'\" '\" Generated from file 'simulation_random\&.man' by tcllib/doctools with format 'nroff' '\" Copyright (c) 2004 Arjen Markus '\" .TH "simulation::random" 3tcl 0\&.4 tcllib "Tcl Simulation Tools" .\" The -*- nroff -*- definitions below are for supplemental macros used .\" in Tcl/Tk manual entries. .\" .\" .AP type name in/out ?indent? .\" Start paragraph describing an argument to a library procedure. .\" type is type of argument (int, etc.), in/out is either "in", "out", .\" or "in/out" to describe whether procedure reads or modifies arg, .\" and indent is equivalent to second arg of .IP (shouldn't ever be .\" needed; use .AS below instead) .\" .\" .AS ?type? ?name? .\" Give maximum sizes of arguments for setting tab stops. Type and .\" name are examples of largest possible arguments that will be passed .\" to .AP later. If args are omitted, default tab stops are used. .\" .\" .BS .\" Start box enclosure. From here until next .BE, everything will be .\" enclosed in one large box. .\" .\" .BE .\" End of box enclosure. .\" .\" .CS .\" Begin code excerpt. .\" .\" .CE .\" End code excerpt. .\" .\" .VS ?version? ?br? .\" Begin vertical sidebar, for use in marking newly-changed parts .\" of man pages. The first argument is ignored and used for recording .\" the version when the .VS was added, so that the sidebars can be .\" found and removed when they reach a certain age. If another argument .\" is present, then a line break is forced before starting the sidebar. .\" .\" .VE .\" End of vertical sidebar. .\" .\" .DS .\" Begin an indented unfilled display. .\" .\" .DE .\" End of indented unfilled display. .\" .\" .SO ?manpage? .\" Start of list of standard options for a Tk widget. The manpage .\" argument defines where to look up the standard options; if .\" omitted, defaults to "options". The options follow on successive .\" lines, in three columns separated by tabs. .\" .\" .SE .\" End of list of standard options for a Tk widget. .\" .\" .OP cmdName dbName dbClass .\" Start of description of a specific option. cmdName gives the .\" option's name as specified in the class command, dbName gives .\" the option's name in the option database, and dbClass gives .\" the option's class in the option database. .\" .\" .UL arg1 arg2 .\" Print arg1 underlined, then print arg2 normally. .\" .\" .QW arg1 ?arg2? .\" Print arg1 in quotes, then arg2 normally (for trailing punctuation). .\" .\" .PQ arg1 ?arg2? .\" Print an open parenthesis, arg1 in quotes, then arg2 normally .\" (for trailing punctuation) and then a closing parenthesis. .\" .\" # Set up traps and other miscellaneous stuff for Tcl/Tk man pages. .if t .wh -1.3i ^B .nr ^l \n(.l .ad b .\" # Start an argument description .de AP .ie !"\\$4"" .TP \\$4 .el \{\ . ie !"\\$2"" .TP \\n()Cu . el .TP 15 .\} .ta \\n()Au \\n()Bu .ie !"\\$3"" \{\ \&\\$1 \\fI\\$2\\fP (\\$3) .\".b .\} .el \{\ .br .ie !"\\$2"" \{\ \&\\$1 \\fI\\$2\\fP .\} .el \{\ \&\\fI\\$1\\fP .\} .\} .. .\" # define tabbing values for .AP .de AS .nr )A 10n .if !"\\$1"" .nr )A \\w'\\$1'u+3n .nr )B \\n()Au+15n .\" .if !"\\$2"" .nr )B \\w'\\$2'u+\\n()Au+3n .nr )C \\n()Bu+\\w'(in/out)'u+2n .. .AS Tcl_Interp Tcl_CreateInterp in/out .\" # BS - start boxed text .\" # ^y = starting y location .\" # ^b = 1 .de BS .br .mk ^y .nr ^b 1u .if n .nf .if n .ti 0 .if n \l'\\n(.lu\(ul' .if n .fi .. .\" # BE - end boxed text (draw box now) .de BE .nf .ti 0 .mk ^t .ie n \l'\\n(^lu\(ul' .el \{\ .\" Draw four-sided box normally, but don't draw top of .\" box if the box started on an earlier page. .ie !\\n(^b-1 \{\ \h'-1.5n'\L'|\\n(^yu-1v'\l'\\n(^lu+3n\(ul'\L'\\n(^tu+1v-\\n(^yu'\l'|0u-1.5n\(ul' .\} .el \}\ \h'-1.5n'\L'|\\n(^yu-1v'\h'\\n(^lu+3n'\L'\\n(^tu+1v-\\n(^yu'\l'|0u-1.5n\(ul' .\} .\} .fi .br .nr ^b 0 .. .\" # VS - start vertical sidebar .\" # ^Y = starting y location .\" # ^v = 1 (for troff; for nroff this doesn't matter) .de VS .if !"\\$2"" .br .mk ^Y .ie n 'mc \s12\(br\s0 .el .nr ^v 1u .. .\" # VE - end of vertical sidebar .de VE .ie n 'mc .el \{\ .ev 2 .nf .ti 0 .mk ^t \h'|\\n(^lu+3n'\L'|\\n(^Yu-1v\(bv'\v'\\n(^tu+1v-\\n(^Yu'\h'-|\\n(^lu+3n' .sp -1 .fi .ev .\} .nr ^v 0 .. .\" # Special macro to handle page bottom: finish off current .\" # box/sidebar if in box/sidebar mode, then invoked standard .\" # page bottom macro. .de ^B .ev 2 'ti 0 'nf .mk ^t .if \\n(^b \{\ .\" Draw three-sided box if this is the box's first page, .\" draw two sides but no top otherwise. .ie !\\n(^b-1 \h'-1.5n'\L'|\\n(^yu-1v'\l'\\n(^lu+3n\(ul'\L'\\n(^tu+1v-\\n(^yu'\h'|0u'\c .el \h'-1.5n'\L'|\\n(^yu-1v'\h'\\n(^lu+3n'\L'\\n(^tu+1v-\\n(^yu'\h'|0u'\c .\} .if \\n(^v \{\ .nr ^x \\n(^tu+1v-\\n(^Yu \kx\h'-\\nxu'\h'|\\n(^lu+3n'\ky\L'-\\n(^xu'\v'\\n(^xu'\h'|0u'\c .\} .bp 'fi .ev .if \\n(^b \{\ .mk ^y .nr ^b 2 .\} .if \\n(^v \{\ .mk ^Y .\} .. .\" # DS - begin display .de DS .RS .nf .sp .. .\" # DE - end display .de DE .fi .RE .sp .. .\" # SO - start of list of standard options .de SO 'ie '\\$1'' .ds So \\fBoptions\\fR 'el .ds So \\fB\\$1\\fR .SH "STANDARD OPTIONS" .LP .nf .ta 5.5c 11c .ft B .. .\" # SE - end of list of standard options .de SE .fi .ft R .LP See the \\*(So manual entry for details on the standard options. .. .\" # OP - start of full description for a single option .de OP .LP .nf .ta 4c Command-Line Name: \\fB\\$1\\fR Database Name: \\fB\\$2\\fR Database Class: \\fB\\$3\\fR .fi .IP .. .\" # CS - begin code excerpt .de CS .RS .nf .ta .25i .5i .75i 1i .. .\" # CE - end code excerpt .de CE .fi .RE .. .\" # UL - underline word .de UL \\$1\l'|0\(ul'\\$2 .. .\" # QW - apply quotation marks to word .de QW .ie '\\*(lq'"' ``\\$1''\\$2 .\"" fix emacs highlighting .el \\*(lq\\$1\\*(rq\\$2 .. .\" # PQ - apply parens and quotation marks to word .de PQ .ie '\\*(lq'"' (``\\$1''\\$2)\\$3 .\"" fix emacs highlighting .el (\\*(lq\\$1\\*(rq\\$2)\\$3 .. .\" # QR - quoted range .de QR .ie '\\*(lq'"' ``\\$1''\\-``\\$2''\\$3 .\"" fix emacs highlighting .el \\*(lq\\$1\\*(rq\\-\\*(lq\\$2\\*(rq\\$3 .. .\" # MT - "empty" string .de MT .QW "" .. .BS .SH NAME simulation::random \- Pseudo-random number generators .SH SYNOPSIS package require \fBTcl ?8\&.4?\fR .sp package require \fBsimulation::random 0\&.4\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_Triangular\fR \fImin\fR \fImax\fR .sp \fB::simulation::random::prng_SymmTriangular\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: .CS set p [::simulation::random::prng_Normal -1\&.0 10\&.0] .CE 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_Triangular\fR \fImin\fR \fImax\fR 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 \fIf(x) = 2(1-x)\fR and the other case it is of the form \fIf(x) = 2x\fR\&. .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_SymmTriangular\fR \fImin\fR \fImax\fR Create a command (PRNG) that generates numbers distributed according to a symmetric triangle around the mean of "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: .CS P(v) = exp( -exp(f*(v-min))) .CE .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,z)-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 CATEGORY Mathematics .SH COPYRIGHT .nf Copyright (c) 2004 Arjen Markus .fi