def testTruncatedNormal(self):
for dtype in self._random_types():
with self.cached_session() as sess, self.test_scope():
seed_t = array_ops.placeholder(dtypes.int32, shape=[2])
n = 10000000
x = stateless.stateless_truncated_normal(
shape=[n], seed=seed_t, dtype=dtype)
y = sess.run(x, {seed_t: [0x12345678, 0xabcdef12]})
random_test_util.test_truncated_normal(
self.assertEqual, self.assertAllClose, dtype, n, y)
def testTruncatedNormalIsInRange(self):
for dtype in self._random_types():
with self.cached_session() as sess, self.test_scope():
seed_t = array_ops.placeholder(dtypes.int32, shape=[2])
n = 10000000
x = stateless.stateless_truncated_normal(shape=[n],
seed=seed_t,
dtype=dtype)
y = sess.run(x, {seed_t: [0x12345678, 0xabcdef12]})
def normal_cdf(x):
return .5 * math.erfc(-x / math.sqrt(2))
def normal_pdf(x):
return math.exp(-(x**2) / 2.) / math.sqrt(2 * math.pi)
def probit(x):
return self.evaluate(special_math.ndtri(x))
a = -2.
b = 2.
mu = 0.
sigma = 1.
alpha = (a - mu) / sigma
beta = (b - mu) / sigma
z = normal_cdf(beta) - normal_cdf(alpha)
self.assertEqual((y >= a).sum(), n)
self.assertEqual((y <= b).sum(), n)
# For more information on these calculations, see:
# Burkardt, John. "The Truncated Normal Distribution".
# Department of Scientific Computing website. Florida State University.
expected_mean = mu + (normal_pdf(alpha) -
normal_pdf(beta)) / z * sigma
y = y.astype(float)
actual_mean = np.mean(y)
self.assertAllClose(actual_mean, expected_mean, atol=5e-4)
expected_median = mu + probit(
(normal_cdf(alpha) + normal_cdf(beta)) / 2.) * sigma
actual_median = np.median(y)
self.assertAllClose(actual_median, expected_median, atol=8e-4)
expected_variance = sigma**2 * (1 + (
(alpha * normal_pdf(alpha) - beta * normal_pdf(beta)) /
z) - ((normal_pdf(alpha) - normal_pdf(beta)) / z)**2)
actual_variance = np.var(y)
self.assertAllClose(
actual_variance,
expected_variance,
rtol=5e-3 if dtype == dtypes.bfloat16 else 1e-3)
def testTruncatedNormalIsInRange(self):
for dtype in self._random_types():
with self.cached_session() as sess, self.test_scope():
seed_t = array_ops.placeholder(dtypes.int32, shape=[2])
n = 10000000
x = stateless.stateless_truncated_normal(
shape=[n], seed=seed_t, dtype=dtype)
y = sess.run(x, {seed_t: [0x12345678, 0xabcdef12]})
def normal_cdf(x):
return .5 * math.erfc(-x / math.sqrt(2))
def normal_pdf(x):
return math.exp(-(x**2) / 2.) / math.sqrt(2 * math.pi)
def probit(x, sess=sess):
return self.evaluate(special_math.ndtri(x))
a = -2.
b = 2.
mu = 0.
sigma = 1.
alpha = (a - mu) / sigma
beta = (b - mu) / sigma
z = normal_cdf(beta) - normal_cdf(alpha)
self.assertTrue((y >= a).sum() == n)
self.assertTrue((y <= b).sum() == n)
# For more information on these calculations, see:
# Burkardt, John. "The Truncated Normal Distribution".
# Department of Scientific Computing website. Florida State University.
expected_mean = mu + (normal_pdf(alpha) - normal_pdf(beta)) / z * sigma
y = y.astype(float)
actual_mean = np.mean(y)
self.assertAllClose(actual_mean, expected_mean, atol=5e-4)
expected_median = mu + probit(
(normal_cdf(alpha) + normal_cdf(beta)) / 2.) * sigma
actual_median = np.median(y)
self.assertAllClose(actual_median, expected_median, atol=8e-4)
expected_variance = sigma**2 * (1 + (
(alpha * normal_pdf(alpha) - beta * normal_pdf(beta)) / z) - (
(normal_pdf(alpha) - normal_pdf(beta)) / z)**2)
actual_variance = np.var(y)
self.assertAllClose(actual_variance, expected_variance,
rtol=5e-3 if dtype == dtypes.bfloat16 else 1e-3)