SRC/ztgevc.f(3)

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version 3.12.1 · 7 versions
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okay bestie, welcome to the manual page for SRC/ztgevc.f(3) from the Library Functions Manual — generalized Schur eigenvector realness is about to happen, and yes, we’re keeping every single detail. ✨💅

🌸 NAME 🌸

SRC/ztgevc.f — that’s the name, periodt. 💅

🦋 SYNOPSIS 🦋

✨ Functions/Subroutines ✨

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

ZTGEVC — iconic. 👑

💅 Function/Subroutine Documentation 💅

subroutine ztgevc (character side, character howmny, logical, dimension( * )
    select, integer n, complex*16, dimension( lds, * ) s, integer lds,
    complex*16, dimension( ldp, * ) p, integer ldp, complex*16, dimension(
    ldvl, * ) vl, integer ldvl, complex*16, dimension( ldvr, * ) vr, integer
    ldvr, integer mm, integer m, complex*16, dimension( * ) work, double
    precision, dimension( * ) rwork, integer info)

ZTGEVC

🧚 Purpose 🧚

okay so here’s the vibe: ZTGEVC 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 ZGGHRD + ZHGEQZ.

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. 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.

pick your fave, bestie.

💙 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*16 array, dimension (LDS,N)

The upper triangular matrix S from a generalized Schur factorization, as computed by ZHGEQZ.

🌈 LDS 🌈

LDS is INTEGER

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

🍓 P 🍓

P is COMPLEX*16 array, dimension (LDP,N)

The upper triangular matrix P from a generalized Schur factorization, as computed by ZHGEQZ. P must have real diagonal elements.

🧚 LDP 🧚

LDP is INTEGER

The leading dimension of array P. LDP >= max(1,N).

💜 VL 💜

VL is COMPLEX*16 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 ZHGEQZ).

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*16 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 ZHGEQZ).

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*16 array, dimension (2*N)

🧚 RWORK 🧚

RWORK is DOUBLE PRECISION 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.

Definition at line 217 of file ztgevc.f.

🌟 Author 🌟

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mwah 💋 source/version: LAPACK Version 3.12.0; page: SRC/ztgevc.f(3); date: the footer doesn’t give a separate one, bestie. That’s the cute little sign-off. 🫶✨🎀

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