ZTGEVC(3)

okay so welcome to ztgevc.f(3) from the Library Functions Manual — this is where LAPACK does eigenvector math and we’re gonna make it make sense, bestie. 💅✨

💖 NAME 💖

the whole NAME section is literally just this file path: /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/ztgevc.f — periodt. 🎀

🌸 SYNOPSIS 🌸

🧚 Functions/Subroutines 🧚

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

✨ Function/Subroutine Documentation ✨

🫶 ZTGEVC 🫶

   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 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. this matrix-pair situation is 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. slay. 💅

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. no cap. 🦋

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. and 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). iconic behavior. 👑

🎀 Parameters 🎀

• SIDE — CHARACTER*1. the side selector, bestie:
  • = 'R': compute right eigenvectors only;
  • = 'L': compute left eigenvectors only;
  • = 'B': compute both right and left eigenvectors.
• HOWMNY — CHARACTER*1. how many / which ones:
  • = '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 — 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 — INTEGER. the order of the matrices S and P. N >= 0.
• S — COMPLEX*16 array, dimension (LDS,N). the upper triangular matrix S from a generalized Schur factorization, as computed by ZHGEQZ.
• LDS — INTEGER. the leading dimension of array S. LDS >= max(1,N).
• P — 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. yes, real ones. 🌸
• LDP — INTEGER. the leading dimension of array P. LDP >= max(1,N).
• VL — 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 — INTEGER. the leading dimension of array VL. LDVL >= 1, and if SIDE = 'L' or 'l' or 'B' or 'b', LDVL >= N. (yes lowercase 'l' and 'b' are in there too, iykyk.)
• VR — 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 — INTEGER. the leading dimension of the array VR. LDVR >= 1, and if SIDE = 'R' or 'B', LDVR >= N.
• MM — INTEGER. the number of columns in the arrays VL and/or VR. MM >= M.
• M — 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. one column per selected eigenvector, slay. 🎀
• WORK — COMPLEX*16 array, dimension (2*N).
• RWORK — DOUBLE PRECISION array, dimension (2*N).
• INFO — INTEGER. the exit-status bestie:
  • = 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 📜

yes, that’s the line. 💅

🧚 Author 🧚

generated automatically by Doxygen for LAPACK from the source code. iconic.

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xoxo, LAPACK Version 3.12.0, source /home/abui...RC/ztgevc.f(3) 💖✨