DDRGVX(3)

📦 version 3.12.0, in opensuse-leap 16.0

💅 NAME 💅

so this whole page is literally about the file /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/ddrgvx.f — and it lives in the Library Functions Manual, bestie, that's the manual name, putting it here so it's not lost 💖

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

subroutine DDRGVX (nsize, thresh, nin, nout, a, lda, b, ai, bi, alphar,
    alphai, beta, vl, vr, ilo, ihi, lscale, rscale, s, dtru, dif,
    diftru, work, lwork, iwork, liwork, result, bwork, info)
    DDRGVX

🎀 Function/Subroutine Documentation 🎀

🌸 subroutine DDRGVX 🌸

okay so here's the full signature, every single type and dimension, no cap:

subroutine DDRGVX (integer nsize, double precision thresh, integer nin,
    integer nout, double precision, dimension( lda, * ) a, integer lda,
    double precision, dimension( lda, * ) b, double precision, dimension(
    lda, * ) ai, double precision, dimension( lda, * ) bi, double precision,
    dimension( * ) alphar, double precision, dimension( * ) alphai, double
    precision, dimension( * ) beta, double precision, dimension( lda, * )
    vl, double precision, dimension( lda, * ) vr, integer ilo, integer ihi,
    double precision, dimension( * ) lscale, double precision, dimension( *
    ) rscale, double precision, dimension( * ) s, double precision,
    dimension( * ) dtru, double precision, dimension( * ) dif, double
    precision, dimension( * ) diftru, double precision, dimension( * ) work,
    integer lwork, integer, dimension( * ) iwork, integer liwork, double
    precision, dimension( 4 ) result, logical, dimension( * ) bwork, integer
    info)
    DDRGVX

💜 Purpose 💜

okay so the whole point of DDRGVX is that it checks the nonsymmetric generalized eigenvalue problem expert driver DGGEVX. it's a tester, she's the vibe check 👑

what DGGEVX actually does: 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. a whole multitasking icon ✨

when DDRGVX is called with NSIZE > 0, two types of test matrix pairs are generated by the subroutine DLATM6 and test the driver DGGEVX. 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 DLATM6).

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. conjugate transpose representation, we love to see it 🫶

  1. max over all right eigenvalue/-vector pairs (beta/alpha,r) of
     | (beta A - alpha B) r | / ( ulp max( |beta A|, |alpha B| ) )
  1. the condition number S(i) of eigenvalues computed by DGGEVX differs less than a factor THRESH from the exact S(i) (see DLATM6).
  2. DIF(i) computed by DTGSNA 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)) }. those are the exact characters, do not touch them 🌈

🌟 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. zero is a valid lifestyle choice 💅
  • THRESH — THRESH is DOUBLE PRECISION. A test will count as if the , computed as described above, exceeds THRESH. (ngl the original page literally has gaps right there, not me, I'm just the messenger 🙈). 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 DOUBLE PRECISION array, dimension (LDA, NSIZE). Used to hold the matrix whose eigenvalues are to be computed. On exit, A contains the last matrix actually used. she stays 👑
  • 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDA, NSIZE). Copy of A, modified by DGGEVX.
  • BI — BI is DOUBLE PRECISION array, dimension (LDA, NSIZE). Copy of B, modified by DGGEVX.
  • ALPHAR — ALPHAR is DOUBLE PRECISION array, dimension (NSIZE).
  • ALPHAI — ALPHAI is DOUBLE PRECISION array, dimension (NSIZE).
  • BETA — BETA is DOUBLE PRECISION array, dimension (NSIZE). On exit, (ALPHAR + ALPHAI*i)/BETA are the eigenvalues. the math is mathing ✨
  • VL — VL is DOUBLE PRECISION array, dimension (LDA, NSIZE). VL holds the left eigenvectors computed by DGGEVX.
  • VR — VR is DOUBLE PRECISION array, dimension (LDA, NSIZE). VR holds the right eigenvectors computed by DGGEVX.
  • ILO — ILO is INTEGER.
  • IHI — IHI is INTEGER.
  • LSCALE — LSCALE is DOUBLE PRECISION array, dimension (N).
  • RSCALE — RSCALE is DOUBLE PRECISION array, dimension (N).
  • S — S is DOUBLE PRECISION array, dimension (N).
  • DTRU — DTRU is DOUBLE PRECISION array, dimension (N).
  • DIF — DIF is DOUBLE PRECISION array, dimension (N).
  • DIFTRU — DIFTRU is DOUBLE PRECISION array, dimension (N).
  • WORK — WORK is DOUBLE PRECISION array, dimension (LWORK).
  • LWORK — LWORK is INTEGER. Leading dimension of WORK. LWORK >= 2*N*N+12*N+16. write that down fr fr 📝
  • IWORK — IWORK is INTEGER array, dimension (LIWORK).
  • LIWORK — LIWORK is INTEGER. Leading dimension of IWORK. Must be at least N+6.
  • RESULT — RESULT is DOUBLE PRECISION array, dimension (4).
  • BWORK — BWORK is LOGICAL array, dimension (N).
  • INFO — INFO is INTEGER. exit status time, pay attention:
    • = 0: successful exit 🎉
    • < 0: if INFO = -i, the i-th argument had an illegal value.
    • > 0: A routine returned an error code.
lowkey obsessed with INFO having three whole moods. main character exit status energy 👑

💖 Author 💖

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

Definition at line 296 of file ddrgvx.f.

🌸 Author 🌸

Generated automatically by Doxygen for LAPACK from the source code. (yes the author section happens twice, that's how the page is built, no notes 💀)

okay that's the whole page bestie, you ate that 💅🫶 this was LAPACK, Version 3.12.0, signed off from /home/abui...IG/ddrgvx.f(3) — go forth and test those generalized eigenvalue problems, mwah 🎀💜

📦 where this page comes from