def parameterized_expectations(model,
verbose=False,
dr0=None,
pert_order=1,
with_complementarities=True,
grid={},
distribution={},
maxit=100,
tol=1e-8,
inner_maxit=10,
direct=False):
'''
Find global solution for ``model`` via parameterized expectations.
Controls must be expressed as a direct function of equilibrium objects.
Algorithm iterates over the expectations function in the arbitrage equation.
Parameters:
----------
model : NumericModel
``dtcscc`` model to be solved
verbose : boolean
if True, display iterations
dr0 : decision rule
initial guess for the decision rule
pert_order : {1}
if no initial guess is supplied, the perturbation solution at order
``pert_order`` is used as initial guess
grid : grid options
distribution : distribution options
maxit : maximum number of iterations
tol : tolerance criterium for successive approximations
inner_maxit : maximum number of iteration for inner solver
direct : if True, solve with direct method. If false, solve indirectly
Returns
-------
decision rule :
approximated solution
'''
t1 = time.time()
g = model.functions['transition']
h = model.functions['expectation']
d = model.functions['direct_response']
f = model.functions['arbitrage_exp'] # f(s, x, z, p, out)
parms = model.calibration['parameters']
if dr0 is None:
if pert_order == 1:
dr0 = approximate_controls(model)
if pert_order > 1:
raise Exception("Perturbation order > 1 not supported (yet).")
approx = model.get_endo_grid(**grid)
grid = approx.grid
interp_type = approx.interpolation
dr = create_interpolator(approx, interp_type)
expect = create_interpolator(approx, interp_type)
distrib = model.get_distribution(**distribution)
nodes, weights = distrib.discretize()
N = grid.shape[0]
z = np.zeros((N, len(model.symbols['expectations'])))
x_0 = dr0(grid)
x_0 = x_0.real # just in case ...
h_0 = h(grid, x_0, parms)
it = 0
err = 10
err_0 = 10
verbit = True if verbose == 'full' else False
if with_complementarities is True:
lbfun = model.functions['controls_lb']
ubfun = model.functions['controls_ub']
lb = lbfun(grid, parms)
ub = ubfun(grid, parms)
else:
lb = None
ub = None
if verbose:
headline = '|{0:^4} | {1:10} | {2:8} | {3:8} |'
headline = headline.format('N', ' Error', 'Gain', 'Time')
stars = '-' * len(headline)
print(stars)
print(headline)
print(stars)
# format string for within loop
fmt_str = '|{0:4} | {1:10.3e} | {2:8.3f} | {3:8.3f} |'
while err > tol and it <= maxit:
it += 1
t_start = time.time()
# dr.set_values(x_0)
expect.set_values(h_0)
# evaluate expectation over the future state
z[...] = 0
for i in range(weights.shape[0]):
e = nodes[i, :]
S = g(grid, x_0, e, parms)
z += weights[i] * expect(S)
if direct is True:
# Use control as direct function of arbitrage equation
new_x = d(grid, z, parms)
if with_complementarities is True:
new_x = np.minimum(new_x, ub)
new_x = np.maximum(new_x, lb)
else:
# Find control by solving arbitrage equation
def fun(x):
return f(grid, x, z, parms)
sdfun = SerialDifferentiableFunction(fun)
if with_complementarities is True:
[new_x, nit] = ncpsolve(sdfun,
lb,
ub,
x_0,
verbose=verbit,
maxit=inner_maxit)
else:
[new_x, nit] = serial_newton(sdfun, x_0, verbose=verbit)
new_h = h(grid, new_x, parms)
# update error
err = (abs(new_h - h_0).max())
# Update guess for decision rule and expectations function
x_0 = new_x
h_0 = new_h
# print error infomation if `verbose`
err_SA = err / err_0
err_0 = err
t_finish = time.time()
elapsed = t_finish - t_start
if verbose:
print(fmt_str.format(it, err, err_SA, elapsed))
if it == maxit:
import warnings
warnings.warn(UserWarning("Maximum number of iterations reached"))
# compute final fime and do final printout if `verbose`
t2 = time.time()
if verbose:
print(stars)
print('Elapsed: {} seconds.'.format(t2 - t1))
print(stars)
# Interpolation for the decision rule
dr.set_values(x_0)
return dr
def parameterized_expectations(model, verbose=False, initial_dr=None,
pert_order=1, with_complementarities=True,
grid={}, distribution={},
maxit=100, tol=1e-8, inner_maxit=10,
direct=False):
'''
Find global solution for ``model`` via parameterized expectations.
