def _cho_solve(c, b, lower): c, b = np_linalg._promote_arg_dtypes(jnp.asarray(c), jnp.asarray(b)) lax_linalg._check_solve_shapes(c, b) b = lax_linalg.triangular_solve(c, b, left_side=True, lower=lower, transpose_a=not lower, conjugate_a=not lower) b = lax_linalg.triangular_solve(c, b, left_side=True, lower=lower, transpose_a=lower, conjugate_a=lower) return b
def _solve(a, b, sym_pos, lower): if not sym_pos: return np_linalg.solve(a, b) a, b = _promote_dtypes_inexact(jnp.asarray(a), jnp.asarray(b)) lax_linalg._check_solve_shapes(a, b) # With custom_linear_solve, we can reuse the same factorization when # computing sensitivities. This is considerably faster. factors = cho_factor(lax.stop_gradient(a), lower=lower) custom_solve = partial(lax.custom_linear_solve, lambda x: lax_linalg._matvec_multiply(a, x), solve=lambda _, x: cho_solve(factors, x), symmetric=True) if a.ndim == b.ndim + 1: # b.shape == [..., m] return custom_solve(b) else: # b.shape == [..., m, k] return vmap(custom_solve, b.ndim - 1, max(a.ndim, b.ndim) - 1)(b)