Generated Code

# Size of variable arrays:
sizeAlgebraic = 27
sizeStates = 6
sizeConstants = 27
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] = "C_m in component environment (fF)"
    legend_states[0] = "q_Ca_o in component environment (fmol)"
    legend_states[1] = "q_Ca_i in component environment (fmol)"
    legend_states[2] = "q_s00_TCC in component environment (fmol)"
    legend_states[3] = "q_s10_TCC in component environment (fmol)"
    legend_states[4] = "q_s01_TCC in component environment (fmol)"
    legend_states[5] = "q_s11_TCC in component environment (fmol)"
    legend_constants[1] = "q_mem in component environment (fC)"
    legend_constants[23] = "V_mem in component environment (volt)"
    legend_constants[2] = "R in component environment (J_per_K_per_mol)"
    legend_constants[3] = "T in component environment (kelvin)"
    legend_constants[4] = "F in component environment (C_per_mol)"
    legend_algebraic[18] = "v_TCC in component TCC (fmol_per_sec)"
    legend_algebraic[24] = "I_mem_TCC in component TCC (fA)"
    legend_constants[24] = "I_stim in component environment (fA)"
    legend_constants[5] = "stimPeriod in component environment (second)"
    legend_constants[6] = "stimDuration in component environment (second)"
    legend_algebraic[0] = "tPeriod in component environment (second)"
    legend_constants[7] = "kappa_TCC in component TCC_parameters (fmol_per_sec)"
    legend_constants[8] = "kappa_R1_TCC in component TCC_parameters (fmol_per_sec)"
    legend_constants[9] = "kappa_R2_TCC in component TCC_parameters (fmol_per_sec)"
    legend_constants[10] = "kappa_R3_TCC in component TCC_parameters (fmol_per_sec)"
    legend_constants[11] = "kappa_R4_TCC in component TCC_parameters (fmol_per_sec)"
    legend_constants[12] = "K_Ca_i in component TCC_parameters (per_fmol)"
    legend_constants[13] = "K_Ca_o in component TCC_parameters (per_fmol)"
    legend_constants[14] = "K_S00_TCC in component TCC_parameters (per_fmol)"
    legend_constants[15] = "K_S10_TCC in component TCC_parameters (per_fmol)"
    legend_constants[16] = "K_S01_TCC in component TCC_parameters (per_fmol)"
    legend_constants[17] = "K_S11_TCC in component TCC_parameters (per_fmol)"
    legend_constants[18] = "zCa in component TCC_parameters (dimensionless)"
    legend_constants[19] = "z_df in component TCC_parameters (dimensionless)"
    legend_constants[20] = "z_ff in component TCC_parameters (dimensionless)"
    legend_constants[21] = "z_dr in component TCC_parameters (dimensionless)"
    legend_constants[22] = "z_fr in component TCC_parameters (dimensionless)"
    legend_algebraic[1] = "u_Ca_i in component TCC (J_per_mol)"
    legend_algebraic[2] = "u_Ca_o in component TCC (J_per_mol)"
    legend_constants[25] = "V_mem in component TCC (J_per_C)"
    legend_constants[26] = "Am_TCC in component TCC (J_per_mol)"
    legend_algebraic[16] = "Af_Ca in component TCC (J_per_mol)"
    legend_algebraic[17] = "Ar_Ca in component TCC (J_per_mol)"
    legend_algebraic[14] = "v_s00_TCC in component TCC (fmol_per_sec)"
    legend_algebraic[25] = "v_s10_TCC in component TCC (fmol_per_sec)"
    legend_algebraic[22] = "v_s01_TCC in component TCC (fmol_per_sec)"
    legend_algebraic[26] = "v_s11_TCC in component TCC (fmol_per_sec)"
    legend_algebraic[9] = "v_R1_TCC in component TCC (fmol_per_sec)"
    legend_algebraic[21] = "v_R2_TCC in component TCC (fmol_per_sec)"
    legend_algebraic[13] = "v_R3_TCC in component TCC (fmol_per_sec)"
    legend_algebraic[23] = "v_R4_TCC in component TCC (fmol_per_sec)"
    legend_algebraic[3] = "mu_s00_TCC in component TCC (J_per_mol)"
    legend_algebraic[6] = "mu_s10_TCC in component TCC (J_per_mol)"
    legend_algebraic[10] = "mu_s01_TCC in component TCC (J_per_mol)"
    legend_algebraic[15] = "mu_s11_TCC in component TCC (J_per_mol)"
    legend_algebraic[4] = "Af_R1_TCC in component TCC (J_per_mol)"
    legend_algebraic[7] = "Ar_R1_TCC in component TCC (J_per_mol)"
    legend_algebraic[11] = "Af_R2_TCC in component TCC (J_per_mol)"
    legend_algebraic[19] = "Ar_R2_TCC in component TCC (J_per_mol)"
    legend_algebraic[5] = "Af_R3_TCC in component TCC (J_per_mol)"
    legend_algebraic[12] = "Ar_R3_TCC in component TCC (J_per_mol)"
    legend_algebraic[8] = "Af_R4_TCC in component TCC (J_per_mol)"
    legend_algebraic[20] = "Ar_R4_TCC in component TCC (J_per_mol)"
    legend_rates[1] = "d/dt q_Ca_i in component environment (fmol)"
    legend_rates[0] = "d/dt q_Ca_o in component environment (fmol)"
    legend_rates[2] = "d/dt q_s00_TCC in component environment (fmol)"
    legend_rates[3] = "d/dt q_s10_TCC in component environment (fmol)"
    legend_rates[4] = "d/dt q_s01_TCC in component environment (fmol)"
