So, to get us started with Theano and get a feel of what we’re working with, let’s make a simple function: add two numbers together. Here is how you do it:
>>> x = T.dscalar('x')
>>> y = T.dscalar('y')
>>> z = x + y
>>> f = function([x, y], z)
And now that we’ve created our function we can use it:
>>> f(2, 3)
array(5.0)
>>> f(16.3, 12.1)
array(28.4)
Let’s break this down into several steps. The first step is to define two symbols (Variables) representing the quantities that you want to add. Note that from now on, we will use the term Variable to mean “symbol” (in other words, x, y, z are all Variable objects). The output of the function f is a numpy.ndarray with zero dimensions.
If you are following along and typing into an interpreter, you may have noticed that there was a slight delay in executing the function instruction. Behind the scenes, f was being compiled into C code.
Step 1
>>> x = T.dscalar('x')
>>> y = T.dscalar('y')
In Theano, all symbols must be typed. In particular, T.dscalar is the type we assign to “0-dimensional arrays (scalar) of doubles (d)”. It is a Theano Type.
dscalar is not a class. Therefore, neither x nor y are actually instances of dscalar. They are instances of TensorVariable. x and y are, however, assigned the theano Type dscalar in their type field, as you can see here:
>>> type(x)
<class 'theano.tensor.basic.TensorVariable'>
>>> x.type
TensorType(float64, scalar)
>>> T.dscalar
TensorType(float64, scalar)
>>> x.type == T.dscalar
True
You can learn more about the structures in Theano in Graph Structures.
By calling T.dscalar with a string argument, you create a Variable representing a floating-point scalar quantity with the given name. If you provide no argument, the symbol will be unnamed. Names are not required, but they can help debugging.
Step 2
The second step is to combine x and y into their sum z:
>>> z = x + y
z is yet another Variable which represents the addition of x and y. You can use the pp function to pretty-print out the computation associated to z.
>>> print pp(z)
(x + y)
Step 3
The last step is to create a function taking x and y as inputs and giving z as output:
>>> f = function([x, y], z)
The first argument to function is a list of Variables that will be provided as inputs to the function. The second argument is a single Variable or a list of Variables. For either case, the second argument is what we want to see as output when we apply the function.
f may then be used like a normal Python function.
You might already have guessed how to do this. Indeed, the only change from the previous example is that you need to instantiate x and y using the matrix Types:
>>> x = T.dmatrix('x')
>>> y = T.dmatrix('y')
>>> z = x + y
>>> f = function([x, y], z)
dmatrix is the Type for matrices of doubles. And then we can use our new function on 2D arrays:
>>> f([[1, 2], [3, 4]], [[10, 20], [30, 40]])
array([[ 11., 22.],
[ 33., 44.]])
The variable is a numpy array. We can also use numpy arrays directly as inputs:
>>> import numpy
>>> f(numpy.array([[1, 2], [3, 4]]), numpy.array([[10, 20], [30, 40]]))
array([[ 11., 22.],
[ 33., 44.]])
It is possible to add scalars to matrices, vectors to matrices, scalars to vectors, etc. The behavior of these operations is defined by broadcasting.
The following types are available:
The previous list is not exhaustive. A guide to all types compatible with numpy arrays may be found here.
Note
You, the user—not the system architecture—have to choose whether your program will use 32- or 64-bit integers (i prefix vs. the l prefix) and floats (f prefix vs. the d prefix).