# Size of variable arrays:
sizeAlgebraic = 39
sizeStates = 11
sizeConstants = 48
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_constants[0] = "q_Cai_init in component environment (fmol)"
    legend_constants[1] = "q_TRPN_init in component environment (fmol)"
    legend_constants[2] = "q_Ca_TRPN_init in component environment (fmol)"
    legend_constants[3] = "q_B_init in component environment (fmol)"
    legend_constants[4] = "q_U_init in component environment (fmol)"
    legend_constants[5] = "q_W_init in component environment (fmol)"
    legend_constants[6] = "q_S_init in component environment (fmol)"
    legend_algebraic[2] = "q_TRPN in component environment (fmol)"
    legend_algebraic[5] = "q_Cai in component environment (fmol)"
    legend_algebraic[8] = "q_Ca_TRPN in component environment (fmol)"
    legend_algebraic[9] = "q_B in component environment (fmol)"
    legend_algebraic[10] = "q_U in component environment (fmol)"
    legend_algebraic[11] = "q_W in component environment (fmol)"
    legend_algebraic[12] = "q_S in component environment (fmol)"
    legend_states[0] = "q_TRPN in component crossbridge_TRPN (fmol)"
    legend_states[1] = "q_Cai in component crossbridge_TRPN (fmol)"
    legend_states[2] = "q_Ca_TRPN in component crossbridge_TRPN (fmol)"
    legend_states[3] = "q_B in component crossbridge_TRPN (fmol)"
    legend_states[4] = "q_U in component crossbridge_TRPN (fmol)"
    legend_states[5] = "q_W in component crossbridge_TRPN (fmol)"
    legend_states[6] = "q_S in component crossbridge_TRPN (fmol)"
    legend_algebraic[35] = "T_total in component crossbridge_TRPN (kPa)"
    legend_states[7] = "SL in component crossbridge_TRPN (metre)"
    legend_constants[7] = "kappa_R_TRPNCa in component crossbridge_TRPN_parameters (fmol_per_sec)"
    legend_constants[8] = "kappa_R_BU in component crossbridge_TRPN_parameters (fmol_per_sec)"
    legend_constants[9] = "kappa_R_UW in component crossbridge_TRPN_parameters (fmol_per_sec)"
    legend_constants[10] = "kappa_R_WS in component crossbridge_TRPN_parameters (fmol_per_sec)"
    legend_constants[11] = "kappa_R_SU in component crossbridge_TRPN_parameters (fmol_per_sec)"
    legend_constants[12] = "K_TRPN in component crossbridge_TRPN_parameters (per_fmol)"
    legend_constants[13] = "K_Cai in component crossbridge_TRPN_parameters (per_fmol)"
    legend_constants[14] = "K_Ca_TRPN in component crossbridge_TRPN_parameters (per_fmol)"
    legend_constants[15] = "K_B in component crossbridge_TRPN_parameters (per_fmol)"
    legend_constants[16] = "K_U in component crossbridge_TRPN_parameters (per_fmol)"
    legend_constants[17] = "K_W in component crossbridge_TRPN_parameters (per_fmol)"
    legend_constants[18] = "K_S in component crossbridge_TRPN_parameters (per_fmol)"
    legend_constants[19] = "R in component constants (J_per_K_per_mol)"
    legend_constants[20] = "T in component constants (kelvin)"
    legend_constants[21] = "n_Tm in component crossbridge_TRPN (dimensionless)"
    legend_algebraic[13] = "mu_TRPN in component crossbridge_TRPN (J_per_mol)"
    legend_algebraic[14] = "mu_Cai in component crossbridge_TRPN (J_per_mol)"
    legend_algebraic[15] = "mu_Ca_TRPN in component crossbridge_TRPN (J_per_mol)"
    legend_algebraic[16] = "mu_B in component crossbridge_TRPN (J_per_mol)"
    legend_algebraic[18] = "mu_U in component crossbridge_TRPN (J_per_mol)"
    legend_algebraic[20] = "mu_W in component crossbridge_TRPN (J_per_mol)"
