Creating a new Op: Python implementation¶
So suppose you have looked through the library documentation and you don’t see a function that does what you want.
If you can implement something in terms of existing Ops, you should do that. Odds are your function that uses existing Theano expressions is short, has no bugs, and potentially profits from optimizations that have already been implemented.
However, if you cannot implement an Op in terms of existing Ops, you have to write a new one. Don’t worry, Theano was designed to make it easy to add new Ops, Types, and Optimizations.
As an illustration, this tutorial shows how to write a simple Python-based
operations which performs operations on
.. It also shows how to implement tests that
.. ensure the proper working of an op.
This is an introductury tutorial and as such it does not cover how to make
an op that returns a view or modifies the values in its inputs. Thus, all
ops created with the instructions described here MUST return newly
allocated memory or reuse the memory provided in the parameter
output_storage of the
perform() function. See
Views and inplace operations for an explanation on how to do this.
If your op returns a view or changes the value of its inputs without doing as prescribed in that page, Theano will run, but will return correct results for some graphs and wrong results for others.
It is recommended that you run your tests in DebugMode (Theano flag
mode=DebugMode) since it verifies if your op behaves correctly in this
Theano Graphs refresher¶
Theano represents symbolic mathematical computations as graphs. Those graphs are bi-partite graphs (graphs with 2 types of nodes), they are composed of interconnected Apply and Variable nodes. Variable nodes represent data in the graph, either inputs, outputs or intermediary values. As such, Inputs and Outputs of a graph are lists of Theano Variable nodes. Apply nodes perform computation on these variables to produce new variables. Each Apply node has a link to an instance of Op which describes the computation to perform. This tutorial details how to write such an Op instance. Please refers to Graph Structures for a more detailed explanation about the graph structure.
Op’s basic methods¶
An op is any Python object which inherits from
This section provides an overview of the basic methods you typically have to
implement to make a new op. It does not provide extensive coverage of all the
possibilities you may encounter or need. For that refer to
import theano class MyOp(theano.Op): # Properties attribute __props__ = () #itypes and otypes attributes are #compulsory if make_node method is not defined. #They're the type of input and output respectively itypes = None otypes = None #Compulsory if itypes and otypes are not defined def make_node(self, *inputs): pass # Python implementation: def perform(self, node, inputs_storage, output_storage): pass # Other type of implementation # C implementation: [see theano web site for other functions] def c_code(self, node, inputs, outputs, sub): pass # Other implementations: def make_thunk(self, node, storage_map, _, _2, impl=None): pass # optional: check_input = True def __init__(self, *args): pass def grad(self, inputs, g): pass def R_op(self, inputs, eval_points): pass def infer_shape(node, input_shapes): pass
An op has to implement some methods defined in the the interface of
gof.Op. More specifically, it is mandatory for an op to define either
otypes and one of the
implementation methods, either
make_node()method creates an Apply node representing the application of the op on the inputs provided. This method is reponsible for three things:
it first checks that the input Variables types are compatible with the current op. If the op cannot be applied on the provided input types, it must raises an exception (such as
it operates on the Variables found in
*inputsin Theano’s symbolic language to infer the type of the symbolic output Variables. It creates output Variables of a suitable symbolic Type to serve as the outputs of this op’s application.
it creates an Apply instance with the input and output Variable, and return the Apply instance.
perform()method defines the Python implementation of an op. It takes several arguments:
nodeis a reference to an Apply node which was previously obtained via the
make_node()method. It is typically not used in simple ops, but it contains symbolic information that could be required for complex ops.
inputsis a list of references to data which can be operated on using non-symbolic statements, (i.e., statements in Python, Numpy).
output_storageis a list of storage cells where the output is to be stored. There is one storage cell for each output of the op. The data put in
output_storagemust match the type of the symbolic output. It is forbidden to change the length of the list(s) contained in
output_storage. A function Mode may allow
output_storageelements to persist between evaluations, or it may reset
output_storagecells to hold a value of
None. It can also pre-allocate some memory for the op to use. This feature can allow
performto reuse memory between calls, for example. If there is something preallocated in the
output_storage, it will be of the good dtype, but can have the wrong shape and have any stride pattern.
perform()method must be determined by the inputs. That is to say, when applied to identical inputs the method must return the same outputs.
