| /* |
| * Licensed to the Apache Software Foundation (ASF) under one or more |
| * contributor license agreements. See the NOTICE file distributed with |
| * this work for additional information regarding copyright ownership. |
| * The ASF licenses this file to You under the Apache License, Version 2.0 |
| * (the "License"); you may not use this file except in compliance with |
| * the License. You may obtain a copy of the License at |
| * |
| * http://www.apache.org/licenses/LICENSE-2.0 |
| * |
| * Unless required by applicable law or agreed to in writing, software |
| * distributed under the License is distributed on an "AS IS" BASIS, |
| * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| * See the License for the specific language governing permissions and |
| * limitations under the License. |
| */ |
| package org.apache.commons.math.analysis.interpolation; |
| |
| import org.apache.commons.math.exception.DimensionMismatchException; |
| import org.apache.commons.math.exception.NoDataException; |
| import org.apache.commons.math.MathException; |
| import org.apache.commons.math.util.MathUtils; |
| |
| /** |
| * Generates a tricubic interpolating function. |
| * |
| * @version $Revision$ $Date$ |
| * @since 2.2 |
| */ |
| public class TricubicSplineInterpolator |
| implements TrivariateRealGridInterpolator { |
| /** |
| * {@inheritDoc} |
| */ |
| public TricubicSplineInterpolatingFunction interpolate(final double[] xval, |
| final double[] yval, |
| final double[] zval, |
| final double[][][] fval) |
| throws MathException { |
| if (xval.length == 0 || yval.length == 0 || zval.length == 0 || fval.length == 0) { |
| throw new NoDataException(); |
| } |
| if (xval.length != fval.length) { |
| throw new DimensionMismatchException(xval.length, fval.length); |
| } |
| |
| MathUtils.checkOrder(xval); |
| MathUtils.checkOrder(yval); |
| MathUtils.checkOrder(zval); |
| |
| final int xLen = xval.length; |
| final int yLen = yval.length; |
| final int zLen = zval.length; |
| |
| // Samples, re-ordered as (z, x, y) and (y, z, x) tuplets |
| // fvalXY[k][i][j] = f(xval[i], yval[j], zval[k]) |
| // fvalZX[j][k][i] = f(xval[i], yval[j], zval[k]) |
| final double[][][] fvalXY = new double[zLen][xLen][yLen]; |
| final double[][][] fvalZX = new double[yLen][zLen][xLen]; |
| for (int i = 0; i < xLen; i++) { |
| if (fval[i].length != yLen) { |
| throw new DimensionMismatchException(fval[i].length, yLen); |
| } |
| |
| for (int j = 0; j < yLen; j++) { |
| if (fval[i][j].length != zLen) { |
| throw new DimensionMismatchException(fval[i][j].length, zLen); |
| } |
| |
| for (int k = 0; k < zLen; k++) { |
| final double v = fval[i][j][k]; |
| fvalXY[k][i][j] = v; |
| fvalZX[j][k][i] = v; |
| } |
| } |
| } |
| |
| final BicubicSplineInterpolator bsi = new BicubicSplineInterpolator(); |
| |
| // For each line x[i] (0 <= i < xLen), construct a 2D spline in y and z |
| final BicubicSplineInterpolatingFunction[] xSplineYZ |
| = new BicubicSplineInterpolatingFunction[xLen]; |
| for (int i = 0; i < xLen; i++) { |
| xSplineYZ[i] = bsi.interpolate(yval, zval, fval[i]); |
| } |
| |
| // For each line y[j] (0 <= j < yLen), construct a 2D spline in z and x |
| final BicubicSplineInterpolatingFunction[] ySplineZX |
| = new BicubicSplineInterpolatingFunction[yLen]; |
| for (int j = 0; j < yLen; j++) { |
| ySplineZX[j] = bsi.interpolate(zval, xval, fvalZX[j]); |
| } |
| |
| // For each line z[k] (0 <= k < zLen), construct a 2D spline in x and y |
