inner matrix dimensions must agree error in the function?

function [f] = objfun(W,VCVMatx)

%function for varience of the portfolio with swtN stocks

 f =W*VCVMatx*W';

this is my function I am trying to run in the main program. However, when run in the main program, it keeps giving me :

Error using * Inner matrix dimensions must agree.

W is a 10(N)X1 vector, while VCVMatx is an NXN vector?

Does anyone see anything wrong, considering I multiplied it by a transposed W'

I tried running fmincon, but in the main program it says the function matrix dimensions do not agree.

f = (W'*VCVMatx)*W;

i=1; 
while i<=rows(ERGrid); 
  ExpectedReturn = ERInc(i); 
  [W] = fmincon('objfun',x0,swtOther_A,swtOther_b,swtOther_Aeq,swtOther_beq,swtMinWt1,swtMaxWt1,[],options); 
  ERGrid(2:swtN+1,i) = W; 
  i=i+1; 
end;

W' is a 1X10 vector while VCVMatx is a 10X10 matrix and W is 10X1 vector

fmincon cannot run as a result.

Answer 1

[Geoff Hayes]

The first matrix product (in the equation) is the problem. Since W is Nx1 and VCVMatx is NxN, then W*VCVMtx will fail due to the incompatible dimensions of the two matrices. If you are just expecting a single value, then the equation should be re-written as

 f = W'*VCVMtx*W;

[Sameer]

I changed it up, but it still does not work for some reason.

[Star Strider]

If you type:

W_size = size(W)
VCVMatx_size(VCVMatx)

what are the results?

[Sameer]

where should i type that?

[Geoff Hayes]

Type the commands that Star Strider indicated just prior to evaluating f to ensure that the dimensions of the matrices are compatible.

[Sameer]

well, it says 'VCVMatx_size' is undefined. but W_size is 1 and 10.

[Geoff Hayes]

Try the following to get the number of rows and columns of VCVMatx

 VCVMatx_size = size(VCVMatx)

[Sameer]

i did that, and it says

Inner matrix dimensions must agree.

Error in objfun (line 8) f = (W'*VCVMatx)*W;

so it is basically giving me the same error as before.

[Star Strider]

I’ve never seen the size function return ‘undefined’ as output.

Go back and see how you created VCVMtx. If the code creating it is not very long, post it or the relevant part of it.

[Sameer]

swtN = cols(Data); VCVMatx = cov(Data)*252;

data is imported from a .csv file and has 10 (swtN) stocks.

these equation are in the main program

[Geoff Hayes]

@Sameer - you said a couple of comments ago that W is 1x10 (which is different from the original statement of 10x1). If that is the case, and VCVMtx is still 10x10 (what did size(VCVMtx) return?), then your original line of code (not the one I suggested above) should be valid

f = W*VCV*W';

[Sameer]

 W transposed is a 1X10 vector. So you were originally correct.

[Star Strider]

What is:

swtN_size = size(swtN)

[Sameer]

1X1, it is a scalar

[Geoff Hayes]

What then is:

VCVMatx_size = size(VCVMatx)

[Sameer]

10X10

[Sameer]

when i type that same equation in the main program ( f = W'*VCVMtx*W;) it seems to work.

but it does not work when it is in the function.

[Star Strider]

So:

f = W'*VCV*W;

should be a scalar.

[Geoff Hayes]

Strange that it doesn't work in the function. Could you attach the function (m file) to a comment, using the paper clip button?

[Sameer]

yes it does turn out to be a scalar. I am supposed to minimize this for fmincon

[Sameer]

here is the function:

[Sameer]

Here is the error it gives me when i try to run the main program:

[Geoff Hayes]

The code is

 function [f] = objfun(W,VCVMatx)

    %function for varience of the portfolio with swtN stocks
    global VCVMatx;

    W_size = size(W);
    VCVMatx_size = size(VCVMatx);

    f = (W'*VCVMatx)*W;
  end

Why is there a global variable with the same name as the input parameter? If this global variable has not been set then it is probably empty and so the error is thrown. Please comment out the line

 % global VXVMatx;

and try again so that the second input (to the function) is used.

[Sameer]

i took out the globa variable in the function and now it is saying:

Error using objfun (line 7) Not enough input arguments.

Error in fmincon (line 564) initVals.f = feval(funfcn{3},X,varargin{:});

Error in FEHW7 (line 183) [W] = fmincon('objfun',x0,swtOther_A,swtOther_b,swtOther_Aeq,swtOther_beq,swtMinWt1,swtMaxWt1,[],options);

Caused by: Failure in initial user-supplied objective function evaluation. FMINCON cannot continue.

[Geoff Hayes]

Okay - I don't have the fmincon function, but reading the documentation at http://www.mathworks.com/help/optim/ug/fmincon.html indicates that the function handle passed into fmincon must be for a function that accepts a vector and returns a scalar. Is that why you have tried to get around the limitation of only one input being passed - by using a global variable?

If that is the case, then I suppose you have to put that global variable back and remove the second input to your objfun. Then, assuming that the input vector is 1x10 and that the global variable VCVMtx is 10x10, then your f should be changed to

 f = (W*VCVMatx)*W';

and the global variable VCVMatx must be set prior to the evaluation of fmincon.

[Sameer]

what the heck? it works now.....

[Sameer]

could you explain the error in more detail? thanks.

[Geoff Hayes]

I think the problem that you were originally experiencing was the the global variable VCVMatx was not defined to be a 10x10 matrix, it was just empty. And so if you multiply a non-empty matrix ( W ) with an empty matrix ( VCVMatx ) the message Error using * Inner matrix dimensions must agree is thrown. So it didn't matter which combination of f we were using (transpose of W on left or right) it would still fail.

At some point, the global variable must have been set. And now, with the correct order of the matrix multiplications for f, it works as expected.

But you will have to remember to set the global variable VCVMatx...

[Sameer]

would you happen to know how to place two linear equality constraints in one fmincon function? thanks.

[Geoff Hayes]

No, unfortunately I have never used that function (nor have the toolbox for it).