Just another update

Task/Probabilistic-choice/D/probabilistic-choice-2.d

@@ -12,11 +12,8 @@ void main() {
 
   double[pr.length] counts = 0.0;
   auto rnd = Xorshift(unpredictableSeed);
-  foreach (immutable _; 0 .. nTrials) {
-    immutable rnd01 = rnd.front / double(rnd.max);
-    rnd.popFront;
-    counts[cumulatives[].countUntil!(c => c >= rnd01)]++;
-  }
+  foreach (immutable _; 0 .. nTrials)
+    counts[cumulatives[].countUntil!(c => c >= rnd.uniform01)]++;
 
   writeln("Item    Target prob  Attained prob");
   foreach (name, p, co; zip(items, pr, counts[]))

Task/Probabilistic-choice/Erlang/probabilistic-choice.erl

@@ -0,0 +1,31 @@
+-module(probabilistic_choice).
+
+-export([test/0]).
+
+-define(TRIES, 1000000).
+
+test() ->
+	Probs =
+		[{aleph,1/5},
+		{beth,1/6},
+		{gimel,1/7},
+		{daleth,1/8},
+		{he,1/9},
+		{waw,1/10},
+		{zayin,1/11},
+		{heth,1759/27720}],
+    random:seed(now()),
+    Trials =
+    	[get_choice(Probs,random:uniform()) || _ <- lists:seq(1,?TRIES)],
+    [{Glyph,Expected,(length([Glyph || Glyph_ <- Trials, Glyph_ == Glyph])/?TRIES)}
+    	 || {Glyph,Expected} <- Probs].
+
+get_choice([{Glyph,_}],_) ->
+	Glyph;
+get_choice([{Glyph,Prob}|T],Ran) ->
+	case (Ran < Prob) of
+		true ->
+			Glyph;
+		false ->
+			get_choice(T,Ran - Prob)
+	end.

Task/Probabilistic-choice/MATLAB/probabilistic-choice-1.m

@@ -0,0 +1,11 @@
+function probChoice
+    choices = {'aleph' 'beth' 'gimel' 'daleth' 'he' 'waw' 'zayin' 'heth'};
+    w = [1/5 1/6 1/7 1/8 1/9 1/10 1/11 1759/27720];
+    R = randsample(length(w), 1e6, true, w);
+    T = tabulate(R);
+    fprintf('Value\tCount\tPercent\tGoal\n')
+    for k = 1:size(T, 1)
+        fprintf('%6s\t%.f\t%.2f%%\t%.2f%%\n', ...
+            choices{k}, T(k, 2), T(k, 3), 100*w(k))
+    end
+end

Task/Probabilistic-choice/MATLAB/probabilistic-choice-2.m

@@ -0,0 +1,17 @@
+function probChoice
+    choices = {'aleph' 'beth' 'gimel' 'daleth' 'he' 'waw' 'zayin' 'heth'};
+    w = [1/5 1/6 1/7 1/8 1/9 1/10 1/11 1759/27720];
+    nSamp = 1e6;
+    nChoice = length(w);
+    R = rand(nSamp, 1);
+    wCS = cumsum(w);
+    results = zeros(1, nChoice);
+    fprintf('Value\tCount\tPercent\tGoal\n')
+    for k = 1:nChoice
+        choiceKIdxs = R < wCS(k);
+        R(choiceKIdxs) = k;
+        results(k) = sum(choiceKIdxs);
+        fprintf('%6s\t%.f\t%.2f%%\t%.2f%%\n', ...
+            choices{k}, results(k), 100*results(k)/nSamp, 100*w(k))
+    end
+end

Task/Probabilistic-choice/Perl-6/probabilistic-choice.pl6

@@ -1,19 +1,21 @@
 constant TRIALS = 1e4;
 
-my %ps = <aleph beth gimel daleth he waw zayin> Z=> 1 «/« (5 .. 11);
-%ps<heth> = 1 - [+] values %ps;
+my @event = <aleph beth gimel daleth he waw zayin heth>;
 
-my %results;
+my @P = 1 «/« (5 .. 11), 1759/27720;
+my @cP = [\+] @P;
+
+my @results;
 for ^TRIALS {
-    %results{.key}++ given
-    first { .value > state $ = rand },
-    state % = %ps.keys Z=> [\+] %ps.values;
+    @results[
+	first { @cP[$_] > state $ = rand }, ^@P;
+    ]++;
 }
 
-say 'Event   Occurred  Expected  Difference';
-for sort *.value, %results {
-    my ($occurred, $expected) = .value/TRIALS, %ps{.key};
-    printf "%-6s  %f  %f  %f\n",
-        .key, $occurred, $expected,
+say  'Event    Occurred Expected  Difference';
+for ^@results {
+    my ($occurred, $expected) = @results[$_], @P[$_]*TRIALS;
+    printf "%-9s%8.0f%9.1f%12.1f\n",
+        @event[$_], $occurred, $expected,
         abs( $occurred - $expected );
 }

