def dynamic_residuals(X, return_dr=False):
x = X[:, 0]
dx = X[:, 1:]
d = {}
for i in range(n_pfs):
p = pf_parms[i]
v = pf_vars[i]
d[p] = x[i]
d[v] = x[i]
for j in range(n_states):
d[pf_dparms[i][j]] = dx[i, j]
new_model.set_calibration(d)
if return_dr:
dr = approximate_controls(new_model, order=2, lambda_name='lam')
return dr
else:
[X_bar, X_s, X_ss, X_sss] = approximate_controls(new_model,
order=3,
return_dr=False,
lambda_name='lam')
crit = numpy.column_stack([
X_bar[n_controls - n_pfs:n_controls],
X_s[n_controls - n_pfs:n_controls, :],
])
return crit
def constant_residuals(x, return_dr=False):
d = {}
for i in range(n_pfs):
p = pf_parms[i]
v = pf_vars[i]
d[p] = x[i]
d[v] = x[i]
new_model.set_calibration(d)
# new_model.parameters_values[p] = x[i]
# new_model.init_values[v] = x[i]
if return_dr:
dr = approximate_controls(new_model, order=1, return_dr=True, lambda_name='lam')
return dr
X_bar, X_s, X_ss = approximate_controls(new_model, order=2, return_dr=False, lambda_name="lam")
return X_bar[n_controls-n_pfs:n_controls]
def test_second_order_accuracy(self):
# This solves the optimal growth example at second order
# and computes the second order correction to the steady-state
# We test that both the statefree method and the perturbation to states
# yield the same result.
from dolo.algos.perturbations import yaml_import
model = yaml_import('examples/models/compat/rbc.yaml', compiler=None)
from trash.dolo.numeric.perturbations import solve_decision_rule
from trash.dolo.numeric.perturbations_to_states import approximate_controls
coeffs = approximate_controls(model,order=2, return_dr=False)
state_perturb = coeffs[0]
dr = solve_decision_rule(model)
statefree_perturb = dr['ys'] + dr['g_ss']/2.0
ctls = model.symbols_s['controls']
ctls_ind = [model.variables.index(v) for v in ctls]
# the two methods should yield exactly the same result
from numpy.testing import assert_almost_equal
A = statefree_perturb[ctls_ind]
B = state_perturb
assert_almost_equal(A, B) # we compare the risk-adjusted constants
def dynamic_residuals(X, return_dr=False):
x = X[:, 0]
dx = X[:, 1:]
d = {}
for i in range(n_pfs):
p = pf_parms[i]
v = pf_vars[i]
d[p] = x[i]
d[v] = x[i]
for j in range(n_states):
d[pf_dparms[i][j]] = dx[i, j]
new_model.set_calibration(d)
if return_dr:
dr = approximate_controls(new_model, order=2, lambda_name="lam")
return dr
else:
[X_bar, X_s, X_ss, X_sss] = approximate_controls(new_model, order=3, return_dr=False, lambda_name="lam")
crit = numpy.column_stack([X_bar[n_controls - n_pfs : n_controls], X_s[n_controls - n_pfs : n_controls, :]])
return crit
def solve_model_around_risky_ss(model,
verbose=False,
return_dr=True,
initial_sol=None):
if initial_sol == None:
if model.model_spec == 'portfolios':
print(
'This is a portfolio model ! Converting to deterministic one.')
from dolo.algos.portfolio_perturbation import portfolios_to_deterministic
model = portfolios_to_deterministic(model, ['x_1', 'x_2'])
model.check()
from trash.dolo.numeric.perturbations_to_states import approximate_controls
perturb_sol = approximate_controls(model, order=1, return_dr=False)
[X_bar, X_s] = perturb_sol
else:
perturb_sol = initial_sol
[X_bar, X_s] = perturb_sol
# reduce X_s to the real controls (remove auxiliary variables
X_s = X_s[:len(model.symbols['controls']), :]
X_bar = X_bar[:len(model.symbols['controls'])]
X_bar = numpy.array(X_bar)
if abs(X_s.imag).max() < 1e-10:
X_s = X_s.real
else:
raise (Exception('Complex decision rule'))
print('Perturbation solution found')
#print model.parameters
#exit()
X_bar_1 = X_bar
X_s_1 = X_s
#model = yaml_import(filename)
#from dolo.symbolic.symbolic import Parameter
[S_bar, X_bar, X_s, P] = solve_risky_ss(model.model,
X_bar,
X_s,
verbose=verbose)
if return_dr:
cdr = CDR([S_bar, X_bar, X_s])
# cdr.P = P
return cdr
return [S_bar, X_bar, X_s, P]
def solve_model_around_risky_ss(model, verbose=False, return_dr=True, initial_sol=None):
if initial_sol == None:
if model.model_type == 'portfolios':
print('This is a portfolio model ! Converting to deterministic one.')
