Suggestion to use `np.linalg.solve` instead of `torch.linalg.solve`

[Andyccs]

Is your feature request related to a problem? Please describe.

I was trying out the MinimumProfit class. The optimization is really slow due to the usages of np.linalg.solve. By changing np.linalg.solve to torch.linalg.solve, I was able to speed it up by ~2x (on CPU) based on observation. Example codes:

import torch

class CustomMinimumProfit(MinimumProfit):
    def _mean_passage_time(self, lower: int, upper: int, ar_coeff: float, ar_resid: np.array,
                           granularity: float) -> pd.Series:
        # Build the grid for summation
        grid = granularity * np.arange(lower, upper)

        # Calculate the gaussian kernel
        gaussian = self._gaussian_kernel(ar_coeff, grid, ar_resid)

        # Calculate the mean passage time at each grid point
        k_dim = gaussian.shape[0]
        passage_time = torch.linalg.solve(torch.from_numpy(np.eye(k_dim) - gaussian), torch.from_numpy(np.ones(k_dim)))
        # passage_time = np.linalg.solve(np.eye(k_dim) - gaussian, np.ones(k_dim))

        # Return a pandas.Series indexed by grid points for easy retrieval
        passage_time_df = pd.Series(passage_time, index=grid)

        return passage_time_df

The idea is based on the discussion at https://stackoverflow.com/questions/62099939/solving-linear-equations-on-the-gpu-with-numpy-and-pytorch

Describe the solution you'd like I am not sure whether this repo wants to take in new dependency on PyTorch, but if the maintainer is willing to do so, using PyTorch to solve the equations would greatly speed to the optimization process.

Describe alternatives you've considered None.

Additional context None.

[Jackal08]

Thank you for this great suggestion!

I will come back to this - we are very nervous to add more dependencies as it causes a lot of issues in the long term but maybe there is a way.

Can one copy paste code from pytorch to this repo so that we don't have the dependency?