/*
* 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.optimization.fitting;
import java.io.Serializable;
import org.apache.commons.math.exception.DimensionMismatchException;
import org.apache.commons.math.exception.util.LocalizedFormats;
import org.apache.commons.math.exception.ZeroException;
import org.apache.commons.math.exception.NullArgumentException;
import org.apache.commons.math.optimization.fitting.ParametricRealFunction;
/**
* A Gaussian function. Specifically:
* <p>
* <tt>f(x) = a + b*exp(-((x - c)^2 / (2*d^2)))</tt>
* <p>
* The parameters have the following meaning:
* <ul>
* <li><tt>a</tt> is a constant offset that shifts <tt>f(x)</tt> up or down
* <li><tt>b</tt> is the height of the peak
* <li><tt>c</tt> is the position of the center of the peak
* <li><tt>d</tt> is related to the FWHM by <tt>FWHM = 2*sqrt(2*ln(2))*d</tt>
* </ul>
* Notation key:
* <ul>
* <li><tt>x^n</tt>: <tt>x</tt> raised to the power of <tt>n</tt>
* <li><tt>exp(x)</tt>: <i>e</i><tt>^x</tt>
* <li><tt>sqrt(x)</tt>: the square root of <tt>x</tt>
* <li><tt>ln(x)</tt>: the natural logarithm of <tt>x</tt>
* </ul>
* References:
* <ul>
* <li><a href="http://en.wikipedia.org/wiki/Gaussian_function">Wikipedia:
* Gaussian function</a>
* </ul>
*
* @since 2.2
* @version $Revision: 1037327 $ $Date: 2010-11-20 21:57:37 +0100 (sam. 20 nov. 2010) $
*/
public class ParametricGaussianFunction implements ParametricRealFunction, Serializable {
/** Serializable version Id. */
private static final long serialVersionUID = -3875578602503903233L;
/**
* Constructs an instance.
*/
public ParametricGaussianFunction() {
}
/**
* Computes value of function <tt>f(x)</tt> for the specified <tt>x</tt> and
* parameters <tt>a</tt>, <tt>b</tt>, <tt>c</tt>, and <tt>d</tt>.
*
* @param x <tt>x</tt> value
* @param parameters values of <tt>a</tt>, <tt>b</tt>, <tt>c</tt>, and
* <tt>d</tt>
*
* @return value of <tt>f(x)</tt> evaluated at <tt>x</tt> with the specified
* parameters
*
* @throws IllegalArgumentException if <code>parameters</code> is invalid as
* determined by {@link #validateParameters(double[])}
* @throws ZeroException if <code>parameters</code> values are
* invalid as determined by {@link #validateParameters(double[])}
*/
public double value(double x, double[] parameters) throws ZeroException {
validateParameters(parameters);
final double a = parameters[0];
final double b = parameters[1];
final double c = parameters[2];
final double d = parameters[3];
final double xMc = x - c;
return a + b * Math.exp(-xMc * xMc / (2.0 * (d * d)));
}
/**
* Computes the gradient vector for a four variable version of the function
* where the parameters, <tt>a</tt>, <tt>b</tt>, <tt>c</tt>, and <tt>d</tt>,
* are considered the variables, not <tt>x</tt>. That is, instead of
* computing the gradient vector for the function <tt>f(x)</tt> (which would
* just be the derivative of <tt>f(x)</tt> with respect to <tt>x</tt> since
* it's a one-dimensional function), computes the gradient vector for the
* function <tt>f(a, b, c, d) = a + b*exp(-((x - c)^2 / (2*d^2)))</tt>
* treating the specified <tt>x</tt> as a constant.
* <p>
* The components of the computed gradient vector are the partial
* derivatives of <tt>f(a, b, c, d)</tt> with respect to each variable.
* That is, the partial derivative of <tt>f(a, b, c, d)</tt> with respect to
* <tt>a</tt>, the partial derivative of <tt>f(a, b, c, d)</tt> with respect
* to <tt>b</tt>, the partial derivative of <tt>f(a, b, c, d)</tt> with
* respect to <tt>c</tt>, and the partial derivative of <tt>f(a, b, c,
* d)</tt> with respect to <tt>d</tt>.
*
* @param x <tt>x</tt> value to be used as constant in <tt>f(a, b, c,
* d)</tt>
* @param parameters values of <tt>a</tt>, <tt>b</tt>, <tt>c</tt>, and
* <tt>d</tt> for computation of gradient vector of <tt>f(a, b, c,
* d)</tt>
*
* @return gradient vector of <tt>f(a, b, c, d)</tt>
*
* @throws IllegalArgumentException if <code>parameters</code> is invalid as
* determined by {@link #validateParameters(double[])}
* @throws ZeroException if <code>parameters</code> values are
* invalid as determined by {@link #validateParameters(double[])}
*/
public double[] gradient(double x, double[] parameters) throws ZeroException {
validateParameters(parameters);
final double b = parameters[1];
final double c = parameters[2];
final double d = parameters[3];
final double xMc = x - c;
final double d2 = d * d;
final double exp = Math.exp(-xMc * xMc / (2 * d2));
final double f = b * exp * xMc / d2;
return new double[] { 1.0, exp, f, f * xMc / d };
}
/**
* Validates parameters to ensure they are appropriate for the evaluation of
* the <code>value</code> and <code>gradient</code> methods.
*
* @param parameters values of <tt>a</tt>, <tt>b</tt>, <tt>c</tt>, and
* <tt>d</tt>
*
* @throws IllegalArgumentException if <code>parameters</code> is
* <code>null</code> or if <code>parameters</code> does not have
* length == 4
* @throws ZeroException if <code>parameters[3]</code>
* (<tt>d</tt>) is 0
*/
private void validateParameters(double[] parameters) throws ZeroException {
if (parameters == null) {
throw new NullArgumentException(LocalizedFormats.INPUT_ARRAY);
}
if (parameters.length != 4) {
throw new DimensionMismatchException(4, parameters.length);
}
if (parameters[3] == 0.0) {
throw new ZeroException();
}
}
}