Controls must be expressed as a direct function of equilibrium objects.
Algorithm iterates over the expectations function in the arbitrage equation.
Parameters:
----------
model : NumericModel
``dtcscc`` model to be solved
verbose : boolean
if True, display iterations
initial_dr : decision rule
initial guess for the decision rule
pert_order : {1}
if no initial guess is supplied, the perturbation solution at order
``pert_order`` is used as initial guess
grid : grid options
distribution : distribution options
maxit : maximum number of iterations
tol : tolerance criterium for successive approximations
inner_maxit : maximum number of iteration for inner solver
direct : if True, solve with direct method. If false, solve indirectly
Returns
-------
decision rule :
approximated solution
'''
t1 = time.time()
g = model.functions['transition']
h = model.functions['expectation']
d = model.functions['direct_response']
f = model.functions['arbitrage_exp'] # f(s, x, z, p, out)
parms = model.calibration['parameters']
if initial_dr is None:
if pert_order == 1:
initial_dr = approximate_controls(model)
if pert_order > 1:
raise Exception("Perturbation order > 1 not supported (yet).")
approx = model.get_grid(**grid)
grid = approx.grid
interp_type = approx.interpolation
dr = create_interpolator(approx, interp_type)
expect = create_interpolator(approx, interp_type)
distrib = model.get_distribution(**distribution)
nodes, weights = distrib.discretize()
N = grid.shape[0]
z = np.zeros((N, len(model.symbols['expectations'])))
x_0 = initial_dr(grid)
x_0 = x_0.real # just in case ...
h_0 = h(grid, x_0, parms)
it = 0
err = 10
err_0 = 10
verbit = True if verbose == 'full' else False
if with_complementarities is True:
lbfun = model.functions['controls_lb']
ubfun = model.functions['controls_ub']
lb = lbfun(grid, parms)
ub = ubfun(grid, parms)
else:
lb = None
ub = None
if verbose:
headline = '|{0:^4} | {1:10} | {2:8} | {3:8} |'
headline = headline.format('N', ' Error', 'Gain', 'Time')
stars = '-'*len(headline)
print(stars)
print(headline)
print(stars)
# format string for within loop
fmt_str = '|{0:4} | {1:10.3e} | {2:8.3f} | {3:8.3f} |'
while err > tol and it <= maxit:
it += 1
t_start = time.time()
# dr.set_values(x_0)
expect.set_values(h_0)
# evaluate expectation over the future state
z[...] = 0
for i in range(weights.shape[0]):
e = nodes[i, :]
S = g(grid, x_0, e, parms)
z += weights[i]*expect(S)
if direct is True:
# Use control as direct function of arbitrage equation
new_x = d(grid, z, parms)
if with_complementarities is True:
new_x = np.minimum(new_x, ub)
new_x = np.maximum(new_x, lb)
else:
# Find control by solving arbitrage equation
def fun(x): return f(grid, x, z, parms)
sdfun = SerialDifferentiableFunction(fun)
if with_complementarities is True:
[new_x, nit] = ncpsolve(sdfun, lb, ub, x_0, verbose=verbit,
maxit=inner_maxit)
else:
[new_x, nit] = serial_newton(sdfun, x_0, verbose=verbit)
new_h = h(grid, new_x, parms)
# update error
err = (abs(new_h - h_0).max())
# Update guess for decision rule and expectations function
x_0 = new_x
h_0 = new_h
# print error infomation if `verbose`
err_SA = err/err_0
err_0 = err
t_finish = time.time()
elapsed = t_finish - t_start
if verbose:
print(fmt_str.format(it, err, err_SA, elapsed))
if it == maxit:
import warnings
warnings.warn(UserWarning("Maximum number of iterations reached"))
# compute final fime and do final printout if `verbose`
t2 = time.time()
if verbose:
print(stars)
print('Elapsed: {} seconds.'.format(t2 - t1))
print(stars)
# Interpolation for the decision rule
dr.set_values(x_0)
return dr
def time_iteration(model, bounds=None, verbose=False, initial_dr=None,
pert_order=1, with_complementarities=True,
interp_type='smolyak', smolyak_order=3, interp_orders=None,
maxit=500, tol=1e-8, inner_maxit=10,
integration='gauss-hermite', integration_orders=None,
T=200, n_s=3, hook=None):
'''
Finds a global solution for ``model`` using backward time-iteration.
