Problem with using the max while manipulating a 3-dimensional array

[Krzysztof Postek]

Dear Mr. Lofberg,

I have a problem that while defining the optimization problem involving 3 dimensional matrices (attached with data definitions) I get the following message: 

Error using ndsdpvar.max

Too many input arguments.

Could you please help me with this issue?

Thank you

Krzysztof

[Johan Löfberg]

Hmm, I should have run your code first...

[Johan Löfberg]

An easy way out for me is to say that your code is not valid MATLAB syntax

X = randn(2,3,4);
Y = randn(2,3,4);
>> max(X,Y,3)
Error using max
MAX with two matrices to compare and a working dimension is not supported.

[Johan Löfberg]

I don't even understand what it means to take max(X,Y,dim). What would be the answer here for dim=2, i.e, the highest dimension

>> X = [1 2;3 4]

X =

     1     2
     3     4

>> Y = [5 6;7 8]

Y =

     5     6
     7     8

[Krzysztof Postek]

Dear Mr. Löfberg

thank you for your reply. The following code is rather ok with respect to parameters, but gives me exactly the same error:

q=sdpvar(2,1);


objective_proxy = sdpvar;


Constraints = [norm(q,1) <= 1];
Constraints = [Constraints; max(rand(2,2,2).*repmat(q,[1 2 2]), rand(2,2,2).*repmat(q,[1 2 2])) <= objective_proxy];


Objective = objective_proxy;


sol = solvesdp(Objective,Constraints);

I think the reason is that the max.m function from the ndsdpvar folder interprets the 3rd dimension of the matrices as an extra parameter of max, and hence the error. However, I just tackled the problem for my application by interchanging the dimensions of the matrices, so that I no longer compare 3D matrices with max, but only 2D matrices.

[Johan Löfberg]

This case is correct MATLAB syntax, but the case with two arguments is not implemented for ndsdpvars

You can write it as

a = rand(2,2,2).*repmat(q,[1 2 2]);
b = rand(2,2,2).*repmat(q,[1 2 2]);
reshape(max(a(:),b(:)),size(a))

The next version will support this though

[Johan Löfberg]

Ah well, here it is

function Y = max(X,aux,workdim)
% abs (overloaded)

switch nargin
    case 1
        workdim = 1;
    case 2
        Y = max(reshape(X,[],1),reshape(aux,[],1));
        Y = reshape(Y,size(X));
        return
    case 3
        if ~isempty(aux)
            error('MAX with two matrices to compare and a working dimension is not supported in MATLAB.');
        end
    otherwise
        error('Too many input arguments')
end

xdim = size(X);

if workdim > length(xdim)
    error('Index exceeds matrix dimensions.');
end

newdim = xdim;
newdim = circshift(xdim',-(workdim-1))';
newdim(1)=1;
Y = reshape(max(reshape(shiftdim(X,workdim-1),xdim(workdim),[])),newdim);
Y = shiftdim(Y,length(xdim)-workdim+1);

[Krzysztof Postek]

Great! Thank you, I will use the upgraded version in my next numerical example! Sometimes it is just easier to work in mind with entire 3D variables.