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NIFTy -- Numerical Information Field Theory NIFTy Manual
=========================================== ============
**NIFTy** [1]_ [2]_ [3]_, "\ **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 these fields into classes.
This allows for an abstract formulation and programming of inference algorithms, including those derived within information field theory.
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
----------
.. [1] Selig et al., "NIFTY - Numerical Information Field Theory. A versatile PYTHON library for signal inference ", 2013, Astronmy and Astrophysics 554, 26; `[DOI] <https://ui.adsabs.harvard.edu/link_gateway/2013A&A...554A..26S/doi:10.1051/0004-6361/201321236>`_, `[arXiv:1301.4499] <https://arxiv.org/abs/1301.4499>`_
.. [2] Steininger et al., "NIFTy 3 - Numerical Information Field Theory - A Python framework for multicomponent signal inference on HPC clusters", 2017, accepted by Annalen der Physik; `[arXiv:1708.01073] <https://arxiv.org/abs/1708.01073>`_
.. [3] Arras et al., "NIFTy5: Numerical Information Field Theory v5", 2019, Astrophysics Source Code Library; `[ascl:1903.008] <http://ascl.net/1903.008>`_
Contents
........
.. toctree:: .. toctree::
:maxdepth: 2 :maxdepth: 1
ift User Guide <user/index>
volume API reference <mod/nifty7>
Gallery <https://wwwmpa.mpa-garching.mpg.de/~ensslin/nifty-gallery/index.html>
installation
code
citations
Package Documentation <mod/nifty7>
...@@ -145,14 +145,14 @@ Here, the uncertainty of the field and the power spectrum of its generating proc ...@@ -145,14 +145,14 @@ Here, the uncertainty of the field and the power spectrum of its generating proc
+----------------------------------------------------+ +----------------------------------------------------+
| **Output of tomography demo getting_started_3.py** | | **Output of tomography demo getting_started_3.py** |
+----------------------------------------------------+ +----------------------------------------------------+
| .. image:: images/getting_started_3_setup.png | | .. image:: ../images/getting_started_3_setup.png |
| | | |
+----------------------------------------------------+ +----------------------------------------------------+
| Non-Gaussian signal field, | | Non-Gaussian signal field, |
| data backprojected into the image domain, power | | data backprojected into the image domain, power |
| spectrum of underlying Gausssian process. | | spectrum of underlying Gausssian process. |
+----------------------------------------------------+ +----------------------------------------------------+
| .. image:: images/getting_started_3_results.png | | .. image:: ../images/getting_started_3_results.png |
| | | |
+----------------------------------------------------+ +----------------------------------------------------+
| Posterior mean field signal | | Posterior mean field signal |
......
NIFTy user guide
================
This guide is an overview and explains the major idea behind nifty. More
details are found in :ref:`mod`.
.. toctree::
:maxdepth: 1
whatisnifty
installation
ift
volume
code
citations
...@@ -39,4 +39,3 @@ To view the documentation in firefox:: ...@@ -39,4 +39,3 @@ To view the documentation in firefox::
(Note: Make sure that you reinstall nifty after each change since sphinx (Note: Make sure that you reinstall nifty after each change since sphinx
imports nifty from the Python path.) imports nifty from the Python path.)
...@@ -12,7 +12,7 @@ Fields are defined to be scalar functions on the manifold, living in the functio ...@@ -12,7 +12,7 @@ Fields are defined to be scalar functions on the manifold, living in the functio
Unless we find ourselves in the lucky situation that we can solve for the posterior statistics of interest analytically, we need to apply numerical methods. Unless we find ourselves in the lucky situation that we can solve for the posterior statistics of interest analytically, we need to apply numerical methods.
This is where NIFTy comes into play. This is where NIFTy comes into play.
.. figure:: images/inference.png .. figure:: ../images/inference.png
:width: 80% :width: 80%
:align: center :align: center
...@@ -138,7 +138,7 @@ NIFTy is implemented such that in order to change resolution, only the line of c ...@@ -138,7 +138,7 @@ NIFTy is implemented such that in order to change resolution, only the line of c
It automatically takes care of dependent structures like volume factors, discretised operators and responses. It automatically takes care of dependent structures like volume factors, discretised operators and responses.
A visualisation of this can be seen in figure 2, which displays the MAP inference of a signal at various resolutions. A visualisation of this can be seen in figure 2, which displays the MAP inference of a signal at various resolutions.
.. figure:: images/converging_discretization.png .. figure:: ../images/converging_discretization.png
:scale: 80% :scale: 80%
:align: center :align: center
......
What is NIFTy?
==============
**NIFTy** [1]_ [2]_ [3]_, "\ **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 these fields into classes.
This allows for an abstract formulation and programming of inference algorithms, including those derived within information field theory.
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.
Examples of nifty applications can be found in the `nifty gallery (external link) <https://wwwmpa.mpa-garching.mpg.de/~ensslin/nifty-gallery/index.html>`_.
References
----------
.. [1] Selig et al., "NIFTY - Numerical Information Field Theory. A versatile PYTHON library for signal inference ", 2013, Astronmy and Astrophysics 554, 26; `[DOI] <https://ui.adsabs.harvard.edu/link_gateway/2013A&A...554A..26S/doi:10.1051/0004-6361/201321236>`_, `[arXiv:1301.4499] <https://arxiv.org/abs/1301.4499>`_
.. [2] Steininger et al., "NIFTy 3 - Numerical Information Field Theory - A Python framework for multicomponent signal inference on HPC clusters", 2017, accepted by Annalen der Physik; `[arXiv:1708.01073] <https://arxiv.org/abs/1708.01073>`_
.. [3] Arras et al., "NIFTy5: Numerical Information Field Theory v5", 2019, Astrophysics Source Code Library; `[ascl:1903.008] <http://ascl.net/1903.008>`_
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