jax.scipy.linalg.expmΒΆ

jax.scipy.linalg.expm(A, *, upper_triangular=False, max_squarings=16)[source]ΒΆ

Compute the matrix exponential using Pade approximation.

LAX-backend implementation of expm().

In addition to the original NumPy argument(s) listed below, also supports the optional boolean argument upper_triangular to specify whether the A matrix is upper triangular, and the optional argument max_squarings to specify the max number of squarings allowed in the scaling-and-squaring approximation method. Return nan if the actual number of squarings required is more than max_squarings.

The number of required squarings = max(0, ceil(log2(norm(A)) - c) where norm() denotes the L1 norm, and

  • c=2.42 for float64 or complex128,

  • c=1.97 for float32 or complex64

Original docstring below.

Parameters

A ((N, N) array_like or sparse matrix) – Matrix to be exponentiated.

Returns

expm – Matrix exponential of A.

Return type

(N, N) ndarray

References

1

Awad H. Al-Mohy and Nicholas J. Higham (2009) β€œA New Scaling and Squaring Algorithm for the Matrix Exponential.” SIAM Journal on Matrix Analysis and Applications. 31 (3). pp. 970-989. ISSN 1095-7162