1530 lines
52 KiB
Java
1530 lines
52 KiB
Java
/*
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* Copyright (c) 2010 The Broad Institute
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*
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* Permission is hereby granted, free of charge, to any person
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* obtaining a copy of this software and associated documentation
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* files (the "Software"), to deal in the Software without
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* restriction, including without limitation the rights to use,
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* copy, modify, merge, publish, distribute, sublicense, and/or sell
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* copies of the Software, and to permit persons to whom the
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* Software is furnished to do so, subject to the following
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* conditions:
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*
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* The above copyright notice and this permission notice shall be
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* included in all copies or substantial portions of the Software.
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*
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
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* OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
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* HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
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* WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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* FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR
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* THE USE OR OTHER DEALINGS IN THE SOFTWARE.
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*/
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package org.broadinstitute.sting.utils;
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import com.google.java.contract.Ensures;
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import com.google.java.contract.Requires;
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import net.sf.samtools.SAMRecord;
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import org.broadinstitute.sting.gatk.GenomeAnalysisEngine;
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import org.broadinstitute.sting.utils.exceptions.UserException;
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import java.math.BigDecimal;
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import java.util.*;
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/**
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* MathUtils is a static class (no instantiation allowed!) with some useful math methods.
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*
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* @author Kiran Garimella
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*/
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public class MathUtils {
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/**
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* Private constructor. No instantiating this class!
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*/
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private MathUtils() {
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}
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public static final double[] log10Cache;
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private static final double[] jacobianLogTable;
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private static final double JACOBIAN_LOG_TABLE_STEP = 0.001;
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private static final double MAX_JACOBIAN_TOLERANCE = 10.0;
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private static final int JACOBIAN_LOG_TABLE_SIZE = (int) (MAX_JACOBIAN_TOLERANCE / JACOBIAN_LOG_TABLE_STEP) + 1;
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private static final int MAXN = 11000;
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private static final int LOG10_CACHE_SIZE = 4 * MAXN; // we need to be able to go up to 2*(2N) when calculating some of the coefficients
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static {
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log10Cache = new double[LOG10_CACHE_SIZE];
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jacobianLogTable = new double[JACOBIAN_LOG_TABLE_SIZE];
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log10Cache[0] = Double.NEGATIVE_INFINITY;
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for (int k = 1; k < LOG10_CACHE_SIZE; k++)
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log10Cache[k] = Math.log10(k);
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for (int k = 0; k < JACOBIAN_LOG_TABLE_SIZE; k++) {
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jacobianLogTable[k] = Math.log10(1.0 + Math.pow(10.0, -((double) k) * JACOBIAN_LOG_TABLE_STEP));
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}
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}
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// A fast implementation of the Math.round() method. This method does not perform
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// under/overflow checking, so this shouldn't be used in the general case (but is fine
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// if one is already make those checks before calling in to the rounding).
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public static int fastRound(double d) {
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return (d > 0) ? (int) (d + 0.5d) : (int) (d - 0.5d);
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}
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public static double approximateLog10SumLog10(final double[] vals) {
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return approximateLog10SumLog10(vals, vals.length);
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}
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public static double approximateLog10SumLog10(final double[] vals, final int endIndex) {
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final int maxElementIndex = MathUtils.maxElementIndex(vals, endIndex);
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double approxSum = vals[maxElementIndex];
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if (approxSum == Double.NEGATIVE_INFINITY)
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return approxSum;
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for (int i = 0; i < endIndex; i++) {
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if (i == maxElementIndex || vals[i] == Double.NEGATIVE_INFINITY)
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continue;
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final double diff = approxSum - vals[i];
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if (diff < MathUtils.MAX_JACOBIAN_TOLERANCE) {
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// See notes from the 2-inout implementation below
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final int ind = fastRound(diff / MathUtils.JACOBIAN_LOG_TABLE_STEP); // hard rounding
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approxSum += MathUtils.jacobianLogTable[ind];
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}
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}
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return approxSum;
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}
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public static double approximateLog10SumLog10(double small, double big) {
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// make sure small is really the smaller value
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if (small > big) {
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final double t = big;
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big = small;
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small = t;
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}
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if (small == Double.NEGATIVE_INFINITY || big == Double.NEGATIVE_INFINITY)
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return big;
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final double diff = big - small;
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if (diff >= MathUtils.MAX_JACOBIAN_TOLERANCE)
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return big;
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// OK, so |y-x| < tol: we use the following identity then:
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// we need to compute log10(10^x + 10^y)
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// By Jacobian logarithm identity, this is equal to
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// max(x,y) + log10(1+10^-abs(x-y))
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// we compute the second term as a table lookup with integer quantization
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// we have pre-stored correction for 0,0.1,0.2,... 10.0
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final int ind = fastRound(diff / MathUtils.JACOBIAN_LOG_TABLE_STEP); // hard rounding
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return big + MathUtils.jacobianLogTable[ind];
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}
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public static double sum(Collection<? extends Number> numbers) {
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return sum(numbers, false);
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}
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public static double sum(Collection<? extends Number> numbers, boolean ignoreNan) {
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double sum = 0;
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for (Number n : numbers) {
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if (!ignoreNan || !Double.isNaN(n.doubleValue())) {
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sum += n.doubleValue();
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}
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}
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return sum;
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}
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public static int nonNanSize(Collection<Number> numbers) {
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int size = 0;
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for (Number n : numbers) {
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size += Double.isNaN(n.doubleValue()) ? 0 : 1;
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}
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return size;
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}
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public static double average(Collection<? extends Number> x) {
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return sum(x) / x.size();
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}
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public static double average(Collection<Number> numbers, boolean ignoreNan) {
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if (ignoreNan) {
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return sum(numbers, true) / nonNanSize(numbers);
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}
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else {
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return sum(numbers, false) / nonNanSize(numbers);
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}
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}
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public static double variance(Collection<Number> numbers, Number mean, boolean ignoreNan) {
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double mn = mean.doubleValue();
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double var = 0;
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for (Number n : numbers) {
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var += (!ignoreNan || !Double.isNaN(n.doubleValue())) ? (n.doubleValue() - mn) * (n.doubleValue() - mn) : 0;
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}
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if (ignoreNan) {
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return var / (nonNanSize(numbers) - 1);
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}
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return var / (numbers.size() - 1);
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}
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public static double variance(Collection<Number> numbers, Number mean) {
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return variance(numbers, mean, false);
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}
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public static double variance(Collection<Number> numbers, boolean ignoreNan) {
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return variance(numbers, average(numbers, ignoreNan), ignoreNan);
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}
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public static double variance(Collection<Number> numbers) {
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return variance(numbers, average(numbers, false), false);
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}
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public static double sum(double[] values) {
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double s = 0.0;
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for (double v : values)
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s += v;
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return s;
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}
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public static long sum(int[] x) {
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long total = 0;
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for (int v : x)
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total += v;
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return total;
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}
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/**
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* Calculates the log10 cumulative sum of an array with log10 probabilities
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*
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* @param log10p the array with log10 probabilites
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* @param upTo index in the array to calculate the cumsum up to
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* @return the log10 of the cumulative sum
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*/
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public static double log10CumulativeSumLog10(double[] log10p, int upTo) {
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return log10sumLog10(log10p, 0, upTo);
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}
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/**
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* Converts a real space array of probabilities into a log10 array
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*
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* @param prRealSpace
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* @return
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*/
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public static double[] toLog10(double[] prRealSpace) {
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double[] log10s = new double[prRealSpace.length];
