core/src/main/java/hivemall/utils/math/MathUtils.java - incubator-hivemall - Git at Google

 /*
  * 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 static java.lang.Math.abs;

 import java.util.Random;

 import javax.annotation.Nonnegative;
 import javax.annotation.Nonnull;
 import javax.annotation.Nullable;

 import org.apache.commons.math3.special.Gamma;

 public final class MathUtils {
     public static final double LOG2 = Math.log(2);

     private MathUtils() {}

     /**
      * @return secant 1 / cos(d)
      */
     public static double sec(final double d) {
         return 1.d / Math.cos(d);
     }

     public static int divideAndRoundUp(final int num, final int divisor) {
         if (divisor == 0) {
             throw new ArithmeticException("/ by zero");
         }
         final int sign = (num > 0 ? 1 : -1) * (divisor > 0 ? 1 : -1);
         final int div = abs(divisor);
         return sign * (abs(num) + div - 1) / div;
     }

     /**
      * 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 int sign(final float v) {
         return v < 0.f ? -1 : 1;
     }

     public static double square(final double d) {
         return d * d;
     }

     public static double log(final double n, final int base) {
         return Math.log(n) / Math.log(base);
     }

     public static double log2(final double n) {
         return Math.log(n) / LOG2;
     }

     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(final float value, final float expected, final float delta) {
         if (Double.isNaN(value)) {
             return false;
         }
         if (Math.abs(expected - value) > delta) {
             return false;
         }
         return true;
     }

     public static boolean equals(final double value, final double expected, final double delta) {
         if (Double.isNaN(value)) {
             return false;
         }
         if (Math.abs(expected - value) > delta) {
             return false;
         }
         return true;
     }

     public static boolean almostEquals(final float value, final float expected) {
         return equals(value, expected, 1E-15f);
     }

     public static boolean almostEquals(final double value, final double expected) {
         return equals(value, expected, 1E-15d);
     }

     public static boolean closeToZero(final float value) {
         return closeToZero(value, 1E-15f);
     }

     public static boolean closeToZero(final float value, @Nonnegative final float tol) {
         if (value == 0.f) {
             return true;
         }
         return Math.abs(value) <= tol;
     }

     public static boolean closeToZero(final double value) {
         return closeToZero(value, 1E-15d);
     }

     public static boolean closeToZero(final double value, @Nonnegative final double tol) {
         if (value == 0.d) {
             return true;
         }
         return Math.abs(value) <= tol;
     }

     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
     }

     @Nonnull
     public static int[] permutation(@Nonnegative final int size) {
         final int[] perm = new int[size];
         for (int i = 0; i < size; i++) {
             perm[i] = i;
         }
         return perm;
     }

     @Nonnull
     public static int[] permutation(@Nonnegative final int start, @Nonnegative final int size) {
         final int[] perm = new int[size];
         for (int i = 0; i < size; i++) {
             perm[i] = start + i;
         }
         return perm;
     }

     public static double sum(@Nullable final float[] arr) {
         if (arr == null) {
             return 0.d;
         }

         double sum = 0.d;
         for (float v : arr) {
             sum += v;
         }
         return sum;
     }

     public static void add(@Nonnull final float[] src, @Nonnull final float[] dst, final int size) {
         for (int i = 0; i < size; i++) {
             dst[i] += src[i];
         }
     }

     public static void add(@Nonnull final float[] src, @Nonnull final double[] dst,
             final int size) {
         for (int i = 0; i < size; i++) {
             dst[i] += src[i];
         }
     }

     @Nonnull
     public static float[] digamma(@Nonnull final float[] arr) {
         final int k = arr.length;
         final float[] ret = new float[k];
         for (int i = 0; i < k; i++) {
             ret[i] = (float) Gamma.digamma(arr[i]);
         }
         return ret;
     }

