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Message-ID: <406AF01A.3030109@steitz.com>
Date: Wed, 31 Mar 2004 09:21:46 -0700
From: Phil Steitz <phil@steitz.com>
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To: Jakarta Commons Developers List <commons-dev@jakarta.apache.org>
Subject: Re: [math] Some changes to Polynomial
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Al Chou wrote:
> --- Phil Steitz <phil@steitz.com> wrote:
> 
>>0. To help debug the SplineInterpolater (PR #28019 et al), I need to 
>>expose the coefficients in o.a.c.m.analysis.Polynomial as a read-only 
>>property (returning an array copy). Any objections to adding this?
> 
> 
> +1 if you do it by adding a package-level-accessible (i.e., no access modifier
> keyword; the JUnit test would be able to access it by being in the same
> package) getter method -- which sounds like what you're proposing.
> 
> 
I actually intended to make this public, but read-only and using copy 
semantics. Any client should have (read-only) access to this basic 
property of the Polynomial, IMHO.

Phil


> 
>>While reviewing the code, I also noticed that the current impl uses 
>>"naive" evaluation (using Math.pow, etc.).  I would like to change this to 
>>use Horner's Method.  Here is what I have ready to commit:
>>
>>1. Add protected static double evaluate(double[] coefficients, double 
>>argument) implementing Horner to get the function value; and change 
>>value(double) to just call this.
>>
>>2. Add protected static double[] differentiate(double[] coefficients) to 
>>return the coefficients of the derivative of the polynomial with 
>>coefficients equal to the actual parameter.  Then change 
>>firstDerivative(x) to just return
>>evaluate(differentiate(coefficients), x).  Similar for secondDerivative.
>>I could adapt Horner for the derivatives, but that seems messy to me and 
>>the slight memory cost to create the temp arrays seems worth it.
>>
>>3. I would also like to add
>>public PolynomialFunction derivative() {
>>   return new PolynomialFunction(differentiate(coefficients));
>>}
>>
>>Any objections to this?
> 
> 
> +1, these sound reasonable.
> 
> 
> 
>>Interestingly, while Horner's method should give better numerics, it 
>>actually fails to get within 1E-15 for one of the quintic test cases, 
>>performing worse than the "naive" impl. The error is in the 16th 
>>significant digit, which is not surprising.  I would like to change the 
>>tolerance to 1E-12 (current tests actually succeed at 1E-14).
>>
>>Phil
> 
> 
> I wonder why that is?  Does Math.pow() use higher-than-double precision and
> then cast down to double?  I think we should consider carefully what is implied
> by the fact that Horner's method has worse precision.  Also, I would in
> principle like to leave the tolerance as tight as possible, 1E-14 in this case.
> 
> 
> 
> Al
> 
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