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for (int i = 0; i < prRealSpace.length; i++)
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log10s[i] = Math.log10(prRealSpace[i]);
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return log10s;
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}
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public static double log10sumLog10(double[] log10p, int start) {
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return log10sumLog10(log10p, start, log10p.length);
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}
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public static double log10sumLog10(double[] log10p, int start, int finish) {
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double sum = 0.0;
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double maxValue = Utils.findMaxEntry(log10p);
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for (int i = start; i < finish; i++) {
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sum += Math.pow(10.0, log10p[i] - maxValue);
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}
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return Math.log10(sum) + maxValue;
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}
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public static double sumDoubles(List<Double> values) {
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double s = 0.0;
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for (double v : values)
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s += v;
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return s;
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}
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public static int sumIntegers(List<Integer> values) {
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int s = 0;
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for (int v : values)
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s += v;
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return s;
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}
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public static double sumLog10(double[] log10values) {
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return Math.pow(10.0, log10sumLog10(log10values));
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// double s = 0.0;
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// for ( double v : log10values) s += Math.pow(10.0, v);
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// return s;
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}
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public static double log10sumLog10(double[] log10values) {
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return log10sumLog10(log10values, 0);
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}
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public static boolean wellFormedDouble(double val) {
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return !Double.isInfinite(val) && !Double.isNaN(val);
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}
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public static double bound(double value, double minBoundary, double maxBoundary) {
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return Math.max(Math.min(value, maxBoundary), minBoundary);
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}
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public static boolean isBounded(double val, double lower, double upper) {
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return val >= lower && val <= upper;
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}
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public static boolean isPositive(double val) {
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return !isNegativeOrZero(val);
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}
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public static boolean isPositiveOrZero(double val) {
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return isBounded(val, 0.0, Double.POSITIVE_INFINITY);
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}
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public static boolean isNegativeOrZero(double val) {
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return isBounded(val, Double.NEGATIVE_INFINITY, 0.0);
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}
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public static boolean isNegative(double val) {
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return !isPositiveOrZero(val);
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}
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/**
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* Compares double values for equality (within 1e-6), or inequality.
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*
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* @param a the first double value
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* @param b the second double value
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* @return -1 if a is greater than b, 0 if a is equal to be within 1e-6, 1 if b is greater than a.
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*/
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public static byte compareDoubles(double a, double b) {
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return compareDoubles(a, b, 1e-6);
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}
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/**
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* Compares double values for equality (within epsilon), or inequality.
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*
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* @param a the first double value
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* @param b the second double value
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* @param epsilon the precision within which two double values will be considered equal
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* @return -1 if a is greater than b, 0 if a is equal to be within epsilon, 1 if b is greater than a.
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*/
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public static byte compareDoubles(double a, double b, double epsilon) {
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if (Math.abs(a - b) < epsilon) {
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return 0;
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}
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if (a > b) {
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return -1;
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}
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return 1;
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}
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/**
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* Compares float values for equality (within 1e-6), or inequality.
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*
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* @param a the first float value
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* @param b the second float value
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* @return -1 if a is greater than b, 0 if a is equal to be within 1e-6, 1 if b is greater than a.
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*/
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public static byte compareFloats(float a, float b) {
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return compareFloats(a, b, 1e-6f);
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}
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/**
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* Compares float values for equality (within epsilon), or inequality.
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*
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* @param a the first float value
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* @param b the second float value
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* @param epsilon the precision within which two float values will be considered equal
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* @return -1 if a is greater than b, 0 if a is equal to be within epsilon, 1 if b is greater than a.
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*/
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public static byte compareFloats(float a, float b, float epsilon) {
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if (Math.abs(a - b) < epsilon) {
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return 0;
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}
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if (a > b) {
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return -1;
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}
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return 1;
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}
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public static double NormalDistribution(double mean, double sd, double x) {
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double a = 1.0 / (sd * Math.sqrt(2.0 * Math.PI));
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double b = Math.exp(-1.0 * (Math.pow(x - mean, 2.0) / (2.0 * sd * sd)));
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return a * b;
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}
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public static double binomialCoefficient(int n, int k) {
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return Math.pow(10, log10BinomialCoefficient(n, k));
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}
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/**
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* Computes a binomial probability. This is computed using the formula
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* <p/>
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* B(k; n; p) = [ n! / ( k! (n - k)! ) ] (p^k)( (1-p)^k )
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* <p/>
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* where n is the number of trials, k is the number of successes, and p is the probability of success
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*
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* @param n number of Bernoulli trials
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* @param k number of successes
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* @param p probability of success
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* @return the binomial probability of the specified configuration. Computes values down to about 1e-237.
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*/
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public static double binomialProbability(int n, int k, double p) {
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return Math.pow(10, log10BinomialProbability(n, k, Math.log10(p)));
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}
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/**
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* Performs the cumulative sum of binomial probabilities, where the probability calculation is done in log space.
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*
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* @param start - start of the cumulant sum (over hits)
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* @param end - end of the cumulant sum (over hits)
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* @param total - number of attempts for the number of hits
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* @param probHit - probability of a successful hit
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* @return - returns the cumulative probability
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*/
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public static double binomialCumulativeProbability(int start, int end, int total, double probHit) {
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double cumProb = 0.0;
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double prevProb;
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BigDecimal probCache = BigDecimal.ZERO;
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for (int hits = start; hits < end; hits++) {
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prevProb = cumProb;
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double probability = binomialProbability(total, hits, probHit);
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cumProb += probability;
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if (probability > 0 && cumProb - prevProb < probability / 2) { // loss of precision
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probCache = probCache.add(new BigDecimal(prevProb));
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cumProb = 0.0;
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hits--; // repeat loop
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// prevProb changes at start of loop
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}
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}
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return probCache.add(new BigDecimal(cumProb)).doubleValue();
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}
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/**
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* Computes a multinomial coefficient efficiently avoiding overflow even for large numbers.
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* This is computed using the formula:
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* <p/>
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* M(x1,x2,...,xk; n) = [ n! / (x1! x2! ... xk!) ]
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* <p/>
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* where xi represents the number of times outcome i was observed, n is the number of total observations.
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* In this implementation, the value of n is inferred as the sum over i of xi.
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*
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* @param k an int[] of counts, where each element represents the number of times a certain outcome was observed
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* @return the multinomial of the specified configuration.
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*/
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public static double multinomialCoefficient(int[] k) {
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int n = 0;
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for (int xi : k) {
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n += xi;
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}
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return Math.pow(10, log10MultinomialCoefficient(n, k));
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}
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/**
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* Computes a multinomial probability efficiently avoiding overflow even for large numbers.
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* This is computed using the formula:
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* <p/>
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* M(x1,x2,...,xk; n; p1,p2,...,pk) = [ n! / (x1! x2! ... xk!) ] (p1^x1)(p2^x2)(...)(pk^xk)
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* <p/>
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* where xi represents the number of times outcome i was observed, n is the number of total observations, and
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* pi represents the probability of the i-th outcome to occur. In this implementation, the value of n is
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* inferred as the sum over i of xi.
