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Posted to issues@commons.apache.org by "Andreas mueller (JIRA)" <ji...@apache.org> on 2009/12/25 13:08:29 UTC
[jira] Updated: (MATH-325) Improvement of Romberg extrapolation
[ https://issues.apache.org/jira/browse/MATH-325?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel ]
Andreas mueller updated MATH-325:
---------------------------------
Description:
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.
<pre>
/**
* 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);
}
</pre>
was:
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);
}
> 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
>
>
> 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.
> <pre>
> /**
> * 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);
> }
> </pre>
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