Multiplication of SDPVAR and vectorized version

[jhua...@hawk.iit.edu]

Hi professor,

I get the following message:

Multiplication of SDPVAR object caused memory error

Continuing using unvectorized version which is extremely slow

They are related with my code as follow,

FIM1=w_2*H_m'*(diag(p))*H_m

where w_2 is a constant, H_m is a m-by-n matrix.

How can I solve these 2 problems? By the way, I think my code is vectorized, right?

Thanks,

Jianqiao Huang

[Johan Löfberg]

You re simply creating a way too large symbolic expression. What do you intend to use it for? If it is a semidefinite constraint, you re screwed anyway as you never would be able to solve anything that large. If you are creating it to use it later for something else, you might not need to construct this first but do things in a more clever way

A simple thing like this

>> x = sdpvar(100);

>> R = randn(100);

>> x'*R*x

will have on the order of 10000 expressions, each involving on the order of 10000 monomials, and this will probably take a GB or so to represent

[jhua...@hawk.iit.edu]

Hi professor,

FIM1=w_2*H_m'*(diag(p))*H_m , where only p is a variable vector (8878-by-1), w_2 and H_m are constant number and matrix. It's a semidefinite model. Last year, I used a similar model and it worked. But I don't know why it doesn't work this time.

Thanks,

Jianqiao Huang

[jhua...@hawk.iit.edu]

Hi professor,

Do you think the model is large given that only p is a 8878-by-1 vector and the others are constant number or matrix? Do I need to send you my code?

Thanks,

Jianqiao Huang

[jhua...@hawk.iit.edu]

I mean only p is a 8878-by-1 variable vector. H_m is a 8878-by-7410 constant matrix and w_m is a constant number.

[Johan Löfberg]

Still going to a massive object to create and hold symbollically if h is dense. As I said, are you actually using this matrix, or is it a partial result before doing something else

>> clear all

>> h = randn(250);

>> p = sdpvar(250,1);

>> q = h'*diag(p)*h;

>> whos

  Name        Size                 Bytes  Class     Attributes

  h         250x250               500000  double              

  p         250x1                  10552  sdpvar              

  q         250x250            250006536  sdpvar              

[jhua...@hawk.iit.edu]

My model is very similar to the D-optimal design convex relaxed problem https://yalmip.github.io/example/experimentdesign/. variable vector p is like variable m in the link.

In this case, am I actually using this matrix, or is it a partial result?

[Johan Löfberg]

So you intend to solve a 7410x7410 semidefinite program involving 8878 variables? That's just not going to fly

[jhua...@hawk.iit.edu]

Hi professor,

SDPT3 can work now when replace the matrix vector multiplication with the following for loop,

for i=1: m

      hi=H(i,:);

      A=A+p(i)*hi'*hi;

end.

Thanks,

Jianqiao Huang

[Johan Löfberg]

That loop has to be absolutely awfully slow, as it will manipulate an increasingly complex object. Some recursive calls at least to avoid that. THe last method below has roughly the same time as H'*diag(p)*H

m = 300;

H = randn(m);

p = sdpvar(m,1);

tic

A = 0;

for i=1:m

    hi = H(i,:);

    A = A+p(i)*hi'*hi;

end

toc

tic

A = recursivesum1(H,p)

toc

tic

A = recursivesum2(H,p)

toc

function B = recursivesum1(A,p)

if length(p) > 10

    n = ceil(length(p)/2);

    B1 = recursivesum1(A(1:n,:),p(1:n));

    B2 = recursivesum1(A(n+1:end,:),p(n+1:end));

    B = B1 + B2;

else

    B = 0;

    for i = 1:length(p)       

        B = B+p(i)*A(i,:)'*A(i,:);

    end

end

    

function B = recursivesum2(A,p)

if length(p) > 10

    n = ceil(length(p)/2);

    B1 = recursivesum2(A(1:n,:),p(1:n));

    B2 = recursivesum2(A(n+1:end,:),p(n+1:end));

    B = B1 + B2;

else

    B = A'*diag(p)*A;   

end