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*
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* @param k an int[] of counts, where each element represents the number of times a certain outcome was observed
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* @param p a double[] of probabilities, where each element represents the probability a given outcome can occur
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* @return the multinomial probability of the specified configuration.
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*/
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public static double multinomialProbability(int[] k, double[] p) {
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if (p.length != k.length)
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throw new UserException.BadArgumentValue("p and k", "Array of log10 probabilities must have the same size as the array of number of sucesses: " + p.length + ", " + k.length);
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int n = 0;
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double[] log10P = new double[p.length];
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for (int i = 0; i < p.length; i++) {
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log10P[i] = Math.log10(p[i]);
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n += k[i];
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}
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return Math.pow(10, log10MultinomialProbability(n, k, log10P));
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}
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/**
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* calculate the Root Mean Square of an array of integers
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*
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* @param x an byte[] of numbers
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* @return the RMS of the specified numbers.
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*/
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public static double rms(byte[] x) {
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if (x.length == 0)
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return 0.0;
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double rms = 0.0;
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for (int i : x)
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rms += i * i;
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rms /= x.length;
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return Math.sqrt(rms);
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}
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/**
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* calculate the Root Mean Square of an array of integers
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*
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* @param x an int[] of numbers
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* @return the RMS of the specified numbers.
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*/
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public static double rms(int[] x) {
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if (x.length == 0)
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return 0.0;
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double rms = 0.0;
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for (int i : x)
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rms += i * i;
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rms /= x.length;
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return Math.sqrt(rms);
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}
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/**
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* calculate the Root Mean Square of an array of doubles
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*
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* @param x a double[] of numbers
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* @return the RMS of the specified numbers.
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*/
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public static double rms(Double[] x) {
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if (x.length == 0)
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return 0.0;
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double rms = 0.0;
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|
for (Double i : x)
|
|
rms += i * i;
|
|
rms /= x.length;
|
|
return Math.sqrt(rms);
|
|
}
|
|
|
|
public static double rms(Collection<Integer> l) {
|
|
if (l.size() == 0)
|
|
return 0.0;
|
|
|
|
double rms = 0.0;
|
|
for (int i : l)
|
|
rms += i * i;
|
|
rms /= l.size();
|
|
return Math.sqrt(rms);
|
|
}
|
|
|
|
public static double distanceSquared(final double[] x, final double[] y) {
|
|
double dist = 0.0;
|
|
for (int iii = 0; iii < x.length; iii++) {
|
|
dist += (x[iii] - y[iii]) * (x[iii] - y[iii]);
|
|
}
|
|
return dist;
|
|
}
|
|
|
|
public static double round(double num, int digits) {
|
|
double result = num * Math.pow(10.0, (double) digits);
|
|
result = Math.round(result);
|
|
result = result / Math.pow(10.0, (double) digits);
|
|
return result;
|
|
}
|
|
|
|
/**
|
|
* normalizes the log10-based array. ASSUMES THAT ALL ARRAY ENTRIES ARE <= 0 (<= 1 IN REAL-SPACE).
|
|
*
|
|
* @param array the array to be normalized
|
|
* @param takeLog10OfOutput if true, the output will be transformed back into log10 units
|
|
* @return a newly allocated array corresponding the normalized values in array, maybe log10 transformed
|
|
*/
|
|
public static double[] normalizeFromLog10(double[] array, boolean takeLog10OfOutput) {
|
|
return normalizeFromLog10(array, takeLog10OfOutput, false);
|
|
}
|
|
|
|
public static double[] normalizeFromLog10(double[] array, boolean takeLog10OfOutput, boolean keepInLogSpace) {
|
|
|
|
// for precision purposes, we need to add (or really subtract, since they're
|
|
// all negative) the largest value; also, we need to convert to normal-space.
|
|
double maxValue = Utils.findMaxEntry(array);
|
|
|
|
// we may decide to just normalize in log space without converting to linear space
|
|
if (keepInLogSpace) {
|
|
for (int i = 0; i < array.length; i++)
|
|
array[i] -= maxValue;
|
|
return array;
|
|
}
|
|
|
|
// default case: go to linear space
|
|
double[] normalized = new double[array.length];
|
|
|
|
for (int i = 0; i < array.length; i++)
|
|
normalized[i] = Math.pow(10, array[i] - maxValue);
|
|
|
|
// normalize
|
|
double sum = 0.0;
|
|
for (int i = 0; i < array.length; i++)
|
|
sum += normalized[i];
|
|
for (int i = 0; i < array.length; i++) {
|
|
double x = normalized[i] / sum;
|
|
if (takeLog10OfOutput)
|
|
x = Math.log10(x);
|
|
normalized[i] = x;
|
|
}
|
|
|
|
return normalized;
|
|
}
|
|
|
|
/**
|
|
* normalizes the log10-based array. ASSUMES THAT ALL ARRAY ENTRIES ARE <= 0 (<= 1 IN REAL-SPACE).
|
|
*
|
|
* @param array the array to be normalized
|
|
* @return a newly allocated array corresponding the normalized values in array
