gatk-3.8/java/src/org/broadinstitute/sting/utils/MathUtils.java

824 lines
29 KiB
Java
Executable File

/*
* Copyright (c) 2010 The Broad Institute
*
* Permission is hereby granted, free of charge, to any person
* obtaining a copy of this software and associated documentation
* files (the "Software"), to deal in the Software without
* restriction, including without limitation the rights to use,
* copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the
* Software is furnished to do so, subject to the following
* conditions:
*
* The above copyright notice and this permission notice shall be
* included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
* OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
* HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
* WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
* FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR
* THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*/
package org.broadinstitute.sting.utils;
import cern.jet.math.Arithmetic;
import java.math.BigDecimal;
import java.util.*;
import net.sf.samtools.SAMRecord;
/**
* MathUtils is a static class (no instantiation allowed!) with some useful math methods.
*
* @author Kiran Garimella
*/
public class MathUtils {
/** Public constants - used for the Lanczos approximation to the factorial function
* (for the calculation of the binomial/multinomial probability in logspace)
* @param LANC_SEQ[] - an array holding the constants which correspond to the product
* of Chebyshev Polynomial coefficients, and points on the Gamma function (for interpolation)
* [see A Precision Approximation of the Gamma Function J. SIAM Numer. Anal. Ser. B, Vol. 1 1964. pp. 86-96]
* @param LANC_G - a value for the Lanczos approximation to the gamma function that works to
* high precision
*/
/** Private constructor. No instantiating this class! */
private MathUtils() {}
public static double sum(double[] values) {
double s = 0.0;
for ( double v : values) s += v;
return s;
}
public static double log10sumLog10(double[] log10p, int start) {
double sum = 0.0;
double maxValue = Utils.findMaxEntry(log10p);
for ( int i = start; i < log10p.length; i++ ) {
sum += Math.pow(10.0, log10p[i] - maxValue);
}
return Math.log10(sum) + maxValue;
}
public static double sum(List<Double> values) {
double s = 0.0;
for ( double v : values) s += v;
return s;
}
public static double sumLog10(double[] log10values) {
return Math.pow(10.0, log10sumLog10(log10values));
// double s = 0.0;
// for ( double v : log10values) s += Math.pow(10.0, v);
// return s;
}
public static double log10sumLog10(double[] log10values) {
return log10sumLog10(log10values, 0);
}
public static boolean wellFormedDouble(double val) {
return ! Double.isInfinite(val) && ! Double.isNaN(val);
}
public static boolean isBounded(double val, double lower, double upper) {
return val >= lower && val <= upper;
}
public static boolean isPositive(double val) {
return ! isNegativeOrZero(val);
}
public static boolean isPositiveOrZero(double val) {
return isBounded(val, 0.0, Double.POSITIVE_INFINITY);
}
public static boolean isNegativeOrZero(double val) {
return isBounded(val, Double.NEGATIVE_INFINITY, 0.0);
}
public static boolean isNegative(double val) {
return ! isPositiveOrZero(val);
}
/**
* Compares double values for equality (within 1e-6), or inequality.
*
* @param a the first double value
* @param b the second double value
* @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.
*/
public static byte compareDoubles(double a, double b) { return compareDoubles(a, b, 1e-6); }
/**
* Compares double values for equality (within epsilon), or inequality.
*
* @param a the first double value
* @param b the second double value
* @param epsilon the precision within which two double values will be considered equal
* @return -1 if a is greater than b, 0 if a is equal to be within epsilon, 1 if b is greater than a.
*/
public static byte compareDoubles(double a, double b, double epsilon)
{
if (Math.abs(a - b) < epsilon) { return 0; }
if (a > b) { return -1; }
return 1;
}
/**
* Compares float values for equality (within 1e-6), or inequality.
*
* @param a the first float value
* @param b the second float value
* @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.