    legend_algebraic[22] = "mu_S in component crossbridge_TRPN (J_per_mol)"
    legend_algebraic[38] = "v_R_TRPNCa in component crossbridge_TRPN (fmol_per_sec)"
    legend_algebraic[24] = "v_R_BU in component crossbridge_TRPN (fmol_per_sec)"
    legend_algebraic[30] = "v_R_UW in component crossbridge_TRPN (fmol_per_sec)"
    legend_algebraic[32] = "v_R_WS in component crossbridge_TRPN (fmol_per_sec)"
    legend_algebraic[34] = "v_R_SU in component crossbridge_TRPN (fmol_per_sec)"
    legend_algebraic[36] = "tension in component crossbridge_TRPN (N_per_mm2)"
    legend_algebraic[37] = "mu_tension in component crossbridge_TRPN (J_per_mol)"
    legend_constants[22] = "kf_coeff in component crossbridge_TRPN (dimensionless)"
    legend_constants[43] = "n in component crossbridge_TRPN (J_per_mol)"
    legend_constants[23] = "hh in component crossbridge_TRPN (mm2_per_N)"
    legend_constants[24] = "SL_0 in component crossbridge_TRPN (metre)"
    legend_constants[25] = "q_MS in component crossbridge_TRPN (fmol)"
    legend_constants[26] = "r_s in component crossbridge_TRPN (dimensionless)"
    legend_constants[27] = "r_w in component crossbridge_TRPN (dimensionless)"
    legend_constants[28] = "A_eff in component crossbridge_TRPN (dimensionless)"
    legend_constants[29] = "phi in component crossbridge_TRPN (dimensionless)"
    legend_constants[30] = "k_uw in component crossbridge_TRPN (per_sec)"
    legend_constants[31] = "k_ws in component crossbridge_TRPN (per_sec)"
    legend_states[8] = "G_w in component crossbridge_TRPN (metre)"
    legend_states[9] = "G_s in component crossbridge_TRPN (metre)"
    legend_constants[40] = "c_w in component crossbridge_TRPN (per_sec)"
    legend_constants[41] = "c_s in component crossbridge_TRPN (per_sec)"
    legend_constants[42] = "A_w in component crossbridge_TRPN (dimensionless)"
    legend_constants[44] = "A_s in component crossbridge_TRPN (dimensionless)"
    legend_algebraic[3] = "mu_1 in component crossbridge_TRPN (J_per_m)"
    legend_constants[45] = "mu_2 in component crossbridge_TRPN (J_per_m)"
    legend_algebraic[0] = "mu_3 in component crossbridge_TRPN (J_per_m)"
    legend_algebraic[4] = "mu_4 in component crossbridge_TRPN (J_per_m)"
    legend_constants[46] = "mu_5 in component crossbridge_TRPN (J_per_m)"
    legend_algebraic[1] = "mu_6 in component crossbridge_TRPN (J_per_m)"
    legend_algebraic[6] = "v_1 in component crossbridge_TRPN (m_per_s)"
    legend_constants[32] = "v_2 in component crossbridge_TRPN (m_per_s)"
    legend_algebraic[7] = "v_4 in component crossbridge_TRPN (m_per_s)"
    legend_constants[33] = "v_to_mu in component crossbridge_TRPN (Js_per_m2)"
    legend_algebraic[23] = "T_active in component crossbridge_TRPN (kPa)"
    legend_constants[34] = "T_ref in component crossbridge_TRPN (kPa)"
    legend_algebraic[21] = "mu_T_a in component crossbridge_TRPN (kPa)"
    legend_algebraic[17] = "mu_T_S in component crossbridge_TRPN (kPa)"
    legend_algebraic[19] = "mu_T_W in component crossbridge_TRPN (kPa)"
    legend_states[10] = "Cdd in component crossbridge_TRPN (metre)"
    legend_algebraic[25] = "eta in component crossbridge_TRPN (per_sec)"
    legend_constants[35] = "eta_l in component crossbridge_TRPN (per_sec)"
    legend_constants[36] = "eta_s in component crossbridge_TRPN (per_sec)"
    legend_constants[37] = "k in component crossbridge_TRPN (dimensionless)"
    legend_constants[38] = "alpha in component crossbridge_TRPN (kPa)"
