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From Tanguy Yannick <Yannick.Tan...@cnes.fr>
Subject RE: [math] Adding some methods in Precision class (oacm.util)
Date Wed, 19 Sep 2012 15:31:57 GMT
As I said, our solution first uses equals() method, to distinguish wether number are "strictly"
equals (thanks to existing methods) before dividing the difference by the max value of (x,y).

So I tested the use case proposed by Luc with our implementation and with Luc's one (see here
after).

About the default value (1e-14), I know the tolerance is case-dependant, but some times, we
don't precisely know the order of magnitude (ex : jacobians matrices) and it's quite practical
to have a default value.
In our tools, we use this value in the test classes, but also for specific algorithm convergence
threshold.

If you agree, I'll open a ticket and attach our patch.

Best regards,

Yannick

--
Here are the results obtained with various methods : CommonsMath equals (one ulp), our method
with a relative 1e-14 threshold, and another method (abs(x1-x2) <= eps * max(abs(x1),abs(x2)
)

-------------------
X: 0.0 vs Y: -0.0
Equals (CM) 		true
EqualsWithRelativeTol 	true
EqualsOtherSolution	 false
-------------------
X: 0.1 vs Y: 0.1000000000001
Equals (CM) 		false
EqualsWithRelativeTol 	false
EqualsOtherSolution	 false
-------------------
X: 1.7976931348623157E308 vs Y: 1.7976931348623157E308
Equals (CM) 		true
EqualsWithRelativeTol 	true
EqualsOtherSolution	 true
-------------------
X: 4.9E-324 vs Y: 4.9E-324
Equals (CM) 		true
EqualsWithRelativeTol 	true
EqualsOtherSolution	 false
-------------------
X: Infinity vs Y: Infinity
Equals (CM) 		true
EqualsWithRelativeTol 	true
EqualsOtherSolution	 false
-------------------
X: NaN vs Y: NaN
Equals (CM) 		false
EqualsWithRelativeTol 	false
EqualsOtherSolution	 false
-------------------
X: 0.0 vs Y: 0.0
Equals (CM) 		true
EqualsWithRelativeTol 	true
EqualsOtherSolution	 false
-------------------
X: -Infinity vs Y: -Infinity
Equals (CM) 		true
EqualsWithRelativeTol 	true
EqualsOtherSolution	 false
-------------------
X: 0.100000000000001 vs Y: 0.1
Equals (CM) 		false
EqualsWithRelativeTol 	true
EqualsOtherSolution	 true
-------------------
X: 0.1000000000000011 vs Y: 0.1
Equals (CM) 		false
EqualsWithRelativeTol 	false
EqualsOtherSolution	 false

-----Message d'origine-----
Envoyé : mercredi 19 septembre 2012 16:38
À : dev@commons.apache.org
Objet : Re: [math] Adding some methods in Precision class (oacm.util)

Hi.

>
> >
> > This message is about some methods in Precision class, and follows a
> > (https://issues.apache.org/jira/browse/MATH-863).
> >
> > Recently, we slightly modified our Precision class, by adding a
> > specific epsilon value to compute a relative deviation and also some
> > methods. --- /** Epsilon used for doubles relative comparison */
> > public static final double DOUBLE_COMPARISON_EPSILON = 1.0e-14; ---
> >
> > This value is quite useful to compare two values. It's
> > approximatively 100 times larger than the previous EPSILON value
> > (1e-16, the difference between 1. and the next closest value).
> >
> > We also added static methods, to compute a relative difference : if
> > x1 and x2 are not equal (according to the equals(x1,x2, "1 ulp")
> > function), then we compute a relative deviation
> > ("abs(x1-x2)/max(abs(x1),abs(x2))" and see if it's lower than an
> > epsilon value.
>
> The comparison should probably rather be:
>   abs(x1-x2) <= eps * max(abs(x1),abs(x2)
>
> The reason for that is that with your implementation when both x1 and x2
> are 0 (either +0 or -0), then the result would be false, despite the
> numbers are equal. The division 0/0 leads to a NaN and all comparisons
> involving NaN return false.

Unfotunately, that version makes the comparison fail when one of the
argument is infinite; in that case we get for the proposed code
inf / inf < eps  --> false thanks to NaN
inf <= inf       --> true

Also, the proposed implementation first checks for strict equality: when the
arguments are equal, the division is not performed.

[I wanted to replace the proposed implementation with a call to the existing
"absolute" comparison method, but because of that problem, it doesn't seem

> >
> > --- public static boolean equalsWithRelativeTolerance(final double x,
> > final double y) -> uses the DOUBLE_COMPARISON_EPSILON public static
> > boolean equalsWithRelativeTolerance(final double x, final double y,
> > final double eps) ---
> >
> > These kind of methods are used in some of our tools (space dynamic
> > libraries) to assert equality between values, when we don't know the
> > order of magnitude.
> >
> > Do you think it's useful for Commons Math users ? Shall I open a
> > ticket on JIRA and contribute the corresponding code source ?
>
> Yes, along with test cases, including special cases (+/-0, +/-infinity,
> NaNs, +/-Double.MAX_VALUE, +/-Double.MIN_VALUE ...)

I think that we should focus on the second version (with an explicit
tolerance).
The tolerance is very much case-dependent, so that the default value is not
widely useful: Why 1e-14 rather than 1e-15 or 1e-13 or even 1e-7 ?

Best regards,
Gilles

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