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.math3.analysis.interpolation;
018    
019    import org.apache.commons.math3.exception.DimensionMismatchException;
020    import org.apache.commons.math3.exception.NoDataException;
021    import org.apache.commons.math3.exception.NonMonotonicSequenceException;
022    import org.apache.commons.math3.util.MathArrays;
023    
024    /**
025     * Generates a tricubic interpolating function.
026     *
027     * @since 2.2
028     * @version $Id: TricubicSplineInterpolator.java 1379904 2012-09-01 23:54:52Z erans $
029     */
030    public class TricubicSplineInterpolator
031        implements TrivariateGridInterpolator {
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 NoDataException,
040                   DimensionMismatchException,
041                   NonMonotonicSequenceException {
042            if (xval.length == 0 || yval.length == 0 || zval.length == 0 || fval.length == 0) {
043                throw new NoDataException();
044            }
045            if (xval.length != fval.length) {
046                throw new DimensionMismatchException(xval.length, fval.length);
047            }
048    
049            MathArrays.checkOrder(xval);
050            MathArrays.checkOrder(yval);
051            MathArrays.checkOrder(zval);
052    
053            final int xLen = xval.length;
054            final int yLen = yval.length;
055            final int zLen = zval.length;
056    
057            // Samples, re-ordered as (z, x, y) and (y, z, x) tuplets
058            // fvalXY[k][i][j] = f(xval[i], yval[j], zval[k])
059            // fvalZX[j][k][i] = f(xval[i], yval[j], zval[k])
060            final double[][][] fvalXY = new double[zLen][xLen][yLen];
061            final double[][][] fvalZX = new double[yLen][zLen][xLen];
062            for (int i = 0; i < xLen; i++) {
063                if (fval[i].length != yLen) {
064                    throw new DimensionMismatchException(fval[i].length, yLen);
065                }
066    
067                for (int j = 0; j < yLen; j++) {
068                    if (fval[i][j].length != zLen) {
069                        throw new DimensionMismatchException(fval[i][j].length, zLen);
070                    }
071    
072                    for (int k = 0; k < zLen; k++) {
073                        final double v = fval[i][j][k];
074                        fvalXY[k][i][j] = v;
075                        fvalZX[j][k][i] = v;
076                    }
077                }
078            }
079    
080            final BicubicSplineInterpolator bsi = new BicubicSplineInterpolator();
081    
082            // For each line x[i] (0 <= i < xLen), construct a 2D spline in y and z
083            final BicubicSplineInterpolatingFunction[] xSplineYZ
084                = new BicubicSplineInterpolatingFunction[xLen];
085            for (int i = 0; i < xLen; i++) {
086                xSplineYZ[i] = bsi.interpolate(yval, zval, fval[i]);
087            }
088    
089            // For each line y[j] (0 <= j < yLen), construct a 2D spline in z and x
090            final BicubicSplineInterpolatingFunction[] ySplineZX
091                = new BicubicSplineInterpolatingFunction[yLen];
092            for (int j = 0; j < yLen; j++) {
093                ySplineZX[j] = bsi.interpolate(zval, xval, fvalZX[j]);
094            }
095    
096            // For each line z[k] (0 <= k < zLen), construct a 2D spline in x and y
097            final BicubicSplineInterpolatingFunction[] zSplineXY
098                = new BicubicSplineInterpolatingFunction[zLen];
099            for (int k = 0; k < zLen; k++) {
100                zSplineXY[k] = bsi.interpolate(xval, yval, fvalXY[k]);
101            }
102    
103            // Partial derivatives wrt x and wrt y
104            final double[][][] dFdX = new double[xLen][yLen][zLen];
105            final double[][][] dFdY = new double[xLen][yLen][zLen];
106            final double[][][] d2FdXdY = new double[xLen][yLen][zLen];
107            for (int k = 0; k < zLen; k++) {
108                final BicubicSplineInterpolatingFunction f = zSplineXY[k];
109                for (int i = 0; i < xLen; i++) {
110                    final double x = xval[i];
111                    for (int j = 0; j < yLen; j++) {
