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https://issues.apache.org/jira/browse/MATH-1138?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=14137174#comment-14137174
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Hank Grabowski commented on MATH-1138:
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Actually, the source they used for that derivation was not that link, but this
one (also in their references section):
http://www.geovista.psu.edu/sites/geocomp99/Gc99/082/gc_082.htm
You can see in Section 3.8 how they are sampling just the corner points (0,0),
(1,0), (0,1) and (1,1) in determining coefficients, just like their derivation.
The reference you cited is sampling a 4x4 grid, which makes more sense to me.
The methodology I was talking about existing in the Octave code is the same as
the methodology in his site as well. Specifically, to do a 2D interpolation you
call a series of 1D interpolations. The coefficient term version at the bottom
of the reference you cited is useful for when the region being sampled between
iterations often stays the same.
I am aware that Octave uses GPL, which is not compatible with the Apache
license, so I was not going to be using their code (it is written in Matlab
scripting language and FORTRAN too). I was simply looking at which math
algorithm they chose to use. I did not want to use the code off of the site
you listed as a baseline either because there is no mention of licensing rights
at all. It simply says, "Anything at this page may be copied and modified." but
it doesn't list what the requirements are for when you do that.
My implementation strategy was going to be as follows: I was therefore going to
be implementing the algorithm using existing Apache Math 1D interpolation
functions after I created my own validating implementation in Octave source
code and a test set of data in Octave as well. I would then create versions of
the test that does random samplings of the interpolation region in Octave to
figure out what the statistical distributions of errors are. I would then use
that for the tolerances of the same test implementation in Apache.
I believe the public API for this should be fine, but I will not change it
without consulting team members here. I would also like to implement lower
order BivariateGridInterpolators. This can be overkill for a lot of
applications. That would be done in a seperate story/issue though.
> 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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