    legend_algebraic[29] = "v_Cdd in component crossbridge_TRPN (m_per_s)"
    legend_algebraic[26] = "mu_d in component crossbridge_TRPN (J_per_m)"
    legend_algebraic[27] = "mu_k in component crossbridge_TRPN (J_per_m)"
    legend_algebraic[28] = "mu_f in component crossbridge_TRPN (J_per_m)"
    legend_algebraic[31] = "mu_T_passive in component crossbridge_TRPN (kPa)"
    legend_algebraic[33] = "T_passive in component crossbridge_TRPN (kPa)"
    legend_constants[39] = "F in component constants (C_per_mol)"
    legend_rates[1] = "d/dt q_Cai in component crossbridge_TRPN (fmol)"
    legend_rates[0] = "d/dt q_TRPN in component crossbridge_TRPN (fmol)"
    legend_rates[2] = "d/dt q_Ca_TRPN in component crossbridge_TRPN (fmol)"
    legend_rates[3] = "d/dt q_B in component crossbridge_TRPN (fmol)"
    legend_rates[4] = "d/dt q_U in component crossbridge_TRPN (fmol)"
    legend_rates[5] = "d/dt q_W in component crossbridge_TRPN (fmol)"
    legend_rates[6] = "d/dt q_S in component crossbridge_TRPN (fmol)"
    legend_rates[8] = "d/dt G_w in component crossbridge_TRPN (metre)"
    legend_rates[7] = "d/dt SL in component crossbridge_TRPN (metre)"
    legend_rates[9] = "d/dt G_s in component crossbridge_TRPN (metre)"
    legend_rates[10] = "d/dt Cdd in component crossbridge_TRPN (metre)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    constants[0] = 6.82e-1
    constants[1] = 2.57
    constants[2] = 1e-6
    constants[3] = 1
    constants[4] = 0
    constants[5] = 0
    constants[6] = 0
    states[0] = 1e-16
    states[1] = 1e-16
    states[2] = 1e-16
    states[3] = 1e-16
    states[4] = 1e-16
    states[5] = 1e-16
    states[6] = 1e-16
    states[7] = 1e-6
    constants[7] = 52.0453
    constants[8] = 2.90875
    constants[9] = 0.332501
    constants[10] = 0.00782356
    constants[11] = 140824
    constants[12] = 1.27424
    constants[13] = 1.27424
    constants[14] = 0.11171
    constants[15] = 6.06164
    constants[16] = 2.27312
    constants[17] = 14.8627
    constants[18] = 3.71567e-06
    constants[19] = 8.31
    constants[20] = 310
    constants[21] = 1.1
    constants[22] = -0.0118
    constants[23] = 1
    constants[24] = 2e-6
    constants[25] = 1e-6
    constants[26] = 0.25
    constants[27] = 0.5
    constants[28] = 25
    constants[29] = 2.23
    constants[30] = 26
    constants[31] = 4
    states[8] = 1e-6
    states[9] = 1e-6
    constants[32] = 0
    constants[33] = 1
    constants[34] = 40.5
    states[10] = 0
    constants[35] = 200e3
    constants[36] = 200e3
    constants[37] = 7
    constants[38] = 2.1
    constants[39] = 96485
    constants[40] = (constants[29]*constants[30]*(1.00000-constants[27]))/constants[27]
    constants[41] = (constants[29]*constants[31]*(1.00000-constants[26])*constants[27])/constants[26]
    constants[42] = (constants[28]*constants[26])/((1.00000-constants[26])*constants[27]+constants[26])
    constants[43] = constants[22]*constants[19]*constants[20]
    constants[47] = constants[32]
    constants[44] = constants[42]
    constants[45] = -constants[42]*constants[32]*constants[33]
    constants[46] = -constants[44]*constants[32]*constants[33]
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    rates[7] = constants[47]
    algebraic[0] = constants[40]*states[8]*constants[33]
    algebraic[3] = -constants[45]-algebraic[0]
    algebraic[6] = algebraic[3]/constants[33]
    rates[8] = algebraic[6]
    algebraic[1] = constants[41]*states[9]*constants[33]
