Source code for pyproximal.utils.moreau

import numpy as np
from pyproximal.ProxOperator import _check_tau

[docs]def moreau(prox, x, tau, tol=1e-5, raiseerror=True, verb=False): r"""Moreau Identity. The Moreau identity defines a relation between the vector :math:`\mathbf{u}`, its proximal operator and its dual proximal operator and can be used to estimate one of the two operators given the knowledge of the other. Parameters ---------- prox : :obj:`pyprox.ProxOperator` Proximal operator x : :obj:`np.ndarray` Vector tau : :obj:`float` Positive scalar weight tol : :obj:`float`, optional Moreau identity tolerance raiseerror : :obj:`bool`, optional Raise error or simply return ``False`` when Moreau identity is not satisfied verb : :obj:`bool`, optional Verbosity Notes ----- The Moreau decomposition (or identity) is defined as: .. math:: \mathbf{x} = \prox_{\tau f} (\mathbf{x}) + \tau \prox_{\frac{1}{\tau} f^*} (\frac{\mathbf{x}}{\tau}) This routine is used to evaluate if the prox and dualprox implementations of a ``pyprox.ProxOperator`` satisfy such identity. """ # compute prox p = prox.prox(x, tau) # compute dualprox pdual = tau * prox.proxdual(x / tau, 1. / tau) if verb: print('x: ', x) print('p + pdual: ', p + pdual) print('error: ', x - (p + pdual)) if np.allclose(x, p + pdual, atol=tol): return True else: if raiseerror: raise ValueError('Moreau identity not verified') return False