# Size of variable arrays:
sizeAlgebraic = 49
sizeStates = 7
sizeConstants = 60
from math import *
from numpy import *

def createLegends():
    legend_states = [""] * sizeStates
    legend_rates = [""] * sizeStates
    legend_algebraic = [""] * sizeAlgebraic
    legend_voi = ""
    legend_constants = [""] * sizeConstants
    legend_voi = "t in component params_BG (second)"
    legend_constants[0] = "R in component params_BG (J_per_K_mol)"
    legend_constants[1] = "T in component params_BG (kelvin)"
    legend_constants[2] = "F in component params_BG (C_per_mol)"
    legend_constants[3] = "K_Hi in component params_BG (per_fmol)"
    legend_constants[55] = "q_Hi in component params_BG (fmol)"
    legend_constants[4] = "K_Ho in component params_BG (per_fmol)"
    legend_constants[57] = "q_Ho in component params_BG (fmol)"
    legend_constants[5] = "K_Cai in component params_BG (per_fmol)"
    legend_constants[45] = "q_Cai in component params_BG (fmol)"
    legend_constants[6] = "K_Cao in component params_BG (per_fmol)"
    legend_constants[47] = "q_Cao in component params_BG (fmol)"
    legend_constants[7] = "K_Pi in component params_BG (per_fmol)"
    legend_constants[49] = "q_Pi in component params_BG (fmol)"
    legend_constants[8] = "K_ATPi in component params_BG (per_fmol)"
    legend_constants[51] = "q_ATPi in component params_BG (fmol)"
    legend_constants[9] = "K_ADPi in component params_BG (per_fmol)"
    legend_constants[53] = "q_ADPi in component params_BG (fmol)"
    legend_constants[10] = "K_1 in component params_BG (per_fmol)"
    legend_constants[11] = "q_init_1 in component params_BG (fmol)"
    legend_constants[12] = "K_2 in component params_BG (per_fmol)"
    legend_constants[13] = "q_init_2 in component params_BG (fmol)"
    legend_constants[14] = "K_3 in component params_BG (per_fmol)"
    legend_constants[15] = "q_init_3 in component params_BG (fmol)"
    legend_constants[16] = "K_4 in component params_BG (per_fmol)"
    legend_constants[17] = "q_init_4 in component params_BG (fmol)"
    legend_constants[18] = "K_5 in component params_BG (per_fmol)"
    legend_constants[19] = "q_init_5 in component params_BG (fmol)"
    legend_constants[20] = "K_6 in component params_BG (per_fmol)"
    legend_constants[21] = "q_init_6 in component params_BG (fmol)"
    legend_constants[22] = "kappa_r1 in component params_BG (fmol_per_s)"
    legend_constants[23] = "kappa_r2 in component params_BG (fmol_per_s)"
    legend_constants[24] = "kappa_r3 in component params_BG (fmol_per_s)"
    legend_constants[25] = "kappa_r4 in component params_BG (fmol_per_s)"
    legend_constants[26] = "kappa_r5 in component params_BG (fmol_per_s)"
    legend_constants[27] = "kappa_r6 in component params_BG (fmol_per_s)"
    legend_constants[56] = "mu_Hi in component BG_SERCA (J_per_mol)"
    legend_constants[58] = "mu_Ho in component BG_SERCA (J_per_mol)"
    legend_constants[46] = "mu_Cai in component BG_SERCA (J_per_mol)"
    legend_constants[48] = "mu_Cao in component BG_SERCA (J_per_mol)"
    legend_constants[50] = "mu_Pi in component BG_SERCA (J_per_mol)"
    legend_constants[52] = "mu_ATPi in component BG_SERCA (J_per_mol)"
    legend_constants[54] = "mu_ADPi in component BG_SERCA (J_per_mol)"
    legend_algebraic[0] = "mu_1 in component BG_SERCA (J_per_mol)"
    legend_algebraic[21] = "v_1 in component BG_SERCA (fmol_per_s)"
    legend_algebraic[1] = "mu_2 in component BG_SERCA (J_per_mol)"
    legend_algebraic[42] = "v_2 in component BG_SERCA (fmol_per_s)"
