matflow.subset_simulation.subset_simulation.cumsum_transformation_adjoint

matflow.subset_simulation.subset_simulation.cumsum_transformation_adjoint(grad_xt)

Adjoint (transpose-Jacobian action) for transformation = lambda x: np.cumsum(x, axis=-1). Since cumsum is linear with Jacobian J_ij = 1 if j <= i else 0, J^T @ v is a reversed cumulative sum – maps a gradient computed in the transformed (“physical”) space back to the original (untransformed) sampling space. Required whenever a proposal/gradient-based correction is computed in transformed space but applied to untransformed states (as in generate_next_level_samples_MLDA_gradient/_spsa).