lets say i have 4 vectors {x1, x2, x3, x4} and i m interested in the
following quantity

v = kron(x1, kron(x2, kron(x3, x4))))

which is easy to write down for a small number of vectors but how can
one generalize this?

the following is a solution using for loop:

x = rand(2,4); % 4 vectors each of length 2
v = kron(x(:,3), x(:,4));
for n=1:2
    v = kron(x(:,3-n), v);
end
v - kron(x(:,1), kron(x(:,2), kron(x(:,3), x(:,4)))) % check

is there any other way?

the order of the kron products is important of course.

What's wrong using the for-loop?

Bruno

Here is a vectorized engine, but honestly I don't see the point of insisting on vectorization:

% Random data
x1 = ceil(5*rand(1,3))
x2 = ceil(5*rand(1,2))
x3 = ceil(5*rand(1,4))

X1 = kron(x1,kron(x2,x3))

% Vectorize engine
x={x1 x2 x3};
n=length(x);
c = cell(size(x));
[c{:}]=ndgrid(x{end:-1:1});
c = cat(n+1,c{:});
X2 = reshape(prod(c,n+1),1,[])

isequal(X1,X2)

% Bruno

On 22 Okt., 14:45, "Bruno Luong" <b.lu...@fogale.findmycountry> wrote:
> Here is a vectorized engine, but honestly I don't see the point of insisting on vectorization:
>
> % Random data
> x1 = ceil(5*rand(1,3))
> x2 = ceil(5*rand(1,2))
> x3 = ceil(5*rand(1,4))
>
> X1 = kron(x1,kron(x2,x3))
>
> % Vectorize engine
> x={x1 x2 x3};
> n=length(x);
> c = cell(size(x));
> [c{:}]=ndgrid(x{end:-1:1});
> c = cat(n+1,c{:});
> X2 = reshape(prod(c,n+1),1,[])
>
> isequal(X1,X2)
>
> % Bruno

Hi,

the  v = kron(x1, kron(x2, kron(x3, x4))))  is a typical recursive
problem.
You can write a recursive function, which calculates your result. But
it probably wouldn't really be faster.
Since you have a working solution, I'm not sure it would be worthwile.

Here's the wikipedia article on recursion :
http://en.wikipedia.org/wiki/Recursion_%28computer_science%29

And here's the pseusocode for a recursive implementation of the
factorial function, just as an example:


factorial(n)
if (n <= 1)
    return 1;
else
    return n * factorial(n-1);

Awhan Patnaik <awimagic@gmail.com> wrote in message <64ee5575-c0f8-4faf-bbb5-db488ed49654@k13g2000prg.googlegroups.com>...
> lets say i have 4 vectors {x1, x2, x3, x4} and i m interested in the
> following quantity
> 
> v = kron(x1, kron(x2, kron(x3, x4))))
> 
> which is easy to write down for a small number of vectors but how can
> one generalize this?
==============

Consider not expanding out the kronecker product at all (unless you really need to) using this tool:

http://www.mathworks.com/matlabcentral/fileexchange/25969-efficient-object-oriented-kronecker-product-manipulation

In your case it would be

v=KronProd({x4,x3,x2,x1});

If you really need to, you can expand it using   
full(v) or sparse(v), as appropriate. This will use a for-loop, but like Bruno says, I don't see why vectorizing is preferable.

The fastest is for-loop using matrix product:

n = 10;
m = 5;
x = rand(m,n); % 10 vectors of length 5

tic
X1 = 1;
for k=1:size(x,2) 
    X1 = kron(X1,x(:,k));
end
toc

% Fastest method
tic
X2 = 1;
for k=1:size(x,2) 
    X2 = x(:,k)*X2;
    X2 = X2(:)';
end
X2 = X2';
toc

% Bruno

thanks for the answers and comments. nothing wrong with the for loop
as it gets the job done. just wanted to see if any alternate approach
was possible. thanks again.