Commit c6c876cf authored by Martin Reinecke's avatar Martin Reinecke

Merge branch 'docs_lp' into 'NIFTy_5'

Docs improvements

See merge request ift/nifty-dev!208
parents e6b87b06 dc1dfb6c
......@@ -41,7 +41,6 @@ Abstract base class
One of the fundamental building blocks of the NIFTy5 framework is the *domain*.
Its required capabilities are expressed by the abstract :py:class:`Domain` class.
A domain must be able to answer the following queries:
m
- its total number of data entries (pixels), which is accessible via the
:attr:`~Domain.size` property
......@@ -129,7 +128,7 @@ specify full field domains. In principle, a :class:`~domain_tuple.DomainTuple`
can even be empty, which implies that the field living on it is a scalar.
A :class:`~domain_tuple.DomainTuple` supports iteration and indexing, and also
provides the properties :attr:`~domain_tuple.DomainTuple.shape`,
provides the properties :attr:`~domain_tuple.DomainTuple.shape` and
:attr:`~domain_tuple.DomainTuple.size` in analogy to the elementary
:class:`~domains.domain.Domain`.
......@@ -159,10 +158,11 @@ Contractions (like summation, integration, minimum/maximum, computation of
statistical moments) can be carried out either over an entire field (producing
a scalar result) or over sub-domains (resulting in a field defined on a smaller
domain). Scalar products of two fields can also be computed easily.
See the documentation of :class:`~field.Field` for details.
There is also a set of convenience functions to generate fields with constant
values or fields filled with random numbers according to a user-specified
distribution.
distribution: :attr:`~sugar.full`, :attr:`~sugar.from_random`.
Like almost all NIFTy objects, fields are immutable: their value or any other
attribute cannot be modified after construction. To manipulate a field in ways
......@@ -311,11 +311,15 @@ and ``f1`` and ``f2`` are of type :class:`~field.Field`, writing::
will perform the operation suggested intuitively by the notation, checking
domain compatibility while building the composed operator.
The combined operator infers its domain and target from its constituents,
as well as the set of operations it can support.
The properties :attr:`~LinearOperator.adjoint` and
:attr:`~LinearOperator.inverse` return a new operator which behaves as if it
were the original operator's adjoint or inverse, respectively.
The combined operator infers its domain and target from its constituents,
as well as the set of operations it can support.
Instantiating operator adjoints or inverses by :attr:`~LinearOperator.adjoint`
and similar methods is to be distinguished from the instant application of
operators performed by :attr:`~LinearOperator.adjoint_times` and similar
methods.
.. _minimization:
......@@ -368,8 +372,8 @@ failure.
Sensible stopping criteria can vary significantly with the problem being
solved; NIFTy provides one concrete sub-class of :class:`IterationController`
called :class:`GradientNormController`, which should be appropriate in many
circumstances, but users have complete freedom to implement custom sub-classes
for their specific applications.
circumstances, but users have complete freedom to implement custom
:class:`IterationController` sub-classes for their specific applications.
Minimization algorithms
......@@ -424,11 +428,13 @@ the information propagator whose inverse is defined as:
:math:`D^{-1} = \left(R^\dagger N^{-1} R + S^{-1}\right)`.
It needs to be applied in forward direction in order to calculate the Wiener
filter solution. Only its inverse application is straightforward; to use it in
forward direction, we make use of NIFTy's
filter solution, but only its inverse application is straightforward.
To use it in forward direction, we make use of NIFTy's
:class:`~operators.inversion_enabler.InversionEnabler` class, which internally
performs a minimization of a
:class:`~minimization.quadratic_energy.QuadraticEnergy` by means of the
:class:`~minimization.conjugate_gradient.ConjugateGradient` algorithm. An
example is provided in
applies the (approximate) inverse of the given operator :math:`x = Op^{-1} (y)` by
solving the equation :math:`y = Op (x)` for :math:`x`.
This is accomplished by minimizing a suitable
:class:`~minimization.quadratic_energy.QuadraticEnergy`
with the :class:`~minimization.conjugate_gradient.ConjugateGradient`
