def solve_risky_ss(model, X_bar, X_s, verbose=False):
import numpy
from dolo.compiler.function_compiler import compile_function
import time
from dolo.compiler.compiler_functions import simple_global_representation
parms = model.calibration['parameters']
sigma = model.calibration['covariances']
sgm = simple_global_representation(model)
states = sgm['states']
controls = sgm['controls']
shocks = sgm['shocks']
parameters = sgm['parameters']
f_eqs = sgm['f_eqs']
g_eqs = sgm['g_eqs']
g_args = [s(-1) for s in states] + [c(-1) for c in controls] + shocks
f_args = states + controls + [v(1)
for v in states] + [v(1) for v in controls]
p_args = parameters
g_fun = compile_function(g_eqs, g_args, p_args, 2)
f_fun = compile_function(f_eqs, f_args, p_args, 3)
epsilons_0 = np.zeros((sigma.shape[0]))
from numpy import dot
from dolo.numeric.tensor import sdot, mdot
def residuals(X, sigma, parms, g_fun, f_fun):
import numpy
dummy_x = X[0:1, 0]
X_bar = X[1:, 0]
S_bar = X[0, 1:]
X_s = X[1:, 1:]
[n_x, n_s] = X_s.shape
n_e = sigma.shape[0]
xx = np.concatenate([S_bar, X_bar, epsilons_0])
[g_0, g_1, g_2] = g_fun(xx, parms)
[f_0, f_1, f_2,
f_3] = f_fun(np.concatenate([S_bar, X_bar, S_bar, X_bar]), parms)
res_g = g_0 - S_bar
# g is a first order function
g_s = g_1[:, :n_s]
g_x = g_1[:, n_s:n_s + n_x]
g_e = g_1[:, n_s + n_x:]
g_se = g_2[:, :n_s, n_s + n_x:]
g_xe = g_2[:, n_s:n_s + n_x, n_s + n_x:]
# S(s,e) = g(s,x,e)
S_s = g_s + dot(g_x, X_s)
S_e = g_e
S_se = g_se + mdot(g_xe, [X_s, numpy.eye(n_e)])
# V(s,e) = [ g(s,x,e) ; x( g(s,x,e) ) ]
V_s = np.row_stack([S_s, dot(X_s, S_s)]) # ***
V_e = np.row_stack([S_e, dot(X_s, S_e)])
V_se = np.row_stack([S_se, dot(X_s, S_se)])
# v(s) = [s, x(s)]
v_s = np.row_stack([numpy.eye(n_s), X_s])
# W(s,e) = [xx(s,e); yy(s,e)]
W_s = np.row_stack([v_s, V_s])
#return
nn = n_s + n_x
f_v = f_1[:, :nn]
f_V = f_1[:, nn:]
f_1V = f_2[:, :, nn:]
f_VV = f_2[:, nn:, nn:]
f_1VV = f_3[:, :, nn:, nn:]
# E = lambda v: np.tensordot(v, sigma, axes=((2,3),(0,1)) ) # expectation operator
F = f_0 + 0.5 * np.tensordot(
mdot(f_VV, [V_e, V_e]), sigma, axes=((1, 2), (0, 1)))
F_s = sdot(f_1, W_s)
f_see = mdot(f_1VV, [W_s, V_e, V_e]) + 2 * mdot(f_VV, [V_se, V_e])
F_s += 0.5 * np.tensordot(f_see, sigma, axes=(
(2, 3), (0, 1))) # second order correction
resp = np.row_stack(
[np.concatenate([dummy_x, res_g]),
np.column_stack([F, F_s])])
return resp
# S_bar = s_fun_init( numpy.atleast_2d(X_bar).T ,parms).flatten()
# S_bar = S_bar.flatten()
S_bar = model.calibration['states']
S_bar = np.array(S_bar)
X0 = np.row_stack(
[np.concatenate([np.zeros(1), S_bar]),
np.column_stack([X_bar, X_s])])
fobj = lambda X: residuals(X, sigma, parms, g_fun, f_fun)
if verbose:
val = fobj(X0)
print('val')
print(val)
# exit()
t = time.time()
sol = solver(fobj,
X0,
method='lmmcp',
verbose=verbose,
options={
'preprocess': False,
'eps1': 1e-15,
'eps2': 1e-15
})
if verbose:
print('initial guess')
print(X0)
print('solution')
print sol
print('initial residuals')
print(fobj(X0))
print('residuals')
print fobj(sol)
s = time.time()
if verbose:
print('Elapsed : {0}'.format(s - t))
#sol = solver(fobj,X0, method='fsolve', verbose=True, options={'preprocessor':False})
norm = lambda x: numpy.linalg.norm(x, numpy.inf)
if verbose:
print("Initial error: {0}".format(norm(fobj(X0))))
