# Size of variable arrays:
sizeAlgebraic = 14
sizeStates = 4
sizeConstants = 46
from math import *
from numpy import *

def createLegends():
    legend_states = [""] * sizeStates
    legend_rates = [""] * sizeStates
    legend_algebraic = [""] * sizeAlgebraic
    legend_voi = ""
    legend_constants = [""] * sizeConstants
    legend_voi = "time in component environment (msec)"
    legend_algebraic[0] = "t_modulo in component environment (msec)"
    legend_constants[0] = "Acap in component general_parameters (cm2)"
    legend_constants[1] = "V_myo in component general_parameters (uL)"
    legend_constants[2] = "C_m in component general_parameters (uF_per_cm2)"
    legend_constants[3] = "F in component general_parameters (C_per_mmole)"
    legend_constants[4] = "T in component general_parameters (kelvin)"
    legend_constants[5] = "R in component general_parameters (J_per_K_per_mol)"
    legend_constants[6] = "CaM_tot in component general_parameters (uM)"
    legend_constants[7] = "Km_CaM in component general_parameters (uM)"
    legend_constants[8] = "Ca_o in component general_parameters (uM)"
    legend_constants[9] = "Na_o in component general_parameters (uM)"
    legend_constants[10] = "Ca_NSR in component general_parameters (uM)"
    legend_constants[11] = "J_leak in component general_parameters (uM_per_msec)"
    legend_algebraic[1] = "V in component action_potential (mV)"
    legend_constants[12] = "t1 in component action_potential (msec)"
    legend_constants[13] = "t2 in component action_potential (msec)"
    legend_constants[14] = "p in component action_potential (dimensionless)"
    legend_constants[15] = "A in component action_potential (mV)"
    legend_constants[16] = "A1 in component action_potential (msec)"
    legend_constants[17] = "rest in component action_potential (mV)"
    legend_algebraic[3] = "Ca_input in component calcium_input (uM_per_msec)"
    legend_algebraic[2] = "tcalcium in component calcium_input (msec)"
    legend_constants[18] = "Ca_tau1 in component calcium_input (msec)"
    legend_constants[19] = "Ca_tau2 in component calcium_input (msec)"
    legend_constants[20] = "Ca_pow in component calcium_input (dimensionless)"
    legend_constants[21] = "Ca_amp in component calcium_input (uM_per_msec)"
    legend_algebraic[4] = "INaCa in component NCX_current (uA_per_uF)"
    legend_constants[22] = "Na_i in component NCX_current (uM)"
    legend_constants[23] = "KmNa in component NCX_current (uM)"
    legend_constants[24] = "KmCa in component NCX_current (uM)"
    legend_constants[25] = "ksat in component NCX_current (dimensionless)"
    legend_constants[26] = "eta in component NCX_current (dimensionless)"
    legend_constants[27] = "kNaCa in component NCX_current (uA_per_uF)"
    legend_states[0] = "Ca_cyt in component differential_equations (uM)"
    legend_constants[28] = "SERCA_TOT in component serca_parameters (uM)"
    legend_constants[29] = "CaMKII_reg in component serca_parameters (dimensionless)"
    legend_constants[30] = "PKA_reg in component serca_parameters (dimensionless)"
    legend_constants[31] = "PSR in component serca_parameters (dimensionless)"
    legend_constants[32] = "Kmf_PLBKO in component serca_parameters (uM)"
    legend_constants[33] = "Kmf_PLB in component serca_parameters (uM)"
    legend_constants[34] = "Kmr_PLBKO in component serca_parameters (uM)"
    legend_constants[35] = "Kmr_PLB in component serca_parameters (uM)"
    legend_constants[36] = "PLB_tot in component serca_parameters (uM)"
    legend_constants[37] = "kplb_pos in component serca_parameters (per_msec)"
    legend_constants[38] = "kplb_neg in component serca_parameters (per_msec)"
    legend_algebraic[5] = "EC_50_fwd in component serca_parameters (uM)"
