N_PERMUTE_K

All possible permutations of the elements of set N, taken K at a time, with repetition.

Description

MAT = NPERMUTEK(N,K) returns all possible permutations of the elements taken from vector N of length K. This type of sampling is an ordered sample with replacement.
This is also known as the permutations with repetition.
MAT has size (length(N)^K)-by-K, where K must be a scalar.
  
[MAT, IDX] = NPERMUTEK(N,K) also returns IDX such that MAT = N(IDX).

If N is of class single, MAT and IDX will be also.

Please email me about bugs in the code.
Thanks

Acknowledgements

The author wishes to acknowledge the following in the creation of this submission:
COMBN (4.2)
This submission has inspired the following:
VChooseKRO

• MATLAB release: MATLAB 7.4 (R2007a)

[matt fig (author)]

I noticed that I missed a comment line in the help... this is fixed.

[Jos vdG]

Did you know <combnk> also here on the FEX? (File # 7147).
Looks like that does exactly the same.

[Jos vdG]

sorry .. didn't see the acknowledgement ...
Jos

[matt fig (author)]

I thought that by defining the last column of the Index matrix first, there would be no advantage to pre-allocation. I was wrong, live and learn. File updated.

[V. M.]

Fast and a good description of what it does.

[Husam Aldahiyat]

Very helpful.

[Hoda El Mahallawy]

what's nume1? that's used for calculating the index. where's the help that you said you missed sth in ? Thanks

[Matt Fig]

Hoda,

numel is a built-in Matlab function which returns the Number of ELements in the argument. If your version of Matlab is too old to have numel, you may have to write your own. For vector inputs to npermutek, you can also replace numel with length.

[Hoda El Mahallawy]

Dear Sir Matt,
What's nargin? Thanks

[Matt Fig]

nargin is a built-in Matlab function, as is numel. Take these questions to email please! My email address is in the file.

[Gareth]

just what I wanted, worked as I expected, great comments. Thanks

[Syed Galib]

It is really a nice thing...it helped me a lot.
Thank you author for this

[Juliette Salexa]

Does this not work for large arrays ??

>> nuc='ABCD';
>> clear('R');n=1;R=zeros(4^n,n);R=nuc(npermutek(1:n,n));
works.
>> clear('R');n=2;R=zeros(4^n,n);R=nuc(npermutek(1:n,n));
works.
>> clear('R');n=3;R=zeros(4^n,n);R=nuc(npermutek(1:n,n));
works.
>> clear('R');n=4;R=zeros(4^n,n);R=nuc(npermutek(1:n,n));
works.
>> clear('R');n=5;R=zeros(4^n,n);R=nuc(npermutek(1:n,n));
??? Index exceeds matrix dimensions.

------------------
I'm not entirely sure where the index is exceeding matrix dimensions.... if only matlab was more specific with error listings.
------------------
But maybe this is only happening on my machine... can someone try and let me know ???

[Matt Fig]

Juliette,

You cannot index the output of npermutek(1:5,5) into an array (nuc) of length 4! The index exceeds dimensions because the output of the above call to NPERMUTEK will have many '5's in it. You will get the same error by doing this:

nuc = 'ABCD'
R = nuc(5) % or nuc(6) or nuc(7), etc. nuc only has 4 elements!

This is not an NPERMUTEK problem, it a user misunderstanding the output problem.

[Mark]

totally terrific, works as advertised and saves me a bunch of hassle.

[GERMÁN]

HOW TO CALCULATE THIS FUNCTION?

MAT = npermutek(['a' 'b' 'c' '!' 'l' 't' 's' '0' '1' 'e' 'o' 'i' ],16)

[Jan Simon]

Why is the index IDX a SINGLE array, if N is a SINGLE? Isn't this an unnecessary limitation when working with large arrays on a 64-bit Matlab? UINT32 would accept larger arrays with using all 32 bits for adressing. And addressing with UINT32 might be faster than with SINGLEs (depending on Matlab version?!).
--- But of course: The number of permutations will explode at far smaller limits, I know.

Is it helpful to cast CHAR to DOUBLEs temporarily, or would it be better to store them in smaller INT16?

[Matt Fig]

Jan,
With the single class we are ok up to 16,000,000 elements. Even finding the number taken two at a time would lead to an array of size 5.12e+014 elements. I think this is beyond the reasonable, even with 64-bit computing! The other problem is that cumsum isn't supported for the integer classes, at least in 2007b. If you look at my COMBINATOR file, you will see that I have included a MEX which performs cumsum on integer classes.
Thanks.

[Jan Simon]

Thanks Matt! Now I got it.
For small arrays, this function is faster than your COMBINATOR.
H1-Line, help, example, contact address, "see also", input checks, extensive comments, works correct and efficiently => nice for teaching and computing!

[zampala ballarini]

Works great, thanks

[rahman]

Excellent