     @Nonnull
     public static double[] digamma(@Nonnull final double[] arr) {
         final int k = arr.length;
         final double[] ret = new double[k];
         for (int i = 0; i < k; i++) {
             ret[i] = Gamma.digamma(arr[i]);
         }
         return ret;
     }

     public static float logsumexp(@Nonnull final float[] arr) {
         if (arr.length == 0) {
             return 0.f;
         }
         float max = 0.f;
         for (final float v : arr) {
             if (v > max) {
                 max = v;
             }
         }
         return logsumexp(arr, max);
     }

     public static float logsumexp(@Nonnull final float[] arr, final float max) {
         double logsumexp = 0.d;
         for (final float v : arr) {
             logsumexp += Math.exp(v - max);
         }
         logsumexp = Math.log(logsumexp) + max;
         return (float) logsumexp;
     }

     public static double logsumexp(@Nonnull final double[] arr) {
         if (arr.length == 0) {
             return 0.d;
         }
         double max = 0.d;
         for (final double v : arr) {
             if (v > max) {
                 max = v;
             }
         }
         return logsumexp(arr, max);
     }

     public static double logsumexp(@Nonnull final double[] arr, final double max) {
         double logsumexp = 0.d;
         for (final double v : arr) {
             logsumexp += Math.exp(v - max);
         }
         return Math.log(logsumexp) + max;
     }

     @Nonnull
     public static float[] l1normalize(@Nonnull final float[] arr) {
         double sum = 0.d;
         int size = arr.length;
         for (int i = 0; i < size; i++) {
             sum += Math.abs(arr[i]);
         }
         if (sum == 0.d) {
             return new float[size];
         }
         // floating point multiplication is faster than division
         final double multiplier = 1.d / sum;
         for (int i = 0; i < size; i++) {
             arr[i] *= multiplier;
         }
         return arr;
     }

     public static float clip(final float v, final float min, final float max) {
         return Math.max(Math.min(v, max), min);
     }

     public static double clip(final double v, final double min, final double max) {
         return Math.max(Math.min(v, max), min);
     }

 }
	/*
	* 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 static java.lang.Math.abs;

	import java.util.Random;

	import javax.annotation.Nonnegative;
	import javax.annotation.Nonnull;
	import javax.annotation.Nullable;

	import org.apache.commons.math3.special.Gamma;

	public final class MathUtils {
	public static final double LOG2 = Math.log(2);

	private MathUtils() {}

	/**
	* @return secant 1 / cos(d)
	*/
	public static double sec(final double d) {
	return 1.d / Math.cos(d);
	}

	public static int divideAndRoundUp(final int num, final int divisor) {
	if (divisor == 0) {
	throw new ArithmeticException("/ by zero");
	}
	final int sign = (num > 0 ? 1 : -1) * (divisor > 0 ? 1 : -1);
	final int div = abs(divisor);
	return sign * (abs(num) + div - 1) / div;
	}

	/**
	* 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 int sign(final float v) {
	return v < 0.f ? -1 : 1;
	}

	public static double square(final double d) {
	return d * d;
	}

	public static double log(final double n, final int base) {
	return Math.log(n) / Math.log(base);
	}

	public static double log2(final double n) {
	return Math.log(n) / LOG2;
	}

	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(final float value, final float expected, final float delta) {
	if (Double.isNaN(value)) {
	return false;
	}
	if (Math.abs(expected - value) > delta) {
	return false;
	}
	return true;
	}

	public static boolean equals(final double value, final double expected, final double delta) {
	if (Double.isNaN(value)) {
	return false;
	}
	if (Math.abs(expected - value) > delta) {
	return false;
	}
	return true;
	}

	public static boolean almostEquals(final float value, final float expected) {
	return equals(value, expected, 1E-15f);
	}

	public static boolean almostEquals(final double value, final double expected) {
	return equals(value, expected, 1E-15d);
	}

	public static boolean closeToZero(final float value) {
	return closeToZero(value, 1E-15f);
	}

	public static boolean closeToZero(final float value, @Nonnegative final float tol) {
	if (value == 0.f) {
	return true;
	}
	return Math.abs(value) <= tol;
	}

	public static boolean closeToZero(final double value) {
	return closeToZero(value, 1E-15d);
	}

	public static boolean closeToZero(final double value, @Nonnegative final double tol) {
	if (value == 0.d) {
	return true;
	}
	return Math.abs(value) <= tol;
	}

	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
	}

	@Nonnull
	public static int[] permutation(@Nonnegative final int size) {
	final int[] perm = new int[size];
	for (int i = 0; i < size; i++) {
	perm[i] = i;
	}
	return perm;
	}

	@Nonnull
	public static int[] permutation(@Nonnegative final int start, @Nonnegative final int size) {
	final int[] perm = new int[size];
	for (int i = 0; i < size; i++) {
	perm[i] = start + i;
	}
	return perm;
	}

	public static double sum(@Nullable final float[] arr) {
	if (arr == null) {
	return 0.d;
	}

	double sum = 0.d;
	for (float v : arr) {
	sum += v;
	}
	return sum;
	}

	public static void add(@Nonnull final float[] src, @Nonnull final float[] dst, final int size) {
	for (int i = 0; i < size; i++) {
	dst[i] += src[i];
	}
	}

	public static void add(@Nonnull final float[] src, @Nonnull final double[] dst,
	final int size) {
	for (int i = 0; i < size; i++) {
	dst[i] += src[i];
	}
	}

	@Nonnull
	public static float[] digamma(@Nonnull final float[] arr) {
	final int k = arr.length;
	final float[] ret = new float[k];
	for (int i = 0; i < k; i++) {
	ret[i] = (float) Gamma.digamma(arr[i]);
	}
	return ret;
	}

	@Nonnull
	public static double[] digamma(@Nonnull final double[] arr) {
	final int k = arr.length;
	final double[] ret = new double[k];
	for (int i = 0; i < k; i++) {
	ret[i] = Gamma.digamma(arr[i]);
	}
	return ret;
	}

	public static float logsumexp(@Nonnull final float[] arr) {
	if (arr.length == 0) {
	return 0.f;
	}
	float max = 0.f;
	for (final float v : arr) {
	if (v > max) {
	max = v;
	}
	}
	return logsumexp(arr, max);
	}

	public static float logsumexp(@Nonnull final float[] arr, final float max) {
	double logsumexp = 0.d;
	for (final float v : arr) {
	logsumexp += Math.exp(v - max);
	}
	logsumexp = Math.log(logsumexp) + max;
	return (float) logsumexp;
	}

	public static double logsumexp(@Nonnull final double[] arr) {
	if (arr.length == 0) {
	return 0.d;
	}
	double max = 0.d;
	for (final double v : arr) {
	if (v > max) {
	max = v;
	}
	}
	return logsumexp(arr, max);
	}

	public static double logsumexp(@Nonnull final double[] arr, final double max) {
	double logsumexp = 0.d;
	for (final double v : arr) {
	logsumexp += Math.exp(v - max);
	}
	return Math.log(logsumexp) + max;
	}

	@Nonnull
	public static float[] l1normalize(@Nonnull final float[] arr) {
	double sum = 0.d;
	int size = arr.length;
	for (int i = 0; i < size; i++) {
	sum += Math.abs(arr[i]);
	}
	if (sum == 0.d) {
	return new float[size];
	}
	// floating point multiplication is faster than division
	final double multiplier = 1.d / sum;
	for (int i = 0; i < size; i++) {
	arr[i] *= multiplier;
	}
	return arr;
	}

	public static float clip(final float v, final float min, final float max) {
	return Math.max(Math.min(v, max), min);
	}

	public static double clip(final double v, final double min, final double max) {
	return Math.max(Math.min(v, max), min);
	}

	}