.. include:: ../../wlsubstitutions.rst
.. _TwoPCFWLShearShear2D:

Output Product: Tomographic Cosmic Shear Correlation
==================================================

$SetSchemaPath le3/wl/twopcf/out/euc-le3-wl-twopcf-ShearShear2D.xsd

Data Product Name
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.. DataProductNameStart

$PrintDataProductName

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Data Product Custodian
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.. DataProductCustodianStart

$PrintDataProductCustodian

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Name of the Schema File
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.. NameSchemaStart

$PrintSchemaFilename

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Last Edited for DPDD Version
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.. DpddVersionlTagStart

1.1

.. DpddVersionTagEnd

Processing Elements Creating / Updating / Using the Product
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.. PECreatorStart

**Creators:**

* LE3_2PCF_WL_ShearShear_Pipeline
* LE3_CM_2PCF_WL_ShearShear_Pipeline

**Consumers:**

* WL-SWG

.. PECreatorEnd

Processing Function using the products
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.. PFUsingStart

SGS pipeline output product to be used by LE3 and SWGs

.. PFUsingEnd

Proposed for inclusion in EAS/SAS
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.. IncludeInSASStart

This product is proposed for inclusion in the SAS: Yes

Motivation: the product contains the two-point shear-shear tomographic real-space correlation functions requested by the RSD document.

.. IncludeInSASEnd

Data Product Elements
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.. DataProductElementsStart

$PrintDataProductElements

.. DataProductElementsEnd

Detailed Description of the Data Product
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.. DetailedDescStart

This product contains the tomographic cosmic shear 2PCF.

This output product is a fits file (see ``le3.wl.2pcf.output.shearshear2d`` in |XSD-FITS-WL|_).

Extra metadata associated to the FITS container are the following:

* **SpatialCoverage** a description of the spatial footprint [optional, cot:spatialFootprint],
* **CatalogSelection**: describing the selection in the input catalogues [optional, up to 1 element]

  *  **CatalogFileName**: the name of the input catalogue [sys:dataFileName]
  *  **CatalogSHE**: type of input catalogue [string among "BFD", "KSB",
     "LensMC","MomentsML","REGAUSS","MER_PHZ", "OTHER" ]
  *  **Selection**: selection associated to catalogue [string]
  *  **CatalogUse**: for which use case the catalog is employed (=["ShearShear"])
     [string among "PosPos", "PosShear", "ShearShear"]
  *  **CatalogInfo**:  whether position or shear information is used in this catalogue
     [string among "Pos", "Shear"]  (=["Shear"])
  * **CatalogOrder**: order associated to catalogue for reporting (e.g. BIN_ID1)[int32]

The fits file contains:

- a primary array containing important computation parameters as keywords,
- binary tables in the next HDUs with cosmic shear 2-PCF for specific redshift bins.

Primary Array
+++++++++++++

This fits table is expected to contain the following keywords in primary HDU,
characterizing the important parameters of the product:

$PrintPrimaryHeader fit/euc-le3-wl.xml le3.wl.2pcf.output.shearshear2d

#. **THMIN**: minimal angular value chosen for spatial binning [DoubleKeyword]
#. **THMAX**: maximal angular value chosen for spatial binning [DoubleKeyword]
#. **OATH**: maximal open angle value used for the approximation [DoubleKeyword]
#. **THUNIT**: unit of spatial distance [StringKeyword]
#. **BINSCALE**: if linear or logarithmic scales are used for output [StringKeyword]
#. **COORDSYS**: if spherical or cartesian computation of distances [StringKeyword]
#. **SHE_SOFT**: which SHE catalogue used [StringKeyword]
#. **SHE_SEL**: selection for shear catalogue [StringKeyword]
#. **SOFTNAME**: name of software used for 2PCF [StringKeyword]
#. **SOFTVERS**: version of software used for 2PCF [StringKeyword]

Table (HDU=1...)
++++++++++++++++

The following keywords are added to the header of the HDUs:

$PrintHDUTableContents fit/euc-le3-wl.xml le3.wl.2pcf.output.shearshear2d SHEARSHEAR2D_2PCF_n

#. **BIN_ID1**: bin for first catalog [IntegerKeyword]
#. **BIN_ID2**: bin for second catalog [IntegerKeyword]
#. **EXTNAME**: "SHEARSHEAR2D_2PCF"

and the columns are:

#. **THETA**: mean angular separation in the bin [D, float64]
#. **XI_P**: cosmic shear 2PCF :math:`\xi_+` [D, float64]
#. **XI_M**: cosmic shear 2PCF :math:`\xi_-` [D, float64]
#. **XI_X**: cosmic shear 2PCF :math:`\xi_x` [D, float64]
#. **WEIGHT**: total weight for the bin [D, float64]
#. **SQRT_D**:  Poisson error associated to the bin [D, float64]
#. **SQRT_DCOR**:  Poisson error associated to the bin, down-weighted by the ratio
   of number of galaxy pairs by the number of nodes [D, float64].
#. **N_PAIR**:  Number of pairs [D, float64]

The correlation functions are defined as:

.. math::
    \xi_\pm &=\langle \epsilon_t \epsilon_t\rangle \pm \langle \epsilon_x \epsilon_x\rangle\\
    \xi_x &= \langle  \epsilon_t \epsilon_x \rangle

with :math:`\epsilon_t` tangential component and :math:`\epsilon_x` cross component of ellipticity.

.. note::
    Under discussion is the possibility in the future of having as first HDU a summary table with information
    on the binning for 2PCF tables (HDU>2):

    #. **THETA**: angular separation (center of spatial bin)  [D, float64]
    #. **MIN_THETA**:  minimal angular separation in the bin [D, float64]
    #. **MAX_THETA**:  maximal angular separation in the bin [D, float64]


    and in the second hdu a summary table to allow fast access to the HDU corresponding to a particular
    bin combination:

    #. **BIN_ID1**: bin for first catalog [J, int32]
    #. **BIN_ID2**: bin for second catalog [J, int32]
    #. **HDU**: HDU index [J, int32]

.. DetailedDescEnd