def test_setup_no_bounds(self):
dist = StandardNormal()
u_bound = np.exp(-0.5) * np.sqrt(2)
v_max = 1.0
# no bound
rng = NaiveRatioUniforms(dist, random_state=7303)
check_cont_samples(rng, dist, (0, 1))
# just v_max
rng = NaiveRatioUniforms(dist, v_max=v_max, random_state=7303)
check_cont_samples(rng, dist, (0, 1))
# just one u-bound is missing
msg = 'Only one of the values of u_min and u_max is None.'
with pytest.warns(RuntimeWarning, match=msg):
rng = NaiveRatioUniforms(dist, u_max=u_bound, random_state=7303)
check_cont_samples(rng, dist, (0, 1))
def test_rv_generation_r(self, r):
# test different values of r
# note: u_max, u_min are attained at the points -/+ sqrt((r+1)/r)
dist = StandardNormal()
y = np.sqrt((r + 1) / r)
u = (dist.pdf(y))**(r / (r + 1)) * y
v_max = (dist.pdf(0))**(1 / (r + 1))
rng = NaiveRatioUniforms(dist,
r=r,
u_min=-u,
u_max=u,
v_max=v_max,
random_state=7303)
check_cont_samples(rng, dist, (0, 1))
def test_rv_generation_default(self):
# use default settings (r=1, center=0)
# exponential distribution
class Exponential():
def pdf(self, x):
return np.exp(-x)
def cdf(self, x):
return 1 - np.exp(-x)
dist = Exponential()
rng = NaiveRatioUniforms(dist,
v_max=1,
u_min=0,
u_max=2 * np.exp(-1),
random_state=76525)
check_cont_samples(rng, dist, (1, 1))
def test_rv_generation_mode_shift(self, p):
# test mode shift with Gamma(p) distribution, mode=p-1
# note: the pdf is bounded only if p >= 1
# note: u_max, u_min can be computed explicitly
def u_bound(x, p, m):
if x < 0:
return 0
return (x - m) * x**((p - 1) / 2) * math.exp(-x / 2)
dist = Gamma(p)
m = p - 1
h = (p + 1 + m) / 2
k = np.sqrt(h**2 - m * (p - 1))
u_min, u_max = u_bound(h - k, p, m), u_bound(h + k, p, m)
v_max = np.sqrt(dist.pdf(m))
rng = NaiveRatioUniforms(dist,
center=m,
u_min=u_min,
u_max=u_max,
v_max=v_max,
random_state=357)
check_cont_samples(rng, dist, (p, p))
def test_exceptions(self):
dist = StandardNormal()
# need u_min < u_max
msg = r"`u_min` must be smaller than `u_max`."
with pytest.raises(ValueError, match=msg):
NaiveRatioUniforms(dist, v_max=1, u_min=3, u_max=1)
with pytest.raises(ValueError, match=msg):
NaiveRatioUniforms(dist, v_max=1, u_min=1, u_max=1)
# need v_max > 0
msg = r'`v_max` must be positive.'
with pytest.raises(ValueError, match=msg):
NaiveRatioUniforms(dist, v_max=-1, u_min=1, u_max=3)
with pytest.raises(ValueError, match=msg):
NaiveRatioUniforms(dist, v_max=0, u_min=1, u_max=3)
# need r > 0
msg = r'`r` must be positive.'
with pytest.raises(ValueError, match=msg):
NaiveRatioUniforms(dist, r=0, v_max=1, u_min=1, u_max=3)
with pytest.raises(ValueError, match=msg):
NaiveRatioUniforms(dist, r=-0.24, v_max=1, u_min=1, u_max=3)