Percolation/Mean run density: Difference between revisions

{{task|Percolation Simulations}}{{Percolation Simulation}}

Let <math>v</math> be a vector of <math>n</math> values of either <tt>1</tt> or <tt>0</tt> where the probability of any

vector of length <math>n</math> be <math>R_n</math>.

 

<pre>

[1 1 0 0 0 1 0 1 1 1]

on the accuracy of simulated <math>K(p)</math>.

 

 

;See also

* [http://mathworld.wolfram.com/s-Run.html s-Run] on Wolfram mathworld.

 

=={{header|C++}}==

#include <random>

#include <vector>

}

return 0 ;

{{out}}

<pre>t = 100

=={{header|D}}==

{{trans|python}}

 

enum n = 100, p = 0.5, t = 500;

 

double meanRunDensity(in size_t n, in double prob) {

}

 

immutable n = 2 ^^ n2;

immutable sim = t.iota.map!(_ => meanRunDensity(n, p))

writefln("t=%3d, p=%4.2f, n=%5d, p(1-p)=%5.5f, " ~

"sim=%5.5f, delta=%3.1f%%", t, p, n, limit, sim,

}

}

{{out}}

<pre>t=500, p=0.10, n= 1024, p(1-p)=0.09000, sim=0.08949, delta=0.6%

t=500, p=0.90, n=16384, p(1-p)=0.09000, sim=0.09007, delta=0.1%</pre>

 

! loosely translated from python. We do not need to generate and store the entire vector at once.

! compilation: gfortran -Wall -std=f2008 -o thisfile thisfile.f08

 

end program percolation_mean_run_density

 

<pre>

500 0.90 4096 0.090 0.090 0.4

500 0.90 16384 0.090 0.090 0.1

</pre>

 

The following works in both languages:

 

t := integer(A[2]) | 500

 

write(left(p,8)," ",left(n,8)," ",left(p*(1-p),10)," ",left(Ka/t, 10))

}

 

Output:

 

=={{header|J}}==

NB. translation of python

T =. y

smoutput' T P N P(1-P) SIM DELTA%'

smoutput ''

for_N. 2 ^ 10 + +: i. 3 do.

smoutput 4 5j2 6 6j3 6j3 4j1 ": T, P, N, LIMIT, SIM, SIM (100 * [`(|@:(- % ]))@.(0 ~: ])) LIMIT

end.

EMPTY

)

Session:

<pre>

500 0.90 4096 0.090 0.090 0.1

500 0.90 16384 0.090 0.090 0.1

</pre>

 

=={{header|Perl}}==

my ($n, $p) = @_;

my $r = join '',

printf " R(n, p)= %f\n", $r / t;

}

{{out}}

<pre>t= 100

R(n, p)= 0.091730</pre>

 

 

 

 

=={{header|Python}}==

from random import random

from math import fsum

sim = fsum(mean_run_density(n, p) for i in range(t)) / t

print('t=%3i p=%4.2f n=%5i p(1-p)=%5.3f sim=%5.3f delta=%3.1f%%'

 

{{out}}

=={{header|Racket}}==

 

(require racket/fixnum)

(define t (make-parameter 100))

(module+ test

(require rackunit)

{{out}}

<pre>

mean(R_10000/10000) = 89939/1000000 0.0899

 

</pre>

 

=={{header|Tcl}}==

for {set s ""} {[string length $s] < $length} {} {

append s [expr {rand() < $probability}]

}

puts ""

{{out}}

<pre>

t=500, p=0.90, n= 4096, p(1-p)=0.090, sim=0.090, delta=0.08%

t=500, p=0.90, n=16384, p(1-p)=0.090, sim=0.090, delta=0.09%

</pre>