====================
Emulator Parameters
====================

This page details the parameters used by ``Aletheia``. It is important to distinguish between the user-facing *input parameters* and the internal *emulated parameters* upon which the emulator is trained.

User Input: The Cosmology Dictionary
------------------------------------

The main way to provide a cosmology is through a Python dictionary, created by the ``AletheiaEmu.create_cosmo_dict()`` static method. This method ensures all parameters are correctly formatted.

**Example 1: Using Physical Densities (Default)**
This is the recommended method, as it uses physical density parameters (e.g., :math:`\omega_{\mathrm{b}}`) that are independent of the dimensionless Hubble parameter :math:`h`.

.. code-block:: python

   cosmo_params = AletheiaEmu.create_cosmo_dict(
       h=0.67,
       omega_b=0.0224,
       omega_c=0.120,
       n_s=0.96,
       A_s=2.1e-9,
       model='LCDM'
   )

**Example 2: Using Fractional Densities**
The helper function can also accept fractional densities (e.g., :math:`\Omega_{\mathrm{b}}=\omega_{\mathrm{b}}/h^2`) by setting the ``density_type`` flag.

.. code-block:: python

   cosmo_params = AletheiaEmu.create_cosmo_dict(
       h=0.7,
       Omega_b=0.05,
       Omega_c=0.267,
       n_s=0.97,
       A_s=2.1e-9,
       model='LCDM',
       density_type='fractional'
   )

The user provides standard cosmological parameters (like ``A_s``, ``w_0``, ``w_a``, ``omega_k``) and the ``get_pnl()`` method also takes a ``redshift``.

Internal Conversion
-------------------

The emulator does **not** use all of these input parameters directly. Instead, it internally calculates the specific set of parameters upon which its Gaussian Process models were trained.

The primary emulated parameters are:

1.  **Shape Parameters:** ``omega_b``, ``omega_c``, ``n_s``

2.  **Clustering Amplitude:** ``sigma12`` (the RMS of matter fluctuations at z=0)

The user-provided values for ``A_s``, ``w_0``, ``w_a``, ``omega_DE``, ``omega_k``, and ``z`` are used by the internal ``Cosmology`` and ``GrowthCalculator`` classes to compute the correct values of ``sigma12`` and ``xtilde`` for the given cosmology at the specified redshift. This ``sigma12`` value is then passed to the emulators.

Emulator Training Range
-----------------------

The ``get_pnl()`` method will raise a ``ValueError`` if the input cosmology results in emulated parameters that are outside the training domain.

* **Shape Parameters** :math:`(\omega_{\mathrm{b}}, \omega_{\mathrm{c}}, n_{\mathrm{s}})`:
    The emulator is trained on a parameter space spanning :math:`\pm 5\sigma` of the Planck 2018 constraints, projected onto the eigenvectors of the covariance matrix. The ``_validate_params`` method checks this internally.

* **Clustering Amplitude** :math:`(\sigma12)`:
    The valid range for the clustering amplitude is:
    :math:`0.2 < \sigma_{12} < 1.0`

* **Wavenumber** :math:`(k)`:
    The emulator provides predictions within the wavenumber range:
    :math:`0.006\, {\rm Mpc}^{-1} < k < 2.0 \, {\rm Mpc}^{-1}`

This design, based on the **evolution mapping framework**, allows the emulator to robustly handle dark energy and curvature models without having been explicitly trained on them.