Skip to content
GitLab
Menu
Projects
Groups
Snippets
Loading...
Help
Help
Support
Community forum
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in
Toggle navigation
Menu
Open sidebar
ift
NIFTy
Commits
ba6dc97b
Commit
ba6dc97b
authored
Aug 08, 2018
by
Martin Reinecke
Browse files
some documentation work
parent
012feede
Changes
1
Show whitespace changes
Inline
Side-by-side
Showing
1 changed file
with
49 additions
and
13 deletions
+49
-13
docs/source/code.rst
docs/source/code.rst
+49
-13
No files found.
docs/source/code.rst
View file @
ba6dc97b
...
...
@@ -99,6 +99,7 @@ Combinations of domains
The fundamental classes described above are often sufficient to specify the
domain of a field. In some cases, however, it will be necessary to have the
field live on a product of elementary domains instead of a single one.
More sophisticated models also require a set of several such fields.
Some examples are:
- sky emission depending on location and energy. This could be represented by
...
...
@@ -107,6 +108,9 @@ Some examples are:
- a polarised field, which could be modeled as a product of any structured
domain (representing location) with a four-element
:class:`UnstructuredDomain` holding Stokes I, Q, U and V components.
- a model for the sky emission, which holds both the current realization
(on a harmonic domain) and a few inferred model parameters (e.g. on an
unstructured grid).
Consequently, NIFTy defines a class called :class:`DomainTuple` holding
a sequence of :class:`Domain` objects, which is used to specify full field
...
...
@@ -117,10 +121,15 @@ A :class:`DomainTuple` supports iteration and indexing, and also provides the
properties :attr:`~DomainTuple.shape`, :attr:`~DomainTuple.size` in analogy to
the elementary :class:`Domain`.
An aggregation of several :class:`DomainTuple`s, each member identified by a
name, is described by the :class:`MultiDomain` class.
Fields
======
Fields on a single DomainTuple
------------------------------
A :class:`Field` object consists of the following components:
- a domain in form of a :class:`DomainTuple` object
...
...
@@ -148,14 +157,44 @@ that are not covered by the provided standard operations, its data content must
be extracted first, then changed, and a new field has to be created from the
result.
Fields living on a MultiDomain
------------------------------
The :class:`MultiField` class can be seen as a dictionary of individual
:class:`Field`s, each identified by a name, which lives on an associated
:class:`MultiDomain`.
Operators
=========
All transformations between different NIFTy fields are expressed (explicitly
or implicitly) in the form of :class:`Operator` objects. The interface of this
class is very minimalistic: it has a property called `domain` which returns
a `Domaintuple` or `MultiDomain` object specifying the structure of the
`Field`s or `MultiField`s it expects as input, another property `target`
describing its output, and finally an overloaded `apply` method, which can
take
- a `Field`/`MultiField`object, in which case it returns the transformed
`Field`/`MultiField`
- a `Linearization` object, in which case it returns the transformed
`Linearization`
This is the interface that all objects derived from `Operator` must implement.
In addition, `Operator` objects can be added/subtracted, multiplied, chained
(via the `__call__` method) and support pointwise application of functions like
`exp()`, `log()`, `sqrt()`, `conjugate()` etc.
Linear Operators
================
A linear operator (represented by NIFTy5's abstract :class:`LinearOperator`
class) can be interpreted as an (implicitly defined) matrix.
It can be applied to :class:`Field` instances, resulting in other :class:`Field`
instances that potentially live on other domains.
class) is derived from `Operator` and can be interpreted as an
(implicitly defined) matrix. Since its operation is linear, it can provide some
additional functionality which is not available for the more generic `Operator`
class.
Operator basics
...
...
@@ -163,13 +202,13 @@ Operator basics
There are four basic ways of applying an operator :math:`A` to a field :math:`f`:
- direct
multi
plication: :math:`A\cdot f`
- adjoint
multi
plication: :math:`A^\dagger \cdot f`
- inverse
multi
plication: :math:`A^{-1}\cdot f`
- adjoint inverse
multi
plication: :math:`(A^\dagger)^{-1}\cdot f`
- direct
ap
plication: :math:`A\cdot f`
- adjoint
ap
plication: :math:`A^\dagger \cdot f`
- inverse
ap
plication: :math:`A^{-1}\cdot f`
- adjoint inverse
ap
plication: :math:`(A^\dagger)^{-1}\cdot f`
(
For linear operators
, inverse adjoint
multiplication
and adjoint inverse
multiplication
are equivalent.)
(
Because of the linearity
, inverse adjoint and adjoint inverse
application
are equivalent.)
These different actions of an operator ``Op`` on a field ``f`` can be invoked
in various ways:
...
...
@@ -190,9 +229,6 @@ enhanced by this approach to support the complete set. This functionality is
provided by NIFTy's :class:`InversionEnabler` class, which is itself a linear
operator.
There are two :class:`DomainTuple` objects associated with a
:class:`LinearOperator`: a :attr:`~LinearOperator.domain` and a
:attr:`~LinearOperator.target`.
Direct multiplication and adjoint inverse multiplication transform a field
living on the operator's :attr:`~LinearOperator.domain` to one living on the operator's :attr:`~LinearOperator.target`, whereas adjoint multiplication
and inverse multiplication transform from :attr:`~LinearOperator.target` to :attr:`~LinearOperator.domain`.
...
...
@@ -221,7 +257,7 @@ operators.
As an example, if ``A``, ``B`` and ``C`` are of type :class:`LinearOperator`
and ``f1`` and ``f2`` are of type :class:`Field`, writing::
X = A
*
B.inverse
*
A.adjoint + C
X = A
(
B.inverse
(
A.adjoint
))
+ C
f2 = X(f1)
will perform the operation suggested intuitively by the notation, checking
...
...
Write
Preview
Markdown
is supported
0%
Try again
or
attach a new file
.
Attach a file
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Cancel
Please
register
or
sign in
to comment