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/*
* 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.math3.analysis.function;
import org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;
import org.apache.commons.math3.analysis.FunctionUtils;
import org.apache.commons.math3.analysis.ParametricUnivariateFunction;
import org.apache.commons.math3.analysis.UnivariateFunction;
import org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
import org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.NullArgumentException;
import org.apache.commons.math3.exception.OutOfRangeException;
import org.apache.commons.math3.util.FastMath;
/**
* <a href="http://en.wikipedia.org/wiki/Logit">
* Logit</a> function.
* It is the inverse of the {@link Sigmoid sigmoid} function.
*
* @since 3.0
*/
public class Logit implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction {
/** Lower bound. */
private final double lo;
/** Higher bound. */
private final double hi;
/**
* Usual logit function, where the lower bound is 0 and the higher
* bound is 1.
*/
public Logit() {
this(0, 1);
}
/**
* Logit function.
*
* @param lo Lower bound of the function domain.
* @param hi Higher bound of the function domain.
*/
public Logit(double lo,
double hi) {
this.lo = lo;
this.hi = hi;
}
/** {@inheritDoc} */
public double value(double x)
throws OutOfRangeException {
return value(x, lo, hi);
}
/** {@inheritDoc}
* @deprecated as of 3.1, replaced by {@link #value(DerivativeStructure)}
*/
@Deprecated
public UnivariateFunction derivative() {
return FunctionUtils.toDifferentiableUnivariateFunction(this).derivative();
}
/**
* Parametric function where the input array contains the parameters of
* the logit function, ordered as follows:
* <ul>
* <li>Lower bound</li>
* <li>Higher bound</li>
* </ul>
*/
public static class Parametric implements ParametricUnivariateFunction {
/**
* Computes the value of the logit at {@code x}.
*
* @param x Value for which the function must be computed.
* @param param Values of lower bound and higher bounds.
* @return the value of the function.
* @throws NullArgumentException if {@code param} is {@code null}.
* @throws DimensionMismatchException if the size of {@code param} is
* not 2.
*/
public double value(double x, double ... param)
throws NullArgumentException,
DimensionMismatchException {
validateParameters(param);
return Logit.value(x, param[0], param[1]);
}
/**
* Computes the value of the gradient at {@code x}.
* The components of the gradient vector are the partial
* derivatives of the function with respect to each of the
* <em>parameters</em> (lower bound and higher bound).
*
* @param x Value at which the gradient must be computed.
* @param param Values for lower and higher bounds.
* @return the gradient vector at {@code x}.
* @throws NullArgumentException if {@code param} is {@code null}.
* @throws DimensionMismatchException if the size of {@code param} is
* not 2.
*/
public double[] gradient(double x, double ... param)
throws NullArgumentException,
DimensionMismatchException {
validateParameters(param);
final double lo = param[0];
final double hi = param[1];
return new double[] { 1 / (lo - x), 1 / (hi - x) };
}
/**
* Validates parameters to ensure they are appropriate for the evaluation of
* the {@link #value(double,double[])} and {@link #gradient(double,double[])}
* methods.
*
* @param param Values for lower and higher bounds.
* @throws NullArgumentException if {@code param} is {@code null}.
* @throws DimensionMismatchException if the size of {@code param} is
* not 2.
*/
private void validateParameters(double[] param)
throws NullArgumentException,
DimensionMismatchException {
if (param == null) {
throw new NullArgumentException();
}
if (param.length != 2) {
throw new DimensionMismatchException(param.length, 2);
}
}
}
/**
* @param x Value at which to compute the logit.
* @param lo Lower bound.
* @param hi Higher bound.
* @return the value of the logit function at {@code x}.
* @throws OutOfRangeException if {@code x < lo} or {@code x > hi}.
*/
private static double value(double x,
double lo,
double hi)
throws OutOfRangeException {
if (x < lo || x > hi) {
throw new OutOfRangeException(x, lo, hi);
}
return FastMath.log((x - lo) / (hi - x));
}
/** {@inheritDoc}
* @since 3.1
* @exception OutOfRangeException if parameter is outside of function domain
*/
public DerivativeStructure value(final DerivativeStructure t)
throws OutOfRangeException {
final double x = t.getValue();
if (x < lo || x > hi) {
throw new OutOfRangeException(x, lo, hi);
}
double[] f = new double[t.getOrder() + 1];
// function value
f[0] = FastMath.log((x - lo) / (hi - x));
if (Double.isInfinite(f[0])) {
if (f.length > 1) {
f[1] = Double.POSITIVE_INFINITY;
}
// fill the array with infinities
// (for x close to lo the signs will flip between -inf and +inf,
// for x close to hi the signs will always be +inf)
// this is probably overkill, since the call to compose at the end
// of the method will transform most infinities into NaN ...
for (int i = 2; i < f.length; ++i) {
f[i] = f[i - 2];
}
} else {
// function derivatives
final double invL = 1.0 / (x - lo);
double xL = invL;
final double invH = 1.0 / (hi - x);
double xH = invH;
for (int i = 1; i < f.length; ++i) {
f[i] = xL + xH;
xL *= -i * invL;
xH *= i * invH;
}
}
return t.compose(f);
}
}
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