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for
       GE matrices

       Purpose:

	    This routine is deprecated and has been replaced by routine DGGEV.

	    DGEGV computes the eigenvalues and, optionally, the left and/or right
	    eigenvectors of a real matrix pair (A,B).
	    Given two square matrices A and B,
	    the generalized nonsymmetric eigenvalue problem (GNEP) is to find the
	    eigenvalues lambda and corresponding (non-zero) eigenvectors x such
	    that

	       A*x = lambda*B*x.

	    An alternate form is to find the eigenvalues mu and corresponding
	    eigenvectors y such that

	       mu*A*y = B*y.

	    These two forms are equivalent with mu = 1/lambda and x = y if
	    neither lambda nor mu is zero.  In order to deal with the case that
	    lambda or mu is zero or small, two values alpha and beta are returned
	    for each eigenvalue, such that lambda = alpha/beta and
	    mu = beta/alpha.

	    The vectors x and y in the above equations are right eigenvectors of
	    the matrix pair (A,B).  Vectors u and v satisfying

	       u**H*A = lambda*u**H*B  or  mu*v**H*A = v**H*B

	    are left eigenvectors of (A,B).

	    Note: this routine performs "full balancing" on A and B

       Parameters:
	   JOBVL

		     JOBVL is CHARACTER*1
		     = 'N':  do not compute the left generalized eigenvectors;
		     = 'V':  compute the left generalized eigenvectors (returned
			     in VL).

	   JOBVR

		     JOBVR is CHARACTER*1
		     = 'N':  do not compute the right generalized eigenvectors;
		     = 'V':  compute the right generalized eigenvectors (returned
			     in VR).

	   N

		     N is INTEGER
		     The order of the matrices A, B, VL, and VR.  N >= 0.

	   A

		     A is DOUBLE PRECISION array, dimension (LDA, N)
		     On entry, the matrix A.
		     If JOBVL = 'V' or JOBVR = 'V', then on exit A
		     contains the real Schur form of A from the generalized Schur
		     factorization of the pair (A,B) after balancing.
		     If no eigenvectors were computed, then only the diagonal
		     blocks from the Schur form will be correct.  See DGGHRD and
		     DHGEQZ for details.

	   LDA

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

	   B

		     B is DOUBLE PRECISION array, dimension (LDB, N)
		     On entry, the matrix B.
		     If JOBVL = 'V' or JOBVR = 'V', then on exit B contains the
		     upper triangular matrix obtained from B in the generalized
		     Schur factorization of the pair (A,B) after balancing.
		     If no eigenvectors were computed, then only those elements of
		     B corresponding to the diagonal blocks from the Schur form of
		     A will be correct.  See DGGHRD and DHGEQZ for details.

	   LDB

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

	   ALPHAR

		     ALPHAR is DOUBLE PRECISION array, dimension (N)
		     The real parts of each scalar alpha defining an eigenvalue of
		     GNEP.

	   ALPHAI

		     ALPHAI is DOUBLE PRECISION array, dimension (N)
		     The imaginary parts of each scalar alpha defining an
		     eigenvalue of GNEP.  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) = -ALPHAI(j).

	   BETA

		     BETA is DOUBLE PRECISION array, dimension (N)
		     The scalars beta that define the eigenvalues of GNEP.

		     Together, the quantities alpha = (ALPHAR(j),ALPHAI(j)) and
		     beta = BETA(j) represent the j-th eigenvalue of the matrix
		     pair (A,B), in one of the forms lambda = alpha/beta or
		     mu = beta/alpha.  Since either lambda or mu may overflow,
		     they should not, in general, be computed.

	   VL

		     VL is DOUBLE PRECISION array, dimension (LDVL,N)
		     If JOBVL = 'V', the left eigenvectors u(j) are stored
		     in the columns of VL, in the same order as their eigenvalues.
		     If the j-th eigenvalue is real, then u(j) = VL(:,j).
		     If the j-th and (j+1)-st eigenvalues form a complex conjugate
		     pair, then
			u(j) = VL(:,j) + i*VL(:,j+1)
		     and
		       u(j+1) = VL(:,j) - i*VL(:,j+1).

		     Each eigenvector is scaled so that its largest component has
		     abs(real part) + abs(imag. part) = 1, except for eigenvectors
		     corresponding to an eigenvalue with alpha = beta = 0, which
		     are set to zero.
		     Not referenced if JOBVL = 'N'.

	   LDVL

		     LDVL is INTEGER
		     The leading dimension of the matrix VL. LDVL >= 1, and
		     if JOBVL = 'V', LDVL >= N.

	   VR

		     VR is DOUBLE PRECISION array, dimension (LDVR,N)
		     If JOBVR = 'V', the right eigenvectors x(j) are stored
		     in the columns of VR, in the same order as their eigenvalues.
		     If the j-th eigenvalue is real, then x(j) = VR(:,j).
		     If the j-th and (j+1)-st eigenvalues form a complex conjugate
		     pair, then
		       x(j) = VR(:,j) + i*VR(:,j+1)
		     and
		       x(j+1) = VR(:,j) - i*VR(:,j+1).

		     Each eigenvector is scaled so that its largest component has
		     abs(real part) + abs(imag. part) = 1, except for eigenvalues
		     corresponding to an eigenvalue with alpha = beta = 0, which
		     are set to zero.
		     Not referenced if JOBVR = 'N'.

	   LDVR

		     LDVR is INTEGER
		     The leading dimension of the matrix VR. LDVR >= 1, and
		     if JOBVR = 'V', LDVR >= N.

	   WORK

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

	   LWORK

		     LWORK is INTEGER
		     The dimension of the array WORK.  LWORK >= max(1,8*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 + MAX( 6*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

		     INFO is INTEGER
		     = 0:  successful exit
		     < 0:  if INFO = -i, the i-th argument had an illegal value.
		     = 1,...,N:
			   The QZ iteration failed.  No eigenvectors have been
			   calculated, 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 DTGEVC
			   =N+8: error return from DGGBAK (computing VL)
			   =N+9: error return from DGGBAK (computing VR)
			   =N+10: error return from DLASCL (various calls)

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Further Details:

	     Balancing
	     ---------

	     This driver calls DGGBAL to both permute and scale rows and columns
	     of A and B.  The permutations PL and PR are chosen so that PL*A*PR
	     and PL*B*R will be upper triangular except for the diagonal blocks
	     A(i:j,i:j) and B(i:j,i:j), with i and j as close together as
	     possible.	The diagonal scaling matrices DL and DR are chosen so
	     that the pair  DL*PL*A*PR*DR, DL*PL*B*PR*DR have elements close to
	     one (except for the elements that start out zero.)

	     After the eigenvalues and eigenvectors of the balanced matrices
	     have been computed, DGGBAK transforms the eigenvectors back to what
	     they would have been (in perfect arithmetic) if they had not been
	     balanced.

	     Contents of A and B on Exit
	     -------- -- - --- - -- ----

	     If any eigenvectors are computed (either JOBVL='V' or JOBVR='V' or
	     both), then on exit the arrays A and B will contain the real Schur
	     form[*] of the "balanced" versions of A and B.  If no eigenvectors
	     are computed, then only the diagonal blocks will be correct.

	     [*] See DHGEQZ, DGEGS, or read the book "Matrix Computations",
		 by Golub & van Loan, pub. by Johns Hopkins U. Press.

       Definition at line 306 of file dgegv.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			       dgegv.f(3)
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