|
|
*/
|
|
public static double[] normalizeFromLog10(double[] array) {
|
|
return normalizeFromLog10(array, false);
|
|
}
|
|
|
|
public static int maxElementIndex(final double[] array) {
|
|
return maxElementIndex(array, array.length);
|
|
}
|
|
|
|
public static int maxElementIndex(final double[] array, final int endIndex) {
|
|
if (array == null)
|
|
throw new IllegalArgumentException("Array cannot be null!");
|
|
|
|
int maxI = -1;
|
|
for (int i = 0; i < endIndex; i++) {
|
|
if (maxI == -1 || array[i] > array[maxI])
|
|
maxI = i;
|
|
}
|
|
|
|
return maxI;
|
|
}
|
|
|
|
public static int maxElementIndex(final int[] array) {
|
|
return maxElementIndex(array, array.length);
|
|
}
|
|
|
|
public static int maxElementIndex(final int[] array, int endIndex) {
|
|
if (array == null)
|
|
throw new IllegalArgumentException("Array cannot be null!");
|
|
|
|
int maxI = -1;
|
|
for (int i = 0; i < endIndex; i++) {
|
|
if (maxI == -1 || array[i] > array[maxI])
|
|
maxI = i;
|
|
}
|
|
|
|
return maxI;
|
|
}
|
|
|
|
public static double arrayMax(double[] array) {
|
|
return array[maxElementIndex(array)];
|
|
}
|
|
|
|
public static double arrayMin(double[] array) {
|
|
return array[minElementIndex(array)];
|
|
}
|
|
|
|
public static int arrayMin(int[] array) {
|
|
return array[minElementIndex(array)];
|
|
}
|
|
|
|
public static byte arrayMin(byte[] array) {
|
|
return array[minElementIndex(array)];
|
|
}
|
|
|
|
public static int minElementIndex(double[] array) {
|
|
if (array == null)
|
|
throw new IllegalArgumentException("Array cannot be null!");
|
|
|
|
int minI = -1;
|
|
for (int i = 0; i < array.length; i++) {
|
|
if (minI == -1 || array[i] < array[minI])
|
|
minI = i;
|
|
}
|
|
|
|
return minI;
|
|
}
|
|
|
|
public static int minElementIndex(byte[] array) {
|
|
if (array == null)
|
|
throw new IllegalArgumentException("Array cannot be null!");
|
|
|
|
int minI = -1;
|
|
for (int i = 0; i < array.length; i++) {
|
|
if (minI == -1 || array[i] < array[minI])
|
|
minI = i;
|
|
}
|
|
|
|
return minI;
|
|
}
|
|
|
|
public static int minElementIndex(int[] array) {
|
|
if (array == null)
|
|
throw new IllegalArgumentException("Array cannot be null!");
|
|
|
|
int minI = -1;
|
|
for (int i = 0; i < array.length; i++) {
|
|
if (minI == -1 || array[i] < array[minI])
|
|
minI = i;
|
|
}
|
|
|
|
return minI;
|
|
}
|
|
|
|
public static int arrayMaxInt(List<Integer> array) {
|
|
if (array == null)
|
|
throw new IllegalArgumentException("Array cannot be null!");
|
|
if (array.size() == 0)
|
|
throw new IllegalArgumentException("Array size cannot be 0!");
|
|
|
|
int m = array.get(0);
|
|
for (int e : array)
|
|
m = Math.max(m, e);
|
|
return m;
|
|
}
|
|
|
|
public static double arrayMaxDouble(List<Double> array) {
|
|
if (array == null)
|
|
throw new IllegalArgumentException("Array cannot be null!");
|
|
if (array.size() == 0)
|
|
throw new IllegalArgumentException("Array size cannot be 0!");
|
|
|
|
double m = array.get(0);
|
|
for (double e : array)
|
|
m = Math.max(m, e);
|
|
return m;
|
|
}
|
|
|
|
public static double average(List<Long> vals, int maxI) {
|
|
long sum = 0L;
|
|
|
|
int i = 0;
|
|
for (long x : vals) {
|
|
if (i > maxI)
|
|
break;
|
|
sum += x;
|
|
i++;
|
|
//System.out.printf(" %d/%d", sum, i);
|
|
}
|
|
|
|
//System.out.printf("Sum = %d, n = %d, maxI = %d, avg = %f%n", sum, i, maxI, (1.0 * sum) / i);
|
|
|
|
return (1.0 * sum) / i;
|
|
}
|
|
|
|
public static double averageDouble(List<Double> vals, int maxI) {
|
|
double sum = 0.0;
|
|
|
|
int i = 0;
|
|
for (double x : vals) {
|
|
if (i > maxI)
|
|
break;
|
|
sum += x;
|
|
i++;
|
|
}
|
|
return (1.0 * sum) / i;
|
|
}
|
|
|
|
public static double average(List<Long> vals) {
|
|
return average(vals, vals.size());
|
|
}
|
|
|
|
public static double average(int[] x) {
|
|
int sum = 0;
|
|
for (int v : x)
|
|
sum += v;
|
|
return (double) sum / x.length;
|
|
}
|
|
|
|
public static byte average(byte[] vals) {
|
|
int sum = 0;
|
|
for (byte v : vals) {
|
|
sum += v;
|
|
}
|
|
return (byte) Math.floor(sum / vals.length);
|
|
}
|
|
|
|
public static double averageDouble(List<Double> vals) {
|
|
return averageDouble(vals, vals.size());
|
|
}
|
|
|
|
// Java Generics can't do primitive types, so I had to do this the simplistic way
|
|
|
|
public static Integer[] sortPermutation(final int[] A) {
|
|
class comparator implements Comparator<Integer> {
|
|
public int compare(Integer a, Integer b) {
|
|
if (A[a.intValue()] < A[b.intValue()]) {
|
|
return -1;
|
|
}
|
|
if (A[a.intValue()] == A[b.intValue()]) {
|
|
return 0;
|
|
}
|
|
if (A[a.intValue()] > A[b.intValue()]) {
|
|
return 1;
|
|
}
|
|
return 0;
|
|
}
|
|
}
|
|
Integer[] permutation = new Integer[A.length];
|
|
for (int i = 0; i < A.length; i++) {
|
|
permutation[i] = i;
|
|
}
|
|
Arrays.sort(permutation, new comparator());
|
|
return permutation;
|
|
}
|
|
|
|
public static Integer[] sortPermutation(final double[] A) {
|
|
class comparator implements Comparator<Integer> {
|
|
public int compare(Integer a, Integer b) {
|
|
if (A[a.intValue()] < A[b.intValue()]) {
|
|
return -1;
|
|
}
|
|
if (A[a.intValue()] == A[b.intValue()]) {
|
|
return 0;
|
|
}
|
|
if (A[a.intValue()] > A[b.intValue()]) {
|
|
return 1;
|
|
}
|
|
return 0;
|
|
}
|
|
}
|
|
Integer[] permutation = new Integer[A.length];
|
|
for (int i = 0; i < A.length; i++) {
|
|
permutation[i] = i;
|
|
}
|
|
Arrays.sort(permutation, new comparator());
|
|
return permutation;
|
|
}
|
|
|
|
public static <T extends Comparable> Integer[] sortPermutation(List<T> A) {
|
|
final Object[] data = A.toArray();
|
|
|
|
class comparator implements Comparator<Integer> {
|
|
public int compare(Integer a, Integer b) {
|
|
return ((T) data[a]).compareTo(data[b]);
|
|
}
|
|
}
|
|
Integer[] permutation = new Integer[A.size()];
|
|
for (int i = 0; i < A.size(); i++) {
|
|
permutation[i] = i;
|
|
}
|
|
Arrays.sort(permutation, new comparator());
|
|
return permutation;
|
|
}
|
|
|
|
public static int[] permuteArray(int[] array, Integer[] permutation) {
|
|
int[] output = new int[array.length];
|
|
for (int i = 0; i < output.length; i++) {
|
|
output[i] = array[permutation[i]];
|
|
}
|
|
return output;
|
|
}
|
|
|
|
public static double[] permuteArray(double[] array, Integer[] permutation) {
|
|
double[] output = new double[array.length];
|
|
for (int i = 0; i < output.length; i++) {
|
|
output[i] = array[permutation[i]];
|
|
}
|
|
return output;
|
|
}
|
|
|
|
public static Object[] permuteArray(Object[] array, Integer[] permutation) {
|
|
Object[] output = new Object[array.length];
|
|
for (int i = 0; i < output.length; i++) {
|
|
output[i] = array[permutation[i]];
|
|
}
|
|
return output;
|
|
}
|
|
|
|
public static String[] permuteArray(String[] array, Integer[] permutation) {
|
|
String[] output = new String[array.length];
|
|
for (int i = 0; i < output.length; i++) {
|
|
output[i] = array[permutation[i]];
|
|
}
|
|
return output;
|
|
}
|
|
|
|
public static <T> List<T> permuteList(List<T> list, Integer[] permutation) {
|
|
List<T> output = new ArrayList<T>();
|
|
for (int i = 0; i < permutation.length; i++) {
|
|
output.add(list.get(permutation[i]));
|
|
}
|
|
return output;
|
|
}
|
|
|
|
/**
|
|
* Draw N random elements from list.
