expm_frechet_block_enlarge¶

torch_sim.math.expm_frechet_block_enlarge(A, E)[source]¶

Block-enlarge helper for Frechet derivative via matrix exponential.

Builds M = [[A, E], [0, A]], computes exp(M), and extracts: - exp(A) from the top-left block - L_exp(A, E) from the top-right block

Reference:: Nicholas J. Higham (2008), “Functions of Matrices: Theory and Computation”, SIAM. (Frechet derivative block-matrix identity.)

Parameters:

A (Tensor) – (B, N, N) Batch of input matrices.
E (Tensor) – (B, N, N) Batch of direction matrices. Must have same shape as A.

Returns:

Matrix exponential of A expm_frechet_AE: torch.Tensor

Frechet derivative of the matrix exponential of A in the direction E

Return type:

expm_A