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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.

If the final answer in the paper is correct, then the length of the end-effector arm should be 1 unit and you did not mention this. Also in the code, you should multiply the final answer by the M matrix. So the code should be:

It puts the value -realmax in every entry of A which is -Inf.

For instance, let's say

You misplaced a }.

In fact, using the package geomstats, I found a solution.

This is exclusively for SPD matrices.

There is a function to directly compute the riemannian exponential, and even one to compute A**t for A SPD and t real.

I recommend using the last version of geomstats (from GitHub).

Here, N is the order of the square matrices (so that their sizes are N x N).

Well, as pointed out in the comments, your (more complicated) ODE is nonlinear. Therefore, a matrix exponential approach will not work anymore.

In general, there are two general approaches to solving ODEs. First, you can try to find a symbolic solution. In most cases, you follow some approach based on an educated guess. There are several types of ODEs for which symbolic solutions are known.

However, this is not the case for the vast majority of ODEs. Hence, we generally contend ourselves with a numeric solution, essentially numerically integrating the ODE based on the right hand side.

The result is not an explicit function, but instead an approximation on the function values at certain point. In python, you can use scipy to solve ODEs this way. Based on your right hand side (barring any errors on my part), this would look something like this: