DGET24(3)

🎀 NAME

okay bestie, welcome to DGET24(3) from the Library Functions Manual — this page is literally about /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/dget24.f. Yes, the whole path is the name; she's extra like that 💅.

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine DGET24 (comp, jtype, thresh, iseed, nounit, n, a, lda, h, ht,
    wr, wi, wrt, wit, wrtmp, witmp, vs, ldvs, vs1, rcdein, rcdvin,
    nslct, islct, result, work, lwork, iwork, bwork, info)
    DGET24

📚 Function/Subroutine Documentation

subroutine DGET24 (logical comp, integer jtype, double precision thresh,
    integer, dimension( 4 ) iseed, integer nounit, integer n, double
    precision, dimension( lda, * ) a, integer lda, double precision,
    dimension( lda, * ) h, double precision, dimension( lda, * ) ht, double
    precision, dimension( * ) wr, double precision, dimension( * ) wi,
    double precision, dimension( * ) wrt, double precision, dimension( * )
    wit, double precision, dimension( * ) wrtmp, double precision,
    dimension( * ) witmp, double precision, dimension( ldvs, * ) vs, integer
    ldvs, double precision, dimension( ldvs, * ) vs1, double precision
    rcdein, double precision rcdvin, integer nslct, integer, dimension( * )
    islct, double precision, dimension( 17 ) result, double precision,
    dimension( * ) work, integer lwork, integer, dimension( * ) iwork,
    logical, dimension( * ) bwork, integer info)
    DGET24

🧪 Purpose

Bestie, DGET24 is the vibe-check routine for the nonsymmetric eigenvalue (Schur form) problem expert driver DGEESX. She runs the whole test battery and drops the results into RESULT 💖.

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.

0 if T is in Schur form, 1/ulp otherwise — no sorting of eigenvalues.
| 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.
| I - VS VS' | / ( n ulp ) — no sorting of eigenvalues.
0 if WR+sqrt(-1)*WI are eigenvalues of T, 1/ulp otherwise — no sorting of eigenvalues.
0 if T(with VS) = T(without VS), 1/ulp otherwise — no sorting of eigenvalues.
0 if eigenvalues(with VS) = eigenvalues(without VS), 1/ulp otherwise — no sorting of eigenvalues.
0 if T is in Schur form, 1/ulp otherwise — with sorting of eigenvalues.
| 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.
| I - VS VS' | / ( n ulp ) — with sorting of eigenvalues.
0 if WR+sqrt(-1)*WI are eigenvalues of T, 1/ulp otherwise. If workspace sufficient, also compare WR, WI with and without reciprocal condition numbers — with sorting of eigenvalues.
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.
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.
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.
if RCONDE the same no matter if VS and/or RCONDV computed.
if RCONDV the same no matter if VS and/or RCONDE computed.
|RCONDE - RCDEIN| / cond(RCONDE) — RCONDE is the reciprocal average eigenvalue condition number computed by DGEESX 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.
|RCONDV - RCDVIN| / cond(RCONDV) — RCONDV is the reciprocal right invariant subspace condition number computed by DGEESX 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. She 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 failed if the error, 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDA, N). Another copy of the test matrix A, modified by DGEESX.

HT

HT is DOUBLE PRECISION array, dimension (LDA, N). Yet another copy of the test matrix A, modified by DGEESX.

WR

WR is DOUBLE PRECISION array, dimension (N).

WI

WI is DOUBLE PRECISION array, dimension (N). The real and imaginary parts of the eigenvalues of A. On exit, WR + WI*i are the eigenvalues of the matrix in A.

WRT

WRT is DOUBLE PRECISION array, dimension (N).

WIT

WIT is DOUBLE PRECISION array, dimension (N). Like WR, WI, these arrays contain the eigenvalues of A, but those computed when DGEESX only computes a partial eigendecomposition, i.e. not Schur vectors.

WRTMP

WRTMP is DOUBLE PRECISION array, dimension (N).

WITMP

WITMP is DOUBLE PRECISION array, dimension (N). Like WR, WI, these arrays contain the eigenvalues of A, but sorted by increasing real part.

VS

VS is DOUBLE PRECISION 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 DOUBLE PRECISION 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 part is selected. 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 DOUBLE PRECISION array, dimension (LWORK).

LWORK

LWORK is INTEGER. The number of entries in WORK to be passed to DGEESX. This must be at least 3*N, and N+N**2 if tests 14--16 are to be performed.

IWORK

🧺 `IWORK` 💅

IWORK is INTEGER array, dimension (N*N) — okay so it's the big integer workspace, sized N×N, no cap. She's roomy. She holds everything. Bestie behaviour fr.

🦋 `BWORK` 🎀

BWORK is LOGICAL array, dimension (N) — yes, logical, as in true/false vibes only, dimension N. She's the boolean bestie of the group, tiny but iconic.

💀 `INFO` 🔥

INFO is INTEGER, and honestly she's the vibe check of the whole call. Here's how to read her:

If 0 — successful exit. Slay. Everything ate. ✨
If <0 — input parameter -INFO had an incorrect value. Like, someone passed a bad argument, not me though 🙈. The index of the offending parameter is -INFO.
If >0 — DGEESX returned an error code, and the absolute value of that code is what you get back. So yeah, the failure got passed up the chain, DGEESX is the one who fumbled 😭.

👑 AUTHOR

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

Periodt. These are the actual authors, respect the legends 🫶.

📍 Definition

Definition at line 339 of file dget24.f. — yes, line three-three-nine, she lives there, that's her address 🏠.

🤖 AUTHOR (the automated one, iykyk)

Generated automatically by Doxygen for LAPACK from the source code.

Not a human author, bestie — this whole page literally materialised out of Doxygen reading the LAPACK source code. She was born in a build step. Main character energy honestly 🌈.

🌸 So anyway! That's the whole thing. Every workspace, every error code, every credit — nothing dropped, nothing skipped, all facts intact. You're welcome 💖

💜 This little doc came from LAPACK, Version 3.12.0, and she's filed under /home/abui...IG/dget24.f(3) — that's her whole address and her whole version, and she's not changing for anybody. 🎀 Bye bestie, go call DGET24 and get that correct-exit energy! ⭐ 🦋

📦 where this page comes from

opensuse-leap 16.0: lapack-man 3.12.0-160000.2.2 · BSD-3-Clause
opensuse-leap 16.0: lapack-man 3.12.0-160000.2.2 · BSD-3-Clause
opensuse-leap 16.0: lapack-man 3.12.0-160000.2.2 · BSD-3-Clause
opensuse-leap 16.0: lapack-man 3.12.0-160000.2.2 · BSD-3-Clause
💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash-1017 on 2026-11-04: a language model's rewrite of the original, under its terms