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 }