def test_subgradient(self):
"""Check if the subgradient is computed correctly
Subgradient should lie in the cone made up by the subgradients.
"""
c = CConstraintL1(center=0, radius=1)
x0 = CArray([0, 1])
p_min = CArray([1, 1])
p_max = CArray([-1, 1])
gradient = c.gradient(x0)
# normalize the points
norm_center = x0 / x0.norm(2)
norm_p_min = p_min / p_min.norm(2)
norm_p_max = p_max / p_max.norm(2)
norm_gradient = gradient / gradient.norm(2)
angl1 = round(acos(norm_center.dot(norm_gradient)), 5)
angl2 = round(acos(norm_p_min.dot(norm_p_max)) / 2.0, 5)
self.logger.info("Subgrad in {:} is:\n{:}".format(x0, gradient))
self.assertLessEqual(angl1, angl2, "Subgrad is not inside the cone of "
"{:} and {:}".format(p_min, p_max))
def _xk(self, x, fx, *args):
"""Returns a new point after gradient descent."""
# compute gradient
grad = self._fun.gradient(x, *args)
self._grad = grad # only used for visualization/convergence
norm = grad.norm()
if norm < 1e-20:
return x, fx # return same point (and exit optimization)
grad = grad / norm
# filter modifications that would violate bounds (to sparsify gradient)
grad = self._box_projected_gradient(x, grad)
if self.constr is not None and self.constr.class_type == 'l1':
# project z onto l1 constraint (via dual norm)
grad = self._l1_projected_gradient(grad)
next_point = CArray(x - grad * self._line_search.eta,
dtype=self._dtype,
tosparse=x.issparse)
if self.constr is not None and self.constr.is_violated(next_point):
self.logger.debug("Line-search on distance constraint.")
grad = CArray(x - self.constr.projection(next_point))
grad_norm = grad.norm(order=2)
if grad_norm > 1e-20:
grad /= grad_norm
if self.constr.class_type == 'l1':
grad = grad.sign() # to move along the l1 ball surface
z, fz = self._line_search.minimize(x, -grad, fx)
return z, fz
if self.bounds is not None and self.bounds.is_violated(next_point):
self.logger.debug("Line-search on box constraint.")
grad = CArray(x - self.bounds.projection(next_point))
grad_norm = grad.norm(order=2)
if grad_norm > 1e-20:
grad /= grad_norm
z, fz = self._line_search.minimize(x, -grad, fx)
return z, fz
z, fz = self._line_search.minimize(x, -grad, fx)
return z, fz
