/*
 * 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.statistics.distribution;

import org.apache.commons.numbers.gamma.Erf;
import org.apache.commons.numbers.gamma.ErfDifference;
import org.apache.commons.rng.UniformRandomProvider;
import org.apache.commons.rng.sampling.distribution.LogNormalSampler;
import org.apache.commons.rng.sampling.distribution.ZigguratNormalizedGaussianSampler;

/**
 * Implementation of the <a href="http://en.wikipedia.org/wiki/Log-normal_distribution">log-normal distribution</a>.
 *
 * <p>
 * <strong>Parameters:</strong>
 * {@code X} is log-normally distributed if its natural logarithm {@code log(X)}
 * is normally distributed. The probability distribution function of {@code X}
 * is given by (for {@code x > 0})
 * </p>
 * <p>
 * {@code exp(-0.5 * ((ln(x) - m) / s)^2) / (s * sqrt(2 * pi) * x)}
 * </p>
 * <ul>
 * <li>{@code m} is the <em>scale</em> parameter: this is the mean of the
 * normally distributed natural logarithm of this distribution,</li>
 * <li>{@code s} is the <em>shape</em> parameter: this is the standard
 * deviation of the normally distributed natural logarithm of this
 * distribution.
 * </ul>
 */
public class LogNormalDistribution extends AbstractContinuousDistribution {
    /** &radic;(2 &pi;). */
    private static final double SQRT2PI = Math.sqrt(2 * Math.PI);
    /** &radic;(2). */
    private static final double SQRT2 = Math.sqrt(2);
    /** The scale parameter of this distribution. */
    private final double scale;
    /** The shape parameter of this distribution. */
    private final double shape;
    /** The value of {@code log(shape) + 0.5 * log(2*PI)} stored for faster computation. */
    private final double logShapePlusHalfLog2Pi;

    /**
     * Creates a log-normal distribution.
     *
     * @param scale Scale parameter of this distribution.
     * @param shape Shape parameter of this distribution.
     * @throws IllegalArgumentException if {@code shape <= 0}.
     */
    public LogNormalDistribution(double scale,
                                 double shape) {
        if (shape <= 0) {
            throw new DistributionException(DistributionException.NOT_STRICTLY_POSITIVE, shape);
        }

        this.scale = scale;
        this.shape = shape;
        this.logShapePlusHalfLog2Pi = Math.log(shape) + 0.5 * Math.log(2 * Math.PI);
    }

    /**
     * Returns the scale parameter of this distribution.
     *
     * @return the scale parameter
     */
    public double getScale() {
        return scale;
    }

    /**
     * Returns the shape parameter of this distribution.
     *
     * @return the shape parameter
     */
    public double getShape() {
        return shape;
    }

    /**
     * {@inheritDoc}
     *
     * For scale {@code m}, and shape {@code s} of this distribution, the PDF
     * is given by
     * <ul>
     * <li>{@code 0} if {@code x <= 0},</li>
     * <li>{@code exp(-0.5 * ((ln(x) - m) / s)^2) / (s * sqrt(2 * pi) * x)}
     * otherwise.</li>
     * </ul>
     */
    @Override
    public double density(double x) {
        if (x <= 0) {
            return 0;
        }
        final double x0 = Math.log(x) - scale;
        final double x1 = x0 / shape;
        return Math.exp(-0.5 * x1 * x1) / (shape * SQRT2PI * x);
    }

    /** {@inheritDoc}
     *
     * See documentation of {@link #density(double)} for computation details.
     */
    @Override
    public double logDensity(double x) {
        if (x <= 0) {
            return Double.NEGATIVE_INFINITY;
        }
        final double logX = Math.log(x);
        final double x0 = logX - scale;
        final double x1 = x0 / shape;
        return -0.5 * x1 * x1 - (logShapePlusHalfLog2Pi + logX);
    }

    /**
     * {@inheritDoc}
     *
     * For scale {@code m}, and shape {@code s} of this distribution, the CDF
     * is given by
     * <ul>
     * <li>{@code 0} if {@code x <= 0},</li>
     * <li>{@code 0} if {@code ln(x) - m < 0} and {@code m - ln(x) > 40 * s}, as
     * in these cases the actual value is within {@code Double.MIN_VALUE} of 0,
     * <li>{@code 1} if {@code ln(x) - m >= 0} and {@code ln(x) - m > 40 * s},
     * as in these cases the actual value is within {@code Double.MIN_VALUE} of
     * 1,</li>
     * <li>{@code 0.5 + 0.5 * erf((ln(x) - m) / (s * sqrt(2))} otherwise.</li>
     * </ul>
     */
    @Override
    public double cumulativeProbability(double x)  {
        if (x <= 0) {
            return 0;
        }
        final double dev = Math.log(x) - scale;
        if (Math.abs(dev) > 40 * shape) {
            return dev < 0 ? 0.0d : 1.0d;
        }
        return 0.5 + 0.5 * Erf.value(dev / (shape * SQRT2));
    }

    /** {@inheritDoc} */
    @Override
    public double probability(double x0,
                              double x1) {
        if (x0 > x1) {
            throw new DistributionException(DistributionException.INVALID_RANGE_LOW_GT_HIGH,
                                            x0, x1);
        }
        if (x0 <= 0) {
            return super.probability(x0, x1);
        }
        // Assumes x1 >= x0 && x0 > 0
        final double denom = shape * SQRT2;
        final double v0 = (Math.log(x0) - scale) / denom;
        final double v1 = (Math.log(x1) - scale) / denom;
        return 0.5 * ErfDifference.value(v0, v1);
    }

    /**
     * {@inheritDoc}
     *
     * For scale {@code m} and shape {@code s}, the mean is
     * {@code exp(m + s^2 / 2)}.
     */
    @Override
    public double getMean() {
        final double s = shape;
        return Math.exp(scale + (s * s / 2));
    }

    /**
     * {@inheritDoc}
     *
     * For scale {@code m} and shape {@code s}, the variance is
     * {@code (exp(s^2) - 1) * exp(2 * m + s^2)}.
     */
    @Override
    public double getVariance() {
        final double s = shape;
        final double ss = s * s;
        return (Math.expm1(ss)) * Math.exp(2 * scale + ss);
    }

    /**
     * {@inheritDoc}
     *
     * The lower bound of the support is always 0 no matter the parameters.
     *
     * @return lower bound of the support (always 0)
     */
    @Override
    public double getSupportLowerBound() {
        return 0;
    }

    /**
     * {@inheritDoc}
     *
     * The upper bound of the support is always positive infinity
     * no matter the parameters.
     *
     * @return upper bound of the support (always
     * {@code Double.POSITIVE_INFINITY})
     */
    @Override
    public double getSupportUpperBound() {
        return Double.POSITIVE_INFINITY;
    }

    /**
     * {@inheritDoc}
     *
     * The support of this distribution is connected.
     *
     * @return {@code true}
     */
    @Override
    public boolean isSupportConnected() {
        return true;
    }

    /** {@inheritDoc} */
    @Override
    public ContinuousDistribution.Sampler createSampler(final UniformRandomProvider rng) {
        // Log normal distribution sampler.
        return new LogNormalSampler(new ZigguratNormalizedGaussianSampler(rng), scale, shape)::sample;
    }
}