This algorithm iterates on the residuals of the arbitrage equations
Parameters
----------
model : NumericModel
"fg" or "fga" model to be solved
bounds : ndarray
boundaries for approximations. First row contains minimum values.
Second row contains maximum values.
verbose : boolean
if True, display iterations
initial_dr : decision rule
initial guess for the decision rule
pert_order : {1}
if no initial guess is supplied, the perturbation solution at order
``pert_order`` is used as initial guess
with_complementarities : boolean (True)
if False, complementarity conditions are ignored
interp_type : {`smolyak`, `spline`}
type of interpolation to use for future controls
smolyak_orders : int
parameter ``l`` for Smolyak interpolation
interp_orders : 1d array-like
list of integers specifying the number of nodes in each dimension if
``interp_type="spline" ``
Returns
-------
decision rule :
approximated solution
'''
def vprint(t):
if verbose:
print(t)
parms = model.calibration['parameters']
sigma = model.covariances
if initial_dr is None:
if pert_order == 1:
initial_dr = approximate_controls(model)
if pert_order > 1:
raise Exception("Perturbation order > 1 not supported (yet).")
if interp_type == 'perturbations':
return initial_dr
if bounds is not None:
pass
elif model.options and 'approximation_space' in model.options:
vprint('Using bounds specified by model')
approx = model.options['approximation_space']
a = approx['a']
b = approx['b']
bounds = np.row_stack([a, b])
bounds = np.array(bounds, dtype=float)
if interp_orders is None:
interp_orders = approx.get('orders', [5] * bounds.shape[1])
else:
vprint('Using asymptotic bounds given by first order solution.')
from dolo.numeric.timeseries import asymptotic_variance
# this will work only if initial_dr is a Taylor expansion
Q = asymptotic_variance(initial_dr.A.real, initial_dr.B.real,
initial_dr.sigma, T=T)
devs = np.sqrt(np.diag(Q))
bounds = np.row_stack([
initial_dr.S_bar - devs * n_s,
initial_dr.S_bar + devs * n_s,
])
if interp_orders is None:
interp_orders = [5] * bounds.shape[1]
if interp_type == 'smolyak':
from dolo.numeric.interpolation.smolyak import SmolyakGrid
dr = SmolyakGrid(bounds[0, :], bounds[1, :], smolyak_order)
elif interp_type == 'spline':
from dolo.numeric.interpolation.splines import MultivariateSplines
dr = MultivariateSplines(bounds[0, :], bounds[1, :], interp_orders)
if integration == 'optimal_quantization':
from dolo.numeric.discretization import quantization_nodes
# number of shocks
[epsilons, weights] = quantization_nodes(N_e, sigma)
elif integration == 'gauss-hermite':
from dolo.numeric.discretization import gauss_hermite_nodes
if not integration_orders:
integration_orders = [3] * sigma.shape[0]
[epsilons, weights] = gauss_hermite_nodes(integration_orders, sigma)
vprint('Starting time iteration')
# TODO: transpose
grid = dr.grid
xinit = initial_dr(grid)
xinit = xinit.real # just in case...
