# This script calculates the bond graph parameters for the SERCA model of
# Tran et al. (2009) by using the kinetic parameters and stoichiometric
# matrix.
# translated from MATLAB to Python by SF using Pan's original code

import os
import csv
import json
import math
import numpy as np
import sympy
from scipy.linalg import null_space
from kinetic_parameters_SERCA import kinetic_parameters

def read_IDs(path):
    data = []
    with open(path,'r') as f:
        reader = csv.reader(f)
        for row in reader:
            data.append(row[0])
        f.close()
    return data


def load_matrix(stoich_path):
    matrix = []
    with open(stoich_path,'r') as f:
        reader = csv.reader(f,delimiter=',')
        for row in reader:
            matrix.append([int(r) for r in row])
        f.close()
    return matrix


if __name__ == "__main__":

    ## booleans
    write_parameters_file = True
    include_constraints = True

    ## Set directories
    current_dir = os.getcwd()
    data_dir = current_dir + '\data'
    output_dir = current_dir + '\output'
    modname = os.path.dirname(current_dir).split('\\')[-1].split('_')[-1]

    ## Define the volumes of each compartment (units pL)
    W_i = 38.0 # Intracellular volume
    W_sr = 2.28 # SR volume
    W_isr = W_i + W_sr # Intracellular volume + SR volume
    V = dict()
    V['V_myo'] = W_i
    V['V_SR'] = W_sr
    V['V_ISR'] = W_isr

    ## Load forward matrix
    stoich_path = data_dir + '\\all_forward_matrix.txt'

    N_f = load_matrix(stoich_path)

    ## Load reverse matrix
    stoich_path = data_dir + '\\all_reverse_matrix.txt'
    
    N_r = load_matrix(stoich_path)

    N_fT = np.transpose(N_f)
    N_rT = np.transpose(N_r)


    ## Calculate stoichiometric matrix
    N = [[N_r[j][i] - N_f[j][i] for i in range(len(N_f[0]))] for j in range(len(N_f))]
    N_T = [[N_rT[j][i] - N_fT[j][i] for i in range(len(N_fT[0]))] for j in range(len(N_fT))]

    num_rows = len(N)
    num_cols = len(N[0])
    dims = dict()
    dims['num_rows'] = num_rows
    dims['num_cols'] = num_cols

    I = np.identity(num_cols)

    M = np.append(np.append(I, N_fT,1), np.append(I, N_rT,1),0)

    [k_kinetic, N_cT, K_C, W] = kinetic_parameters(M, True, dims, V)

    if not include_constraints:
        N_cT = []

    try:
        M = np.append(M, N_cT,0)
        k = np.append(k_kinetic, K_C, 0)
    except:
        k = k_kinetic

    # FIND PARAMETERS HERE
    lambda_expo = np.matmul(np.linalg.pinv(M), [math.log(ik) for ik in k])
    lambdaW = [math.exp(l) for l in lambda_expo]


    # Check that kinetic parameters are reproduced by bond graph parameters
    k_est = np.matmul(M,[math.log(k) for k in lambdaW])
    k_est = [math.exp(k) for k in k_est]
    diff = [(k[i] - k_est[i])/k[i] for i in range(len(k))]

    error = np.sum([abs(d) for d in diff])


    # Check that there is a detailed balance constraint
    Z = null_space(np.transpose(M))

    N_rref = sympy.Matrix(N).rref()
    R_mat = null_space(N)
    kf = k_kinetic[:num_cols]
    kr = k_kinetic[num_cols:]
    K_eq = [kf[i]/kr[i] for i in range(len(kr))]
    zero_est = np.matmul(np.transpose(R_mat),K_eq)
    zero_est_log = np.matmul(np.transpose(R_mat),[math.log(k) for k in K_eq])

    lambdak = [lambdaW[i]/W[i] for i in range(len(W))]
    kappa = lambdak[:len(N[0])]
    K = lambdak[len(N[0]):]

    rxnID = read_IDs('data\\rxnID.txt')
    Kname = read_IDs('data\\Kname.txt')
    
    # ### print outputs ###
    for ik in range(len(kappa)):
        print('var kappa_%s: fmol_per_sec {init: %g, pub: out};' %(rxnID[ik],kappa[ik]))
    for ik in range(len(Kname)):
        print('var K_%s: per_fmol {init: %g, pub: out};' %(Kname[ik],K[ik]))

    file = open(output_dir + '/all_parameters_out.json', 'w')
    data = { "K": K, "kappa": kappa, "k_kinetic": k_kinetic }
    json.dump(data, file)