Theano is an open source Python based tool that allows you to define, optimize, and efficiently evaluate mathematical expressions involving multi-dimensional arrays. Using Theano, it is not uncommon to see speed improvements of ten-fold over using pure NumPy.

Theano melds some aspects of a computer algebra system (CAS) with aspects of an optimizing compiler. Theano can even transform some or all of the mathematical expression into C code and compile it into native machine instructions.

This combination of CAS with optimizing compilation is particularly useful for computational fields in which complicated mathematical expressions are evaluated repeatedly and evaluation speed is critical.

Theano supports a range of numerical types in multiple dimensions and a number of well-tested operations. It also allows you to compute the gradient of an expression with respect to another. Symbolic expressions may be compiled into functions, which work on the same data structures as numpy, allowing for easy interoperability.

Theano’s compiler applies many optimizations of varying complexity to these symbolic expressions. These optimizations include, but are not limited to:
· constant folding
· merging of similar subgraphs, to avoid calculating the same values more than once
· arithmetic simplification (x*y/x -> y)
· inserting efficient BLAS operations
· using inplace operations wherever it is safe to do so.