DGEEVX man page on IRIX

Man page or keyword search:  
man Server   31559 pages
apropos Keyword Search (all sections)
Output format
IRIX logo
[printable version]



DGEEVX(3F)							    DGEEVX(3F)

NAME
     DGEEVX - compute for an N-by-N real nonsymmetric matrix A, the
     eigenvalues and, optionally, the left and/or right eigenvectors

SYNOPSIS
     SUBROUTINE DGEEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, WR, WI, VL,
			LDVL, VR, LDVR, ILO, IHI, SCALE, ABNRM, RCONDE,
			RCONDV, WORK, LWORK, IWORK, INFO )

	 CHARACTER	BALANC, JOBVL, JOBVR, SENSE

	 INTEGER	IHI, ILO, INFO, LDA, LDVL, LDVR, LWORK, N

	 DOUBLE		PRECISION ABNRM

	 INTEGER	IWORK( * )

	 DOUBLE		PRECISION A( LDA, * ), RCONDE( * ), RCONDV( * ),
			SCALE( * ), VL( LDVL, * ), VR( LDVR, * ), WI( * ),
			WORK( * ), WR( * )

PURPOSE
     DGEEVX computes for an N-by-N real nonsymmetric matrix A, the eigenvalues
     and, optionally, the left and/or right eigenvectors.

     Optionally also, it computes a balancing transformation to improve the
     conditioning of the eigenvalues and eigenvectors (ILO, IHI, SCALE, and
     ABNRM), reciprocal condition numbers for the eigenvalues (RCONDE), and
     reciprocal condition numbers for the right
     eigenvectors (RCONDV).

     The right eigenvector v(j) of A satisfies
		      A * v(j) = lambda(j) * v(j)
     where lambda(j) is its eigenvalue.
     The left eigenvector u(j) of A satisfies
		   u(j)**H * A = lambda(j) * u(j)**H
     where u(j)**H denotes the conjugate transpose of u(j).

     The computed eigenvectors are normalized to have Euclidean norm equal to
     1 and largest component real.

     Balancing a matrix means permuting the rows and columns to make it more
     nearly upper triangular, and applying a diagonal similarity
     transformation D * A * D**(-1), where D is a diagonal matrix, to make its
     rows and columns closer in norm and the condition numbers of its
     eigenvalues and eigenvectors smaller.  The computed reciprocal condition
     numbers correspond to the balanced matrix.	 Permuting rows and columns
     will not change the condition numbers (in exact arithmetic) but diagonal
     scaling will.  For further explanation of balancing, see section 4.10.2
     of the LAPACK Users' Guide.

									Page 1

DGEEVX(3F)							    DGEEVX(3F)

ARGUMENTS
     BALANC  (input) CHARACTER*1
	     Indicates how the input matrix should be diagonally scaled and/or
	     permuted to improve the conditioning of its eigenvalues.  = 'N':
	     Do not diagonally scale or permute;
	     = 'P': Perform permutations to make the matrix more nearly upper
	     triangular. Do not diagonally scale; = 'S': Diagonally scale the
	     matrix, i.e. replace A by D*A*D**(-1), where D is a diagonal
	     matrix chosen to make the rows and columns of A more equal in
	     norm. Do not permute; = 'B': Both diagonally scale and permute A.

	     Computed reciprocal condition numbers will be for the matrix
	     after balancing and/or permuting. Permuting does not change
	     condition numbers (in exact arithmetic), but balancing does.

     JOBVL   (input) CHARACTER*1
	     = 'N': left eigenvectors of A are not computed;
	     = 'V': left eigenvectors of A are computed.  If SENSE = 'E' or
	     'B', JOBVL must = 'V'.

     JOBVR   (input) CHARACTER*1
	     = 'N': right eigenvectors of A are not computed;
	     = 'V': right eigenvectors of A are computed.  If SENSE = 'E' or
	     'B', JOBVR must = 'V'.

     SENSE   (input) CHARACTER*1
	     Determines which reciprocal condition numbers are computed.  =
	     'N': None are computed;
	     = 'E': Computed for eigenvalues only;
	     = 'V': Computed for right eigenvectors only;
	     = 'B': Computed for eigenvalues and right eigenvectors.

	     If SENSE = 'E' or 'B', both left and right eigenvectors must also
	     be computed (JOBVL = 'V' and JOBVR = 'V').

     N	     (input) INTEGER
	     The order of the matrix A. N >= 0.

