CDRGVX(3)

📦 version 3.12.0, in opensuse-leap 16.0

🦋 CDRGVX(3) — the girlies' guide to the LAPACK test driver 🦋

okay so real quick, bestie — this is a page from the Library Functions Manual, section 3, and it's documenting a file that lives at

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

(yes the path is That Long, we don't judge, she's doing her best 💅)

✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/cdrgvx.f — that's the whole name, that's the file, that's her 💖

🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine CDRGVX (nsize, thresh, nin, nout, a, lda, b, ai, bi, alpha,
    beta, vl, vr, ilo, ihi, lscale, rscale, s, stru, dif, diftru, work,
    lwork, rwork, iwork, liwork, result, bwork, info)

CDRGVX — that's it, that's the name, icon behavior 👑

🎀 Function/Subroutine Documentation 🎀

subroutine CDRGVX (integer nsize, real thresh, integer nin, integer nout,
    complex, dimension( lda, * ) a, integer lda, complex, dimension( lda, *
    ) b, complex, dimension( lda, * ) ai, complex, dimension( lda, * ) bi,
    complex, dimension( * ) alpha, complex, dimension( * ) beta, complex,
    dimension( lda, * ) vl, complex, dimension( lda, * ) vr, integer ilo,
    integer ihi, real, dimension( * ) lscale, real, dimension( * ) rscale,
    real, dimension( * ) s, real, dimension( * ) stru, real, dimension( * )
    dif, real, dimension( * ) diftru, complex, dimension( * ) work, integer
    lwork, real, dimension( * ) rwork, integer, dimension( * ) iwork,
    integer liwork, real, dimension( 4 ) result, logical, dimension( * )
    bwork, integer info)

CDRGVX 🫶

💜 Purpose 💜

okay so picture this: CDRGVX is the vibe-checker for the nonsymmetric generalized eigenvalue problem expert driver CGGEVX.

CGGEVX computes the generalized eigenvalues, (optionally) the left and/or right eigenvectors, (optionally) computes a balancing transformation to improve the conditioning, and (optionally) reciprocal condition numbers for the eigenvalues and eigenvectors.

When CDRGVX is called with NSIZE > 0, two types of test matrix pairs are generated by the subroutine SLATM6 and test the driver CGGEVX. The test matrices have the known exact condition numbers for eigenvalues. For the condition numbers of the eigenvectors corresponding the first and last eigenvalues are also know "exactly" (see CLATM6).

For each matrix pair, the following tests will be performed and compared with the threshold THRESH. 🔥

(1) max over all left eigenvalue/-vector pairs (beta/alpha,l) of

   | l**H * (beta A - alpha B) | / ( ulp max( |beta A|, |alpha B| ) )

where l**H is the conjugate transpose of l.

(2) max over all right eigenvalue/-vector pairs (beta/alpha,r) of

      | (beta A - alpha B) r | / ( ulp max( |beta A|, |alpha B| ) )

(3) The condition number S(i) of eigenvalues computed by CGGEVX differs less than a factor THRESH from the exact S(i) (see CLATM6).

(4) DIF(i) computed by CTGSNA differs less than a factor 10*THRESH from the exact value (for the 1st and 5th vectors only).

🧚 Test Matrices 🧚

Two kinds of test matrix pairs

     (A, B) = inverse(YH) * (Da, Db) * inverse(X)

are used in the tests:

1: Da = 1+a   0    0    0    0    Db = 1   0   0   0   0
         0   2+a   0    0    0         0   1   0   0   0
         0    0   3+a   0    0         0   0   1   0   0
         0    0    0   4+a   0         0   0   0   1   0
         0    0    0    0   5+a ,      0   0   0   0   1 , and
2: Da =  1   -1    0    0    0    Db = 1   0   0   0   0
         1    1    0    0    0         0   1   0   0   0
         0    0    1    0    0         0   0   1   0   0
         0    0    0   1+a  1+b        0   0   0   1   0
         0    0    0  -1-b  1+a ,      0   0   0   0   1 .

