Matrix inverse in objective function

Question

Sai Srikar 2023-11-17

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2048417-matrix-inverse-in-objective-function

编辑： Sai Srikar 2023-11-17

采纳的回答： Bruno Luong

在 MATLAB Online 中打开

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);

5 个评论
显示 3更早的评论隐藏 3更早的评论

Walter Roberson 2023-11-17

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

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.

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Bruno Luong 2023-11-17

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2048417-matrix-inverse-in-objective-function#answer_1354757

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

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

Sai Srikar 2023-11-17

编辑：Sai Srikar 2023-11-17

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

请先登录，再进行评论。

Answer 2

Himanshu 2023-11-17

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2048417-matrix-inverse-in-objective-function#answer_1354517

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
显示 -1更早的评论隐藏 -1更早的评论

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.

请先登录，再进行评论。

Answer 3

Pratyush 2023-11-17

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2048417-matrix-inverse-in-objective-function#answer_1354567

在 MATLAB Online 中打开

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);