    algebraic[4] = -constants[46]-algebraic[1]
    algebraic[7] = algebraic[4]/constants[33]
    rates[9] = algebraic[7]
    algebraic[8] = states[2]+constants[2]
    algebraic[15] = constants[19]*constants[20]*log(constants[14]*algebraic[8])
    algebraic[9] = states[3]+constants[3]
    algebraic[16] = constants[19]*constants[20]*log(constants[15]*algebraic[9])
    algebraic[10] = states[4]+constants[4]
    algebraic[18] = constants[19]*constants[20]*log(constants[16]*algebraic[10])
    algebraic[24] = constants[8]*(exp((algebraic[16]+constants[21]*algebraic[15])/(constants[19]*constants[20]))-exp((algebraic[18]+constants[21]*algebraic[15])/(constants[19]*constants[20])))
    rates[3] = -algebraic[24]
    rootfind_0(voi, constants, rates, states, algebraic)
    algebraic[29] = algebraic[26]/constants[33]
    rates[10] = algebraic[29]
    algebraic[11] = states[5]+constants[5]
    algebraic[20] = constants[19]*constants[20]*log(constants[17]*algebraic[11])
    algebraic[30] = constants[9]*(exp(algebraic[18]/(constants[19]*constants[20]))-exp(algebraic[20]/(constants[19]*constants[20])))
    algebraic[12] = states[6]+constants[6]
    algebraic[22] = constants[19]*constants[20]*log(constants[18]*algebraic[12])
    algebraic[32] = constants[10]*(exp(algebraic[20]/(constants[19]*constants[20]))-exp(algebraic[22]/(constants[19]*constants[20])))
    rates[5] = algebraic[30]-algebraic[32]
    algebraic[34] = constants[11]*(exp(algebraic[22]/(constants[19]*constants[20]))-exp(algebraic[18]/(constants[19]*constants[20])))
    rates[4] = (algebraic[24]-algebraic[30])+algebraic[34]
    rates[6] = algebraic[32]-algebraic[34]
    algebraic[2] = states[0]+constants[1]
    algebraic[13] = constants[19]*constants[20]*log(constants[12]*algebraic[2])
    algebraic[5] = states[1]+constants[0]
    algebraic[14] = constants[19]*constants[20]*log(constants[13]*algebraic[5])
    algebraic[17] = (constants[34]/(constants[24]*constants[25]*constants[26]))*states[6]*(states[9]+constants[24])
    algebraic[19] = (constants[34]/(constants[24]*constants[25]*constants[26]))*states[5]*states[8]
    algebraic[21] = algebraic[17]+algebraic[19]
    algebraic[23] = algebraic[21]
    algebraic[31] = ((constants[38]*algebraic[25])/constants[24])*algebraic[29]
    algebraic[33] = algebraic[31]
    algebraic[35] = algebraic[23]+algebraic[33]
    algebraic[36] = algebraic[35]*1000.00
    algebraic[37] = constants[23]*constants[43]*algebraic[36]
    algebraic[38] = constants[7]*(exp((algebraic[14]+algebraic[13])/(constants[19]*constants[20]))-exp((algebraic[15]+algebraic[37])/(constants[19]*constants[20])))
    rates[1] = -algebraic[38]
    rates[0] = -algebraic[38]
    rates[2] = algebraic[38]
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[0] = constants[40]*states[8]*constants[33]
    algebraic[3] = -constants[45]-algebraic[0]
    algebraic[6] = algebraic[3]/constants[33]
    algebraic[1] = constants[41]*states[9]*constants[33]
    algebraic[4] = -constants[46]-algebraic[1]
    algebraic[7] = algebraic[4]/constants[33]
    algebraic[8] = states[2]+constants[2]
    algebraic[15] = constants[19]*constants[20]*log(constants[14]*algebraic[8])
    algebraic[9] = states[3]+constants[3]
    algebraic[16] = constants[19]*constants[20]*log(constants[15]*algebraic[9])
    algebraic[10] = states[4]+constants[4]
    algebraic[18] = constants[19]*constants[20]*log(constants[16]*algebraic[10])