|
|
*/
|
|
public static <T> List<T> randomSubset(List<T> list, int N) {
|
|
if (list.size() <= N) {
|
|
return list;
|
|
}
|
|
|
|
int idx[] = new int[list.size()];
|
|
for (int i = 0; i < list.size(); i++) {
|
|
idx[i] = GenomeAnalysisEngine.getRandomGenerator().nextInt();
|
|
}
|
|
|
|
Integer[] perm = sortPermutation(idx);
|
|
|
|
List<T> ans = new ArrayList<T>();
|
|
for (int i = 0; i < N; i++) {
|
|
ans.add(list.get(perm[i]));
|
|
}
|
|
|
|
return ans;
|
|
}
|
|
|
|
/**
|
|
* Draw N random elements from an array.
|
|
*
|
|
* @param array your objects
|
|
* @param n number of elements to select at random from the list
|
|
* @return a new list with the N randomly chosen elements from list
|
|
*/
|
|
@Requires({"array != null", "n>=0"})
|
|
@Ensures({"result != null", "result.length == Math.min(n, array.length)"})
|
|
public static Object[] randomSubset(final Object[] array, final int n) {
|
|
if (array.length <= n)
|
|
return array.clone();
|
|
|
|
Object[] shuffledArray = arrayShuffle(array);
|
|
Object[] result = new Object[n];
|
|
System.arraycopy(shuffledArray, 0, result, 0, n);
|
|
return result;
|
|
}
|
|
|
|
public static double percentage(double x, double base) {
|
|
return (base > 0 ? (x / base) * 100.0 : 0);
|
|
}
|
|
|
|
public static double percentage(int x, int base) {
|
|
return (base > 0 ? ((double) x / (double) base) * 100.0 : 0);
|
|
}
|
|
|
|
public static double percentage(long x, long base) {
|
|
return (base > 0 ? ((double) x / (double) base) * 100.0 : 0);
|
|
}
|
|
|
|
public static int countOccurrences(char c, String s) {
|
|
int count = 0;
|
|
for (int i = 0; i < s.length(); i++) {
|
|
count += s.charAt(i) == c ? 1 : 0;
|
|
}
|
|
return count;
|
|
}
|
|
|
|
public static <T> int countOccurrences(T x, List<T> l) {
|
|
int count = 0;
|
|
for (T y : l) {
|
|
if (x.equals(y))
|
|
count++;
|
|
}
|
|
|
|
return count;
|
|
}
|
|
|
|
public static int countOccurrences(byte element, byte[] array) {
|
|
int count = 0;
|
|
for (byte y : array) {
|
|
if (element == y)
|
|
count++;
|
|
}
|
|
|
|
return count;
|
|
}
|
|
|
|
/**
|
|
* Returns the top (larger) N elements of the array. Naive n^2 implementation (Selection Sort).
|
|
* Better than sorting if N (number of elements to return) is small
|
|
*
|
|
* @param array the array
|
|
* @param n number of top elements to return
|
|
* @return the n larger elements of the array
|
|
*/
|
|
public static Collection<Double> getNMaxElements(double[] array, int n) {
|
|
ArrayList<Double> maxN = new ArrayList<Double>(n);
|
|
double lastMax = Double.MAX_VALUE;
|
|
for (int i = 0; i < n; i++) {
|
|
double max = Double.MIN_VALUE;
|
|
for (double x : array) {
|
|
max = Math.min(lastMax, Math.max(x, max));
|
|
}
|
|
maxN.add(max);
|
|
lastMax = max;
|
|
}
|
|
return maxN;
|
|
}
|
|
|
|
/**
|
|
* Returns n random indices drawn with replacement from the range 0..(k-1)
|
|
*
|
|
* @param n the total number of indices sampled from
|
|
* @param k the number of random indices to draw (with replacement)
|
|
* @return a list of k random indices ranging from 0 to (n-1) with possible duplicates
|
|
*/
|
|
static public ArrayList<Integer> sampleIndicesWithReplacement(int n, int k) {
|
|
|
|
ArrayList<Integer> chosen_balls = new ArrayList<Integer>(k);
|
|
for (int i = 0; i < k; i++) {
|
|
//Integer chosen_ball = balls[rand.nextInt(k)];
|
|
chosen_balls.add(GenomeAnalysisEngine.getRandomGenerator().nextInt(n));
|
|
//balls.remove(chosen_ball);
|
|
}
|
|
|
|
return chosen_balls;
|
|
}
|
|
|
|
/**
|
|
* Returns n random indices drawn without replacement from the range 0..(k-1)
|
|
*
|
|
* @param n the total number of indices sampled from
|
|
* @param k the number of random indices to draw (without replacement)
|
|
* @return a list of k random indices ranging from 0 to (n-1) without duplicates
|
|
*/
|
|
static public ArrayList<Integer> sampleIndicesWithoutReplacement(int n, int k) {
|
|
ArrayList<Integer> chosen_balls = new ArrayList<Integer>(k);
|
|
|
|
for (int i = 0; i < n; i++) {
|
|
chosen_balls.add(i);
|
|
}
|
|
|
|
Collections.shuffle(chosen_balls, GenomeAnalysisEngine.getRandomGenerator());
|
|
|
|
//return (ArrayList<Integer>) chosen_balls.subList(0, k);
|
|
return new ArrayList<Integer>(chosen_balls.subList(0, k));
|
|
}
|
|
|
|
/**
|
|
* Given a list of indices into a list, return those elements of the list with the possibility of drawing list elements multiple times
|
|
*
|
|
* @param indices the list of indices for elements to extract
|
|
* @param list the list from which the elements should be extracted
|
|
* @param <T> the template type of the ArrayList
|
|
* @return a new ArrayList consisting of the elements at the specified indices
|
|
*/
|
|
static public <T> ArrayList<T> sliceListByIndices(List<Integer> indices, List<T> list) {
|
|
ArrayList<T> subset = new ArrayList<T>();
|
|
|
|
for (int i : indices) {
|
|
subset.add(list.get(i));
|
|
}
|
|
|
|
return subset;
|
|
}
|
|
|
|
public static Comparable orderStatisticSearch(int orderStat, List<Comparable> list) {
|
|
// this finds the order statistic of the list (kth largest element)
|
|
// the list is assumed *not* to be sorted
|
|
|
|
final Comparable x = list.get(orderStat);
|
|
ListIterator iterator = list.listIterator();
|
|
ArrayList lessThanX = new ArrayList();
|
|
ArrayList equalToX = new ArrayList();
|
|
ArrayList greaterThanX = new ArrayList();
|
|
|
|
for (Comparable y : list) {
|
|
if (x.compareTo(y) > 0) {
|
|
lessThanX.add(y);
|
|
}
|
|
else if (x.compareTo(y) < 0) {
|
|
greaterThanX.add(y);
|
|
}
|
|
else
|
|
equalToX.add(y);
|
|
}
|
|
|
|
if (lessThanX.size() > orderStat)
|
|
return orderStatisticSearch(orderStat, lessThanX);
|
|
else if (lessThanX.size() + equalToX.size() >= orderStat)
|
|
return orderStat;
|
|
else
|
|
return orderStatisticSearch(orderStat - lessThanX.size() - equalToX.size(), greaterThanX);
|
|
|
|
}
|
|
|
|
public static Object getMedian(List<Comparable> list) {
|
|
return orderStatisticSearch((int) Math.ceil(list.size() / 2), list);
|
|
}
|
|
|
|
public static byte getQScoreOrderStatistic(List<SAMRecord> reads, List<Integer> offsets, int k) {
|
|
// version of the order statistic calculator for SAMRecord/Integer lists, where the
|
|
// list index maps to a q-score only through the offset index
|
|
// returns the kth-largest q-score.