print("Final error: {0}".format(norm(fobj(sol))))
print("Solution")
print(sol)
X_bar = sol[1:, 0]
S_bar = sol[0, 1:]
X_s = sol[1:, 1:]
# compute transitions
n_s = len(states)
n_x = len(controls)
[g, dg, junk] = g_fun(np.concatenate([S_bar, X_bar, epsilons_0]), parms)
g_s = dg[:, :n_s]
g_x = dg[:, n_s:n_s + n_x]
P = g_s + dot(g_x, X_s)
if verbose:
eigenvalues = numpy.linalg.eigvals(P)
print eigenvalues
eigenvalues = [abs(e) for e in eigenvalues]
eigenvalues.sort()
print(eigenvalues)
return [S_bar, X_bar, X_s, P]
def solve_risky_ss(model, X_bar, X_s, verbose=False):
import numpy
from dolo.compiler.compiling import compile_function
import time
from dolo.compiler.compiler_functions import simple_global_representation
[y,x,parms] = model.read_calibration()
sigma = model.read_covariances()
sgm = simple_global_representation(model)
states = sgm['states']
controls = sgm['controls']
shocks = sgm['shocks']
parameters = sgm['parameters']
f_eqs = sgm['f_eqs']
g_eqs = sgm['g_eqs']
g_args = [s(-1) for s in states] + [c(-1) for c in controls] + shocks
f_args = states + controls + [v(1) for v in states] + [v(1) for v in controls]
p_args = parameters
g_fun = compile_function(g_eqs, g_args, p_args, 2)
f_fun = compile_function(f_eqs, f_args, p_args, 3)
epsilons_0 = np.zeros((sigma.shape[0]))
from numpy import dot
from dolo.numeric.tensor import sdot,mdot
def residuals(X, sigma, parms, g_fun, f_fun):
import numpy
dummy_x = X[0:1,0]
X_bar = X[1:,0]
S_bar = X[0,1:]
X_s = X[1:,1:]
[n_x,n_s] = X_s.shape
n_e = sigma.shape[0]
xx = np.concatenate([S_bar, X_bar, epsilons_0])
[g_0, g_1, g_2] = g_fun(xx, parms)
[f_0,f_1,f_2,f_3] = f_fun( np.concatenate([S_bar, X_bar, S_bar, X_bar]), parms)
res_g = g_0 - S_bar
# g is a first order function
g_s = g_1[:,:n_s]
g_x = g_1[:,n_s:n_s+n_x]
g_e = g_1[:,n_s+n_x:]
g_se = g_2[:,:n_s,n_s+n_x:]
g_xe = g_2[:, n_s:n_s+n_x, n_s+n_x:]
# S(s,e) = g(s,x,e)
S_s = g_s + dot(g_x, X_s)
S_e = g_e
S_se = g_se + mdot(g_xe,[X_s, numpy.eye(n_e)])
# V(s,e) = [ g(s,x,e) ; x( g(s,x,e) ) ]
V_s = np.row_stack([
S_s,
dot( X_s, S_s )
]) # ***
V_e = np.row_stack([
S_e,
dot( X_s, S_e )
])
V_se = np.row_stack([
S_se,
dot( X_s, S_se )
])
# v(s) = [s, x(s)]
v_s = np.row_stack([
numpy.eye(n_s),
X_s
])
# W(s,e) = [xx(s,e); yy(s,e)]
W_s = np.row_stack([
v_s,
V_s
])
#return
nn = n_s + n_x
f_v = f_1[:,:nn]
f_V = f_1[:,nn:]
f_1V = f_2[:,:,nn:]
f_VV = f_2[:,nn:,nn:]
f_1VV = f_3[:,:,nn:,nn:]
# E = lambda v: np.tensordot(v, sigma, axes=((2,3),(0,1)) ) # expectation operator
F = f_0 + 0.5*np.tensordot( mdot(f_VV,[V_e,V_e]), sigma, axes=((1,2),(0,1)) )
F_s = sdot(f_1, W_s)
f_see = mdot(f_1VV, [W_s, V_e, V_e]) + 2*mdot(f_VV, [V_se, V_e])
F_s += 0.5 * np.tensordot(f_see, sigma, axes=((2,3),(0,1)) ) # second order correction
resp = np.row_stack([
np.concatenate([dummy_x,res_g]),
np.column_stack([F,F_s])
])
return resp
# S_bar = s_fun_init( numpy.atleast_2d(X_bar).T ,parms).flatten()
# S_bar = S_bar.flatten()
S_bar = [ y[i] for i,v in enumerate(model.variables) if v in model['variables_groups']['states'] ]
S_bar = np.array(S_bar)
X0 = np.row_stack([
np.concatenate([np.zeros(1),S_bar]),
np.column_stack([X_bar,X_s])
])
from dolo.numeric.solver import solver
fobj = lambda X: residuals(X, sigma, parms, g_fun, f_fun)
if verbose:
val = fobj(X0)
print('val')
