nchoosekFS

nchoosekFS returns the Binomial coefficient or matrix containing all combinations

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Syntax

c=nchoosekFS(v,k)example

Description

example

c =nchoosekFS(v, k) Binomial coefficient(s) or all combinations.

Examples

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Binomial coefficient(s) or all combinations.

Profile generation of 2118760 combinations.

v = 1:50; k = 4; 
tic
for i=1:10, nchoosekFS(v,k); end
t_nchoosekFS = toc
tic
for i=1:10, nchoosek(v,k); end
t_nchoosek = toc
fprintf('nchoosekFS has been %5.2f times faster than nchoosek\n\n\n', t_nchoosek/t_nchoosekFS); 
fprintf('Try now again using k=5: in a 32 bit computer\n');
fprintf('nchoosekFS will require about the same time (in order of magnitude)\n');
fprintf('while nchoosek will start swaping into virtual memory.\n');

t_nchoosekFS =

          0.03


t_nchoosek =

          0.09

nchoosekFS has been  3.04 times faster than nchoosek


Try now again using k=5: in a 32 bit computer
nchoosekFS will require about the same time (in order of magnitude)
while nchoosek will start swaping into virtual memory.

Input Arguments

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`v` — Vector of length n. Integer or array of non-negative integers.

Data Types: single|double

`k` — Items to choose from the set of n elements. Non negative integer.

Data Types: single|double

Output Arguments

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`c` —scalar $v!/k!(v-k)!$ if $v$ and $k$ are non-negative integers or matrix with $n!/k!(n-k)!$ rows and $k$ columns if $v$ is a vector of length $n. Binomial coefficient(s) or all combinations

Data Types - single|double

More About

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Additional Details

This function is similar to nchoosek of Statistics Toolbox but it is much faster and makes a more efficient use of memory.

Returns the scalar $v!/k!(v-k)!$ if $v$ and $k$ are non-negative integers.

This is the number of combinations of $v$ things taken $k$ at a time. In this case it makes use of function bc.

Produces a matrix with $n!/k!(n-k)!$ rows and $k$ columns if $v$ is a vector of length $n. Each row contains a combination of k elements taken without repetitions among n. In this case function combsFS is used.

References

Riordan, J. (1958), "An Introduction to Combinatorial Analysis", Wiley & Sons, New York.

Documentation

nchoosekFS

Syntax

Description

Examples

Binomial coefficient(s) or all combinations.

Input Arguments

`v` — Vector of length n. Integer or array of non-negative integers.

`k` — Items to choose from the set of n elements. Non negative integer.

Output Arguments

`c` —scalar $v!/k!(v-k)!$ if $v$ and $k$ are non-negative integers or matrix with $n!/k!(n-k)!$ rows and $k$ columns if $v$ is a vector of length $n. Binomial coefficient(s) or all combinations

More About

Additional Details

References

See Also

Documentation

nchoosekFS

Syntax

Description

Examples

Binomial coefficient(s) or all combinations.

Input Arguments

v — Vector of length n. Integer or array of non-negative integers.

k — Items to choose from the set of n elements. Non negative integer.

Output Arguments

c —scalar v!/k!(v-k)! if vv and kk are non-negative integers or matrix with n!/k!(n-k)!n!/k!(n-k)! rows and kk columns if vv is a vector of length $n. Binomial coefficient(s) or all combinations

More About

Additional Details

References

See Also

`v` — Vector of length n. Integer or array of non-negative integers.

`k` — Items to choose from the set of n elements. Non negative integer.

`c` —scalar $v!/k!(v-k)!$ if $v$ and $k$ are non-negative integers or matrix with $n!/k!(n-k)!$ rows and $k$ columns if $v$ is a vector of length $n. Binomial coefficient(s) or all combinations