    legend_algebraic[6] = "EC_50_rev in component serca_parameters (uM)"
    legend_states[1] = "PLB_dephosph in component differential_equations (uM)"
    legend_constants[45] = "k_cyt_serca in component transition_parameters (per_uM2_per_msec)"
    legend_algebraic[7] = "k_serca_cyt in component transition_parameters (per_msec)"
    legend_constants[43] = "k_serca_sr in component transition_parameters (per_msec)"
    legend_algebraic[8] = "k_sr_serca in component transition_parameters (per_uM2_per_msec)"
    legend_constants[44] = "br_cyt_serca in component transition_parameters (per_uM2_per_msec)"
    legend_constants[39] = "br_serca_sr in component transition_parameters (per_msec)"
    legend_algebraic[12] = "J_up in component calcium_fluxes (uM_per_msec)"
    legend_algebraic[9] = "J_cyt_serca in component calcium_fluxes (uM_per_msec)"
    legend_algebraic[10] = "J_serca_sr in component calcium_fluxes (uM_per_msec)"
    legend_states[2] = "Ca_serca in component differential_equations (uM)"
    legend_constants[40] = "LTRPN_tot in component calcium_buffering (uM)"
    legend_constants[41] = "kltrpn_pos in component calcium_buffering (per_uM_per_msec)"
    legend_constants[42] = "kltrpn_neg in component calcium_buffering (per_msec)"
    legend_algebraic[13] = "J_LTRPN in component calcium_buffering (uM_per_msec)"
    legend_algebraic[11] = "B_i in component calcium_buffering (dimensionless)"
    legend_states[3] = "LTRPN in component differential_equations (uM)"
    legend_rates[0] = "d/dt Ca_cyt in component differential_equations (uM)"
    legend_rates[3] = "d/dt LTRPN in component differential_equations (uM)"
    legend_rates[1] = "d/dt PLB_dephosph in component differential_equations (uM)"
    legend_rates[2] = "d/dt Ca_serca in component differential_equations (uM)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    constants[0] = 1.534e-4
    constants[1] = 25.84e-6
    constants[2] = 1
    constants[3] = 96.5
    constants[4] = 298
    constants[5] = 8.314
    constants[6] = 24
    constants[7] = 2.38
    constants[8] = 1000
    constants[9] = 140000
    constants[10] = 760
    constants[11] = 0.0003
    constants[12] = 0.5
    constants[13] = 200
    constants[14] = 2
    constants[15] = 135
    constants[16] = 110
    constants[17] = -90
    constants[18] = 1.5
    constants[19] = 7.5
    constants[20] = 2
    constants[21] = 10
    constants[22] = 10000
    constants[23] = 87500
    constants[24] = 1380
    constants[25] = 0.1
    constants[26] = 0.35
    constants[27] = 950
    states[0] = 0.1
    constants[28] = 20
    constants[29] = 0.1
    constants[30] = 0.1
    constants[31] = 1
    constants[32] = 0.15
    constants[33] = 0.15
    constants[34] = 2500
    constants[35] = 1110
    constants[36] = 1
    constants[37] = 1
    constants[38] = 6.8
    states[1] = 0.1
    constants[39] = 0.00625
    states[2] = 5
    constants[40] = 70
    constants[41] = 0.1
    constants[42] = 0.06
    states[3] = 11
    constants[43] = constants[39]*(1.00000+0.700000*constants[29])
    constants[44] = 1000.00*constants[39]
    constants[45] = constants[44]*(1.00000+0.700000*constants[29])
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    rates[3] = constants[41]*states[0]*(constants[40]-states[3])-constants[42]*states[3]
    rates[1] = constants[37]*(constants[36]-states[1])-constants[38]*(power(constants[29]+constants[30], 2.00000))*states[1]
    algebraic[5] = (constants[32]+(constants[33]*constants[31]*states[1])/1.00000)*(1.00000+0.270000*constants[29])
    algebraic[7] = (power(algebraic[5], 2.00000))*constants[44]
    algebraic[9] = constants[45]*(power(states[0], 2.00000))*(constants[28]-states[2])-algebraic[7]*states[2]