print(val)
# exit()
t = time.time()
sol = solver(fobj,X0, method='lmmcp', verbose=verbose, options={'preprocess':False, 'eps1':1e-15, 'eps2': 1e-15})
if verbose:
print('initial guess')
print(X0)
print('solution')
print sol
print('initial residuals')
print(fobj(X0))
print('residuals')
print fobj(sol)
s = time.time()
if verbose:
print('Elapsed : {0}'.format(s-t))
#sol = solver(fobj,X0, method='fsolve', verbose=True, options={'preprocessor':False})
norm = lambda x: numpy.linalg.norm(x,numpy.inf)
if verbose:
print( "Initial error: {0}".format( norm( fobj(X0)) ) )
print( "Final error: {0}".format( norm( fobj(sol) ) ) )
print("Solution")
print(sol)
X_bar = sol[1:,0]
S_bar = sol[0,1:]
X_s = sol[1:,1:]
# compute transitions
n_s = len(states)
n_x = len(controls)
[g, dg, junk] = g_fun( np.concatenate( [S_bar, X_bar, epsilons_0] ), parms)
g_s = dg[:,:n_s]
g_x = dg[:,n_s:n_s+n_x]
P = g_s + dot(g_x, X_s)
if verbose:
eigenvalues = numpy.linalg.eigvals(P)
print eigenvalues
eigenvalues = [abs(e) for e in eigenvalues]
eigenvalues.sort()
print(eigenvalues)
return [S_bar, X_bar, X_s, P]
def process_output(self, solution_order=False, fname=None):
from dolo.compiler.compiler_functions import simple_global_representation
data = simple_global_representation(self.model, solve_systems=True)
# print data['a_eqs']
# print data['f_eqs']
dmodel = self.model
model = dmodel
f_eqs = data['f_eqs']
g_eqs = data['g_eqs']
g_eqs = [map_function_to_expression(lambda x: timeshift(x,1),eq) for eq in g_eqs]
# h_eqs = data['h_eqs']
auxiliaries = data['auxiliaries']
states = data['states']
controls = data['controls']
shocks = dmodel.shocks
# exp_vars = data['exp_vars']
#inf_bounds = data['inf_bounds']
#sup_bounds = data['sup_bounds']
controls_f = [v(1) for v in controls]
states_f = [v(1) for v in states]
shocks_f = [v(1) for v in shocks]
sub_list = dict()
# for i,v in enumerate(exp_vars):
# sub_list[v] = 'z(:,{0})'.format(i+1)
for i,v in enumerate(controls):
sub_list[v] = 'x(:,{0})'.format(i+1)
sub_list[v(1)] = 'xnext(:,{0})'.format(i+1)
for i,v in enumerate(states):
sub_list[v] = 's(:,{0})'.format(i+1)
sub_list[v(1)] = 'snext(:,{0})'.format(i+1)
for i,v in enumerate(dmodel.shocks):
sub_list[v] = 'e(:,{0})'.format(i+1)
sub_list[v(1)] = 'enext(:,{0})'.format(i+1)
for i,v in enumerate(dmodel.parameters):
sub_list[v] = 'p({0})'.format(i+1)
text = '''function [model] = get_model()
model = model_info;
model.f = @f;
model.g = @g;
model.a = @a;
end
function [out1,out2,out3,out4,out5] = f(s,x,snext,xnext,enext,p)
n = size(s,1);
{eq_fun_block}
end
function [out1,out2,out3] = g(s,x,e,p)
n = size(s,1);
{state_trans_block}
end
function [out1,out2,out3] = a(s,x,p)
n = size(s,1);
{aux_block}
end
function [out1] = model_info() % informations about the model
{model_info}
end
'''
from dolo.compiler.common import DicPrinter
dp = DicPrinter(sub_list)
def write_eqs(eq_l,outname='out1',ntabs=0):
eq_block = ' ' * ntabs + '{0} = zeros(n,{1});'.format(outname,len(eq_l))
for i,eq in enumerate(eq_l):
eq_block += '\n' + ' ' * ntabs + '{0}(:,{1}) = {2};'.format( outname, i+1, dp.doprint_matlab(eq,vectorize=True) )
return eq_block
def write_der_eqs(eq_l,v_l,lhs,ntabs=0):
eq_block = ' ' * ntabs + '{lhs} = zeros(n,{0},{1});'.format(len(eq_l),len(v_l),lhs=lhs)
eq_l_d = eqdiff(eq_l,v_l)
