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[Octave-bug-tracker] [bug #37613] Octave precision/accuracy is much lowe

From: David Bateman
Subject: [Octave-bug-tracker] [bug #37613] Octave precision/accuracy is much lower for quadgk
Date: Mon, 29 Oct 2012 20:48:28 +0000
User-agent: Mozilla/5.0 (X11; Ubuntu; Linux x86_64; rv:16.0) Gecko/20100101 Firefox/16.0

Follow-up Comment #9, bug #37613 (project octave):

Opps, yes it should be 'transformed' to the 'untransformed' form with @trans.
However, thinking about it, that going to be fairly expensive if we test the
distance between all of the abscissae. Also it seems difficult to understand
what Shampine meant by

... become closer in a relative sense than 100 times the unit roundoff eps.

and my previous test was wrong for yet another reason; It trying to give a
"relative value" I effectively always renormalized the distance between
abscissae by the total length between the abscissae (ie 2) so that the value
returned in the test would be 0.021 (ie the distance between the 1st and 2nd
abscissae divided by 2) so comparing to 100 * eps would always return false.

Thinking about it Shampine probably meant to compare "DeltaX / X < 100 * eps".
As the test is relatively artifical we can get the same effective result by
comparing between any two abscissae in the interval and so a test like

x = trans ([t(:,1), t(:,end)]);
if (any (abs (diff (x, [], 2) ./ max (x, [], 2))) < 100 * myeps)

Should do the right thing. Here is a modified changset


(file #26853)

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