gof.Opallows some other way to define the op implentation. For instance, it is possible to define
Op.c_code()to provide a C-implementation to the op. Please refers to tutorial Extending Theano with a C Op for a description of
Op.c_code()and other related c_methods. Note that an op can provide both Python and C implementation.
make_thunk()method is another alternative to
perform(). It returns a thunk. A thunk is defined as a zero-arguments function which encapsulates the computation to be performed by an op on the arguments of its corresponding node. It takes several parameters:
nodeis the Apply instance for which a thunk is requested,
storage_mapis a dict of lists which maps variables to a one-element lists holding the variable’s current value. The one-element list acts as pointer to the value and allows sharing that “pointer” with other nodes and instances.
compute_mapis also a dict of lists. It maps variables to one-element lists holding booleans. If the value is 0 then the variable has not been computed and the value should not be considered valid. If the value is 1 the variable has been computed and the value is valid. If the value is 2 the variable has been garbage-collected and is no longer valid, but shouldn’t be required anymore for this call. The returned function must ensure that it sets the computed variables as computed in the compute_map.
implallow to select between multiple implementation. It should have a default value of None.
make_thunk()is useful if you want to generate code and compile it yourself.
Op’s auxiliary methods¶
There are other methods that can be optionally defined by the op:
__str__()method provides a meaningful string representation of your op.
__hash__()define respectivelly equality between two ops and the hash of an op instance. They will be used by the optimization phase to merge nodes that are doing equivalent computations (same inputs, same operation). Two ops that are equal according
__eq__()should return the same output when they are applied on the same inputs.
__props__lists the properties that influence how the computation is performed (Ususally these are those that you set in
__init__()). It must be a tuple. If you don’t have any properties, then you should set this attribute to the emtpy tuple ().
__props__enables the automatic generation of appropriate
__hash__(). Given the method
__eq__(), automatically generated from
__props__, two ops will be equal if they have the same values for all the properties listed in
__props__. Given to the method
__hash__()automatically generated from
__props__, two ops will be have the same hash if they have the same values for all the properties listed in
__props__will also generate a suitable
__str__()for your op. This requires development version after September 1st, 2014 or version 0.7.
infer_shape()method allows to infer the shape of the op output variables, without actually computing the outputs. It takes as input
node, a reference to the op Apply node, and a list of Theano symbolic Varables (
i1_shape, …) which are the shape of the op input Variables.
infer_shape()returns a list where each element is a tuple representing the shape of one output. This could be helpful if one only needs the shape of the output instead of the actual outputs, which can be useful, for instance, for optimization procedures.
grad()method is required if you want to differentiate some cost whose expression includes your op. The gradient may be specified symbolically in this method. It takes two arguments
output_gradientswhich are both lists of symbolic Theano Variables and those must be operated on using Theano’s symbolic language. The grad method must return a list containing one Variable for each input. Each returned Variable represents the gradient with respect to that input computed based on the symbolic gradients with respect to each output. If the output is not differentiable with respect to an input then this method should be defined to return a variable of type NullType for that input. Likewise, if you have not implemented the grad computation for some input, you may return a variable of type NullType for that input. Please refer to
grad()for a more detailed view.
R_op()method is needed if you want
theano.tensor.Ropto work with your op. This function implements the application of the R-operator on the function represented by your op. Let assume that function is , with input , applying the R-operator means computing the Jacobian of and right-multiplying it by , the evaluation point, namely: .
The optional boolean
check_inputattribute is used to specify if you want the types used in your op to check their inputs in their c_code. It can be used to speed up compilation, reduce overhead (particularly for scalars) and reduce the number of generated C files.