    algebraic[24] = constants[8]*(exp((algebraic[16]+constants[21]*algebraic[15])/(constants[19]*constants[20]))-exp((algebraic[18]+constants[21]*algebraic[15])/(constants[19]*constants[20])))
    algebraic[29] = algebraic[26]/constants[33]
    algebraic[11] = states[5]+constants[5]
    algebraic[20] = constants[19]*constants[20]*log(constants[17]*algebraic[11])
    algebraic[30] = constants[9]*(exp(algebraic[18]/(constants[19]*constants[20]))-exp(algebraic[20]/(constants[19]*constants[20])))
    algebraic[12] = states[6]+constants[6]
    algebraic[22] = constants[19]*constants[20]*log(constants[18]*algebraic[12])
    algebraic[32] = constants[10]*(exp(algebraic[20]/(constants[19]*constants[20]))-exp(algebraic[22]/(constants[19]*constants[20])))
    algebraic[34] = constants[11]*(exp(algebraic[22]/(constants[19]*constants[20]))-exp(algebraic[18]/(constants[19]*constants[20])))
    algebraic[2] = states[0]+constants[1]
    algebraic[13] = constants[19]*constants[20]*log(constants[12]*algebraic[2])
    algebraic[5] = states[1]+constants[0]
    algebraic[14] = constants[19]*constants[20]*log(constants[13]*algebraic[5])
    algebraic[17] = (constants[34]/(constants[24]*constants[25]*constants[26]))*states[6]*(states[9]+constants[24])
    algebraic[19] = (constants[34]/(constants[24]*constants[25]*constants[26]))*states[5]*states[8]
    algebraic[21] = algebraic[17]+algebraic[19]
    algebraic[23] = algebraic[21]
    algebraic[31] = ((constants[38]*algebraic[25])/constants[24])*algebraic[29]
    algebraic[33] = algebraic[31]
    algebraic[35] = algebraic[23]+algebraic[33]
    algebraic[36] = algebraic[35]*1000.00
    algebraic[37] = constants[23]*constants[43]*algebraic[36]
    algebraic[38] = constants[7]*(exp((algebraic[14]+algebraic[13])/(constants[19]*constants[20]))-exp((algebraic[15]+algebraic[37])/(constants[19]*constants[20])))
    return algebraic

initialGuess0 = None
def rootfind_0(voi, constants, rates, states, algebraic):
    """Calculate values of algebraic variables for DAE"""
    from scipy.optimize import fsolve
    global initialGuess0
    if initialGuess0 is None: initialGuess0 = ones(4)*0.1
    if not iterable(voi):
        soln = fsolve(residualSN_0, initialGuess0, args=(algebraic, voi, constants, rates, states), xtol=1E-6)
        initialGuess0 = soln
        algebraic[25] = soln[0]
        algebraic[26] = soln[1]
        algebraic[27] = soln[2]
        algebraic[28] = soln[3]
    else:
        for (i,t) in enumerate(voi):
            soln = fsolve(residualSN_0, initialGuess0, args=(algebraic[:,i], voi[i], constants, rates[:i], states[:,i]), xtol=1E-6)
            initialGuess0 = soln
            algebraic[25][i] = soln[0]
            algebraic[26][i] = soln[1]
            algebraic[27][i] = soln[2]
            algebraic[28][i] = soln[3]

def residualSN_0(algebraicCandidate, algebraic, voi, constants, rates, states):
    resid = array([0.0] * 4)
    algebraic[25] = algebraicCandidate[0]
    algebraic[26] = algebraicCandidate[1]
    algebraic[27] = algebraicCandidate[2]
    algebraic[28] = algebraicCandidate[3]
    resid[0] = (algebraic[25]-(custom_piecewise([greater(algebraic[26] , 0.00000), constants[35] , True, constants[36]])))
    resid[1] = (algebraic[27]-(constants[37]/algebraic[25])*states[10]*constants[33])
    resid[2] = (algebraic[28]-(constants[37]/algebraic[25])*(states[7]-constants[24])*constants[33])
    resid[3] = (algebraic[26]-(-algebraic[27]+algebraic[28]))
    return resid

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)