    legend_algebraic[2] = "mu_3 in component BG_SERCA (J_per_mol)"
    legend_algebraic[43] = "v_3 in component BG_SERCA (fmol_per_s)"
    legend_algebraic[3] = "mu_4 in component BG_SERCA (J_per_mol)"
    legend_algebraic[32] = "v_4 in component BG_SERCA (fmol_per_s)"
    legend_algebraic[4] = "mu_5 in component BG_SERCA (J_per_mol)"
    legend_algebraic[33] = "v_5 in component BG_SERCA (fmol_per_s)"
    legend_algebraic[5] = "mu_6 in component BG_SERCA (J_per_mol)"
    legend_algebraic[22] = "v_6 in component BG_SERCA (fmol_per_s)"
    legend_algebraic[23] = "V_Vm in component BG_SERCA (volt)"
    legend_algebraic[20] = "V0_Vm in component params_BG (volt)"
    legend_constants[28] = "z_zf1 in component params_BG (dimensionless)"
    legend_constants[29] = "z_zr1 in component params_BG (dimensionless)"
    legend_constants[30] = "z_zf2 in component params_BG (dimensionless)"
    legend_constants[31] = "z_zr2 in component params_BG (dimensionless)"
    legend_algebraic[24] = "Vm_zf1 in component BG_SERCA (volt)"
    legend_algebraic[35] = "I_zf1 in component BG_SERCA (fA)"
    legend_algebraic[27] = "mu_zf1 in component BG_SERCA (J_per_mol)"
    legend_algebraic[34] = "v_zf1 in component BG_SERCA (fmol_per_s)"
    legend_algebraic[26] = "Vm_zr1 in component BG_SERCA (volt)"
    legend_algebraic[37] = "I_zr1 in component BG_SERCA (fA)"
    legend_algebraic[29] = "mu_zr1 in component BG_SERCA (J_per_mol)"
    legend_algebraic[36] = "v_zr1 in component BG_SERCA (fmol_per_s)"
    legend_algebraic[25] = "Vm_zf2 in component BG_SERCA (volt)"
    legend_algebraic[45] = "I_zf2 in component BG_SERCA (fA)"
    legend_algebraic[28] = "mu_zf2 in component BG_SERCA (J_per_mol)"
    legend_algebraic[44] = "v_zf2 in component BG_SERCA (fmol_per_s)"
    legend_algebraic[38] = "Vm_zr2 in component BG_SERCA (volt)"
    legend_algebraic[47] = "I_zr2 in component BG_SERCA (fA)"
    legend_algebraic[39] = "mu_zr2 in component BG_SERCA (J_per_mol)"
    legend_algebraic[46] = "v_zr2 in component BG_SERCA (fmol_per_s)"
    legend_algebraic[6] = "A_f_r1 in component BG_SERCA (J_per_mol)"
    legend_algebraic[16] = "v_r1 in component BG_SERCA (fmol_per_s)"
    legend_algebraic[7] = "A_r_r1 in component BG_SERCA (J_per_mol)"
    legend_algebraic[8] = "A_f_r2 in component BG_SERCA (J_per_mol)"
    legend_algebraic[41] = "v_r2 in component BG_SERCA (fmol_per_s)"
    legend_algebraic[40] = "A_r_r2 in component BG_SERCA (J_per_mol)"
    legend_algebraic[9] = "A_f_r3 in component BG_SERCA (J_per_mol)"
    legend_algebraic[17] = "v_r3 in component BG_SERCA (fmol_per_s)"
    legend_algebraic[10] = "A_r_r3 in component BG_SERCA (J_per_mol)"
    legend_algebraic[11] = "A_f_r4 in component BG_SERCA (J_per_mol)"
    legend_algebraic[31] = "v_r4 in component BG_SERCA (fmol_per_s)"
    legend_algebraic[30] = "A_r_r4 in component BG_SERCA (J_per_mol)"
    legend_algebraic[12] = "A_f_r5 in component BG_SERCA (J_per_mol)"
    legend_algebraic[18] = "v_r5 in component BG_SERCA (fmol_per_s)"
    legend_algebraic[13] = "A_r_r5 in component BG_SERCA (J_per_mol)"
    legend_algebraic[14] = "A_f_r6 in component BG_SERCA (J_per_mol)"
    legend_algebraic[19] = "v_r6 in component BG_SERCA (fmol_per_s)"
    legend_algebraic[15] = "A_r_r6 in component BG_SERCA (J_per_mol)"
    legend_states[0] = "q_1 in component BG_SERCA (fmol)"
    legend_states[1] = "q_2 in component BG_SERCA (fmol)"
    legend_states[2] = "q_3 in component BG_SERCA (fmol)"
    legend_states[3] = "q_4 in component BG_SERCA (fmol)"
    legend_states[4] = "q_5 in component BG_SERCA (fmol)"