f = model.functions['arbitrage']
g = model.functions['transition']
# define objective function (residuals of arbitrage equations)
def fun(x):
return step_residual(grid, x, dr, f, g, parms, epsilons, weights)
##
t1 = time.time()
err = 1
x0 = xinit
it = 0
verbit = True if verbose == 'full' else False
if with_complementarities:
lbfun = model.functions['controls_lb']
ubfun = model.functions['controls_ub']
lb = lbfun(grid, parms)
ub = ubfun(grid, parms)
else:
lb = None
ub = None
if verbose:
headline = '|{0:^4} | {1:10} | {2:8} | {3:8} | {4:3} |'
headline = headline.format('N', ' Error', 'Gain', 'Time', 'nit')
stars = '-'*len(headline)
print(stars)
print(headline)
print(stars)
# format string for within loop
fmt_str = '|{0:4} | {1:10.3e} | {2:8.3f} | {3:8.3f} | {4:3} |'
err_0 = 1
while err > tol and it < maxit:
# update counters
t_start = time.time()
it += 1
# update interpolation coefficients (NOTE: filters through `fun`)
dr.set_values(x0)
# Derivative of objective function
sdfun = SerialDifferentiableFunction(fun)
# Apply solver with current decision rule for controls
if with_complementarities:
[x, nit] = ncpsolve(sdfun, lb, ub, x0, verbose=verbit,
maxit=inner_maxit)
else:
[x, nit] = serial_newton(sdfun, x0, verbose=verbit)
# update error and print if `verbose`
err = abs(x-x0).max()
err_SA = err/err_0
err_0 = err
t_finish = time.time()
elapsed = t_finish - t_start
if verbose:
print(fmt_str.format(it, err, err_SA, elapsed, nit))
# Update control vector
x0[:] = x # x0 = x0 + (x-x0)
# call user supplied hook, if any
if hook:
hook(dr, it, err)
# warn and bail if we get inf
if False in np.isfinite(x0):
print('iteration {} failed : non finite value')
return [x0, x]
if it == maxit:
import warnings
warnings.warn(UserWarning("Maximum number of iterations reached"))
# compute final fime and do final printout if `verbose`
t2 = time.time()
if verbose:
print(stars)
print('Elapsed: {} seconds.'.format(t2 - t1))
print(stars)
return dr
def time_iteration(model, verbose=False, initial_dr=None, pert_order=1,
with_complementarities=True, grid={}, distribution={},
maxit=500, tol=1e-8, inner_maxit=10, hook=None):
'''
Finds a global solution for ``model`` using backward time-iteration.
This algorithm iterates on the residuals of the arbitrage equations
Parameters
----------
model : NumericModel
"dtcscc" model to be solved
verbose : boolean
if True, display iterations
initial_dr : decision rule
initial guess for the decision rule
pert_order : {1}
if no initial guess is supplied, the perturbation solution at order
``pert_order`` is used as initial guess
with_complementarities : boolean (True)
if False, complementarity conditions are ignored
grid: grid options
distribution: distribution options
maxit: maximum number of iterations
inner_maxit: maximum number of iteration for inner solver
tol: tolerance criterium for successive approximations
Returns
-------
decision rule :
approximated solution
'''
def vprint(t):
if verbose:
print(t)
f = model.functions['arbitrage']
g = model.functions['transition']
parms = model.calibration['parameters']
approx = model.get_grid(**grid)
interp_type = approx.interpolation
dr = create_interpolator(approx, interp_type)
distrib = model.get_distribution(**distribution)
nodes, weights = distrib.discretize()
if initial_dr is None:
if pert_order == 1:
initial_dr = approximate_controls(model)
if pert_order > 1:
raise Exception("Perturbation order > 1 not supported (yet).")
vprint('Starting time iteration')
# TODO: transpose
grid = dr.grid
x_0 = initial_dr(grid)
x_0 = x_0.real # just in case...
