Efficient approaches for matrix inverse operation

[faze-geek]

This is not an issue, but a doubt.
I am implementing a matrix method as follows :

s = Symbol('s')
I = eye(A.shape[0])
G = C*(s*I - A).inv()*B + D)          # A,B,C,D are sympy matrices

But I'm not sure using inv() is good practice.
Are there any more efficient methods to calculate the matrix G in Sympy ? Or maybe it could be done manually using LUdecomposition(). Kindly let me know any ways which come to mind. Thanks !

[oscarbenjamin]

I've converted this to a discussion rather than an issue. You need to say something more like what sort of expressions are in the matrices, what are their shapes and sizes etc. Ideally just show some simple code that makes the matrices (or at least something similar to your actual problem).

[faze-geek]

What I am trying to implement is this - https://lpsa.swarthmore.edu/Representations/SysRepTransformations/TF2SS.html
The matrices can consist purely of numbers or can be symbolic with a complex variable.
Consider a model with n states, u inputs and y outputs:
Then the shapes will be -

A : n*n
B : n*u
C : y*x
D : y*u

[oscarbenjamin]

The best approach really depends a lot on what kinds of expressions you have. See e.g. gh-25452 for discussions about performance of matrix inverse.

[sylee957]

Usually, using inv means finding a reusable matrix that solves any instance of B.
If you don't want to reuse the result of (s*I - A).inv(), and only use once for specific instance of B
you'd better try using .rref or .solve.
.solve is the easiest interface (s*I - A).solve(B)

[faze-geek]

Thanks for the reply !