    legend_states[5] = "q_6 in component BG_SERCA (fmol)"
    legend_algebraic[48] = "Ii in component BG_SERCA (fA)"
    legend_constants[32] = "nH in component BG_SERCA (dimensionless)"
    legend_constants[33] = "nCa in component BG_SERCA (dimensionless)"
    legend_constants[34] = "kappa_r7 in component params_BG (fmol_per_s)"
    legend_constants[35] = "Cai in component params_BG (mM)"
    legend_constants[36] = "Cao in component params_BG (mM)"
    legend_constants[37] = "Hi in component params_BG (mM)"
    legend_constants[38] = "Ho in component params_BG (mM)"
    legend_constants[39] = "Pi in component params_BG (mM)"
    legend_constants[40] = "ATPi in component params_BG (mM)"
    legend_constants[41] = "ADPi in component params_BG (mM)"
    legend_constants[42] = "V_i in component params_BG (pL)"
    legend_constants[43] = "V_o in component params_BG (pL)"
    legend_states[6] = "V_E in component params_BG (volt)"
    legend_constants[44] = "dt in component params_BG (second)"
    legend_rates[0] = "d/dt q_1 in component BG_SERCA (fmol)"
    legend_rates[1] = "d/dt q_2 in component BG_SERCA (fmol)"
    legend_rates[2] = "d/dt q_3 in component BG_SERCA (fmol)"
    legend_rates[3] = "d/dt q_4 in component BG_SERCA (fmol)"
    legend_rates[4] = "d/dt q_5 in component BG_SERCA (fmol)"
    legend_rates[5] = "d/dt q_6 in component BG_SERCA (fmol)"
    legend_rates[6] = "d/dt V_E in component params_BG (volt)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    constants[0] = 8.31
    constants[1] = 293
    constants[2] = 96485
    constants[3] = 1e-06
    constants[4] = 1e-06
    constants[5] = 1e-08
    constants[6] = 1e-08
    constants[7] = 1e-08
    constants[8] = 1e-08
    constants[9] = 1e-08
    constants[10] = 1
    constants[11] = 1
    constants[12] = 1
    constants[13] = 1
    constants[14] = 1
    constants[15] = 1
    constants[16] = 1
    constants[17] = 1
    constants[18] = 1
    constants[19] = 1
    constants[20] = 1
    constants[21] = 1
    constants[22] = 1
    constants[23] = 1
    constants[24] = 1
    constants[25] = 1
    constants[26] = 1
    constants[27] = 1
    constants[28] = 1
    constants[29] = 1
    constants[30] = 1
    constants[31] = 1
    constants[32] = 1
    constants[33] = 2
    constants[34] = 1
    constants[35] = 20
    constants[36] = 100
    constants[37] = 10e-3
    constants[38] = 1e-12
    constants[39] = 1e-12
    constants[40] = 1e-12
    constants[41] = 1e-12
    constants[42] = 8.5e5
    constants[43] = 8.5e5
    states[6] = -0.05
    constants[44] = 1e-3
    constants[45] = constants[35]*constants[42]
    constants[59] = 0.00000
    constants[46] = constants[0]*constants[1]*log(constants[5]*constants[45])
    constants[47] = constants[36]*constants[43]
    constants[48] = constants[0]*constants[1]*log(constants[6]*constants[47])
    constants[49] = constants[39]*constants[43]
    constants[50] = constants[0]*constants[1]*log(constants[7]*constants[49])
    constants[51] = constants[40]*constants[43]
    constants[52] = constants[0]*constants[1]*log(constants[8]*constants[51])
    constants[53] = constants[41]*constants[43]
    constants[54] = constants[0]*constants[1]*log(constants[9]*constants[53])
    constants[55] = constants[37]*constants[42]
    constants[56] = constants[0]*constants[1]*log(constants[3]*constants[55])
    constants[57] = constants[38]*constants[43]
    constants[58] = constants[0]*constants[1]*log(constants[4]*constants[57])
    states[0] = constants[11]
    states[1] = constants[13]
