Java tutorial
/* * 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 java.util.Arrays; import org.apache.commons.math3.analysis.BivariateFunction; import org.apache.commons.math3.analysis.polynomials.PolynomialSplineFunction; import org.apache.commons.math3.exception.DimensionMismatchException; import org.apache.commons.math3.exception.InsufficientDataException; import org.apache.commons.math3.exception.NoDataException; import org.apache.commons.math3.exception.NullArgumentException; import org.apache.commons.math3.exception.OutOfRangeException; import org.apache.commons.math3.exception.NonMonotonicSequenceException; import org.apache.commons.math3.util.MathArrays; /** * Function that implements the * <a href="http://www.paulinternet.nl/?page=bicubic">bicubic spline</a> * interpolation. * This implementation currently uses {@link AkimaSplineInterpolator} as the * underlying one-dimensional interpolator, which requires 5 sample points; * insufficient data will raise an exception when the * {@link #value(double,double) value} method is called. * * @since 3.4 */ public class PiecewiseBicubicSplineInterpolatingFunction implements BivariateFunction { /** The minimum number of points that are needed to compute the function. */ private static final int MIN_NUM_POINTS = 5; /** Samples x-coordinates */ private final double[] xval; /** Samples y-coordinates */ private final double[] yval; /** Set of cubic splines patching the whole data grid */ private final double[][] fval; /** * @param x Sample values of the x-coordinate, in increasing order. * @param y Sample values of the y-coordinate, in increasing order. * @param f Values of the function on every grid point. the expected number * of elements. * @throws NonMonotonicSequenceException if {@code x} or {@code y} are not * strictly increasing. * @throws NullArgumentException if any of the arguments are null * @throws NoDataException if any of the arrays has zero length. * @throws DimensionMismatchException if the length of x and y don't match the row, column * height of f */ public PiecewiseBicubicSplineInterpolatingFunction(double[] x, double[] y, double[][] f) throws DimensionMismatchException, NullArgumentException, NoDataException, NonMonotonicSequenceException { if (x == null || y == null || f == null || f[0] == null) { throw new NullArgumentException(); } final int xLen = x.length; final int yLen = y.length; if (xLen == 0 || yLen == 0 || f.length == 0 || f[0].length == 0) { throw new NoDataException(); } if (xLen < MIN_NUM_POINTS || yLen < MIN_NUM_POINTS || f.length < MIN_NUM_POINTS || f[0].length < MIN_NUM_POINTS) { throw new InsufficientDataException(); } if (xLen != f.length) { throw new DimensionMismatchException(xLen, f.length); } if (yLen != f[0].length) { throw new DimensionMismatchException(yLen, f[0].length); } MathArrays.checkOrder(x); MathArrays.checkOrder(y); xval = x.clone(); yval = y.clone(); fval = f.clone(); } /** * {@inheritDoc} */ public double value(double x, double y) throws OutOfRangeException { final AkimaSplineInterpolator interpolator = new AkimaSplineInterpolator(); final int offset = 2; final int count = offset + 3; final int i = searchIndex(x, xval, offset, count); final int j = searchIndex(y, yval, offset, count); final double xArray[] = new double[count]; final double yArray[] = new double[count]; final double zArray[] = new double[count]; final double interpArray[] = new double[count]; for (int index = 0; index < count; index++) { xArray[index] = xval[i + index]; yArray[index] = yval[j + index]; } for (int zIndex = 0; zIndex < count; zIndex++) { for (int index = 0; index < count; index++) { zArray[index] = fval[i + index][j + zIndex]; } final PolynomialSplineFunction spline = interpolator.interpolate(xArray, zArray); interpArray[zIndex] = spline.value(x); } final PolynomialSplineFunction spline = interpolator.interpolate(yArray, interpArray); double returnValue = spline.value(y); return returnValue; } /** * Indicates whether a point is within the interpolation range. * * @param x First coordinate. * @param y Second coordinate. * @return {@code true} if (x, y) is a valid point. * @since 3.3 */ public boolean isValidPoint(double x, double y) { if (x < xval[0] || x > xval[xval.length - 1] || y < yval[0] || y > yval[yval.length - 1]) { return false; } else { return true; } } /** * @param c Coordinate. * @param val Coordinate samples. * @param offset how far back from found value to offset for querying * @param count total number of elements forward from beginning that will be * queried * @return the index in {@code val} corresponding to the interval containing * {@code c}. * @throws OutOfRangeException if {@code c} is out of the range defined by * the boundary values of {@code val}. */ private int searchIndex(double c, double[] val, int offset, int count) { int r = Arrays.binarySearch(val, c); if (r == -1 || r == -val.length - 1) { throw new OutOfRangeException(c, val[0], val[val.length - 1]); } if (r < 0) { // "c" in within an interpolation sub-interval, which returns // negative // need to remove the negative sign for consistency r = -r - offset - 1; } else { r -= offset; } if (r < 0) { r = 0; } if ((r + count) >= val.length) { // "c" is the last sample of the range: Return the index // of the sample at the lower end of the last sub-interval. r = val.length - count; } return r; } }