from dolo.algos.portfolio_perturbation import portfolios_to_deterministic
model = portfolios_to_deterministic(model,['x_1','x_2'])
model.check()
from trash.dolo.numeric.perturbations_to_states import approximate_controls
perturb_sol = approximate_controls(model, order = 1, return_dr=False)
[X_bar,X_s] = perturb_sol
else:
perturb_sol = initial_sol
[X_bar,X_s] = perturb_sol
# reduce X_s to the real controls (remove auxiliary variables
X_s = X_s[:len(model.symbols['controls']),:]
X_bar = X_bar[:len(model.symbols['controls'])]
X_bar = numpy.array(X_bar)
if abs(X_s.imag).max() < 1e-10:
X_s = X_s.real
else:
raise( Exception('Complex decision rule') )
print('Perturbation solution found')
#print model.parameters
#exit()
X_bar_1 = X_bar
X_s_1 = X_s
#model = yaml_import(filename)
#from dolo.symbolic.symbolic import Parameter
[S_bar, X_bar, X_s, P] = solve_risky_ss(model.model, X_bar, X_s, verbose=verbose)
if return_dr:
cdr = CDR([S_bar, X_bar, X_s])
# cdr.P = P
return cdr
return [S_bar, X_bar, X_s, P]
def solve_portfolio_model(model, pf_names, order=2, lambda_name='lam', guess=None):
from dolo.compiler.compiler_python import GModel
if isinstance(model, GModel):
model = model.model
pf_model = model
from dolo import Variable, Parameter, Equation
import re
n_states = len(pf_model.symbols_s['states'])
states = pf_model.symbols_s['states']
steady_states = [Parameter(v.name+'_bar') for v in pf_model.symbols_s['states']]
n_pfs = len(pf_names)
pf_vars = [Variable(v) for v in pf_names]
res_vars = [Variable('res_'+str(i)) for i in range(n_pfs)]
pf_parms = [Parameter('K_'+str(i)) for i in range(n_pfs)]
pf_dparms = [[Parameter('K_'+str(i)+'_'+str(j)) for j in range(n_states)] for i in range(n_pfs)]
from sympy import Matrix
# creation of the new model
import copy
new_model = copy.copy(pf_model)
new_model.symbols_s['controls'] += res_vars
for v in res_vars + pf_vars:
new_model.calibration_s[v] = 0
new_model.symbols_s['parameters'].extend(steady_states)
for p in pf_parms + Matrix(pf_dparms)[:]:
new_model.symbols_s['parameters'].append(p)
new_model.calibration_s[p] = 0
compregex = re.compile('(.*)<=(.*)<=(.*)')
to_be_added_1 = []
to_be_added_2 = []
expressions = Matrix(pf_parms) + Matrix(pf_dparms)*( Matrix(states) - Matrix(steady_states))
for n,eq in enumerate(new_model.equations_groups['arbitrage']):
if 'complementarity' in eq.tags:
tg = eq.tags['complementarity']
[lhs,mhs,rhs] = compregex.match(tg).groups()
mhs = new_model.eval_string(mhs)
else:
mhs = None
if mhs in pf_vars:
i = pf_vars.index(mhs)
neq = Equation(mhs, expressions[i])
neq.tag(**eq.tags)
eq_res = Equation(eq.gap, res_vars[i])
eq_res.tag(eq_type='arbitrage')
to_be_added_2.append(eq_res)
new_model.equations_groups['arbitrage'][n] = neq
to_be_added_1.append(neq)
# new_model.equations_groups['arbitrage'].extend(to_be_added_1)
new_model.equations_groups['arbitrage'].extend(to_be_added_2)
new_model.update()
print("number of equations {}".format(len(new_model.equations)))
print("number of arbitrage equations {}".format( len(new_model.equations_groups['arbitrage'])) )
print('parameters_ordering')
print("number of parameters {}".format(new_model.symbols['parameters']))
print("number of parameters {}".format(new_model.parameters))
# now, we need to solve for the optimal portfolio coefficients
from trash.dolo.numeric.perturbations_to_states import approximate_controls
dr = approximate_controls(new_model)
print('ok')
import numpy
n_controls = len(model.symbols_s['controls'])
def constant_residuals(x, return_dr=False):
d = {}
for i in range(n_pfs):
p = pf_parms[i]
v = pf_vars[i]
d[p] = x[i]
d[v] = x[i]
new_model.set_calibration(d)
