/*
* 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.
*/
//
// 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
// computed 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;
}
public static double sign(final double x) {
if (x < 0.d) {
return -1.d;
} else if (x > 0.d) {
return 1.d;
}
return 0; // 0 or NaN
}
}