    states[2] = constants[15]
    states[3] = constants[17]
    states[4] = constants[19]
    states[5] = constants[21]
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    rates[6] = constants[59]
    algebraic[0] = constants[0]*constants[1]*log(constants[10]*states[0])
    algebraic[6] = constants[52]+algebraic[0]
    algebraic[1] = constants[0]*constants[1]*log(constants[12]*states[1])
    algebraic[7] = algebraic[1]
    algebraic[16] = constants[22]*(exp(algebraic[6]/(constants[0]*constants[1]))-exp(algebraic[7]/(constants[0]*constants[1])))
    algebraic[5] = constants[0]*constants[1]*log(constants[20]*states[5])
    algebraic[14] = algebraic[5]
    algebraic[15] = algebraic[0]+constants[50]
    algebraic[19] = constants[27]*(exp(algebraic[14]/(constants[0]*constants[1]))-exp(algebraic[15]/(constants[0]*constants[1])))
    algebraic[21] = algebraic[19]-algebraic[16]
    rates[0] = algebraic[21]
    algebraic[4] = constants[0]*constants[1]*log(constants[18]*states[4])
    algebraic[12] = algebraic[4]
    algebraic[13] = algebraic[5]+constants[32]*constants[58]
    algebraic[18] = constants[26]*(exp(algebraic[12]/(constants[0]*constants[1]))-exp(algebraic[13]/(constants[0]*constants[1])))
    algebraic[22] = algebraic[18]-algebraic[19]
    rates[5] = algebraic[22]
    algebraic[2] = constants[0]*constants[1]*log(constants[14]*states[2])
    algebraic[9] = algebraic[2]
    algebraic[3] = constants[0]*constants[1]*log(constants[16]*states[3])
    algebraic[10] = algebraic[3]+constants[54]
    algebraic[17] = constants[24]*(exp(algebraic[9]/(constants[0]*constants[1]))-exp(algebraic[10]/(constants[0]*constants[1])))
    algebraic[11] = algebraic[3]
    algebraic[20] = states[6]
    algebraic[23] = algebraic[20]
    algebraic[26] = algebraic[23]
    algebraic[29] = constants[29]*constants[2]*algebraic[26]
    algebraic[30] = algebraic[4]+constants[33]*constants[48]+algebraic[29]
    algebraic[31] = constants[25]*(exp(algebraic[11]/(constants[0]*constants[1]))-exp(algebraic[30]/(constants[0]*constants[1])))
    algebraic[32] = algebraic[17]-algebraic[31]
    rates[3] = algebraic[32]
    algebraic[33] = algebraic[31]-algebraic[18]
    rates[4] = algebraic[33]
    algebraic[8] = algebraic[1]+constants[33]*constants[46]
    algebraic[38] = algebraic[23]
    algebraic[39] = constants[31]*constants[2]*algebraic[38]
    algebraic[40] = algebraic[2]+constants[32]*constants[56]+algebraic[39]
    algebraic[41] = constants[23]*(exp(algebraic[8]/(constants[0]*constants[1]))-exp(algebraic[40]/(constants[0]*constants[1])))
    algebraic[42] = algebraic[16]-algebraic[41]
    rates[1] = algebraic[42]
    algebraic[43] = algebraic[41]-algebraic[17]
    rates[2] = algebraic[43]
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[0] = constants[0]*constants[1]*log(constants[10]*states[0])
    algebraic[6] = constants[52]+algebraic[0]
    algebraic[1] = constants[0]*constants[1]*log(constants[12]*states[1])
    algebraic[7] = algebraic[1]
    algebraic[16] = constants[22]*(exp(algebraic[6]/(constants[0]*constants[1]))-exp(algebraic[7]/(constants[0]*constants[1])))
    algebraic[5] = constants[0]*constants[1]*log(constants[20]*states[5])
    algebraic[14] = algebraic[5]
    algebraic[15] = algebraic[0]+constants[50]
    algebraic[19] = constants[27]*(exp(algebraic[14]/(constants[0]*constants[1]))-exp(algebraic[15]/(constants[0]*constants[1])))
    algebraic[21] = algebraic[19]-algebraic[16]
    algebraic[4] = constants[0]*constants[1]*log(constants[18]*states[4])
    algebraic[12] = algebraic[4]
