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/*******************************************************************************
* Copyright (c) 2015-2018 Skymind, Inc.
*
* This program and the accompanying materials are made available under the
* terms of the Apache License, Version 2.0 which is available at
* https://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.
*
* SPDX-License-Identifier: Apache-2.0
******************************************************************************/
package org.nd4j.linalg.api.rng.distribution.impl;
import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.apache.commons.math3.exception.NumberIsTooLargeException;
import org.apache.commons.math3.exception.OutOfRangeException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.special.Erf;
import org.apache.commons.math3.util.FastMath;
import org.nd4j.linalg.api.iter.NdIndexIterator;
import org.nd4j.linalg.api.ndarray.INDArray;
import org.nd4j.linalg.api.ops.random.impl.GaussianDistribution;
import org.nd4j.linalg.api.rng.Random;
import org.nd4j.linalg.api.rng.distribution.BaseDistribution;
import org.nd4j.linalg.factory.Nd4j;
import java.util.Iterator;
/**
* Base distribution derived from apache commons math
* http://commons.apache.org/proper/commons-math/
*
* (specifically the {@link org.apache.commons.math3.distribution.NormalDistribution}
*
* @author Adam Gibson
*/
public class NormalDistribution extends BaseDistribution {
/**
* Default inverse cumulative probability accuracy.
*
* @since 2.1
*/
public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY = 1e-9;
/**
* Serializable version identifier.
*/
private static final long serialVersionUID = 8589540077390120676L;
/**
* √(2 π)
*/
private static final double SQRT2PI = FastMath.sqrt(2 * FastMath.PI);
/**
* √(2)
*/
private static final double SQRT2 = FastMath.sqrt(2.0);
/**
* Standard deviation of this distribution.
*/
private final double standardDeviation;
/**
* Mean of this distribution.
*/
private double mean;
private INDArray means;
/**
* Inverse cumulative probability accuracy.
*/
private double solverAbsoluteAccuracy;
public NormalDistribution(Random rng, double standardDeviation, INDArray means) {
super(rng);
this.standardDeviation = standardDeviation;
this.means = means;
}
public NormalDistribution(double standardDeviation, INDArray means) {
this.standardDeviation = standardDeviation;
this.means = means;
}
/**
* Create a normal distribution with mean equal to zero and standard
* deviation equal to one.
*/
public NormalDistribution() {
this(0, 1);
}
/**
* Create a normal distribution using the given mean and standard deviation.
*
* @param mean Mean for this distribution.
* @param sd Standard deviation for this distribution.
* @throws org.apache.commons.math3.exception.NotStrictlyPositiveException if {@code sd <= 0}.
*/
public NormalDistribution(double mean, double sd) throws NotStrictlyPositiveException {
this(mean, sd, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
}
public NormalDistribution(Random rng, double mean, double sd) throws NotStrictlyPositiveException {
this(rng, mean, sd, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
}
/**
* Create a normal distribution using the given mean, standard deviation and
* inverse cumulative distribution accuracy.
*
* @param mean Mean for this distribution.
* @param sd Standard deviation for this distribution.
* @param inverseCumAccuracy Inverse cumulative probability accuracy.
* @throws NotStrictlyPositiveException if {@code sd <= 0}.
* @since 2.1
*/
public NormalDistribution(double mean, double sd, double inverseCumAccuracy) throws NotStrictlyPositiveException {
this(Nd4j.getRandom(), mean, sd, inverseCumAccuracy);
}
/**
* Creates a normal distribution.
*
* @param rng Random number generator.
* @param mean Mean for this distribution.
* @param sd Standard deviation for this distribution.
* @param inverseCumAccuracy Inverse cumulative probability accuracy.
* @throws NotStrictlyPositiveException if {@code sd <= 0}.
* @since 3.1
*/
public NormalDistribution(Random rng, double mean, double sd, double inverseCumAccuracy)
throws NotStrictlyPositiveException {
super(rng);
if (sd <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.STANDARD_DEVIATION, sd);
}
this.mean = mean;
standardDeviation = sd;
solverAbsoluteAccuracy = inverseCumAccuracy;
}
public NormalDistribution(INDArray mean, double std) {
this.means = mean;
this.standardDeviation = std;
this.random = Nd4j.getRandom();
}
/**
* Access the mean.
*
* @return the mean for this distribution.
*/
public double getMean() {
return mean;
}
/**
* Access the standard deviation.
*
* @return the standard deviation for this distribution.
