def _newton_rhaphson(self, T, E, precision=1e-5, show_progress=False):
from lifelines.utils import _smart_search
def hessian_function(parameters, T, E):
return np.array([[
_d_lambda_d_lambda_(parameters, T, E),
_d_rho_d_lambda_(parameters, T, E)
],
[
_d_rho_d_lambda_(parameters, T, E),
_d_rho_d_rho(parameters, T, E)
]])
def gradient_function(parameters, T, E):
return np.array([
_lambda_gradient(parameters, T, E),
_rho_gradient(parameters, T, E)
])
# initialize the parameters. This shows dramatic improvements.
parameters = _smart_search(_negative_log_likelihood, 2, T, E)
i = 1
step_size = 0.9
max_steps = 50
converging, completed = True, False
start = time.time()
while converging and i < max_steps:
# Do not override hessian and gradient in case of garbage
h, g = hessian_function(parameters, T,
E), gradient_function(parameters, T, E)
delta = solve(h, -step_size * g.T)
if np.any(np.isnan(delta)):
raise ConvergenceError(
"delta contains nan value(s). Convergence halted.")
parameters += delta
# Save these as pending result
hessian = h
if show_progress:
print(
"Iteration %d: norm_delta = %.5f, seconds_since_start = %.1f"
% (i, norm(delta), time.time() - start))
if norm(delta) < precision:
converging = False
completed = True
i += 1
if show_progress and completed:
print("Convergence completed after %d iterations." % (i))
if not completed:
warnings.warn(
"Newton-Rhapson failed to converge sufficiently in %d steps." %
max_steps, ConvergenceWarning)
return parameters, hessian
def _newton_rhaphson(self, T, E, precision=1e-5):
from lifelines.utils import _smart_search
def jacobian_function(parameters, T, E):
return np.array([[
_d_lambda_d_lambda_(parameters, T, E),
_d_rho_d_lambda_(parameters, T, E)
],
[
_d_rho_d_lambda_(parameters, T, E),
_d_rho_d_rho(parameters, T, E)
]])
def gradient_function(parameters, T, E):
return np.array([
_lambda_gradient(parameters, T, E),
_rho_gradient(parameters, T, E)
])
# initialize the parameters. This shows dramatic improvements.
parameters = _smart_search(_negative_log_likelihood, 2, T, E)
iter = 1
step_size = 1.
converging = True
while converging and iter < 50:
# Do not override hessian and gradient in case of garbage
j, g = jacobian_function(parameters, T,
E), gradient_function(parameters, T, E)
delta = solve(j, -step_size * g.T)
if np.any(np.isnan(delta)):
raise ValueError(
"delta contains nan value(s). Convergence halted.")
parameters += delta
# Save these as pending result
jacobian = j
if norm(delta) < precision:
converging = False
iter += 1
self._jacobian = jacobian
return parameters
def _newton_rhaphson(self, T, E, precision=1e-5):
from lifelines.utils import _smart_search
def jacobian_function(parameters, T, E):
return np.array([
[_d_lambda_d_lambda_(parameters, T, E), _d_rho_d_lambda_(parameters, T, E)],
[_d_rho_d_lambda_(parameters, T, E), _d_rho_d_rho(parameters, T, E)]
])
def gradient_function(parameters, T, E):
return np.array([_lambda_gradient(parameters, T, E), _rho_gradient(parameters, T, E)])
# initialize the parameters. This shows dramatic improvements.
parameters = _smart_search(_negative_log_likelihood, 2, T, E)
iter = 1
step_size = 1.
converging = True
while converging and iter < 50:
# Do not override hessian and gradient in case of garbage
j, g = jacobian_function(parameters, T, E), gradient_function(parameters, T, E)
delta = solve(j, - step_size * g.T)
if np.any(np.isnan(delta)):
raise ValueError("delta contains nan value(s). Convergence halted.")
parameters += delta
# Save these as pending result
jacobian = j
if norm(delta) < precision:
converging = False
iter += 1
self._jacobian = jacobian
return parameters