/*
* 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.MathRuntimeException;
import org.apache.commons.math.MathException;
import org.apache.commons.math.util.MathUtils;
import org.apache.commons.math.util.MathUtils.OrderDirection;
import org.apache.commons.math.analysis.BivariateRealFunction;
import org.apache.commons.math.analysis.UnivariateRealFunction;
import org.apache.commons.math.analysis.polynomials.PolynomialSplineFunction;
import org.apache.commons.math.exception.util.LocalizedFormats;
/**
* Generates a bicubic interpolation function.
* Before interpolating, smoothing of the input data is performed using
* splines.
* See <b>Handbook on splines for the user</b>, ISBN 084939404X,
* chapter 2.
*
* @version $Revision: 1059400 $ $Date: 2011-01-15 20:35:27 +0100 (sam. 15 janv. 2011) $
* @since 2.1
* @deprecated This class does not perform smoothing; the name is thus misleading.
* Please use {@link org.apache.commons.math.analysis.interpolation.BicubicSplineInterpolator}
* instead. If smoothing is desired, a tentative implementation is provided in class
* {@link org.apache.commons.math.analysis.interpolation.SmoothingPolynomialBicubicSplineInterpolator}.
* This class will be removed in math 3.0.
*/
@Deprecated
public class SmoothingBicubicSplineInterpolator
implements BivariateRealGridInterpolator {
/**
* {@inheritDoc}
*/
public BivariateRealFunction interpolate(final double[] xval,
final double[] yval,
final double[][] zval)
throws MathException, IllegalArgumentException {
if (xval.length == 0 || yval.length == 0 || zval.length == 0) {
throw MathRuntimeException.createIllegalArgumentException(LocalizedFormats.NO_DATA);
}
if (xval.length != zval.length) {
throw new DimensionMismatchException(xval.length, zval.length);
}
MathUtils.checkOrder(xval, OrderDirection.INCREASING, true);
MathUtils.checkOrder(yval, OrderDirection.INCREASING, true);
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
// zX[j][i] = f(xval[i], yval[j])
final double[][] zX = new double[yLen][xLen];
for (int i = 0; i < xLen; i++) {
if (zval[i].length != yLen) {
throw new DimensionMismatchException(zval[i].length, yLen);
}
for (int j = 0; j < yLen; j++) {
zX[j][i] = zval[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, zX[j]);
}
// For every knot (xval[i], yval[j]) of the grid, calculate corrected
// values zY_1
final double[][] zY_1 = new double[xLen][yLen];
for (int j = 0; j < yLen; j++) {
final PolynomialSplineFunction f = ySplineX[j];
for (int i = 0; i < xLen; i++) {
zY_1[i][j] = f.value(xval[i]);
}
}
// For each line x[i] (0 <= i < xLen), construct a 1D spline with
// respect to variable y generated by array zY_1[i]
final PolynomialSplineFunction[] xSplineY = new PolynomialSplineFunction[xLen];
for (int i = 0; i < xLen; i++) {
xSplineY[i] = spInterpolator.interpolate(yval, zY_1[i]);
}
// For every knot (xval[i], yval[j]) of the grid, calculate corrected
// values zY_2
final double[][] zY_2 = new double[xLen][yLen];
for (int i = 0; i < xLen; i++) {
final PolynomialSplineFunction f = xSplineY[i];
for (int j = 0; j < yLen; j++) {
zY_2[i][j] = f.value(yval[j]);
}
}
// Partial derivatives with respect to x at the grid knots
final double[][] dZdX = new double[xLen][yLen];
for (int j = 0; j < yLen; j++) {
final UnivariateRealFunction f = ySplineX[j].derivative();
for (int i = 0; i < xLen; i++) {
dZdX[i][j] = f.value(xval[i]);
}
}
// Partial derivatives with respect to y at the grid knots
final double[][] dZdY = new double[xLen][yLen];
for (int i = 0; i < xLen; i++) {
final UnivariateRealFunction f = xSplineY[i].derivative();
for (int j = 0; j < yLen; j++) {
dZdY[i][j] = f.value(yval[j]);
}
}
// Cross partial derivatives
final double[][] dZdXdY = 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);
dZdXdY[i][j] = (zY_2[nI][nJ] - zY_2[nI][pJ] -
zY_2[pI][nJ] + zY_2[pI][pJ]) /
((xval[nI] - xval[pI]) * (yval[nJ] - yval[pJ]));
}
}
// Create the interpolating splines
return new BicubicSplineInterpolatingFunction(xval, yval, zY_2,
dZdX, dZdY, dZdXdY);
}
/**
* 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;
}
}