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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
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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;


 Logit function. It is the inverse of the sigmoid function. 
Since:
3.0/**
 * <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. /** Lower bound. */
    private final double lo;
    
Higher bound. /** Higher bound. */
    private final double hi;

    
Usual logit function, where the lower bound is 0 and the higher
bound is 1.
/**
     * Usual logit function, where the lower bound is 0 and the higher
     * bound is 1.
     */
    public Logit() {
        this(0, 1);
    }

    
Logit function.
Params:
lo – Lower bound of the function domain.
hi – Higher bound of the function domain./**
     * 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} /** {@inheritDoc} */
    public double value(double x)
        throws OutOfRangeException {
        return value(x, lo, hi);
    }

    
{@inheritDoc}
Deprecated:
as of 3.1, replaced by value(DerivativeStructure)/** {@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:

 
Lower bound
 
Higher bound

/**
     * 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 x. 
Params:
x – Value for which the function must be computed.
param – Values of lower bound and higher bounds.
Throws:
NullArgumentException – if param is null.
DimensionMismatchException – if the size of param is not 2.
Returns:
the value of the function./**
         * 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 x. The components of the gradient vector are the partial derivatives of the function with respect to each of the parameters (lower bound and higher bound).
Params:
x – Value at which the gradient must be computed.
param – Values for lower and higher bounds.
Throws:
NullArgumentException – if param is null.
DimensionMismatchException – if the size of param is not 2.
Returns:
the gradient vector at x./**
         * 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 value(double, double[]) and gradient(double, double[]) methods. 
Params:
param – Values for lower and higher bounds.
Throws:
NullArgumentException – if param is null.
DimensionMismatchException – if the size of param is not 2./**
         * 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);
            }
        }
    }

    
Params:
x – Value at which to compute the logit.
lo – Lower bound.
hi – Higher bound.
Throws:
OutOfRangeException – if x < lo or x > hi.
Returns:
the value of the logit function at x./**
     * @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}
Throws:
OutOfRangeException – if parameter is outside of function domain
Since:
3.1/** {@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);
    }
}