def denhaanerrors( cmodel, dr, s0, horizon=100, n_sims=10, sigma=None, seed=0 ):
from dolo.numeric.global_solution import step_residual
from dolo.numeric.quadrature import gauss_hermite_nodes
from dolo.numeric.newton import newton_solver
from dolo.numeric.simulations import simulate
# cmodel should be an fg model
# the code is almost duplicated from simulate_without_error
# dr is used to approximate future steps
# monkey patch:
cmodel = cmodel.as_type('fg')
if sigma is None:
sigma = cmodel.sigma
from dolo.symbolic.model import Model
if isinstance(cmodel,Model):
from dolo.compiler.compiler_global import CModel_fg
model = cmodel
cmodel = CModel_fg(model)
[y,x,parms] = model.read_calibration()
parms = cmodel.model.read_calibration()[2]
mean = sigma[0,:]*0
n_x = len(cmodel.controls)
n_s = len(cmodel.states)
orders = [5]*len(mean)
[nodes, weights] = gauss_hermite_nodes(orders, sigma)
s0 = numpy.atleast_2d(s0.flatten()).T
x0 = dr(s0)
# standard simulation
simul = simulate(cmodel, dr, s0, sigma, horizon=horizon, n_exp=n_sims, parms=parms, seed=seed)
simul_se = simulate(cmodel, dr, s0, sigma, horizon=horizon, n_exp=n_sims, parms=parms, seed=seed, solve_expectations=True, nodes=nodes, weights=weights)
x_simul = simul[n_s:,:,:]
x_simul_se = simul_se[n_s:,:,:]
diff = abs( x_simul_se - x_simul )
error_1 = (diff).max(axis=2).mean(axis=1)
error_2 = (diff).mean(axis=2).mean(axis=1)
return [error_1, error_2]
def omega(dr, model, bounds, orders, exponent='inf', n_exp=10000, time_weight=None, return_everything=False):
N_epsilons = 1000
[y,x,parms] = model.read_calibration()
sigma = model.read_covariances()
mean = numpy.zeros(sigma.shape[0])
N_epsilons=100
numpy.random.seed(1)
epsilons = numpy.random.multivariate_normal(mean, sigma, N_epsilons).T
weights = np.ones(epsilons.shape[1])/N_epsilons
domain = RectangularDomain(bounds[0,:], bounds[1,:], orders)
gc = CModel(model)
f = gc.f
g = gc.g
errors = test_residuals( domain.grid, dr, f, g, parms, epsilons, weights )
errors = abs(errors)
errors = errors.reshape( [errors.shape[0]] + orders )
if exponent == 'inf':
criterium = numpy.max(abs(errors), axis=1)
elif exponent == 'L2':
squared_errors = np.power(errors,2)
criterium = np.sqrt( np.sum(squared_errors,axis=1) ) /(squared_errors.shape[1])
if time_weight:
horizon = time_weight[0]
beta = time_weight[1]
s0 = time_weight[2]
from dolo.numeric.simulations import simulate
simul = simulate( gc ,dr,s0, sigma, n_exp=n_exp, horizon=horizon+1, discard=True)
s_simul = simul[:len(gc.controls),:,:]
densities = [domain.compute_density(s_simul[:,:,i]) for i in range(horizon)]
ergo_dens = densities[-1]
ergo_error = numpy.tensordot( errors, ergo_dens, axes=((1,2),(0,1)))
mean_error = numpy.tensordot( errors, (ergo_dens*0+1)/len(ergo_dens.flatten()), axes=((1,2),(0,1)))
max_error = numpy.max(errors,axis=1)
max_error = numpy.max(max_error,axis=1)
time_weighted_errors = max_error*0
for i in range(horizon):
err = numpy.tensordot( errors, densities[i], axes=((1,2),(0,1)))
time_weighted_errors += beta**i * err
time_weighted_errors /= (1-beta**(horizon-1))/(1-beta)
# print(numpy.mean(errors[0,:,:].flatten()))
# print(numpy.mean(errors[1,:,:].flatten()))
if return_everything:
d = dict(
errors = errors,
densities = densities,
bounds = bounds,
mean = mean_error,
max = max_error,
ergo = ergo_error,
time_weighted = time_weighted_errors,
simulations = s_simul,
domain = domain
)
return d
else:
return [mean_error, max_error, ergo_error, time_weighted_errors]
return criterium
def denhaanerrors(cmodel, dr, s0, horizon=100, n_sims=10, sigma=None, seed=0):
from dolo.numeric.global_solution import step_residual
from dolo.numeric.quadrature import gauss_hermite_nodes
from dolo.numeric.newton import newton_solver
from dolo.numeric.simulations import simulate
# cmodel should be an fg model
# the code is almost duplicated from simulate_without_error
# dr is used to approximate future steps
# monkey patch:
if sigma is None:
sigma = cmodel.sigma
# from dolo.symbolic.model import SModel
#
# if isinstance(cmodel,SModel):
# from dolo.compiler.compiler_global import CModel_fg
# model = cmodel
# cmodel = CModel_fg(model)
# [y,x,parms] = model.read_calibration()
#
# parms = cmodel.model.read_calibration()[2]
parms = cmodel.calibration['parameters']
mean = sigma[0, :] * 0
n_x = len(cmodel.symbols['controls'])
n_s = len(cmodel.symbols['states'])
orders = [5] * len(mean)
[nodes, weights] = gauss_hermite_nodes(orders, sigma)
s0 = numpy.atleast_2d(s0.flatten()).T
x0 = dr(s0)
# standard simulation
simul = simulate(cmodel,
dr,
s0,
sigma,
horizon=horizon,
n_exp=n_sims,
parms=parms,
seed=seed)
simul_se = simulate(cmodel,
dr,
s0,
sigma,
horizon=horizon,
n_exp=n_sims,
parms=parms,
seed=seed,
solve_expectations=True,
nodes=nodes,
weights=weights)
x_simul = simul[n_s:, :, :]
x_simul_se = simul_se[n_s:, :, :]
diff = abs(x_simul_se - x_simul)
error_1 = (diff).max(axis=2).mean(axis=1)
error_2 = (diff).mean(axis=2).mean(axis=1)
return [error_1, error_2]
def omega(dr,
model,
bounds,
orders,
exponent='inf',
n_exp=10000,
time_weight=None,
return_everything=False):
N_epsilons = 1000
#[y,x,parms] = model.read_calibration()
sigma = model.calibration['covariances']
parms = model.calibration['parameters']
mean = numpy.zeros(sigma.shape[0])
N_epsilons = 100
numpy.random.seed(1)
epsilons = numpy.random.multivariate_normal(mean, sigma, N_epsilons).T
weights = np.ones(epsilons.shape[1]) / N_epsilons
domain = RectangularDomain(bounds[0, :], bounds[1, :], orders)
f = model.functions['arbitrage']
g = model.functions['transition']
n_s = len(model.symbols['states'])
with_future_shocks = model.model_type == 'fg2'
errors = test_residuals(domain.grid,
dr,
f,
g,
parms,
epsilons,
weights,
with_future_shocks=with_future_shocks)
errors = abs(errors)
errors = errors.reshape([errors.shape[0]] + orders)
if exponent == 'inf':
criterium = numpy.max(abs(errors), axis=1)
elif exponent == 'L2':
squared_errors = np.power(errors, 2)
criterium = np.sqrt(np.sum(squared_errors,
axis=1)) / (squared_errors.shape[1])
if time_weight:
horizon = time_weight[0]
beta = time_weight[1]
s0 = time_weight[2]
else:
raise Exception()
from dolo.numeric.simulations import simulate
simul = simulate(model,
dr,
s0,
sigma,
n_exp=n_exp,
horizon=horizon + 1,
discard=True)
print(simul.shape)
print(n_s)