Task/Probabilistic-choice/Scala/probabilistic-choice.scala

@@ -0,0 +1,64 @@
+object ProbabilisticChoice extends App {
+  import scala.collection.mutable.LinkedHashMap
+
+  def weightedProb[A](prob: LinkedHashMap[A,Double]): A = {
+    require(prob.forall{case (_, p) => p > 0 && p < 1})
+    assume(prob.values.sum == 1)
+    def weighted(todo: Iterator[(A,Double)], rand: Double, accum: Double = 0): A = todo.next match {
+      case (s, i) if rand < (accum + i) => s
+      case (_, i) => weighted(todo, rand, accum + i)
+    }
+    weighted(prob.toIterator, scala.util.Random.nextDouble)
+  }
+
+  def weightedFreq[A](freq: LinkedHashMap[A,Int]): A = {
+    require(freq.forall{case (_, f) => f >= 0})
+    require(freq.values.sum > 0)
+    def weighted(todo: Iterator[(A,Int)], rand: Int, accum: Int = 0): A = todo.next match {
+      case (s, i) if rand < (accum + i) => s
+      case (_, i) => weighted(todo, rand, accum + i)
+    }
+    weighted(freq.toIterator, scala.util.Random.nextInt(freq.values.sum))
+  }
+
+  // Tests:
+
+  val probabilities = LinkedHashMap(
+    'aleph  -> 1.0/5,
+    'beth   -> 1.0/6,
+    'gimel  -> 1.0/7,
+    'daleth -> 1.0/8,
+    'he     -> 1.0/9,
+    'waw    -> 1.0/10,
+    'zayin  -> 1.0/11,
+    'heth   -> 1759.0/27720
+  )
+
+  val frequencies = LinkedHashMap(
+    'aleph  -> 200,
+    'beth   -> 167,
+    'gimel  -> 143,
+    'daleth -> 125,
+    'he     -> 111,
+    'waw    -> 100,
+    'zayin  -> 91,
+    'heth   -> 63
+  )
+
+  def check[A](original: LinkedHashMap[A,Double], results: Seq[A]) {
+    val freq = results.groupBy(x => x).mapValues(_.size.toDouble/results.size)
+    original.foreach{case (k, v) =>
+      val a = v/original.values.sum
+      val b = freq(k)
+      val c = if (Math.abs(a - b) < 0.001) "ok" else "**"
+      println(f"$k%10s  $a%.4f  $b%.4f  $c")
+    }
+    println(" "*10 + f"  ${1}%.4f  ${freq.values.sum}%.4f")
+  }
+
+  println("Checking weighted probabilities:")
+  check(probabilities, for (i <- 1 to 1000000) yield weightedProb(probabilities))
+  println
+  println("Checking weighted frequencies:")
+  check(frequencies.map{case (a, b) => a -> b.toDouble}, for (i <- 1 to 1000000) yield weightedFreq(frequencies))
+}

Task/Probabilistic-choice/Scheme/probabilistic-choice.ss

@@ -0,0 +1,45 @@
+(use-modules (ice-9 format))
+
+(define (random-choice probs)
+  (define choice (random 1.0))
+  (define (helper val prob-lis)
+    (let ((nval (- val (cadar prob-lis))))
+      (if
+       (< nval 0)
+       (caar prob-lis)
+       (helper nval (cdr prob-lis)))))
+  (helper choice probs))
+
+(define (add-result result delta table)
+  (cond
+   ((null? table) (list (list result delta)))
+   ((eq? (caar table) result)
+    (cons (list result (+ (cadar table) delta)) (cdr table)))
+   (#t (cons (car table) (add-result result delta (cdr table))))))
+
+(define (choices trials probs)
+  (define (helper trial-num freq-table)
+    (if
+     (= trial-num trials)
+     freq-table
+     (helper
+      (+ trial-num 1)
+      (add-result (random-choice probs) (/ 1 trials) freq-table))))
+  (helper 0 '()))
+
+(define (format-results probs results)
+  (for-each
+   (lambda (x)
+     (format
+      #t
+      "~10a~10,5f~10,5f~%"
+      (car x)
+      (cadr x)
+      (cadr (assoc (car x) results))))
+   probs))
+
+(define probs
+  '((aleph 1/5) (beth 1/6) (gimel 1/7) (daleth 1/8)
+    (he 1/9) (waw 1/10) (zayin 1/11) (heth 1759/27720)))
+
+(format-results probs (choices 1000000 probs))