CTGEVC (3) Linux Manual Page

ctgevc.f –

Synopsis

Functions/Subroutines

subroutine ctgevc (SIDE, HOWMNY, SELECT, N, S, LDS, P, LDP, VL, LDVL, VR, LDVR, MM, M, WORK, RWORK, INFO)
CTGEVC

Function/Subroutine Documentation

subroutine ctgevc (characterSIDE, characterHOWMNY, logical, dimension( * )SELECT, integerN, complex, dimension( lds, * )S, integerLDS, complex, dimension( ldp, * )P, integerLDP, complex, dimension( ldvl, * )VL, integerLDVL, complex, dimension( ldvr, * )VR, integerLDVR, integerMM, integerM, complex, dimension( * )WORK, real, dimension( * )RWORK, integerINFO)

CTGEVC

Purpose:

 CTGEVC computes some or all of the right and/or left eigenvectors of

 a pair of complex matrices (S,P), where S and P are upper triangular.

 Matrix pairs of this type are produced by the generalized Schur

 factorization of a complex matrix pair (A,B):

 A = Q*S*Z**H, B = Q*P*Z**H
 as computed by CGGHRD + CHGEQZ.
 The right eigenvector x and the left eigenvector y of (S,P)

 corresponding to an eigenvalue w are defined by:
 S*x = w*P*x, (y**H)*S = w*(y**H)*P,
 where y**H denotes the conjugate tranpose of y.

 The eigenvalues are not input to this routine, but are computed

 directly from the diagonal elements of S and P.
 This routine returns the matrices X and/or Y of right and left

 eigenvectors of (S,P), or the products Z*X and/or Q*Y,

 where Z and Q are input matrices.

 If Q and Z are the unitary factors from the generalized Schur

 factorization of a matrix pair (A,B), then Z*X and Q*Y

 are the matrices of right and left eigenvectors of (A,B).

 

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 by the matrices in VR and/or VL;

 = ‘S’: compute selected right and/or left eigenvectors,

 specified 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 matrices S and P. N >= 0.

S

 S is COMPLEX array, dimension (LDS,N)

 The upper triangular matrix S from a generalized Schur

 factorization, as computed by CHGEQZ.

LDS

 LDS is INTEGER

 The leading dimension of array S. LDS >= max(1,N).

P

 P is COMPLEX array, dimension (LDP,N)

 The upper triangular matrix P from a generalized Schur

 factorization, as computed by CHGEQZ. P must have real

 diagonal elements.

LDP

 LDP is INTEGER

 The leading dimension of array P. LDP >= 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 left Schur vectors returned by CHGEQZ).

 On exit, if SIDE = ‘L’ or ‘B’, VL contains:

 if HOWMNY = ‘A’, the matrix Y of left eigenvectors of (S,P);

 if HOWMNY = ‘B’, the matrix Q*Y;

 if HOWMNY = ‘S’, the left eigenvectors of (S,P) 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 array VL. LDVL >= 1, and if

 SIDE = ‘L’ or ‘l’ or ‘B’ 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 Z

 of right Schur vectors returned by CHGEQZ).

 On exit, if SIDE = ‘R’ or ‘B’, VR contains:

 if HOWMNY = ‘A’, the matrix X of right eigenvectors of (S,P);

 if HOWMNY = ‘B’, the matrix Z*X;

 if HOWMNY = ‘S’, the right eigenvectors of (S,P) 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 (2*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

Definition at line 219 of file ctgevc.f.

Author

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