# Size of variable arrays:
sizeAlgebraic = 9
sizeStates = 1
sizeConstants = 13
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 main (second)"
    legend_states[0] = "omega in component main (per_s)"
    legend_constants[0] = "omega_ref in component main (per_s)"
    legend_algebraic[0] = "logOmega in component main (dimensionless)"
    legend_constants[1] = "E_1 in component main (J_per_C2)"
    legend_constants[2] = "E_2 in component main (J_per_m2)"
    legend_constants[3] = "R_1 in component main (Js_per_C2)"
    legend_constants[4] = "R_2 in component main (Js_per_m2)"
    legend_constants[5] = "L_1 in component main (Js2_per_C2)"
    legend_constants[6] = "L_2 in component main (Js2_per_m2)"
    legend_constants[7] = "Bl in component main (Js_per_C_m)"
    legend_algebraic[1] = "x_1 in component main (J_per_m2)"
    legend_algebraic[2] = "x_2 in component main (J2_per_m4)"
    legend_constants[10] = "omega_3 in component main (per_s)"
    legend_constants[11] = "logOmega_3 in component main (dimensionless)"
    legend_algebraic[3] = "G_real in component main (Js_per_C2)"
    legend_algebraic[4] = "G_imag in component main (Js_per_C2)"
    legend_algebraic[5] = "amplitude in component main (Js_per_C2)"
    legend_constants[8] = "amplitude_ref in component main (Js_per_C2)"
    legend_algebraic[6] = "phase in component main (dimensionless)"
    legend_constants[9] = "phase_ref in component main (dimensionless)"
    legend_algebraic[7] = "phase_degrees in component main (dimensionless)"
    legend_algebraic[8] = "logAmplitude in component main (dimensionless)"
    legend_rates[0] = "d/dt omega in component main (per_s)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    states[0] = 0.1
    constants[0] = 1
    constants[1] = 0
    constants[2] = 2000
    constants[3] = 3.5
    constants[4] = 0.4
    constants[5] = 0.15
    constants[6] = 0.018
    constants[7] = 10
    constants[8] = 1
    constants[9] = 1
    constants[10] = power(constants[2]/constants[6], 1.0/2)
    constants[12] = 1.00000
    constants[11] = log(constants[10]/constants[0], 10)
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    rates[0] = constants[12]
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[0] = log(states[0]/constants[0], 10)
    algebraic[1] = constants[2]-(power(states[0], 2.00000))*constants[6]
    algebraic[2] = power(algebraic[1], 2.00000)+power(states[0]*constants[4], 2.00000)
    algebraic[3] = constants[3]+(constants[4]*(power(states[0]*constants[7], 2.00000)))/algebraic[2]
    algebraic[4] = states[0]*(constants[5]+((power(constants[7], 2.00000))*algebraic[1])/algebraic[2])
    algebraic[5] = power(power(algebraic[3], 2.00000)+power(algebraic[4], 2.00000), 1.0/2)
    algebraic[6] = arctan(algebraic[4]/algebraic[3])
    algebraic[7] = (algebraic[6]*180.000)/ pi
    algebraic[8] = log(algebraic[5]/constants[8], 10)
    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)