*/
public double getStandardDeviation() {
return standardDeviation;
}
/**
* {@inheritDoc}
*/
public double density(double x) {
if (means != null)
throw new IllegalStateException("Unable to sample from more than one mean");
final double x0 = x - mean;
final double x1 = x0 / standardDeviation;
return FastMath.exp(-0.5 * x1 * x1) / (standardDeviation * SQRT2PI);
}
/**
* {@inheritDoc}
*
* If {@code x} is more than 40 standard deviations from the mean, 0 or 1
* is returned, as in these cases the actual value is within
* {@code Double.MIN_VALUE} of 0 or 1.
*/
public double cumulativeProbability(double x) {
if (means != null)
throw new IllegalStateException("Unable to sample from more than one mean");
final double dev = x - mean;
if (FastMath.abs(dev) > 40 * standardDeviation) {
return dev < 0 ? 0.0d : 1.0d;
}
return 0.5 * (1 + Erf.erf(dev / (standardDeviation * SQRT2)));
}
/**
* {@inheritDoc}
*
* @since 3.2
*/
@Override
public double inverseCumulativeProbability(final double p) throws OutOfRangeException {
if (p < 0.0 || p > 1.0) {
throw new OutOfRangeException(p, 0, 1);
}
if (means != null)
throw new IllegalStateException("Unable to sample from more than one mean");
return mean + standardDeviation * SQRT2 * Erf.erfInv(2 * p - 1);
}
/**
* {@inheritDoc}
*
* @deprecated See {@link org.apache.commons.math3.distribution.RealDistribution#cumulativeProbability(double, double)}
*/
@Override
@Deprecated
public double cumulativeProbability(double x0, double x1) throws NumberIsTooLargeException {
return probability(x0, x1);
}
/**
* {@inheritDoc}
*/
@Override
public double probability(double x0, double x1) throws NumberIsTooLargeException {
if (x0 > x1) {
throw new NumberIsTooLargeException(LocalizedFormats.LOWER_ENDPOINT_ABOVE_UPPER_ENDPOINT, x0, x1, true);
}
final double denom = standardDeviation * SQRT2;
final double v0 = (x0 - mean) / denom;
final double v1 = (x1 - mean) / denom;
return 0.5 * Erf.erf(v0, v1);
}
/**
* {@inheritDoc}
*/
@Override
protected double getSolverAbsoluteAccuracy() {
return solverAbsoluteAccuracy;
}
/**
* {@inheritDoc}
*
* For mean parameter {@code mu}, the mean is {@code mu}.
*/
public double getNumericalMean() {
return getMean();
}
/**
* {@inheritDoc}
*
* For standard deviation parameter {@code s}, the variance is {@code s^2}.
*/
public double getNumericalVariance() {
final double s = getStandardDeviation();
return s * s;
}
/**
* {@inheritDoc}
*
* The lower bound of the support is always negative infinity
* no matter the parameters.
*
* @return lower bound of the support (always
* {@code Double.NEGATIVE_INFINITY})
*/
public double getSupportLowerBound() {
return Double.NEGATIVE_INFINITY;
}
/**
* {@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})
*/
public double getSupportUpperBound() {
return Double.POSITIVE_INFINITY;
}
/**
* {@inheritDoc}
*/
public boolean isSupportLowerBoundInclusive() {
return false;
}
/**
* {@inheritDoc}
*/
public boolean isSupportUpperBoundInclusive() {
return false;
}
/**
* {@inheritDoc}
*
* The support of this distribution is connected.
*
* @return {@code true}
*/
public boolean isSupportConnected() {
return true;
}
/**
* {@inheritDoc}
*/
@Override
public double sample() {
if (means != null)
throw new IllegalStateException("Unable to sample from more than one mean");
return standardDeviation * random.nextGaussian() + mean;
}
@Override
public INDArray sample(int[] shape) {
final INDArray ret = Nd4j.createUninitialized(shape, Nd4j.order());
return sample(ret);
}
@Override
public INDArray sample(INDArray ret) {
if (random.getStatePointer() != null) {
if (means != null) {
return Nd4j.getExecutioner().exec(new GaussianDistribution(
ret, means, standardDeviation), random);
} else {
return Nd4j.getExecutioner().exec(new GaussianDistribution(
ret, mean, standardDeviation), random);
}
} else {
Iterator idxIter = new NdIndexIterator(ret.shape()); //For consistent values irrespective of c vs. fortran ordering
long len = ret.length();
if (means != null) {
for (int i = 0; i < len; i++) {
long[] idx = idxIter.next();
ret.putScalar(idx, standardDeviation * random.nextGaussian() + means.getDouble(idx));
}
} else {
for (int i = 0; i < len; i++) {
ret.putScalar(idxIter.next(), standardDeviation * random.nextGaussian() + mean);
}
}
return ret;
}
}
}
