diff git a/docs/source/code.rst b/docs/source/code.rst
index cddd1c9258504dfc7c7599fe3c8bf5546baf6b67..bb14397617701df6c84fa575f1c60e7d4d4e8a0a 100644
 a/docs/source/code.rst
+++ b/docs/source/code.rst
@@ 77,7 +77,7 @@ The additional methods are specified in the abstract class
provide information about the domain's pixel volume(s) and its total volume.
 The property :attr:`~StructuredDomain.harmonic` specifies whether a domain
is harmonic (i.e. describes a frequency space) or not
 Iff the domain is harmonic, the methods
+ If (and only if) the domain is harmonic, the methods
:meth:`~StructuredDomain.get_k_length_array`,
:meth:`~StructuredDomain.get_unique_k_lengths`, and
:meth:`~StructuredDomain.get_fft_smoothing_kernel_function` provide absolute
@@ 90,13 +90,16 @@ NIFTy comes with several concrete subclasses of :class:`StructuredDomain`:
 :class:`~rg_space.RGSpace` represents a regular Cartesian grid with an arbitrary
number of dimensions, which is supposed to be periodic in each dimension.
+ :class:`~log_rg_space.LogRGSpace` implements a Cartesian grid with logarithmically
+ spaced bins and an arbitrary number of dimensions.
 :class:`~hp_space.HPSpace` and :class:`~gl_space.GLSpace` describe pixelisations of the
2sphere; their counterpart in harmonic space is :class:`~lm_space.LMSpace`, which
contains spherical harmonic coefficients.
 :class:`~power_space.PowerSpace` is used to describe onedimensional power spectra.
Among these, :class:`~rg_space.RGSpace` can be harmonic or not (depending on
constructor arguments), :class:`~gl_space.GLSpace`, :class:`~hp_space.HPSpace`,
+Among these, :class:`~rg_space.RGSpace` and :class:`~log_rg_space.LogRGSpace` can
+be harmonic or not (depending on constructor arguments),
+:class:`~gl_space.GLSpace`, :class:`~hp_space.HPSpace`,
and :class:`~power_space.PowerSpace` are pure position domains (i.e.
nonharmonic), and :class:`~lm_space.LMSpace` is always harmonic.
@@ 113,18 +116,20 @@ Some examples are:
 sky emission depending on location and energy. This could be represented by a
product of an :class:`~hp_space.HPSpace` (for location) with an
:class:`~rg_space.RGSpace` (for energy).
 a polarized field, which could be modeled as a product of any structured
+ a polarized field, which could be modelled as a product of any structured
domain (representing location) with a fourelement
:class:`~unstructured_domain.UnstructuredDomain` holding Stokes I, Q, U and V components.
 a model for the sky emission, which holds both the current realization
+ a model for the sky emission, which holds both the current realisation
(on a harmonic domain) and a few inferred model parameters (e.g. on an
unstructured grid).
.. currentmodule:: nifty5
Consequently, NIFTy defines a class called :class:`~domain_tuple.DomainTuple`
holding a sequence of :class:`~domains.domain.Domain` objects, which is used to
specify full field domains. In principle, a :class:`~domain_tuple.DomainTuple`
+holding a sequence of :class:`~domains.domain.Domain` objects. The full domain is
+specified as the product of all elementary domains. Thus, an instance of
+:class:`~domain_tuple.DomainTuple` would be suitable to describe the first two
+examples above. 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
@@ 134,7 +139,10 @@ provides the properties :attr:`~domain_tuple.DomainTuple.shape` and
An aggregation of several :class:`~domain_tuple.DomainTuple` s, each member
identified by a name, is described by the :class:`~multi_domain.MultiDomain`
class.
+class. In contrast to a :class:`~domain_tuple.DomainTuple` a
+:class:`~multi_domain.MultiDomain` is a collection and does not define the
+product space of its elements. It would be the adequate space to use in the
+last of the above examples.
Fields
======
@@ 152,12 +160,22 @@ Usually, the array is stored in the form of a ``numpy.ndarray``, but for very
resourceintensive tasks NIFTy also provides an alternative storage method to
be used with distributed memory processing.
