ZGET24(3)

📦 version 3.12.0, in opensuse-leap 16.0

zget24(3) 💅🦋

okay so bestie, this is zget24(3), and the manual name is Library Functions Manual — she said "put some respect on it." The file this page belongs to is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/zget24.f, and we're keeping the whole path exactly as it is. No edits, no remixes, no lowercase crimes. ✨

🌸 NAME 🌸

  • /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/zget24.f — that's the name line. That's the whole name. She's not a short little command name today; she's a full file path and she's owning it. 💖

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

This section is literally just the subroutine lineup, and the lineup is one icon: ZGET24. The signature is below, and yes, every argument made it into the group chat. 🫶

subroutine ZGET24 (comp, jtype, thresh, iseed, nounit, n, a, lda, h, ht,
           w, wt, wtmp, vs, ldvs, vs1, rcdein, rcdvin, nslct, islct, isrt,
           result, work, lwork, rwork, bwork, info)
           ZGET24
  • subroutine ZGET24 — the subroutine entry. The full argument cast, in order, is comp, jtype, thresh, iseed, nounit, n, a, lda, h, ht, w, wt, wtmp, vs, ldvs, vs1, rcdein, rcdvin, nslct, islct, isrt, result, work, lwork, rwork, bwork, info. 💅
  • ZGET24 — the subroutine name as listed under Functions/Subroutines. Spelled exactly like that, uppercase and unbothered. 👑

💖 Function/Subroutine Documentation 💖

okay bestie, this is where we meet the actual subroutine — say hi to ZGET24 👋. Here's the whole signature exactly as it lives, no edits, no cap:

   subroutine ZGET24 (logical comp, integer jtype, double precision thresh,
       integer, dimension( 4 ) iseed, integer nounit, integer n, complex*16,
       dimension( lda, * ) a, integer lda, complex*16, dimension( lda, * ) h,
       complex*16, dimension( lda, * ) ht, complex*16, dimension( * ) w,
       complex*16, dimension( * ) wt, complex*16, dimension( * ) wtmp,
       complex*16, dimension( ldvs, * ) vs, integer ldvs, complex*16,
       dimension( ldvs, * ) vs1, double precision rcdein, double precision
       rcdvin, integer nslct, integer, dimension( * ) islct, integer isrt,
       double precision, dimension( 17 ) result, complex*16, dimension( * )
       work, integer lwork, double precision, dimension( * ) rwork, logical,
       dimension( * ) bwork, integer info)
       ZGET24

✨ Purpose ✨

ZGET24 checks the nonsymmetric eigenvalue (Schur form) problem expert driver ZGEESX. Like, it's the vibe-check routine for numerical correctness 👑.

  • If COMP = .FALSE., the first 13 of the following tests will be be performed on the input matrix A, and also tests 14 and 15 if LWORK is sufficiently large. (Yes, the source says "be be" — I'm not fixing it, it's iconic 😭.)
  • If COMP = .TRUE., all 17 test will be performed. (Source grammar, not mine 💅.)

Here's the full test lineup, bestie:

  1. (1) 0 if T is in Schur form, 1/ulp otherwise — no sorting of eigenvalues.
  2. (2) | A - VS T VS' | / ( n |A| ulp )

Here VS is the matrix of Schur eigenvectors, and T is in Schur form (no sorting of eigenvalues).

  1. (3) | I - VS VS' | / ( n ulp ) (no sorting of eigenvalues).
  2. (4) 0 if W are eigenvalues of T; 1/ulp otherwise (no sorting of eigenvalues).
  3. (5) 0 if T (with VS) = T (without VS); 1/ulp otherwise (no sorting of eigenvalues).
  4. (6) 0 if eigenvalues (with VS) = eigenvalues (without VS); 1/ulp otherwise (no sorting of eigenvalues).
  5. (7) 0 if T is in Schur form, 1/ulp otherwise (with sorting of eigenvalues).
  6. (8) | A - VS T VS' | / ( n |A| ulp )

Here VS is the matrix of Schur eigenvectors, and T is in Schur form (with sorting of eigenvalues).

  1. (9) | I - VS VS' | / ( n ulp ) (with sorting of eigenvalues).
  2. (10) 0 if W are eigenvalues of T; 1/ulp otherwise. If workspace sufficient, also compare W with and without reciprocal condition numbers (with sorting of eigenvalues).
  3. (11) 0 if T (with VS) = T (without VS); 1/ulp otherwise. If workspace sufficient, also compare T with and without reciprocal condition numbers (with sorting of eigenvalues).
  4. (12) 0 if eigenvalues (with VS) = eigenvalues (without VS); 1/ulp otherwise. If workspace sufficient, also compare VS with and without reciprocal condition numbers (with sorting of eigenvalues).
  5. (13) if sorting worked and SDIM is the number of eigenvalues which were SELECTed. If workspace sufficient, also compare SDIM with and without reciprocal condition numbers.
  6. (14) if RCONDE the same no matter if VS and/or RCONDV computed.
  7. (15) if RCONDV the same no matter if VS and/or RCONDE computed.
  8. (16) |RCONDE - RCDEIN| / cond(RCONDE)

RCONDE is the reciprocal average eigenvalue condition number computed by ZGEESX and RCDEIN (the precomputed true value) is supplied as input. cond(RCONDE) is the condition number of RCONDE, and takes errors in computing RCONDE into account, so that the resulting quantity should be O(ULP). cond(RCONDE) is essentially given by norm(A)/RCONDV.

