Package com.google.common.math

Class Quantiles

java.lang.Object

com.google.common.math.Quantiles

@Beta
@GwtIncompatible
public final class Quantiles
extends java.lang.Object

Provides a fluent API for calculating quantiles.

Examples

To compute the median:

 double myMedian = median().compute(myDataset);
 

where median() has been statically imported.

To compute the 99th percentile:

 double myPercentile99 = percentiles().index(99).compute(myDataset);
 

where percentiles() has been statically imported.

To compute median and the 90th and 99th percentiles:

 Map<Integer, Double> myPercentiles =
     percentiles().indexes(50, 90, 99).compute(myDataset);
 

where percentiles() has been statically imported: myPercentiles maps the keys 50, 90, and 99, to their corresponding quantile values.

To compute quartiles, use quartiles() instead of percentiles(). To compute arbitrary q-quantiles, use scale(q).

These examples all take a copy of your dataset. If you have a double array, you are okay with it being arbitrarily reordered, and you want to avoid that copy, you can use computeInPlace instead of compute.

Definition and notes on interpolation

The definition of the kth q-quantile of N values is as follows: define x = k * (N - 1) / q; if x is an integer, the result is the value which would appear at index x in the sorted dataset (unless there are NaN values, see below); otherwise, the result is the average of the values which would appear at the indexes floor(x) and ceil(x) weighted by (1-frac(x)) and frac(x) respectively. This is the same definition as used by Excel and by S, it is the Type 7 definition in R, and it is described by wikipedia as providing "Linear interpolation of the modes for the order statistics for the uniform distribution on [0,1]."

Handling of non-finite values

If any values in the input are NaN then all values returned are NaN. (This is the one occasion when the behaviour is not the same as you'd get from sorting with Arrays.sort(double[]) or Collections.sort(List<Double>) and selecting the required value(s). Those methods would sort NaN as if it is greater than any other value and place them at the end of the dataset, even after POSITIVE_INFINITY.)

Otherwise, NEGATIVE_INFINITY and POSITIVE_INFINITY sort to the beginning and the end of the dataset, as you would expect.

If required to do a weighted average between an infinity and a finite value, or between an infinite value and itself, the infinite value is returned. If required to do a weighted average between NEGATIVE_INFINITY and POSITIVE_INFINITY, NaN is returned (note that this will only happen if the dataset contains no finite values).

Performance

The average time complexity of the computation is O(N) in the size of the dataset. There is a worst case time complexity of O(N^2). You are extremely unlikely to hit this quadratic case on randomly ordered data (the probability decreases faster than exponentially in N), but if you are passing in unsanitized user data then a malicious user could force it. A light shuffle of the data using an unpredictable seed should normally be enough to thwart this attack.

The time taken to compute multiple quantiles on the same dataset using indexes is generally less than the total time taken to compute each of them separately, and sometimes much less. For example, on a large enough dataset, computing the 90th and 99th percentiles together takes about 55% as long as computing them separately.

When calling Quantiles.ScaleAndIndex.compute(java.util.Collection<? extends java.lang.Number>) (in either form), the memory requirement is 8*N bytes for the copy of the dataset plus an overhead which is independent of N (but depends on the quantiles being computed). When calling computeInPlace (in either form), only the overhead is required. The number of object allocations is independent of N in both cases.

Since:

20.0

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static class	Quantiles.Scale	Describes the point in a fluent API chain where only the scale (i.e.
static class	Quantiles.ScaleAndIndex	Describes the point in a fluent API chain where the scale and a single quantile index (i.e.
static class	Quantiles.ScaleAndIndexes	Describes the point in a fluent API chain where the scale and a multiple quantile indexes (i.e.

Constructor Summary

Constructors

Constructor	Description
Quantiles()

Method Summary

Modifier and Type	Method	Description
private static void	checkIndex(int index, int scale)
private static int	chooseNextSelection(int[] allRequired, int requiredFrom, int requiredTo, int from, int to)	Chooses the next selection to do from the required selections.
private static boolean	containsNaN(double... dataset)	Returns whether any of the values in dataset are NaN.
private static double	interpolate(double lower, double upper, double remainder, double scale)	Returns a value a fraction (remainder / scale) of the way between lower and upper.
private static double[]	intsToDoubles(int[] ints)
private static double[]	longsToDoubles(long[] longs)
static Quantiles.ScaleAndIndex	median()	Specifies the computation of a median (i.e.
private static void	movePivotToStartOfSlice(double[] array, int from, int to)	Selects the pivot to use, namely the median of the values at from, to, and halfway between the two (rounded down), from array, and ensure (by swapping elements if necessary) that that pivot value appears at the start of the slice i.e.
private static int	partition(double[] array, int from, int to)	Performs a partition operation on the slice of array with elements in the range [ from, to].
static Quantiles.Scale	percentiles()	Specifies the computation of percentiles (i.e.
static Quantiles.Scale	quartiles()	Specifies the computation of quartiles (i.e.
static Quantiles.Scale	scale(int scale)	Specifies the computation of q-quantiles.
private static void	selectAllInPlace(int[] allRequired, int requiredFrom, int requiredTo, double[] array, int from, int to)	Performs an in-place selection, like selectInPlace(int, double[], int, int), to select all the indexes allRequired[i] for i in the range [requiredFrom, requiredTo].
private static void	selectInPlace(int required, double[] array, int from, int to)	Performs an in-place selection to find the element which would appear at a given index in a dataset if it were sorted.
private static void	swap(double[] array, int i, int j)	Swaps the values at i and j in array.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

