TESTING/EIG/dget31.f(3)

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💅 TESTING/EIG/dget31.f 💅

okay bestie, welcome to the Library Functions Manual page for TESTING/EIG/dget31.f — yes, it's a whole Fortran testing routine and we're gonna read it together. No cap. 💖

🌸 NAME 🌸

TESTING/EIG/dget31.f

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

subroutine dget31 (rmax, lmax, ninfo, knt)
           DGET31

🧚 Function/Subroutine Documentation 🧚

👑 subroutine dget31 👑

subroutine dget31 (double precision rmax, integer lmax, integer, dimension(
       2 ) ninfo, integer knt)

DGET31

💖 Purpose 💖

Okay so DGET31 tests DLALN2, a routine for solving:

(ca A - w D)X = sB

Here's the tea: A is an NA by NA matrix — and bestie, NA=1 or 2 only, those are the only sizes on the menu. w is a real constant when NW=1 or a complex constant when NW=2. ca is a real constant. D is an NA by NA real diagonal matrix, and B is an NA by NW matrix — when NW=2, the second column of B contains the imaginary part of the solution. The code returns X and s, where s is a scale factor, less than or equal to 1, chosen to avoid overflow in X.

If any singular values of ca A-w D are less than another input parameter SMIN, they are perturbed up to SMIN.

The test condition is that the scaled residual:

norm( (ca A-w D)*X - s*B ) /
      ( max( ulp*norm(ca A-w D), SMIN )*norm(X) )

should be on the order of 1. Here, ulp is the machine precision. Also, it is verified that SCALE is less than or equal to 1, and that XNORM = infinity-norm(X).

🌸 Parameters 🌸

  • RMAX — DOUBLE PRECISION; this is the value of the largest test ratio.
  • LMAX — INTEGER; this is the example number where the largest test ratio was achieved.
  • NINFO — INTEGER array, dimension (2); NINFO(1) = number of examples with INFO less than 0, and NINFO(2) = number of examples with INFO greater than 0.
  • KNT — INTEGER; total number of examples tested.

💖 Author 💖

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

Definition at line 90 of file dget31.f.

🎀 Author 🎀

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