.. include:: ../wlsubstitutions.rst
.. _PF-2PCF-WL-intro:

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Introduction
============

From the SHE/PHZ catalog :ref:`WLLensMCCatalog <WLLensMCCatalog>`, the 2PCF-WL PF will provide the following output products:

* The 3x2PCF: the :ref:`tomographic cosmic shear 2PCF <TwoPCFWLShearShear2D>`,
  the :ref:`tomographic galaxy-galaxy lensing 2PCF <TwoPCFWLPosShear2D>`
  and the :ref:`tomographic angular 2PCF <TwoPCFWLPosPos2D>` using the
  :ref:`random catalog <WLRandomCatalog>`
* The 3 spectra: the :ref:`tomographic E/B cosmic shear spectra <TwoPCFWLPEBShearShear2D>`,
  the :ref:`tomographic E/B galaxy-galaxy lensing spectra <TwoPCFWLPEBPosShear2D>`
  and the :ref:`tomographic angular spectra <TwoPCFWLClPosPos2D>`
* For cosmic shear, :ref:`the COSEBI decomposition <TwoPCFWLCOSEBIShearShear2D>`

Optionally, if selection is different for the lens galaxies than for the source galaxies,
a MER/PHZ position catalog :ref:`WLPosCatalog <WLPosCatalog>`.

In the following, we first present :ref:`tomographic cosmic shear products<2PCFWLIntroShearShear>`,
:ref:`tomographic galaxy-galaxy lensing products<2PCFWLIntroPosShear>`  and finally
:ref:`tomographic angular products<2PCFWLIntroPosPos>`.


.. _2PCFWLIntroShearShear:

Tomographic cosmic shear
++++++++++++++++++++++++

To derive the tomographic cosmic shear 2PCF,  an input fits catalog
:ref:`WLLensMCCatalog <WLLensMCCatalog>` collecting information from
SHE/PHZ is needed.
Running parameters are collected in :ref:`TwoPCFWLParamsShearShear2D <TwoPCFWLParamsShearShear2D>`
for cosmic shear correlation, specifying in particular the binning, open angle
used by the algorithm.

Once the 2PCF :ref:`TwoPCFWLShearShear2D <TwoPCFWLShearShear2D>` is computed,
with running parameters :ref:`TwoPCFWLParamsPEBShearShear2D <TwoPCFWLParamsPEBShearShear2D>`,
the tomographic E/B cosmic shear power spectra :ref:`TwoPCFWLPEBShearShear2D <TwoPCFWLPEBShearShear2D>`
can then be computed.

Finally, from the 2PCF :ref:`TwoPCFWLShearShear2D <TwoPCFWLShearShear2D>` and parameters
:ref:`TwoPCFWLParamsCOSEBIShearShear2D <TwoPCFWLParamsCOSEBIShearShear2D>`, the COSEBI
decomposition :ref:`TwoPCFWLCOSEBIShearShear2D <TwoPCFWLCOSEBIShearShear2D>` can be computed as well.

The flowchart is described in the following:

.. image:: DPDD-shearshear2d.png

.. _2PCFWLIntroPosShear:

Tomographic galaxy-galaxy lensing
+++++++++++++++++++++++++++++++++

To derive the tomographic galaxy-galaxy lensing 2PCF,  an input fits catalog
:ref:`WLLensMCCatalog <WLLensMCCatalog>` collecting information from
SHE/PHZ is needed and (optionally) a MER/PHZ position catalog :ref:`WLPosCatalog <WLPosCatalog>`.
Running parameters are collected in :ref:`TwoPCFWLParamsPosShear2D <TwoPCFWLParamsPosShear2D>`
for galaxy-galaxy lensing correlation, specifying in particular the binning,
open angle used by the algorithm.

Once the 2PCF :ref:`TwoPCFWLPosShear2D <TwoPCFWLPosShear2D>` is computed,  using
running parameters :ref:`TwoPCFWLParamsPEBPosShear2D <TwoPCFWLParamsPEBPosShear2D>`,
the tomographic E/B galaxy-galaxy lensing power spectra :ref:`TwoPCFWLPEBPosShear2D <TwoPCFWLPEBPosShear2D>`
can then be computed.

For galaxy-galaxy lensing, the flowchart contains is then described in the following:

.. image:: DPDD-shearpos2d.png

.. _2PCFWLIntroPosPos:

Tomographic angular correlation
++++++++++++++++++++++++++++++++

To derive the tomographic angular 2PCF,  an input fits catalog :ref:`WLLensMCCatalog <WLLensMCCatalog>`
(or a MER/PHZ position catalog :ref:`WLPosCatalog <WLPosCatalog>`)
collecting information from SHE/PHZ is needed, as well as a random catalog
:ref:`WLRandomCatalog <WLRandomCatalog>` originating from VMPZ-ID.
Running parameters are collected in :ref:`TwoPCFWLParamsPosPos2D <TwoPCFWLParamsPosPos2D>`
for angular correlation, specifying in particular which estimator is chosen.

Once :ref:`TwoPCFWLPosPos2D <TwoPCFWLPosPos2D>` is computed,  using running parameters
:ref:`TwoPCFWLParamsClPosPos2D <TwoPCFWLParamsClPosPos2D>`, the tomographic angular power spectra
:ref:`TwoPCFWLClPosPos2D <TwoPCFWLClPosPos2D>` can then be computed.

The flowchart is the following:

.. image:: DPDD-pospos2d.png


Inputs products

* :ref:`WLCosebiFilter`

* :ref:`TwoPCFWLParamsClPosPos2D`

* :ref:`TwoPCFWLParamsCOSEBIShearShear2D`

* :ref:`TwoPCFWLParamsPEBPosShear2D`

* :ref:`TwoPCFWLParamsPEBShearShear2D`

* :ref:`TwoPCFWLParamsPosPos2D`

* :ref:`TwoPCFWLParamsPosShear2D`

* :ref:`TwoPCFWLParamsShearShear2D`

Outputs products

* :ref:`TwoPCFWLClPosPos2D`

* :ref:`TwoPCFWLCOSEBIShearShear2D`

* :ref:`TwoPCFWLPEBPosShear2D`

* :ref:`TwoPCFWLPEBShearShear2D`

* :ref:`TwoPCFWLPosPos2D`

* :ref:`TwoPCFWLPosShear2D`

* :ref:`TwoPCFWLShearShear2D`



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