# Size of variable arrays:
sizeAlgebraic = 2
sizeStates = 1
sizeConstants = 17
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_constants[0] = "Ca_cyt in component general_parameters (uM)"
    legend_constants[1] = "Ca_NSR in component general_parameters (uM)"
    legend_constants[2] = "CaMKII_reg in component general_parameters (dimensionless)"
    legend_constants[3] = "SERCA_TOT in component serca_parameters (uM)"
    legend_constants[4] = "PSR in component serca_parameters (dimensionless)"
    legend_constants[5] = "Kmf_PLBKO in component serca_parameters (uM)"
    legend_constants[6] = "Kmf_PLB in component serca_parameters (uM)"
    legend_constants[7] = "Kmr_PLBKO in component serca_parameters (uM)"
    legend_constants[8] = "Kmr_PLB in component serca_parameters (uM)"
    legend_constants[12] = "EC_50_fwd in component serca_parameters (uM)"
    legend_constants[10] = "EC_50_rev in component serca_parameters (uM)"
    legend_constants[15] = "k_cyt_serca in component transition_parameters (per_msec_per_uM2)"
    legend_constants[16] = "k_serca_cyt in component transition_parameters (per_msec)"
    legend_constants[11] = "k_serca_sr in component transition_parameters (per_msec)"
    legend_constants[13] = "k_sr_serca in component transition_parameters (per_msec_per_uM2)"
    legend_constants[14] = "br_cyt_serca in component transition_parameters (per_msec_per_uM2)"
    legend_constants[9] = "br_serca_sr in component transition_parameters (per_msec)"
    legend_algebraic[0] = "J_cyt_serca in component calcium_fluxes (uM_per_msec)"
    legend_algebraic[1] = "J_serca_sr in component calcium_fluxes (uM_per_msec)"
    legend_states[0] = "Ca_serca in component calcium_bound_serca (uM)"
    legend_rates[0] = "d/dt Ca_serca in component calcium_bound_serca (uM)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    constants[0] = 0.25
    constants[1] = 760
    constants[2] = 0
    constants[3] = 47
    constants[4] = 1
    constants[5] = 0.15
    constants[6] = 0.15
    constants[7] = 2500
    constants[8] = 1110
    constants[9] = 0.00625
    states[0] = 12
    constants[10] = constants[7]-constants[8]*constants[4]
    constants[11] = constants[9]*(1.00000+0.700000*constants[2])
    constants[12] = (constants[5]+constants[6]*constants[4])*(1.00000+0.270000*constants[2])
    constants[13] = constants[9]/(power(constants[10], 2.00000))
    constants[14] = 1000.00*constants[9]
    constants[15] = constants[14]*(1.00000+0.700000*constants[2])
    constants[16] = (power(constants[12], 2.00000))*constants[14]
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    algebraic[0] = constants[15]*(power(constants[0], 2.00000))*(constants[3]-states[0])-constants[16]*states[0]
    algebraic[1] = constants[11]*states[0]-constants[13]*(power(constants[1], 2.00000))*(constants[3]-states[0])
    rates[0] = algebraic[0]-algebraic[1]
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[0] = constants[15]*(power(constants[0], 2.00000))*(constants[3]-states[0])-constants[16]*states[0]
    algebraic[1] = constants[11]*states[0]-constants[13]*(power(constants[1], 2.00000))*(constants[3]-states[0])
    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)