Unix and Linux Discussions Tagged with amp |
|
Thread / Thread Starter |
Last Post |
Replies |
Views |
Forum |
|
|
|
1 |
11,072 |
UNIX for Beginners Questions & Answers |
|
|
|
1 |
4,245 |
UNIX for Beginners Questions & Answers |
|
|
|
6 |
4,141 |
UNIX for Beginners Questions & Answers |
|
|
|
2 |
11,473 |
UNIX for Beginners Questions & Answers |
|
|
|
1 |
3,316 |
UNIX for Beginners Questions & Answers |
|
|
|
2 |
3,336 |
UNIX for Beginners Questions & Answers |
|
|
|
8 |
42,990 |
Solaris |
|
|
|
5 |
3,106 |
UNIX for Beginners Questions & Answers |
|
|
|
0 |
1,801 |
What is on Your Mind? |
|
|
|
33 |
35,713 |
Solaris |
|
|
|
2 |
3,672 |
Solaris |
|
|
|
2 |
3,885 |
IP Networking |
|
|
|
2 |
3,168 |
AIX |
|
|
|
0 |
1,991 |
Software Releases - RSS News |
|
|
|
2 |
7,578 |
Solaris |
|
|
|
2 |
2,196 |
UNIX for Dummies Questions & Answers |
|
|
|
1 |
3,060 |
Programming |
|
|
|
0 |
2,367 |
OS X Support RSS |
|
|
|
1 |
29,442 |
Shell Programming and Scripting |
|
|
|
0 |
1,989 |
Solaris BigAdmin RSS |
|
|
|
7 |
13,266 |
Ubuntu |
|
|
|
0 |
1,376 |
Complex Event Processing RSS News |
|
|
|
0 |
1,909 |
Cartoons for Geeks |
|
|
|
0 |
1,281 |
Software Releases - RSS News |
|
|
|
6 |
4,742 |
UNIX for Dummies Questions & Answers |
|
|
|
1 |
1,514 |
UNIX for Dummies Questions & Answers |
|
|
|
0 |
2,451 |
Cartoons for Geeks |
|
|
|
0 |
1,800 |
Complex Event Processing RSS News |
|
|
|
0 |
2,403 |
Cartoons for Geeks |
|
|
|
0 |
3,120 |
HP Server News and Podcasts RSS |
|
|
|
0 |
1,678 |
MySQL DevZone RSS |
|
|
|
5 |
6,461 |
UNIX for Advanced & Expert Users |
|
|
|
0 |
1,716 |
Complex Event Processing RSS News |
|
|
|
3 |
6,355 |
UNIX and Linux Applications |
|
|
|
6 |
10,038 |
Solaris |
|
|
|
0 |
2,338 |
Cartoons for Geeks |
|
|
|
0 |
1,808 |
Cartoons for Geeks |
|
|
|
2 |
5,677 |
OS X (Apple) |
|
|
|
3 |
2,218 |
Shell Programming and Scripting |
|
|
|
0 |
1,060 |
Software Releases - RSS News |
math::combinatorics(n) Tcl Math Library math::combinatorics(n)
__________________________________________________________________________________________________________________________________________________
NAME
math::combinatorics - Combinatorial functions in the Tcl Math Library
SYNOPSIS
package require Tcl 8.2
package require math ?1.2.3?
::math::ln_Gamma z
::math::factorial x
::math::choose n k
::math::Beta z w
_________________________________________________________________
DESCRIPTION
The math package contains implementations of several functions useful in combinatorial problems.
COMMANDS
::math::ln_Gamma z
Returns the natural logarithm of the Gamma function for the argument z.
The Gamma function is defined as the improper integral from zero to positive infinity of
t**(x-1)*exp(-t) dt
The approximation used in the Tcl Math Library is from Lanczos, ISIAM J. Numerical Analysis, series B, volume 1, p. 86. For "x >
1", the absolute error of the result is claimed to be smaller than 5.5*10**-10 -- that is, the resulting value of Gamma when
exp( ln_Gamma( x) )
is computed is expected to be precise to better than nine significant figures.
::math::factorial x
Returns the factorial of the argument x.
For integer x, 0 <= x <= 12, an exact integer result is returned.
For integer x, 13 <= x <= 21, an exact floating-point result is returned on machines with IEEE floating point.
For integer x, 22 <= x <= 170, the result is exact to 1 ULP.
For real x, x >= 0, the result is approximated by computing Gamma(x+1) using the ::math::ln_Gamma function, and the result is
expected to be precise to better than nine significant figures.
It is an error to present x <= -1 or x > 170, or a value of x that is not numeric.
::math::choose n k
Returns the binomial coefficient C(n, k)
C(n,k) = n! / k! (n-k)!
If both parameters are integers and the result fits in 32 bits, the result is rounded to an integer.
Integer results are exact up to at least n = 34. Floating point results are precise to better than nine significant figures.
::math::Beta z w
Returns the Beta function of the parameters z and w.
Beta(z,w) = Beta(w,z) = Gamma(z) * Gamma(w) / Gamma(z+w)
Results are returned as a floating point number precise to better than nine significant digits provided that w and z are both at
least 1.
BUGS, IDEAS, FEEDBACK
This document, and the package it describes, will undoubtedly contain bugs and other problems. Please report such in the category math of
the Tcllib SF Trackers [http://sourceforge.net/tracker/?group_id=12883]. Please also report any ideas for enhancements you may have for
either package and/or documentation.
CATEGORY
Mathematics
math 1.2.3 math::combinatorics(n)