def armijo_backtracking(self, func, alpha, maxiter=20):
"""
Returns step and next point, minimizing given functional
Parameters
----------
func : function
function to minimize
x : ManifoldElement
initial point
alpha : float
estimated line search parameter
direction : TangentVector
direction to move from initial point
conj_direction : TangentVector
conjugated direction
Returns
-------
x_new :
next point (x + step * direction)
step : float
optimal step
"""
scale = -0.0001 * alpha
for i in range(maxiter):
x_new = svd_retraction(self.x + (0.5 ** i * alpha) * self.conj.release(), self.x.r)
bound = (0.5 ** i * scale) * self.grad.release().scalar_product(self.conj.release())
if self.cost_raw(self.x) - self.cost_raw(x_new) >= bound:
return x_new, 0.5 ** i * scale
return x_new, 0.5 ** maxiter * scale
def gd_step(self):
alpha = minimize_scalar(lambda x: self.cost_func(x), bounds=(0.0, 10.0), method="bounded")["x"]
if alpha is None:
alpha = 1.0
print(alpha)
self.x = svd_retraction(self.x + alpha * self.grad.release(), self.x.r)
# self.armijo_backtracking(lambda x: self.cost_raw(x), alpha)[0]
return None
def cost_func(self, param):
retracted = svd_retraction(self.x + param * self.grad.release(), self.x.r)
return self.cost_raw(retracted)