# the first two arguments are required and the last two are
# optional and initialized to 42 and 0, respectively.
# The last argument, w, is updated with w + x each time the
# function is called.
fn(1) # illegal because there are two required arguments
fn(1, 2) # legal, z is 42, w goes 0 -> 1 (because w <- w + x), returns array(45.0)
fn(1, y = 2) # legal, z is 42, w goes 1 -> 2, returns array(45.0)
fn(x = 1, y = 2) # illegal because x was not named
fn(1, 2, 3) # legal, z is 3, w goes 2 -> 3, returns array(6.0)
fn(1, z = 3, y = 2) # legal, z is 3, w goes 3 -> 4, returns array(6.0)
fn(1, 2, w = 400) # legal, z is 42 again, w goes 400 -> 401, returns array(45.0)
fn(1, 2) # legal, z is 42, w goes 401 -> 402, returns array(45.0)
>>> import theano
>>> from theano import tensor as T
>>> from theano.compile.io import In
>>> x = T.scalar()
>>> y = T.scalar('y')
>>> z = T.scalar('z')
>>> w = T.scalar('w')
>>> fn = theano.function(inputs=[x, y, In(z, value=42), ((w, w+x), 0)],
... outputs=x + y + z)
>>> # the first two arguments are required and the last two are
>>> # optional and initialized to 42 and 0, respectively.
>>> # The last argument, w, is updated with w + x each time the
>>> # function is called.
>>> fn(1) # illegal because there are two required arguments # doctest: +ELLIPSIS
Traceback (most recent call last):
...
TypeError: Missing required input: y
>>> fn(1, 2) # legal, z is 42, w goes 0 -> 1 (because w <- w + x)
array(45.0)
>>> fn(1, y=2) # legal, z is 42, w goes 1 -> 2
array(45.0)
>>> fn(x=1, y=2) # illegal because x was not named # doctest: +ELLIPSIS
Traceback (most recent call last):
...
TypeError: Unknown input or state: x. The function has 3 named inputs (y, z, w), and 1 unnamed input which thus cannot be accessed through keyword argument (use 'name=...' in a variable's constructor to give it a name).
>>> fn(1, 2, 3) # legal, z is 3, w goes 2 -> 3
array(6.0)
>>> fn(1, z=3, y=2) # legal, z is 3, w goes 3 -> 4
array(6.0)
>>> fn(1, 2, w=400) # legal, z is 42 again, w goes 400 -> 401
array(45.0)
>>> fn(1, 2) # legal, z is 42, w goes 401 -> 402
array(45.0)
In the example above, ``z`` has value 42 when no value is explicitly given.
This default value is potentially used at every function invocation, because
...
...
@@ -282,20 +306,25 @@ If a single ``Variable`` or ``Out`` instance is given as argument, then the comp
If a list of ``Variable`` or ``Out`` instances is given as argument, then the compiled function will return a list of their values.
HINT: Re-running with most Theano optimization disabled could give you a back-traces when this node was created. This can be done with by setting the Theano flags 'optimizer=fast_compile'. If that does not work, Theano optimization can be disabled with 'optimizer=None'.
HINT: Use the Theano flag 'exception_verbosity=high' for a debugprint of this apply node.
HINT: Re-running with most Theano optimization disabled could give you a back-traces when this node was created. This can be done with by setting the Theano flags 'optimizer=fast_compile'. If that does not work, Theano optimization can be disabled with 'optimizer=None'.
HINT: Use the Theano flag 'exception_verbosity=high' for a debugprint of this apply node.
Arguably the most useful information is approximately half-way through
the error message, where the kind of error is displayed along with its
...
...
@@ -71,7 +67,7 @@ the faulty line, while ``exception_verbosity=high`` will display a
debugprint of the apply node. Using these hints, the end of the error
message becomes :
.. code-block:: bash
.. code-block:: none
Backtrace when the node is created:
File "test0.py", line 8, in <module>
...
...
@@ -101,7 +97,7 @@ following example. Here, we use ``exception_verbosity=high`` and
``optimizer=None`` would and it could therefore be used instead of test values.
.. code-block:: python
.. testcode:: testvalue
import numpy
import theano
...
