# 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
Type, `double<Double>`

.
.. It also shows how to implement tests that
.. ensure the proper working of an op.

Note

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
regard.

## 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 `gof.Op`

.
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
Op’s contract.

```
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
the method `make_node()`

or `itypes`

, `otypes`

and one of the
implementation methods, either `perform()`

, `Op.c_code()`

or `make_thunk()`

.

`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
`TypeError`

).- it operates on the Variables found in
`*inputs`

in 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:

`node`

is a reference to an Apply node which was previously obtained via the`Op`

‘s`make_node()`

method. It is typically not used in simple ops, but it contains symbolic information that could be required for complex ops.`inputs`

is a list of references to data which can be operated on using non-symbolic statements, (i.e., statements in Python, Numpy).`output_storage`

is 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_storage`

must 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_storage`

elements to persist between evaluations, or it may reset`output_storage`

cells to hold a value of`None`

. It can also pre-allocate some memory for the op to use. This feature can allow`perform`

to 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.Op`

allows 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:

`node`

is the Apply instance for which a thunk is requested,`storage_map`

is 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_map`

is 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.`impl`

allow 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.If

`make_thunk()`

is defined by an op, it will be used by Theano to obtain the op’s implementation.`perform()`

and`Op.c_code()`

will be ignored.If

`make_node()`

is not defined, the`itypes`

and`otypes`

are used by the Op’s`make_node()`

method to implement the functionality of`make_node()`

method mentioned above.

## Op’s auxiliary methods¶

There are other methods that can be optionally defined by the op:

The

`__str__()`

method provides a meaningful string representation of your op.

`__eq__()`

and`__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.The

`__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`__eq__()`

and`__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__`

.`__props__`

will also generate a suitable`__str__()`

for your op. This requires development version after September 1st, 2014 or version 0.7.The

`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 (`i0_shape`

,`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.The

`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`inputs`

and`output_gradients`

which 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.The

`R_op()`

method is needed if you want`theano.tensor.Rop`

to 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_input`

attribute 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[0]
z = output_storage[0]
z[0] = x * 2
def infer_shape(self, node, i0_shapes):
return i0_shapes
def grad(self, inputs, output_grads):
return [output_grads[0] * 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[0] 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[0]
z = output_storage[0]
z[0] = x * 2
def infer_shape(self, node, i0_shapes):
return i0_shapes
def grad(self, inputs, output_grads):
return [output_grads[0] * 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[0] 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., `doubleOp1`

).

We often gloss over this distinction, but will be precise here:
`doubleOp1`

(the instance) is an Op, not `DoubleOp1`

(the class which is a
subclass of `theano.Op`

). You can call `doubleOp1(tensor.vector())`

on a
Variable to build an expression, and in the expression there will be
a `.op`

attribute that refers to `doubleOp1`

.

The `make_node`

method creates a node to be included in the expression graph.
It runs when we apply our Op (`doubleOp1`

) to the Variable (`x`

), as
in `doubleOp1(tensor.vector())`

.
When an Op has multiple inputs, their order in the inputs argument to `Apply`

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.

All the `inputs`

and `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 `numpy.ndarray`

into
the storage for a TensorType Constant. The `make_node`

method dictates the
appropriate Type for all output variables.

The `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 `doubleOp1`

had
a second output, it would be stored in `output_storage[1][0]`

.

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 `__props__`

attribute.

We create an Op that takes a variable `x`

and returns `a*x+b`

.
We want to say that two such ops are equal when their values of `a`

and `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[0]
z = output_storage[0]
z[0] = 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[0] + b]
```

The use of `__props__`

saves
the user the trouble of implementing `__eq__()`

and `__hash__()`

manually. It also generates a default `__str__()`

method that prints the
attribute names and their values.

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
`infer_shape`

, `grad`

and `R_op`

methods. Put the following code
in a file and execute it with the `theano-nose`

program.

### Basic Tests¶

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
`AssertionError`

.

```
import numpy
import theano
from theano.tests import unittest_tools as utt
from theano import config
class test_Double(utt.InferShapeTester):
def setUp(self):
super(test_Double, self).setUp()
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)
```

We call `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
comparison.

### 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 `infer_shape`

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
output.

`self._compile_and_check`

compiles a Theano function. It takes as
parameters the lists of input and output Theano variables, as would be
provided to `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 `infer_shape`

.

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
`warn=False`

parameter.

```
from theano.tests import unittest_tools as utt
from theano import config
class test_Double(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):
theano.tests.unittest_tools.verify_grad(self.op,
[numpy.random.rand(5, 7, 2)])
```

### Testing the Rop¶

The class `RopLop_checker`

defines the functions
`RopLop_checker.check_mat_rop_lop()`

, `RopLop_checker.check_rop_lop()`

and
`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 theano.tests
from theano.tests.test_rop import RopLop_checker
class test_DoubleRop(RopLop_checker):
def setUp(self):
super(test_DoubleRop, self).setUp()
def test_double_rop(self):
self.check_rop_lop(DoubleRop()(self.x), self.in_shape)
```

### Running Your Tests¶

To perform your tests, you may select either one of the three following methods:

#### theano-nose¶

The method of choice to conduct tests is to run the file
`theano-nose`

. In a regular Theano installation, the latter will be
on the operating system’s path and directly accessible from any
folder. Otherwise, it can be accessed in the `Theano/bin`

folder. The following command lines may be used for the corresponding
purposes:

`theano-nose --theano`

: Run every test found in Theano’s path.`theano-nose folder_name`

: Run every test found in the folder*folder_name*.`theano-nose test_file.py`

: Run every test found in the file*test_file.py*.

The following are particularly useful for development purposes since they call for particular classes or even for particular tests:

`theano-nose test_file.py:test_DoubleRop`

: Run every test found inside the class*test_DoubleRop*.`theano-nose test_file.py:test_DoubleRop.test_double_op`

: Run only the test*test_double_op*in the class*test_DoubleRop*.

Help with the use and functionalities of `theano-nose`

may be
obtained by running it with the command line parameter ```
--help
(-h)
```

.

#### nosetests¶

The command `nosetests`

can also be used. Although it lacks the
useful functionalities that `theano-nose`

provides, `nosetests`

can be called similarly to `theano-nose`

from any folder in Python’s
path like so:

`nosetests [suffix similar to the above]`

.

More documentation on `nosetests`

is available here:
nosetests.

#### In-file¶

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 *test_DoubleRop* in the class
*test_double_op* would be performed.

```
if __name__ == '__main__':
t = test_DoubleRop("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()
```

#### Exercise¶

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 `setUp`

function,
don’t forget to call the parent `setUp`

function.

For more details see Using Random Values in Test Cases.

## as_op¶

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
signature:

```
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.
```

Note

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.

Note

As no grad is defined, this means you won’t be able to differentiate paths that include this op.

Note

It converts the Python function to a callable object that takes as inputs Theano variables that were declared.

Note

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.

### as_op Example¶

```
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)
```

### Exercise¶

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
tag.

## Final Note¶

A more extensive discussion of this section’s content may be found in the advanced tutorial Extending Theano.

The section Other ops includes more instructions for the following specific cases: