def getV(lam, tau):
n = len(lam)
V = np.zeros((n, n))
ones = np.ones((n, n))
delta = tau * (lam - lam[:, np.newaxis]) # delta_ij = lam_j-lam_i
positive = delta >= 0
negative = delta < 0
a1 = tau * np.exp(tau * lam)[:, np.newaxis] * ones # tau*e^l_i
b1 = exprel(delta)
V[negative] = a1[negative] * b1[negative]
a2 = tau * np.exp(tau * lam)[np.newaxis, :] * ones # tau*e^l_j *
b2 = exprel(-delta)
V[positive] = a2[positive] * b2[positive]
return V
def pexpunif(t, tau, T):
"""
Convolution of an exponential with scale tau and a uniform in (0, T).
"""
if t <= 0:
return 0
elif 0 < t <= T:
return -np.expm1(-t / tau) / T
else:
return np.exp(-(t - T) / tau) * special.exprel(-T / tau) / tau
def test_dwell():
d = copy.deepcopy(D)
s = arbplf_dwell(json.dumps(d))
df = pd.read_json(StringIO(s), orient='split', precise_float=True)
actual = df.pivot('edge', 'state', 'value').values
# compute the desired closed form solution
u = np.cumsum([0] + rates)
a, b = u[:-1], u[1:]
v = exprel(b - a) * exp(-b)
desired = np.vstack([v, 1-v]).T
# compare actual and desired result
assert_allclose(actual, desired)
def test_truncated_dwell():
d = copy.deepcopy(D)
d['model_and_data']['probability_array'][0][-1] = [0, 1]
s = arbplf_dwell(json.dumps(d))
df = pd.read_json(StringIO(s), orient='split', precise_float=True)
actual = df.pivot('edge', 'state', 'value').values
# compute the desired closed form solution
u = np.cumsum([0] + rates)
a, b = u[:-1], u[1:]
T = u[-1]
# this way is not robust when a == b.
def F(x):
return -(exp(T - x) + x) / expm1(T)
v = (F(b) - F(a)) / (b - a)
desired = np.vstack([v, 1-v]).T
# this way is better
v = (exprel(b-a)*exp(T-b) - 1) / expm1(T)
desired = np.vstack([v, 1-v]).T
# compare actual and desired result
assert_allclose(actual, desired)
def gen(x, name):
"""Generate fixture data and write to file.
# Arguments
* `x`: domain
* `name::str`: output filename
# Examples
``` python
python> x = linspace(-1000, 1000, 2001)
python> gen(x, './data.json')
```
"""
y = exprel(x)
data = {"x": x.tolist(), "expected": y.tolist()}
# Based on the script directory, create an output filepath:
filepath = os.path.join(DIR, name)
# Write the data to the output filepath as JSON:
with open(filepath, "w") as outfile:
json.dump(data, outfile)
def XfPar (self, fin, ini):
r = log( fin["Lambda"] / ini["Lambda"] )
yc = log( fin["Alpha"] / ini["Alpha"] )
ys = -fin["Alpha"] * r / exprel(yc)
return { "Alpha": yc, "Lambda": ys }
def lam(eps):
''' Calculates lambda eps (used for Jaakola & Jordan local bound) '''
eps = -abs(eps)
return 0.25 * exprel(eps) / (np.exp(eps) + 1)