MULTINOMIAL

Multinomial coefficients.

Description

MULTINOMIAL(N, K1, K2, ..., Km) where N and Ki are numeric arrays of non-negative integers satisfying N = K1 + K2 + ... + Km, returns the multinomial coefficient N!/( K1!* K2! ... *Km!).

MULTINOMIAL(N, [K1 K2 ... Km]) when Ki's are all scalar, returns the same as MULTINOMIAL(N, K1, K2, ..., Km).

Non-integer input arguments are pre-rounded by FLOOR function.

EXAMPLES:
multinomial(8, 2, 6) returns 28
binomial(8, 2) returns 28

multinomial(8, 2, 3, 3) returns 560
multinomial(8, [2, 3, 3]) returns 560

multinomial([8 10], 2, [6 8]) returns [28 45]

• MATLAB release: MATLAB 7 (R14)
• Other requirements: uses scalarexpand.m(by the same author) available in this file-exchange.

[Antonio Trujillo-Ortiz]

As a user, it is frustrating to run this function due that we get several ERROR display messages and abort function. Such as:

Undefined function or variable 'isfloat'.

Error in ==> C:\Documents and Settings\multinomial.m
On line 29 ==> if ~isreal(n) || ~isfloat(n) || any(n(:)<0)

??? Undefined function or variable 'sclrexpnd'.

Error in ==> C:\Documents and Settings\multinomial.m
On line 42 ==> [arg2{:},sizk] = sclrexpnd(arg2{:});

This last ERROR message is due that you have already created the m-file called scalarexpand not sclrexpnd.

Besides,there exists a much more parsimoniously way to calculate it you can find on this same site as multcoef.

So the users became frustrated.

[Mukhtar Ullah]

ISFLOAT is a built-in function in MATLAB 7. For earlier versions, ~isfloat(n) can be replaced by ~isa(n,'double') | ~isa(n,'single').
I have renamed scalarexpand to fix the bug.
Thanks once again to Antonio Trujillo-Ortiz.

[Mukhtar Ullah]

Another problem that can be faced by earlier versions is the short-circuit AND and OR functions (&&, ||). These can simple be replaced by the usual AND,OR (&,|).

[Min Poh]

The update addresses the bugs mentioned in the comments. The function is also well documented.

[George richardson]

well documented, simple function

[Kammoun]

good work