|
|
|
|
if (reads.size() == 0) {
|
|
return 0;
|
|
}
|
|
|
|
ArrayList lessThanQReads = new ArrayList();
|
|
ArrayList equalToQReads = new ArrayList();
|
|
ArrayList greaterThanQReads = new ArrayList();
|
|
ArrayList lessThanQOffsets = new ArrayList();
|
|
ArrayList greaterThanQOffsets = new ArrayList();
|
|
|
|
final byte qk = reads.get(k).getBaseQualities()[offsets.get(k)];
|
|
|
|
for (int iter = 0; iter < reads.size(); iter++) {
|
|
SAMRecord read = reads.get(iter);
|
|
int offset = offsets.get(iter);
|
|
byte quality = read.getBaseQualities()[offset];
|
|
|
|
if (quality < qk) {
|
|
lessThanQReads.add(read);
|
|
lessThanQOffsets.add(offset);
|
|
}
|
|
else if (quality > qk) {
|
|
greaterThanQReads.add(read);
|
|
greaterThanQOffsets.add(offset);
|
|
}
|
|
else {
|
|
equalToQReads.add(reads.get(iter));
|
|
}
|
|
}
|
|
|
|
if (lessThanQReads.size() > k)
|
|
return getQScoreOrderStatistic(lessThanQReads, lessThanQOffsets, k);
|
|
else if (equalToQReads.size() + lessThanQReads.size() >= k)
|
|
return qk;
|
|
else
|
|
return getQScoreOrderStatistic(greaterThanQReads, greaterThanQOffsets, k - lessThanQReads.size() - equalToQReads.size());
|
|
|
|
}
|
|
|
|
public static byte getQScoreMedian(List<SAMRecord> reads, List<Integer> offsets) {
|
|
return getQScoreOrderStatistic(reads, offsets, (int) Math.floor(reads.size() / 2.));
|
|
}
|
|
|
|
/**
|
|
* A utility class that computes on the fly average and standard deviation for a stream of numbers.
|
|
* The number of observations does not have to be known in advance, and can be also very big (so that
|
|
* it could overflow any naive summation-based scheme or cause loss of precision).
|
|
* Instead, adding a new number <code>observed</code>
|
|
* to a sample with <code>add(observed)</code> immediately updates the instance of this object so that
|
|
* it contains correct mean and standard deviation for all the numbers seen so far. Source: Knuth, vol.2
|
|
* (see also e.g. http://www.johndcook.com/standard_deviation.html for online reference).
|
|
*/
|
|
public static class RunningAverage {
|
|
private double mean = 0.0;
|
|
private double s = 0.0;
|
|
private long obs_count = 0;
|
|
|
|
public void add(double obs) {
|
|
obs_count++;
|
|
double oldMean = mean;
|
|
mean += (obs - mean) / obs_count; // update mean
|
|
s += (obs - oldMean) * (obs - mean);
|
|
}
|
|
|
|
public void addAll(Collection<Number> col) {
|
|
for (Number o : col) {
|
|
add(o.doubleValue());
|
|
}
|
|
}
|
|
|
|
public double mean() {
|
|
return mean;
|
|
}
|
|
|
|
public double stddev() {
|
|
return Math.sqrt(s / (obs_count - 1));
|
|
}
|
|
|
|
public double var() {
|
|
return s / (obs_count - 1);
|
|
}
|
|
|
|
public long observationCount() {
|
|
return obs_count;
|
|
}
|
|
|
|
public RunningAverage clone() {
|
|
RunningAverage ra = new RunningAverage();
|
|
ra.mean = this.mean;
|
|
ra.s = this.s;
|
|
ra.obs_count = this.obs_count;
|
|
return ra;
|
|
}
|
|
|
|
public void merge(RunningAverage other) {
|
|
if (this.obs_count > 0 || other.obs_count > 0) { // if we have any observations at all
|
|
this.mean = (this.mean * this.obs_count + other.mean * other.obs_count) / (this.obs_count + other.obs_count);
|
|
this.s += other.s;
|
|
}
|
|
this.obs_count += other.obs_count;
|
|
}
|
|
}
|
|
|
|
//
|
|
// useful common utility routines
|
|
//
|
|
public static double rate(long n, long d) {
|
|
return n / (1.0 * Math.max(d, 1));
|
|
}
|
|
|
|
public static double rate(int n, int d) {
|
|
return n / (1.0 * Math.max(d, 1));
|
|
}
|
|
|
|
public static long inverseRate(long n, long d) {
|
|
return n == 0 ? 0 : d / Math.max(n, 1);
|
|
}
|
|
|
|
public static long inverseRate(int n, int d) {
|
|
return n == 0 ? 0 : d / Math.max(n, 1);
|
|
}
|
|
|
|
public static double ratio(int num, int denom) {
|
|
return ((double) num) / (Math.max(denom, 1));
|
|
}
|
|
|
|
public static double ratio(long num, long denom) {
|
|
return ((double) num) / (Math.max(denom, 1));
|
|
}
|
|
|
|
static public double max(double x0, double x1, double x2) {
|
|
double a = Math.max(x0, x1);
|
|
return Math.max(a, x2);
|
|
}
|
|
|
|
public static double phredScaleToProbability(byte q) {
|
|
return Math.pow(10, (-q) / 10.0);
|
|
}
|
|
|
|
public static double phredScaleToLog10Probability(byte q) {
|
|
return ((-q) / 10.0);
|
|
}
|
|
|
|
/**
|
|
* Returns the phred scaled value of probability p
|
|
*
|
|
* @param p probability (between 0 and 1).
|
|
* @return phred scaled probability of p
|
|
*/
|
|
public static byte probabilityToPhredScale(double p) {
|
|
return (byte) ((-10) * Math.log10(p));
|
|
}
|
|
|
|
public static double log10ProbabilityToPhredScale(double log10p) {
|
|
return (-10) * log10p;
|
|
}
|
|
|
|
/**
|
|
* Converts LN to LOG10
|
|
*
|
|
* @param ln log(x)
|
|
* @return log10(x)
|
|
*/
|
|
public static double lnToLog10(double ln) {
|
|
return ln * Math.log10(Math.exp(1));
|
|
}
|
|
|
|
/**
|
|
* Constants to simplify the log gamma function calculation.
