jax.lax.linalg.qdwh#
- jax.lax.linalg.qdwh(x, *, is_hermitian=False, max_iterations=None, eps=None, dynamic_shape=None)[source]#
QR-based dynamically weighted Halley iteration for polar decomposition.
- Parameters:
x – A full-rank matrix, with shape M x N. The matrix may be padded up to that size from a smaller true shape (
dynamic_shape).is_hermitian – True if x is Hermitian. Default to False.
eps – The final result will satisfy
|x_k - x_k-1| < |x_k| * (4*eps)**(1/3)where x_k is the iterate.max_iterations – Iterations will terminate after this many steps even if the above is unsatisfied.
dynamic_shape (tuple[int, int] | None) – the unpadded shape as an
(m, n)tuple; optional.
- Returns:
A four-tuple of (u, h, num_iters, is_converged) containing the polar decomposition of x = u * h, the number of iterations to compute u, and is_converged, whose value is True when the convergence is achieved within the maximum number of iterations.