def test_denhaan_errors(self):
from dolo.misc.yamlfile import yaml_import
from dolo.numeric.global_solve import global_solve
model = yaml_import('examples/global_models/rbc.yaml')
from dolo.compiler.compiler_global import CModel
from dolo.numeric.perturbations_to_states import approximate_controls
dr = approximate_controls(model)
dr_global = global_solve(model, smolyak_order=4, verbose=False, pert_order=1)
sigma = model.read_covariances()
cmodel = CModel(model)
cmodel.sigma = sigma
s_0 = dr.S_bar
from dolo.numeric.error_measures import denhaanerrors
[error_1, error_2] = denhaanerrors(cmodel, dr, s_0)
[error_1_glob, error_2_glob] = denhaanerrors(cmodel, dr_global, s_0)
print(error_1)
print(error_1_glob)
assert( max(error_1_glob) < 10-7) # errors with solyak colocations at order 4 are very small
assert( max(error_2_glob) < 10-7)
def global_solve(model,
bounds=None, verbose=False,
initial_dr=None, pert_order=2,
interp_type='smolyak', smolyak_order=3, interp_orders=None,
maxit=500, numdiff=True, polish=True, tol=1e-8,
integration='gauss-hermite', integration_orders=[],
compiler='numpy', memory_hungry=True,
T=200, n_s=2, N_e=40 ):
def vprint(t):
if verbose:
print(t)
[y, x, parms] = model.read_calibration()
sigma = model.read_covariances()
if initial_dr == None:
initial_dr = approximate_controls(model, order=pert_order)
if interp_type == 'perturbations':
return initial_dr
if bounds is not None:
pass
elif 'approximation' in model['original_data']:
vprint('Using bounds specified by model')
# this should be moved to the compiler
ssmin = model['original_data']['approximation']['bounds']['smin']
ssmax = model['original_data']['approximation']['bounds']['smax']
ssmin = [model.eval_string(str(e)) for e in ssmin]
ssmax = [model.eval_string(str(e)) for e in ssmax]
ssmin = [model.eval_string(str(e)) for e in ssmin]
ssmax = [model.eval_string(str(e)) for e in ssmax]
[y, x, p] = model.read_calibration()
d = {v: y[i] for i, v in enumerate(model.variables)}
d.update({v: p[i] for i, v in enumerate(model.parameters)})
smin = [expr.subs(d) for expr in ssmin]
smax = [expr.subs(d) for expr in ssmax]
smin = numpy.array(smin, dtype=numpy.float)
smax = numpy.array(smax, dtype=numpy.float)
bounds = numpy.row_stack([smin, smax])
bounds = numpy.array(bounds, dtype=float)
else:
vprint('Using bounds given by second 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,
])
smin = bounds[0, :]
smax = bounds[1, :]
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)
elif interp_type == 'sparse_linear':
from dolo.numeric.interpolation.interpolation import SparseLinear
dr = SparseLinear(bounds[0, :], bounds[1, :], smolyak_order)
elif interp_type == 'linear':
from dolo.numeric.interpolation.interpolation import LinearTriangulation, TriangulatedDomain, RectangularDomain
rec = RectangularDomain(smin, smax, interp_orders)
domain = TriangulatedDomain(rec.grid)
dr = LinearTriangulation(domain)
from dolo.compiler.compiler_global import CModel
cm = CModel(model, solve_systems=True, compiler=compiler)
cm = cm.as_type('fg')
if integration == 'optimal_quantization':
from dolo.numeric.quantization import quantization_nodes
# number of shocks
[epsilons, weights] = quantization_nodes(N_e, sigma)
elif integration == 'gauss-hermite':
from dolo.numeric.quadrature 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')
from dolo.numeric.global_solution import time_iteration
from dolo.numeric.global_solution import stochastic_residuals_2, stochastic_residuals_3
xinit = initial_dr(dr.grid)
xinit = xinit.real # just in case...
dr = time_iteration(dr.grid, dr, xinit, cm.f, cm.g, parms, epsilons, weights, x_bounds=cm.x_bounds, maxit=maxit,
tol=tol, nmaxit=50, numdiff=numdiff, verbose=verbose)
if polish and interp_type == 'smolyak': # this works with smolyak only
vprint('\nStarting global optimization')
import time
t1 = time.time()
if cm.x_bounds is not None:
lb = cm.x_bounds[0](dr.grid, parms)
ub = cm.x_bounds[1](dr.grid, parms)
else:
lb = None
ub = None
xinit = dr(dr.grid)
dr.set_values(xinit)
shape = xinit.shape
if not memory_hungry:
fobj = lambda t: stochastic_residuals_3(dr.grid, t, dr, cm.f, cm.g, parms, epsilons, weights, shape, deriv=False)
dfobj = lambda t: stochastic_residuals_3(dr.grid, t, dr, cm.f, cm.g, parms, epsilons, weights, shape, deriv=True)[1]
else:
fobj = lambda t: stochastic_residuals_2(dr.grid, t, dr, cm.f, cm.g, parms, epsilons, weights, shape, deriv=False)
dfobj = lambda t: stochastic_residuals_2(dr.grid, t, dr, cm.f, cm.g, parms, epsilons, weights, shape, deriv=True)[1]
from dolo.numeric.solver import solver
x = solver(fobj, xinit, lb=lb, ub=ub, jac=dfobj, verbose=verbose, method='ncpsolve', serial_problem=False)
dr.set_values(x) # just in case
t2 = time.time()
# test solution
res = stochastic_residuals_2(dr.grid, x, dr, cm.f, cm.g, parms, epsilons, weights, shape, deriv=False)
if numpy.isinf(res.flatten()).sum() > 0:
raise ( Exception('Non finite values in residuals.'))
