def ergodic_distribution(model,
dr,
exo_grid: UnstructuredGrid,
endo_grid: CartesianGrid,
dp: MarkovChain,
compute_μ=True):
N_m = exo_grid.n_nodes()
N_s = endo_grid.n_nodes()
dims_s = tuple(endo_grid.n) # we have N_s = prod(dims_s)
s = endo_grid.nodes()
N = N_m * N_s
Π = np.zeros((N_m, N_m, N_s) + dims_s)
g = model.functions['transition']
p = model.calibration['parameters']
a = endo_grid.min
b = endo_grid.max
for i_m in range(N_m):
m = exo_grid.node(i_m)
x: np.array = dr(i_m, s)
for i_M in range(dp.n_inodes(i_m)):
w = dp.iweight(i_m, i_M)
M = dp.inode(i_m, i_M)
S = g(m, s, x, M, p)
#renormalize
S = (S - a[None, :]) / (b[None, :] - a[None, :])
# allocate weights
dest = Π[i_m, i_M, ...]
trembling_hand(dest, S, w)
# these seem to be a bit expensive...
Π = Π.reshape((N_m, N_m, N_s, N_s))
Π = Π.swapaxes(1, 2)
Π = Π.reshape((N, N))
if not compute_μ:
return Π.reshape((N_m, N_s, N_m, N_s))
else:
B = np.zeros(N)
B[-1] = 1.0
A = Π.T - np.eye(Π.shape[0])
A[-1, :] = 1.0
μ = np.linalg.solve(A, B)
μ = μ.reshape((N_m, ) + dims_s)
labels = [
np.linspace(endo_grid.min[i], endo_grid.max[i], endo_grid.n[i])
for i in range(len(endo_grid.max))
]
μ = xarray.DataArray(
μ, [('i_m', np.arange(N_m))] +
list({s: labels[i]
for i, s in enumerate(model.symbols['states'])}.items()))
return Π.reshape((N_m, N_s, N_m, N_s)), μ
def ergodic_distribution(model,
dr,
exo_grid: EmptyGrid,
endo_grid: CartesianGrid,
dp: DiscretizedIIDProcess,
compute_μ=True):
N_s = endo_grid.n_nodes()
dims_s = tuple(endo_grid.n) # we have N_s = prod(dims_s)
s = endo_grid.nodes()
m = model.calibration['exogenous']
Π = np.zeros((N_s, ) + dims_s)
g = model.functions['transition']
p = model.calibration['parameters']
a = endo_grid.min
b = endo_grid.max
x: np.array = dr(s)
for i_M in range(dp.n_inodes(0)):
w = dp.iweight(0, i_M)
M = dp.inode(0, i_M)
S = g(m, s, x, M, p)
#renormalize
S = (S - a[None, :]) / (b[None, :] - a[None, :])
# allocate weights
trembling_hand(Π, S, w)
Π = Π.reshape((N_s, N_s))
if not compute_μ:
return Π
else:
B = np.zeros(N_s)
B[-1] = 1.0
A = Π.T - np.eye(Π.shape[0])
A[-1, :] = 1.0
μ = np.linalg.solve(A, B)
μ = μ.reshape(dims_s)
labels = [
np.linspace(endo_grid.min[i], endo_grid.max[i], endo_grid.n[i])
for i in range(len(endo_grid.max))
]
μ = xarray.DataArray(
μ,
list({s: labels[i]
for i, s in enumerate(model.symbols['states'])}.items()))
return Π, μ