*/
public static byte compareFloats(float a, float b) { return compareFloats(a, b, 1e-6f); }
/**
* Compares float values for equality (within epsilon), or inequality.
*
* @param a the first float value
* @param b the second float value
* @param epsilon the precision within which two float values will be considered equal
* @return -1 if a is greater than b, 0 if a is equal to be within epsilon, 1 if b is greater than a.
*/
public static byte compareFloats(float a, float b, float epsilon)
{
if (Math.abs(a - b) < epsilon) { return 0; }
if (a > b) { return -1; }
return 1;
}
public static double NormalDistribution(double mean, double sd, double x)
{
double a = 1.0 / (sd*Math.sqrt(2.0 * Math.PI));
double b = Math.exp(-1.0 * (Math.pow(x - mean,2.0)/(2.0 * sd * sd)));
return a * b;
}
/**
* Computes a binomial probability. This is computed using the formula
*
* B(k; n; p) = [ n! / ( k! (n - k)! ) ] (p^k)( (1-p)^k )
*
* where n is the number of trials, k is the number of successes, and p is the probability of success
*
* @param k number of successes
* @param n number of Bernoulli trials
* @param p probability of success
*
* @return the binomial probability of the specified configuration. Computes values down to about 1e-237.
*/
public static double binomialProbability(int k, int n, double p) {
return Arithmetic.binomial(n, k)*Math.pow(p, k)*Math.pow(1.0 - p, n - k);
//return (new cern.jet.random.Binomial(n, p, cern.jet.random.engine.RandomEngine.makeDefault())).pdf(k);
}
/**
* Performs the calculation for a binomial probability in logspace, preventing the blowups of the binomial coefficient
* consistent with moderately large n and k.
*
* @param k - number of successes/observations
* @param n - number of Bernoulli trials
* @param p - probability of success/observations
*
* @return the probability mass associated with a binomial mass function for the above configuration
*/
public static double binomialProbabilityLog(int k, int n, double p) {
double log_coef = 0.0;
int min;
int max;
if(k < n - k) {
min = k;
max = n-k;
} else {
min = n - k;
max = k;
}
for(int i=2; i <= min; i++) {
log_coef -= Math.log((double)i);
}
for(int i = max+1; i <= n; i++) {
log_coef += Math.log((double)i);
}
return Math.exp(log_coef + ((double)k)*Math.log(p) + ((double)(n-k))*Math.log(1-p));
// in the future, we may want to precompile a table of exact values, where the entry (a,b) indicates
// the sum of log(i) from i = (1+(50*a)) to i = 50+(50*b) to increase performance on binomial coefficients
// which may require many sums.
}
/**
* Performs the cumulative sum of binomial probabilities, where the probability calculation is done in log space.
* @param start - start of the cumulant sum (over hits)
* @param end - end of the cumulant sum (over hits)
* @param total - number of attempts for the number of hits
* @param probHit - probability of a successful hit
* @return - returns the cumulative probability
*/
public static double cumBinomialProbLog(int start, int end, int total, double probHit) {
double cumProb = 0.0;
double prevProb;
BigDecimal probCache = BigDecimal.ZERO;
for(int hits = start; hits < end; hits++) {
prevProb = cumProb;
double probability = binomialProbabilityLog(hits,total,probHit);
cumProb += probability;
if ( probability > 0 && cumProb - prevProb < probability/2 ) { // loss of precision
probCache = probCache.add(new BigDecimal(prevProb));
cumProb = 0.0;
hits--; // repeat loop
// prevProb changes at start of loop
}
}
return probCache.add(new BigDecimal(cumProb)).doubleValue();
}
/**
* Computes a multinomial. This is computed using the formula
*
* M(x1,x2,...,xk; n) = [ n! / (x1! x2! ... xk!) ]
*
* where xi represents the number of times outcome i was observed, n is the number of total observations.
* In this implementation, the value of n is inferred as the sum over i of xi.
