DTRSNA man page on Oracle

Man page or keyword search:  
man Server   33470 pages
apropos Keyword Search (all sections)
Output format
Oracle logo
[printable version]

dtrsna.f(3)			    LAPACK			   dtrsna.f(3)

NAME
       dtrsna.f -

SYNOPSIS
   Functions/Subroutines
       subroutine dtrsna (JOB, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, LDVR,
	   S, SEP, MM, M, WORK, LDWORK, IWORK, INFO)
	   DTRSNA

Function/Subroutine Documentation
   subroutine dtrsna (characterJOB, characterHOWMNY, logical, dimension( *
       )SELECT, integerN, double precision, dimension( ldt, * )T, integerLDT,
       double precision, dimension( ldvl, * )VL, integerLDVL, double
       precision, dimension( ldvr, * )VR, integerLDVR, double precision,
       dimension( * )S, double precision, dimension( * )SEP, integerMM,
       integerM, double precision, dimension( ldwork, * )WORK, integerLDWORK,
       integer, dimension( * )IWORK, integerINFO)
       DTRSNA

       Purpose:

	    DTRSNA estimates reciprocal condition numbers for specified
	    eigenvalues and/or right eigenvectors of a real upper
	    quasi-triangular matrix T (or of any matrix Q*T*Q**T with Q
	    orthogonal).

	    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-diagonal elements of opposite sign.

       Parameters:
	   JOB

		     JOB is CHARACTER*1
		     Specifies whether condition numbers are required for
		     eigenvalues (S) or eigenvectors (SEP):
		     = 'E': for eigenvalues only (S);
		     = 'V': for eigenvectors only (SEP);
		     = 'B': for both eigenvalues and eigenvectors (S and SEP).

	   HOWMNY

		     HOWMNY is CHARACTER*1
		     = 'A': compute condition numbers for all eigenpairs;
		     = 'S': compute condition numbers for selected eigenpairs
			    specified by the array SELECT.

	   SELECT

		     SELECT is LOGICAL array, dimension (N)
		     If HOWMNY = 'S', SELECT specifies the eigenpairs for which
		     condition numbers are required. To select condition numbers
		     for the eigenpair corresponding to a real eigenvalue w(j),
		     SELECT(j) must be set to .TRUE.. To select condition numbers
		     corresponding to a complex conjugate pair of eigenvalues w(j)
		     and w(j+1), either SELECT(j) or SELECT(j+1) or both, must be
		     set to .TRUE..
		     If HOWMNY = 'A', SELECT is not referenced.

	   N

		     N is INTEGER
		     The order of the matrix T. N >= 0.

	   T

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

	   LDT

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

	   VL

		     VL is DOUBLE PRECISION array, dimension (LDVL,M)
		     If JOB = 'E' or 'B', VL must contain left eigenvectors of T
		     (or of any Q*T*Q**T with Q orthogonal), corresponding to the
		     eigenpairs specified by HOWMNY and SELECT. The eigenvectors
		     must be stored in consecutive columns of VL, as returned by
		     DHSEIN or DTREVC.
		     If JOB = 'V', VL is not referenced.

	   LDVL

		     LDVL is INTEGER
		     The leading dimension of the array VL.
		     LDVL >= 1; and if JOB = 'E' or 'B', LDVL >= N.

	   VR

		     VR is DOUBLE PRECISION array, dimension (LDVR,M)
		     If JOB = 'E' or 'B', VR must contain right eigenvectors of T
		     (or of any Q*T*Q**T with Q orthogonal), corresponding to the
		     eigenpairs specified by HOWMNY and SELECT. The eigenvectors
		     must be stored in consecutive columns of VR, as returned by
		     DHSEIN or DTREVC.
		     If JOB = 'V', VR is not referenced.

	   LDVR

		     LDVR is INTEGER
		     The leading dimension of the array VR.
		     LDVR >= 1; and if JOB = 'E' or 'B', LDVR >= N.

	   S

		     S is DOUBLE PRECISION array, dimension (MM)
		     If JOB = 'E' or 'B', the reciprocal condition numbers of the
		     selected eigenvalues, stored in consecutive elements of the
		     array. For a complex conjugate pair of eigenvalues two
		     consecutive elements of S are set to the same value. Thus
		     S(j), SEP(j), and the j-th columns of VL and VR all
		     correspond to the same eigenpair (but not in general the
		     j-th eigenpair, unless all eigenpairs are selected).
		     If JOB = 'V', S is not referenced.

	   SEP

		     SEP is DOUBLE PRECISION array, dimension (MM)
		     If JOB = 'V' or 'B', the estimated reciprocal condition
		     numbers of the selected eigenvectors, stored in consecutive
		     elements of the array. For a complex eigenvector two
		     consecutive elements of SEP are set to the same value. If
		     the eigenvalues cannot be reordered to compute SEP(j), SEP(j)
		     is set to 0; this can only occur when the true value would be
		     very small anyway.
		     If JOB = 'E', SEP is not referenced.

	   MM

		     MM is INTEGER
		     The number of elements in the arrays S (if JOB = 'E' or 'B')
		      and/or SEP (if JOB = 'V' or 'B'). MM >= M.

	   M

		     M is INTEGER
		     The number of elements of the arrays S and/or SEP actually
		     used to store the estimated condition numbers.
		     If HOWMNY = 'A', M is set to N.

	   WORK

		     WORK is DOUBLE PRECISION array, dimension (LDWORK,N+6)
		     If JOB = 'E', WORK is not referenced.

	   LDWORK

		     LDWORK is INTEGER
		     The leading dimension of the array WORK.
		     LDWORK >= 1; and if JOB = 'V' or 'B', LDWORK >= N.

	   IWORK

		     IWORK is INTEGER array, dimension (2*(N-1))
		     If JOB = 'E', IWORK is not referenced.

	   INFO

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

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Further Details:

	     The reciprocal of the condition number of an eigenvalue lambda is
	     defined as

		     S(lambda) = |v**T*u| / (norm(u)*norm(v))

	     where u and v are the right and left eigenvectors of T corresponding
	     to lambda; v**T denotes the transpose of v, and norm(u)
	     denotes the Euclidean norm. These reciprocal condition numbers always
	     lie between zero (very badly conditioned) and one (very well
	     conditioned). If n = 1, S(lambda) is defined to be 1.

	     An approximate error bound for a computed eigenvalue W(i) is given by

				 EPS * norm(T) / S(i)

	     where EPS is the machine precision.

	     The reciprocal of the condition number of the right eigenvector u
	     corresponding to lambda is defined as follows. Suppose

			 T = ( lambda  c  )
			     (	 0    T22 )

	     Then the reciprocal condition number is

		     SEP( lambda, T22 ) = sigma-min( T22 - lambda*I )

	     where sigma-min denotes the smallest singular value. We approximate
	     the smallest singular value by the reciprocal of an estimate of the
	     one-norm of the inverse of T22 - lambda*I. If n = 1, SEP(1) is
	     defined to be abs(T(1,1)).

	     An approximate error bound for a computed right eigenvector VR(i)
	     is given by

				 EPS * norm(T) / SEP(i)

       Definition at line 264 of file dtrsna.f.

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

Version 3.4.2			Tue Sep 25 2012			   dtrsna.f(3)
[top]

List of man pages available for Oracle

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