Matrix inverse in objective function

Hi,

I am trying to find the matrix X, which minimizes the objective function. However, I see the following error:

Error using inv

Invalid data type. Input matrix must be double or single.

Error in t2 (line 11)

prob.Objective=trace(R - R*X'*inv(X*R*X' + sigma2*eye(T))*X*R);

My code snippet: (Here, T, N and sigma2 are constants and R is an NxN PSD matrix)

prob=optimproblem("Description","MSE min")
X=optimvar("X",T,N,"Type",'continuous');
prob.Objective=trace(R - R*X'*inv(X*R*X' + sigma2*eye(T))*X*R);

[Rik]

Can you edit your question to provide example variables that will reproduce the error? You can use the run button to run the code in the editor.

[Brahmadev]

Hi, I was trying to reproduce this error and I used the following code below.

% Set the dimensions
T = 5;
N = 4;

% Generate a random value for sigma2
sigma2 = rand;

% Generate a random NxN PSD matrix for R
R = rand(N, N);
R = R'*R;  % This ensures that R is positive semi-definite

prob=optimproblem("Description","MSE min");
X=optimvar("X",T,N,"Type",'continuous')

X = 
  5×4 OptimizationVariable array with properties:

  Array-wide properties:
          Name: 'X'
          Type: 'continuous'
    IndexNames: {{}  {}}

  Elementwise properties:
    LowerBound: [5×4 double]
    UpperBound: [5×4 double]

  See variables with show.
  See bounds with showbounds.

prob.Objective=trace(R - R*X'*inv(X*R*X' + sigma2*eye(T))*X*R);

Error using inv
Invalid data type. Input matrix must be double or single.

In your case, the expression X*R*X' + sigma2*eye(T) is not a double or single matrix, it's an optimization expression, because "X" is an optimization variable. The inv function cannot handle optimization expressions, hence the error. You might need to reconsider the formulation of your problem without the use of 'inv'

[Sai Srikar]

Hi @Rik, Brahmadev has provided the code with some example variables

Hi @Brahmadev, Can you suggest some way which helps me get rid of this error? My objective function and its optimal solution were discussed in an IEEE paper. I am trying to reproduce the same result using MATLAB's optimization toolbox.

[Walter Roberson]

Do not use inv() here. Use the \ operator

[Sai Srikar]

Hi, I tried \ operator like: prob.Objective = trace(R - R*X'*(X*R*X' + sigma2*eye(T))/(X*R)). I still get an error as follows:

Error using /

Division of an OptimizationVariable by nonscalar not supported.

Answer 1

[Bruno Luong]

The inv() is not supported by optimization expression see https://www.mathworks.com/help/optim/ug/supported-operations-on-optimization-variables-expressions.html

Workaround using https://www.mathworks.com/help/optim/ug/fcn2optimexpr.html

[Sai Srikar]

Thanks Bruno, I am able to get rid of the error.

Answer 2

[Himanshu]

Hey,

I understand that you are an encountering an error while running the given code snippet.

The error message indicates that the error occurs because the ‘inv’ function is being called with inputs of invalid datatype. The ‘inv’ function only accepts inputs of type double or single. In the given code, ‘inv’ function is trying to operate on an expression involving an optimization variable (X), which is not of type double or single.

Please refer to the following documentation page for more information on the ‘inv’ function:

https://www.mathworks.com/help/matlab/ref/inv.html?s_tid=doc_ta

[Sai Srikar]

Thanks Himanshu. Is there any way to address this issue in MATLAB?, I do know the analytical solution for this optimization problem, I wanted to reproduce the same using MATALAB's optimization toolbox for my work.

Answer 3

[Pratyush]

Hi Sai,

I understand that you are getting an error using the "inv" function.

The error you receive is because the "inv" function accepts matrix of data type single or double as argument, but it seems your "X*R*X' + sigma2*eye(T)" expression is not of the correct type.

To fix this issue, you can explicitly convert the matrix to the desired type using the "double" function. Try modifying the last line of your script to :

prob.Objective = trace(R - R*X'*inv(double(X*R*X' + sigma2*eye(T)))*X*R);

[Sai Srikar]

Thanks Pratyush, I tried this. I get a new error: "Error using double

Conversion to double from optim.problemdef.OptimizationExpression is not possible."