TESTING/LIN/cebchvxx.f(3)

📦
version 3.12.1 · 3 versions
, in arch rolling

💅 TESTING/LIN/cebchvxx.f(3) 💅

Welcome to the glow-up of TESTING/LIN/cebchvxx.f(3) from the Library Functions Manual. This is the page for the Fortran test routine that wants your linear algebra to be honest. 🫶

🌸 NAME 🌸

TESTING/LIN/cebchvxx.f — that’s the whole name, bestie. Iconic brevity.

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine cebchvxx (thresh, path)
    CEBCHVXX

🦋 Function/Subroutine Documentation 🦋

subroutine cebchvxx (real thresh, character*3 path)

CEBCHVXX Purpose:

Okay so CEBCHVXX is the vibe-check for CGESVXX: it runs CGESVXX on a series of Hilbert matrices, then compares the error bounds returned by CGESVXX to see if the returned answer actually falls within those bounds. No cap, we’re checking the receipts. 💅

Eight test ratios will be computed. The tests pass if they are .LT. THRESH. There are two cases, and they’re determined by 1 / (SQRT( N ) * EPS). If that value is .LE. to the component wise reciprocal condition number, it uses the guaranteed case; otherwise it uses the unguaranteed case. The norm used is the infinity norm. Let Xc be X_computed and Xt be X_truth. Let A be the guaranteed case and B be the unguaranteed case. 🧚

Test ratios:

  1. Normwise guaranteed forward error bound.
    • A: norm ( abs( Xc - Xt ) / norm ( Xt ) .LE. ERRBND( *, nwise_i, bnd_i ) and ERRBND( *, nwise_i, bnd_i ) .LE. MAX(SQRT(N),10) * EPS. If these conditions are met, the test ratio is set to be ERRBND( *, nwise_i, bnd_i ) / MAX(SQRT(N), 10). Otherwise it is 1/EPS.
    • B: For this case, CGESVXX should just return 1. If it is less than one, treat it the same as in 1A. Otherwise it fails. (Set test ratio to ERRBND( *, nwise_i, bnd_i ) * THRESH?)
  2. Componentwise guaranteed forward error bound.
    • A: norm ( abs( Xc(j) - Xt(j) ) ) / norm (Xt(j)) .LE. ERRBND( *, cwise_i, bnd_i ) for all j .AND. ERRBND( *, cwise_i, bnd_i ) .LE. MAX(SQRT(N), 10) * EPS. If these conditions are met, the test ratio is set to be ERRBND( *, cwise_i, bnd_i ) / MAX(SQRT(N), 10). Otherwise it is 1/EPS.
    • B: Same as normwise test ratio.
  3. Backwards error.
    • A: The test ratio is set to BERR/EPS.
    • B: Same test ratio.
  4. Reciprocal condition number.
    • A: A condition number is computed with Xt and compared with the one returned from CGESVXX. Let RCONDc be the RCOND returned by CGESVXX and RCONDt be the RCOND from the truth value. Test ratio is set to MAX(RCONDc/RCONDt, RCONDt/RCONDc).
    • B: Test ratio is set to 1 / (EPS * RCONDc).
  5. Reciprocal normwise condition number.
    • A: The test ratio is set to MAX(ERRBND( *, nwise_i, cond_i ) / NCOND, NCOND / ERRBND( *, nwise_i, cond_i )).
    • B: Test ratio is set to 1 / (EPS * ERRBND( *, nwise_i, cond_i )).
  6. Reciprocal componentwise condition number.
    • A: The test ratio is set to MAX(ERRBND( *, cwise_i, cond_i ) / CCOND, CCOND / ERRBND( *, cwise_i, cond_i )).
    • B: Test ratio is set to 1 / (EPS * ERRBND( *, cwise_i, cond_i )).

.. Parameters ..

Quick parameter tea: NMAX is determined by the largest number in the inverse of the hilbert matrix. Precision is exhausted when the largest entry in it is greater than 2 to the power of the number of bits in the fraction of the data type used plus one, which is 24 for single precision. NMAX should be 6 for single and 11 for double.

Author

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

Definition at line 95 of file cebchvxx.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

Stay slay, bestie — this page is stamped from LAPACK Version 3.12.0 and TESTING/LIN/cebchvxx.f(3). 🫶✨💖

📦 where this page comes from