In both cases the same inverse(YH) and inverse(X) are used to compute (A, B), giving the exact eigenvectors to (A,B) as (YH, X):

YH:  =  1    0   -y    y   -y    X =  1   0  -x  -x   x
        0    1   -y    y   -y         0   1   x  -x  -x
        0    0    1    0    0         0   0   1   0   0
        0    0    0    1    0         0   0   0   1   0
        0    0    0    0    1,        0   0   0   0   1 , where

a, b, x and y will have all values independently of each other from

{ sqrt(sqrt(ULP)),  0.1,  1,  10,  1/sqrt(sqrt(ULP)) }.

like, the range is giving chaotic-and-scientific at the same time, we love her 🌈

💅 PARAMETERS 💅

  • NSIZE — NSIZE is INTEGER. The number of sizes of matrices to use. NSIZE must be at least zero. If it is zero, no randomly generated matrices are tested, but any test matrices read from NIN will be tested. If it is not zero, then N = 5.
  • THRESH — THRESH is REAL. A test will count as 😭 if the (blank), computed as described above, exceeds THRESH. (bestie, the original source literally has a word missing right there — "A test will count as if the , computed as" — I'm not making it up, ngl 🙈). 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.
  • NIN — NIN is INTEGER. The FORTRAN unit number for reading in the data file of problems to solve.
  • NOUT — NOUT is INTEGER. The FORTRAN unit number for printing out error messages (e.g., if a routine returns IINFO not equal to 0.)
  • A — A is COMPLEX array, dimension (LDA, NSIZE). Used to hold the matrix whose eigenvalues are to be computed. On exit, A contains the last matrix actually used.
  • LDA — LDA is INTEGER. The leading dimension of A, B, AI, BI, Ao, and Bo. It must be at least 1 and at least NSIZE.
  • B — B is COMPLEX array, dimension (LDA, NSIZE). Used to hold the matrix whose eigenvalues are to be computed. On exit, B contains the last matrix actually used.
  • AI — AI is COMPLEX array, dimension (LDA, NSIZE). Copy of A, modified by CGGEVX.
  • BI — BI is COMPLEX array, dimension (LDA, NSIZE). Copy of B, modified by CGGEVX.
  • ALPHA — ALPHA is COMPLEX array, dimension (NSIZE).
  • BETA — BETA is COMPLEX array, dimension (NSIZE). On exit, ALPHA/BETA are the eigenvalues.
  • VL — VL is COMPLEX array, dimension (LDA, NSIZE). VL holds the left eigenvectors computed by CGGEVX.
  • VR — VR is COMPLEX array, dimension (LDA, NSIZE). VR holds the right eigenvectors computed by CGGEVX.
  • ILO — ILO is INTEGER.
  • IHI — IHI is INTEGER.
  • LSCALE — LSCALE is REAL array, dimension (N).
  • RSCALE — RSCALE is REAL array, dimension (N).
  • S — S is REAL array, dimension (N).
  • STRU — STRU is REAL array, dimension (N).
  • DIF — DIF is REAL array, dimension (N).
  • DIFTRU — DIFTRU is REAL array, dimension (N).
  • WORK — WORK is COMPLEX array, dimension (LWORK).
  • LWORK — LWORK is INTEGER. Leading dimension of WORK. LWORK >= 2*N*N + 2*N
  • RWORK — RWORK is REAL array, dimension (6*N).
  • IWORK — IWORK is INTEGER array, dimension (LIWORK).
  • LIWORK — LIWORK is INTEGER. Leading dimension of IWORK. LIWORK >= N+2.
  • RESULT — RESULT is REAL array, dimension (4).
  • BWORK — BWORK is LOGICAL array, dimension (N).
  • INFO — INFO is INTEGER
    • = 0: successful exit ✨
    • < 0: if INFO = -i, the i-th argument had an illegal value. 💀
    • > 0: A routine returned an error code.

👑 Author 👑

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

Definition at line 294 of file cdrgvx.f.

⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code.

ok and that's the whole page, bestie — every flag, every dimension, every (N), every (LDA, NSIZE), all of it, no cap 🫶

and finally, the cute sign-off: this gorgeous thing is LAPACK, Version 3.12.0, and its file header/footer do the (3) thing — /home/abui...IG/cdrgvx.f(3) — which we've now fully covered. mwah 💋💖

📦 where this page comes from