112                        final double y = yval[j];
113                        dFdX[i][j][k] = f.partialDerivativeX(x, y);
114                        dFdY[i][j][k] = f.partialDerivativeY(x, y);
115                        d2FdXdY[i][j][k] = f.partialDerivativeXY(x, y);
116                    }
117                }
118            }
119    
120            // Partial derivatives wrt y and wrt z
121            final double[][][] dFdZ = new double[xLen][yLen][zLen];
122            final double[][][] d2FdYdZ = new double[xLen][yLen][zLen];
123            for (int i = 0; i < xLen; i++) {
124                final BicubicSplineInterpolatingFunction f = xSplineYZ[i];
125                for (int j = 0; j < yLen; j++) {
126                    final double y = yval[j];
127                    for (int k = 0; k < zLen; k++) {
128                        final double z = zval[k];
129                        dFdZ[i][j][k] = f.partialDerivativeY(y, z);
130                        d2FdYdZ[i][j][k] = f.partialDerivativeXY(y, z);
131                    }
132                }
133            }
134    
135            // Partial derivatives wrt x and wrt z
136            final double[][][] d2FdZdX = new double[xLen][yLen][zLen];
137            for (int j = 0; j < yLen; j++) {
138                final BicubicSplineInterpolatingFunction f = ySplineZX[j];
139                for (int k = 0; k < zLen; k++) {
140                    final double z = zval[k];
141                    for (int i = 0; i < xLen; i++) {
142                        final double x = xval[i];
143                        d2FdZdX[i][j][k] = f.partialDerivativeXY(z, x);
144                    }
145                }
146            }
147    
148            // Third partial cross-derivatives
149            final double[][][] d3FdXdYdZ = new double[xLen][yLen][zLen];
150            for (int i = 0; i < xLen ; i++) {
151                final int nI = nextIndex(i, xLen);
152                final int pI = previousIndex(i);
153                for (int j = 0; j < yLen; j++) {
154                    final int nJ = nextIndex(j, yLen);
155                    final int pJ = previousIndex(j);
156                    for (int k = 0; k < zLen; k++) {
157                        final int nK = nextIndex(k, zLen);
158                        final int pK = previousIndex(k);
159    
160                        // XXX Not sure about this formula
161                        d3FdXdYdZ[i][j][k] = (fval[nI][nJ][nK] - fval[nI][pJ][nK] -
162                                              fval[pI][nJ][nK] + fval[pI][pJ][nK] -
163                                              fval[nI][nJ][pK] + fval[nI][pJ][pK] +
164                                              fval[pI][nJ][pK] - fval[pI][pJ][pK]) /
165                            ((xval[nI] - xval[pI]) * (yval[nJ] - yval[pJ]) * (zval[nK] - zval[pK])) ;
166                    }
167                }
168            }
169    
170            // Create the interpolating splines
171            return new TricubicSplineInterpolatingFunction(xval, yval, zval, fval,
172                                                           dFdX, dFdY, dFdZ,
173                                                           d2FdXdY, d2FdZdX, d2FdYdZ,
174                                                           d3FdXdYdZ);
175        }
176    
177        /**
178         * Compute the next index of an array, clipping if necessary.
179         * It is assumed (but not checked) that {@code i} is larger than or equal to 0}.
180         *
181         * @param i Index
182         * @param max Upper limit of the array
183         * @return the next index
184         */
185        private int nextIndex(int i, int max) {
186            final int index = i + 1;
187            return index < max ? index : index - 1;
188        }
189        /**
190         * Compute the previous index of an array, clipping if necessary.
191         * It is assumed (but not checked) that {@code i} is smaller than the size of the array.
192         *
193         * @param i Index
194         * @return the previous index
195         */
196        private int previousIndex(int i) {
197            final int index = i - 1;
198            return index >= 0 ? index : 0;
199        }
200    }