A class for successive matrix products

A class representing products of matrices, internally storing/manipulating them separately.

This submission defines a class for representing products of matrices (or of any objects that know how to multiply) when it is more efficient to store and manipulate the matrices separately. Below is a basic example, but more can be found in the Examples tab.

N=3e4;
u=rand(N,1);
v=rand(N,1);
x=rand(N,1);

Pmat=u*v.';

and let us also represent Pmat as a ProdCascade object.

P=ProdCascade({u,v.'});

Now, compare the execution time from multiplying with Pmat and its transpose,

tic;
 y1=Pmat*x; 
 z1=Pmat.'*y1;
toc; %Elapsed time is 0.347683 seconds.

with the same operations using a ProdCascade representation,

tic 
 y2=P*x; 
 z2=P.'*y2;
toc %Elapsed time is 0.005741 seconds.

DISCAIMER: Error checking is never done to see whether the operators in a ProdCascade are compatible for successive multiplication.