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From "Johnathan Kool (JIRA)" <j...@apache.org>
Subject [jira] [Commented] (MATH-985) BicubicSpline interpolation returns unexpected values (BicubicSplineInterpolator/BicubicSplineInterpolationFunction)
Date Wed, 22 Jan 2014 22:52:19 GMT

    [ https://issues.apache.org/jira/browse/MATH-985?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13879306#comment-13879306
] 

Johnathan Kool commented on MATH-985:
-------------------------------------

I believe so - it's been a while since I checked it.  I'd say go ahead and close it.  If anything
else crops up, I'll generate a new ticket.

Thanks!

Dr. Johnathan Kool 
Marine Ecologist  |  Coastal, Marine and Climate Change
Environmental Geoscience Division  |  GEOSCIENCE AUSTRALIA


> BicubicSpline interpolation returns unexpected values (BicubicSplineInterpolator/BicubicSplineInterpolationFunction)
> --------------------------------------------------------------------------------------------------------------------
>
>                 Key: MATH-985
>                 URL: https://issues.apache.org/jira/browse/MATH-985
>             Project: Commons Math
>          Issue Type: Bug
>    Affects Versions: 3.1.1
>         Environment: Windows 7 64 bit, 64 bit JVM
>            Reporter: Johnathan Kool
>         Attachments: math985.png
>
>
> I've been testing out the Tricubic spline functions, and have been getting some strange
values.  I dug down a bit, and it seems like they start at the Bicubic level.  SplineInterpolator/PolynomialSplineFunction
seem to be returning correct values.  I set up a block of data that increases linearly, so
you'd expect the interpolated values to follow the same trend, except the values tend to overshoot
to half the distance between knot points, and then undershoot for the remaining half.  Probably
the easiest thing would be to show some tests.  First - 1D which works fine:
> {code:title=SplineTest.java|borderStyle=solid}
> import org.apache.commons.math3.analysis.interpolation.SplineInterpolator;
> import org.apache.commons.math3.analysis.polynomials.PolynomialSplineFunction;
> public class SplineTest {
> 	double[] x = new double[]{.52,.54,.56,.58,.6};
> 	double[] y = new double[]{76,77,78,79,80};
> 	
> 	public static void main(String[] args){
> 		SplineTest st = new SplineTest();
> 		st.go();
> 	}
> 	
> 	public void go(){
> 		SplineInterpolator si = new SplineInterpolator();
> 		PolynomialSplineFunction sf = si.interpolate(x, y);
> 		
> 		System.out.println(sf.value(0.52));
> 		System.out.println(sf.value(0.5225));
> 		System.out.println(sf.value(0.525));
> 		System.out.println(sf.value(0.5275));
> 		System.out.println(sf.value(0.53));
> 		System.out.println(sf.value(0.5325));
> 		System.out.println(sf.value(0.535));
> 		System.out.println(sf.value(0.5375));
> 		System.out.println(sf.value(0.54));
> 		System.out.println(sf.value(0.5425));
> 		System.out.println(sf.value(0.545));
> 		System.out.println(sf.value(0.5475));
> 		System.out.println(sf.value(0.55));
> 		System.out.println(sf.value(0.5525));
> 		System.out.println(sf.value(0.555));
> 		System.out.println(sf.value(0.5575));
> 		System.out.println(sf.value(0.56));
> 	}
> }
> {code}
> and next, 2D which doesn't:
> {code:title=BicubicSplineTest.java|borderStyle=solid}
> import org.apache.commons.math3.analysis.interpolation.BicubicSplineInterpolatingFunction;
> import org.apache.commons.math3.analysis.interpolation.BicubicSplineInterpolator;
> public class BicubicSplineTest {
> 	double[] x = new double[]{0,1,2};
> 	double[] y = new double[]{.52,.54,.56,.58,.6};
> 	double[] v1 = new double[]{76,77,78,79,80};
> 	double[][] v2 = new double[][]{v1,v1,v1};
> 	
> 	public static void main(String[] args){
> 		BicubicSplineTest bt = new BicubicSplineTest();
> 		bt.go();
> 	}
> 	
> 	public void go(){
> 		BicubicSplineInterpolator bi = new BicubicSplineInterpolator();
> 		BicubicSplineInterpolatingFunction bf = bi.interpolate(x, y, v2);
> 		
> 		System.out.println(bf.value(1, 0.52));
> 		System.out.println(bf.value(1, 0.5225));
> 		System.out.println(bf.value(1, 0.525));
> 		System.out.println(bf.value(1, 0.5275));
> 		System.out.println(bf.value(1, 0.53));
> 		System.out.println(bf.value(1, 0.5325));
> 		System.out.println(bf.value(1, 0.535));
> 		System.out.println(bf.value(1, 0.5375));
> 		System.out.println(bf.value(1, 0.54));
> 		System.out.println(bf.value(1, 0.5425));
> 		System.out.println(bf.value(1, 0.545));
> 		System.out.println(bf.value(1, 0.5475));
> 		System.out.println(bf.value(1, 0.55));
> 		System.out.println(bf.value(1, 0.5525));
> 		System.out.println(bf.value(1, 0.555));
> 		System.out.println(bf.value(1, 0.5575));
> 		System.out.println(bf.value(1, 0.56));
> 	}
> }
> {code}
> The data points increase from 76 to 80 in a linear way.  Incrementing by 1/8 the distance
to the next point, the 1D spline returns:
> 76.0
> 76.125
> 76.25
> 76.375
> 76.5
> 76.625
> 76.75
> 76.875
> 77.0
> 77.125
> 77.25
> 77.375
> 77.5
> 77.625
> 77.75
> 77.875
> 78.0
> The 2D spline returns:
> 76.0
> 80.14453124999996
> 80.84375000000003
> 79.24609375000007
> 76.50000000000003
> 73.75390625000007
> 72.15625000000001
> 72.85546874999996
> 76.99999999999997
> 81.14453124999993
> 81.84374999999997
> 80.24609375000006
> 77.50000000000003
> 74.75390625000009
> 73.15625000000004
> 73.85546874999997
> 78.0
> Even though it's still effectively a 1D problem.  I'm not sure exactly what's causing
it - maybe something when multiplying the coefficients, but thought I should flag it.



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