Random numbers: Difference between revisions
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=={{header|Ada}}== |
=={{header|Ada}}== |
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<Ada> |
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with Ada.Numerics; use Ada.Numerics; |
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with Ada.Numerics.Elementary_Functions; use Ada.Numerics.Elementary_Functions; |
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package Elementary_Flt is new |
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Ada.Numerics.Generic_Elementary_Functions(Float); |
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use Elementary_Flt; |
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use Ada.Numerics; |
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Sigma : constant Float := 0.5; |
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R1 := Random(Seed); |
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R2 := Random(Seed); |
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type Normal_Array is array(1..1000) of Float; |
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return |
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</Ada> |
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=={{header|BASIC}}== |
=={{header|BASIC}}== |
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{{works with|QuickBasic|4.5}} |
{{works with|QuickBasic|4.5}} |
Revision as of 13:10, 7 June 2008
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>
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
#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
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 temp = 0.0 DO i = 1, n temp = temp + (array(i) - mean)**2 END DO sd = SQRT(temp/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
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() }
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;
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 )
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 ());;
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 // Cycle array values foreach(range(1,1000) as $i){ $a[$i] = 1 + sqrt(-2 * log(mt_rand())) * cos(2 * $pi * mt_rand()); }
Pop11
;;; Choose radians as arguments to trigonometic functions true -> popradians;
;;; procedure generating standard normal distribution define random_normal() -> result; lvars r1 = random0(1.0), r2 = random0(1.0); cos(2*pi*r1)*sqrt(-2*log(r2)) -> result enddefine;
lvars array, i;
;;; Put numbers on the stack for i from 1 to 1000 do 1.0+0.5*random_normal() endfor; ;;; collect them into array consvector(1000) -> array;
Python
import random randList = [random.gauss(1, .5) for i in range(1000)] # or [ random.normalvariate(1, 0.5) for i in range(1000)]
Note that the random module in the Python standard library supports a number of statistical distribution methods.
Tcl
proc nrand {} {return [expr sqrt(-2*log(rand()))*cos(4*acos(0)*rand())]} for {set i 0} {$i < 1000} {incr i} {lappend result [expr 1+.5*nrand()]}
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