| final BicubicSplineInterpolatingFunction[] zSplineXY |
| = new BicubicSplineInterpolatingFunction[zLen]; |
| for (int k = 0; k < zLen; k++) { |
| zSplineXY[k] = bsi.interpolate(xval, yval, fvalXY[k]); |
| } |
| |
| // Partial derivatives wrt x and wrt y |
| final double[][][] dFdX = new double[xLen][yLen][zLen]; |
| final double[][][] dFdY = new double[xLen][yLen][zLen]; |
| final double[][][] d2FdXdY = new double[xLen][yLen][zLen]; |
| for (int k = 0; k < zLen; k++) { |
| final BicubicSplineInterpolatingFunction f = zSplineXY[k]; |
| for (int i = 0; i < xLen; i++) { |
| final double x = xval[i]; |
| for (int j = 0; j < yLen; j++) { |
| final double y = yval[j]; |
| dFdX[i][j][k] = f.partialDerivativeX(x, y); |
| dFdY[i][j][k] = f.partialDerivativeY(x, y); |
| d2FdXdY[i][j][k] = f.partialDerivativeXY(x, y); |
| } |
| } |
| } |
| |
| // Partial derivatives wrt y and wrt z |
| final double[][][] dFdZ = new double[xLen][yLen][zLen]; |
| final double[][][] d2FdYdZ = new double[xLen][yLen][zLen]; |
| for (int i = 0; i < xLen; i++) { |
| final BicubicSplineInterpolatingFunction f = xSplineYZ[i]; |
| for (int j = 0; j < yLen; j++) { |
| final double y = yval[j]; |
| for (int k = 0; k < zLen; k++) { |
| final double z = zval[k]; |
| dFdZ[i][j][k] = f.partialDerivativeY(y, z); |
| d2FdYdZ[i][j][k] = f.partialDerivativeXY(y, z); |
| } |
| } |
| } |
| |
| // Partial derivatives wrt x and wrt z |
| final double[][][] d2FdZdX = new double[xLen][yLen][zLen]; |
| for (int j = 0; j < yLen; j++) { |
| final BicubicSplineInterpolatingFunction f = ySplineZX[j]; |
| for (int k = 0; k < zLen; k++) { |
| final double z = zval[k]; |
| for (int i = 0; i < xLen; i++) { |
| final double x = xval[i]; |
| d2FdZdX[i][j][k] = f.partialDerivativeXY(z, x); |
| } |
| } |
| } |
| |
| // Third partial cross-derivatives |
| final double[][][] d3FdXdYdZ = new double[xLen][yLen][zLen]; |
| for (int i = 0; i < xLen ; i++) { |
| final int nI = nextIndex(i, xLen); |
| final int pI = previousIndex(i); |
| for (int j = 0; j < yLen; j++) { |
| final int nJ = nextIndex(j, yLen); |
| final int pJ = previousIndex(j); |
| for (int k = 0; k < zLen; k++) { |
| final int nK = nextIndex(k, zLen); |
| final int pK = previousIndex(k); |
| |
| // XXX Not sure about this formula |
| d3FdXdYdZ[i][j][k] = (fval[nI][nJ][nK] - fval[nI][pJ][nK] - |
| fval[pI][nJ][nK] + fval[pI][pJ][nK] - |
| fval[nI][nJ][pK] + fval[nI][pJ][pK] + |
| fval[pI][nJ][pK] - fval[pI][pJ][pK]) / |
| ((xval[nI] - xval[pI]) * (yval[nJ] - yval[pJ]) * (zval[nK] - zval[pK])) ; |
| } |
| } |
| } |
| |
| // Create the interpolating splines |
| return new TricubicSplineInterpolatingFunction(xval, yval, zval, fval, |
| dFdX, dFdY, dFdZ, |
| d2FdXdY, d2FdZdX, d2FdYdZ, |
| d3FdXdYdZ); |
| } |
| |
| /** |
| * Compute the next index of an array, clipping if necessary. |
| * It is assumed (but not checked) that {@code i} is larger than or equal to 0}. |
| * |
| * @param i Index |
| * @param max Upper limit of the array |
| * @return the next index |
| */ |
| private int nextIndex(int i, int max) { |
| final int index = i + 1; |
| return index < max ? index : index - 1; |
| } |
| /** |
| * Compute the previous index of an array, clipping if necessary. |
| * It is assumed (but not checked) that {@code i} is smaller than the size of the array. |
| * |
| * @param i Index |
| * @return the previous index |
| */ |
| private int previousIndex(int i) { |
| final int index = i - 1; |
| return index >= 0 ? index : 0; |
| } |
| } |