# Size of variable arrays:
sizeAlgebraic = 5
sizeStates = 2
sizeConstants = 7
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 (second)"
    legend_algebraic[0] = "kappa_L1 in component rate_constants (per_second)"
    legend_constants[0] = "kappa_P1 in component rate_constants (per_second)"
    legend_algebraic[2] = "kappa_L2 in component rate_constants (per_second)"
    legend_constants[1] = "kappa_P2 in component rate_constants (per_second)"
    legend_constants[2] = "kappa_L2_0 in component rate_constants (per_second)"
    legend_constants[3] = "kappa_L2_1 in component rate_constants (per_second)"
    legend_algebraic[1] = "Kd_Ca in component rate_constants (nanomolar)"
    legend_constants[4] = "n in component rate_constants (dimensionless)"
    legend_states[0] = "Ca_i in component cytosolic_calcium (nanomolar)"
    legend_constants[5] = "Ca_o in component cytosolic_calcium (nanomolar)"
    legend_algebraic[3] = "Ca_i_ss in component cytosolic_calcium (nanomolar)"
    legend_constants[6] = "gamma in component cytosolic_calcium (dimensionless)"
    legend_states[1] = "Ca_s in component subspace_calcium (nanomolar)"
    legend_algebraic[4] = "Ca_s_ss in component subspace_calcium (nanomolar)"
    legend_rates[0] = "d/dt Ca_i in component cytosolic_calcium (nanomolar)"
    legend_rates[1] = "d/dt Ca_s in component subspace_calcium (nanomolar)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    constants[0] = 0.132
    constants[1] = 3.78
    constants[2] = 0.054
    constants[3] = 2.4
    constants[4] = 3
    states[0] = 75
    constants[5] = 2000000.0
    constants[6] = 0.24
    states[1] = 5300.0
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    algebraic[0] = custom_piecewise([greater_equal(voi , 0.00000) & less(voi , 40.0000), 5.00000e-06 , True, 2.00000e-05])
    algebraic[1] = custom_piecewise([greater_equal(voi , 0.00000) & less(voi , 80.0000), 1.00000 , True, 0.500000])
    algebraic[2] = constants[2]+constants[3]/(1.00000+power((1000.00*algebraic[1])/states[0], constants[4]))
    rates[0] = -(algebraic[0]+constants[0]+constants[6]*(algebraic[2]+constants[1]))*states[0]+constants[6]*algebraic[2]*states[1]+algebraic[0]*constants[5]
    rates[1] = (algebraic[2]+constants[1])*states[0]-algebraic[2]*states[1]
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[0] = custom_piecewise([greater_equal(voi , 0.00000) & less(voi , 40.0000), 5.00000e-06 , True, 2.00000e-05])
    algebraic[1] = custom_piecewise([greater_equal(voi , 0.00000) & less(voi , 80.0000), 1.00000 , True, 0.500000])
    algebraic[2] = constants[2]+constants[3]/(1.00000+power((1000.00*algebraic[1])/states[0], constants[4]))
    algebraic[3] = constants[5]/(1.00000+constants[0]/algebraic[0])
    algebraic[4] = algebraic[3]*(1.00000+constants[1]/algebraic[2])
    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)