# new_model.parameters_values[p] = x[i]
# new_model.init_values[v] = x[i]
if return_dr:
dr = approximate_controls(new_model, order=1, return_dr=True, lambda_name='lam')
return dr
X_bar, X_s, X_ss = approximate_controls(new_model, order=2, return_dr=False, lambda_name="lam")
return X_bar[n_controls-n_pfs:n_controls]
if guess is not None:
x0 = numpy.array(guess)
else:
x0 = numpy.zeros(n_pfs)
print('Zero order portfolios')
print('Initial guess: {}'.format(x0))
print('Initial error: {}'.format( constant_residuals(x0) ))
portfolios_0 = solver(constant_residuals, x0)
print('Solution: {}'.format(portfolios_0))
print('Final error: {}'.format( constant_residuals(portfolios_0) ))
if order == 1:
dr = constant_residuals(portfolios_0, return_dr=True)
return dr
def dynamic_residuals(X, return_dr=False):
x = X[:,0]
dx = X[:,1:]
d = {}
for i in range(n_pfs):
p = pf_parms[i]
v = pf_vars[i]
d[p] = x[i]
d[v] = x[i]
for j in range(n_states):
d[pf_dparms[i][j]] = dx[i,j]
new_model.set_calibration(d)
if return_dr:
dr = approximate_controls(new_model, order=2, lambda_name='lam')
return dr
else:
[X_bar, X_s, X_ss, X_sss] = approximate_controls(new_model, order=3, return_dr=False, lambda_name='lam')
crit = numpy.column_stack([
X_bar[n_controls-n_pfs:n_controls],
X_s[n_controls-n_pfs:n_controls,:],
])
return crit
y0 = numpy.column_stack([x0, numpy.zeros((n_pfs, n_states))])
print('Initial error:')
err = (dynamic_residuals(y0))
print( abs(err).max() )
portfolios_1 = solver(dynamic_residuals, y0)
print('First order portfolios : ')
print(portfolios_1)
print('Final error:')
print(dynamic_residuals(portfolios_1))
dr = dynamic_residuals(portfolios_1, return_dr=True)
# TODO: remove coefficients of criteria
return dr
z0 = z1
print('finished in {} iterations'.format(it))
return [x0,z0]
from dolo import yaml_import
from trash.dolo.numeric.perturbations_to_states import approximate_controls
model = yaml_import('../../../examples/models/rbc_fgah.yaml')
dr_pert = approximate_controls(model, order=1, substitute_auxiliary=True)
print(dr_pert.X_bar)
from dolo.numeric.interpolation.smolyak import SmolyakGrid
from dolo.numeric.time_iteration import time_iteration
dr_smol = time_iteration(model, smolyak_order=2, maxit=2, polish=True)
smin = dr_smol.bounds[0,:]
smax = dr_smol.bounds[1,:]
dr_x = SmolyakGrid( smin, smax, 3)
print(err, err2)
x0 = x1
z0 = z1
print('finished in {} iterations'.format(it))
return [x0, z0]
from dolo import yaml_import
from trash.dolo.numeric.perturbations_to_states import approximate_controls
model = yaml_import('../../../examples/models/rbc_fgah.yaml')
dr_pert = approximate_controls(model, order=1, substitute_auxiliary=True)
print(dr_pert.X_bar)
from dolo.numeric.interpolation.smolyak import SmolyakGrid
from dolo.numeric.time_iteration import time_iteration
dr_smol = time_iteration(model, smolyak_order=2, maxit=2, polish=True)
smin = dr_smol.bounds[0, :]
smax = dr_smol.bounds[1, :]
dr_x = SmolyakGrid(smin, smax, 3)
dr_h = SmolyakGrid(smin, smax, 3)
grid = dr_x.grid
def test_perturbation_3(self):
from dolo import yaml_import
from dolo.algos.perturbations import approximate_controls
model = yaml_import('examples/models/compat/rbc.yaml')
dr = approximate_controls(model,order=3)
def test_perturbation_1_old(self):
from dolo import yaml_import
model = yaml_import('examples/models/rbc.yaml')
from dolo.algos.perturbations import approximate_controls
dr = approximate_controls(model, order=1)
def test_perturbation_1_old(self):
from dolo import yaml_import
model = yaml_import('examples/models/rbc.yaml')
from dolo.algos.perturbations import approximate_controls
dr = approximate_controls(model,order=1)