wl_spectra_ppf
================================================

Compute weak lensing C_ell from P(k,z) and MG D(k,z) with the Limber integral

+-------------+--------------------------------+
| File        | shear/spectra-ppf/interface.so |
+-------------+--------------------------------+
| Attribution | CosmoSIS team                  |
+-------------+--------------------------------+
|             | Matt Becker                    |
+-------------+--------------------------------+
| URL         |                                |
+-------------+--------------------------------+

DEPRECATED: You should use the module cosmosis-standard-library/structure/projection_ppf/project_2d_ppf.py instead.
This variant of the wl_spectra module includes modified gravity via the phenomenological D(k,z) which modifies the lensing kernel. Compare equations 33 and 34 of http://arxiv.org/pdf/1109.4583v3.pdf
Intrinsic alignments under modified gravity are not correctly supported; please use intrinsic_alignments=F

The Limber approximation integrates a 3D power spectrum over the radial direction to get a 2D angular power spectrum.  It is an approximation  which is only valid on smaller scales.
:math:`C_\ell =  A \int_0^{\chi_1} W_1(\chi) W_2(\chi) P(k=l/\chi, z(\chi)) / \chi^2 d\chi`

The full integral must integrate over k(\ell) also.
For weak lensing, the power spectrum is the matter power spectrum and the two kernel functions W depend on the redshift bins being used and the geometry.
Parts of this code and the underlying implementation of limber are based on cosmocalc: https://bitbucket.org/beckermr/cosmocalc-public


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

 - The Limber integral is valid on the scales in question



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

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

   * - Name
     - Type
     - Default
     - Description

   * - n_ell
     - int
     - 
     - Number of log-spaced ell values to compute
   * - ell_min
     - real
     - 
     - Minimum ell value to compute
   * - ell_max
     - real
     - 
     - Maximum ell value to compute


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

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

   * - Section
     - Name
     - Type
     - Default
     - Description

   * - modified_gravity
     - k_h
     - real 1d
     - 
     - Wavenumber k/h sample points for D(k,z)
   * - 
     - z
     - real 1d
     - 
     - Redshift sample points for D(k,z)
   * - 
     - D
     - real 2d
     - 
     - D(k,z) values at sample points
   * - cosmological_parameters
     - omega_m
     - real
     - 
     - Density fraction of all matter; used in the prefactor
   * - 
     - h0
     - real
     - 
     - Hubble factor H0 / 100 km/s/Mpc.
   * - distances
     - z
     - real 1d
     - 
     - Redshift values of distance samples
   * - 
     - d_m
     - real 1d
     - 
     - Comoving distnace to redshift values in units of Mpc (no factor h)
   * - matter_power_nl
     - z
     - real 1d
     - 
     - Redshift values of P(k,z) samples
   * - 
     - k_h
     - real 1d
     - 
     - Wavenumber k values of P(k,z) samples in units of Mpc/h
   * - 
     - P_k
     - real 2d
     - 
     - Non-linear matter power spectrum at samples in (Mpc/h)^{-3}
   * - wl_number_density
     - nbin
     - int
     - 
     - Number of redshift bins
   * - 
     - z
     - real 1d
     - 
     - Redshift values of n(z) samples
   * - 
     - bin_{i}
     - real 1d
     - 
     - Bin n(z) values.  Need not be normalized. bin_1, bin_2, bin_3, ....


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


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

   * - Section
     - Name
     - Type
     - Description

   * - shear_cl
     - ell
     - int 1d
     - Sample ell values for output C_ell
   * - 
     - nbin
     - int
     - Number of redshift bins used
   * - 
     - bin_{i}_{j}
     - real 1d
     - C_ell (no l(l+1) factor) for (auto-correlation) bin i and j. Only stores j<=i.