# Size of variable arrays:
sizeAlgebraic = 0
sizeStates = 0
sizeConstants = 18
from math import *
from numpy import *

def createLegends():
    legend_states = [""] * sizeStates
    legend_rates = [""] * sizeStates
    legend_algebraic = [""] * sizeAlgebraic
    legend_voi = ""
    legend_constants = [""] * sizeConstants
    legend_constants[0] = "E11 in component interface (strain)"
    legend_constants[1] = "E22 in component interface (strain)"
    legend_constants[2] = "E33 in component interface (strain)"
    legend_constants[3] = "E12 in component interface (strain)"
    legend_constants[4] = "E13 in component interface (strain)"
    legend_constants[5] = "E23 in component interface (strain)"
    legend_constants[6] = "c1 in component interface (strain)"
    legend_constants[7] = "c2 in component interface (strain)"
    legend_constants[8] = "c3 in component interface (strain)"
    legend_constants[9] = "c4 in component interface (strain)"
    legend_constants[10] = "c5 in component interface (strain)"
    legend_constants[12] = "Tdev11 in component equations (stress)"
    legend_constants[13] = "Tdev22 in component equations (stress)"
    legend_constants[14] = "Tdev33 in component equations (stress)"
    legend_constants[15] = "Tdev12 in component equations (stress)"
    legend_constants[16] = "Tdev13 in component equations (stress)"
    legend_constants[17] = "Tdev23 in component equations (stress)"
    legend_constants[11] = "Q in component equations (strain)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    constants[0] = 0
    constants[1] = 0
    constants[2] = 0
    constants[3] = 0
    constants[4] = 0
    constants[5] = 0
    constants[6] = 0.88
    constants[7] = 0
    constants[8] = 18.5
    constants[9] = 3.58
    constants[10] = 3.26
    constants[11] = 2.00000*constants[7]*(constants[0]+constants[1]+constants[2])+constants[8]*(power(constants[0], 2.00000))+constants[9]*(power(constants[2], 2.00000)+power(constants[1], 2.00000)+(power(constants[5], 2.00000))*2.00000)+2.00000*constants[10]*(power(constants[4], 2.00000)+power(constants[3], 2.00000))
    constants[12] = constants[6]*exp(constants[11])*(constants[7]+constants[8]*constants[0])
    constants[13] = constants[6]*exp(constants[11])*(constants[7]+constants[9]*constants[1])
    constants[14] = constants[6]*exp(constants[11])*(constants[7]+constants[9]*constants[2])
    constants[15] = constants[6]*exp(constants[11])*constants[10]*constants[3]
    constants[16] = constants[6]*exp(constants[11])*constants[10]*constants[4]
    constants[17] = constants[6]*exp(constants[11])*constants[9]*constants[5]
    return (states, constants)

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

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