dtrevc man page on YellowDog

Man page or keyword search:  
man Server   18644 pages
apropos Keyword Search (all sections)
Output format
YellowDog logo
[printable version]

DTREVC(l)			       )			     DTREVC(l)

NAME
       DTREVC - compute some or all of the right and/or left eigenvectors of a
       real upper quasi-triangular matrix T

SYNOPSIS
       SUBROUTINE DTREVC( SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, LDVR,
			  MM, M, WORK, INFO )

	   CHARACTER	  HOWMNY, SIDE

	   INTEGER	  INFO, LDT, LDVL, LDVR, M, MM, N

	   LOGICAL	  SELECT( * )

	   DOUBLE	  PRECISION T( LDT, * ), VL( LDVL, * ), VR( LDVR, * ),
			  WORK( * )

PURPOSE
       DTREVC computes some or all of the right and/or left eigenvectors of  a
       real  upper quasi-triangular matrix T.  The right eigenvector x and the
       left eigenvector y of T corresponding to an eigenvalue  w  are  defined
       by:

		    T*x = w*x,	   y'*T = w*y'

       where y' denotes the conjugate transpose of the vector y.

       If  all	eigenvectors  are requested, the routine may either return the
       matrices X and/or Y of right or left eigenvectors of T, or the products
       Q*X and/or Q*Y, where Q is an input orthogonal
       matrix. If T was obtained from the real-Schur factorization of an orig‐
       inal matrix A = Q*T*Q', then Q*X and Q*Y are the matrices of  right  or
       left eigenvectors of A.

       T  must	be  in	Schur canonical form (as returned by DHSEQR), that is,
       block upper triangular with 1-by-1 and  2-by-2  diagonal	 blocks;  each
       2-by-2 diagonal block has its diagonal elements equal and its off-diag‐
       onal elements of opposite sign.	Corresponding to each 2-by-2  diagonal
       block is a complex conjugate pair of eigenvalues and eigenvectors; only
       one eigenvector of the pair is computed, namely the  one	 corresponding
       to the eigenvalue with positive imaginary part.

ARGUMENTS
       SIDE    (input) CHARACTER*1
	       = 'R':  compute right eigenvectors only;
	       = 'L':  compute left eigenvectors only;
	       = 'B':  compute both right and left eigenvectors.

       HOWMNY  (input) CHARACTER*1
	       = 'A':  compute all right and/or left eigenvectors;
	       =  'B':	 compute all right and/or left eigenvectors, and back‐
	       transform them using the input matrices supplied in  VR	and/or
	       VL;  =  'S':   compute selected right and/or left eigenvectors,
	       specified by the logical array SELECT.

       SELECT  (input/output) LOGICAL array, dimension (N)
	       If HOWMNY = 'S', SELECT specifies the eigenvectors to  be  com‐
	       puted.	If  HOWMNY = 'A' or 'B', SELECT is not referenced.  To
	       select the real eigenvector corresponding to a real  eigenvalue
	       w(j),  SELECT(j)	 must be set to .TRUE..	 To select the complex
	       eigenvector corresponding to a complex conjugate pair w(j)  and
	       w(j+1),	either SELECT(j) or SELECT(j+1) must be set to .TRUE.;
	       then on exit SELECT(j) is .TRUE. and SELECT(j+1) is .FALSE..

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

       T       (input) DOUBLE PRECISION array, dimension (LDT,N)
	       The upper quasi-triangular matrix T in Schur canonical form.

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

       VL      (input/output) DOUBLE PRECISION array, dimension (LDVL,MM)
	       On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL  must  con‐
	       tain  an	 N-by-N	 matrix	 Q (usually the orthogonal matrix Q of
	       Schur vectors returned by DHSEQR).  On exit, if SIDE =  'L'  or
	       'B',  VL contains: if HOWMNY = 'A', the matrix Y of left eigen‐
	       vectors of T; VL has the same quasi-lower  triangular  form  as
	       T'.  If T(i,i) is a real eigenvalue, then the i-th column VL(i)
	       of VL  is its corresponding eigenvector. If T(i:i+1,i:i+1) is a
	       2-by-2  block whose eigenvalues are complex-conjugate eigenval‐
	       ues of T, then VL(i)+sqrt(-1)*VL(i+1) is the complex  eigenvec‐
	       tor  corresponding  to  the eigenvalue with positive real part.
	       if HOWMNY = 'B', the matrix Q*Y; if  HOWMNY  =  'S',  the  left
	       eigenvectors  of T specified by SELECT, stored consecutively in
	       the columns of VL, in the same order as their  eigenvalues.   A
	       complex	eigenvector  corresponding  to a complex eigenvalue is
	       stored in two consecutive columns, the first holding  the  real
	       part,  and the second the imaginary part.  If SIDE = 'R', VL is
	       not referenced.

       LDVL    (input) INTEGER
	       The leading dimension of the array VL.	LDVL  >=  max(1,N)  if
	       SIDE = 'L' or 'B'; LDVL >= 1 otherwise.

       VR      (input/output) DOUBLE PRECISION array, dimension (LDVR,MM)
	       On  entry,  if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must con‐
	       tain an N-by-N matrix Q (usually the  orthogonal	 matrix	 Q  of
	       Schur  vectors  returned by DHSEQR).  On exit, if SIDE = 'R' or
	       'B', VR contains: if HOWMNY = 'A', the matrix X of right eigen‐
	       vectors of T; VR has the same quasi-upper triangular form as T.
	       If T(i,i) is a real eigenvalue, then the i-th column  VR(i)  of
	       VR   is	its  corresponding eigenvector. If T(i:i+1,i:i+1) is a
	       2-by-2 block whose eigenvalues are complex-conjugate  eigenval‐
	       ues  of T, then VR(i)+sqrt(-1)*VR(i+1) is the complex eigenvec‐
	       tor corresponding to the eigenvalue with	 positive  real	 part.
	       if  HOWMNY  =  'B',  the matrix Q*X; if HOWMNY = 'S', the right
	       eigenvectors of T specified by SELECT, stored consecutively  in
	       the  columns  of VR, in the same order as their eigenvalues.  A
	       complex eigenvector corresponding to a  complex	eigenvalue  is
	       stored  in  two consecutive columns, the first holding the real
	       part and the second the imaginary part.	If SIDE = 'L',	VR  is
	       not referenced.

       LDVR    (input) INTEGER
	       The  leading  dimension	of  the array VR.  LDVR >= max(1,N) if
	       SIDE = 'R' or 'B'; LDVR >= 1 otherwise.

       MM      (input) INTEGER
	       The number of columns in the arrays VL and/or VR. MM >= M.

       M       (output) INTEGER
	       The number of columns in the arrays VL and/or VR actually  used
	       to store the eigenvectors.  If HOWMNY = 'A' or 'B', M is set to
	       N.  Each selected real eigenvector occupies one column and each
	       selected complex eigenvector occupies two columns.

       WORK    (workspace) DOUBLE PRECISION array, dimension (3*N)

       INFO    (output) INTEGER
	       = 0:  successful exit
	       < 0:  if INFO = -i, the i-th argument had an illegal value

FURTHER DETAILS
       The algorithm used in this program is basically backward (forward) sub‐
       stitution, with scaling to make the the code  robust  against  possible
       overflow.

       Each eigenvector is normalized so that the element of largest magnitude
       has magnitude 1; here the magnitude of a complex number (x,y) is	 taken
       to be |x| + |y|.

LAPACK version 3.0		 15 June 2000			     DTREVC(l)
[top]

List of man pages available for YellowDog

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