Example: Op definition¶
import theano #Using make_node class DoubleOp1(theano.Op): __props__ = () def make_node(self, x): x = theano.tensor.as_tensor_variable(x) # Note: using x_.type() is dangerous, as it copies x's broadcasting # behaviour return theano.Apply(self, [x], [x.type()]) def perform(self, node, inputs, output_storage): x = inputs z = output_storage z = x * 2 def infer_shape(self, node, i0_shapes): return i0_shapes def grad(self, inputs, output_grads): return [output_grads * 2] def R_op(self, inputs, eval_points): # R_op can receive None as eval_points. # That mean there is no diferientiable path through that input # If this imply that you cannot compute some outputs, # return None for those. if eval_points is None: return eval_points return self.grad(inputs, eval_points) doubleOp1 = DoubleOp1() #Using itypes and otypes class DoubleOp2(theano.Op): __props__ = () itypes = [theano.tensor.dmatrix] otypes = [theano.tensor.dmatrix] def perform(self, node, inputs, output_storage): x = inputs z = output_storage z = x * 2 def infer_shape(self, node, i0_shapes): return i0_shapes def grad(self, inputs, output_grads): return [output_grads * 2] def R_op(self, inputs, eval_points): # R_op can receive None as eval_points. # That mean there is no diferientiable path through that input # If this imply that you cannot compute some outputs, # return None for those. if eval_points is None: return eval_points return self.grad(inputs, eval_points) doubleOp2 = DoubleOp2()
At a high level, the code fragment declares a class (e.g.,
DoubleOp1) and then
creates one instance of it (e.g.,
We often gloss over this distinction, but will be precise here:
doubleOp1 (the instance) is an Op, not
DoubleOp1 (the class which is a
theano.Op). You can call
doubleOp1(tensor.vector()) on a
Variable to build an expression, and in the expression there will be
.op attribute that refers to
make_node method creates a node to be included in the expression graph.
It runs when we apply our Op (
doubleOp1) to the Variable (
When an Op has multiple inputs, their order in the inputs argument to
is important: Theano will call
make_node(*inputs) to copy the graph,
so it is important not to change the semantics of the expression by changing
the argument order.
outputs arguments to
Apply must be Variables.
A common and easy way to ensure inputs are variables is to run them through
as_tensor_variable. This function leaves TensorType variables alone, raises
an error for non-TensorType variables, and copies any
the storage for a TensorType Constant. The
make_node method dictates the
appropriate Type for all output variables.
perform method implements the Op’s mathematical logic in Python.
The inputs (here
x) are passed by value, but a single output is returned
indirectly as the first element of single-element lists. If
a second output, it would be stored in
In some execution modes, the output storage might contain the return value of a previous call. That old value can be reused to avoid memory re-allocation, but it must not influence the semantics of the Op output.
You can try the new Op as follows:
import theano x = theano.tensor.matrix() f = theano.function([x], DoubleOp1()(x)) import numpy inp = numpy.random.rand(5, 4) out = f(inp) assert numpy.allclose(inp * 2, out) print(inp) print(out)
[[ 0.08257206 0.34308357 0.5288043 0.06582951] [ 0.65977826 0.10040307 0.5402353 0.55472296] [ 0.82358552 0.29502171 0.97387481 0.0080757 ] [ 0.77327215 0.65401857 0.76562992 0.94145702] [ 0.8452076 0.30500101 0.88430501 0.95818655]] [[ 0.16514411 0.68616713 1.0576086 0.13165902] [ 1.31955651 0.20080613 1.08047061 1.10944593] [ 1.64717104 0.59004341 1.94774962 0.0161514 ] [ 1.5465443 1.30803715 1.53125983 1.88291403] [ 1.6904152 0.61000201 1.76861002 1.9163731 ]]
import theano x = theano.tensor.matrix() f = theano.function([x], DoubleOp2()(x)) import numpy inp = numpy.random.rand(5, 4) out = f(inp) assert numpy.allclose(inp * 2, out) print(inp) print(out)
[[ 0.02443785 0.67833979 0.91954769 0.95444365] [ 0.60853382 0.7770539 0.78163219 0.92838837] [ 0.04427765 0.37895602 0.23155797 0.4934699 ] [ 0.20551517 0.7419955 0.34500905 0.49347629] [ 0.24082769 0.49321452 0.24566545 0.15351132]] [[ 0.04887571 1.35667957 1.83909538 1.90888731] [ 1.21706764 1.55410779 1.56326439 1.85677674] [ 0.08855531 0.75791203 0.46311594 0.9869398 ] [ 0.41103034 1.48399101 0.69001811 0.98695258] [ 0.48165539 0.98642904 0.4913309 0.30702264]]
Example: __props__ definition¶
We can modify the previous piece of code in order to demonstrate
the usage of the
We create an Op that takes a variable
x and returns
We want to say that two such ops are equal when their values of
b are equal.