Fields support a wide range of arithmetic operations, either involving two
fields with equal domains, or a field and a scalar.
+Fields support a wide range of arithmetic operations, either involving
+two fields of equal domains or a field and a scalar. Arithmetic operations are
+performed pointwise, and the returned field has the same domain as the input field(s).
+Available operators are addition ("+"), subtraction (""),
+multiplication ("*"), division ("/"), floor division ("//") and
+exponentiation ("**"). Inplace operators ("+=", etc.) are not supported.
+Further, boolean operators, performing a pointwise comparison of a field with
+either another field of equal domain or a scalar, are available as well. These
+include equals ("=="), not equals ("!="), less ("<"), less or equal ("<="),
+greater (">") and greater or equal (">=). The domain of the field returned equals
+that of the input field(s), while the stored data is of boolean type.
+
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 subdomains (resulting in a field defined on a smaller
domain). Scalar products of two fields can also be computed easily.
+domain). Scalar products of two fields can also be computed easily as well.
See the documentation of :class:`~field.Field` for details.
There is also a set of convenience functions to generate fields with constant
@@ 215,8 +233,8 @@ specific inference problems. Currently these are:
 :class:`~smooth_linear_amplitude.SLAmplitude`, which returns a smooth power spectrum.
 :class:`~inverse_gamma_operator.InverseGammaOperator`, which models point sources which are
distributed according to a inversegamma distribution.
 :class:`~correlated_fields.CorrelatedField`, which models a diffuse lognormal field. It takes an
 amplitude operator to specify the correlation structure of the field.
+ :class:`~correlated_fields.CorrelatedField`, which models a diffuse field whose correlation
+ structure is described by an amplitude operator.
Linear Operators
@@ 351,13 +369,34 @@ tackling new IFT problems. An example of concrete energy classes delivered with
NIFTy5 is :class:`~minimization.quadratic_energy.QuadraticEnergy` (with
positionindependent metric, mainly used with conjugate gradient minimization).
+For MGVI, NIFTy provides the :class:`~energy.Energy` subclass
+:class:`~minimization.metric_gaussian_kl.MetricGaussianKL`,
+which computes the sampled estimated of the KL divergence, its gradient and the
+Fisher metric. The constructor of
+:class:`~minimization.metric_gaussian_kl.MetricGaussianKL` requires an instance
+of :class:`~operators.energy_operators.StandardHamiltonian`, an operator to
+compute the negative loglikelihood of the problem in standardized coordinates
+at a given position in parameter space.
+Finally, the :class:`~operators.energy_operators.StandardHamiltonian`
+can be constructed from the likelihood, represented by an
+:class:`~operators.energy_operators.EnergyOperator` instance.
+Several commonly used forms of the likelihoods are already provided in
+NIFTy, such as :class:`~operators.energy_operators.GaussianEnergy`,
+:class:`~operators.energy_operators.PoissonianEnergy`,
+:class:`~operators.energy_operators.InverseGammaLikelihood` or
+:class:`~operators.energy_operators.BernoulliEnergy`, but the user
+is free to implement any likelihood customized to the problem at hand.
+The demo code `demos/getting_started_3.py` illustrates how to set up an energy
+functional for MGVI and minimize it.
+
+
Iteration control

.. currentmodule:: nifty5.minimization.iteration_controllers
Iterative minimization of an energy reqires some means of
+Iterative minimization of an energy requires some means of
checking the quality of the current solution estimate and stopping once
it is sufficiently accurate. In case of numerical problems, the iteration needs
to be terminated as well, returning a suitable error description.
@@ 370,12 +409,12 @@ the minimization or return the current estimate indicating convergence or
failure.
Sensible stopping criteria can vary significantly with the problem being
solved; NIFTy provides one concrete subclass of :class:`IterationController`
+solved; NIFTy provides a concrete subclass of :class:`IterationController`
called :class:`GradientNormController`, which should be appropriate in many
circumstances, but users have complete freedom to implement custom
+circumstances. A full list of the available :class:`IterationController` s
+in NIFTy can be found below, but users have complete freedom to implement custom
:class:`IterationController` subclasses for their specific applications.

