def test_truncated_gaussian_prior_cdf_icdf(self):
mean = 10.0
std = 2.0
a = -1.0
b = 14.0
p = pints.TruncatedGaussianLogPrior(mean, std, a, b)
ndtr = scipy.special.ndtr
x = 3.0
theoretical_cdf = (ndtr((x - mean) / std) - ndtr((a - mean) / std)) \
/ (ndtr((b - mean) / std) - ndtr((a - mean) / std))
self.assertAlmostEqual(p.cdf(x), theoretical_cdf)
mean = 0.0
std = 2.0
a = -4.0
b = 4.0
p = pints.TruncatedGaussianLogPrior(mean, std, a, b)
self.assertAlmostEqual(p.icdf(0.5), 0.0)
self.assertTrue(2.0 < p.icdf(0.99) < 4.0)
self.assertTrue(-4.0 < p.icdf(0.01) < -2.0)
def test_truncated_gaussian_prior_sampling(self):
mean = 10.0
std = 2.0
a = -1.0
b = 14.0
p = pints.TruncatedGaussianLogPrior(mean, std, a, b)
# Check number of samples
d = 1
n = 1
x = p.sample(n)
self.assertEqual(x.shape, (n, d))
n = 10
x = p.sample(n)
self.assertEqual(x.shape, (n, d))
# Check that the positions of samples are within truncation limits
np.random.seed(1)
x = p.sample(10000)
self.assertTrue(np.max(x) <= 14.0)
self.assertTrue(np.min(x) >= -1.0)
def test_truncated_gaussian_prior(self):
mean = 10
std = 2
a = -1.0
b = 14.0
p = pints.TruncatedGaussianLogPrior(mean, std, a, b)
n = 10000
# Test left half of distribution
x = np.linspace(mean - 5.5 * std, mean, n)
px = [p([i]) for i in x]
self.assertTrue(np.all(px[1:] >= px[:-1]))
# Test right half of distribution
y = np.linspace(mean, mean + 2 * std, n)
py = [p([i]) for i in y]
self.assertTrue(np.all(py[1:] <= py[:-1]))
# Test means
mean = 1.0
std = 1.5
a = 2.0
b = 11.0
p = pints.TruncatedGaussianLogPrior(mean, std, a, b)
phi = scipy.stats.norm.pdf
ndtr = scipy.special.ndtr
theoretical_mean = \
mean + std / (ndtr((b - mean) / std) - ndtr((a - mean) / std)) \
* (phi((a - mean) / std) - phi((b - mean) / std))
self.assertAlmostEqual(p.mean(), theoretical_mean)
# Test derivatives
x = [4.5]
y, dy = p.evaluateS1(x)
self.assertEqual(y, p(x))
self.assertEqual(dy.shape, (1, ))
dx = 1e-6
self.assertAlmostEqual(dy[0], (p([x[0] + dx]) - p(x)) / dx, places=4)
# Test inputs outside the truncation limits
x = [11.5]
y, dy = p.evaluateS1(x)
self.assertTrue(np.isneginf(p(x)))
self.assertTrue(np.isneginf(y))
self.assertTrue(np.isnan(dy))
x = [-1.0]
y, dy = p.evaluateS1(x)
self.assertTrue(np.isneginf(p(x)))
self.assertTrue(np.isneginf(y))
self.assertTrue(np.isnan(dy))
# Test specific points
mean = 5.0
std = 2.5
a = 0.0
b = 10.0
p = pints.TruncatedGaussianLogPrior(mean, std, a, b)
self.assertAlmostEqual(
p([5.0]),
scipy.stats.truncnorm.logpdf(5.0, -2, 2, loc=mean, scale=std)
)
self.assertAlmostEqual(
p([0.1]),
scipy.stats.truncnorm.logpdf(0.1, -2, 2, loc=mean, scale=std)
)
# Test input at each bound, this should return a finite number
x = [b]
self.assertTrue(np.isfinite(p(x)))
x = [a]
self.assertTrue(np.isfinite(p(x)))
# Test n_parameters
self.assertEqual(p.n_parameters(), 1)
# Test one sided truncation
mean = 5.0
std = 2.5
a = 0.0
b = np.inf
p = pints.TruncatedGaussianLogPrior(mean, std, a, b)
result = p([1e5])
self.assertTrue(np.isfinite(result))
mean = 5.0
std = 2.5
a = -np.inf
b = 10.0
p = pints.TruncatedGaussianLogPrior(mean, std, a, b)
result = p([-1e5])
self.assertTrue(np.isfinite(result))
# Test bad truncation
self.assertRaises(
ValueError, pints.TruncatedGaussianLogPrior, 0.0, 1.0, 10.0, 9.0)
self.assertRaises(
ValueError, pints.TruncatedGaussianLogPrior, 0.0, 1.0, 10.0, 10.0)
