Add some doctests to transforms (#1300)

* add some doctest to transforms

* make format

numpyro/distributions/transforms.py

@@ -654,6 +654,19 @@ class LowerCholeskyAffine(Transform):
 
     :param loc: a real vector.
     :param scale_tril: a lower triangular matrix with positive diagonal.
+
+    **Example**
+
+    .. doctest::
+
+       >>> import jax.numpy as jnp
+       >>> from numpyro.distributions.transforms import LowerCholeskyAffine
+       >>> base = jnp.ones(2)
+       >>> loc = jnp.zeros(2)
+       >>> scale_tril = jnp.array([[0.3, 0.0], [1.0, 0.5]])
+       >>> affine = LowerCholeskyAffine(loc=loc, scale_tril=scale_tril)
+       >>> affine(base)
+       DeviceArray([0.3, 1.5], dtype=float32)
     """
     domain = constraints.real_vector
     codomain = constraints.real_vector
@@ -773,6 +786,17 @@ class OrderedTransform(Transform):
 
     1. *Stan Reference Manual v2.20, section 10.6*,
        Stan Development Team
+
+    **Example**
+
+    .. doctest::
+
+       >>> import jax.numpy as jnp
+       >>> from numpyro.distributions.transforms import OrderedTransform
+       >>> base = jnp.ones(3)
+       >>> transform = OrderedTransform()
+       >>> assert jnp.allclose(transform(base), jnp.array([1., 3.7182817, 6.4365635]), rtol=1e-3, atol=1e-3)
+
     """
 
     domain = constraints.real_vector
@@ -863,6 +887,16 @@ class SimplexToOrderedTransform(Transform):
     1. *Ordinal Regression Case Study, section 2.2*,
        M. Betancourt, https://betanalpha.github.io/assets/case_studies/ordinal_regression.html
 
+    **Example**
+
+    .. doctest::
+
+       >>> import jax.numpy as jnp
+       >>> from numpyro.distributions.transforms import SimplexToOrderedTransform
+       >>> base = jnp.array([0.3, 0.1, 0.4, 0.2])
+       >>> transform = SimplexToOrderedTransform()
+       >>> assert jnp.allclose(transform(base), jnp.array([-0.8472978, -0.40546507, 1.3862944]), rtol=1e-3, atol=1e-3)
+
     """
 
     domain = constraints.simplex