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