| /* |
| * 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.DimensionMismatchException; |
| import org.apache.commons.math.MathException; |
| import org.apache.commons.math.analysis.UnivariateRealFunction; |
| import org.apache.commons.math.analysis.polynomials.PolynomialSplineFunction; |
| import org.apache.commons.math.exception.NoDataException; |
| import org.apache.commons.math.util.MathUtils; |
| |
| /** |
| * Generates a bicubic interpolating function. |
| * |
| * @version $Revision: 980944 $ $Date: 2010-07-30 22:31:11 +0200 (ven. 30 juil. 2010) $ |
| * @since 2.2 |
| */ |
| public class BicubicSplineInterpolator |
| implements BivariateRealGridInterpolator { |
| /** |
| * {@inheritDoc} |
| */ |
| public BicubicSplineInterpolatingFunction interpolate(final double[] xval, |
| final double[] yval, |
| final double[][] fval) |
| throws MathException, IllegalArgumentException { |
| if (xval.length == 0 || yval.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); |
| |
| final int xLen = xval.length; |
| final int yLen = yval.length; |
| |
| // Samples (first index is y-coordinate, i.e. subarray variable is x) |
| // 0 <= i < xval.length |
| // 0 <= j < yval.length |
| // fX[j][i] = f(xval[i], yval[j]) |
| final double[][] fX = new double[yLen][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++) { |
| fX[j][i] = fval[i][j]; |
| } |
| } |
| |
| final SplineInterpolator spInterpolator = new SplineInterpolator(); |
| |
| // For each line y[j] (0 <= j < yLen), construct a 1D spline with |
| // respect to variable x |
| final PolynomialSplineFunction[] ySplineX = new PolynomialSplineFunction[yLen]; |
| for (int j = 0; j < yLen; j++) { |
| ySplineX[j] = spInterpolator.interpolate(xval, fX[j]); |
| } |
| |
| // For each line x[i] (0 <= i < xLen), construct a 1D spline with |
| // respect to variable y generated by array fY_1[i] |
| final PolynomialSplineFunction[] xSplineY = new PolynomialSplineFunction[xLen]; |
| for (int i = 0; i < xLen; i++) { |
| xSplineY[i] = spInterpolator.interpolate(yval, fval[i]); |
| } |
| |
| // Partial derivatives with respect to x at the grid knots |
| final double[][] dFdX = new double[xLen][yLen]; |
| for (int j = 0; j < yLen; j++) { |
| final UnivariateRealFunction f = ySplineX[j].derivative(); |
| for (int i = 0; i < xLen; i++) { |
| dFdX[i][j] = f.value(xval[i]); |
| } |
| } |
| |
| // Partial derivatives with respect to y at the grid knots |
| final double[][] dFdY = new double[xLen][yLen]; |
| for (int i = 0; i < xLen; i++) { |
| final UnivariateRealFunction f = xSplineY[i].derivative(); |
| for (int j = 0; j < yLen; j++) { |
| dFdY[i][j] = f.value(yval[j]); |
| } |
| } |
| |
| // Cross partial derivatives |
| final double[][] d2FdXdY = new double[xLen][yLen]; |
| 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); |
| d2FdXdY[i][j] = (fval[nI][nJ] - fval[nI][pJ] - |
| fval[pI][nJ] + fval[pI][pJ]) / |
| ((xval[nI] - xval[pI]) * (yval[nJ] - yval[pJ])); |
| } |
| } |
| |
| // Create the interpolating splines |
| return new BicubicSplineInterpolatingFunction(xval, yval, fval, |
| dFdX, dFdY, d2FdXdY); |
| } |
| |
| /** |
| * 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; |
| } |
| } |