    algebraic[13] = algebraic[5]+constants[32]*constants[58]
    algebraic[18] = constants[26]*(exp(algebraic[12]/(constants[0]*constants[1]))-exp(algebraic[13]/(constants[0]*constants[1])))
    algebraic[22] = algebraic[18]-algebraic[19]
    algebraic[2] = constants[0]*constants[1]*log(constants[14]*states[2])
    algebraic[9] = algebraic[2]
    algebraic[3] = constants[0]*constants[1]*log(constants[16]*states[3])
    algebraic[10] = algebraic[3]+constants[54]
    algebraic[17] = constants[24]*(exp(algebraic[9]/(constants[0]*constants[1]))-exp(algebraic[10]/(constants[0]*constants[1])))
    algebraic[11] = algebraic[3]
    algebraic[20] = states[6]
    algebraic[23] = algebraic[20]
    algebraic[26] = algebraic[23]
    algebraic[29] = constants[29]*constants[2]*algebraic[26]
    algebraic[30] = algebraic[4]+constants[33]*constants[48]+algebraic[29]
    algebraic[31] = constants[25]*(exp(algebraic[11]/(constants[0]*constants[1]))-exp(algebraic[30]/(constants[0]*constants[1])))
    algebraic[32] = algebraic[17]-algebraic[31]
    algebraic[33] = algebraic[31]-algebraic[18]
    algebraic[8] = algebraic[1]+constants[33]*constants[46]
    algebraic[38] = algebraic[23]
    algebraic[39] = constants[31]*constants[2]*algebraic[38]
    algebraic[40] = algebraic[2]+constants[32]*constants[56]+algebraic[39]
    algebraic[41] = constants[23]*(exp(algebraic[8]/(constants[0]*constants[1]))-exp(algebraic[40]/(constants[0]*constants[1])))
    algebraic[42] = algebraic[16]-algebraic[41]
    algebraic[43] = algebraic[41]-algebraic[17]
    algebraic[24] = algebraic[23]
    algebraic[25] = algebraic[23]
    algebraic[27] = constants[28]*constants[2]*algebraic[24]
    algebraic[28] = constants[30]*constants[2]*algebraic[25]
    algebraic[34] = algebraic[31]
    algebraic[35] = constants[28]*constants[2]*algebraic[34]
    algebraic[36] = algebraic[31]
    algebraic[37] = constants[29]*constants[2]*algebraic[36]
    algebraic[44] = algebraic[41]
    algebraic[45] = constants[30]*constants[2]*algebraic[44]
    algebraic[46] = algebraic[41]
    algebraic[47] = constants[31]*constants[2]*algebraic[46]
    algebraic[48] = algebraic[35]+algebraic[37]+algebraic[45]+algebraic[47]
    return algebraic

def solve_model():
    """Solve model with ODE solver"""
    from scipy.integrate import ode
    # Initialise constants and state variables
    (init_states, constants) = initConsts()

    # Set timespan to solve over
    voi = linspace(0, 10, 500)

    # Construct ODE object to solve
    r = ode(computeRates)
    r.set_integrator('vode', method='bdf', atol=1e-06, rtol=1e-06, max_step=1)
    r.set_initial_value(init_states, voi[0])
    r.set_f_params(constants)

    # Solve model
    states = array([[0.0] * len(voi)] * sizeStates)
    states[:,0] = init_states
    for (i,t) in enumerate(voi[1:]):
        if r.successful():
            r.integrate(t)
            states[:,i+1] = r.y
        else:
            break

    # Compute algebraic variables
    algebraic = computeAlgebraic(constants, states, voi)
    return (voi, states, algebraic)

def plot_model(voi, states, algebraic):
    """Plot variables against variable of integration"""
    import pylab
    (legend_states, legend_algebraic, legend_voi, legend_constants) = createLegends()
    pylab.figure(1)
    pylab.plot(voi,vstack((states,algebraic)).T)
    pylab.xlabel(legend_voi)
    pylab.legend(legend_states + legend_algebraic, loc='best')
    pylab.show()

if __name__ == "__main__":
    (voi, states, algebraic) = solve_model()
    plot_model(voi, states, algebraic)