def _log_prob(self, x):
alpha0 = tf.convert_to_tensor(self.concentration1_numerator)
beta0 = tf.convert_to_tensor(self.concentration0_numerator)
alpha1 = tf.convert_to_tensor(self.concentration1_denominator)
beta1 = tf.convert_to_tensor(self.concentration0_denominator)
alpha_sum = alpha0 + alpha1
log_normalization = (tfp_math.lbeta(alpha0, beta0) +
tfp_math.lbeta(alpha1, beta1))
log_normalization = log_normalization - tfp_math.lbeta(
alpha_sum, tf.where(x > 1., beta0, beta1))
b = tf.where(x > 1., 1. - beta1, 1 - beta0)
c = alpha_sum + tf.where(x > 1., beta0, beta1)
z = tf.where(x > 1., tf.math.reciprocal(x), x)
# Here, c - a - b = beta0 + beta1 - 1, so the series always converges
# conditionally.
log_unnormalized_prob = tf.math.log(
hypgeo.hyp2f1_small_argument(alpha_sum, b, c, z))
log_unnormalized_prob = log_unnormalized_prob + tf.math.xlogy(
tf.where(x > 1., -(alpha1 + 1.), alpha0 - 1.), x)
return log_unnormalized_prob - log_normalization
def testHyp2F1AtOne(self, dtype, rtol):
seed_stream = test_util.test_seed_stream()
a = self.GenParam(-10., 10., dtype, seed_stream())
b = self.GenParam(-10., 10., dtype, seed_stream())
# Ensure c > a + b so the evaluation is defined.
c = a + b + 1.
hyp2f1, a, b, c = self.evaluate(
[tfp_math.hyp2f1_small_argument(a, b, c, dtype(1.)), a, b, c])
scipy_hyp2f1 = scipy_special.hyp2f1(a, b, c, dtype(1.))
self.assertAllClose(hyp2f1, scipy_hyp2f1, rtol=rtol)
def testHyp2F1ShapeBroadcast(self, a_shape, b_shape, c_shape, z_shape):
a = tf.zeros(a_shape, dtype=tf.float32)
b = tf.zeros(b_shape, dtype=tf.float32)
c = 10.5 * tf.ones(c_shape, dtype=tf.float32)
z = tf.zeros(z_shape, dtype=tf.float32)
broadcast_shape = functools.reduce(
tf.broadcast_dynamic_shape, [a_shape, b_shape, c_shape, z_shape])
hyp2f1 = tfp_math.hyp2f1_small_argument(a, b, c, z)
broadcast_shape = self.evaluate(broadcast_shape)
self.assertAllEqual(hyp2f1.shape, broadcast_shape)
def VerifyHyp2F1(
self,
dtype,
rtol,
a,
b,
c,
z_lower=-0.9,
z_upper=0.9):
seed_stream = test_util.test_seed_stream()
z = tf.random.uniform(
[int(1e4)], seed=seed_stream(),
minval=z_lower, maxval=z_upper, dtype=dtype)
hyp2f1, a, b, c, z = self.evaluate([
tfp_math.hyp2f1_small_argument(a, b, c, z), a, b, c, z])
scipy_hyp2f1 = scipy_special.hyp2f1(a, b, c, z)
self.assertAllClose(hyp2f1, scipy_hyp2f1, rtol=rtol)
def VerifyHyp2F1(
self,
dtype,
rtol,
a,
b,
c,
z_lower=-0.9,
z_upper=0.9,
use_mpmath=False):
comparison_hyp2f1 = self._mpmath_hyp2f1 if use_mpmath else scipy_special.hyp2f1
seed_stream = test_util.test_seed_stream()
z = tf.random.uniform(
[int(1e4)], seed=seed_stream(),
minval=z_lower, maxval=z_upper, dtype=dtype)
hyp2f1, a, b, c, z = self.evaluate([
tfp_math.hyp2f1_small_argument(a, b, c, z), a, b, c, z])
expected = comparison_hyp2f1(a, b, c, z)
self.assertAllClose(hyp2f1, expected, rtol=rtol)