linear combination of vector and permutation

Hi, i' m developing a program where I find myself with this problem that I couldn't solve nem with combntns(v,k) or with nchoosek .

Anyone here to help me?

Let A=[-1,1] and B=3

I need to find all possible combinations taking from B to B vector element A ( It can be with repetition of the vector element )

I have done it manually, but I need it automatically, or a Matlab function does it.

Let A and B the output of this function has to be:

Out=[-1,-1,-1; 
     -1,-1, 1
     -1, 1,-1
     -1, 1, 1
      1,-1,-1
      1,-1, 1
      1, 1,-1
      1, 1, 1],  

Answer 1

[Torsten]

values = [-1 1];                            %//  data
k = 3;                                      %//  data
n = numel(values);                          %//  number of values
combs = values(dec2base(0:n^k-1,n)-'0'+1)   %//  generate all tuples

combs = 8×3

-1 -1 -1 -1 -1 1 -1 1 -1 -1 1 1 1 -1 -1 1 -1 1 1 1 -1 1 1 1

[Fidele Adanvo]

thank you

[Matt J]

This approach is rather slow, if that matters...

values = -2:2;                            %//  data
k = 9; 

timeit(@()version1(values,k))

ans = 0.5780

timeit(@()version2(values,k))

ans = 0.0763

function version1(values,k)

 n = numel(values);                          %//  number of values
 combs = values(dec2base(0:n^k-1,n)-'0'+1);   %//  generate all tuples

end

function version2(A,B)

 [Out{1:B}]=ndgrid(A);
 Out=reshape( cat(B+1,Out{:}),[],B);

end

Answer 2

[Matt J]

One way:

A=[-1,1];B=3;

[Out{1:B}]=ndgrid(A);

Out=reshape( cat(B+1,Out{:}),[],B)

Out = 8×3

-1 -1 -1 1 -1 -1 -1 1 -1 1 1 -1 -1 -1 1 1 -1 1 -1 1 1 1 1 1

[Fidele Adanvo]

thank you

[Stephen23]

+1 very neat usage of CAT and RESHAPE.

Answer 3

[James Tursa]

Another way very similar to Torsten's method, limited to two desired values:

n = 3;
2*(dec2bin(0:2^n-1)-'0')-1

ans = 8×3

-1 -1 -1 -1 -1 1 -1 1 -1 -1 1 1 1 -1 -1 1 -1 1 1 1 -1 1 1 1