algorithm. An example is provided in
:func:`~library.wiener_filter_curvature.WienerFilterCurvature`.
NIFTy -- Numerical Information Field Theory
===========================================
**NIFTy** [1]_, [2]_, "\ **N**\umerical **I**\nformation **F**\ield **T**\heor\ **y**\ ", is a versatile library designed to enable the development of signal inference algorithms that are independent of the underlying spatial grid and its resolution.
**NIFTy** [1]_, [2]_, "\ **N**\umerical **I**\nformation **F**\ield **T**\heor\ **y**\ ", is a versatile library designed to enable the development of signal inference algorithms that are independent of the underlying grids (spatial, spectral, temporal, …) and their resolutions.
Its object-oriented framework is written in Python, although it accesses libraries written in C++ and C for efficiency.
NIFTy offers a toolkit that abstracts discretized representations of continuous spaces, fields in these spaces, and operators acting on fields into classes.
Thereby, the correct normalization of operations on fields is taken care of automatically without concerning the user.
NIFTy offers a toolkit that abstracts discretized representations of continuous spaces, fields in these spaces, and operators acting on these fields into classes.
This allows for an abstract formulation and programming of inference algorithms, including those derived within information field theory.
Thus, NIFTy permits its user to rapidly prototype algorithms in 1D and then apply the developed code in higher-dimensional settings to real world problems.
NIFTy's interface is designed to resemble IFT formulae in the sense that the user implements algorithms in NIFTy independent of the topology of the underlying spaces and the discretization scheme.
Thus, the user can develop algorithms on subsets of problems and on spaces where the detailed performance of the algorithm can be properly evaluated and then easily generalize them to other, more complex spaces and the full problem, respectively.
The set of spaces on which NIFTy operates comprises point sets, *n*-dimensional regular grids, spherical spaces, their harmonic counterparts, and product spaces constructed as combinations of those.
NIFTy takes care of numerical subtleties like the normalization of operations on fields and the numerical representation of model components, allowing the user to focus on formulating the abstract inference procedures and process-specific model properties.
References
----------
......
......@@ -14,12 +14,13 @@ Plotting support is added via::
pip3 install --user matplotlib
FFTW support is added via::
NIFTy uses Numpy's FFT implementation by default. For large problems FFTW may be
used because of its higher performance. It can be installed via::
sudo apt-get install libfftw3-dev
pip3 install --user pyfftw
To actually use FFTW in your Nifty calculations, you need to call::
To enable FFTW usage in NIFTy, call::
nifty5.fft.enable_fftw()
......
......@@ -86,7 +86,10 @@ class Domain(metaclass=NiftyMeta):
@property
def local_shape(self):
"""tuple of int: number of pixels along each axis on the local task
"""tuple of int: number of pixels along each axis on the local task,
mainly relevant for MPI.
See :meth:`.shape()` for general explanation of property.
The shape of the array-like object required to store information
defined on part of the domain which is stored on the local MPI task.
......
......@@ -87,11 +87,11 @@ class StructuredDomain(Domain):
def get_fft_smoothing_kernel_function(self, sigma):
"""Helper for Gaussian smoothing.
This method, which is only implemented for harmonic domains, helps
smoothing fields that are defined on a domain that has this domain as
its harmonic partner. The returned function multiplies field values of
a field with a zero centered Gaussian which corresponds to a
convolution with a Gaussian kernel and sigma standard deviation in
This method, which is only implemented for harmonic domains, helps to
smoothe fields that are defined on a domain that has this domain as
its harmonic partner. The returned function does a pointwise evaluation
of a zero-centered Gaussian on the field values, which corresponds to a
convolution with a Gaussian kernel with sigma standard deviation in
position space.
Parameters
......
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