Minimization algorithms

@@ 407,10 +446,12 @@ generally usable concrete implementations:
:class:`~descent_minimizers.VL_BFGS`. Of these algorithms, only
:class:`~descent_minimizers.NewtonCG` requires the energy object to provide
a :attr:`~energy.Energy.metric` property, the others only need energy values and
gradients.
+gradients. Further available descent minimizers are
+:class:`~descent_minimizers.RelaxedNewton`
+and :class:`~descent_minimizers.SteepestDescent`.
The flexibility of NIFTy's design allows using externally provided minimizers.
With only small effort, adapters for two SciPy minimizers were written; they are
+With only small effort, adaptors for two SciPy minimizers were written; they are
available under the names :class:`~scipy_minimizer.ScipyCG` and
:class:`~scipy_minimizer.L_BFGS_B`.
@@ 438,3 +479,16 @@ This is accomplished by minimizing a suitable
with the :class:`~minimization.conjugate_gradient.ConjugateGradient`
algorithm. An example is provided in
:func:`~library.wiener_filter_curvature.WienerFilterCurvature`.
+
+
+Posterior analysis and visualization
+
+
+After the minimization of an energy functional has converged, samples can be drawn
+from the posterior distribution at the current position to investigate the result.
+The probing module offers class called :class:`~probing.StatCalculator`
+which allows to evaluate the :attr:`~probing.StatCalculator.mean` and the unbiased
+variance :attr:`~probing.StatCalculator.var` of these samples.
+
+Fields can be visualized using the :class:`~plot.Plot` class, which invokes
+matplotlib for plotting.
diff git a/docs/source/installation.rst b/docs/source/installation.rst
index 9882bd334bea4faca0a5509eb690ee1616e6a103..23b3488890b17b3cdcc3170f5ba8e398999101e1 100644
 a/docs/source/installation.rst
+++ b/docs/source/installation.rst
@@ 38,3 +38,17 @@ Support for spherical harmonic transforms is added via::
MPI support is added via::
sudo aptget install python3mpi4py
+
+NIFTy documentation is provided by Sphinx. To build the documentation::
+
+ sudo aptget install python3sphinxrtdtheme dvipng
+ cd
+ sh docs/generate.sh
+
+To view the documentation in firefox::
+
+ firefox docs/build/index.html
+
+(Note: Make sure that you reinstall nifty after each change since sphinx
+imports nifty from the Python path.)
+
diff git a/docs/source/volume.rst b/docs/source/volume.rst
index a00a850234efbe5fb1e1679f835eb22ce838f14c..e12b8b1980ed602ac764d3111a195e9a9d5c8778 100644
 a/docs/source/volume.rst
+++ b/docs/source/volume.rst
@@ 1,4 +1,4 @@
Discretization and Volume in NIFTy
+Discretisation and Volume in NIFTy
==================================
.. note:: Some of this discussion is rather technical and may be skipped in a first readthrough.
@@ 160,15 +160,21 @@ Often, loglikelihoods contain integrals over the quantity of interest :math:`s`
\int_\Omega \text{d}x\, s(x) \approx \sum_i s^i\int_{\Omega_i}\text{d}x\, 1
Here the domain of the integral :math:`\Omega = \dot{\bigcup_q} \; \Omega_i` is the disjoint union over smaller :math:`\Omega_i`, e.g. the pixels of the space, and :math:`s_i` is the discretized field value on the :math:`i`th pixel.
+Here the domain of the integral :math:`\Omega = \dot{\bigcup_q} \; \Omega_i` is the disjoint union over smaller :math:`\Omega_i`, e.g. the pixels of the space, and :math:`s_i` is the discretised field value on the :math:`i`th pixel.
This introduces the weighting :math:`V_i=\int_{\Omega_i}\text{d}x\, 1`, also called the volume factor, a property of the space.
NIFTy aids you in constructing your own loglikelihood by providing methods like :func:`~field.Field.weight`, which weights all pixels of a field with their corresponding volume.
An integral over a :class:`~field.Field` :code:`s` can be performed by calling :code:`s.weight(1).sum()`, which is equivalent to :code:`s.integrate()`.
Volume factors are also applied automatically in the following places:
  :class:`~operators.harmonic_operators.FFTOperator` as well as all other harmonic operators. Here the zero mode of the transformed field is the integral over the original field, thus the whole field is weighted once.
  some response operators, such as the :class:`~library.los_response.LOSResponse`. In this operator a line integral is descritized, so a 1dimensional volume factor is applied.
  In :class:`~library.correlated_fields.CorrelatedField` as well :class:`~library.correlated_fields.MfCorrelatedField`, the field is multiplied by the square root of the total volume in configuration space. This ensures that the same field reconstructed over a larger domain has the same variance in position space in the limit of infinite resolution. It also ensures that power spectra in NIFTy behave according to the definition of a power spectrum, namely the power of a kmode is the expectation of the kmode square, divided by the volume of the space.
+  :class:`~operators.harmonic_operators.FFTOperator` as well as all other harmonic operators.
+ Here the zero mode of the transformed field is the integral over the original field, thus the whole field is weighted once.
+  Some response operators, such as the :class:`~library.los_response.LOSResponse`.
+ In this operator a line integral is discretised, so a 1dimensional volume factor is applied.
+  In :class:`~library.correlated_fields.CorrelatedField` as well as :class:`~library.correlated_fields.MfCorrelatedField`.
+ Both describe fields with a smooth, a priori unknown correlation structure specified by a power spectrum.
+ The field is multiplied by the square root of the total volume of it domain's harmonic counterpart.
+ This ensures that the same power spectrum can be used regardless of the chosen resolution, provided the total volume of the space remains the same.
+ It also guarantees that the power spectra in NIFTy behave according to their definition, i.e. the power of a mode :math:`s_k` is the expectation value of that mode squared, divided by the volume of its space :math:`P(k) = \left\langle s_k^2 \right\rangle / V_k`.
Note that in contrast to some older versions of NIFTy, the dot product :code:`s.vdot(t)` of fields does **not** apply a volume factor, but instead just sums over the field components,
diff git a/nifty5/operators/convolution_operators.py b/nifty5/operators/convolution_operators.py
index 26a2faea3956423bb229a935153169644c7212bd..ef2a368cc41fa3c88509b2175f6eded982791e67 100644
 a/nifty5/operators/convolution_operators.py
+++ b/nifty5/operators/convolution_operators.py
@@ 45,6 +45,13 @@ def FuncConvolutionOperator(domain, func, space=None):
The index of the subdomain on which the operator should act
If None, it is set to 0 if `domain` contains exactly one space.
`domain[space]` must be of type `RGSpace`, `HPSpace`, or `GLSpace`.
+
+ Notes
+ 
+ The operator assumes periodic boundaries in the input domain. This means
+ for a sufficiently broad function a point source close to the boundary will
+ blur into the opposite side of the image. Zero padding can be applied to
+ avoid this behaviour.
"""
domain = DomainTuple.make(domain)
space = utilities.infer_space(domain, space)
diff git a/nifty5/operators/harmonic_operators.py b/nifty5/operators/harmonic_operators.py
index f7a536ac6cf0aa4601f0655f9a17bf8c52e4bb4d..a957d56dfb7238b9864118a7dbbe9e9b7735d7cf 100644
 a/nifty5/operators/harmonic_operators.py
+++ b/nifty5/operators/harmonic_operators.py
@@ 361,6 +361,13 @@ class HarmonicTransformOperator(LinearOperator):
The index of the domain on which the operator should act
If None, it is set to 0 if domain contains exactly one subdomain.
domain[space] must be a harmonic domain.
+
+ Notes
+ 
+ HarmonicTransformOperator uses a Hartley transformation to transform
+ between harmonic and nonharmonic RGSpaces. This has the advantage that all
+ field values are real in either space. If you require a true Fourier
+ transform you should use FFTOperator instead.
"""
def __init__(self, domain, target=None, space=None):