    001    /*
    002     * Licensed to the Apache Software Foundation (ASF) under one or more
    003     * contributor license agreements.  See the NOTICE file distributed with
    004     * this work for additional information regarding copyright ownership.
    005     * The ASF licenses this file to You under the Apache License, Version 2.0
    006     * (the "License"); you may not use this file except in compliance with
    007     * the License.  You may obtain a copy of the License at
    008     *
    009     *      http://www.apache.org/licenses/LICENSE-2.0
    010     *
    011     * Unless required by applicable law or agreed to in writing, software
    012     * distributed under the License is distributed on an "AS IS" BASIS,
    013     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    014     * See the License for the specific language governing permissions and
    015     * limitations under the License.
    016     */
    017    package org.apache.commons.math.analysis.interpolation;
    018
    019    import org.apache.commons.math.DimensionMismatchException;
    020    import org.apache.commons.math.MathException;
    021    import org.apache.commons.math.analysis.UnivariateRealFunction;
    022    import org.apache.commons.math.analysis.polynomials.PolynomialSplineFunction;
    023    import org.apache.commons.math.exception.NoDataException;
    024    import org.apache.commons.math.util.MathUtils;
    025
    026    /**
    027     * Generates a bicubic interpolating function.
    028     *
    029     * @version $Revision: 980944 $ $Date: 2010-07-30 22:31:11 +0200 (ven. 30 juil. 2010) $
    030     * @since 2.2
    031     */
    032    public class BicubicSplineInterpolator
    033        implements BivariateRealGridInterpolator {
    034        /**
    035         * {@inheritDoc}
    036         */
    037        public BicubicSplineInterpolatingFunction interpolate(final double[] xval,
    038                                                              final double[] yval,
    039                                                              final double[][] fval)
    040            throws MathException, IllegalArgumentException {
    041            if (xval.length == 0 || yval.length == 0 || fval.length == 0) {
    042                throw new NoDataException();
    043            }
    044            if (xval.length != fval.length) {
    045                throw new DimensionMismatchException(xval.length, fval.length);
    046            }
    047
    048            MathUtils.checkOrder(xval);
    049            MathUtils.checkOrder(yval);
    050
    051            final int xLen = xval.length;
    052            final int yLen = yval.length;
    053
    054            // Samples (first index is y-coordinate, i.e. subarray variable is x)
    055            // 0 <= i < xval.length
    056            // 0 <= j < yval.length
    057            // fX[j][i] = f(xval[i], yval[j])
    058            final double[][] fX = new double[yLen][xLen];
    059            for (int i = 0; i < xLen; i++) {
    060                if (fval[i].length != yLen) {
    061                    throw new DimensionMismatchException(fval[i].length, yLen);
    062                }
    063
    064                for (int j = 0; j < yLen; j++) {
    065                    fX[j][i] = fval[i][j];
    066                }
    067            }
    068
    069            final SplineInterpolator spInterpolator = new SplineInterpolator();
    070
    071            // For each line y[j] (0 <= j < yLen), construct a 1D spline with
    072            // respect to variable x
    073            final PolynomialSplineFunction[] ySplineX = new PolynomialSplineFunction[yLen];
    074            for (int j = 0; j < yLen; j++) {
    075                ySplineX[j] = spInterpolator.interpolate(xval, fX[j]);
    076            }
    077
    078            // For each line x[i] (0 <= i < xLen), construct a 1D spline with
    079            // respect to variable y generated by array fY_1[i]
    080            final PolynomialSplineFunction[] xSplineY = new PolynomialSplineFunction[xLen];
    081            for (int i = 0; i < xLen; i++) {
    082                xSplineY[i] = spInterpolator.interpolate(yval, fval[i]);
    083            }
    084
    085            // Partial derivatives with respect to x at the grid knots
    086            final double[][] dFdX = new double[xLen][yLen];
    087            for (int j = 0; j < yLen; j++) {
    088                final UnivariateRealFunction f = ySplineX[j].derivative();
    089                for (int i = 0; i < xLen; i++) {
    090                    dFdX[i][j] = f.value(xval[i]);
    091                }
    092            }
    093
    094            // Partial derivatives with respect to y at the grid knots
    095            final double[][] dFdY = new double[xLen][yLen];
    096            for (int i = 0; i < xLen; i++) {
    097                final UnivariateRealFunction f = xSplineY[i].derivative();
    098                for (int j = 0; j < yLen; j++) {
    099                    dFdY[i][j] = f.value(yval[j]);
    100                }
    101            }
    102
    103            // Cross partial derivatives
    104            final double[][] d2FdXdY = new double[xLen][yLen];
    105            for (int i = 0; i < xLen ; i++) {
    106                final int nI = nextIndex(i, xLen);
    107                final int pI = previousIndex(i);
    108                for (int j = 0; j < yLen; j++) {
    109                    final int nJ = nextIndex(j, yLen);
    110                    final int pJ = previousIndex(j);
    111                    d2FdXdY[i][j] = (fval[nI][nJ] - fval[nI][pJ] -
    112                                     fval[pI][nJ] + fval[pI][pJ]) /
    113                        ((xval[nI] - xval[pI]) * (yval[nJ] - yval[pJ]));
    114                }
    115            }
    116
    117            // Create the interpolating splines
    118            return new BicubicSplineInterpolatingFunction(xval, yval, fval,
    119                                                          dFdX, dFdY, d2FdXdY);
    120        }
    121
    122        /**
    123         * Compute the next index of an array, clipping if necessary.
    124         * It is assumed (but not checked) that {@code i} is larger than or equal to 0}.
    125         *
    126         * @param i Index
    127         * @param max Upper limit of the array
    128         * @return the next index
    129         */
    130        private int nextIndex(int i, int max) {
    131            final int index = i + 1;
    132            return index < max ? index : index - 1;
    133        }
    134        /**
    135         * Compute the previous index of an array, clipping if necessary.
    136         * It is assumed (but not checked) that {@code i} is smaller than the size of the array.
    137         *
    138         * @param i Index
    139         * @return the previous index
    140         */
    141        private int previousIndex(int i) {
    142            final int index = i - 1;
    143            return index >= 0 ? index : 0;
    144        }
    145    }