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https://issues.apache.org/jira/browse/MATH-1138?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=14160303#comment-14160303
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Hank Grabowski commented on MATH-1138:
--------------------------------------
Reviewing Octave and Math.NET I have identified the source of the discrepancy.
It appears that Octave uses B-splines for their spline interpolation. The
implementation in Apache Math is the Natural Spline. When I use the Math.NET
natural spline interpolator I get the same results as I get with the Apache
Math method. However if I use the Akima Cubic Spline algorithm from Math.NET I
get valid numbers. The only disadvantage of the Akima Spline that I see that
we don't have with the standard cubic spline is that it needs a minimum of five
elements, not four.
Because the current spline works I was going to code up an Akima spline based
on the Math.NET implementation (referencing that source (they are a compatible
MIT license), plus a book source. I will then use that as the basis for the
splines in the BicubicSpline Interpolation.
> BicubicSplineInterpolator is returning incorrect interpolated values
> --------------------------------------------------------------------
>
> Key: MATH-1138
> URL: https://issues.apache.org/jira/browse/MATH-1138
> Project: Commons Math
> Issue Type: Bug
> Affects Versions: 3.3
> Reporter: Adam Bedrossian
> Attachments: Interpolated Values from CM and MatLab.docx
>
>
> I have encountered a use case with the BicubicSplineInterpolator where the
> interpolated values that are being returned seem incorrect. Furthermore, the
> values do not match those generated by MatLab using the interp2 'cubic'
> method.
> Here is a snippet of code that uses the interpolator:
> double[] xValues = new double[] {36, 36.001, 36.002};
> double[] yValues = new double[] {-108.00, -107.999, -107.998};
> double[][] fValues = new double[][] {{1915, 1906, 1931},
> {1877, 1889, 1894},
> {1878, 1873, 1888}};
> BicubicSplineInterpolator interpolator = new
> BicubicSplineInterpolator();
> BicubicSplineInterpolatingFunction interpolatorFunction =
> interpolator.interpolate(xValues, yValues, fValues);
> double[][] results = new double[9][9];
> double x = 36;
> int arrayIndexX = 0, arrayIndexY = 0;
> while(x <= 36.002) {
> double y = -108;
> arrayIndexY = 0;
> while (y <= -107.998) {
> results[arrayIndexX][arrayIndexY] =
> interpolatorFunction.value(x, y);
> System.out.println(results[arrayIndexX][arrayIndexY]);
> y = y + 0.00025;
> arrayIndexY++;
> }
> x = x + 0.00025;
> arrayIndexX++;
> }
> Attached is a grid showing x and y values and the corresponding interpolated
> value from both commons math and MatLab.
> The values produced by commons math are far off from those created by MatLab.
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