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/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.math3.analysis.interpolation;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.NoDataException;
import org.apache.commons.math3.exception.NonMonotonicSequenceException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.util.MathArrays;
/**
* Generates a {@link BicubicInterpolatingFunction bicubic interpolating
* function}.
* <p>
* Caveat: Because the interpolation scheme requires that derivatives be
* specified at the sample points, those are approximated with finite
* differences (using the 2-points symmetric formulae).
* Since their values are undefined at the borders of the provided
* interpolation ranges, the interpolated values will be wrong at the
* edges of the patch.
* The {@code interpolate} method will return a function that overrides
* {@link BicubicInterpolatingFunction#isValidPoint(double,double)} to
* indicate points where the interpolation will be inaccurate.
* </p>
*
* @since 3.4
*/
public class BicubicInterpolator
implements BivariateGridInterpolator {
/**
* {@inheritDoc}
*/
public BicubicInterpolatingFunction interpolate(final double[] xval,
final double[] yval,
final double[][] fval)
throws NoDataException, DimensionMismatchException,
NonMonotonicSequenceException, NumberIsTooSmallException {
if (xval.length == 0 || yval.length == 0 || fval.length == 0) {
throw new NoDataException();
}
if (xval.length != fval.length) {
throw new DimensionMismatchException(xval.length, fval.length);
}
MathArrays.checkOrder(xval);
MathArrays.checkOrder(yval);
final int xLen = xval.length;
final int yLen = yval.length;
// Approximation to the partial derivatives using finite differences.
final double[][] dFdX = new double[xLen][yLen];
final double[][] dFdY = new double[xLen][yLen];
final double[][] d2FdXdY = new double[xLen][yLen];
for (int i = 1; i < xLen - 1; i++) {
final int nI = i + 1;
final int pI = i - 1;
final double nX = xval[nI];
final double pX = xval[pI];
final double deltaX = nX - pX;
for (int j = 1; j < yLen - 1; j++) {
final int nJ = j + 1;
final int pJ = j - 1;
final double nY = yval[nJ];
final double pY = yval[pJ];
final double deltaY = nY - pY;
dFdX[i][j] = (fval[nI][j] - fval[pI][j]) / deltaX;
dFdY[i][j] = (fval[i][nJ] - fval[i][pJ]) / deltaY;
final double deltaXY = deltaX * deltaY;
d2FdXdY[i][j] = (fval[nI][nJ] - fval[nI][pJ] - fval[pI][nJ] + fval[pI][pJ]) / deltaXY;
}
}
// Create the interpolating function.
return new BicubicInterpolatingFunction(xval, yval, fval,
dFdX, dFdY, d2FdXdY) {
/** {@inheritDoc} */
@Override
public boolean isValidPoint(double x, double y) {
if (x < xval[1] ||
x > xval[xval.length - 2] ||
y < yval[1] ||
y > yval[yval.length - 2]) {
return false;
} else {
return true;
}
}
};
}
}
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