Eigen Decomposition of Hermitian symmetric matrix using MATLAB Coder

Question

AJ 2022-6-5

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1734185-eigen-decomposition-of-hermitian-symmetric-matrix-using-matlab-coder

评论： AJ 2022-6-8

采纳的回答： Steven Lord

I'm planning to implement the eig function as part of a MATLAB coder project.

The input matrix is complex, and Hermitian symmetric and positive definite.

My worry is about timing, how long the algorithm requires, since I'll be calling it a lot.

My assumption is that the C-code implementation will employ the "full-blown" eigen decompsition, without considering that the problem could simplified using the knowledge of the matrix properties. For example, all the eigen-values will be positive and real-valued.

I have not yet looked into BLAS or LAPACK, etc., to see of there is a special case of eig for symmetric, positive definite matrices.

Any ideas?

2 个评论
显示无隐藏无

Bruno Luong 2022-6-5

Your decription is confused:

Hermitian is not symmetric if the matrix is complex (not pure real).
Symmetric is not positive in general, one cannot even speak about positiveness since x'*H*x is complex.

AJ 2022-6-5

Yes, I (perhaps wrongly) use the term "Hermitian Symmetric" meaning "Hermitian" when the real parts are symmetric and the imaginary parts are "anti-symmetric", i.e. the matrix is its own conjugate transpose.

The matrix is also positive definite, due to the way it is generated; think sample covariance matrix.

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Steven Lord 2022-6-5

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1734185-eigen-decomposition-of-hermitian-symmetric-matrix-using-matlab-coder#answer_979380

According to the Extended Capabilities section of the documentation page for the eig function it already supports C/C++ code generation with MATLAB Coder.

5 个评论
显示 3更早的评论隐藏 3更早的评论

Christine Tobler 2022-6-6

The coder version of EIG does not support special branches for the Hermitian case. In fact, it will treat most simple eigenvalue problems as if they were generalized eigenvalue problems, in the implementation.

See the Extended Capabilities section, which notes

"For the standard eigenvalue problem, [V,D] = eig(A), when A is Hermitian or skew-Hermitian, code generation uses schur to calculate V and D. Otherwise, the results of [V,D] = eig(A) are similar to the results obtained by using [V,D] = eig(A,eye(size(A)),'qz') in MATLAB, except that the columns of V are normalized."

Note there are differences in behavior based on whether you specify the LAPACK library callback class.

AJ 2022-6-8