:py:mod:`BioSANS2020.propagation.symbolic.analytical_sol`
=========================================================

.. py:module:: BioSANS2020.propagation.symbolic.analytical_sol

.. autoapi-nested-parse::

                   This module is the analytical_sol module

   This module handles analytical expression derivation

   The following are the functions in this module

   1. solve_with_timeout
   2. get_sets
   3. grab_steady_state
   4. cs_to_csr
   5. analyt_soln



Module Contents
---------------


Functions
~~~~~~~~~

.. autoapisummary::

   BioSANS2020.propagation.symbolic.analytical_sol.solve_with_timeout
   BioSANS2020.propagation.symbolic.analytical_sol.get_sets
   BioSANS2020.propagation.symbolic.analytical_sol.grab_steady_state
   BioSANS2020.propagation.symbolic.analytical_sol.cs_to_csr
   BioSANS2020.propagation.symbolic.analytical_sol.analyt_soln



.. py:function:: solve_with_timeout(f_e, j_s)

   resturn solution to the system of equation in f_e with variables
   symbos in the list j_s

   Args:
       f_e (list): equations
       j_s (list): Symbols

   Returns:
       dict: sometimes list but normally {variable : value}


.. py:function:: get_sets(r_dict, p_dict)

   [summary]

   Args:
       r_dict (dict): dictionary of reactants
       p_dict (dict): dictionary of products

   Returns:
       set: sets to sum that will be used as constraints


.. py:function:: grab_steady_state(r_dict, p_dict, c_s, c_so, da_dt, j_s)

   This function return steady state amounts of components

   Args:
       r_dict (dict): reactants dictionary
       p_dict (dict): products dictionary
       c_s (dict): dictionary of concentration Symbols/values
       c_so (dict): dictionary of initial concentration Symbols/values
       da_dt ([type]): ode expression
       j_s ([type]): list of components

   Returns:
       Matrix: steady state result


.. py:function:: cs_to_csr(f_x, c_s, cs_r, not_semi)

   [summary]

   Args:
       f_x (expression): sympy expression
       c_s (Symbol): sympy symbols
       cs_r (Symbol): equivalent of c_s
       not_semi (boolean): if True, use pure symbolic

   Returns:
       expression: substituted expression


.. py:function:: analyt_soln(sp_comp, ks_dict, conc, r_dict, p_dict, stch_var, items=None, rfile='', not_semi=True, mode=None)

   This function finds an analytical solution to a system of ODE.

   Args:
       sp_comp (dict): dictionary of components
       ks_dict (dict):  dictionary of rate constant
       conc (dict): dictionary of concentrations
       r_dict (dict): dictionary of reactants
       p_dict (dict): dictionary of products
       stch_var (Matrix): stoichiomentric matrix
       items (tuple, optional): (canvas, scroll_x, scrolly).
       rfile (str, optional): BioSANS topology file.
       not_semi (bool, optional): if True, use pure symbolic solution;
               which is a function of time, initial concentration, and
               rate constant. Defaults to True.
       mode (str, optional): mode of computation;
               ftxo - function of time and initial condition
               ftks - function of time and rate constant
           Defaults to None.

   Returns:
       dict: dictionary of solution