Java tutorial
/* * Hivemall: Hive scalable Machine Learning Library * * Copyright (C) 2015 Makoto YUI * Copyright (C) 2013-2015 National Institute of Advanced Industrial Science and Technology (AIST) * * 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. */ // // 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 hivemall.utils.math; import java.util.Random; import javax.annotation.Nonnull; public final class MathUtils { private MathUtils() { } /** * Returns a bit mask for the specified number of bits. */ public static int bitMask(final int numberOfBits) { if (numberOfBits >= 32) { return -1; } return (numberOfBits == 0 ? 0 : powerOf(2, numberOfBits) - 1); } /** * Power of method for integer math. */ public static int powerOf(final int value, final int powerOf) { if (powerOf == 0) { return 0; } int r = value; for (int x = 1; x < powerOf; x++) { r = r * value; } return r; } /** * Returns the number of bits required to store a number. */ public static int bitsRequired(int value) { int bits = 0; while (value != 0) { bits++; value >>= 1; } return bits; } public static double sigmoid(final double x) { double x2 = Math.max(Math.min(x, 23.d), -23.d); return 1.d / (1.d + Math.exp(-x2)); } public static double lnSigmoid(final double x) { double ex = Math.exp(-x); return ex / (1.d + ex); } /** * <a href="https://en.wikipedia.org/wiki/Logit">Logit</a> is the inverse of * {@link #sigmoid(double)} function. */ public static double logit(final double p) { return Math.log(p / (1.d - p)); } public static double logit(final double p, final double hi, final double lo) { return Math.log((p - lo) / (hi - p)); } /** * Returns the inverse erf. This code is based on erfInv() in * org.apache.commons.math3.special.Erf. * <p> * This implementation is described in the paper: <a * href="http://people.maths.ox.ac.uk/gilesm/files/gems_erfinv.pdf">Approximating the erfinv * function</a> by Mike Giles, Oxford-Man Institute of Quantitative Finance, which was published * in GPU Computing Gems, volume 2, 2010. The source code is available <a * href="http://gpucomputing.net/?q=node/1828">here</a>. * </p> * * @param x the value * @return t such that x = erf(t) */ public static double inverseErf(final double x) { // beware that the logarithm argument must be // commputed as (1.0 - x) * (1.0 + x), // it must NOT be simplified as 1.0 - x * x as this // would induce rounding errors near the boundaries +/-1 double w = -Math.log((1.0 - x) * (1.0 + x)); double p; if (w < 6.25) { w = w - 3.125; p = -3.6444120640178196996e-21; p = -1.685059138182016589e-19 + p * w; p = 1.2858480715256400167e-18 + p * w; p = 1.115787767802518096e-17 + p * w; p = -1.333171662854620906e-16 + p * w; p = 2.0972767875968561637e-17 + p * w; p = 6.6376381343583238325e-15 + p * w; p = -4.0545662729752068639e-14 + p * w; p = -8.1519341976054721522e-14 + p * w; p = 2.6335093153082322977e-12 + p * w; p = -1.2975133253453532498e-11 + p * w; p = -5.4154120542946279317e-11 + p * w; p = 1.051212273321532285e-09 + p * w; p = -4.1126339803469836976e-09 + p * w; p = -2.9070369957882005086e-08 + p * w; p = 4.2347877827932403518e-07 + p * w; p = -1.3654692000834678645e-06 + p * w; p = -1.3882523362786468719e-05 + p * w; p = 0.0001867342080340571352 + p * w; p = -0.00074070253416626697512 + p * w; p = -0.0060336708714301490533 + p * w; p = 0.24015818242558961693 + p * w; p = 1.6536545626831027356 + p * w; } else if (w < 16.0) { w = Math.sqrt(w) - 3.25; p = 2.2137376921775787049e-09; p = 9.0756561938885390979e-08 + p * w; p = -2.7517406297064545428e-07 + p * w; p = 1.8239629214389227755e-08 + p * w; p = 1.5027403968909827627e-06 + p * w; p = -4.013867526981545969e-06 + p * w; p = 2.9234449089955446044e-06 + p * w; p = 1.2475304481671778723e-05 + p * w; p = -4.7318229009055733981e-05 + p * w; p = 6.8284851459573175448e-05 + p * w; p = 2.4031110387097893999e-05 + p * w; p = -0.0003550375203628474796 + p * w; p = 0.00095328937973738049703 + p * w; p = -0.0016882755560235047313 + p * w; p = 0.0024914420961078508066 + p * w; p = -0.0037512085075692412107 + p * w; p = 0.005370914553590063617 + p * w; p = 1.0052589676941592334 + p * w; p = 3.0838856104922207635 + p * w; } else if (!Double.isInfinite(w)) { w = Math.sqrt(w) - 5.0; p = -2.7109920616438573243e-11; p = -2.5556418169965252055e-10 + p * w; p = 1.5076572693500548083e-09 + p * w; p = -3.7894654401267369937e-09 + p * w; p = 7.6157012080783393804e-09 + p * w; p = -1.4960026627149240478e-08 + p * w; p = 2.9147953450901080826e-08 + p * w; p = -6.7711997758452339498e-08 + p * w; p = 2.2900482228026654717e-07 + p * w; p = -9.9298272942317002539e-07 + p * w; p = 4.5260625972231537039e-06 + p * w; p = -1.9681778105531670567e-05 + p * w; p = 7.5995277030017761139e-05 + p * w; p = -0.00021503011930044477347 + p * w; p = -0.00013871931833623122026 + p * w; p = 1.0103004648645343977 + p * w; p = 4.8499064014085844221 + p * w; } else { // this branch does not appears in the original code, it // was added because the previous branch does not handle // x = +/-1 correctly. In this case, w is positive infinity // and as the first coefficient (-2.71e-11) is negative. // Once the first multiplication is done, p becomes negative // infinity and remains so throughout the polynomial evaluation. // So the branch above incorrectly returns negative infinity // instead of the correct positive infinity. p = Double.POSITIVE_INFINITY; } return p * x; } public static int moduloPowerOfTwo(final int x, final int powerOfTwoY) { return x & (powerOfTwoY - 1); } public static float l2norm(final float[] elements) { double sqsum = 0.d; for (float e : elements) { sqsum += (e * e); } return (float) Math.sqrt(sqsum); } public static double gaussian(final double mean, final double stddev, @Nonnull final Random rnd) { return mean + (stddev * rnd.nextGaussian()); } public static double lognormal(final double mean, final double stddev, @Nonnull final Random rnd) { return Math.exp(gaussian(mean, stddev, rnd)); } public static int sign(final short v) { return v < 0 ? -1 : 1; } public static float sign(final float v) { return v < 0.f ? -1.f : 1.f; } public static double log(final double n, final int base) { return Math.log(n) / Math.log(base); } public static int floorDiv(final int x, final int y) { int r = x / y; // if the signs are different and modulo not zero, round down if ((x ^ y) < 0 && (r * y != x)) { r--; } return r; } public static long floorDiv(final long x, final long y) { long r = x / y; // if the signs are different and modulo not zero, round down if ((x ^ y) < 0 && (r * y != x)) { r--; } return r; } public static boolean equals(@Nonnull final float value, final float expected, final float delta) { if (Math.abs(expected - value) > delta) { return false; } return true; } public static boolean equals(@Nonnull final double value, final double expected, final double delta) { if (Math.abs(expected - value) > delta) { return false; } return true; } public static boolean almostEquals(@Nonnull final float value, final float expected, final float delta) { return equals(value, expected, 1E-15f); } public static boolean almostEquals(@Nonnull final double value, final double expected, final double delta) { return equals(value, expected, 1E-15d); } public static boolean closeToZero(@Nonnull final float value) { if (Math.abs(value) > 1E-15f) { return false; } return true; } public static boolean closeToZero(@Nonnull final double value) { if (Math.abs(value) > 1E-15d) { return false; } return true; } }