import theano class AXPBOp(theano.Op): """ This creates an Op that takes x to a*x+b. """ __props__ = ("a", "b") def __init__(self, a, b): self.a = a self.b = b super(AXPBOp, self).__init__() def make_node(self, x): x = theano.tensor.as_tensor_variable(x) return theano.Apply(self, [x], [x.type()]) def perform(self, node, inputs, output_storage): x = inputs z = output_storage z = self.a * x + self.b def infer_shape(self, node, i0_shapes): return i0_shapes def grad(self, inputs, output_grads): return [a * output_grads + b]
We can test this by running the following segment:
mult4plus5op = AXPBOp(4, 5) another_mult4plus5op = AXPBOp(4, 5) mult2plus3op = AXPBOp(2, 3) assert mult4plus5op == another_mult4plus5op assert mult4plus5op != mult2plus3op x = theano.tensor.matrix() f = theano.function([x], mult4plus5op(x)) g = theano.function([x], mult2plus3op(x)) import numpy inp = numpy.random.rand(5, 4).astype(numpy.float32) assert numpy.allclose(4 * inp + 5, f(inp)) assert numpy.allclose(2 * inp + 3, g(inp))
How To Test it¶
Theano has some functionalities to simplify testing. These help test the
R_op methods. Put the following code
in a file and execute it with the
Basic tests are done by you just by using the op and checking that it
returns the right answer. If you detect an error, you must raise an
exception. You can use the
assert keyword to automatically raise an
import numpy import theano from tests import unittest_tools as utt from theano import config class TestDouble(utt.InferShapeTester): def setup_method(self): super().setup_method() self.op_class = DoubleOp self.op = DoubleOp() def test_basic(self): x = theano.tensor.matrix() f = theano.function([x], self.op(x)) inp = numpy.asarray(numpy.random.rand(5, 4), dtype=config.floatX) out = f(inp) # Compare the result computed to the expected value. utt.assert_allclose(inp * 2, out)
utt.assert_allclose(expected_value, value) to compare
NumPy ndarray.This raise an error message with more information. Also,
the default tolerance can be changed with the Theano flags
config.tensor.cmp_sloppy that take values in 0, 1 and 2. The
defaul value do the most strict comparison, 1 and 2 make less strict
Testing the infer_shape¶
When a class inherits from the
InferShapeTester class, it gets the
self._compile_and_check method that tests the op’s
method. It tests that the op gets optimized out of the graph if only
the shape of the output is needed and not the output
itself. Additionally, it checks that the optimized graph computes
the correct shape, by comparing it to the actual shape of the computed
self._compile_and_check compiles a Theano function. It takes as
parameters the lists of input and output Theano variables, as would be
theano.function, and a list of real values to pass to the
compiled function. It also takes the op class as a parameter
in order to verify that no instance of it appears in the shape-optimized graph.
If there is an error, the function raises an exception. If you want to
see it fail, you can implement an incorrect
When testing with input values with shapes that take the same value
over different dimensions (for instance, a square matrix, or a tensor3
with shape (n, n, n), or (m, n, m)), it is not possible to detect if
the output shape was computed correctly, or if some shapes with the
same value have been mixed up. For instance, if the infer_shape uses
the width of a matrix instead of its height, then testing with only
square matrices will not detect the problem. This is why the
self._compile_and_check method prints a warning in such a case. If
your op works only with such matrices, you can disable the warning with the
from tests import unittest_tools as utt from theano import config class TestDouble(utt.InferShapeTester): # [...] as previous tests. def test_infer_shape(self): x = theano.tensor.matrix() self._compile_and_check([x], # theano.function inputs [self.op(x)], # theano.function outputs # Always use not square matrix! # inputs data [numpy.asarray(numpy.random.rand(5, 4), dtype=config.floatX)], # Op that should be removed from the graph. self.op_class)
Testing the gradient¶
The function verify_grad verifies the gradient of an op or Theano graph. It compares the analytic (symbolically computed) gradient and the numeric gradient (computed through the Finite Difference Method).
