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 */ 017package org.apache.commons.math3.analysis.interpolation; 018 019import org.apache.commons.math3.exception.DimensionMismatchException; 020import org.apache.commons.math3.exception.NoDataException; 021import org.apache.commons.math3.exception.NonMonotonicSequenceException; 022import org.apache.commons.math3.exception.NumberIsTooSmallException; 023import org.apache.commons.math3.util.MathArrays; 024 025/** 026 * Generates a {@link BicubicInterpolatingFunction bicubic interpolating 027 * function}. 028 * <p> 029 * Caveat: Because the interpolation scheme requires that derivatives be 030 * specified at the sample points, those are approximated with finite 031 * differences (using the 2-points symmetric formulae). 032 * Since their values are undefined at the borders of the provided 033 * interpolation ranges, the interpolated values will be wrong at the 034 * edges of the patch. 035 * The {@code interpolate} method will return a function that overrides 036 * {@link BicubicInterpolatingFunction#isValidPoint(double,double)} to 037 * indicate points where the interpolation will be inaccurate. 038 * </p> 039 * 040 * @since 3.4 041 */ 042public class BicubicInterpolator 043 implements BivariateGridInterpolator { 044 /** 045 * {@inheritDoc} 046 */ 047 public BicubicInterpolatingFunction interpolate(final double[] xval, 048 final double[] yval, 049 final double[][] fval) 050 throws NoDataException, DimensionMismatchException, 051 NonMonotonicSequenceException, NumberIsTooSmallException { 052 if (xval.length == 0 || yval.length == 0 || fval.length == 0) { 053 throw new NoDataException(); 054 } 055 if (xval.length != fval.length) { 056 throw new DimensionMismatchException(xval.length, fval.length); 057 } 058 059 MathArrays.checkOrder(xval); 060 MathArrays.checkOrder(yval); 061 062 final int xLen = xval.length; 063 final int yLen = yval.length; 064 065 // Approximation to the partial derivatives using finite differences. 066 final double[][] dFdX = new double[xLen][yLen]; 067 final double[][] dFdY = new double[xLen][yLen]; 068 final double[][] d2FdXdY = new double[xLen][yLen]; 069 for (int i = 1; i < xLen - 1; i++) { 070 final int nI = i + 1; 071 final int pI = i - 1; 072 073 final double nX = xval[nI]; 074 final double pX = xval[pI]; 075 076 final double deltaX = nX - pX; 077 078 for (int j = 1; j < yLen - 1; j++) { 079 final int nJ = j + 1; 080 final int pJ = j - 1; 081 082 final double nY = yval[nJ]; 083 final double pY = yval[pJ]; 084 085 final double deltaY = nY - pY; 086 087 dFdX[i][j] = (fval[nI][j] - fval[pI][j]) / deltaX; 088 dFdY[i][j] = (fval[i][nJ] - fval[i][pJ]) / deltaY; 089 090 final double deltaXY = deltaX * deltaY; 091 092 d2FdXdY[i][j] = (fval[nI][nJ] - fval[nI][pJ] - fval[pI][nJ] + fval[pI][pJ]) / deltaXY; 093 } 094 } 095 096 // Create the interpolating function. 097 return new BicubicInterpolatingFunction(xval, yval, fval, 098 dFdX, dFdY, d2FdXdY) { 099 /** {@inheritDoc} */ 100 @Override 101 public boolean isValidPoint(double x, double y) { 102 if (x < xval[1] || 103 x > xval[xval.length - 2] || 104 y < yval[1] || 105 y > yval[yval.length - 2]) { 106 return false; 107 } else { 108 return true; 109 } 110 } 111 }; 112 } 113}