# Size of variable arrays:
sizeAlgebraic = 4
sizeStates = 2
sizeConstants = 3
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] = "q_1 in component main (metre)"
    legend_states[1] = "v_1 in component main (m_per_s)"
    legend_algebraic[3] = "a_1 in component main (m_per_s2)"
    legend_algebraic[0] = "u_C in component main (J_per_m)"
    legend_algebraic[1] = "u_R in component main (J_per_m)"
    legend_algebraic[2] = "u_L in component main (J_per_m)"
    legend_constants[0] = "C in component main (m2_per_J)"
    legend_constants[1] = "R in component main (Js_per_m2)"
    legend_constants[2] = "L in component main (Js2_per_m2)"
    legend_rates[0] = "d/dt q_1 in component main (metre)"
    legend_rates[1] = "d/dt v_1 in component main (m_per_s)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    states[0] = 1
    states[1] = 0
    constants[0] = 20
    constants[1] = 0.1
    constants[2] = 10
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    rates[0] = states[1]
    algebraic[0] = states[0]/constants[0]
    algebraic[1] = states[1]*constants[1]
    rootfind_0(voi, constants, rates, states, algebraic)
    rootfind_1(voi, constants, rates, states, algebraic)
    rates[1] = algebraic[3]
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[0] = states[0]/constants[0]
    algebraic[1] = states[1]*constants[1]
    return algebraic

initialGuess0 = None
def rootfind_0(voi, constants, states, algebraic):
    """Calculate value of algebraic variable for DAE"""
    from scipy.optimize import fsolve
    global initialGuess0
    if initialGuess0 is None: initialGuess0 = 0.1
    if not iterable(voi):
        algebraic[2] = fsolve(residualSN_0, initialGuess0, args=(algebraic, voi, constants, rates, states), xtol=1E-6)
        initialGuess0 = algebraic[2]
    else:
        for (i,t) in enumerate(voi):
            algebraic[2][i] = fsolve(residualSN_0, initialGuess0, args=(algebraic[:,i], voi[i], constants, rates, states[:,i]), xtol=1E-6)
            initialGuess0 = algebraic[2][i]

def residualSN_0(algebraicCandidate, algebraic, voi, constants, rates, states):
    algebraic[2] = algebraicCandidate
    return (algebraic[0]) - (-algebraic[1]-algebraic[2])

initialGuess1 = None
def rootfind_1(voi, constants, states, algebraic):
    """Calculate value of algebraic variable for DAE"""
    from scipy.optimize import fsolve
    global initialGuess1
    if initialGuess1 is None: initialGuess1 = 0.1
    if not iterable(voi):
        algebraic[3] = fsolve(residualSN_1, initialGuess1, args=(algebraic, voi, constants, rates, states), xtol=1E-6)
        initialGuess1 = algebraic[3]
    else:
        for (i,t) in enumerate(voi):
            algebraic[3][i] = fsolve(residualSN_1, initialGuess1, args=(algebraic[:,i], voi[i], constants, rates, states[:,i]), xtol=1E-6)
            initialGuess1 = algebraic[3][i]

def residualSN_1(algebraicCandidate, algebraic, voi, constants, rates, states):
    algebraic[3] = algebraicCandidate
    return (algebraic[2]) - (algebraic[3]*constants[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)