From dff85f3d6fdb4b3453d863bf9208073564a9fcf2 Mon Sep 17 00:00:00 2001 From: Guilherme Andrade Date: Sat, 18 Mar 2017 19:48:23 +0000 Subject: rand: Support arbitrary normal distributions --- lib/stdlib/doc/src/rand.xml | 23 +++++++++++++++ lib/stdlib/src/rand.erl | 16 ++++++++++- lib/stdlib/test/rand_SUITE.erl | 65 +++++++++++++++++++++++++++++++++--------- 3 files changed, 90 insertions(+), 14 deletions(-) diff --git a/lib/stdlib/doc/src/rand.xml b/lib/stdlib/doc/src/rand.xml index 8745e16908..3a5d18dc35 100644 --- a/lib/stdlib/doc/src/rand.xml +++ b/lib/stdlib/doc/src/rand.xml @@ -119,6 +119,11 @@ S0 = rand:seed_s(exsplus), 
 {SND0, S2} = rand:normal_s(S1),
+

Create a normal deviate with mean -3 and variance 0.5:

+ + 
+{ND0, S3} = rand:normal_s(-3, 0.5, S2),
+

This random number generator is not cryptographically strong. If a strong cryptographic random number generator is @@ -200,6 +205,15 @@ S0 = rand:seed_s(exsplus), + + + Return a normal distributed random float. + +

Returns a normal N(Mean, Variance) deviate float + and updates the state in the process dictionary.

+ + + Return a standard normal distributed random float. @@ -210,6 +224,15 @@ S0 = rand:seed_s(exsplus), + + + Return a normal distributed random float. + +

Returns, for a specified state, a normal N(Mean, Variance) + deviate float and a new state.