|
|
*/
|
|
private static final double zero = 0.0, one = 1.0, half = .5, a0 = 7.72156649015328655494e-02, a1 = 3.22467033424113591611e-01, a2 = 6.73523010531292681824e-02, a3 = 2.05808084325167332806e-02, a4 = 7.38555086081402883957e-03, a5 = 2.89051383673415629091e-03, a6 = 1.19270763183362067845e-03, a7 = 5.10069792153511336608e-04, a8 = 2.20862790713908385557e-04, a9 = 1.08011567247583939954e-04, a10 = 2.52144565451257326939e-05, a11 = 4.48640949618915160150e-05, tc = 1.46163214496836224576e+00, tf = -1.21486290535849611461e-01, tt = -3.63867699703950536541e-18, t0 = 4.83836122723810047042e-01, t1 = -1.47587722994593911752e-01, t2 = 6.46249402391333854778e-02, t3 = -3.27885410759859649565e-02, t4 = 1.79706750811820387126e-02, t5 = -1.03142241298341437450e-02, t6 = 6.10053870246291332635e-03, t7 = -3.68452016781138256760e-03, t8 = 2.25964780900612472250e-03, t9 = -1.40346469989232843813e-03, t10 = 8.81081882437654011382e-04, t11 = -5.38595305356740546715e-04, t12 = 3.15632070903625950361e-04, t13 = -3.12754168375120860518e-04, t14 = 3.35529192635519073543e-04, u0 = -7.72156649015328655494e-02, u1 = 6.32827064025093366517e-01, u2 = 1.45492250137234768737e+00, u3 = 9.77717527963372745603e-01, u4 = 2.28963728064692451092e-01, u5 = 1.33810918536787660377e-02, v1 = 2.45597793713041134822e+00, v2 = 2.12848976379893395361e+00, v3 = 7.69285150456672783825e-01, v4 = 1.04222645593369134254e-01, v5 = 3.21709242282423911810e-03, s0 = -7.72156649015328655494e-02, s1 = 2.14982415960608852501e-01, s2 = 3.25778796408930981787e-01, s3 = 1.46350472652464452805e-01, s4 = 2.66422703033638609560e-02, s5 = 1.84028451407337715652e-03, s6 = 3.19475326584100867617e-05, r1 = 1.39200533467621045958e+00, r2 = 7.21935547567138069525e-01, r3 = 1.71933865632803078993e-01, r4 = 1.86459191715652901344e-02, r5 = 7.77942496381893596434e-04, r6 = 7.32668430744625636189e-06, w0 = 4.18938533204672725052e-01, w1 = 8.33333333333329678849e-02, w2 = -2.77777777728775536470e-03, w3 = 7.93650558643019558500e-04, w4 = -5.95187557450339963135e-04, w5 = 8.36339918996282139126e-04, w6 = -1.63092934096575273989e-03;
|
|
|
|
/**
|
|
* Efficient rounding functions to simplify the log gamma function calculation
|
|
* double to long with 32 bit shift
|
|
*/
|
|
private static final int HI(double x) {
|
|
return (int) (Double.doubleToLongBits(x) >> 32);
|
|
}
|
|
|
|
/**
|
|
* Efficient rounding functions to simplify the log gamma function calculation
|
|
* double to long without shift
|
|
*/
|
|
private static final int LO(double x) {
|
|
return (int) Double.doubleToLongBits(x);
|
|
}
|
|
|
|
/**
|
|
* Most efficent implementation of the lnGamma (FDLIBM)
|
|
* Use via the log10Gamma wrapper method.
|
|
*/
|
|
private static double lnGamma(double x) {
|
|
double t, y, z, p, p1, p2, p3, q, r, w;
|
|
int i;
|
|
|
|
int hx = HI(x);
|
|
int lx = LO(x);
|
|
|
|
/* purge off +-inf, NaN, +-0, and negative arguments */
|
|
int ix = hx & 0x7fffffff;
|
|
if (ix >= 0x7ff00000)
|
|
return Double.POSITIVE_INFINITY;
|
|
if ((ix | lx) == 0 || hx < 0)
|
|
return Double.NaN;
|
|
if (ix < 0x3b900000) { /* |x|<2**-70, return -log(|x|) */
|
|
return -Math.log(x);
|
|
}
|
|
|
|
/* purge off 1 and 2 */
|
|
if ((((ix - 0x3ff00000) | lx) == 0) || (((ix - 0x40000000) | lx) == 0))
|
|
r = 0;
|
|
/* for x < 2.0 */
|
|
else if (ix < 0x40000000) {
|
|
if (ix <= 0x3feccccc) { /* lgamma(x) = lgamma(x+1)-log(x) */
|
|
r = -Math.log(x);
|
|
if (ix >= 0x3FE76944) {
|
|
y = one - x;
|
|
i = 0;
|
|
}
|
|
else if (ix >= 0x3FCDA661) {
|
|
y = x - (tc - one);
|
|
i = 1;
|
|
}
|
|
else {
|
|
y = x;
|
|
i = 2;
|
|
}
|
|
}
|
|
else {
|
|
r = zero;
|
|
if (ix >= 0x3FFBB4C3) {
|
|
y = 2.0 - x;
|
|
i = 0;
|
|
} /* [1.7316,2] */
|
|
else if (ix >= 0x3FF3B4C4) {
|
|
y = x - tc;
|
|
i = 1;
|
|
} /* [1.23,1.73] */
|
|
else {
|
|
y = x - one;
|
|
i = 2;
|
|
}
|
|
}
|
|
|
|
switch (i) {
|
|
case 0:
|
|
z = y * y;
|
|
p1 = a0 + z * (a2 + z * (a4 + z * (a6 + z * (a8 + z * a10))));
|
|
p2 = z * (a1 + z * (a3 + z * (a5 + z * (a7 + z * (a9 + z * a11)))));
|
|
p = y * p1 + p2;
|
|
r += (p - 0.5 * y);
|
|
break;
|
|
case 1:
|
|
z = y * y;
|
|
w = z * y;
|
|
p1 = t0 + w * (t3 + w * (t6 + w * (t9 + w * t12))); /* parallel comp */
|
|
p2 = t1 + w * (t4 + w * (t7 + w * (t10 + w * t13)));
|
|
p3 = t2 + w * (t5 + w * (t8 + w * (t11 + w * t14)));
|
|
p = z * p1 - (tt - w * (p2 + y * p3));
|
|
r += (tf + p);
|
|
break;
|
|
case 2:
|
|
p1 = y * (u0 + y * (u1 + y * (u2 + y * (u3 + y * (u4 + y * u5)))));
|
|
p2 = one + y * (v1 + y * (v2 + y * (v3 + y * (v4 + y * v5))));
|
|
r += (-0.5 * y + p1 / p2);
|
|
}
|
|
}
|
|
else if (ix < 0x40200000) { /* x < 8.0 */
|
|
i = (int) x;
|
|
t = zero;
|
|
y = x - (double) i;
|
|
p = y * (s0 + y * (s1 + y * (s2 + y * (s3 + y * (s4 + y * (s5 + y * s6))))));
|
|
q = one + y * (r1 + y * (r2 + y * (r3 + y * (r4 + y * (r5 + y * r6)))));
|
|
r = half * y + p / q;
|
|
z = one; /* lgamma(1+s) = log(s) + lgamma(s) */
|
|
switch (i) {
|
|
case 7:
|
|
z *= (y + 6.0); /* FALLTHRU */
|
|
case 6:
|
|
z *= (y + 5.0); /* FALLTHRU */
|
|
case 5:
|
|
z *= (y + 4.0); /* FALLTHRU */
|
|
case 4:
|
|
z *= (y + 3.0); /* FALLTHRU */
|
|
case 3:
|
|
z *= (y + 2.0); /* FALLTHRU */
|
|
r += Math.log(z);
|
|
break;
|
|
}
|
|
/* 8.0 <= x < 2**58 */
|
|
}
|
|
else if (ix < 0x43900000) {
|
|
t = Math.log(x);
|
|
z = one / x;
|
|
y = z * z;
|
|
w = w0 + z * (w1 + y * (w2 + y * (w3 + y * (w4 + y * (w5 + y * w6)))));
|
|
r = (x - half) * (t - one) + w;
|
|
}
|
|
else
|
|
/* 2**58 <= x <= inf */
|
|
r = x * (Math.log(x) - one);
|
|
return r;
|
|
}
|
|
|
|
/**
|
|
* Calculates the log10 of the gamma function for x using the efficient FDLIBM
|
|
* implementation to avoid overflows and guarantees high accuracy even for large
|
|
* numbers.
