    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.exception.DimensionMismatchException;
    020    import org.apache.commons.math.exception.NoDataException;
    021    import org.apache.commons.math.MathException;
    022    import org.apache.commons.math.util.MathUtils;
    023
    024    /**
    025     * Generates a tricubic interpolating function.
    026     *
    027     * @version $Revision$ $Date$
    028     * @since 2.2
    029     */
    030    public class TricubicSplineInterpolator
    031        implements TrivariateRealGridInterpolator {
    032        /**
    033         * {@inheritDoc}
    034         */
    035        public TricubicSplineInterpolatingFunction interpolate(final double[] xval,
    036                                                               final double[] yval,
    037                                                               final double[] zval,
    038                                                               final double[][][] fval)
    039            throws MathException {
    040            if (xval.length == 0 || yval.length == 0 || zval.length == 0 || fval.length == 0) {
    041                throw new NoDataException();
    042            }
    043            if (xval.length != fval.length) {
    044                throw new DimensionMismatchException(xval.length, fval.length);
    045            }
    046
    047            MathUtils.checkOrder(xval);
    048            MathUtils.checkOrder(yval);
    049            MathUtils.checkOrder(zval);
    050
    051            final int xLen = xval.length;
    052            final int yLen = yval.length;
    053            final int zLen = zval.length;
    054
    055            // Samples, re-ordered as (z, x, y) and (y, z, x) tuplets
    056            // fvalXY[k][i][j] = f(xval[i], yval[j], zval[k])
    057            // fvalZX[j][k][i] = f(xval[i], yval[j], zval[k])
    058            final double[][][] fvalXY = new double[zLen][xLen][yLen];
    059            final double[][][] fvalZX = new double[yLen][zLen][xLen];
    060            for (int i = 0; i < xLen; i++) {
    061                if (fval[i].length != yLen) {
    062                    throw new DimensionMismatchException(fval[i].length, yLen);
    063                }
    064
    065                for (int j = 0; j < yLen; j++) {
    066                    if (fval[i][j].length != zLen) {
    067                        throw new DimensionMismatchException(fval[i][j].length, zLen);
    068                    }
    069
    070                    for (int k = 0; k < zLen; k++) {
    071                        final double v = fval[i][j][k];
    072                        fvalXY[k][i][j] = v;
    073                        fvalZX[j][k][i] = v;
    074                    }
    075                }
    076            }
    077
    078            final BicubicSplineInterpolator bsi = new BicubicSplineInterpolator();
    079
    080            // For each line x[i] (0 <= i < xLen), construct a 2D spline in y and z
    081            final BicubicSplineInterpolatingFunction[] xSplineYZ
    082                = new BicubicSplineInterpolatingFunction[xLen];
    083            for (int i = 0; i < xLen; i++) {
    084                xSplineYZ[i] = bsi.interpolate(yval, zval, fval[i]);
    085            }
    086
    087            // For each line y[j] (0 <= j < yLen), construct a 2D spline in z and x
    088            final BicubicSplineInterpolatingFunction[] ySplineZX
    089                = new BicubicSplineInterpolatingFunction[yLen];
    090            for (int j = 0; j < yLen; j++) {
    091                ySplineZX[j] = bsi.interpolate(zval, xval, fvalZX[j]);
    092            }
    093
    094            // For each line z[k] (0 <= k < zLen), construct a 2D spline in x and y
    095            final BicubicSplineInterpolatingFunction[] zSplineXY
    096                = new BicubicSplineInterpolatingFunction[zLen];
    097            for (int k = 0; k < zLen; k++) {
    098                zSplineXY[k] = bsi.interpolate(xval, yval, fvalXY[k]);
    099            }
    100
    101            // Partial derivatives wrt x and wrt y
    102            final double[][][] dFdX = new double[xLen][yLen][zLen];
    103            final double[][][] dFdY = new double[xLen][yLen][zLen];
    104            final double[][][] d2FdXdY = new double[xLen][yLen][zLen];
    105            for (int k = 0; k < zLen; k++) {
    106                final BicubicSplineInterpolatingFunction f = zSplineXY[k];
    107                for (int i = 0; i < xLen; i++) {
    108                    final double x = xval[i];