...
@@ -137,7 +133,7 @@ following example. Here, we use ``exception_verbosity=high`` and
Running the above code generates the following error message:
.. code-block:: bash
.. testoutput:: testvalue
Traceback (most recent call last):
File "test1.py", line 31, in <module>
...
...
@@ -185,7 +181,7 @@ of error can thus be identified with much more precision and much earlier in
the compilation pipeline. For example, running the above code yields the
following error message, which properly identifies *line 24* as the culprit.
.. code-block:: bash
.. code-block:: node
Traceback (most recent call last):
File "test2.py", line 24, in <module>
...
...
@@ -228,7 +224,10 @@ The ``compute_test_value`` mechanism works as follows:
Theano provides a 'Print' op to do this.
.. code-block:: python
.. testcode::
import numpy
import theano
x = theano.tensor.dvector('x')
...
...
@@ -243,6 +242,9 @@ Theano provides a 'Print' op to do this.
#this runs the graph with the message, and value printed
**Scan Example: Computing the Jacobian of y = tanh(v.dot(A)) wrt x**
.. code-block:: python
.. testcode::
import theano
import theano.tensor as T
...
...
@@ -221,13 +280,22 @@ The full documentation can be found in the library: :ref:`Scan <lib_scan>`.
print compute_jac_t(w, x)[0]
# compare with numpy
print ((1 - np.tanh(x.dot(w)) ** 2) * w).T
print(((1 - np.tanh(x.dot(w)) ** 2) * w).T)
.. testoutput::
[[ 0.41997434 0. 0.41997434 0. 0. ]
[ 0. 1. 1. 0. 0. ]
[ 0. 0. 1. 0. 0. ]]
[[ 0.41997434 0. 0.41997434 0. 0. ]
[ 0. 1. 1. 0. 0. ]
[ 0. 0. 1. 0. 0. ]]
Note that we need to iterate over the indices of ``y`` and not over the elements of ``y``. The reason is that scan create a placeholder variable for its internal function and this placeholder variable does not have the same dependencies than the variables that will replace it.
**Scan Example: Accumulate number of loop during a scan**
.. code-block:: python
.. testcode::
import theano
import theano.tensor as T
...
...
@@ -246,7 +314,7 @@ Note that we need to iterate over the indices of ``y`` and not over the elements
**Scan Example: Computing tanh(v.dot(W) + b) * d where d is binomial**
.. code-block:: python
.. testcode::
import theano
import theano.tensor as T
...
...
@@ -268,13 +336,26 @@ Note that we need to iterate over the indices of ``y`` and not over the elements
w = np.ones((2, 2), dtype=theano.config.floatX)
b = np.ones((2), dtype=theano.config.floatX)
print compute_with_bnoise(x, w, b)
print(compute_with_bnoise(x, w, b))
.. testoutput::
[array([[ 0.96402758, 0. ],
[ 0. , 0.96402758],
[ 0. , 0. ],
[ 0.76159416, 0.76159416],
[ 0.76159416, 0. ],
[ 0. , 0.76159416],
[ 0. , 0.76159416],
[ 0. , 0.76159416],
[ 0. , 0. ],
[ 0.76159416, 0.76159416]])]
Note that if you want to use a random variable ``d`` that will not be updated through scan loops, you should pass this variable as a ``non_sequences`` arguments.
**Scan Example: Computing pow(A, k)**
.. code-block:: python
.. testcode::
import theano
import theano.tensor as T
...
...
@@ -298,13 +379,16 @@ Note that if you want to use a random variable ``d`` that will not be updated th
power = theano.function(inputs=[A, k], outputs=final_result,
updates=updates)
print power(range(10), 2)
#[ 0. 1. 4. 9. 16. 25. 36. 49. 64. 81.]
print(power(range(10), 2))
.. testoutput::
[ 0. 1. 4. 9. 16. 25. 36. 49. 64. 81.]
**Scan Example: Calculating a Polynomial**
.. code-block:: python
.. testcode::
import numpy
import theano
...
...
@@ -329,7 +413,10 @@ Note that if you want to use a random variable ``d`` that will not be updated th
