You are viewing a plain text version of this content. The canonical link for it is here.
Posted to issues@commons.apache.org by "Luc Maisonobe (JIRA)" <ji...@apache.org> on 2009/12/27 20:37:29 UTC
[jira] Commented: (MATH-325) Improvement of Romberg extrapolation
[ https://issues.apache.org/jira/browse/MATH-325?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=12794719#action_12794719 ]
Luc Maisonobe commented on MATH-325:
------------------------------------
I think this issue has already been solved since 2009-10-13. Could you check the current implementation from subversion repository ?
The fix was introduced in r824822 with the following comment:
{quote}
improved array structure in Romberg integrator
since the integrator uses only two rows at a time, we allocate only two arrays and reuse them
{quote}
> Improvement of Romberg extrapolation
> ------------------------------------
>
> Key: MATH-325
> URL: https://issues.apache.org/jira/browse/MATH-325
> Project: Commons Math
> Issue Type: Improvement
> Affects Versions: 2.0
> Reporter: Andreas mueller
> Fix For: 2.1
>
> Original Estimate: 2h
> Remaining Estimate: 2h
>
> One can use a one-dimensional array (instead of Romberg's tableau) for extrapolating subsequent values.
> Please have a look at following code fragments (which I've taken form the class RombergExtrapolator of
> my MathLibrary). Feel free to use this code.
> /**
> * Default number of maximal extrapolation steps.
> */
> public static int DEF_MAXIMAL_EXTRAPOLATION_COUNT = 8;
> /**
> * The approximation order. <br>
> * Assume that f(h) is approximated by a function a(h), so that f(h) = a(h) +
> * O(h<sup>p</sup>). We say that p is the approximation order.
> */
> private int approximationOrder;
> private int extrapolationCount = 0;
> private double prevResult;
>
> /**
> * The estimate and tolerance may be used to deside wether to finalize the
> * iteration process (|estimate| < tolerance).
> */
>
> /** Holds the current estimated error. */
> private double estimate;
> /** Holds the current reached tolerance. */
> private double tolerance;
>
> private double result[] = new double[DEF_MAXIMAL_EXTRAPOLATION_COUNT + 1];;
> /**
> * Set the maximal number of subsequent extrapolation steps.
> *
> * @param maximalExtrapolationCount
> * maximal extrapolation steps
> */
> public void setMaximalExtrapolationCount(int maximalExtrapolationCount)
> {
> result = new double[maximalExtrapolationCount + 1];
> }
> /**
> * Extrapolate a sequence of values by means of Romberg's algorithm.
> * Therefore a polynomial of degree maximalExtraploationCount
> * is used. Calculates the current estimate and tolerance using the
> * approximation order.
> *
> * @param value
> * value to extrapolate
> * @return extrapolated value
> */
> public double extrapolate(double value)
> {
> if (extrapolationCount == 0) {
> // first estimate
> estimate = value;
> tolerance = -1.0;
> prevResult = 0;
> }
>
> int i, m, m1 = idx(extrapolationCount);
> long k = (1 << approximationOrder);
> int imin = Math.max(0, extrapolationCount - (result.length - 1));
> result[m1] = value;
> for (i = extrapolationCount - 1; i >= imin; i--) {
> m = idx(i);
> m1 = idx(i + 1);
> result[m] = (k * result[m1] - result[m]) / (k - 1);
> k <<= approximationOrder;
> }
> m1 = idx(i + 1);
> estimate = result[m1] - prevResult;
> tolerance = Math.abs(result[m1]) * relativeAccuracy + absoluteAccuracy;
> prevResult = result[m1];
> extrapolationCount++;
> return result[m1];
> }
> /**
> * Ring buffer index
> */
> private int idx(int i)
> {
> return (i % result.length);
> }
--
This message is automatically generated by JIRA.
-
You can reply to this email to add a comment to the issue online.