Random numbers: Difference between revisions
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foreach(range(1,1000) as $i){ |
foreach(range(1,1000) as $i){ |
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$a[$i] = 1 + sqrt(-2 * log(mt_rand())) * cos(2 * $pi * mt_rand()); |
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} |
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Revision as of 05:15, 28 November 2007
Random numbers
You are encouraged to solve this task according to the task description, using any language you may know.
You are encouraged to solve this task according to the task description, using any language you may know.
The goal of this task is to generate a collection filled with 1000 normally distributed random numbers with a mean of 1.0 and a standard deviation of 0.5
Many libraries only generate uniformly distributed random numbers. If so, use this formula to convert them to a normal distribution.
Ada
with Ada.Numerics.Float_Random; use Ada.Numerics.Float_Random; with Ada.Numerics.Generic_Elementary_Functions; procedure Normal_Random is Seed : Generator; function Normal_Distribution(Seed : Generator) return Float is package Elementary_Flt is new Ada.Numerics.Generic_Elementary_Functions(Float); use Elementary_Flt; use Ada.Numerics; R1 : Float; R2 : Float; Mu : constant Float := 1.0; Sigma : constant Float := 0.5; begin R1 := Random(Seed); R2 := Random(Seed); return Mu + (Sigma * Sqrt(-2.0 * Log(X => R1, Base => 10.0)) * Cos(2.0 * Pi * R2)); end Normal_Distribution; type Normal_Array is array(1..1000) of Float; Distribution : Normal_Array; begin Reset(Seed); for I in Distribution'range loop Distribution(I) := Normal_Distribution(Seed); end loop; end Normal_Random;
BASIC
Compiler: QuickBasic 4.5
RANDOMIZE TIMER pi = 3.141592653589793# DIM a(1 TO 1000) AS DOUBLE CLS FOR i = 1 TO 1000 a(i) = 1 + SQR(-2 * LOG(RND)) * COS(2 * pi * RND) NEXT i
C
#include <stdlib.h> #include <math.h> double drand() /* uniform distribution, (0..1] */ { return (rand()+1.0)/(RAND_MAX+1.0); } double random_normal() /* normal distribution, centered on 0, std dev 1 */ { return sqrt(-2*log(drand())) * cos(2*M_PI*drand()); } int main() { int i; double rands[1000]; for (i=0; i<1000; i++) rands[i] = 1.0 + 0.5*random_normal(); return 0; }
C++
#include <cstdlib> // for rand #include <cmath> // for atan, sqrt, log, cos #include <algorithm> // for generate_n double const pi = 4*std::atan(1.0); // simple functor for normal distribution class normal_distribution { public: normal_distribution(double m, double s): mu(m), sigma(s) {} double operator() // returns a single normally distributed number { double r1 = (std::rand() + 1.0)/(RAND_MAX + 1.0); // gives equal distribution in (0, 1] double r2 = (std::rand() + 1.0)/(RAND_MAX + 1.0); return mu + sigma * std::sqrt(-2*std::log(r1))*std::cos(2*pi*r2); } private: double mu, sigma; }; int main() { double array[1000]; std::generate_n(array, 1000, normal_distribution(1.0, 0.5)); }
E
accum [] for _ in 1..1000 { _.with(entropy.nextGaussian()) }
Forth
Interpreter: gforth 0.6.2
require random.fs here to seed -1. 1 rshift 2constant MAX-D \ or s" MAX-D" ENVIRONMENT? drop : frnd ( -- f ) \ uniform distribution 0..1 rnd rnd dabs d>f MAX-D d>f f/ ; : frnd-normal ( -- f ) \ centered on 0, std dev 1 frnd pi f* 2e f* fcos frnd fln -2e f* fsqrt f* ; : ,normals ( n -- ) \ store many, centered on 1, std dev 0.5 0 do frnd-normal 0.5e f* 1e f+ f, loop ; create rnd-array 1000 ,normals
Haskell
import System.Random pairs :: [a] -> [(a,a)] pairs (x:y:zs) = (x,y):pairs zs pairs _ = [] gauss mu sigma (r1,r2) = mu + sigma * sqrt (-2 * log r1) * cos (2 * pi * r2) gaussians :: (RandomGen g, Random a, Floating a) => Int -> g -> [a] gaussians n g = take n $ map (gauss 1.0 0.5) $ pairs $ randoms g
result :: IO [Double] result = getStdGen >>= \g -> return $ gaussians 1000 g
Groovy
rnd = new Random() result = (1..1000).inject([]) { r, i -> r << rnd.nextGaussian() }
IDL
result = 1.0 + 0.5*randomn(seed,1000)
Java
double[] list = new double[1000]; Random rng = new Random(); for(int i = 0;i<list.length;i++) { list[i] = 1.0 + 0.5 * rng.nextGaussian() }
MAXScript
arr = #() for i in 1 to 1000 do ( a = random 0.0 1.0 b = random 0.0 1.0 c = 1.0 + 0.5 * sqrt (-2*log a) * cos (360*b) -- Maxscript cos takes degrees append arr c )
Perl
use Math::Cephes qw($PI); map { 1.0 + 0.5 * sqrt (-2 * log rand) * cos (2 * $PI * rand) } 1..1000
PHP
$pi = pi(); // Set PI $a = range(1,1000); // Create array
foreach(range(1,1000) as $i){ $a[$i] = 1 + sqrt(-2 * log(mt_rand())) * cos(2 * $pi * mt_rand()); }
Pop11
;;; Choose radians as arguments to trigonometic functions true -> popradians;
;;; procedure generating standard normal distribution define random_normal() -> result; lvars r1 = random0(1.0), r2 = random0(1.0); cos(2*pi*r1)*sqrt(-2*log(r2)) -> result enddefine;
lvars array, i;
;;; Put numbers on the stack for i from 1 to 1000 do 1.0+0.5*random_normal() endfor; ;;; collect them into array consvector(1000) -> array;
Python
Interpreter: Python 2.5
import random randList = [random.gauss(1, .5) for i in range(1000)] # or [ random.normalvariate(1, 0.5) for i in range(1000)]
Note that the random module in the Python standard library supports a number of statistical distribution methods.
Tcl
proc nrand {} {return [expr sqrt(-2*log(rand()))*cos(4*acos(0)*rand())]} for {set i 0} {$i < 1000} {incr i} {lappend result [expr 1+.5*nrand()]}