Reducing memory storage through matrix computation
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I need to compute a matrix and the following code does exactly what I want. However, the operator creates O(n^2) storage but I want it to store the matrix linearly i.e., create O(n) storage (less storage space). I think this could be done using permutations but how could you modify the code in those terms:
ele=100;
x=(0:ele)'/2;
nlength= length(x);
p=ones(nlength,1);
for i=1:nlength-1
p=horzcat(p,x.^i);
end
g=p*x;
2 Comments
Answers (1)
Matt J
on 2 Mar 2014
Edited: Matt J
on 2 Mar 2014
If you only intend to operate on vectors, by matrix-vector multiplication, you could use MatrixObj as below (or just use POLYVAL directly),
p=MatrixObj;
p.Ops.mtimes=@(~,y) polyval(flipud(y), x);
p.Ops.size=[nlength,nlength];
However, I don't see when it would ever be practical to use such a matrix for very large n. Expressions like x.^n are very numerically sensitive when n is large.
2 Comments
Matt J
on 2 Mar 2014
Edited: Matt J
on 2 Mar 2014
I didn't understand your comment. The code you've posted is equivalent to the single line,
g=polyval(flipud(x),x);
So, if you want to use built-in functions only, this would be the way.
The advantage of MatrixObj is that it allows you to do the same thing with the same matrix multiplication syntax as in your original code,
p=MatrixObj;
p.Ops.mtimes=@(~,y) polyval(flipud(y), x);
p.Ops.size=[nlength,nlength];
g=p*x;
which sounded like what you were looking for.
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