vprint('Finished in {} s'.format(t2 - t1))
return dr
pyplot.xlabel(state)
if __name__ == '__main__':
from dolo import yaml_import, approximate_controls
model = yaml_import('../../examples/global_models/capital.yaml')
dr = approximate_controls(model)
[y, x, parms] = model.read_calibration()
sigma = model.read_covariances()
from dolo.compiler.compiler_global import CModel
import numpy
cmodel = CModel(model)
s0 = numpy.atleast_2d(dr.S_bar).T
horizon = 50
simul = simulate(cmodel,
dr,
s0,
sigma,
n_exp=500,
parms=parms,
seed=1,
horizon=horizon)
from dolo.numeric.quantization import quantization_nodes
N = 80
[x, w] = quantization_nodes(N, sigma)
def simulate(cmodel, dr, s0=None, sigma=None, n_exp=0, horizon=40, parms=None, seed=1, discard=False, stack_series=True,
solve_expectations=False, nodes=None, weights=None):
'''
:param cmodel: compiled model
:param dr: decision rule
:param s0: initial state where all simulations start
:param sigma: covariance matrix of the normal multivariate distribution describing the random shocks
:param n_exp: number of draws to simulate. Use 0 for impulse-response functions
:param horizon: horizon for the simulation
:param parms: (vector) value for the parameters of the model
:param seed: used to initialize the random number generator. Use it to replicate exact same results among simulations
:param discard: (default: False) if True, then all simulations containing at least one non finite value are discarded
:param stack_series: return simulated series for different types of variables separately (in a list)
:return: a ``n_s x n_exp x horizon`` array where ``n_s`` is the number of states. The second dimension is omitted if
n_exp = 0.
'''
from dolo.compiler.compiler_global import CModel
from dolo.symbolic.model import Model
if isinstance(cmodel, Model):
from dolo.symbolic.model import Model
model = cmodel
cmodel = CModel(model)
[y,x,parms] = model.read_calibration()
else:
cmodel = cmodel.as_type('fg')
if n_exp ==0:
irf = True
n_exp = 1
else:
irf = False
calib = cmodel.model.calibration
if parms is None:
parms = numpy.array( calib['parameters'] ) # TODO : remove reference to symbolic model
if sigma is None:
sigma = numpy.array( calib['sigma'] )
if s0 is None:
s0 = numpy.array( calib['steady_state']['states'] )
s0 = numpy.atleast_2d(s0.flatten()).T
x0 = dr(s0)
s_simul = numpy.zeros( (s0.shape[0],n_exp,horizon) )
x_simul = numpy.zeros( (x0.shape[0],n_exp,horizon) )
s_simul[:,:,0] = s0
x_simul[:,:,0] = x0
numpy.random.seed(seed)
for i in range(horizon):
mean = numpy.zeros(sigma.shape[0])
if irf:
epsilons = numpy.zeros( (sigma.shape[0],1) )
else:
epsilons = numpy.random.multivariate_normal(mean, sigma, n_exp).T
s = s_simul[:,:,i]
x = dr(s)
if solve_expectations:
from dolo.numeric.solver import solver
from dolo.numeric.newton import newton_solver
fobj = lambda t: step_residual(s, t, dr, cmodel.f, cmodel.g, parms, nodes, weights, with_derivatives=False) #
# x = solver(fobj, x, serial_problem=True)
x = newton_solver(fobj, x, numdiff=True)
x_simul[:,:,i] = x
ss = cmodel.g(s,x,epsilons,parms)
if i<(horizon-1):
s_simul[:,:,i+1] = ss
from numpy import any,isnan,all
if not hasattr(cmodel,'__a__'): # TODO: find a better test than this
l = [s_simul, x_simul]
else:
n_s = s_simul.shape[0]
n_x = x_simul.shape[0]
a_simul = cmodel.a( s_simul.reshape((n_s,n_exp*horizon)), x_simul.reshape( (n_x,n_exp*horizon) ), parms)
n_a = a_simul.shape[0]
a_simul = a_simul.reshape(n_a,n_exp,horizon)
l = [s_simul, x_simul, a_simul]
if not stack_series:
return l
else:
simul = numpy.row_stack(l)
if discard:
iA = -isnan(x_simul)
valid = all( all( iA, axis=0 ), axis=1 )
simul = simul[:,valid,:]
n_kept = s_simul.shape[1]
if n_exp > n_kept:
print( 'Discarded {}/{}'.format(n_exp-n_kept,n_exp))
if irf:
simul = simul[:,0,:]
return simul
bounds[:, 1] += s0[1]
print('bounds')
print bounds
P = eigs[1]
sg = SmolyakGrid(bounds, 5, P)
[y, x, parms] = model.read_calibration()
xinit = dr(sg.grid)
sg.fit_values(xinit)
from dolo.compiler.compiler_global import CModel, time_iteration, deterministic_residuals
gc = CModel(model)
res = deterministic_residuals(sg.grid, xinit, sg, gc.f, gc.g, dr.sigma, parms)
n_e = 5
epsilons = np.zeros((1, n_e))
weights = np.ones(n_e) / n_e
dr_smol = time_iteration(sg.grid,
sg,
xinit,
gc.f,
gc.g,
parms,
epsilons,
weights,