If there is an error, the function raises an exception. If you want to see it fail, you can implement an incorrect gradient (for instance, by removing the multiplication by 2).
def test_grad(self): tests.unittest_tools.verify_grad(self.op, [numpy.random.rand(5, 7, 2)])
Testing the Rop¶
RopLop_checker defines the functions
RopLop_checker.check_nondiff_rop(). These allow to test the
implementation of the Rop method of a particular op.
For instance, to verify the Rop method of the DoubleOp, you can use this:
import numpy import tests from tests.test_rop import RopLop_checker class TestDoubleRop(RopLop_checker): def setUp(self): super(TestDoubleRop, self).setUp() def test_double_rop(self): self.check_rop_lop(DoubleRop()(self.x), self.in_shape)
Running Your Tests¶
To perform your tests, simply run
One may also add a block of code similar to the following at the end of the file containing a specific test of interest and run the file. In this example, the test TestDoubleRop in the class test_double_op would be performed.
if __name__ == '__main__': t = TestDoubleRop("test_double_rop") t.setUp() t.test_double_rop()
We recommend that when we execute a file, we run all tests in that file. This can be done by adding this at the end of your test files:
if __name__ == '__main__': unittest.main()
Run the code of the DoubleOp example above.
Modify and execute to compute: x * y.
Modify and execute the example to return two outputs: x + y and x - y.
You can omit the Rop functions. Try to implement the testing apparatus described above.
(Notice that Theano’s current elemwise fusion optimization is only applicable to computations involving a single output. Hence, to gain efficiency over the basic solution that is asked here, the two operations would have to be jointly optimized explicitly in the code.)
Random numbers in tests¶
Making tests errors more reproducible is a good practice. To make your tests more reproducible, you need a way to get the same random numbers. You can do this by seeding NumPy’s random number generator.
For convenience, the classes InferShapeTester and RopLop_checker
already do this for you. If you implement your own
don’t forget to call the parent
For more details see Using Random Values in Test Cases.
as_op is a python decorator that converts a python function into a basic Theano op that will call the supplied function during execution.
This isn’t the recommended way to build an op, but allows for a quick implementation.
It takes an optional
infer_shape() parameter that must have this
def infer_shape(node, input_shapes): # ... return output_shapes - `input_shapes` and `output_shapes` are lists of tuples that represent the shape of the corresponding inputs/outputs.
Not providing the infer_shape method prevents shape-related optimizations from working with this op. For example your_op(inputs, …).shape will need the op to be executed just to get the shape.
As no grad is defined, this means you won’t be able to differentiate paths that include this op.
It converts the Python function to a callable object that takes as inputs Theano variables that were declared.
The python function wrapped by the as_op decorator needs to return a new data allocation, no views or in place modification of the input.
import theano import numpy from theano import function from theano.compile.ops import as_op def infer_shape_numpy_dot(node, input_shapes): ashp, bshp = input_shapes return [ashp[:-1] + bshp[-1:]] @as_op(itypes=[theano.tensor.fmatrix, theano.tensor.fmatrix], otypes=[theano.tensor.fmatrix], infer_shape=infer_shape_numpy_dot) def numpy_dot(a, b): return numpy.dot(a, b)
You can try it as follows:
x = theano.tensor.fmatrix() y = theano.tensor.fmatrix() f = function([x, y], numpy_dot(x, y)) inp1 = numpy.random.rand(5, 4).astype('float32') inp2 = numpy.random.rand(4, 7).astype('float32') out = f(inp1, inp2)
Run the code of the numpy_dot example above.
Modify and execute to compute: numpy.add and numpy.subtract.
- Modify and execute the example to return two outputs: x + y
and x - y.
Documentation and Coding Style¶
Please always respect the Requirements for Quality Contributions or your contribution will not be accepted.
NanGuardMode and AllocEmpty¶
NanGuardMode help users find where in the graph NaN appear. But sometimes, we want some variables to not be checked. For example, in the old GPU back-end, we use a float32 CudaNdarray to store the MRG random number generator state (they are integers). So if NanGuardMode check it, it will generate false positive. Another case is related to [Gpu]AllocEmpty or some computation on it (like done by Scan).
You can tell NanGuardMode to do not check a variable with:
variable.tag.nan_guard_mode_check. Also, this tag automatically
follow that variable during optimization. This mean if you tag a
variable that get replaced by an inplace version, it will keep that