title: Jax vectorization: vmap and/or numpy.vectorize?
body: <p>what are the differences between <code>jax.numpy.vectorize</code>and <code>jax.vmap</code>?
  Here is a small snipset</p>
  <pre><code>import jax
  import jax.numpy as jnp
  
  def f(x):
       return jnp.exp(-x)*jnp.sin(x)
  
  gf = jax.grad(f)
  x = jnp.arange(0,1,0.1)
  
  jax.vmap(gf)(x)
  jnp.vectorize(gf)(x)
  </code></pre>
  <p>Both computations give the same results:</p>
  <p>DeviceArray([ 1.        ,  0.80998397,  0.63975394,  0.4888039 ,
  0.35637075,  0.24149445,  0.14307144,  0.05990037,
  -0.00927836, -0.06574923], dtype=float32)</p>
  <p>How to decide which one to use, and if there is a  difference in terms of performance?</p>