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.MathRuntimeException;
021    import org.apache.commons.math.MathException;
022    import org.apache.commons.math.util.MathUtils;
023    import org.apache.commons.math.util.MathUtils.OrderDirection;
024    import org.apache.commons.math.analysis.BivariateRealFunction;
025    import org.apache.commons.math.analysis.UnivariateRealFunction;
026    import org.apache.commons.math.analysis.polynomials.PolynomialSplineFunction;
027    import org.apache.commons.math.exception.util.LocalizedFormats;
028    
029    /**
030     * Generates a bicubic interpolation function.
031     * Before interpolating, smoothing of the input data is performed using
032     * splines.
033     * See <b>Handbook on splines for the user</b>, ISBN 084939404X,
034     * chapter 2.
035     *
036     * @version $Revision: 1059400 $ $Date: 2011-01-15 20:35:27 +0100 (sam. 15 janv. 2011) $
037     * @since 2.1
038     * @deprecated This class does not perform smoothing; the name is thus misleading.
039     * Please use {@link org.apache.commons.math.analysis.interpolation.BicubicSplineInterpolator}
040     * instead. If smoothing is desired, a tentative implementation is provided in class
041     * {@link org.apache.commons.math.analysis.interpolation.SmoothingPolynomialBicubicSplineInterpolator}.
042     * This class will be removed in math 3.0.
043     */
044    @Deprecated
045    public class SmoothingBicubicSplineInterpolator
046        implements BivariateRealGridInterpolator {
047        /**
048         * {@inheritDoc}
049         */
050        public BivariateRealFunction interpolate(final double[] xval,
051                                                              final double[] yval,
052                                                              final double[][] zval)
053            throws MathException, IllegalArgumentException {
054            if (xval.length == 0 || yval.length == 0 || zval.length == 0) {
055                throw MathRuntimeException.createIllegalArgumentException(LocalizedFormats.NO_DATA);
056            }
057            if (xval.length != zval.length) {
058                throw new DimensionMismatchException(xval.length, zval.length);
059            }
060    
061            MathUtils.checkOrder(xval, OrderDirection.INCREASING, true);
062            MathUtils.checkOrder(yval, OrderDirection.INCREASING, true);
063    
064            final int xLen = xval.length;
065            final int yLen = yval.length;
066    
067            // Samples (first index is y-coordinate, i.e. subarray variable is x)
068            // 0 <= i < xval.length
069            // 0 <= j < yval.length
070            // zX[j][i] = f(xval[i], yval[j])
071            final double[][] zX = new double[yLen][xLen];
072            for (int i = 0; i < xLen; i++) {
073                if (zval[i].length != yLen) {
074                    throw new DimensionMismatchException(zval[i].length, yLen);
075                }
076    
077                for (int j = 0; j < yLen; j++) {
078                    zX[j][i] = zval[i][j];
079                }
080            }
081    
082            final SplineInterpolator spInterpolator = new SplineInterpolator();
083    
084            // For each line y[j] (0 <= j < yLen), construct a 1D spline with
085            // respect to variable x
086            final PolynomialSplineFunction[] ySplineX = new PolynomialSplineFunction[yLen];
087            for (int j = 0; j < yLen; j++) {
088                ySplineX[j] = spInterpolator.interpolate(xval, zX[j]);
089            }
090    
091            // For every knot (xval[i], yval[j]) of the grid, calculate corrected
092            // values zY_1
093            final double[][] zY_1 = new double[xLen][yLen];
094            for (int j = 0; j < yLen; j++) {
095                final PolynomialSplineFunction f = ySplineX[j];
096                for (int i = 0; i < xLen; i++) {
097                    zY_1[i][j] = f.value(xval[i]);
098                }
099            }
100    
101            // For each line x[i] (0 <= i < xLen), construct a 1D spline with
102            // respect to variable y generated by array zY_1[i]
103            final PolynomialSplineFunction[] xSplineY = new PolynomialSplineFunction[xLen];
104            for (int i = 0; i < xLen; i++) {
105                xSplineY[i] = spInterpolator.interpolate(yval, zY_1[i]);
106            }
107    
108            // For every knot (xval[i], yval[j]) of the grid, calculate corrected
109            // values zY_2
110            final double[][] zY_2 = new double[xLen][yLen];
111            for (int i = 0; i < xLen; i++) {
112                final PolynomialSplineFunction f = xSplineY[i];
113                for (int j = 0; j < yLen; j++) {
114                    zY_2[i][j] = f.value(yval[j]);
115                }
116            }
117    
118            // Partial derivatives with respect to x at the grid knots
119            final double[][] dZdX = new double[xLen][yLen];
120            for (int j = 0; j < yLen; j++) {
121                final UnivariateRealFunction f = ySplineX[j].derivative();
122                for (int i = 0; i < xLen; i++) {
123                    dZdX[i][j] = f.value(xval[i]);
124                }
125            }
126    
127            // Partial derivatives with respect to y at the grid knots
128            final double[][] dZdY = new double[xLen][yLen];
129            for (int i = 0; i < xLen; i++) {
130                final UnivariateRealFunction f = xSplineY[i].derivative();
131                for (int j = 0; j < yLen; j++) {
132                    dZdY[i][j] = f.value(yval[j]);
133                }
134            }
135    
136            // Cross partial derivatives
137            final double[][] dZdXdY = new double[xLen][yLen];
138            for (int i = 0; i < xLen ; i++) {
139                final int nI = nextIndex(i, xLen);
140                final int pI = previousIndex(i);
141                for (int j = 0; j < yLen; j++) {
142                    final int nJ = nextIndex(j, yLen);
143                    final int pJ = previousIndex(j);
144                    dZdXdY[i][j] = (zY_2[nI][nJ] - zY_2[nI][pJ] -
145                                    zY_2[pI][nJ] + zY_2[pI][pJ]) /
146                        ((xval[nI] - xval[pI]) * (yval[nJ] - yval[pJ]));
147                }
148            }
149    
150            // Create the interpolating splines
151            return new BicubicSplineInterpolatingFunction(xval, yval, zY_2,
152                                                          dZdX, dZdY, dZdXdY);
153        }
154    
155        /**
156         * Compute the next index of an array, clipping if necessary.
157         * It is assumed (but not checked) that {@code i} is larger than or equal to 0}.
158         *
159         * @param i Index
160         * @param max Upper limit of the array
161         * @return the next index
162         */
163        private int nextIndex(int i, int max) {
164            final int index = i + 1;
165            return index < max ? index : index - 1;
166        }
167        /**
168         * Compute the previous index of an array, clipping if necessary.
169         * It is assumed (but not checked) that {@code i} is smaller than the size of the array.
170         *
171         * @param i Index
172         * @return the previous index
173         */
174        private int previousIndex(int i) {
175            final int index = i - 1;
176            return index >= 0 ? index : 0;
177        }
178    }