*
* @param x an int[] of counts, where each element represents the number of times a certain outcome was observed
* @return the multinomial of the specified configuration.
*/
public static double multinomial(int[] x) {
// In order to avoid overflow in computing large factorials in the multinomial
// coefficient, we split the calculation up into the product of a bunch of
// binomial coefficients.
double multinomialCoefficient = 1.0;
for (int i = 0; i < x.length; i++) {
int n = 0;
for (int j = 0; j <= i; j++) { n += x[j]; }
double multinomialTerm = Arithmetic.binomial(n, x[i]);
multinomialCoefficient *= multinomialTerm;
}
return multinomialCoefficient;
}
/**
* Computes a multinomial probability. This is computed using the formula
*
* M(x1,x2,...,xk; n; p1,p2,...,pk) = [ n! / (x1! x2! ... xk!) ] (p1^x1)(p2^x2)(...)(pk^xk)
*
* where xi represents the number of times outcome i was observed, n is the number of total observations, and
* pi represents the probability of the i-th outcome to occur. In this implementation, the value of n is
* inferred as the sum over i of xi.
*
* @param x an int[] of counts, where each element represents the number of times a certain outcome was observed
* @param p a double[] of probabilities, where each element represents the probability a given outcome can occur
* @return the multinomial probability of the specified configuration.
*/
public static double multinomialProbability(int[] x, double[] p) {
// In order to avoid overflow in computing large factorials in the multinomial
// coefficient, we split the calculation up into the product of a bunch of
// binomial coefficients.
double multinomialCoefficient = multinomial(x);
double probs = 1.0, totalprob = 0.0;
for (int obsCountsIndex = 0; obsCountsIndex < x.length; obsCountsIndex++) {
probs *= Math.pow(p[obsCountsIndex], x[obsCountsIndex]);
totalprob += p[obsCountsIndex];
}
assert(MathUtils.compareDoubles(totalprob, 1.0, 0.01) == 0);
return multinomialCoefficient*probs;
}
/**
* calculate the Root Mean Square of an array of integers
* @param x an int[] of numbers
* @return the RMS of the specified numbers.
*/
public static double rms(int[] x) {
if ( x.length == 0 )
return 0.0;
double rms = 0.0;
for (int i : x)
rms += i * i;
rms /= x.length;
return Math.sqrt(rms);
}
/**
* calculate the Root Mean Square of an array of doubles
* @param x a double[] of numbers
* @return the RMS of the specified numbers.
*/
public static double rms(Double[] x) {
if ( x.length == 0 )
return 0.0;
double rms = 0.0;
for (Double i : x)
rms += i * i;
rms /= x.length;
return Math.sqrt(rms);
}
/**
* 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) {
double[] normalized = new double[array.length];
// 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);
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(double[] array) {
if ( array == null ) throw new IllegalArgumentException("Array cannot be null!");
int maxI = -1;
for ( int i = 0; i < array.length; 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 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 arrayMax(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 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 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;
}
java.util.Random random = new java.util.Random();
int idx[] = new int[list.size()];
for (int i = 0; i < list.size(); i++) {
idx[i] = random.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;
}
// lifted from the internet
// http://www.cs.princeton.edu/introcs/91float/Gamma.java.html
public static double logGamma(double x) {
double tmp = (x - 0.5) * Math.log(x + 4.5) - (x + 4.5);
double ser = 1.0 + 76.18009173 / (x + 0) - 86.50532033 / (x + 1)
+ 24.01409822 / (x + 2) - 1.231739516 / (x + 3)
+ 0.00120858003 / (x + 4) - 0.00000536382 / (x + 5);
return tmp + Math.log(ser * Math.sqrt(2 * Math.PI));
}
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;
}
static Random rand = new Random(12321); //System.currentTimeMillis());
/**
* 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(rand.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, rand);
//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 double mean() { return mean; }
public double stddev() { return Math.sqrt(s/(obs_count - 1)); }
public long observationCount() { return 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)); }
}