smail
================================================

Compute window functions for photometric n(z)

+-------------+-------------------------------------------+
| File        | number_density/smail/photometric_smail.py |
+-------------+-------------------------------------------+
| Attribution | Donnacha Kirk                             |
+-------------+-------------------------------------------+
|             | Simon Samuroff                            |
+-------------+-------------------------------------------+
|             | Jessica Muir                              |
+-------------+-------------------------------------------+
| URL         |                                           |
+-------------+-------------------------------------------+

This module takes inputs that specify the underlying spectroscopic (true) redshift distribution of the galaxies in the survey.  It then convolves this with a photometric error :math:`\sigma(z) = \sigma_0 (1+z)` and optionally biases it.  It computes bin edges in the survey assuming equal numbers in each.
You can also specify fixed bin edges.


Assumptions
-----------

 - Underlying true number density has Smail distribution
 - Photometric errors are sigma(z) = sigma_0 (1+z)
 - Bias fixed with redshift (if included)
 - Galaxies evenly divided between bins



Setup Parameters
----------------

.. list-table::
   :header-rows: 1

   * - Name
     - Type
     - Default
     - Description

   * - nbin
     - int
     - 
     - Number of redshift bins with equal number of gals in each
   * - zmin
     - real
     - 0.0
     - Minimum redshift to compute
   * - zmax
     - real
     - 4.0
     - Maximum redshift to compute
   * - dz
     - real
     - 0.01
     - Spacing of samples to compute n(z) at.
   * - enforce_equal_numbers
     - bool
     - F
     - No matter how n(z) gets divided, specify that each bin has equal number density
   * - z_edges
     - real 1d
     - None
     - Manually specified redshift bin edges. If nbin - 1 values passed, these are the bounds of photometric selection for those nbin bins. If 2 values are passed, they specify a minimum and maximum redshift between which galaxies are divided into equal number samples.



Input values
----------------

.. list-table::
   :header-rows: 1

   * - Section
     - Name
     - Type
     - Default
     - Description

   * - number_density_params
     - alpha
     - real
     - 
     - Smail distribution parameter. n(z) = z^{alpha} exp{-(z/z0)^beta}
   * - 
     - beta
     - real
     - 
     - Smail distribution parameter
   * - 
     - z0
     - real
     - 
     - Smail distribution parameter
   * - 
     - sigz
     - real
     - 
     - Photometric error at z=0
   * - 
     - ngal
     - real
     - 
     - Total number density of galaxies per square arcmin
   * - 
     - bias
     - real
     - 
     - Bias on all photometric measurements


Output values
----------------


.. list-table:: Output values
   :header-rows: 1

   * - Section
     - Name
     - Type
     - Description

   * - wl_number_density
     - nz
     - int
     - Number of redshift samples
   * - 
     - nbin
     - int
     - Number of bins
   * - 
     - z
     - real 1d
     - Redshift sample values
   * - 
     - bin_{i}
     - real 1d
     - n(z) at redshift sample values.  bin_1, bin_2, ...
   * - 
     - edge_{i}
     - real 1d
     - The nominal edges of the redshift bins (i.e. edges if no photometric errors)
   * - 
     - ngal_{i}
     - real
     - number density of redshift bin i