expm | Differentiable and numerically stable implementation of expm

x %^% n computes the nth power of x efficiently, but it is inefficient to compute x %^% i for all i from 0 to n, because each x %^% i requires O(log(i)) matrix multiplications.

In general, the most efficient way to compute all of the powers of x up to the nth is recursive multiplication by x, possibly taking advantage of the diagonalizability of x.

The difference is nontrivial for large n: whereas

Your variance function is returning the difference, and if you want the absolute value (variance) just wrap it inside abs() like this:

I think the python equivalent is scipy.linalg.expm

See scipy documentation: https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.expm.html

The following code replicates the Matlab example given in your link to the documentation.

There is no function, however, it is possible to decompose the matrix into eigenvalues and use the exp(inMat, outMat) function, namely,

According to the traceback T[k, k+1] doesn't work because T is a bsr format sparse matrix, which does not implement indexing. (coo is a more common format that doesn't have this either).

Looking at the sp.kron code, https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.kron.html

Fixed. Error was in the definition of matrices to be generated. From what I gather in Python you must specifically define each array, while in MATLAB you can set matrix equivalences and run them through a for-loop.

Your problem is that you are multiplying a 3x3 (a and b variables) matrix with a 50x50 (xx and yy) matrix element wise. Therefore, fix this issue and everything should be okay.

Example:

np.array([1,2,3])*np.array([1,2,3])

Output: array([1,4,9])

np.array([1,2,3])*np.array([1,2,3,4])

Output: ValueError: operands could not be broadcast together with shapes (3,) (4,)

I think this is ultimately a small bug in renv. Here's my guess at what's happening:

1. While this project has been initialized as an renv project, it does not have a lockfile for some reason. (Perhaps renv::activate() was called to initialize renv without explicitly creating a lockfile?)

2. The project has an renv autoloader; this is from a script at renv/activate.R. That script is configured to load renv 0.11.0.

3. When the project is loaded, renv finds that renv 0.12.0 is installed in the project library, not the expected version 0.11.0. This causes the warning to be emitted. (Perhaps renv was updated in that project previously?)

So, ultimately, the warning is misleading here -- the request for renv 0.11.0 comes directly from the autoloader, not from the lockfile (which does not exist). As for why the lockfile does not exist, I'm not sure -- but it most likely implies the project was initialized via renv::activate(), and not by renv::init().

All that said -- you can safely re-generate the lockfile via renv::snapshot().

Here's an answer to the question "how to scale a matrix by multiple scalars without a for-loop". This disregards the matrix exponentiation, since I don't think there's a way to do that without the for-loop, but the question doesn't seem to be asking about the exponentiation step.

You can use 3D arrays to use numpy's vectorized multiplication.