TESTING/EIG/zget24.f(3)

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version 3.12.1 · 3 versions
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🦋 TESTING/EIG/zget24.f(3) 🦋

Ok bestie, welcome to the glow-up of TESTING/EIG/zget24.f(3) from the Library Functions Manual. This is part 1, and the energy is immaculate.

💖 NAME 💖

TESTING/EIG/zget24.f — that's the name, literally. No cap, that's the whole NAME section. 🎀

✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

  • subroutine zget24 — the subroutine entry, with the full exact signature looking like this:
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
  • ZGET24 — the label that shows up right after the signature in the synopsis, uppercase and iconic. 👑

💅 Function/Subroutine Documentation 💅

okay so here's the signature, preserved exactly because we do not play with code, bestie:

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 ✨

okay so ZGET24 is the vibe check for the nonsymmetric eigenvalue (Schur form) problem expert driver ZGEESX. iconic.

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.

If COMP = .TRUE., all 17 test will be performed. <em>yes, bestie, the original said “test,” we are keeping the facts and moving.</em>

  1. Test (1): 0 if T is in Schur form, 1/ulp otherwise — no sorting of eigenvalues.
  2. Test (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. Test (3): | I - VS VS' | / ( n ulp ) — no sorting of eigenvalues.
  2. Test (4): 0 if W are eigenvalues of T, 1/ulp otherwise — no sorting of eigenvalues.
  3. Test (5): 0 if T(with VS) = T(without VS), 1/ulp otherwise — no sorting of eigenvalues.
  4. Test (6): 0 if eigenvalues(with VS) = eigenvalues(without VS), 1/ulp otherwise — no sorting of eigenvalues.
  5. Test (7): 0 if T is in Schur form, 1/ulp otherwise — with sorting of eigenvalues.
  6. Test (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. Test (9): | I - VS VS' | / ( n ulp ) — with sorting of eigenvalues.
  2. Test (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. Test (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. Test (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. Test (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. Test (14): if RCONDE the same no matter if VS and/or RCONDV computed.
  7. Test (15): if RCONDV the same no matter if VS and/or RCONDE computed.
  8. Test (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. Test (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. A test will count as a fail if the value, computed as described above, exceeds 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).
  • 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 🦋

Definition at line 331 of file zget24.f.

✨ Author ✨

So like… nobody actually wrote this page by hand, bestie 😭 it's generated automatically by Doxygen for LAPACK from the source code. That's it, that's the whole author situation — the source code is the main character here and Doxygen just did its lil copy-paste slay 💅

🎀 real talk: if you're citing this, cite the source code, not the auto-generated page. Doxygen is just the messenger, no cap.

And that's a wrap on TESTING/EIG/zget24.f! 🦋 Go forth and vibe check your eigenvalues, bestie — you've got this, fr fr ✨

This page lived its best life as part of LAPACK, Version 3.12.0, specifically TESTING/EIG/zget24.f(3) — and it was generated from the source code with love (and by Doxygen, not by a human 🫶). Byeee! 💖👑

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