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Operators and solvers for high-performance computing.

## Project description

=========
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 decorators, Operator
... @decorators.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(ones(5))
Info: Allocating (5,) float64 = 40 bytes in Operator.
array([ 2., 2., 2., 2., 2.])
>>> A(ones((2,3)))
Info: Allocating (2,3) float64 = 48 bytes in Operator.
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

To output a corresponding dense matrix, one needs to specify the input shape:

>>> A.todense(shapein=2)
array([[ 2., 0.],
[ 0., 2.]])

Operators do not have to be linear, but if they are not, they cannot be seen
as matrices. Some operators are already predefined, such as the
``IdentityOperator``, the ``DiagonalOperator`` or the nonlinear
``ClippingOperator``.

The previous ``A`` matrix could be defined more easily like this :

>>> A = 2 * pyoperators.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 ``*`` sign stands for composition):

>>> B = 2 * pyoperators.I + pyoperators.DiagonalOperator(arange(3))
>>> B.todense()
array([[ 2., 0., 0.],
[ 0., 3., 0.],
[ 0., 0., 4.]])

Algebraic rules are used to simplify an expression involving operators, so to speed up its execution:

>>> B
DiagonalOperator(array([ 2., 3., 4.]))
>>> C = pyoperators.Operator(flags='idempotent')
>>> C * C is C
True
>>> D = pyoperators.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

## Release historyRelease notifications

0.13.16

0.13.15

0.13.14

0.13.13.post04

0.13.13

0.13.12

0.13.11

0.13.10

0.13.9

0.13.8

0.13.7

0.13.6.post06

0.13.6.post05

0.13.6.post04

0.13.6

0.13.5

0.13.4.post01

0.13.4

0.13.3

0.13.2

0.13.1

0.13

0.12.14

0.12.13

0.12.12

0.12.11

0.12.9

0.12.8

0.12.7

0.12.6

0.12.5

0.12.4

0.12.3

0.12.2

0.12.1

0.12

0.11.1

0.11

0.10.2

0.10.1

0.10

0.9

0.8.2

This version

0.7.3

0.7.2

0.7.1

0.7

0.6.3

0.6.2

0.6.1

0.6

0.5

0.4

0.3

0.2

0.1

0.12.8-dirty

0.11.dev11-g64ac6

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