def _log_cdf(self, x):
loc, scale, low, high = self._loc_scale_low_high()
std_low, std_high = self._standardized_low_and_high(
low=low, high=high, loc=loc, scale=scale)
return (_log_sub_exp(
special_math.log_ndtr(
(x - loc) / scale), special_math.log_ndtr(std_low)) -
self._log_normalizer(std_low=std_low, std_high=std_high))
def _normal_cdf_log_difference(x, y):
"""Computes log(ndtr(x) - ndtr(y)) assuming that x >= y."""
# When x >= y >= 0, we will return log(ndtr(-y) - ndtr(-x))
# because ndtr does not have a good precision for large positive x, y.
is_y_positive = y >= 0
x_hat = tf.where(is_y_positive, -y, x)
y_hat = tf.where(is_y_positive, -x, y)
return _log_sub_exp(special_math.log_ndtr(x_hat),
special_math.log_ndtr(y_hat))
def _log_cdf(self, x):
rate = tf.convert_to_tensor(self.rate)
x_centralized = x - self.loc
u = rate * x_centralized
v = rate * self.scale
vsquared = tf.square(v)
return tfp_math.log_sub_exp(
special_math.log_ndtr(x_centralized / self.scale),
-u + vsquared / 2. + special_math.log_ndtr((u - vsquared) / v))
def _log_normalizer(self,
loc=None,
scale=None,
low=None,
high=None,
std_low=None,
std_high=None):
if std_low is None or std_high is None:
std_low, std_high = self._standardized_low_and_high(
loc=loc, scale=scale, low=low, high=high)
return _log_sub_exp(
special_math.log_ndtr(std_high), special_math.log_ndtr(std_low))
def _test_grid_log(self, dtype, grid_spec, error_spec):
if not special:
return
grid = _make_grid(dtype, grid_spec)
actual = self.evaluate(special_math.log_ndtr(grid))
# Basic tests.
# isfinite checks for NaN and Inf.
self.assertTrue(np.isfinite(actual).all())
# On the grid, -inf < log_cdf(x) < 0. In this case, we should be able
# to use a huge grid because we have used tricks to escape numerical
# difficulties.
self.assertTrue((actual < 0).all())
_check_strictly_increasing(actual)
# Versus scipy.
expected = special.log_ndtr(grid)
# Scipy prematurely goes to zero at some places that we don't. So don't
# include these in the comparison.
self.assertAllClose(
expected.astype(np.float64)[expected < 0],
actual.astype(np.float64)[expected < 0],
rtol=error_spec.rtol,
atol=error_spec.atol)
def _log_prob(self, x):
loc = tf.convert_to_tensor(self.loc)
rate = tf.convert_to_tensor(self.rate)
scale = tf.convert_to_tensor(self.scale)
two = dtype_util.as_numpy_dtype(x.dtype)(2.)
z = (x - loc) / scale
w = rate * scale
return (tf.math.log(rate) + w / two * (w - 2 * z) +
special_math.log_ndtr(z - w))
def _test_grad_finite(self, dtype):
x = tf.constant([-100., 0., 100.], dtype=dtype)
output = (special_math.log_ndtr(x) if self._use_log
else special_math.ndtr(x))
fn = special_math.log_ndtr if self._use_log else special_math.ndtr
# Not having the lambda sanitzer means we'd get an `IndexError` whenever
# the user supplied function has default args.
output, grad_output = value_and_gradient(fn, x)
# isfinite checks for NaN and Inf.
output_, grad_output_ = self.evaluate([output, grad_output])
self.assert_all_true(np.isfinite(output_))
self.assert_all_true(np.isfinite(grad_output_[0]))
def _log_survival_function(self, x):
return special_math.log_ndtr(-self._z(x))
def _log_cdf(self, x):
return special_math.log_ndtr(self._z(x))
def _outcome_log_probs(self):
if self._probits is None:
p = tf.convert_to_tensor(self._probs)
return tf.math.log1p(-p), tf.math.log(p)
s = tf.convert_to_tensor(self._probits)
return special_math.log_ndtr(-s), special_math.log_ndtr(s)
def _log_survival_function(self, x): return special_math.log_ndtr(-self._z(x))
def _log_cdf(self, x): return special_math.log_ndtr(self._z(x))