def test_ps_roots():
weightf = orth.sh_legendre(5).weight_func
verify_gauss_quad(orth.ps_roots, orth.eval_sh_legendre, weightf, 0., 1., 5)
verify_gauss_quad(orth.ps_roots,
orth.eval_sh_legendre,
weightf,
0.,
1.,
25,
atol=1e-13)
verify_gauss_quad(orth.ps_roots,
orth.eval_sh_legendre,
weightf,
0.,
1.,
100,
atol=1e-12)
x, w = orth.ps_roots(5, False)
y, v, m = orth.ps_roots(5, True)
assert_allclose(x, y, 1e-14, 1e-14)
assert_allclose(w, v, 1e-14, 1e-14)
muI, muI_err = integrate.quad(weightf, 0, 1)
assert_allclose(m, muI, rtol=muI_err)
assert_raises(ValueError, orth.ps_roots, 0)
assert_raises(ValueError, orth.ps_roots, 3.3)
def solve_retirement_model(
num_grid,
n_quad_points,
r,
coeffs_age_poly,
theta,
cost_work,
beta,
lambda_,
sigma,
mmax,
num_periods,
cfloor=0.001,
):
# Initialize grids
quadstnorm = scps.norm.ppf(ps_roots(n_quad_points)[0])
quadw = ps_roots(n_quad_points)[1]
# define savingsgrid
savingsgrid = np.linspace(0, mmax, num_grid)
# Set up list containers
policy, value = create_container(num_grid, num_periods, savingsgrid, theta,
cost_work)
# state = 0 retirement
# state = 1 worker
for period in range(num_periods - 2, -1, -1):
# TODO: For state = 0, no need to solve egm.
for state in [1, 0]:
value, policy, ev = egm_step(
value,
policy,
state,
savingsgrid,
quadstnorm,
period,
num_periods,
num_grid,
cfloor,
n_quad_points,
r,
coeffs_age_poly,
theta,
cost_work,
beta,
lambda_,
sigma,
quadw,
)
if state == 1:
value_, policy_ = secondary_envelope_wrapper(
value, policy, period, theta, cost_work, beta, ev,
num_grid)
value[period][state] = value_
policy[period][state] = policy_
return value, policy
def test_ps_roots():
verify_gauss_quad(orth.ps_roots, orth.eval_sh_legendre, 5)
verify_gauss_quad(orth.ps_roots, orth.eval_sh_legendre, 25, atol=1e-13)
verify_gauss_quad(orth.ps_roots, orth.eval_sh_legendre, 100, atol=1e-12)
x, w = orth.ps_roots(5, False)
y, v, m = orth.ps_roots(5, True)
assert_allclose(x, y, 1e-14, 1e-14)
assert_allclose(w, v, 1e-14, 1e-14)
assert_raises(ValueError, orth.ps_roots, 0)
assert_raises(ValueError, orth.ps_roots, 3.3)
def test_ps_roots():
verify_gauss_quad(orth.ps_roots, orth.eval_sh_legendre, 5)
verify_gauss_quad(orth.ps_roots, orth.eval_sh_legendre, 25, atol=1e-13)
verify_gauss_quad(orth.ps_roots, orth.eval_sh_legendre, 100, atol=1e-12)
x, w = orth.ps_roots(5, False)
y, v, m = orth.ps_roots(5, True)
assert_allclose(x, y, 1e-14, 1e-14)
assert_allclose(w, v, 1e-14, 1e-14)
assert_raises(ValueError, orth.ps_roots, 0)
assert_raises(ValueError, orth.ps_roots, 3.3)
def test_ps_roots():
weightf = orth.sh_legendre(5).weight_func
verify_gauss_quad(orth.ps_roots, orth.eval_sh_legendre, weightf, 0.0, 1.0, 5)
verify_gauss_quad(orth.ps_roots, orth.eval_sh_legendre, weightf, 0.0, 1.0, 25, atol=1e-13)
verify_gauss_quad(orth.ps_roots, orth.eval_sh_legendre, weightf, 0.0, 1.0, 100, atol=1e-12)
x, w = orth.ps_roots(5, False)
y, v, m = orth.ps_roots(5, True)
assert_allclose(x, y, 1e-14, 1e-14)
assert_allclose(w, v, 1e-14, 1e-14)
muI, muI_err = integrate.quad(weightf, 0, 1)
assert_allclose(m, muI, rtol=muI_err)
assert_raises(ValueError, orth.ps_roots, 0)
assert_raises(ValueError, orth.ps_roots, 3.3)
def set_ngauss(self):
k, w = ps_roots(self.ng)
self.knots, self.weights = k * pi, w * pi
self.thetas = self.knots
self.sint = sin(self.thetas)
self.cost = cos(self.thetas)
self.tgt = tan(self.thetas)
self.ctgt = 1 / self.tgt
def set_ngauss(self):
k, w = ps_roots(self.ng)
self.knots, self.weights = k * pi, w * pi
self.thetas = self.knots
self.sint = sin(self.thetas)
self.cost = cos(self.thetas)
self.tgt = tan(self.thetas)
self.ctgt = 1 / self.tgt
def __init__(self, order):
"""
Parameters:
----------
order:
Quadrature Order
"""
self._order = order
# The integration rules for the unit square can be constructed
# by taking tensor products of the standard one-dimensional
# Gauss-Legendre quadrature o the domain [0, 1]
x, w = ps_roots(self._order)
self._size = x.size * x.size
self._points = (numpy.array(numpy.meshgrid(
x, x, indexing="ij")).transpose().reshape(self._size, 2))
self._weights = numpy.outer(w, w).reshape((self._size, 1))
def GaussLegendre(degree):
return sso.ps_roots(degree)