Quantiles

public Quantiles()

Method Detail

median

public static Quantiles.ScaleAndIndex median()

Specifies the computation of a median (i.e. the 1st 2-quantile).

quartiles

public static Quantiles.Scale quartiles()

Specifies the computation of quartiles (i.e. 4-quantiles).

percentiles

public static Quantiles.Scale percentiles()

Specifies the computation of percentiles (i.e. 100-quantiles).

scale

public static Quantiles.Scale scale(int scale)

Specifies the computation of q-quantiles.

Parameters:

scale - the scale for the quantiles to be calculated, i.e. the q of the q-quantiles, which must be positive

containsNaN

private static boolean containsNaN(double... dataset)

Returns whether any of the values in dataset are NaN.

interpolate

private static double interpolate(double lower,
                                  double upper,
                                  double remainder,
                                  double scale)

Returns a value a fraction (remainder / scale) of the way between lower and upper. Assumes that lower <= upper. Correctly handles infinities (but not NaN).

checkIndex

private static void checkIndex(int index,
                               int scale)

longsToDoubles

private static double[] longsToDoubles(long[] longs)

intsToDoubles

private static double[] intsToDoubles(int[] ints)

selectInPlace

private static void selectInPlace(int required,
                                  double[] array,
                                  int from,
                                  int to)

Performs an in-place selection to find the element which would appear at a given index in a dataset if it were sorted. The following preconditions should hold:

• required, from, and to should all be indexes into array;
• required should be in the range [from, to];
• all the values with indexes in the range [0, from) should be less than or equal to all the values with indexes in the range [from, to];
• all the values with indexes in the range (to, array.length - 1] should be greater than or equal to all the values with indexes in the range [from, to].

This method will reorder the values with indexes in the range [from, to] such that all the values with indexes in the range [from, required) are less than or equal to the value with index required, and all the values with indexes in the range (required, to] are greater than or equal to that value. Therefore, the value at required is the value which would appear at that index in the sorted dataset.

partition

private static int partition(double[] array,
                             int from,
                             int to)

Performs a partition operation on the slice of array with elements in the range [ from, to]. Uses the median of from, to, and the midpoint between them as a pivot. Returns the index which the slice is partitioned around, i.e. if it returns ret then we know that the values with indexes in [from, ret) are less than or equal to the value at ret and the values with indexes in (ret, to] are greater than or equal to that.

movePivotToStartOfSlice

private static void movePivotToStartOfSlice(double[] array,
                                            int from,
                                            int to)

Selects the pivot to use, namely the median of the values at from, to, and halfway between the two (rounded down), from array, and ensure (by swapping elements if necessary) that that pivot value appears at the start of the slice i.e. at from. Expects that from is strictly less than to.

selectAllInPlace

private static void selectAllInPlace(int[] allRequired,
                                     int requiredFrom,
                                     int requiredTo,
                                     double[] array,
                                     int from,
                                     int to)

Performs an in-place selection, like selectInPlace(int, double[], int, int), to select all the indexes allRequired[i] for i in the range [requiredFrom, requiredTo]. These indexes must be sorted in the array and must all be in the range [from, to].

chooseNextSelection

private static int chooseNextSelection(int[] allRequired,
                                       int requiredFrom,
                                       int requiredTo,
                                       int from,
                                       int to)

Chooses the next selection to do from the required selections. It is required that the array allRequired is sorted and that allRequired[i] are in the range [from, to] for all i in the range [requiredFrom, requiredTo]. The value returned by this method is the i in that range such that allRequired[i] is as close as possible to the center of the range [from, to]. Choosing the value closest to the center of the range first is the most efficient strategy because it minimizes the size of the subranges from which the remaining selections must be done.

swap

private static void swap(double[] array,
                         int i,
                         int j)

Swaps the values at i and j in array.