|
|
*
|
|
* @param x the x parameter
|
|
* @return the log10 of the gamma function at x.
|
|
*/
|
|
public static double log10Gamma(double x) {
|
|
return lnToLog10(lnGamma(x));
|
|
}
|
|
|
|
/**
|
|
* Calculates the log10 of the binomial coefficient. Designed to prevent
|
|
* overflows even with very large numbers.
|
|
*
|
|
* @param n total number of trials
|
|
* @param k number of successes
|
|
* @return the log10 of the binomial coefficient
|
|
*/
|
|
public static double log10BinomialCoefficient(int n, int k) {
|
|
return log10Gamma(n + 1) - log10Gamma(k + 1) - log10Gamma(n - k + 1);
|
|
}
|
|
|
|
public static double log10BinomialProbability(int n, int k, double log10p) {
|
|
double log10OneMinusP = Math.log10(1 - Math.pow(10, log10p));
|
|
return log10BinomialCoefficient(n, k) + log10p * k + log10OneMinusP * (n - k);
|
|
}
|
|
|
|
/**
|
|
* Calculates the log10 of the multinomial coefficient. Designed to prevent
|
|
* overflows even with very large numbers.
|
|
*
|
|
* @param n total number of trials
|
|
* @param k array of any size with the number of successes for each grouping (k1, k2, k3, ..., km)
|
|
* @return
|
|
*/
|
|
public static double log10MultinomialCoefficient(int n, int[] k) {
|
|
double denominator = 0.0;
|
|
for (int x : k) {
|
|
denominator += log10Gamma(x + 1);
|
|
}
|
|
return log10Gamma(n + 1) - denominator;
|
|
}
|
|
|
|
/**
|
|
* Computes the log10 of the multinomial distribution probability given a vector
|
|
* of log10 probabilities. Designed to prevent overflows even with very large numbers.
|
|
*
|
|
* @param n number of trials
|
|
* @param k array of number of successes for each possibility
|
|
* @param log10p array of log10 probabilities
|
|
* @return
|
|
*/
|
|
public static double log10MultinomialProbability(int n, int[] k, double[] log10p) {
|
|
if (log10p.length != k.length)
|
|
throw new UserException.BadArgumentValue("p and k", "Array of log10 probabilities must have the same size as the array of number of sucesses: " + log10p.length + ", " + k.length);
|
|
double log10Prod = 0.0;
|
|
for (int i = 0; i < log10p.length; i++) {
|
|
log10Prod += log10p[i] * k[i];
|
|
}
|
|
return log10MultinomialCoefficient(n, k) + log10Prod;
|
|
}
|
|
|
|
public static double factorial(int x) {
|
|
return Math.pow(10, log10Gamma(x + 1));
|
|
}
|
|
|
|
public static double log10Factorial(int x) {
|
|
return log10Gamma(x + 1);
|
|
}
|
|
|
|
/**
|
|
* Adds two arrays together and returns a new array with the sum.
|
|
*
|
|
* @param a one array
|
|
* @param b another array
|
|
* @return a new array with the sum of a and b
|
|
*/
|
|
@Requires("a.length == b.length")
|
|
@Ensures("result.length == a.length")
|
|
public static int[] addArrays(int[] a, int[] b) {
|
|
int[] c = new int[a.length];
|
|
for (int i = 0; i < a.length; i++)
|
|
c[i] = a[i] + b[i];
|
|
return c;
|
|
}
|
|
|
|
/**
|
|
* Quick implementation of the Knuth-shuffle algorithm to generate a random
|
|
* permutation of the given array.
|
|
*
|
|
* @param array the original array
|
|
* @return a new array with the elements shuffled
|
|
*/
|
|
public static Object[] arrayShuffle(Object[] array) {
|
|
int n = array.length;
|
|
Object[] shuffled = array.clone();
|
|
for (int i = 0; i < n; i++) {
|
|
int j = i + GenomeAnalysisEngine.getRandomGenerator().nextInt(n - i);
|
|
Object tmp = shuffled[i];
|
|
shuffled[i] = shuffled[j];
|
|
shuffled[j] = tmp;
|
|
}
|
|
return shuffled;
|
|
}
|
|
|
|
/**
|
|
* Vector operations
|
|
*
|
|
* @param v1 first numerical array
|
|
* @param v2 second numerical array
|
|
* @return a new array with the elements added
|
|
*/
|
|
public static <E extends Number> Double[] vectorSum(E v1[], E v2[]) {
|
|
if (v1.length != v2.length)
|
|
throw new UserException("BUG: vectors v1, v2 of different size in vectorSum()");
|
|
|
|
Double[] result = new Double[v1.length];
|
|
for (int k = 0; k < v1.length; k++)
|
|
result[k] = v1[k].doubleValue() + v2[k].doubleValue();
|
|
|
|
return result;
|
|
}
|
|
|
|
public static <E extends Number> Double[] scalarTimesVector(E a, E[] v1) {
|
|
|
|
Double result[] = new Double[v1.length];
|
|
for (int k = 0; k < v1.length; k++)
|
|
result[k] = a.doubleValue() * v1[k].doubleValue();
|
|
|
|
return result;
|
|
}
|
|
|
|
public static <E extends Number> Double dotProduct(E[] v1, E[] v2) {
|
|
if (v1.length != v2.length)
|
|
throw new UserException("BUG: vectors v1, v2 of different size in vectorSum()");
|
|
|
|
Double result = 0.0;
|
|
for (int k = 0; k < v1.length; k++)
|
|
result += v1[k].doubleValue() * v2[k].doubleValue();
|
|
|
|
return result;
|
|
|
|
}
|
|
|
|
public static double[] vectorLog10(double v1[]) {
|
|
double result[] = new double[v1.length];
|
|
for (int k = 0; k < v1.length; k++)
|
|
result[k] = Math.log10(v1[k]);
|
|
|
|
return result;
|
|
|
|
}
|
|
|
|
// todo - silly overloading, just because Java can't unbox/box arrays of primitive types, and we can't do generics with primitive types!
|
|
public static Double[] vectorLog10(Double v1[]) {
|
|
Double result[] = new Double[v1.length];
|
|
for (int k = 0; k < v1.length; k++)
|
|
result[k] = Math.log10(v1[k]);
|
|
|
|
return result;
|
|
|
|
}
|
|
|
|
}
|