SysTutorials

Linux Manual Pages › Section 3

ctrevc-f(3)

ctrevc.f –

Synopsis

Functions/Subroutines

subroutine ctrevc (SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, LDVR, MM, M, WORK, RWORK, INFO)
CTREVC

Function/Subroutine Documentation

subroutine ctrevc (characterSIDE, characterHOWMNY, logical, dimension( * )SELECT, integerN, complex, dimension( ldt, * )T, integerLDT, complex, dimension( ldvl, * )VL, integerLDVL, complex, dimension( ldvr, * )VR, integerLDVR, integerMM, integerM, complex, dimension( * )WORK, real, dimension( * )RWORK, integerINFO)

CTREVC

Purpose:

 CTREVC computes some or all of the right and/or left eigenvectors of
 a complex upper triangular matrix T.
 Matrices of this type are produced by the Schur factorization of
 a complex general matrix: A = Q*T*Q**H, as computed by CHSEQR.

The right eigenvector x and the left eigenvector y of T corresponding
to an eigenvalue w are defined by:


Tx = wx, (yH)T = w(yH)


where y**H denotes the conjugate transpose of the vector y.
The eigenvalues are not input to this routine, but are read directly
from the diagonal of T.


This routine returns the matrices X and/or Y of right and left
eigenvectors of T, or the products QX and/or QY, where Q is an
input matrix. If Q is the unitary factor that reduces a matrix A to
Schur form T, then QX and QY are the matrices of right and left
eigenvectors of A.

 

Parameters:

SIDE

 SIDE is CHARACTER*1
 = 'R': compute right eigenvectors only;
 = 'L': compute left eigenvectors only;
 = 'B': compute both right and left eigenvectors.

HOWMNY

 HOWMNY is CHARACTER*1
 = 'A': compute all right and/or left eigenvectors;
 = 'B': compute all right and/or left eigenvectors,
 backtransformed using the matrices supplied in
 VR and/or VL;
 = 'S': compute selected right and/or left eigenvectors,
 as indicated by the logical array SELECT.

SELECT

 SELECT is LOGICAL array, dimension (N)
 If HOWMNY = 'S', SELECT specifies the eigenvectors to be
 computed.
 The eigenvector corresponding to the j-th eigenvalue is
 computed if SELECT(j) = .TRUE..
 Not referenced if HOWMNY = 'A' or 'B'.

N

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

T

 T is COMPLEX array, dimension (LDT,N)
 The upper triangular matrix T. T is modified, but restored
 on exit.

LDT

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

VL

 VL is COMPLEX array, dimension (LDVL,MM)
 On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must
 contain an N-by-N matrix Q (usually the unitary matrix Q of
 Schur vectors returned by CHSEQR).
 On exit, if SIDE = 'L' or 'B', VL contains:
 if HOWMNY = 'A', the matrix Y of left eigenvectors of T;
 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.
 Not referenced if SIDE = 'R'.

LDVL

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

VR

 VR is COMPLEX array, dimension (LDVR,MM)
 On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must
 contain an N-by-N matrix Q (usually the unitary matrix Q of
 Schur vectors returned by CHSEQR).
 On exit, if SIDE = 'R' or 'B', VR contains:
 if HOWMNY = 'A', the matrix X of right eigenvectors of T;
 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.
 Not referenced if SIDE = 'L'.

LDVR

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

MM

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

M

 M is 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 eigenvector occupies one
 column.

WORK

 WORK is COMPLEX array, dimension (2*N)

RWORK

 RWORK is REAL array, dimension (N)

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 algorithm used in this program is basically backward (forward)
 substitution, 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|.

 

Definition at line 218 of file ctrevc.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.