dexpmv

dexpmv(M, dM)[source]

Compute the Matrix exponential F = e^M and its derivative dF.

User must provide M and its derivative dM. If the argument dM is a vector of partials then dF will be the respective partial vector. This is done using a Pade Approximation with scaling and squaring.

Parameters:

  • M (npt.NDArray[np.complex128]) – Matrix to exponentiate.

  • dM (npt.NDArray[np.complex128]) – Derivative(s) of M.

Returns:

Tuple containing

  • F (np.ndarray): Exponentiated matrix, i.e. e^M.

  • dF (np.ndarray): Derivative(s) of F.

Return type:

tuple[npt.NDArray[np.complex128], npt.NDArray[np.complex128]]

References

Brančík, Lubomír. “Matlab programs for matrix exponential function derivative evaluation.” Proc. of Technical Computing Prague 2008 (2008): 17-24.