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The Apache Commons RNG Sampling module provides samplers for various distributions.
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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.rng.sampling.distribution;

import org.apache.commons.rng.UniformRandomProvider;

/**
 * Sampling from a Gaussian distribution with given mean and
 * standard deviation.
 *
 * Note
 *
 * The mean and standard deviation are validated to ensure they are finite. This prevents
 * generation of NaN samples by avoiding invalid arithmetic (inf * 0 or inf - inf).
 * However use of an extremely large standard deviation and/or mean may result in samples that are
 * infinite; that is the parameters are not validated to prevent truncation of the output
 * distribution.
 *
 * @since 1.1
 */
public class GaussianSampler implements SharedStateContinuousSampler {
    /** Mean. */
    private final double mean;
    /** standardDeviation. */
    private final double standardDeviation;
    /** Normalized Gaussian sampler. */
    private final NormalizedGaussianSampler normalized;

    /**
     * Create an instance.
     *
     * @param normalized Generator of N(0,1) Gaussian distributed random numbers.
     * @param mean Mean of the Gaussian distribution.
     * @param standardDeviation Standard deviation of the Gaussian distribution.
     * @throws IllegalArgumentException if {@code standardDeviation <= 0} or is infinite;
     * or {@code mean} is infinite
     */
    public GaussianSampler(NormalizedGaussianSampler normalized,
                           double mean,
                           double standardDeviation) {
        // Validation before java.lang.Object constructor exits prevents partially initialized object
        this(InternalUtils.requireFinite(mean, "mean"),
             InternalUtils.requireStrictlyPositiveFinite(standardDeviation, "standardDeviation"),
             normalized);
    }

    /**
     * @param mean Mean of the Gaussian distribution.
     * @param standardDeviation Standard deviation of the Gaussian distribution.
     * @param normalized Generator of N(0,1) Gaussian distributed random numbers.
     */
    private GaussianSampler(double mean,
                            double standardDeviation,
                            NormalizedGaussianSampler normalized) {
        this.normalized = normalized;
        this.mean = mean;
        this.standardDeviation = standardDeviation;
    }

    /** {@inheritDoc} */
    @Override
    public double sample() {
        return standardDeviation * normalized.sample() + mean;
    }

    /** {@inheritDoc} */
    @Override
    public String toString() {
        return "Gaussian deviate [" + normalized.toString() + "]";
    }

    /**
     * {@inheritDoc}
     *
     * 
Note: This function is available if the underlying {@link NormalizedGaussianSampler}
     * is a {@link org.apache.commons.rng.sampling.SharedStateSampler SharedStateSampler}.
     * Otherwise a run-time exception is thrown.
     *
     * @throws UnsupportedOperationException if the underlying sampler is not a
     * {@link org.apache.commons.rng.sampling.SharedStateSampler SharedStateSampler} or
     * does not return a {@link NormalizedGaussianSampler} when sharing state.
     *
     * @since 1.3
     */
    @Override
    public SharedStateContinuousSampler withUniformRandomProvider(UniformRandomProvider rng) {
        return new GaussianSampler(mean, standardDeviation,
            InternalUtils.newNormalizedGaussianSampler(normalized, rng));
    }

    /**
     * Create a new normalised Gaussian sampler.
     *
     * Note: The shared-state functionality is available if the {@link NormalizedGaussianSampler}
     * is a {@link org.apache.commons.rng.sampling.SharedStateSampler SharedStateSampler}.
     * Otherwise a run-time exception will be thrown when the sampler is used to share state.
     *
     * @param normalized Generator of N(0,1) Gaussian distributed random numbers.
     * @param mean Mean of the Gaussian distribution.
     * @param standardDeviation Standard deviation of the Gaussian distribution.
     * @return the sampler
     * @throws IllegalArgumentException if {@code standardDeviation <= 0} or is infinite;
     * or {@code mean} is infinite
     * @see #withUniformRandomProvider(UniformRandomProvider)
     * @since 1.3
     */
    public static SharedStateContinuousSampler of(NormalizedGaussianSampler normalized,
                                                  double mean,
                                                  double standardDeviation) {
        return new GaussianSampler(normalized, mean, standardDeviation);
    }
}