Matrix inverse in objective function

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Sai Srikar
Sai Srikar 2023-11-17
编辑： Sai Srikar 2023-11-17
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);
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Walter Roberson
Walter Roberson 2023-11-17
Do not use inv() here. Use the \ operator
Sai Srikar
Sai Srikar 2023-11-17
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.

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采纳的回答

Bruno Luong
Bruno Luong 2023-11-17

更多回答（2 个）

Himanshu
Himanshu 2023-11-17
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
  1 个评论
Sai Srikar
Sai Srikar 2023-11-17
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.

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Pratyush
Pratyush 2023-11-17
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);
  1 个评论
Sai Srikar
Sai Srikar 2023-11-17
Thanks Pratyush, I tried this. I get a new error: "Error using double
Conversion to double from optim.problemdef.OptimizationExpression is not possible."

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