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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}.
 * 

* 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. *

* * @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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