# define objective function (residuals of arbitrage equations)
def fun(x):
return step_residual(grid, x, dr, f, g, parms, nodes, weights)
##
t1 = time.time()
err = 1
err_0 = 1
it = 0
verbit = True if verbose == 'full' else False
if with_complementarities:
lbfun = model.functions['controls_lb']
ubfun = model.functions['controls_ub']
lb = lbfun(grid, parms)
ub = ubfun(grid, parms)
else:
lb = None
ub = None
if verbose:
headline = '|{0:^4} | {1:10} | {2:8} | {3:8} | {4:3} |'
headline = headline.format('N', ' Error', 'Gain', 'Time', 'nit')
stars = '-'*len(headline)
print(stars)
print(headline)
print(stars)
# format string for within loop
fmt_str = '|{0:4} | {1:10.3e} | {2:8.3f} | {3:8.3f} | {4:3} |'
while err > tol and it < maxit:
# update counters
t_start = time.time()
it += 1
# update interpolation coefficients (NOTE: filters through `fun`)
dr.set_values(x_0)
# Derivative of objective function
sdfun = SerialDifferentiableFunction(fun)
# Apply solver with current decision rule for controls
if with_complementarities:
[x, nit] = ncpsolve(sdfun, lb, ub, x_0, verbose=verbit,
maxit=inner_maxit)
else:
[x, nit] = serial_newton(sdfun, x_0, verbose=verbit)
# update error and print if `verbose`
err = abs(x-x_0).max()
err_SA = err/err_0
err_0 = err
t_finish = time.time()
elapsed = t_finish - t_start
if verbose:
print(fmt_str.format(it, err, err_SA, elapsed, nit))
# Update control vector
x_0[:] = x # x0 = x0 + (x-x0)
# call user supplied hook, if any
if hook:
hook(dr, it, err)
# warn and bail if we get inf
if False in np.isfinite(x_0):
print('iteration {} failed : non finite value')
return [x_0, x]
if it == maxit:
import warnings
warnings.warn(UserWarning("Maximum number of iterations reached"))
# compute final time and do final printout if `verbose`
t2 = time.time()
if verbose:
print(stars)
print('Elapsed: {} seconds.'.format(t2 - t1))
print(stars)
return dr
def time_iteration(model, verbose=False, initial_dr=None, pert_order=1,
with_complementarities=True, grid={}, distribution={},
maxit=500, tol=1e-8, inner_maxit=10, hook=None):
'''
Finds a global solution for ``model`` using backward time-iteration.
This algorithm iterates on the residuals of the arbitrage equations
Parameters
----------
model : NumericModel
"dtcscc" model to be solved
verbose : boolean
if True, display iterations
initial_dr : decision rule
initial guess for the decision rule
pert_order : {1}
if no initial guess is supplied, the perturbation solution at order
``pert_order`` is used as initial guess
with_complementarities : boolean (True)
if False, complementarity conditions are ignored
grid: grid options
distribution: distribution options
maxit: maximum number of iterations
inner_maxit: maximum number of iteration for inner solver
tol: tolerance criterium for successive approximations
Returns
-------
decision rule :
approximated solution
'''
def vprint(t):
if verbose:
print(t)
f = model.functions['arbitrage']
g = model.functions['transition']
parms = model.calibration['parameters']
approx = model.get_grid(**grid)
interp_type = approx.interpolation
dr = create_interpolator(approx, interp_type)
distrib = model.get_distribution(**distribution)
nodes, weights = distrib.discretize()
if initial_dr is None:
if pert_order == 1:
initial_dr = approximate_controls(model)
if pert_order > 1:
raise Exception("Perturbation order > 1 not supported (yet).")
vprint('Starting time iteration')
# TODO: transpose
grid = dr.grid
x_0 = initial_dr(grid)
x_0 = x_0.real # just in case...
