In TensorFlow, what is the difference between Session.run() and Tensor.eval()?

The FAQ session on tensor flow has an answer to exactly the same question. I will just go ahead and leave it here:

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If t is a Tensor object, t.eval() is shorthand for sess.run(t) (where sess is the current default session. The two following snippets of code are equivalent:

sess = tf.Session()
c = tf.constant(5.0)
print sess.run(c)

c = tf.constant(5.0)
with tf.Session():
  print c.eval()

In the second example, the session acts as a context manager, which has the effect of installing it as the default session for the lifetime of the with block. The context manager approach can lead to more concise code for simple use cases (like unit tests); if your code deals with multiple graphs and sessions, it may be more straightforward to explicit calls to Session.run().

I'd recommend that you at least skim throughout the whole FAQ, as it might clarify a lot of things.

If you have a Tensor t, calling t.eval() is equivalent to calling tf.get_default_session().run(t).

You can make a session the default as follows:

t = tf.constant(42.0)
sess = tf.Session()
with sess.as_default():   # or `with sess:` to close on exit
    assert sess is tf.get_default_session()
    assert t.eval() == sess.run(t)

The most important difference is that you can use sess.run() to fetch the values of many tensors in the same step:

t = tf.constant(42.0)
u = tf.constant(37.0)
tu = tf.mul(t, u)
ut = tf.mul(u, t)
with sess.as_default():
   tu.eval()  # runs one step
   ut.eval()  # runs one step
   sess.run([tu, ut])  # evaluates both tensors in a single step

Note that each call to eval and run will execute the whole graph from scratch. To cache the result of a computation, assign it to a tf.Variable.

eval() can not handle the list object

tf.reset_default_graph()

a = tf.Variable(0.2, name="a")
b = tf.Variable(0.3, name="b")
z = tf.constant(0.0, name="z0")
for i in range(100):
    z = a * tf.cos(z + i) + z * tf.sin(b - i)
grad = tf.gradients(z, [a, b])

init = tf.global_variables_initializer()

with tf.Session() as sess:
    init.run()
    print("z:", z.eval())
    print("grad", grad.eval())

but Session.run() can

print("grad", sess.run(grad))

correct me if I am wrong