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.math3.analysis.interpolation;
018
019import java.util.Arrays;
020import org.apache.commons.math3.analysis.BivariateFunction;
021import org.apache.commons.math3.analysis.polynomials.PolynomialSplineFunction;
022import org.apache.commons.math3.exception.DimensionMismatchException;
023import org.apache.commons.math3.exception.InsufficientDataException;
024import org.apache.commons.math3.exception.NoDataException;
025import org.apache.commons.math3.exception.NullArgumentException;
026import org.apache.commons.math3.exception.OutOfRangeException;
027import org.apache.commons.math3.exception.NonMonotonicSequenceException;
028import org.apache.commons.math3.util.MathArrays;
029
030/**
031 * Function that implements the
032 * <a href="http://www.paulinternet.nl/?page=bicubic">bicubic spline</a>
033 * interpolation.
034 * This implementation currently uses {@link AkimaSplineInterpolator} as the
035 * underlying one-dimensional interpolator, which requires 5 sample points;
036 * insufficient data will raise an exception when the
037 * {@link #value(double,double) value} method is called.
038 *
039 * @since 3.4
040 */
041public class PiecewiseBicubicSplineInterpolatingFunction
042    implements BivariateFunction {
043    /** The minimum number of points that are needed to compute the function. */
044    private static final int MIN_NUM_POINTS = 5;
045    /** Samples x-coordinates */
046    private final double[] xval;
047    /** Samples y-coordinates */
048    private final double[] yval;
049    /** Set of cubic splines patching the whole data grid */
050    private final double[][] fval;
051
052    /**
053     * @param x Sample values of the x-coordinate, in increasing order.
054     * @param y Sample values of the y-coordinate, in increasing order.
055     * @param f Values of the function on every grid point. the expected number
056     *        of elements.
057     * @throws NonMonotonicSequenceException if {@code x} or {@code y} are not
058     *         strictly increasing.
059     * @throws NullArgumentException if any of the arguments are null
060     * @throws NoDataException if any of the arrays has zero length.
061     * @throws DimensionMismatchException if the length of x and y don't match the row, column
062     *         height of f
063     */
064    public PiecewiseBicubicSplineInterpolatingFunction(double[] x,
065                                                       double[] y,
066                                                       double[][] f)
067        throws DimensionMismatchException,
068               NullArgumentException,
069               NoDataException,
070               NonMonotonicSequenceException {
071        if (x == null ||
072            y == null ||
073            f == null ||
074            f[0] == null) {
075            throw new NullArgumentException();
076        }
077
078        final int xLen = x.length;
079        final int yLen = y.length;
080
081        if (xLen == 0 ||
082            yLen == 0 ||
083            f.length == 0 ||
084            f[0].length == 0) {
085            throw new NoDataException();
086        }
087
088        if (xLen < MIN_NUM_POINTS ||
089            yLen < MIN_NUM_POINTS ||
090            f.length < MIN_NUM_POINTS ||
091            f[0].length < MIN_NUM_POINTS) {
092            throw new InsufficientDataException();
093        }
094
095        if (xLen != f.length) {
096            throw new DimensionMismatchException(xLen, f.length);
097        }
098
099        if (yLen != f[0].length) {
100            throw new DimensionMismatchException(yLen, f[0].length);
101        }
102
103        MathArrays.checkOrder(x);
104        MathArrays.checkOrder(y);
105
106        xval = x.clone();
107        yval = y.clone();
108        fval = f.clone();
109    }
110
111    /**
112     * {@inheritDoc}
113     */
114    public double value(double x,
115                        double y)
116        throws OutOfRangeException {
117        final AkimaSplineInterpolator interpolator = new AkimaSplineInterpolator();
118        final int offset = 2;
119        final int count = offset + 3;
120        final int i = searchIndex(x, xval, offset, count);
121        final int j = searchIndex(y, yval, offset, count);
122
123        final double xArray[] = new double[count];
124        final double yArray[] = new double[count];
125        final double zArray[] = new double[count];
126        final double interpArray[] = new double[count];
127
128        for (int index = 0; index < count; index++) {
129            xArray[index] = xval[i + index];
130            yArray[index] = yval[j + index];
131        }
132
133        for (int zIndex = 0; zIndex < count; zIndex++) {
134            for (int index = 0; index < count; index++) {
135                zArray[index] = fval[i + index][j + zIndex];
136            }
137            final PolynomialSplineFunction spline = interpolator.interpolate(xArray, zArray);
138            interpArray[zIndex] = spline.value(x);
139        }
140
141        final PolynomialSplineFunction spline = interpolator.interpolate(yArray, interpArray);
142
143        double returnValue = spline.value(y);
144
145        return returnValue;
146    }
147
148    /**
149     * Indicates whether a point is within the interpolation range.
150     *
151     * @param x First coordinate.
152     * @param y Second coordinate.
153     * @return {@code true} if (x, y) is a valid point.
154     * @since 3.3
155     */
156    public boolean isValidPoint(double x,
157                                double y) {
158        if (x < xval[0] ||
159            x > xval[xval.length - 1] ||
160            y < yval[0] ||
161            y > yval[yval.length - 1]) {
162            return false;
163        } else {
164            return true;
165        }
166    }
167
168    /**
169     * @param c Coordinate.
170     * @param val Coordinate samples.
171     * @param offset how far back from found value to offset for querying
172     * @param count total number of elements forward from beginning that will be
173     *        queried
174     * @return the index in {@code val} corresponding to the interval containing
175     *         {@code c}.
176     * @throws OutOfRangeException if {@code c} is out of the range defined by
177     *         the boundary values of {@code val}.
178     */
179    private int searchIndex(double c,
180                            double[] val,
181                            int offset,
182                            int count) {
183        int r = Arrays.binarySearch(val, c);
184
185        if (r == -1 || r == -val.length - 1) {
186            throw new OutOfRangeException(c, val[0], val[val.length - 1]);
187        }
188
189        if (r < 0) {
190            // "c" in within an interpolation sub-interval, which returns
191            // negative
192            // need to remove the negative sign for consistency
193            r = -r - offset - 1;
194        } else {
195            r -= offset;
196        }
197
198        if (r < 0) {
199            r = 0;
200        }
201
202        if ((r + count) >= val.length) {
203            // "c" is the last sample of the range: Return the index
204            // of the sample at the lower end of the last sub-interval.
205            r = val.length - count;
206        }
207
208        return r;
209    }
210}