s_simul = simul[:n_s, :, :]
densities = [
domain.compute_density(s_simul[:, :, i]) for i in range(horizon)
]
ergo_dens = densities[-1]
ergo_error = numpy.tensordot(errors, ergo_dens, axes=((1, 2), (0, 1)))
mean_error = numpy.tensordot(errors, (ergo_dens * 0 + 1) /
len(ergo_dens.flatten()),
axes=((1, 2), (0, 1)))
max_error = numpy.max(errors, axis=1)
max_error = numpy.max(max_error, axis=1)
time_weighted_errors = max_error * 0
for i in range(horizon):
err = numpy.tensordot(errors, densities[i], axes=((1, 2), (0, 1)))
time_weighted_errors += beta**i * err
time_weighted_errors /= (1 - beta**(horizon - 1)) / (1 - beta)
# print(numpy.mean(errors[0,:,:].flatten()))
# print(numpy.mean(errors[1,:,:].flatten()))
if return_everything:
d = dict(errors=errors,
densities=densities,
bounds=bounds,
mean=mean_error,
max=max_error,
ergo=ergo_error,
time_weighted=time_weighted_errors,
simulations=s_simul,
domain=domain)
return d
else:
return [mean_error, max_error, ergo_error, time_weighted_errors]
return criterium
def omega(dr,
model,
bounds,
orders,
exponent='inf',
n_exp=10000,
time_weight=None,
return_everything=False):
N_epsilons = 1000
[y, x, parms] = model.read_calibration()
sigma = model.read_covariances()
mean = numpy.zeros(sigma.shape[0])
N_epsilons = 100
numpy.random.seed(1)
epsilons = numpy.random.multivariate_normal(mean, sigma, N_epsilons).T
weights = np.ones(epsilons.shape[1]) / N_epsilons
domain = RectangularDomain(bounds[0, :], bounds[1, :], orders)
gc = GlobalCompiler(model, substitute_auxiliary=True, solve_systems=True)
f = gc.f
g = gc.g
errors = test_residuals(domain.grid, dr, f, g, parms, epsilons, weights)
errors = abs(errors)
errors = errors.reshape([errors.shape[0]] + orders)
if exponent == 'inf':
criterium = numpy.max(abs(errors), axis=1)
elif exponent == 'L2':
squared_errors = np.power(errors, 2)
criterium = np.sqrt(np.sum(squared_errors,
axis=1)) / (squared_errors.shape[1])
if time_weight:
horizon = time_weight[0]
beta = time_weight[1]
s0 = time_weight[2]
from dolo.numeric.simulations import simulate_without_aux as simulate
[s_simul, x_simul] = simulate(model,
dr,
s0,
sigma,
n_exp=n_exp,
horizon=horizon + 1,
discard=True)
densities = [
domain.compute_density(s_simul[:, :, i]) for i in range(horizon)
]
ergo_dens = densities[-1]
ergo_error = numpy.tensordot(errors, ergo_dens, axes=((1, 2), (0, 1)))
mean_error = numpy.tensordot(errors, (ergo_dens * 0 + 1) /
len(ergo_dens.flatten()),
axes=((1, 2), (0, 1)))
max_error = numpy.max(errors, axis=1)
max_error = numpy.max(max_error, axis=1)
time_weighted_errors = max_error * 0
for i in range(horizon):
err = numpy.tensordot(errors, densities[i], axes=((1, 2), (0, 1)))
time_weighted_errors += beta**i * err
time_weighted_errors /= (1 - beta**(horizon - 1)) / (1 - beta)
# print(numpy.mean(errors[0,:,:].flatten()))
# print(numpy.mean(errors[1,:,:].flatten()))
if return_everything:
d = dict(errors=errors,
densities=densities,
bounds=bounds,
mean=mean_error,
max=max_error,
ergo=ergo_error,
time_weighted=time_weighted_errors,
simulations=s_simul,
domain=domain)
return d
else:
return [mean_error, max_error, ergo_error, time_weighted_errors]
return criterium
