Random numbers: Difference between revisions
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Many libraries only generate uniformly distributed random numbers. If so, use [http://en.wikipedia.org/wiki/Normal_distribution#Generating_values_for_normal_random_variables this formula] to convert them to a normal distribution. |
Many libraries only generate uniformly distributed random numbers. If so, use [http://en.wikipedia.org/wiki/Normal_distribution#Generating_values_for_normal_random_variables this formula] to convert them to a normal distribution. |
Revision as of 21:59, 3 January 2009
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
<Ada> with Ada.Numerics; use Ada.Numerics; with Ada.Numerics.Float_Random; use Ada.Numerics.Float_Random; with Ada.Numerics.Elementary_Functions; use Ada.Numerics.Elementary_Functions;
procedure Normal_Random is
function Normal_Distribution ( Seed : Generator; Mu : Float := 1.0; Sigma : Float := 0.5 ) return Float is begin return Mu + (Sigma * Sqrt (-2.0 * Log (Random (Seed), 10.0)) * Cos (2.0 * Pi * Random (Seed))); end Normal_Distribution; Seed : Generator; Distribution : array (1..1_000) of Float;
begin
Reset (Seed); for I in Distribution'Range loop Distribution (I) := Normal_Distribution (Seed); end loop;
end Normal_Random; </Ada>
ALGOL 68
PROC random normal = REAL: # normal distribution, centered on 0, std dev 1 # ( sqrt(-2*log(random)) * cos(2*pi*random) ); main: ( [1000]REAL rands; FOR i TO UPB rands DO rands[i] := 1 + random normal/2 OD; INT limit=10; printf(($"("n(limit-1)(-d.6d",")-d.5d" ... )"$, rands[:limit])) )
Output sample:
( 0.693461, 0.948424, 0.482261, 1.045939, 0.890818, 1.467935, 0.604153, 0.804811, 0.690227, 0.83462 ... )
BASIC
RANDOMIZE TIMER 'seeds random number generator with the system time 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
<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>
C++
<cpp>#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)); return 0;
}</cpp>
Common Lisp
<lisp>(loop for i from 1 to 1000
collect (1+ (* (sqrt (* -2 (log (random 1.0)))) (cos (* 2 pi (random 1.0))))))</lisp>
E
accum [] for _ in 1..1000 { _.with(entropy.nextGaussian()) }
Forth
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
Fortran
PROGRAM Random INTEGER, PARAMETER :: n = 1000 INTEGER :: i REAL :: array(n), pi, temp, mean = 1.0, sd = 0.5 pi = 4.0*ATAN(1.0) CALL RANDOM_NUMBER(array) ! Uniform distribution ! Now convert to normal distribution DO i = 1, n-1, 2 temp = sd * SQRT(-2.0*LOG(array(i))) * COS(2*pi*array(i+1)) + mean array(i+1) = sd * SQRT(-2.0*LOG(array(i))) * SIN(2*pi*array(i+1)) + mean array(i) = temp END DO ! Check mean and standard deviation mean = SUM(array)/n sd = SQRT(SUM((array - mean)**2)/n) WRITE(*, "(A,F8.6)") "Mean = ", mean WRITE(*, "(A,F8.6)") "Standard Deviation = ", sd END PROGRAM Random
Output
Mean = 0.995112 Standard Deviation = 0.503373
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)
J
urand=: ?@$ 0: zrand=: (2 o. 2p1 * urand) * [: %: _2 * [: ^. urand 1 + 0.5 * zrand 100
Java
<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()
}</java>
JavaScript
<javascript>function randomNormal() {
return Math.cos(2 * Math.PI * Math.random()) * Math.sqrt(-2 * Math.log(Math.random()));
}
var a = new Array(1000); for (var i=0; i<a.length; i++)
a[i] = randomNormal() / 2 + 1;</javascript>
Logo
The earliest Logos only have a RANDOM function for picking a random non-negative integer. Many modern Logos have floating point random generators built-in.
to random.float ; 0..1 localmake "max.int lshift -1 -1 output quotient random :max.int :max.int end to random.gaussian output product cos random 360 sqrt -2 / ln random.float end make "randoms cascade 1000 [fput random.gaussian / 2 + 1 ?] []
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 )
Modula-3
MODULE Rand EXPORTS Main; IMPORT Random; FROM Math IMPORT log, cos, sqrt, Pi; VAR rands: ARRAY [1..1000] OF LONGREAL; (* Normal distribution. *) PROCEDURE RandNorm(): LONGREAL = BEGIN WITH rand = NEW(Random.Default).init() DO RETURN sqrt(-2.0D0 * log(rand.longreal())) * cos(2.0D0 * Pi * rand.longreal()); END; END RandNorm; BEGIN FOR i := FIRST(rands) TO LAST(rands) DO rands[i] := 1.0D0 + 0.5D0 * RandNorm(); END; END Rand.
OCaml
<ocaml>let pi = 4. *. atan 1.;; let random_gaussian () =
1. +. sqrt (-2. *. log (Random.float 1.)) *. cos (2. *. pi *. Random.float 1.);;
let a = Array.init 1000 (fun _ -> random_gaussian ());;</ocaml>
Perl
<perl>use Math::Cephes qw($PI);
map {
1.0 + sqrt (-2 * log rand) * cos (2 * $PI * rand)
} 1..1000</perl>
PHP
<php>$pi = pi(); // Set PI $a = range(1,1000); // Create array // Cycle array values foreach(range(1,1000) as $i){
$a[$i] = 1 + sqrt(-2 * log(mt_rand())) * cos(2 * $pi * mt_rand());
}</php>
Pop11
;;; Choose radians as arguments to trigonometic functions true -> popradians;
;;; procedure generating standard normal distribution define random_normal() -> result; lvars r1 = random0(1.0), r2 = random0(1.0); cos(2*pi*r1)*sqrt(-2*log(r2)) -> result enddefine;
lvars array, i;
;;; Put numbers on the stack for i from 1 to 1000 do 1.0+0.5*random_normal() endfor; ;;; collect them into array consvector(1000) -> array;
Python
<python>import random randList = [random.gauss(1, .5) for i in range(1000)]
- or [ random.normalvariate(1, 0.5) for i in range(1000)]</python>
Note that the random module in the Python standard library supports a number of statistical distribution methods.
R
result <- rnorm(1000, mean=1, sd=0.5)
Ruby
(1..1000).map { 1 + Math.sqrt(-2 * Math.log(rand)) * Math.cos(2 * Math::PI * rand) }
Tcl
proc nrand {} {return [expr sqrt(-2*log(rand()))*cos(4*acos(0)*rand())]} for {set i 0} {$i < 1000} {incr i} {lappend result [expr 1+.5*nrand()]}
TI-83 BASIC
Calculator symbol translations:
"STO" arrow: →
Square root sign: √
ClrList L1 Radian For(A,1,1000) √(-2*ln(rand))*cos(2*π*A)→L1(A) End