def compute_dEV_scalar(self, istate, kp):
# Unpack parameters
A, alpha, beta, delta, gamma, rho, sigma = self._unpack_params()
# All possible exogenous states tomorrow
z1 = self.ncgm.z1[istate, :]
phi = complete_polynomial_der(
np.vstack([np.ones(self.ncgm.Qn) * kp, z1]), self.degree, 0).T
val = self.ncgm.weights @ (phi @ self.v_coeffs)
return val
def test_complete_vec_vs_mat():
# Matrix for allocation
temp = np.ones(n_complete(2, 3)) * 5.0
temp_mat = np.ones((n_complete(2, 3), 3))
# Point at which to evaluate
z = np.array([0.9, 1.05])
z_mat = np.array([[0.9, 0.95, 1.0], [1.05, 1.0, 0.95]])
foo = complete_polynomial(z, 2)
bar = complete_polynomial(z_mat, 2)[:, 0]
assert np.allclose(foo, bar)
foo = complete_polynomial_der(z, 2, 0)
bar = complete_polynomial_der(z_mat, 2, 0)[:, 0]
assert np.allclose(foo, bar)
foo = complete_polynomial_der(z, 4, 0)
bar = complete_polynomial_der(z_mat, 4, 0)[:, 0]
assert np.allclose(foo, bar)
def test_complete_derivative():
# Test derivative vector
z = np.array([1, 2, 3])
sol_vec = np.array([0.0, 1.0, 0.0, 0.0, 2.0, 2.0, 3.0, 0.0, 0.0, 0.0])
out_vec = np.empty(n_complete(3, 2))
_complete_poly_der_impl_vec(z, 2, 0, out_vec)
assert (abs(out_vec - sol_vec).max() < 1e-10)
# Test derivative matrix
z = np.arange(1, 7).reshape(3, 2)
out_mat = complete_polynomial_der(z, 2, 1)
assert (abs(out_mat[0, :]).max() < 1e-10)
assert (abs(out_mat[2, :] - np.ones(2)).max() < 1e-10)
assert (abs(out_mat[-2, :] - np.array([5.0, 6.0])).max() < 1e-10)
def test_complete_derivative():
# TODO: Currently if z has a 0 value then it breaks because occasionally
# tries to raise 0 to a negative power -- This can be fixed by
# checking whether coefficient is 0 before trying to do anything...
# Test derivative vector
z = np.array([1, 2, 3])
sol_vec = np.array([0.0, 1.0, 0.0, 0.0, 2.0, 2.0, 3.0, 0.0, 0.0, 0.0])
out_vec = np.empty(n_complete(3, 2))
_complete_poly_der_impl_vec(z, 2, 0, out_vec)
assert (abs(out_vec - sol_vec).max() < 1e-10)
# Test derivative matrix
z = np.arange(1, 7).reshape(3, 2)
out_mat = complete_polynomial_der(z, 2, 1)
assert (abs(out_mat[0, :]).max() < 1e-10)
assert (abs(out_mat[2, :] - np.ones(2)).max() < 1e-10)
assert (abs(out_mat[-2, :] - np.array([5.0, 6.0])).max() < 1e-10)
def __init__(self, ncgm, degree, prev_sol=None):
# Save model and approximation degree
self.ncgm, self.degree = ncgm, degree
# Unpack some info from ncgm
A, alpha, beta, delta, gamma, rho, sigma = self._unpack_params()
grid = self.ncgm.grid
k = grid[:, 0]
z = grid[:, 1]
# Use parameter values from model to create a namedtuple with
# parameters saved inside
self.params = Params(A, alpha, beta, delta, gamma, rho, sigma)
self.Phi = complete_polynomial(grid.T, degree).T
self.dPhi = complete_polynomial_der(grid.T, degree, 0).T
# Update to fill initial value and policy matrices
# If we give it another solution type then use it to
# generate values and policies
if issubclass(type(prev_sol), GeneralSolution):
oldPhi = complete_polynomial(ncgm.grid.T, prev_sol.degree).T
self.VF = oldPhi @ prev_sol.v_coeffs
self.KP = oldPhi @ prev_sol.k_coeffs
# If we give it a tuple then assume it is (policy, value) pair
elif type(prev_sol) is tuple:
self.KP = prev_sol[0]
self.VF = prev_sol[1]
# Otherwise guess a constant value function and a policy
# of roughly steady state
else:
# VF is 0 everywhere
self.VF = np.zeros(ncgm.ns)
# Roughly ss policy
c_pol = f(k, z, A, alpha) * (A - delta) / A
self.KP = expendables_t(k, z, A, alpha, delta) - c_pol
# Coefficients based on guesses
self.v_coeffs = la.lstsq(self.Phi, self.VF)[0]
self.k_coeffs = la.lstsq(self.Phi, self.KP)[0]
def compute_dEV(self, kp=None):
"""
Compute the derivative of the expected value
"""
# Unpack parameters
A, alpha, beta, delta, gamma, rho, sigma = self._unpack_params()
grid = self.ncgm.grid
ns, Qn = self.ncgm.ns, self.ncgm.Qn
# Use policy to compute kp and c
if kp is None:
kp = self.Phi @ self.k_coeffs
# Evaluate E[V_{t+1}]
dVtp1 = np.empty((Qn, grid.shape[0]))
for iztp1 in range(Qn):
grid_tp1 = np.vstack([kp, self.ncgm.z1[:, iztp1]])
dPhi_tp1 = complete_polynomial_der(grid_tp1, self.degree, 0).T
dVtp1[iztp1, :] = dPhi_tp1 @ self.v_coeffs
dEV = self.ncgm.weights @ dVtp1
return dEV