# fast Na module

# Return kinetic parameters, constraints, and vector of volumes in each
# compartment (pL) (1 if gating variable, or in element corresponding to
# kappa)

# Translated from Pan 2018 cardiac AP 

import numpy as np

def kinetic_parameters(M, include_type2_reactions, dims, V):
    # Set the kinetic rate constants

    num_cols = dims['num_cols']
    num_rows = dims['num_rows']

    # load gate transition parameters
    params_K1 = [1.1273394822768654,	0.03356898582323646,	13544.806358561376,	3.115336723982081]

    alpha_K1_bg = params_K1[0] * 1e3 #unit    s ^ -1
    beta_K1_bg = params_K1[2] * 1e3 # unit    s ^ -1

    # constants are stored in V
    F = V['F']
    R = V['R']
    T = V['T']
    N_A = V['N_A']
    cKo = V['cKo']
    G_GHK = 1.578254985192671e-09    # Unit mA/mM
    P_K = G_GHK/F * 1e12 # Unit pL/s . G_GHK [=] Amp/(mol/s)
    x_K_channel = 5369 / N_A * 1e15 # unit    fmol
    x_K_channel = V['numChannels']/N_A*1e15 # unit fmol

    # Calculate bond graph constants from kinetic parameters
    # Note: units of kappa are fmol/s, units of K are fmol^-1
    params_X = [2.231715978758744,	0.5192318115907739,	0.5749888974379704,	-0.731689511547001]
    # Calculate    parameters    for X_i gate
    A = np.exp(-56.26 / 32.1)
    K = 1 / (1 + A * np.exp(-120 / 32.1))
    alpha0 = K # Unit    ms ^ -1
    beta0 = A * K # Unit    ms ^ -1

    zf = 0
    zr = R * T / 32.1 / F
    params_Xi = [alpha0,        zf * 1e3,        beta0,        zr * 1e3]

    alpha_X_bg = params_X[0] # unit    s ^ -1
    beta_X_bg = params_X[2] # unit    s ^ -1
    alpha_Xi_bg = params_Xi[0] * 1e3 # unit    s ^ -1
    beta_Xi_bg = params_Xi[2] * 1e3 # unit    s ^ -1

    kf_K = [P_K / x_K_channel / np.sqrt(cKo) ,    # R_GHK
    2 * alpha_X_bg  ,   # RX00
    alpha_X_bg     ,# RX00
    2 * alpha_X_bg  ,   # RX00
    alpha_X_bg     ,# RX00
    alpha_Xi_bg     ,# RX00
    alpha_Xi_bg     ,# RX00
    alpha_Xi_bg] # RX00

    kr_K = [P_K / x_K_channel / np.sqrt(cKo),     # R_GHK
    beta_X_bg,     # RX00
    2 * beta_X_bg,     # RX00
    beta_X_bg     , # RX00
    2 * beta_X_bg  ,   # RX00
    beta_Xi_bg    , # RX00
    beta_Xi_bg    , # RX00
    beta_Xi_bg] # RX00

    k_kinetic = kf_K + kr_K

    # CONSTRAINTS
    N_cT = []
    K_C = []

    # volume vector
    # W = list(np.append([1] * num_cols, [V['V_myo']] * num_rows))
    W = [1] * num_cols + [V['V_myo'], V['V_o']] + [1] * (num_rows-2)

    return (k_kinetic, N_cT, K_C, W)