'\"
'\" Generated from file '/usr/obj/ports/tcllib-1.11.1/tcllib-1.11.1/modules/simulation/random.man' by tcllib/doctools with format 'nroff'
'\" Copyright (c) 2004 Arjen Markus <arjenmarkus@users.sourceforge.net>
'\"
'\" The definitions below are for supplemental macros used in Tcl/Tk
'\" manual entries.
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.TH "simulation::random" n 0.1 simulation "Tcl Simulation Tools"
.BS
.SH NAME
simulation::random \- Pseudo-random number generators
.SH SYNOPSIS
package require \fBTcl  ?8.4?\fR
.sp
package require \fBsimulation::random  0.1\fR
.sp
\fB::simulation::random::prng_Bernoulli\fR \fIp\fR
.sp
\fB::simulation::random::prng_Discrete\fR \fIn\fR
.sp
\fB::simulation::random::prng_Poisson\fR \fIlambda\fR
.sp
\fB::simulation::random::prng_Uniform\fR \fImin\fR \fImax\fR
.sp
\fB::simulation::random::prng_Exponential\fR \fImin\fR \fImean\fR
.sp
\fB::simulation::random::prng_Normal\fR \fImean\fR \fIstdev\fR
.sp
\fB::simulation::random::prng_Pareto\fR \fImin\fR \fIsteep\fR
.sp
\fB::simulation::random::prng_Gumbel\fR \fImin\fR \fIf\fR
.sp
\fB::simulation::random::prng_chiSquared\fR \fIdf\fR
.sp
\fB::simulation::random::prng_Disk\fR \fIrad\fR
.sp
\fB::simulation::random::prng_Sphere\fR \fIrad\fR
.sp
\fB::simulation::random::prng_Ball\fR \fIrad\fR
.sp
\fB::simulation::random::prng_Rectangle\fR \fIlength\fR \fIwidth\fR
.sp
\fB::simulation::random::prng_Block\fR \fIlength\fR \fIwidth\fR \fIdepth\fR
.sp
.BE
.SH DESCRIPTION
.PP
This package consists of commands to generate pseudo-random number
generators. These new commands deliver
.IP \(bu
numbers that are distributed normally, uniformly, according to a
Pareto or Gumbel distribution and so on
.IP \(bu
coordinates of points uniformly spread inside a sphere or a rectangle
.PP
For example:
.nf

    set p [::simulation::random::prng_Normal -1.0 10.0]

.fi
produces a new command (whose name is stored in the variable "p") that
generates normally distributed numbers with a mean of -1.0 and a
standard deviation of 10.0.
.SH PROCEDURES
The package defines the following public procedures for \fIdiscrete\fR
distributions:
.TP
\fB::simulation::random::prng_Bernoulli\fR \fIp\fR
Create a command (PRNG) that generates numbers with a Bernoulli
distribution: the value is either 1 or 0, with a chance p to be 1
.RS
.TP
float \fIp\fR
Chance the outcome is 1
.RE
.sp
.TP
\fB::simulation::random::prng_Discrete\fR \fIn\fR
Create a command (PRNG) that generates numbers 0 to n-1 with equal
probability.
.RS
.TP
int \fIn\fR
Number of different values (ranging from 0 to n-1)
.RE
.sp
.TP
\fB::simulation::random::prng_Poisson\fR \fIlambda\fR
Create a command (PRNG) that generates numbers according to the Poisson
distribution.
.RS
.TP
float \fIlambda\fR
Mean number per time interval
.RE
.PP
The package defines the following public procedures for \fIcontinuous\fR distributions:
.TP
\fB::simulation::random::prng_Uniform\fR \fImin\fR \fImax\fR
Create a command (PRNG) that generates uniformly distributed numbers
between "min" and "max".
.RS
.TP
float \fImin\fR
Minimum number that will be generated
.TP
float \fImax\fR
Maximum number that will be generated
.RE
.sp
.TP
\fB::simulation::random::prng_Exponential\fR \fImin\fR \fImean\fR
Create a command (PRNG) that generates exponentially distributed numbers
with a given minimum value and a given mean value.
.RS
.TP
float \fImin\fR
Minimum number that will be generated
.TP
float \fImean\fR
Mean value for the numbers
.RE
.sp
.TP
\fB::simulation::random::prng_Normal\fR \fImean\fR \fIstdev\fR
Create a command (PRNG) that generates normally distributed numbers
with a given mean value and a given standard deviation.
.RS
.TP
float \fImean\fR
Mean value for the numbers
.TP
float \fIstdev\fR
Standard deviation
.RE
.sp
.TP
\fB::simulation::random::prng_Pareto\fR \fImin\fR \fIsteep\fR
Create a command (PRNG) that generates numbers distributed according to
Pareto with a given minimum value and a given distribution steepness.
.RS
.TP
float \fImin\fR
Minimum number that will be generated
.TP
float \fIsteep\fR
Steepness of the distribution
.RE
.sp
.TP
\fB::simulation::random::prng_Gumbel\fR \fImin\fR \fIf\fR
Create a command (PRNG) that generates numbers distributed according to
Gumbel with a given minimum value and a given scale factor. The
probability density function is:
.nf

     P(v) = exp( -exp(f*(v-min)))

.fi
.RS
.TP
float \fImin\fR
Minimum number that will be generated
.TP
float \fIf\fR
Scale factor for the values
.RE
.sp
.TP
\fB::simulation::random::prng_chiSquared\fR \fIdf\fR
Create a command (PRNG) that generates numbers distributed according to
the chi-squared distribution with df degrees of freedom. The mean is 0
and the standard deviation is 1.
.RS
.TP
float \fIdf\fR
Degrees of freedom
.RE
.PP
The package defines the following public procedures for random point sets:
.TP
\fB::simulation::random::prng_Disk\fR \fIrad\fR
Create a command (PRNG) that generates (x,y)-coordinates for points
uniformly spread over a disk of given radius.
.RS
.TP
float \fIrad\fR
Radius of the disk
.RE
.sp
.TP
\fB::simulation::random::prng_Sphere\fR \fIrad\fR
Create a command (PRNG) that generates (x,y,z)-coordinates for points
uniformly spread over the surface of a sphere of given radius.
.RS
.TP
float \fIrad\fR
Radius of the disk
.RE
.sp
.TP
\fB::simulation::random::prng_Ball\fR \fIrad\fR
Create a command (PRNG) that generates (x,y,z)-coordinates for points
uniformly spread within a ball of given radius.
.RS
.TP
float \fIrad\fR
Radius of the ball
.RE
.sp
.TP
\fB::simulation::random::prng_Rectangle\fR \fIlength\fR \fIwidth\fR
Create a command (PRNG) that generates (x,y)-coordinates for points
uniformly spread over a rectangle.
.RS
.TP
float \fIlength\fR
Length of the rectangle (x-direction)
.TP
float \fIwidth\fR
Width of the rectangle (y-direction)
.RE
.sp
.TP
\fB::simulation::random::prng_Block\fR \fIlength\fR \fIwidth\fR \fIdepth\fR
Create a command (PRNG) that generates (x,y)-coordinates for points
uniformly spread over a block
.RS
.TP
float \fIlength\fR
Length of the block (x-direction)
.TP
float \fIwidth\fR
Width of the block (y-direction)
.TP
float \fIdepth\fR
Depth of the block (z-direction)
.RE
.PP
.SH KEYWORDS
math, random numbers, simulation, statistical distribution
.SH COPYRIGHT
.nf
Copyright (c) 2004 Arjen Markus <arjenmarkus@users.sourceforge.net>

.fi