    109                    for (int j = 0; j < yLen; j++) {
    110                        final double y = yval[j];
    111                        dFdX[i][j][k] = f.partialDerivativeX(x, y);
    112                        dFdY[i][j][k] = f.partialDerivativeY(x, y);
    113                        d2FdXdY[i][j][k] = f.partialDerivativeXY(x, y);
    114                    }
    115                }
    116            }
    117
    118            // Partial derivatives wrt y and wrt z
    119            final double[][][] dFdZ = new double[xLen][yLen][zLen];
    120            final double[][][] d2FdYdZ = new double[xLen][yLen][zLen];
    121            for (int i = 0; i < xLen; i++) {
    122                final BicubicSplineInterpolatingFunction f = xSplineYZ[i];
    123                for (int j = 0; j < yLen; j++) {
    124                    final double y = yval[j];
    125                    for (int k = 0; k < zLen; k++) {
    126                        final double z = zval[k];
    127                        dFdZ[i][j][k] = f.partialDerivativeY(y, z);
    128                        d2FdYdZ[i][j][k] = f.partialDerivativeXY(y, z);
    129                    }
    130                }
    131            }
    132
    133            // Partial derivatives wrt x and wrt z
    134            final double[][][] d2FdZdX = new double[xLen][yLen][zLen];
    135            for (int j = 0; j < yLen; j++) {
    136                final BicubicSplineInterpolatingFunction f = ySplineZX[j];
    137                for (int k = 0; k < zLen; k++) {
    138                    final double z = zval[k];
    139                    for (int i = 0; i < xLen; i++) {
    140                        final double x = xval[i];
    141                        d2FdZdX[i][j][k] = f.partialDerivativeXY(z, x);
    142                    }
    143                }
    144            }
    145
    146            // Third partial cross-derivatives
    147            final double[][][] d3FdXdYdZ = new double[xLen][yLen][zLen];
    148            for (int i = 0; i < xLen ; i++) {
    149                final int nI = nextIndex(i, xLen);
    150                final int pI = previousIndex(i);
    151                for (int j = 0; j < yLen; j++) {
    152                    final int nJ = nextIndex(j, yLen);
    153                    final int pJ = previousIndex(j);
    154                    for (int k = 0; k < zLen; k++) {
    155                        final int nK = nextIndex(k, zLen);
    156                        final int pK = previousIndex(k);
    157
    158                        // XXX Not sure about this formula
    159                        d3FdXdYdZ[i][j][k] = (fval[nI][nJ][nK] - fval[nI][pJ][nK] -
    160                                              fval[pI][nJ][nK] + fval[pI][pJ][nK] -
    161                                              fval[nI][nJ][pK] + fval[nI][pJ][pK] +
    162                                              fval[pI][nJ][pK] - fval[pI][pJ][pK]) /
    163                            ((xval[nI] - xval[pI]) * (yval[nJ] - yval[pJ]) * (zval[nK] - zval[pK])) ;
    164                    }
    165                }
    166            }
    167
    168            // Create the interpolating splines
    169            return new TricubicSplineInterpolatingFunction(xval, yval, zval, fval,
    170                                                           dFdX, dFdY, dFdZ,
    171                                                           d2FdXdY, d2FdZdX, d2FdYdZ,
    172                                                           d3FdXdYdZ);
    173        }
    174
    175        /**
    176         * Compute the next index of an array, clipping if necessary.
    177         * It is assumed (but not checked) that {@code i} is larger than or equal to 0}.
    178         *
    179         * @param i Index
    180         * @param max Upper limit of the array
    181         * @return the next index
    182         */
    183        private int nextIndex(int i, int max) {
    184            final int index = i + 1;
    185            return index < max ? index : index - 1;
    186        }
    187        /**
    188         * Compute the previous index of an array, clipping if necessary.
    189         * It is assumed (but not checked) that {@code i} is smaller than the size of the array.
    190         *
    191         * @param i Index
    192         * @return the previous index
    193         */
    194        private int previousIndex(int i) {
    195            final int index = i - 1;
    196            return index >= 0 ? index : 0;
    197        }
    198    }