+ + + Seed random number generator. diff --git a/lib/stdlib/src/rand.erl b/lib/stdlib/src/rand.erl index 1f457b9e0e..cef83da287 100644 --- a/lib/stdlib/src/rand.erl +++ b/lib/stdlib/src/rand.erl @@ -28,7 +28,7 @@ export_seed/0, export_seed_s/1, uniform/0, uniform/1, uniform_s/1, uniform_s/2, jump/0, jump/1, - normal/0, normal_s/1 + normal/0, normal/2, normal_s/1, normal_s/3 ]). -compile({inline, [exs64_next/1, exsplus_next/1, @@ -178,6 +178,13 @@ normal() -> _ = seed_put(Seed), X. +%% normal/2: returns a random float with N(μ, σ²) normal distribution +%% updating the state in the process dictionary. + +-spec normal(Mean :: number(), Variance :: number()) -> float(). +normal(Mean, Variance) -> + Mean + (math:sqrt(Variance) * normal()). + %% normal_s/1: returns a random float with standard normal distribution %% The Ziggurat Method for generating random variables - Marsaglia and Tsang %% Paper and reference code: http://www.jstatsoft.org/v05/i08/ @@ -198,6 +205,13 @@ normal_s(State0) -> false -> normal_s(Idx, Sign, -X, State) end. +%% normal_s/3: returns a random float with normal N(μ, σ²) distribution + +-spec normal_s(Mean :: number(), Variance :: number(), state()) -> {float(), NewS :: state()}. +normal_s(Mean, Variance, State0) when Variance > 0 -> + {X, State} = normal_s(State0), + {Mean + (math:sqrt(Variance) * X), State}. + %% ===================================================================== %% Internal functions diff --git a/lib/stdlib/test/rand_SUITE.erl b/lib/stdlib/test/rand_SUITE.erl index fe5eaccda5..cb97d27992 100644 --- a/lib/stdlib/test/rand_SUITE.erl +++ b/lib/stdlib/test/rand_SUITE.erl @@ -27,6 +27,7 @@ -export([interval_int/1, interval_float/1, seed/1, api_eq/1, reference/1, basic_stats_uniform_1/1, basic_stats_uniform_2/1, + basic_stats_standard_normal/1, basic_stats_normal/1, plugin/1, measure/1, reference_jump_state/1, reference_jump_procdict/1]). @@ -52,7 +53,8 @@ all() -> groups() -> [{basic_stats, [parallel], - [basic_stats_uniform_1, basic_stats_uniform_2, basic_stats_normal]}, + [basic_stats_uniform_1, basic_stats_uniform_2, + basic_stats_standard_normal, basic_stats_normal]}, {reference_jump, [parallel], [reference_jump_state, reference_jump_procdict]}]. @@ -294,12 +296,35 @@ basic_stats_uniform_2(Config) when is_list(Config) -> || Alg <- algs()], ok. -basic_stats_normal(Config) when is_list(Config) -> +basic_stats_standard_normal(Config) when is_list(Config) -> ct:timetrap({minutes,6}), %% valgrind needs a lot of time - io:format("Testing normal~n",[]), - [basic_normal_1(?LOOP, rand:seed_s(Alg), 0, 0) || Alg <- algs()], + io:format("Testing standard normal~n",[]), + IntendedMean = 0, + IntendedVariance = 1, + [basic_normal_1(?LOOP, IntendedMean, IntendedVariance, + rand:seed_s(Alg), 0, 0) + || Alg <- algs()], ok. +basic_stats_normal(Config) when is_list(Config) -> + IntendedMeans = [-1.0e6, -50, -math:pi(), -math:exp(-1), + 0.12345678, math:exp(1), 100, 1.0e6], + IntendedVariances = [1.0e-6, math:exp(-1), 1, math:pi(), 1.0e6], + IntendedMeanVariancePairs = + [{Mean, Variance} || Mean <- IntendedMeans, + Variance <- IntendedVariances], + + ct:timetrap({minutes, 6 * length(IntendedMeanVariancePairs)}), %% valgrind needs a lot of time + lists:foreach( + fun ({IntendedMean, IntendedVariance}) -> + io:format("Testing normal(~.2f, ~.2f)~n", + [float(IntendedMean), float(IntendedVariance)]), + [basic_normal_1(?LOOP, IntendedMean, IntendedVariance, + rand:seed_s(Alg), 0, 0) + || Alg <- algs()] + end, + IntendedMeanVariancePairs). + basic_uniform_1(N, S0, Sum, A0) when N > 0 -> {X,S} = rand:uniform_s(S0), I = trunc(X*100), @@ -339,19 +364,33 @@ basic_uniform_2(0, {#{type:=Alg}, _}, Sum, A) -> abs(?LOOP div 100 - Max) < 1000 orelse ct:fail({max, Alg, Max}), ok. -basic_normal_1(N, S0, Sum, Sq) when N > 0 -> - {X,S} = rand:normal_s(S0), - basic_normal_1(N-1, S, X+Sum, X*X+Sq); -basic_normal_1(0, {#{type:=Alg}, _}, Sum, SumSq) -> - Mean = Sum / ?LOOP, - StdDev = math:sqrt((SumSq - (Sum*Sum/?LOOP))/(?LOOP - 1)), - io:format("~.10w: Average: ~7.4f StdDev ~6.4f~n", [Alg, Mean, StdDev]), +basic_normal_1(N, IntendedMean, IntendedVariance, S0, StandardSum, StandardSq) when N > 0 -> + {X,S} = normal_s(IntendedMean, IntendedVariance, S0), + % We now shape X into a standard normal distribution (in case it wasn't already) + % in order to minimise the accumulated error on Sum / SumSq; + % otherwise said error would prevent us of making a fair judgment on + % the overall distribution when targeting large means and variances. + StandardX = (X - IntendedMean) / math:sqrt(IntendedVariance), + basic_normal_1(N-1, IntendedMean, IntendedVariance, S, + StandardX+StandardSum, StandardX*StandardX+StandardSq); +basic_normal_1(0, _IntendedMean, _IntendedVariance, {#{type:=Alg}, _}, StandardSum, StandardSumSq) -> + StandardMean = StandardSum / ?LOOP, + StandardVariance = (StandardSumSq - (StandardSum*StandardSum/?LOOP))/(?LOOP - 1), + StandardStdDev = math:sqrt(StandardVariance), + io:format("~.10w: Standardised Average: ~7.4f, Standardised StdDev ~6.4f~n", + [Alg, StandardMean, StandardStdDev]), %% Verify that the basic statistics are ok %% be gentle we don't want to see to many failing tests - abs(Mean) < 0.005 orelse ct:fail({average, Alg, Mean}), - abs(StdDev - 1.0) < 0.005 orelse ct:fail({stddev, Alg, StdDev}), + abs(StandardMean) < 0.005 orelse ct:fail({average, Alg, StandardMean}), + abs(StandardStdDev - 1.0) < 0.005 orelse ct:fail({stddev, Alg, StandardStdDev}), ok. +normal_s(Mean, Variance, State0) when Mean == 0, Variance == 1 -> + % Make sure we're also testing the standard normal interface + rand:normal_s(State0); +normal_s(Mean, Variance, State0) -> + rand:normal_s(Mean, Variance, State0). + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Test that the user can write algorithms. -- cgit v1.2.3