# imports
from jax import grad
import jax.numpy as jnp

# define the logistic function
def logistic(x):  
    return jnp.exp(x) / (jnp.exp(x) + 1)

# obtain the gradient function of the logistic function
grad_logistic = grad(logistic)

# evaluate the gradient of the logistic function at x = 1 
grad_log_out = grad_logistic(1.0)   
print(grad_log_out)

# imports
from jax import jit
import jax.numpy as jnp

# define the cube function
def cube(x):
    return x * x * x

# generate data
x = jnp.ones((10000, 10000))

# create the jit version of the cube function
jit_cube = jit(cube)

# apply the cube and jit_cube functions to the same data for speed comparison
cube(x)
jit_cube(x)

# imports
from jax import vmap partial
import jax.numpy as jnp

# define function
def grads(self, inputs):
    in_grad_partial = jax.partial(self._net_grads, self._net_params)
    grad_vmap = jax.vmap(in_grad_partial)
    rich_grads = grad_vmap(inputs)
    flat_grads = np.asarray(self._flatten_batch(rich_grads))
    assert flat_grads.ndim == 2 and flat_grads.shape[0] == inputs.shape[0]
    return flat_grads

# import pmap and random from JAX; import JAX NumPy
from jax import pmap, random
import jax.numpy as jnp

# generate 2 random matrices of dimensions 5000 x 6000, one per device
random_keys = random.split(random.PRNGKey(0), 2)
matrices = pmap(lambda key: random.normal(key, (5000, 6000)))(random_keys)

# without data transfer, in parallel, perform a local matrix multiplication on each CPU/GPU
outputs = pmap(lambda x: jnp.dot(x, x.T))(matrices)

# without data transfer, in parallel, obtain the mean for both matrices on each CPU/GPU separately
means = pmap(jnp.mean)(outputs)
print(means)