CGET24(3)

📦 version 3.12.0, in opensuse-leap 16.0

🌸 NAME 🌸

So like, the name of this whole thing is a whole entire file path, bestie — no cute little one-word name, just the full road trip:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/cget24.f

That's it. That's the name. She's a Fortran file chilling in the LAPACK testing directory, and we're reading her manual page from the Library Functions Manual, section 3 (iykyk — section 3 is where the library functions live 💅).

✨ SYNOPSIS ✨

🌈 Functions/Subroutines 🌈

  • subroutine CGET24 (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) — okay so this is the subroutine, and yes, that is a casual twenty-seven arguments. Twenty-seven. Miss girl is not doing minimalism. 🫶

Here it is laid out exactly like the page has it, line breaks and all, so nothing gets lost in the group chat:

subroutine CGET24 (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)

And the one-line tagline the page gives her? Literally just:

CGET24

No notes. No filler. She said "my name is my name." 👑

bestie you're gonna want to actually read the rest of this — that argument list is giving main character energy and we are not done. don't go anywhere 💖

🌸 Function/Subroutine Documentation 🌸

Okay bestie, this is the actual CGET24 signature — yes, the line breaks are part of the look, so keep them cute and exact:

   subroutine CGET24 (logical comp, integer jtype, real thresh, integer,
       dimension( 4 ) iseed, integer nounit, integer n, complex, dimension(
       lda, * ) a, integer lda, complex, dimension( lda, * ) h, complex,
       dimension( lda, * ) ht, complex, dimension( * ) w, complex, dimension( *
       ) wt, complex, dimension( * ) wtmp, complex, dimension( ldvs, * ) vs,
       integer ldvs, complex, dimension( ldvs, * ) vs1, real rcdein, real
       rcdvin, integer nslct, integer, dimension( * ) islct, integer isrt,
       real, dimension( 17 ) result, complex, dimension( * ) work, integer
       lwork, real, dimension( * ) rwork, logical, dimension( * ) bwork,
       integer info)

🎯 Purpose 🎯

CGET24 is the vibe-check routine for the nonsymmetric eigenvalue (Schur form) problem expert driver CGEESX. Like, it runs the tests so you don't have to.

If COMP = .FALSE., the first 13 of the following tests will 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. (Yes, the source says “test” right there. We're not fixing it. It's iconic.)

  1. 0 if T is in Schur form, 1/ulp otherwise — no sorting of eigenvalues.
  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. | I - VS VS' | / ( n ulp ) — no sorting of eigenvalues.
  2. 0 if W are eigenvalues of T, 1/ulp otherwise — no sorting of eigenvalues.
  3. 0 if T(with VS) = T(without VS), 1/ulp otherwise — no sorting of eigenvalues.
  4. 0 if eigenvalues(with VS) = eigenvalues(without VS), 1/ulp otherwise — no sorting of eigenvalues.
  5. 0 if T is in Schur form, 1/ulp otherwise — with sorting of eigenvalues.
  6. | 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. | I - VS VS' | / ( n ulp ) — with sorting of eigenvalues.
  2. 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. 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. 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. 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. if RCONDE the same no matter if VS and/or RCONDV computed.
  7. if RCONDV the same no matter if VS and/or RCONDE computed.
  8. |RCONDE - RCDEIN| / cond(RCONDE)

RCONDE is the reciprocal average eigenvalue condition number computed by CGEESX 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. |RCONDV - RCDVIN| / cond(RCONDV)

RCONDV is the reciprocal right invariant subspace condition number computed by CGEESX 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 REAL. The original text has blanks here, so I'm keeping them as-is: A test will count as if the , 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 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 array, dimension (LDA, N). Another copy of the test matrix A, modified by CGEESX.
  • HT — HT is COMPLEX array, dimension (LDA, N). Yet another copy of the test matrix A, modified by CGEESX.
  • W — W is COMPLEX array, dimension (N). The computed eigenvalues of A.
  • WT — WT is COMPLEX array, dimension (N). Like W, this array contains the eigenvalues of A, but those computed when CGEESX only computes a partial eigendecomposition, i.e. not Schur vectors.
  • WTMP — WTMP is COMPLEX array, dimension (N). Like W, this array contains the eigenvalues of A, but sorted by increasing real or imaginary part.
  • VS — VS is COMPLEX 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 array, dimension (LDVS, N). VS1 holds another copy of the computed Schur vectors.
  • RCDEIN — RCDEIN is REAL. When COMP = .TRUE. RCDEIN holds the precomputed reciprocal condition number for the average of selected eigenvalues.
  • RCDVIN — RCDVIN is REAL. 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 REAL 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 array, dimension (2*N*N).
  • LWORK — LWORK is INTEGER. The number of entries in WORK to be passed to CGEESX. This must be at least 2*N, and N*(N+1)/2 if tests 14--16 are to be performed.
  • RWORK — RWORK is REAL 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, CGEESX 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 cget24.f.

🧚 Author (the Doxygen-generated one) 🧚

Generated automatically by Doxygen for LAPACK from the source code.

💖 That's the whole page, bestie — LAPACK Version 3.12.0, from /home/abui...IG/cget24.f(3). Byeee! 💅

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