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 */
017package org.apache.commons.math4.analysis.interpolation;
018
019import org.apache.commons.math4.exception.DimensionMismatchException;
020import org.apache.commons.math4.exception.NoDataException;
021import org.apache.commons.math4.exception.NonMonotonicSequenceException;
022import org.apache.commons.math4.exception.NumberIsTooSmallException;
023import org.apache.commons.math4.util.MathArrays;
024
025/**
026 * Generates a tricubic interpolating function.
027 *
028 * @since 3.4
029 */
030public class TricubicInterpolator
031    implements TrivariateGridInterpolator {
032    /**
033     * {@inheritDoc}
034     */
035    @Override
036    public TricubicInterpolatingFunction interpolate(final double[] xval,
037                                                     final double[] yval,
038                                                     final double[] zval,
039                                                     final double[][][] fval)
040        throws NoDataException, NumberIsTooSmallException,
041               DimensionMismatchException, 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        // Approximation to the partial derivatives using finite differences.
058        final double[][][] dFdX = new double[xLen][yLen][zLen];
059        final double[][][] dFdY = new double[xLen][yLen][zLen];
060        final double[][][] dFdZ = new double[xLen][yLen][zLen];
061        final double[][][] d2FdXdY = new double[xLen][yLen][zLen];
062        final double[][][] d2FdXdZ = new double[xLen][yLen][zLen];
063        final double[][][] d2FdYdZ = new double[xLen][yLen][zLen];
064        final double[][][] d3FdXdYdZ = new double[xLen][yLen][zLen];
065
066        for (int i = 1; i < xLen - 1; i++) {
067            if (yval.length != fval[i].length) {
068                throw new DimensionMismatchException(yval.length, fval[i].length);
069            }
070
071            final int nI = i + 1;
072            final int pI = i - 1;
073
074            final double nX = xval[nI];
075            final double pX = xval[pI];
076
077            final double deltaX = nX - pX;
078
079            for (int j = 1; j < yLen - 1; j++) {
080                if (zval.length != fval[i][j].length) {
081                    throw new DimensionMismatchException(zval.length, fval[i][j].length);
082                }
083
084                final int nJ = j + 1;
085                final int pJ = j - 1;
086
087                final double nY = yval[nJ];
088                final double pY = yval[pJ];
089
090                final double deltaY = nY - pY;
091                final double deltaXY = deltaX * deltaY;
092
093                for (int k = 1; k < zLen - 1; k++) {
094                    final int nK = k + 1;
095                    final int pK = k - 1;
096
097                    final double nZ = zval[nK];
098                    final double pZ = zval[pK];
099
100                    final double deltaZ = nZ - pZ;
101
102                    dFdX[i][j][k] = (fval[nI][j][k] - fval[pI][j][k]) / deltaX;
103                    dFdY[i][j][k] = (fval[i][nJ][k] - fval[i][pJ][k]) / deltaY;
104                    dFdZ[i][j][k] = (fval[i][j][nK] - fval[i][j][pK]) / deltaZ;
105
106                    final double deltaXZ = deltaX * deltaZ;
107                    final double deltaYZ = deltaY * deltaZ;
108
109                    d2FdXdY[i][j][k] = (fval[nI][nJ][k] - fval[nI][pJ][k] - fval[pI][nJ][k] + fval[pI][pJ][k]) / deltaXY;
110                    d2FdXdZ[i][j][k] = (fval[nI][j][nK] - fval[nI][j][pK] - fval[pI][j][nK] + fval[pI][j][pK]) / deltaXZ;
111                    d2FdYdZ[i][j][k] = (fval[i][nJ][nK] - fval[i][nJ][pK] - fval[i][pJ][nK] + fval[i][pJ][pK]) / deltaYZ;
112
113                    final double deltaXYZ = deltaXY * deltaZ;
114
115                    d3FdXdYdZ[i][j][k] = (fval[nI][nJ][nK] - fval[nI][pJ][nK] -
116                                          fval[pI][nJ][nK] + fval[pI][pJ][nK] -
117                                          fval[nI][nJ][pK] + fval[nI][pJ][pK] +
118                                          fval[pI][nJ][pK] - fval[pI][pJ][pK]) / deltaXYZ;
119                }
120            }
121        }
122
123        // Create the interpolating function.
124        return new TricubicInterpolatingFunction(xval, yval, zval, fval,
125                                                 dFdX, dFdY, dFdZ,
126                                                 d2FdXdY, d2FdXdZ, d2FdYdZ,
127                                                 d3FdXdYdZ) {
128            /** {@inheritDoc} */
129            @Override
130            public boolean isValidPoint(double x, double y, double z) {
131                if (x < xval[1] ||
132                    x > xval[xval.length - 2] ||
133                    y < yval[1] ||
134                    y > yval[yval.length - 2] ||
135                    z < zval[1] ||
136                    z > zval[zval.length - 2]) {
137                    return false;
138                } else {
139                    return true;
140                }
141            }
142        };
143    }
144}