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From "Alex (JIRA)" <j...@apache.org>
Subject [jira] [Comment Edited] (MATH-832) Brent solver calculates incorrect root (namley Double.MAX_VALUE)
Date Thu, 26 Jul 2012 09:28:34 GMT

    [ https://issues.apache.org/jira/browse/MATH-832?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13422980#comment-13422980
] 

Alex edited comment on MATH-832 at 7/26/12 9:27 AM:
----------------------------------------------------

I tried testMath832() and there was no error (although i'm not sure if i did it right - i
never worked with JUnit before). But now i think i know where the problem is: It isn't the
difference between optimizing and solving (minimizing a function (that derivative has only
one root) => finding the root of the derivative) but a numerical issue:
[http://www.wolframalpha.com/input/?i=Plot(100*sqrt%28x%29%2B1000000%2Fx%2B10000%2Fsqrt%28x%29%2C+{x%2C+0%2C+1000})]

[http://www.wolframalpha.com/input/?i=Plot(d%2Fdx+100*sqrt%28x%29%2B1000000%2Fx%2B10000%2Fsqrt%28x%29%2C+{x%2C+0%2C+1000})]

[http://www.wolframalpha.com/input/?i=Plot(d%2Fdx+100*sqrt%28x%29%2B1000000%2Fx%2B10000%2Fsqrt%28x%29%2C+{x%2C+10^10%2C+10^100})]

An upper bound for the interval sufficiently smaller than infinity causes no problems:{code:borderStyle=solid}
System.out.println(
            (new BrentSolver()).solve(Integer.MAX_VALUE, uf, 1/Double.MAX_VALUE, *1.0e10*,
startValue2)
        );{code}
                
      was (Author: alex87):
    I tried testMath832() and there was no error (although i'm not sure if i did it right
- i never worked with JUnit before). But now i think i know where the problem is: It isn't
the difference between optimizing and solving (minimizing a function (that derivative has
only one root) => finding the root of the derivative) but a numerical issue:
[http://www.wolframalpha.com/input/?i=Plot(100*sqrt%28x%29%2B1000000%2Fx%2B10000%2Fsqrt%28x%29%2C+{x%2C+0%2C+1000})]
[http://www.wolframalpha.com/input/?i=Plot(d%2Fdx+100*sqrt%28x%29%2B1000000%2Fx%2B10000%2Fsqrt%28x%29%2C+{x%2C+0%2C+1000})]
[http://www.wolframalpha.com/input/?i=Plot(d%2Fdx+100*sqrt%28x%29%2B1000000%2Fx%2B10000%2Fsqrt%28x%29%2C+{x%2C+10^10%2C+10^100})]

An upper bound for the interval sufficiently smaller than infinity causes no problems:{code:borderStyle=solid}
System.out.println(
            (new BrentSolver()).solve(Integer.MAX_VALUE, uf, 1/Double.MAX_VALUE, *1.0e10*,
startValue2)
        );{code}
                  
> Brent solver calculates incorrect root (namley Double.MAX_VALUE)
> ----------------------------------------------------------------
>
>                 Key: MATH-832
>                 URL: https://issues.apache.org/jira/browse/MATH-832
>             Project: Commons Math
>          Issue Type: Bug
>    Affects Versions: 3.0
>         Environment: Netbeans 7.1.2
>            Reporter: Alex
>
> *Wolfram-Alpha-Solution:*
> [http://www.wolframalpha.com/input/?i=min+100*sqrt%28x%29%2B1000000%2Fx%2B10000%2Fsqrt%28x%29+with+x%3E0]
> {code:borderStyle=solid}min{100 sqrt(x)+1000000/x+10000/sqrt(x)|x>0}~~4431.94 at x~~804.936{code}
> *Java-Input:*{code:borderStyle=solid}
> int startValue1 = 100 + 1000000 + 10000;
> int startValue2 = 100;
> UnivariateFunction uf = new UnivariateFunction() {
>     @Override
>     public double value(double x) {
>         return 100/(2*Math.sqrt(x)) - 1000000/Math.pow(x,2) - 10000/(2*Math.pow(x,(double)
3/2));
>     }
> };
> System.out.println(
>     (new BrentSolver()).solve(Integer.MAX_VALUE, uf, 1/Double.MAX_VALUE, Double.MAX_VALUE,
startValue1)
> );
> System.out.println(
>     (new BrentSolver()).solve(Integer.MAX_VALUE, uf, 1/Double.MAX_VALUE, Double.MAX_VALUE,
startValue2)
> );{code}
> *Java-Output:*{code:borderStyle=solid}
> 804.9355821866686
> 1.7976931348623157E308 (= Double.MAX_VALUE){code} 

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