def _forward(self, x):
tailweight = tf.convert_to_tensor(self.tailweight)
multiplier = self._output_multiplier(tailweight)
bijector_output = tf.sinh((tf.asinh(x) + self.skewness) * tailweight)
return bijector_output * multiplier
def _inverse(self, y):
tailweight = tf.convert_to_tensor(self.tailweight)
multiplier = self._output_multiplier(tailweight)
return tf.sinh(tf.asinh(y / multiplier) / tailweight - self.skewness)
def _output_multiplier(self, tailweight):
return self._scale_number / tf.sinh(
tf.asinh(self._scale_number) * tailweight)
lower=-10.0,
upper=100.0,
antiderivative=lambda x: x**6 / 6,
),
IntegrationTestCase(
func=lambda x: (x**3 + x**2 - 4 * x + 1) / (x**2 + 1)**2,
lower=0.0,
upper=10.0,
antiderivative=lambda x: sum([
2.5 / (x**2 + 1),
0.5 * np.log(x**2 + 1),
np.arctan(x),
]),
),
IntegrationTestCase(
func=lambda x: (tf.sinh(2 * x) + 3 * tf.sinh(x)) /
(tf.cosh(x)**2 + 2 * tf.cosh(0.5 * x)**2),
lower=2.0,
upper=4.0,
antiderivative=lambda x: sum([
np.log(np.cosh(x)**2 + np.cosh(x) + 1),
(4 / np.sqrt(3)) * np.arctan((1 + 2 * np.cosh(x)) / np.sqrt(3.0)),
]),
),
IntegrationTestCase(
func=lambda x: tf.exp(2 * x) * tf.math.sqrt(tf.exp(x) + tf.exp(2 * x)),
lower=2.0,
upper=4.0,
antiderivative=lambda x: sum([
np.sqrt((np.exp(x) + np.exp(2 * x))**3) / 3,
-(1 + 2 * np.exp(x)) * np.sqrt(np.exp(x) + np.exp(2 * x)) / 8,
def _inverse(self, y):
return tf.sinh(tf.asinh(y) / self.tailweight - self.skewness)
def _forward(self, x):
return tf.sinh((tf.asinh(x) + self.skewness) * self.tailweight)
def _forward(self, x):
return tf.sinh(x)