  1. (17) |RCONDV - RCDVIN| / cond(RCONDV)

RCONDV is the reciprocal right invariant subspace condition number computed by ZGEESX and RCDVIN (the precomputed true value) is supplied as input. cond(RCONDV) is the condition number of RCONDV, and takes errors in computing RCONDV into account, so that the resulting quantity should be O(ULP). cond(RCONDV) is essentially given by norm(A)/RCONDE.

🎀 Parameters 🎀

COMP

COMP is LOGICAL — COMP describes which input tests to perform:

  • = .FALSE. if the computed condition numbers are not to be tested against RCDVIN and RCDEIN
  • = .TRUE. if they are to be compared

JTYPE

JTYPE is INTEGER — Type of input matrix. Used to label output if error occurs.

ISEED

ISEED is INTEGER array, dimension (4) — If COMP = .FALSE., the random number generator seed used to produce matrix. If COMP = .TRUE., ISEED(1) = the number of the example. Used to label output if error occurs.

THRESH

THRESH is DOUBLE PRECISION — The source literally says: "A test will count as if the , computed as described above, exceeds THRESH." So yeah, a test flags when its computed thing goes over THRESH 🚩. Note that the error is scaled to be O(1), so THRESH should be a reasonably small multiple of 1, e.g., 10 or 100. In particular, it should not depend on the precision (single vs. double) or the size of the matrix. It must be at least zero.

NOUNIT

NOUNIT is INTEGER — The FORTRAN unit number for printing out error messages (e.g., if a routine returns INFO not equal to 0.)

N

N is INTEGER — The dimension of A. N must be at least 0.

A

A is COMPLEX*16 array, dimension (LDA, N) — Used to hold the matrix whose eigenvalues are to be computed.

LDA

LDA is INTEGER — The leading dimension of A, and H. LDA must be at least 1 and at least N.

H

H is COMPLEX*16 array, dimension (LDA, N) — Another copy of the test matrix A, modified by ZGEESX.

HT

HT is COMPLEX*16 array, dimension (LDA, N) — Yet another copy of the test matrix A, modified by ZGEESX.

W

W is COMPLEX*16 array, dimension (N) — The computed eigenvalues of A.

WT

WT is COMPLEX*16 array, dimension (N) — Like W, this array contains the eigenvalues of A, but those computed when ZGEESX only computes a partial eigendecomposition, i.e. not Schur vectors.

WTMP

WTMP is COMPLEX*16 array, dimension (N) — Like W, this array contains the eigenvalues of A, but sorted by increasing real or imaginary part.

VS

VS is COMPLEX*16 array, dimension (LDVS, N) — VS holds the computed Schur vectors.

LDVS

LDVS is INTEGER — Leading dimension of VS. Must be at least max(1, N).

VS1

VS1 is COMPLEX*16 array, dimension (LDVS, N) — VS1 holds another copy of the computed Schur vectors.

RCDEIN

RCDEIN is DOUBLE PRECISION — When COMP = .TRUE. RCDEIN holds the precomputed reciprocal condition number for the average of selected eigenvalues.

RCDVIN

RCDVIN is DOUBLE PRECISION — When COMP = .TRUE. RCDVIN holds the precomputed reciprocal condition number for the selected right invariant subspace.

NSLCT

NSLCT is INTEGER — When COMP = .TRUE. the number of selected eigenvalues corresponding to the precomputed values RCDEIN and RCDVIN.

ISLCT

ISLCT is INTEGER array, dimension (NSLCT) — When COMP = .TRUE. ISLCT selects the eigenvalues of the input matrix corresponding to the precomputed values RCDEIN and RCDVIN. For I=1, ... ,NSLCT, if ISLCT(I) = J, then the eigenvalue with the J-th largest real or imaginary part is selected. The real part is used if ISRT = 0, and the imaginary part if ISRT = 1. Not referenced if COMP = .FALSE.

ISRT

ISRT is INTEGER — When COMP = .TRUE., ISRT describes how ISLCT is used to choose a subset of the spectrum. Not referenced if COMP = .FALSE.

RESULT

RESULT is DOUBLE PRECISION array, dimension (17) — The values computed by the 17 tests described above. The values are currently limited to 1/ulp, to avoid overflow.

WORK

WORK is COMPLEX*16 array, dimension (2*N*N) — that's the whole description, bestie. It's a big ol' workspace array 💜.

LWORK

LWORK is INTEGER — The number of entries in WORK to be passed to ZGEESX. This must be at least 2*N, and N*(N+1)/2 if tests 14--16 are to be performed.

RWORK

RWORK is DOUBLE PRECISION array, dimension (N)

BWORK

BWORK is LOGICAL array, dimension (N)

INFO

INFO is INTEGER — If 0, successful exit. If <0, input parameter -INFO had an incorrect value. If >0, ZGEESX returned an error code, the absolute value of which is returned.

🌟 Author 🌟

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 331 of file zget24.f.

✨ Author ✨

Auto-generated, bestie. 💅 No human typed this by hand — Doxygen did the whole thing for LAPACK, straight from the source code. So if the vibes are immaculate and the formatting is flawless, that's the tool. If something's weird, it's also the tool. 🙈

That's genuinely it — no mysterious author bio, no "written by a person in 1988," just a lil program doing its thing and eating. 🫶

Lowkey iconic that a whole manual page can be a bot's main character moment. 🤖💖

And that's a wrap on ZGET24! 🎀 Thanks for reading all three parts, bestie — the way you stuck with it through every routine signature, argument, and generated-by-Doxygen footnote? Obsessed. 🌸

Signing off from LAPACK, Version 3.12.0, with the page living at /home/abui...IG/zget24.f(3) — go forth, call your routines correctly, and slay. 🔥👑💜

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