# define objective function (residuals of arbitrage equations)
def fun(x):
return step_residual(grid, x, dr, f, g, parms, nodes, weights)
##
t1 = time.time()
err = 1
err_0 = 1
it = 0
verbit = True if verbose == 'full' else False
if with_complementarities:
lbfun = model.functions['controls_lb']
ubfun = model.functions['controls_ub']
lb = lbfun(grid, parms)
ub = ubfun(grid, parms)
else:
lb = None
ub = None
if verbose:
headline = '|{0:^4} | {1:10} | {2:8} | {3:8} | {4:3} |'
headline = headline.format('N', ' Error', 'Gain', 'Time', 'nit')
stars = '-'*len(headline)
print(stars)
print(headline)
print(stars)
# format string for within loop
fmt_str = '|{0:4} | {1:10.3e} | {2:8.3f} | {3:8.3f} | {4:3} |'
while err > tol and it < maxit:
# update counters
t_start = time.time()
it += 1
# update interpolation coefficients (NOTE: filters through `fun`)
dr.set_values(x_0)
# Derivative of objective function
sdfun = SerialDifferentiableFunction(fun)
# Apply solver with current decision rule for controls
if with_complementarities:
[x, nit] = ncpsolve(sdfun, lb, ub, x_0, verbose=verbit,
maxit=inner_maxit)
else:
[x, nit] = serial_newton(sdfun, x_0, verbose=verbit)
# update error and print if `verbose`
err = abs(x-x_0).max()
err_SA = err/err_0
err_0 = err
t_finish = time.time()
elapsed = t_finish - t_start
if verbose:
print(fmt_str.format(it, err, err_SA, elapsed, nit))
# Update control vector
x_0[:] = x # x0 = x0 + (x-x0)
# call user supplied hook, if any
if hook:
hook(dr, it, err)
# warn and bail if we get inf
if False in np.isfinite(x_0):
print('iteration {} failed : non finite value')
return [x_0, x]
if it == maxit:
import warnings
warnings.warn(UserWarning("Maximum number of iterations reached"))
# compute final time and do final printout if `verbose`
t2 = time.time()
if verbose:
print(stars)
print('Elapsed: {} seconds.'.format(t2 - t1))
print(stars)
return dr
def time_iteration(model,
bounds=None,
verbose=False,
initial_dr=None,
pert_order=1,
with_complementarities=True,
interp_type='smolyak',
smolyak_order=3,
interp_orders=None,
maxit=500,
tol=1e-8,
integration='gauss-hermite',
integration_orders=None,
T=200,
n_s=3,
hook=None):
"""Finds a global solution for ``model`` using backward time-iteration.
Parameters:
-----------
model: NumericModel
"fg" or "fga" model to be solved
bounds: ndarray
boundaries for approximations. First row contains minimum values. Second row contains maximum values.
verbose: boolean
if True, display iterations
initial_dr: decision rule
initial guess for the decision rule
pert_order: {1}
if no initial guess is supplied, the perturbation solution at order ``pert_order`` is used as initial guess
with_complementarities: boolean (True)
if False, complementarity conditions are ignored
interp_type: {`smolyak`, `spline`}
type of interpolation to use for future controls
smolyak_orders: int
parameter ``l`` for Smolyak interpolation
interp_orders: 1d array-like
list of integers specifying the number of nods in each dimension if ``interp_type="spline" ``
Returns:
--------
decision rule object (SmolyakGrid or MultivariateSplines)
"""
def vprint(t):
if verbose:
print(t)
parms = model.calibration['parameters']
sigma = model.covariances
if initial_dr == None:
if pert_order == 1:
from dolo.algos.perturbations import approximate_controls
initial_dr = approximate_controls(model)
if pert_order > 1:
raise Exception("Perturbation order > 1 not supported (yet).")