     A	     (input/output) DOUBLE PRECISION array, dimension (LDA,N)
	     On entry, the N-by-N matrix A.  On exit, A has been overwritten.
	     If JOBVL = 'V' or JOBVR = 'V', A contains the real Schur form of
	     the balanced version of the input matrix A.

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

     WR	     (output) DOUBLE PRECISION array, dimension (N)
	     WI	     (output) DOUBLE PRECISION array, dimension (N) WR and WI
	     contain the real and imaginary parts, respectively, of the
	     computed eigenvalues.  Complex conjugate pairs of eigenvalues
	     will appear consecutively with the eigenvalue having the positive
	     imaginary part first.

									Page 2

DGEEVX(3F)							    DGEEVX(3F)

     VL	     (output) DOUBLE PRECISION array, dimension (LDVL,N)
	     If JOBVL = 'V', the left eigenvectors u(j) are stored one after
	     another in the columns of VL, in the same order as their
	     eigenvalues.  If JOBVL = 'N', VL is not referenced.  If the j-th
	     eigenvalue is real, then u(j) = VL(:,j), the j-th column of VL.
	     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).

     LDVL    (input) INTEGER
	     The leading dimension of the array VL.  LDVL >= 1; if JOBVL =
	     'V', LDVL >= N.

     VR	     (output) DOUBLE PRECISION array, dimension (LDVR,N)
	     If JOBVR = 'V', the right eigenvectors v(j) are stored one after
	     another in the columns of VR, in the same order as their
	     eigenvalues.  If JOBVR = 'N', VR is not referenced.  If the j-th
	     eigenvalue is real, then v(j) = VR(:,j), the j-th column of VR.
	     If the j-th and (j+1)-st eigenvalues form a complex conjugate
	     pair, then v(j) = VR(:,j) + i*VR(:,j+1) and
	     v(j+1) = VR(:,j) - i*VR(:,j+1).

     LDVR    (input) INTEGER
	     The leading dimension of the array VR.  LDVR >= 1, and if JOBVR =
	     'V', LDVR >= N.

	     ILO,IHI (output) INTEGER ILO and IHI are integer values
	     determined when A was balanced.  The balanced A(i,j) = 0 if I > J
	     and J = 1,...,ILO-1 or I = IHI+1,...,N.

     SCALE   (output) DOUBLE PRECISION array, dimension (N)
	     Details of the permutations and scaling factors applied when
	     balancing A.  If P(j) is the index of the row and column
	     interchanged with row and column j, and D(j) is the scaling
	     factor applied to row and column j, then SCALE(J) = P(J),	  for
	     J = 1,...,ILO-1 = D(J),	for J = ILO,...,IHI = P(J)     for J =
	     IHI+1,...,N.  The order in which the interchanges are made is N
	     to IHI+1, then 1 to ILO-1.

     ABNRM   (output) DOUBLE PRECISION
	     The one-norm of the balanced matrix (the maximum of the sum of
	     absolute values of elements of any column).

     RCONDE  (output) DOUBLE PRECISION array, dimension (N)
	     RCONDE(j) is the reciprocal condition number of the j-th
	     eigenvalue.

     RCONDV  (output) DOUBLE PRECISION array, dimension (N)
	     RCONDV(j) is the reciprocal condition number of the j-th right
	     eigenvector.

									Page 3

DGEEVX(3F)							    DGEEVX(3F)

     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.	If SENSE = 'N' or 'E', LWORK
	     >= max(1,2*N), and if JOBVL = 'V' or JOBVR = 'V', LWORK >= 3*N.
	     If SENSE = 'V' or 'B', LWORK >= N*(N+6).  For good performance,
	     LWORK must generally be larger.

     IWORK   (workspace) INTEGER array, dimension (2*N-2)
	     If SENSE = 'N' or 'E', not referenced.

     INFO    (output) INTEGER
	     = 0:  successful exit
	     < 0:  if INFO = -i, the i-th argument had an illegal value.
	     > 0:  if INFO = i, the QR algorithm failed to compute all the
	     eigenvalues, and no eigenvectors or condition numbers have been
	     computed; elements 1:ILO-1 and i+1:N of WR and WI contain
	     eigenvalues which have converged.

									Page 4

[top]

List of man pages available for IRIX

Copyright (c) for man pages and the logo by the respective OS vendor.

For those who want to learn more, the polarhome community provides shell access and support.

[legal] [privacy] [GNU] [policy] [cookies] [netiquette] [sponsors] [FAQ]
Tweet
Polarhome, production since 1999.
Member of Polarhome portal.
Based on Fawad Halim's script.
....................................................................
Vote for polarhome
Free Shell Accounts :: the biggest list on the net