Java tutorial
/* * * * Copyright 2015 Skymind,Inc. * * * * Licensed 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.nd4j.linalg.api.rng.distribution; import java.util.Iterator; import org.apache.commons.math3.analysis.UnivariateFunction; import org.apache.commons.math3.analysis.solvers.UnivariateSolverUtils; 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.util.FastMath; import org.nd4j.linalg.api.iter.NdIndexIterator; import org.nd4j.linalg.api.ndarray.INDArray; import org.nd4j.linalg.api.rng.Random; import org.nd4j.linalg.factory.Nd4j; /** * Base distribution derived from apache commons math * http://commons.apache.org/proper/commons-math/ * <p/> * (specifically the {@link org.apache.commons.math3.distribution.AbstractRealDistribution} * * @author Adam Gibson */ public abstract class BaseDistribution implements Distribution { protected Random random; protected double solverAbsoluteAccuracy; public BaseDistribution(Random rng) { this.random = rng; } public BaseDistribution() { this(Nd4j.getRandom()); } /** * For a random variable {@code X} whose values are distributed according * to this distribution, this method returns {@code P(x0 < X <= x1)}. * * @param x0 Lower bound (excluded). * @param x1 Upper bound (included). * @return the probability that a random variable with this distribution * takes a value between {@code x0} and {@code x1}, excluding the lower * and including the upper endpoint. * @throws org.apache.commons.math3.exception.NumberIsTooLargeException if {@code x0 > x1}. * <p/> * The default implementation uses the identity * {@code P(x0 < X <= x1) = P(X <= x1) - P(X <= x0)} * @since 3.1 */ public double probability(double x0, double x1) { if (x0 > x1) { throw new NumberIsTooLargeException(LocalizedFormats.LOWER_ENDPOINT_ABOVE_UPPER_ENDPOINT, x0, x1, true); } return cumulativeProbability(x1) - cumulativeProbability(x0); } /** * {@inheritDoc} * <p/> * The default implementation returns * <ul> * <li>{@link #getSupportLowerBound()} for {@code p = 0},</li> * <li>{@link #getSupportUpperBound()} for {@code p = 1}.</li> * </ul> */ @Override public double inverseCumulativeProbability(final double p) throws OutOfRangeException { /* * IMPLEMENTATION NOTES * -------------------- * Where applicable, use is made of the one-sided Chebyshev inequality * to bracket the root. This inequality states that * P(X - mu >= k * sig) <= 1 / (1 + k^2), * mu: mean, sig: standard deviation. Equivalently * 1 - P(X < mu + k * sig) <= 1 / (1 + k^2), * F(mu + k * sig) >= k^2 / (1 + k^2). * * For k = sqrt(p / (1 - p)), we find * F(mu + k * sig) >= p, * and (mu + k * sig) is an upper-bound for the root. * * Then, introducing Y = -X, mean(Y) = -mu, sd(Y) = sig, and * P(Y >= -mu + k * sig) <= 1 / (1 + k^2), * P(-X >= -mu + k * sig) <= 1 / (1 + k^2), * P(X <= mu - k * sig) <= 1 / (1 + k^2), * F(mu - k * sig) <= 1 / (1 + k^2). * * For k = sqrt((1 - p) / p), we find * F(mu - k * sig) <= p, * and (mu - k * sig) is a lower-bound for the root. * * In cases where the Chebyshev inequality does not apply, geometric * progressions 1, 2, 4, ... and -1, -2, -4, ... are used to bracket * the root. */ if (p < 0.0 || p > 1.0) { throw new OutOfRangeException(p, 0, 1); } double lowerBound = getSupportLowerBound(); if (p == 0.0) { return lowerBound; } double upperBound = getSupportUpperBound(); if (p == 1.0) { return upperBound; } final double mu = getNumericalMean(); final double sig = FastMath.sqrt(getNumericalVariance()); final boolean chebyshevApplies; chebyshevApplies = !(Double.isInfinite(mu) || Double.isNaN(mu) || Double.isInfinite(sig) || Double.isNaN(sig)); if (lowerBound == Double.NEGATIVE_INFINITY) { if (chebyshevApplies) { lowerBound = mu - sig * FastMath.sqrt((1. - p) / p); } else { lowerBound = -1.0; while (cumulativeProbability(lowerBound) >= p) { lowerBound *= 2.0; } } } if (upperBound == Double.POSITIVE_INFINITY) { if (chebyshevApplies) { upperBound = mu + sig * FastMath.sqrt(p / (1. - p)); } else { upperBound = 1.0; while (cumulativeProbability(upperBound) < p) { upperBound *= 2.0; } } } final UnivariateFunction toSolve = new UnivariateFunction() { public double value(final double x) { return cumulativeProbability(x) - p; } }; double x = UnivariateSolverUtils.solve(toSolve, lowerBound, upperBound, getSolverAbsoluteAccuracy()); if (!isSupportConnected()) { /* Test for plateau. */ final double dx = getSolverAbsoluteAccuracy(); if (x - dx >= getSupportLowerBound()) { double px = cumulativeProbability(x); if (cumulativeProbability(x - dx) == px) { upperBound = x; while (upperBound - lowerBound > dx) { final double midPoint = 0.5 * (lowerBound + upperBound); if (cumulativeProbability(midPoint) < px) { lowerBound = midPoint; } else { upperBound = midPoint; } } return upperBound; } } } return x; } /** * Returns the solver absolute accuracy for inverse cumulative computation. * You can override this method in order to use a Brent solver with an * absolute accuracy different from the default. * * @return the maximum absolute error in inverse cumulative probability estimates */ protected double getSolverAbsoluteAccuracy() { return solverAbsoluteAccuracy; } /** * {@inheritDoc} */ @Override public void reseedRandomGenerator(long seed) { random.setSeed(seed); } /** * {@inheritDoc} * <p/> * The default implementation uses the * <a href="http://en.wikipedia.org/wiki/Inverse_transform_sampling"> * inversion method. * </a> */ @Override public double sample() { return inverseCumulativeProbability(random.nextDouble()); } /** * {@inheritDoc} * <p/> * The default implementation generates the sample by calling * {@link #sample()} in a loop. */ @Override public double[] sample(int sampleSize) { if (sampleSize <= 0) { throw new NotStrictlyPositiveException(LocalizedFormats.NUMBER_OF_SAMPLES, sampleSize); } double[] out = new double[sampleSize]; for (int i = 0; i < sampleSize; i++) { out[i] = sample(); } return out; } /** * {@inheritDoc} * * @return zero. * @since 3.1 */ @Override public double probability(double x) { return 0d; } @Override public INDArray sample(int[] shape) { INDArray ret = Nd4j.create(shape); Iterator<int[]> idxIter = new NdIndexIterator(shape); //For consistent values irrespective of c vs. fortran ordering int len = ret.length(); for (int i = 0; i < len; i++) { ret.putScalar(idxIter.next(), sample()); } return ret; } }