Sums of sdpvars and sparse assignment limited to 2D

[Collin Lutz]

Hello,

I am getting the error "Sparse assignment is limited to 2 dimensions" stemming from line 27 below. Could the tildeX assignment on line 20 be causing issues from double/sdpvar confusion as discussed here? If so, how do you build a sum of sdpvars?

Also, what is the correct way to initialize variables that will have sdpvars in their structure (e.g., XBlock)? If I initialize XBlock = zeros(nx+nw,nx+nw,N), I run into troubles with the double/sdpvar confusion. Should I instead initialize XBlock = sdpvar(nx+nw,nx+nw,N)? In the code below, I do not initialize XBlock, tildeX, or brl at all.

1. global A
2. global B
3. global C
4. global D
5. global N
6. 
   
7. loadSystemMats();
8. 
   
9. P = [ 0.3 0.7 ; 0.3 0.7 ];
10. 
    
11. [nx,dum]=size(A(:,:,1));
12. [nz,dum]=size(C(:,:,1));
13. [dum,nw]=size(D(:,:,1));
14. 
    
15. X = sdpvar(nx,nx,N,'symmetric','real');
16. F = [];
17. 
    
18. for i = 1:N
19.    M(:,:,i) = [ A(:,:,i), B(:,:,i) ; C(:,:,i), D(:,:,i) ];
20.    tildeX(:,:,i) = zeros(nx,nx);
21. 
    
22.    for j = 1:N
23.       tildeX(:,:,i) = tildeX(:,:,i) + P(i,j).*X(:,:,j);
24.    end
25. 
    
26.    tildeBlock(:,:,i) = [ tildeX(:,:,i), zeros(nx,nz) ; zeros(nz,nx), eye(nz) ];
27.    XBlock(:,:,i) = [ X(:,:,i), zeros(nx,nw) ; zeros(nw,nx), eye(nw) ];
28.    brl(:,:,i) = M(:,:,i)' * tildeBlock(:,:,i) * M(:,:,i) - XBlock(:,:,i);
29. 
    
30.    F = [ F, X(:,:,i) >= 0, brl(:,:,i) <= 0 ];
31. end
32. options = sdpsettings('solver','sedumi');
33. diagnostics = solvesdp(F,[],options)
34. checkset(F)

Thank you.
Collin

[Johan Löfberg]

The easiest for you is to simply avoid using a 3D matrix. Just put the slices in cells instead, Xtilde{i} = ...

The way you define Xtilde (etc) does not work anyway do to a design feature in MATLAB
http://users.isy.liu.se/johanl/yalmip/pmwiki.php?n=Extra.NANInModel

[Collin Lutz]

Thanks for the quick response! Should I initialize blocks that will contain other sdpvars as sdpvars or doubles? For example, which of the following would be correct?

for i = 1:N

   XBlock{i} = zeros(nx+nw,nx+nw);
end

OR

for i = 1:N

   XBlock{i} = sdpvar(nx+nw,nx+nw);
end

In the code below, I initialize tildeX{i} to be zeros and it seems to work. Here's the code in case it will help anyone else in the future:

1. global A
2. global B
3. global C
4. global D
5. global N
6. loadSystemMats();
7. P = [ 0.3 0.7 ; 0.3 0.7 ];

1. [nx,dum]=size(A{1});
2. [nz,dum]=size(C{1});
3. [dum,nw]=size(D{1});

1. for i = 1:N

1.     X{i} = sdpvar(nx,nx,'symmetric','real');
2. end

1. F = [];
2. for i = 1:N

1.    M{i} = [ A{i}, B{i} ; C{i}, D{i} ];
2.    tildeX{i} = zeros(nx,nx);

1.    for j = 1:N

1.       tildeX{i} = tildeX{i} + P(i,j).*X{j};
2.    end
3.    tildeBlock{i} = [ tildeX{i}, zeros(nx,nz) ; zeros(nz,nx), eye(nz) ];
4.    XBlock{i} = [ X{i}, zeros(nx,nw) ; zeros(nw,nx), eye(nw) ];
5.    brl{i} = M{i}' * tildeBlock{i} * M{i} - XBlock{i};
6.    F = [ F, X{i} >= 0, brl{i} <= 0 ];

[Johan Löfberg]

you don't have to predefine anything when you work with cells

This is perfectly ok code in MATLAB

for i = 1:10
 Z{i} = something
end

where something is what ever you want, and Z is undefined when you start

[Johan Löfberg]

line 17 is completely redundant

[Collin Lutz]

If I comment out line 17, I get an "Undefined variable "tildeX" or class "tildeX" error.

[Johan Löfberg]

Of course, since you (redundantly) reference the zero object Xtilde on line 19

[Collin Lutz]

Is there a better way to build \sum_{j=1}^{N} P(i,j) .* X_j ? Thanks for your comments and patience.

[Johan Löfberg]

Looks like the easiest approach. You can probably write it using kron and some nasty reshapes, but I don't see why one would like to do that

[Collin Lutz]

Okay. Thanks. Under the hood, is tildeX{i} being cast as an sdpvar each time X{j} is added?

[Johan Löfberg]

tildeX{i} is what ever you have placed in tildeX. No casting or anything happening. A cell object is a container for anything

X{1} = sdpvar(2);
X{2} = pi;
X{3} = 'bananas';

[Collin Lutz]

Ok. Thanks again!