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|
-module(quantile).
-author('Florian Odronitz <odo@mac.com>').
-ifdef(TEST).
-include_lib("eunit/include/eunit.hrl").
-export([ceil/1]).
-define(DEBUG, true).
-endif.
-type sample() :: number().
-type samples() :: [sample()].
-export([quantile/2]).
-export([rank_average/2]).
-spec quantile(float(), samples()) -> sample().
quantile(0.0, [First|_]) ->
First;
quantile(1.0, Samples) ->
lists:last(Samples);
quantile(Quantile, Samples) ->
case ranks(length(Samples), Quantile) of
[Index] ->
lists:nth(Index, Samples);
[Index1, Index2] ->
(lists:nth(Index1, Samples) + lists:nth(Index2, Samples)) / 2
end.
-spec even(integer()) -> boolean().
even(Value) ->
Value rem 2 =:= 0.
-spec natural(float()) -> boolean().
natural(Value) ->
(erlang:trunc(Value) * 1.0) =:= Value.
-spec ranks(integer(), float()) -> [integer()] | [integer()|integer()].
ranks(Size, _Quantile) when Size < 1 ->
throw({error, {Size, size_smaller_one}});
ranks(_Size, Quantile) when Quantile < 0 ->
throw({error, {Quantile, quantile_smaller_zero}});
ranks(_Size, Quantile) when Quantile > 1 ->
throw({error, {Quantile, quantile_larger_one}});
ranks(Size, Quantile) ->
case natural(Size * Quantile) andalso even(Size) of
true ->
[round(Size * Quantile), round(Size * Quantile) + 1];
false ->
[ceil(Size * Quantile)]
end.
-spec ceil(float()) -> integer().
ceil(X) ->
T = erlang:trunc(X),
case (X - T) of
Neg when Neg < 0 -> T;
Pos when Pos > 0 -> T + 1;
_ -> T
end.
% TESTS
rank_average(Size, Quantile) ->
case ranks(Size, Quantile) of
[V] ->
V;
[V1, V2] ->
(V1 + V2) / 2
end.
-ifdef(TEST).
quantile_test_() ->
[{foreach, local,
fun test_setup/0,
fun test_teardown/1,
[
{"test ceil", fun ceil_test/0}
,{"test ranks", fun ranks_test/0}
,{"test natural", fun natural_test/0}
,{"test even", fun even_test/0}
,{"test quantiles", fun quantile_test/0}
]}
].
test_setup() ->
undefined.
test_teardown(_) ->
undefined.
ranks_test() ->
?assertEqual([3], ranks(10, 0.25))
,?assertEqual([5, 6], ranks(10, 0.5))
,?assertEqual([8], ranks(10, 0.75))
,?assertEqual([3], ranks(11, 0.25))
,?assertEqual([6], ranks(11, 0.5))
,?assertEqual([9], ranks(11, 0.75)).
natural_test() ->
?assertEqual(true, natural(10.0))
,?assertEqual(true, natural(-10.0))
,?assertEqual(false, natural(10.1))
,?assertEqual(false, natural(-10.1)).
even_test() ->
?assertEqual(true, even(10))
,?assertEqual(true, even(-10))
,?assertEqual(false, even(11))
,?assertEqual(false, even(-11)).
ceil_test() ->
?assertEqual(1, ceil(1.0))
,?assertEqual(2, ceil(1.1))
,?assertEqual(2, ceil(1.8))
,?assertEqual(-1, ceil(-1.8))
,?assertEqual(-1, ceil(-1.1)).
quantile_test() ->
Samples1 = [3.0, 6.0, 7.0, 8.0, 8.0, 10.0, 13.0, 15.0, 16.0, 20.0]
,?assertEqual(7.0, quantile(1/4, Samples1))
,?assertEqual(9.0, quantile(1/2, Samples1))
,?assertEqual(15.0, quantile(3/4, Samples1))
,Samples2 = [3.0, 6.0, 7.0, 8.0, 8.0, 9.0, 10.0, 13.0, 15.0, 16.0, 20.0]
,?assertEqual(7.0, quantile(1/4, Samples2))
,?assertEqual(9.0, quantile(1/2, Samples2))
,?assertEqual(15.0, quantile(3/4, Samples2))
,?assertEqual(1.0, quantile(1/4, [1.0]))
,?assertEqual(1.0, quantile(2/4, [1.0]))
,?assertEqual(1.0, quantile(3/4, [1.0])).
-endif.
|
