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FACTORIALRATIO

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FACTORIALRATIO

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18 Feb 2009 (Updated )

Ratio of factorials, as in (a!b!c!...) / (d!e!f!g!...) (version 2.0, oct 2012)

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Description

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

MATLAB release MATLAB 6.5 (R13)
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Comments and Ratings (4)
26 Oct 2012 Jos (10584)

Version 2.0 (oct 2012) fixed the bug mentioned by Charles.

17 Oct 2012 Charles

Version 1.1 (feb 2009) of this code has a bug.

x(1)=factorialratio(2,1); %should be 2
x(2)=factorialratio(1,2) %should be .5

x =

1 1

18 Feb 2009 John D'Errico

Sorry, I forgot to point out what I feel to be one of the best features of this code - the copious internal comments that explain how it works.

I've often argued that the best MATLAB code should aim for a 1-1 ratio of comments to lines of code. That is, each line of code should have an associated comment line, at least in those places where the code is doing something tricky. This code goes beyond my aim. People interested in how to write good comments should look at what the author did here and learn from it.

18 Feb 2009 John D'Errico

Good help as you would expect from Jos. Well written. An interesting solution for the computation itself.

Updates
18 Feb 2009

fixed small bug in error checks

25 Oct 2012

fixed bug for inputs with only 2's

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