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.analysis.UnivariateFunction;
020 import org.apache.commons.math3.analysis.polynomials.PolynomialSplineFunction;
021 import org.apache.commons.math3.exception.DimensionMismatchException;
022 import org.apache.commons.math3.exception.NoDataException;
023 import org.apache.commons.math3.exception.NonMonotonicSequenceException;
024 import org.apache.commons.math3.util.MathArrays;
025
026 /**
027 * Generates a bicubic interpolating function.
028 *
029 * @version $Id: BicubicSplineInterpolator.java 1385313 2012-09-16 16:35:23Z tn $
030 * @since 2.2
031 */
032 public class BicubicSplineInterpolator
033 implements BivariateGridInterpolator {
034 /**
035 * {@inheritDoc}
036 */
037 public BicubicSplineInterpolatingFunction interpolate(final double[] xval,
038 final double[] yval,
039 final double[][] fval)
040 throws NoDataException,
041 DimensionMismatchException,
042 NonMonotonicSequenceException {
043 if (xval.length == 0 || yval.length == 0 || fval.length == 0) {
044 throw new NoDataException();
045 }
046 if (xval.length != fval.length) {
047 throw new DimensionMismatchException(xval.length, fval.length);
048 }
049
050 MathArrays.checkOrder(xval);
051 MathArrays.checkOrder(yval);
052
053 final int xLen = xval.length;
054 final int yLen = yval.length;
055
056 // Samples (first index is y-coordinate, i.e. subarray variable is x)
057 // 0 <= i < xval.length
058 // 0 <= j < yval.length
059 // fX[j][i] = f(xval[i], yval[j])
060 final double[][] fX = new double[yLen][xLen];
061 for (int i = 0; i < xLen; i++) {
062 if (fval[i].length != yLen) {
063 throw new DimensionMismatchException(fval[i].length, yLen);
064 }
065
066 for (int j = 0; j < yLen; j++) {
067 fX[j][i] = fval[i][j];
068 }
069 }
070
071 final SplineInterpolator spInterpolator = new SplineInterpolator();
072
073 // For each line y[j] (0 <= j < yLen), construct a 1D spline with
074 // respect to variable x
075 final PolynomialSplineFunction[] ySplineX = new PolynomialSplineFunction[yLen];
076 for (int j = 0; j < yLen; j++) {
077 ySplineX[j] = spInterpolator.interpolate(xval, fX[j]);
078 }
079
080 // For each line x[i] (0 <= i < xLen), construct a 1D spline with
081 // respect to variable y generated by array fY_1[i]
082 final PolynomialSplineFunction[] xSplineY = new PolynomialSplineFunction[xLen];
083 for (int i = 0; i < xLen; i++) {
084 xSplineY[i] = spInterpolator.interpolate(yval, fval[i]);
085 }
086
087 // Partial derivatives with respect to x at the grid knots
088 final double[][] dFdX = new double[xLen][yLen];
089 for (int j = 0; j < yLen; j++) {
090 final UnivariateFunction f = ySplineX[j].derivative();
091 for (int i = 0; i < xLen; i++) {
092 dFdX[i][j] = f.value(xval[i]);
093 }
094 }
095
096 // Partial derivatives with respect to y at the grid knots
097 final double[][] dFdY = new double[xLen][yLen];
098 for (int i = 0; i < xLen; i++) {
099 final UnivariateFunction f = xSplineY[i].derivative();
100 for (int j = 0; j < yLen; j++) {
101 dFdY[i][j] = f.value(yval[j]);
102 }
103 }
104
105 // Cross partial derivatives
106 final double[][] d2FdXdY = new double[xLen][yLen];
107 for (int i = 0; i < xLen ; i++) {
108 final int nI = nextIndex(i, xLen);
109 final int pI = previousIndex(i);
110 for (int j = 0; j < yLen; j++) {
111 final int nJ = nextIndex(j, yLen);
112 final int pJ = previousIndex(j);
113 d2FdXdY[i][j] = (fval[nI][nJ] - fval[nI][pJ] -
114 fval[pI][nJ] + fval[pI][pJ]) /
115 ((xval[nI] - xval[pI]) * (yval[nJ] - yval[pJ]));
116 }
117 }
118
119 // Create the interpolating splines
120 return new BicubicSplineInterpolatingFunction(xval, yval, fval,
121 dFdX, dFdY, d2FdXdY);
122 }
123
124 /**
125 * Computes the next index of an array, clipping if necessary.
126 * It is assumed (but not checked) that {@code i >= 0}.
127 *
128 * @param i Index.
129 * @param max Upper limit of the array.
130 * @return the next index.
131 */
132 private int nextIndex(int i, int max) {
133 final int index = i + 1;
134 return index < max ? index : index - 1;
135 }
136 /**
137 * Computes the previous index of an array, clipping if necessary.
138 * It is assumed (but not checked) that {@code i} is smaller than the size
139 * of the array.
140 *
141 * @param i Index.
142 * @return the previous index.
143 */
144 private int previousIndex(int i) {
145 final int index = i - 1;
146 return index >= 0 ? index : 0;
147 }
148 }