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ift
NIFTy
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ebb0f027
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ebb0f027
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Jul 02, 2018
by
Sebastian Hutschenreuter
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add toplevel model docs
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ebb0f027
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@@ -13,8 +13,10 @@ recognized from a large distance, ignoring all technical details.
From such a perspective,
- IFT problems largely consist of *minimization* problems involving a large
number of equations.
- IFT problems largely consist of the combination of several high dimensional
*minimization* problems.
- Within NIFTy, *models* are used to define the characteristic equations and
properties of the problems.
- The equations are built mostly from the application of *linear operators*,
but there may also be nonlinear functions involved.
- The unknowns in the equations represent either continuous physical *fields*,
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@@ -232,6 +234,60 @@ The properties :attr:`~LinearOperator.adjoint` and
were the original operator's adjoint or inverse, respectively.
Models
======
Model classes (represented by NIFTy5's abstract :class:`Model` class) are used to construct
the equations of a specific inference problem.
Most models are defined via a position, which is a :class:`MultiField` object,
their value at these positions, 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 model classes one can construct more complicated models, as
NIFTy allows for easy and self-consinstent combination via pointwise multiplication,
addition and subtraction. The resulting model of these operations then automatically
contains the correct jacobians, positions and values.
Notably, :class:`Constant` and :class:`Variable` allows for an easy way to turn on and off the
inference of specific quantities.
The basic model classes also allow for more complex operations on models such as
the application of :class:`LinearOperators` or local non-linearities.
As an example one may consider the following combination of ``x``, which is a model of type
:class:`Variable` and ``y``, which is a model of type :class:`Constant`::
z = x*x + y
``z`` will then be a model with position::
z.value = x.value*x.value + y.value
z.position = x.position*x.position + y.position
z.jacobian = 2*makeOp(x.value)
Basic models
------------
Basic model classes provided by NIFTy are
- :class:`Constant` contains a constant value and has a zero valued jacobian.
It has no position (?currently it still has one?), as the value is the same everywhere.
- :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 non-linearity locally on the model.
- :class:`MultiModel` combines various models into one. In this case the position,
value and jacobian get combined into corresponding :class:`MultiFields` and operators.
Advanced models
---------------
NIFTy also provides a library of more sophisticated models which are used for more
specific inference problems. Currently these are:
- :class:'AmplitudeModel', which returns a smooth power spectrum.
- :class:'PointModel', which models points sources which follow a inverse gamma distribution.
- :class:'SmoothSkyModel', which models a diffuse lognormal field. It takes an amplitude model
to specify the correlation structure of the field.
.. _minimization:
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