if interp_type == 'perturbations':
return initial_dr
if bounds is not None:
pass
elif model.options and 'approximation_space' in model.options:
vprint('Using bounds specified by model')
approx = model.options['approximation_space']
a = approx['a']
b = approx['b']
bounds = numpy.row_stack([a, b])
bounds = numpy.array(bounds, dtype=float)
else:
vprint('Using asymptotic bounds given by first order solution.')
from dolo.numeric.timeseries import asymptotic_variance
# this will work only if initial_dr is a Taylor expansion
Q = asymptotic_variance(initial_dr.A.real,
initial_dr.B.real,
initial_dr.sigma,
T=T)
devs = numpy.sqrt(numpy.diag(Q))
bounds = numpy.row_stack([
initial_dr.S_bar - devs * n_s,
initial_dr.S_bar + devs * n_s,
])
if interp_orders == None:
interp_orders = [5] * bounds.shape[1]
if interp_type == 'smolyak':
from dolo.numeric.interpolation.smolyak import SmolyakGrid
dr = SmolyakGrid(bounds[0, :], bounds[1, :], smolyak_order)
elif interp_type == 'spline':
from dolo.numeric.interpolation.splines import MultivariateSplines
dr = MultivariateSplines(bounds[0, :], bounds[1, :], interp_orders)
elif interp_type == 'multilinear':
from dolo.numeric.interpolation.multilinear import MultilinearInterpolator
dr = MultilinearInterpolator(bounds[0, :], bounds[1, :], interp_orders)
if integration == 'optimal_quantization':
from dolo.numeric.discretization import quantization_nodes
# number of shocks
[epsilons, weights] = quantization_nodes(N_e, sigma)
elif integration == 'gauss-hermite':
from dolo.numeric.discretization import gauss_hermite_nodes
if not integration_orders:
integration_orders = [3] * sigma.shape[0]
[epsilons, weights] = gauss_hermite_nodes(integration_orders, sigma)
vprint('Starting time iteration')
# TODO: transpose
grid = dr.grid
xinit = initial_dr(grid)
xinit = xinit.real # just in case...
from dolo.algos.convert import get_fg_functions
f, g = get_fg_functions(model)
import time
fun = lambda x: step_residual(grid, x, dr, f, g, parms, epsilons, weights)
##
t1 = time.time()
err = 1
x0 = xinit
it = 0
verbit = True if verbose == 'full' else False
if with_complementarities:
lbfun = model.functions['arbitrage_lb']
ubfun = model.functions['arbitrage_ub']
lb = lbfun(grid, parms)
ub = ubfun(grid, parms)
else:
lb = None
ub = None
if verbose:
headline = '|{0:^4} | {1:10} | {2:8} | {3:8} | {4:3} |'.format(
'N', ' Error', 'Gain', 'Time', 'nit')
stars = '-' * len(headline)
print(stars)
print(headline)
print(stars)
err_0 = 1
while err > tol and it < maxit:
t_start = time.time()
it += 1
dr.set_values(x0)
from dolo.numeric.optimize.newton import serial_newton, SerialDifferentiableFunction
from dolo.numeric.optimize.ncpsolve import ncpsolve
sdfun = SerialDifferentiableFunction(fun)
if with_complementarities:
[x, nit] = ncpsolve(sdfun, lb, ub, x0, verbose=verbit)
else:
[x, nit] = serial_newton(sdfun, x0, verbose=verbit)
err = abs(x - x0).max()
err_SA = err / err_0
err_0 = err
t_finish = time.time()
elapsed = t_finish - t_start
if verbose:
print('|{0:4} | {1:10.3e} | {2:8.3f} | {3:8.3f} | {4:3} |'.format(
it, err, err_SA, elapsed, nit))
x0 = x0 + (x - x0)
if hook:
hook(dr, it, err)
if False in np.isfinite(x0):
print('iteration {} failed : non finite value')
return [x0, x]
if it == maxit:
import warnings
warnings.warn(UserWarning("Maximum number of iterations reached"))
t2 = time.time()
if verbose:
print(stars)
print('Elapsed: {} seconds.'.format(t2 - t1))
print(stars)
return dr
