sandbox.linalg – Linear Algebra Ops

API

class theano.sandbox.linalg.ops.Hint(**kwargs)

Provide arbitrary information to the optimizer.

These ops are removed from the graph during canonicalization in order to not interfere with other optimizations. The idea is that prior to canonicalization, one or more Features of the fgraph should register the information contained in any Hint node, and transfer that information out of the graph.

make_node(x)

Create a “apply” nodes for the inputs in that order.

perform(node, inputs, outstor)

Required: Calculate the function on the inputs and put the variables in the output storage. Return None.

Parameters

• node (Apply instance) – Contains the symbolic inputs and outputs.

• inputs (list) – Sequence of inputs (immutable).

• output_storage (list) – List of mutable 1-element lists (do not change the length of these lists)

Notes

The output_storage list might contain data. If an element of output_storage is not None, it has to be of the right type, for instance, for a TensorVariable, it has to be a Numpy ndarray, with the right number of dimensions, and the correct dtype. Its shape and stride pattern, can be arbitrary. It not is guaranteed that it was produced by a previous call to impl. It could be allocated by another Op impl is free to reuse it as it sees fit, or to discard it and allocate new memory.

Raises

MethodNotDefined – The subclass does not override this method.

class theano.sandbox.linalg.ops.HintsFeature

FunctionGraph Feature to track matrix properties.

This is a similar feature to variable ‘tags’. In fact, tags are one way to provide hints.

This class exists because tags were not documented well, and the semantics of how tag information should be moved around during optimizations was never clearly spelled out.

Hints are assumptions about mathematical properties of variables. If one variable is substituted for another by an optimization, then it means that the assumptions should be transferred to the new variable.

Hints are attached to ‘positions in a graph’ rather than to variables in particular, although Hints are originally attached to a particular positition in a graph via a variable in that original graph.

Examples of hints are: - shape information - matrix properties (e.g. symmetry, psd, banded, diagonal)

Hint information is propagated through the graph similarly to graph optimizations, except that adding a hint does not change the graph. Adding a hint is not something that debugmode will check.

#TODO: should a Hint be an object that can actually evaluate its # truthfulness? # Should the PSD property be an object that can check the # PSD-ness of a variable?

class theano.sandbox.linalg.ops.HintsOptimizer

Optimizer that serves to add HintsFeature as an fgraph feature.

add_requirements(fgraph)

Add features to the fgraph that are required to apply the optimization. For example:

fgraph.attach_feature(History()) fgraph.attach_feature(MyFeature()) etc.

apply(fgraph)

Applies the optimization to the provided L{FunctionGraph}. It may use all the methods defined by the L{FunctionGraph}. If the L{Optimizer} needs to use a certain tool, such as an L{InstanceFinder}, it can do so in its L{add_requirements} method.

theano.sandbox.linalg.ops.psd(v)

Apply a hint that the variable v is positive semi-definite, i.e. it is a symmetric matrix and for any vector x.

theano.sandbox.linalg.ops.spectral_radius_bound(X, log2_exponent)

Returns upper bound on the largest eigenvalue of square symmetrix matrix X.

log2_exponent must be a positive-valued integer. The larger it is, the slower and tighter the bound. Values up to 5 should usually suffice. The algorithm works by multiplying X by itself this many times.

From V.Pan, 1990. “Estimating the Extremal Eigenvalues of a Symmetric Matrix”, Computers Math Applic. Vol 20 n. 2 pp 17-22. Rq: an efficient algorithm, not used here, is defined in this paper.