image thumbnail

FACTORIALRATIO

version 1.4.0.0 (2.81 KB) by Jos (10584)
Ratio of factorials, as in (a!b!c!...) / (d!e!f!g!...) (version 2.0, oct 2012)

1.9K Downloads

Updated 25 Oct 2012

View License

FACTORIALRATIO - ratio of factorial numbers

FR = FACTORIALRATIO (A,B) calculates the ratio between products of
factorials specified by A and B. A and B are lists of positive
integers, with N and M elements, respectively. The number of values in
each list may differ. The factorial ratio is based on the following formula:

(A1! * A2! * ... * AN!)
FR = -------------------------
(B1! * B2! * ... * BM!)

However, an approach is taken that increases the accuracy when A or B
contain larger values, as mentioned in the help of FACTORIAL.

Examples:

f1 = factorialratio([10 8 6],[9 6 5]) ;
f2 = 10 * 8 * 7 * 6 ; % by hand
f3 = (factorial(10) * factorial(8) * factorial(6)) ./ ...
(factorial(9) * factorial(6) * factorial(5)) ;
disp('f1, f2, f3 = ') ; disp([f1 f2 f3])


% Also for larger values FACTORIALRATIO works correctly
f1 = factorialratio(150,143) ;
f2 = prod(144:150) ; % by hand
% where FACTORIAL lacks precision
f3 = factorial(150) ./ factorial(143) ;
disp('f1, f2, f3 = ') ; disp([f1 f2 f3])
disp(' Differences with f2 = ') ; disp([f1-f2 f2-f2 f3-f2])

% and even for extreme numbers things turn out well
f1 = factorialratio(30000,29998) ;
f2 = (30000 * 29999) ; % by hand
% whereas calls to FACTORIAL fail miserably ...
f3 = factorial(30000) ./ factorial(29998) ;
disp('f1, f2, f3 = ') ; disp([f1 f2 f3])

Note that, for instance, factorialratio(200,1) also fails, of course.
For such occasions other engines have to be used.

See also prod, factorial, gammaln

Cite As

Jos (10584) (2021). FACTORIALRATIO (https://www.mathworks.com/matlabcentral/fileexchange/23018-factorialratio), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R13
Compatible with any release
Platform Compatibility
Windows macOS Linux

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!