diff --git a/docs/source/code.rst b/docs/source/code.rst
index 4cc3fc5c7ccde74144d9a7ec7b356cabd0be641b..90e17c376391510238f2eac34adaf511d67e0866 100644
--- a/docs/source/code.rst
+++ b/docs/source/code.rst
@@ -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`.
diff --git a/docs/source/index.rst b/docs/source/index.rst
index c8c88cd51ce92501200509ec6db079ecbb2cc0f0..6df9bd1e94a70cb8d9fb49b63410c57c6a2d1274 100644
--- a/docs/source/index.rst
+++ b/docs/source/index.rst
@@ -1,14 +1,16 @@
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
----------
diff --git a/docs/source/installation.rst b/docs/source/installation.rst
index cc1206d32840c8db52d1aaabc4c3e948d712e0b9..e531b92bb376e258e6f43dbb24d24063cb873f99 100644
--- a/docs/source/installation.rst
+++ b/docs/source/installation.rst
@@ -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()
diff --git a/nifty5/domains/domain.py b/nifty5/domains/domain.py
index de88089718d9577b700ab5cb2adc6e9cacee47cf..c5c332eda249976b0de2495ebdd3de92f0bf7951 100644
--- a/nifty5/domains/domain.py
+++ b/nifty5/domains/domain.py
@@ -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.
diff --git a/nifty5/domains/structured_domain.py b/nifty5/domains/structured_domain.py
index be5deb75b23ca6f7bbac1c3160da250557aacd51..491d0aa0f3368fc69b33b460a46818cd4b25aafa 100644
--- a/nifty5/domains/structured_domain.py
+++ b/nifty5/domains/structured_domain.py
@@ -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