for i,eqq in enumerate(eq_l_d):
for j,eq in enumerate(eqq):
s = dp.doprint_matlab( eq, vectorize=True )
eq_block += '\n' + ' ' * ntabs + '{lhs}(:,{0},{1}) = {2}; % d eq_{eq_n} w.r.t. {vname}'.format(i+1,j+1,s,lhs=lhs,eq_n=i+1,vname=str(v_l[j]) )
return eq_block
# eq_bounds_block = write_eqs(inf_bounds,ntabs=2)
# eq_bounds_block += '\n'
# eq_bounds_block += write_eqs(sup_bounds,'out2',ntabs=2)
eq_f_block = '''
% f
{0}
if nargout >= 2
% df/ds
{1}
% df/dx
{2}
% df/dsnext
{3}
% df/dxnext
{4}
end
'''.format( write_eqs(f_eqs,'out1',3),
write_der_eqs(f_eqs,states,'out2',3),
write_der_eqs(f_eqs,controls,'out3',3),
write_der_eqs(f_eqs,states_f,'out4',3),
write_der_eqs(f_eqs,controls_f,'out5',3),
write_der_eqs(f_eqs, shocks_f, 'out6',3)
# write_der_eqs(f_eqs,exp_vars,'out4',3)
)
eq_g_block = '''
% g
{0}
if nargout >=2
% dg/ds
{1}
% dg/dx
{2}
end
'''.format( write_eqs(g_eqs,'out1',3),
write_der_eqs(g_eqs,states,'out2',3),
write_der_eqs(g_eqs,controls,'out3',3)
)
if 'a_eqs' in data:
a_eqs = data['a_eqs']
eq_a_block = '''
% a
{0}
if nargout >=2
% da/ds
{1}
% da/dx
{2}
end
'''.format( write_eqs(a_eqs,'out1',3),
write_der_eqs(a_eqs,states,'out2',3),
write_der_eqs(a_eqs,controls,'out3',3)
)
else:
eq_a_block = ''
# if not with_param_names:
# eq_h_block = 's=snext;\nx=xnext;\n'+eq_h_block
# param_def = 'p = [ ' + str.join(',',[p.name for p in dmodel.parameters]) + '];'
from dolo.misc.matlab import value_to_mat
# read model informations
[y,x,params_values] = model.read_calibration()
#params_values = '[' + str.join( ',', [ str( p ) for p in params] ) + '];'
vvs = model.variables
s_ss = [ y[vvs.index(v)] for v in model['variables_groups']['states'] ]
x_ss = [ y[vvs.index(v)] for v in model['variables_groups']['controls'] ]
model_info = '''
mod = struct;
mod.states = {states};
mod.controls = {controls};
mod.auxiliaries = {auxiliaries};
mod.parameters = {parameters};
mod.shocks = {shocks};
mod.s_ss = {s_ss};
mod.x_ss = {x_ss};
mod.params = {params_values};
'''.format(
states = '{{ {} }}'.format(str.join(',', ["'{}'".format(v) for v in states])),
controls = '{{ {} }}'.format(str.join(',', ["'{}'".format(v) for v in controls])),
auxiliaries = '{{ {} }}'.format(str.join(',', ["'{}'".format(v) for v in auxiliaries])),
parameters = '{{ {} }}'.format(str.join(',', ["'{}'".format(v) for v in model.parameters])),
shocks = '{{ {} }}'.format(str.join(',', ["'{}'".format(v) for v in model.shocks])),
s_ss = value_to_mat(s_ss),
x_ss = value_to_mat(x_ss),
params_values = value_to_mat(params_values)
)
if solution_order:
from dolo.numeric.perturbations_to_states import approximate_controls
ZZ = approximate_controls(self.model,order=solution_order, return_dr=False)
n_c = len(controls)
ZZ = [np.array(e) for e in ZZ]
ZZ = [e[:n_c,...] for e in ZZ] # keep only control vars. (x) not expectations (h)
solution = " mod.X = cell({0},1);\n".format(len(ZZ))
for i,zz in enumerate(ZZ):
solution += " mod.X{{{0}}} = {1};\n".format(i+1,value_to_mat(zz.real))
model_info += solution
model_info += ' out1 = mod;\n'
text = text.format(
# eq_bounds_block = eq_bounds_block,
mfname = fname if fname else 'mf_' + model.fname,
eq_fun_block=eq_f_block,
state_trans_block=eq_g_block,
aux_block=eq_a_block,
# exp_fun_block=eq_h_block,
# solution = solution,
model_info = model_info
)
return text