def test_prox_star(self):
n = 10
x = 3 * np.random.randn(n, 1)
f = functions.norm_l1()
f2 = functions.dummy()
f2.prox = lambda x, T: functions._prox_star(f, x, T)
gamma = np.random.rand()
p1 = f.prox(x, gamma)
p2 = functions._prox_star(f2, x, gamma)
np.testing.assert_array_almost_equal(p1, p2)
p1 = f.prox(x, gamma) - x
p2 = -gamma * f2.prox(x / gamma, 1 / gamma)
np.testing.assert_array_almost_equal(p1, p2)
def _algo(self):
# Forward steps (in both primal and dual spaces)
y1 = self.sol - self.step * (self.smooth_funs[0].grad(self.sol) +
self.Lt(self.dual_sol))
y2 = self.dual_sol + self.step * self.L(self.sol)
# Backward steps (in both primal and dual spaces)
p1 = self.non_smooth_funs[0].prox(y1, self.step)
p2 = _prox_star(self.non_smooth_funs[1], y2, self.step)
# Forward steps (in both primal and dual spaces)
q1 = p1 - self.step * (self.smooth_funs[0].grad(p1) + self.Lt(p2))
q2 = p2 + self.step * self.L(p1)
# Update solution (in both primal and dual spaces)
self.sol[:] = self.sol - y1 + q1
self.dual_sol[:] = self.dual_sol - y2 + q2
def _algo(self):
# Forward steps (in both primal and dual spaces)
y1 = self.sol - self.step * (self.smooth_funs[0].grad(self.sol) +
self.Lt(self.dual_sol))
y2 = self.dual_sol + self.step * self.L(self.sol)
# Backward steps (in both primal and dual spaces)
p1 = self.non_smooth_funs[0].prox(y1, self.step)
p2 = _prox_star(self.non_smooth_funs[1], y2, self.step)
# Forward steps (in both primal and dual spaces)
q1 = p1 - self.step * (self.smooth_funs[0].grad(p1) + self.Lt(p2))
q2 = p2 + self.step * self.L(p1)
# Update solution (in both primal and dual spaces)
self.sol[:] = self.sol - y1 + q1
self.dual_sol[:] = self.dual_sol - y2 + q2