    algebraic[6] = constants[34]-(constants[35]*constants[31]*states[1])/1.00000
    algebraic[8] = constants[39]/(power(algebraic[6], 2.00000))
    algebraic[10] = constants[43]*states[2]-algebraic[8]*(power(constants[10], 2.00000))*(constants[28]-states[2])
    rates[2] = algebraic[9]-algebraic[10]
    algebraic[0] =  voi % 1000.00
    algebraic[2] = custom_piecewise([less_equal(algebraic[0]-1.20000 , 0.00000), 0.00000 , True, algebraic[0]-1.20000])
    algebraic[3] = constants[21]*(power(1.00000-exp(-algebraic[2]/constants[18]), constants[20]))*exp(-algebraic[2]/constants[19])
    algebraic[1] = constants[17]+constants[15]*(power(1.00000-exp(-algebraic[0]/constants[12]), constants[14]))*exp(-algebraic[0]/constants[13])*(1.00000-(power(algebraic[0], 10.0000))/(power(constants[16], 10.0000)+power(algebraic[0], 10.0000)))
    algebraic[4] = (constants[27]/((power(constants[23], 3.00000)+power(constants[9], 3.00000))*(constants[24]+constants[8])*(1.00000+constants[25]*exp(((constants[26]-1.00000)*algebraic[1]*constants[3])/(constants[5]*constants[4])))))*(exp((constants[26]*algebraic[1]*constants[3])/(constants[5]*constants[4]))*(power(constants[22], 3.00000))*constants[8]-exp(((constants[26]-1.00000)*algebraic[1]*constants[3])/(constants[5]*constants[4]))*(power(constants[9], 3.00000))*states[0])
    algebraic[13] = constants[41]*states[0]*(constants[40]-states[3])-constants[42]*states[3]
    algebraic[11] = power(1.00000+(constants[6]*constants[7])/(power(constants[7]+states[0], 2.00000)), -1.00000)
    rates[0] = algebraic[11]*((((algebraic[4]*constants[0]*constants[2])/(2.00000*constants[1]*constants[3])-algebraic[9])+constants[11]+algebraic[3])-algebraic[13])
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[5] = (constants[32]+(constants[33]*constants[31]*states[1])/1.00000)*(1.00000+0.270000*constants[29])
    algebraic[7] = (power(algebraic[5], 2.00000))*constants[44]
    algebraic[9] = constants[45]*(power(states[0], 2.00000))*(constants[28]-states[2])-algebraic[7]*states[2]
    algebraic[6] = constants[34]-(constants[35]*constants[31]*states[1])/1.00000
    algebraic[8] = constants[39]/(power(algebraic[6], 2.00000))
    algebraic[10] = constants[43]*states[2]-algebraic[8]*(power(constants[10], 2.00000))*(constants[28]-states[2])
    algebraic[0] =  voi % 1000.00
    algebraic[2] = custom_piecewise([less_equal(algebraic[0]-1.20000 , 0.00000), 0.00000 , True, algebraic[0]-1.20000])
    algebraic[3] = constants[21]*(power(1.00000-exp(-algebraic[2]/constants[18]), constants[20]))*exp(-algebraic[2]/constants[19])
    algebraic[1] = constants[17]+constants[15]*(power(1.00000-exp(-algebraic[0]/constants[12]), constants[14]))*exp(-algebraic[0]/constants[13])*(1.00000-(power(algebraic[0], 10.0000))/(power(constants[16], 10.0000)+power(algebraic[0], 10.0000)))
    algebraic[4] = (constants[27]/((power(constants[23], 3.00000)+power(constants[9], 3.00000))*(constants[24]+constants[8])*(1.00000+constants[25]*exp(((constants[26]-1.00000)*algebraic[1]*constants[3])/(constants[5]*constants[4])))))*(exp((constants[26]*algebraic[1]*constants[3])/(constants[5]*constants[4]))*(power(constants[22], 3.00000))*constants[8]-exp(((constants[26]-1.00000)*algebraic[1]*constants[3])/(constants[5]*constants[4]))*(power(constants[9], 3.00000))*states[0])
    algebraic[13] = constants[41]*states[0]*(constants[40]-states[3])-constants[42]*states[3]
    algebraic[11] = power(1.00000+(constants[6]*constants[7])/(power(constants[7]+states[0], 2.00000)), -1.00000)
    algebraic[12] = algebraic[9]-algebraic[10]
    return algebraic

def custom_piecewise(cases):
    """Compute result of a piecewise function"""
    return select(cases[0::2],cases[1::2])

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)