CTGEVC(3)

🌸 CTGEVC(3) 🌸

ok so you're in the Library Functions Manual bestie, and this page is literally about ctgevc.f — yes the whole path is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/ctgevc.f. She lives in LAPACK and she's iconic.

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✨ SYNOPSIS ✨

Functions/Subroutines 💅

subroutine CTGEVC (side, howmny, select, n, s, lds, p, ldp, vl, ldvl,
    vr, ldvr, mm, m, work, rwork, info)

CTGEVC — that's her, that's the name 🫶

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🦋 Function/Subroutine Documentation 🦋

subroutine CTGEVC (character side, character howmny, logical, dimension( * )
    select, integer n, complex, dimension( lds, * ) s, integer lds, complex,
    dimension( ldp, * ) p, integer ldp, complex, dimension( ldvl, * ) vl,
    integer ldvl, complex, dimension( ldvr, * ) vr, integer ldvr, integer
    mm, integer m, complex, dimension( * ) work, real, dimension( * ) rwork,
    integer info)

CTGEVC 😌✨

🎀 Purpose 🎀

ok so 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. no cap.

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 transpose of y. (that little H is doing a LOT of work, respect her 💅)

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). 🌈

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💖 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. (fr fr, don't skip that one 👀)

• 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 Z (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.

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👑 Author 👑

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 217 of file ctgevc.f.

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💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code. (she's auto-generated and still serving looks, obsessed 😭)

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and that's the whole vibe check bestie — LAPACK, Version 3.12.0, page /home/abui...RC/ctgevc.f(3) — go forth and compute those eigenvectors, you absolute main character 🦋💖✨🎀