## pyoperators

**HomePage:** http://pchanial.github.com/pyoperators

**Author:** Pierre Chanial

**Download:** https://pypi.python.org/packages/source/p/pyoperators/pyoperators-0.11.1.tar.gz

=========== PyOperators =========== The PyOperators package defines operators and solvers for high-performance computing. These operators are multi-dimensional functions with optimised and controlled memory management. If linear, they behave like matrices with a sparse storage footprint. Getting started =============== To define an operator, one needs to define a direct function which will replace the usual matrix-vector operation: >>> def f(x, out): ... out[...] = 2 * x Then, you can instantiate an ``Operator``: >>> A = pyoperators.Operator(direct=f, flags='symmetric') An alternative way to define an operator is to define a subclass: >>> from pyoperators import flags, Operator ... @flags.symmetric ... class MyOperator(Operator): ... def direct(x, out): ... out[...] = 2 * x ... ... A = MyOperator() This operator does not have an explicit shape, it can handle inputs of any shape: >>> A(np.ones(5)) array([ 2., 2., 2., 2., 2.]) >>> A(np.ones((2,3))) array([[ 2., 2., 2.], [ 2., 2., 2.]]) By setting the ``symmetric`` flag, we ensure that A's transpose is A: >>> A.T is A True For non-explicit shape operators, we get the corresponding dense matrix by specifying the input shape: >>> A.todense(shapein=2) array([[2, 0], [0, 2]]) Operators do not have to be linear. Many operators are already `predefined <http://pchanial.github.io/pyoperators/2000/doc-operators/#list>`_, such as the ``IdentityOperator``, the ``DiagonalOperator`` or the nonlinear ``ClipOperator``. The previous ``A`` matrix could be defined more easily like this: >>> from pyoperators import I >>> A = 2 * I where ``I`` is the identity operator with no explicit shape. Operators can be combined together by addition, element-wise multiplication or composition. Note that the operator ``*`` stands for matrix multiplication if the two operators are linear, or for element-wise multiplication otherwise: >>> from pyoperators import I, DiagonalOperator >>> B = 2 * I + DiagonalOperator(range(3)) >>> B.todense() array([[2, 0, 0], [0, 3, 0], [0, 0, 4]]) Algebraic rules can easily be attached to operators. They are used to simplify expressions to speed up their execution. The ``B`` Operator has been reduced to: >>> B DiagonalOperator(array([2, ..., 4], dtype=int64), broadcast='disabled', dtype=int64, shapein=3, shapeout=3) Many simplifications are available. For instance: >>> from pyoperators import Operator >>> C = Operator(flags='idempotent,linear') >>> C * C is C True >>> D = Operator(flags='involutary') >>> D(D) IdentityOperator() Requirements ============ List of requirements: - python 2.6 - numpy >= 1.6 - scipy >= 0.9 Optional requirements: - numexpr (>= 2.0 is better) - PyWavelets : wavelet transforms