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ift
NIFTy
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14437d25
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14437d25
authored
Jan 09, 2019
by
Martin Reinecke
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docs/source/code.rst
docs/source/code.rst
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nifty5/sugar.py
nifty5/sugar.py
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docs/source/code.rst
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14437d25
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@@ 158,7 +158,7 @@ be extracted first, then changed, and a new field has to be created from the
result.
Fields defined on a MultiDomain



The :class:`MultiField` class can be seen as a dictionary of individual
:class:`Field` s, each identified by a name, which is defined on a
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@@ 176,17 +176,29 @@ a :class:`DomainTuple` or :class:`MultiDomain` object specifying the structure o
describing its output, and finally an overloaded `apply` method, which can
take
 a :class:`Field`/:class:`MultiField`object, in which case it returns the transformed
 a :class:`Field`/:class:`MultiField`
object, in which case it returns the transformed
:class:`Field`/:class:`MultiField`
 a :class:`Linearization` object, in which case it returns the transformed
:class:`Linearization`
This is the interface that all objects derived from :class:`Operator` must implement.
In addition, :class:`Operator` objects can be added/subtracted, multiplied, chained
(via the :class:`__call__` method) and support pointwise application of functions like
(via the :class:`__call__` method and the `@` operator) and support pointwise
application of functions like
:class:`exp()`, :class:`log()`, :class:`sqrt()`, :class:`conjugate()` etc.
Advanced operators

NIFTy provides a library of more sophisticated operators which are used for more
specific inference problems. Currently these are:
 :class:`AmplitudeOperator`, which returns a smooth power spectrum.
 :class:`InverseGammaOperator`, which models point sources which follow a inverse gamma distribution.
 :class:`CorrelatedField`, which models a diffuse lognormal field. It takes an amplitude operator to specify the correlation structure of the field.
Linear Operators
================
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@@ 197,8 +209,8 @@ additional functionality which is not available for the more generic :class:`Ope
class.
Operator basics

Linear
Operator basics


There are four basic ways of applying an operator :math:`A` to a field :math:`f`:
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@@ 210,8 +222,8 @@ There are four basic ways of applying an operator :math:`A` to a field :math:`f`
(Because of the linearity, inverse adjoint and adjoint inverse application
are equivalent.)
These different actions of a
n
operator ``Op`` on a field ``f`` can be
invoked
in various ways:
These different actions of a
linear
operator ``Op`` on a field ``f`` can be
invoked
in various ways:
 direct multiplication: ``Op(f)`` or ``Op.times(f)`` or ``Op.apply(f, Op.TIMES)``
 adjoint multiplication: ``Op.adjoint_times(f)`` or ``Op.apply(f, Op.ADJOINT_TIMES)``
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@@ 269,62 +281,6 @@ The properties :attr:`~LinearOperator.adjoint` and
were the original operator's adjoint or inverse, respectively.
Operators
=========
Operator classes (represented by NIFTy5's abstract :class:`Operator` class) are used to construct
the equations of a specific inference problem.
Most operators are defined via a position, which is a :class:`MultiField` object,
their value at this position, which is again a :class:`MultiField` object and a Jacobian derivative,
which is a :class:`LinearOperator` and is needed for the minimization procedure.
Using the existing basic operator classes one can construct more complicated operators, as
NIFTy allows for easy and selfconsinstent combination via pointwise multiplication,
addition and subtraction. The operator resulting from these operations then automatically
contains the correct Jacobians, positions and values.
Notably, :class:`Constant` and :class:`Variable` allow for an easy way to turn
inference of specific quantities on and off.
The basic operator classes also allow for more complex operations on operators such as
the application of :class:`LinearOperators` or local nonlinearities.
As an example one may consider the following combination of ``x``, which is an operator of type
:class:`Variable` and ``y``, which is an operator of type :class:`Constant`::
z = x*x + y
``z`` will then be an operator with the following properties::
z.value = x.value*x.value + y.value
z.position = Union(x.position, y.position)
z.jacobian = 2*makeOp(x.value)
Basic operators

# FIXME All this is outdated!
Basic operator classes provided by NIFTy are
 :class:`Constant` contains a constant value and has a zero valued Jacobian.
Like other operators, it has a position, but its value does not depend on it.
 :class:`Variable` returns the position as its value, its derivative is one.
 :class:`LinearModel` applies a :class:`LinearOperator` on the model.
 :class:`LocalModel` applies a nonlinearity locally on the model.
value and Jacobian are combined into corresponding :class:`MultiFields` and operators.
Advanced operators

NIFTy also provides a library of more sophisticated operators which are used for more
specific inference problems. Currently these are:
 :class:`AmplitudeOperator`, which returns a smooth power spectrum.
 :class:`InverseGammaOperator`, which models point sources which follow a inverse gamma distribution.
 :class:`CorrelatedField`, which models a diffuse lognormal field. It takes an amplitude operator
to specify the correlation structure of the field.
.. _minimization:
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nifty5/sugar.py
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14437d25
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@@ 49,6 +49,7 @@ def PS_field(pspace, func):
space at whose `k_lengths` the power spectrum function is evaluated
func : function taking and returning a numpy.ndarray(float)
the power spectrum function
Returns

Field : a field living on (pspace,) containing the computed function values
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@@ 305,8 +306,7 @@ def makeDomain(domain):
Parameters

domain : Domainoid (can be DomainTuple, MultiDomain, dict, Domain or
list of Domains)
domain : Domainoid (can be DomainTuple, MultiDomain, dict, Domain or list of Domains)
the description of the requested (multi)domain
Returns
...
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