Tcl Library Source Code

package ifneeded simulation::random 0.4.0 [list source [file join $dir random.tcl]]
package ifneeded simulation::montecarlo 0.1 [list source [file join $dir montecarlo.tcl]]
package ifneeded simulation::annealing 0.2 [list source [file join $dir annealing.tcl]]

         set z [expr {DEPTH*rand()}]
         return [list $x $y $z]
    }]

    return $name
}


# prng_Triangle --
#     Create a PRNG with a triangular distribution of points on an interval.
#     If the argument min is lower than the argument max, then smaller
#     values have higher probability and vice versa.
#
# Arguments:
#     min       Minimum value
#     max       Maximum value
#
# Result:
#     Name of a procedure that returns the random point
#
proc ::simulation::random::prng_Triangle {min max} {
    variable count

    incr count

    set name ::simulation::random::PRNG_$count

    set diff [expr {$max-$min}]

    if { $diff > 0.0 } {
        proc $name {} [string map [list MIN $min DIFF $diff] \
         {
            set r [expr {1.0 - sqrt(1.0 - rand())}]
            set x [expr {MIN + DIFF*$r}]
            return $x
        }]
    } else {
        proc $name {} [string map [list MAX $max DIFF $diff] \
         {
            set x [expr {MAX - DIFF*sqrt(rand())}]
            return $x
        }]
    }

    return $name
}


# prng_SymmetricTriangle --
#     Create a PRNG with a symmetric triangular distribution of points on an interval.
#
# Arguments:
#     min       Minimum value
#     max       Maximum value
#
# Result:
#     Name of a procedure that returns the random point
#
proc ::simulation::random::prng_SymmetricTriangle {min max} {
    variable count

    incr count

    set name ::simulation::random::PRNG_$count

    set diff2 [expr {0.5 *($max-$min)}]

    proc $name {} [string map [list MIN $min DIFF2 $diff2] \
     {
        return [expr {MIN + DIFF2 * (rand() + rand())}]
    }]

    return $name
}

# Announce the package
#
package provide simulation::random 0.4.0


# main --
#     Test code
#
if { 0 } {
set bin [::simulation::random::prng_Bernoulli 0.2]

test "Block-1.0" "block generator with sides 10, 0.1 and 2.5" \
    -body {
    set p [::simulation::random::prng_Block 10 0.1 2.5]
    set rnd [$p]
    set result [llength $rnd]
} -result 3

test "Triangle-1.0" "triangularly distributed numbers between -1.0 and 1.0" \
    -body {
    set p [::simulation::random::prng_Triangle -1.0 1.0]

    set okay 1
    for {set i 0} {$i < 1000} {incr i} {
        set rnd [$p]

        if { $rnd < -1.0 || $rnd > 1.0 } {
            set okay 0
            break
        }
    }

    set okay
} -result 1

test "Triangle-1.1" "triangularly distributed numbers between -1.0 and 1.0 (alternative)" \
    -body {
    set p [::simulation::random::prng_Triangle 1.0 -1.0]

    set okay 1
    for {set i 0} {$i < 1000} {incr i} {
        set rnd [$p]

        if { $rnd < -1.0 || $rnd > 1.0 } {
            set okay 0
            break
        }
    }

    set okay
} -result 1

# End of test cases
testsuiteCleanup

[comment {-*- tcl -*- doctools manpage}]
[manpage_begin simulation::random n 0.4]
[keywords math]
[keywords {random numbers}]
[keywords simulation]
[keywords {statistical distribution}]
[copyright {2004 Arjen Markus <[email protected]>}]
[moddesc   {Tcl Simulation Tools}]
[titledesc {Pseudo-random number generators}]
[category  Mathematics]
[require Tcl [opt 8.4]]
[require simulation::random 0.4]

[description]
[para]
This package consists of commands to generate pseudo-random number
generators. These new commands deliver

[list_begin itemized]

[list_begin definitions]

[call [cmd ::simulation::random::prng_Uniform] [arg min ] [arg max]]

Create a command (PRNG) that generates uniformly distributed numbers
between "min" and "max".

[list_begin arguments]
[arg_def float min] Minimum number that will be generated
[arg_def float max] Maximum number that will be generated
[list_end]

[para]

[call [cmd ::simulation::random::prng_Triangular] [arg min ] [arg max]]

Create a command (PRNG) that generates triangularly distributed numbers
between "min" and "max". If the argument min is lower than the argument max, then smaller
values have higher probability and vice versa. In the first case the probability
density function is of the form [emph {f(x) = 2(1-x)}] and the other case it is of the form [emph {f(x) = 2x}].

[list_begin arguments]
[arg_def float min] Minimum number that will be generated
[arg_def float max] Maximum number that will be generated
[list_end]

[para]

[call [cmd ::simulation::random::prng_SymmTriangular] [arg min ] [arg max]]

Create a command (PRNG) that generates numbers distributed according to a symmetric triangle
around the mean of "min" and "max".

[list_begin arguments]
[arg_def float min] Minimum number that will be generated
[arg_def float max] Maximum number that will be generated
[list_end]

[para]