SRC/ctgevc.f(3)

🦋 SRC/ctgevc.f 🦋

okay so bestie, this is SRC/ctgevc.f, straight outta the Library Functions Manual, and it's literally the CTGEVC era 💅✨

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💖 NAME 💖

SRC/ctgevc.f — that's the whole name section, no notes, just the file, periodt 🎀

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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

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🦋 Function/Subroutine Documentation 🦋

okay, here's the full signature so you can see every single argument in all its glory:

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 🎯

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 transpose of y 🫶

The eigenvalues are not input to this routine — they're 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 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.

👑 Author 👑

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

🎀 Definition at line 🎀

Definition at line 217 of file ctgevc.f ✨

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code 💅

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xoxo, LAPACK, Version 3.12.0, from SRC/ctgevc.f(3) — mwah, bestie 💋💖