    legend_rates[5] = "d/dt q_s11_TCC in component environment (fmol)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    constants[0] = 153400
    states[0] = 9.3276
    states[1] = 0.00456
    states[2] = 3.653271338425772e-07
    states[3] = 1e-16
    states[4] = 1e-16
    states[5] = 1e-16
    constants[1] = -13039
    constants[2] = 8.31
    constants[3] = 310
    constants[4] = 96500
    constants[5] = 1
    constants[6] = 0.0001
    constants[7] = 11414.6
    constants[8] = 1266.14
    constants[9] = 4.33488
    constants[10] = 1.34962
    constants[11] = 7.44777
    constants[12] = 28.7976
    constants[13] = 211.182
    constants[14] = 2.10659
    constants[15] = 0.381738
    constants[16] = 615.294
    constants[17] = 111.498
    constants[18] = 2
    constants[19] = 0.876568910405296
    constants[20] = -0.576510778245838
    constants[21] = -0.872117216889333
    constants[22] = 1.73582739545622
    rootfind_0(voi, constants, rates, states, algebraic)
    constants[24] = 0.00000
    constants[25] = constants[1]/constants[0]
    constants[26] = constants[18]*constants[4]*constants[25]
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    algebraic[3] = constants[2]*constants[3]*log(constants[14]*states[2])
    algebraic[4] = algebraic[3]+constants[19]*constants[4]*constants[25]
    algebraic[6] = constants[2]*constants[3]*log(constants[15]*states[3])
    algebraic[7] = algebraic[6]+constants[21]*constants[4]*constants[25]
    algebraic[9] = constants[8]*(exp(algebraic[4]/(constants[2]*constants[3]))-exp(algebraic[7]/(constants[2]*constants[3])))
    algebraic[5] = algebraic[3]+constants[20]*constants[4]*constants[25]
    algebraic[10] = constants[2]*constants[3]*log(constants[16]*states[4])
    algebraic[12] = algebraic[10]+constants[22]*constants[4]*constants[25]
    algebraic[13] = constants[10]*(exp(algebraic[5]/(constants[2]*constants[3]))-exp(algebraic[12]/(constants[2]*constants[3])))
    algebraic[14] = -algebraic[9]-algebraic[13]
    rates[2] = algebraic[14]
    algebraic[1] = constants[2]*constants[3]*log(constants[12]*states[1])
    algebraic[15] = constants[2]*constants[3]*log(constants[17]*states[5])
    algebraic[16] = algebraic[15]+algebraic[1]+constants[26]
    algebraic[2] = constants[2]*constants[3]*log(constants[13]*states[0])
    algebraic[17] = algebraic[15]+algebraic[2]
    algebraic[18] = custom_piecewise([equal(constants[26] , 0.00000), constants[7]*(exp(algebraic[16]/(constants[2]*constants[3]))-exp(algebraic[17]/(constants[2]*constants[3]))) , True, (((constants[7]*constants[26])/(constants[2]*constants[3]))/(exp(constants[26]/(constants[2]*constants[3]))-1.00000))*(exp(algebraic[16]/(constants[2]*constants[3]))-exp(algebraic[17]/(constants[2]*constants[3])))])
    rates[1] = -algebraic[18]
    rates[0] = algebraic[18]
    algebraic[11] = algebraic[10]+constants[19]*constants[4]*constants[25]
    algebraic[19] = algebraic[15]+constants[21]*constants[4]*constants[25]
    algebraic[21] = constants[9]*(exp(algebraic[11]/(constants[2]*constants[3]))-exp(algebraic[19]/(constants[2]*constants[3])))
    algebraic[22] = algebraic[13]-algebraic[21]
    rates[4] = algebraic[22]
    algebraic[8] = algebraic[6]+constants[20]*constants[4]*constants[25]
    algebraic[20] = algebraic[15]+constants[22]*constants[4]*constants[25]
    algebraic[23] = constants[11]*(exp(algebraic[8]/(constants[2]*constants[3]))-exp(algebraic[20]/(constants[2]*constants[3])))
    algebraic[25] = algebraic[9]-algebraic[23]
    rates[3] = algebraic[25]
    algebraic[26] = algebraic[21]+algebraic[23]
    rates[5] = algebraic[26]
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[3] = constants[2]*constants[3]*log(constants[14]*states[2])
    algebraic[4] = algebraic[3]+constants[19]*constants[4]*constants[25]
    algebraic[6] = constants[2]*constants[3]*log(constants[15]*states[3])
    algebraic[7] = algebraic[6]+constants[21]*constants[4]*constants[25]
    algebraic[9] = constants[8]*(exp(algebraic[4]/(constants[2]*constants[3]))-exp(algebraic[7]/(constants[2]*constants[3])))
    algebraic[5] = algebraic[3]+constants[20]*constants[4]*constants[25]
    algebraic[10] = constants[2]*constants[3]*log(constants[16]*states[4])
    algebraic[12] = algebraic[10]+constants[22]*constants[4]*constants[25]
    algebraic[13] = constants[10]*(exp(algebraic[5]/(constants[2]*constants[3]))-exp(algebraic[12]/(constants[2]*constants[3])))
    algebraic[14] = -algebraic[9]-algebraic[13]
    algebraic[1] = constants[2]*constants[3]*log(constants[12]*states[1])
    algebraic[15] = constants[2]*constants[3]*log(constants[17]*states[5])
    algebraic[16] = algebraic[15]+algebraic[1]+constants[26]
    algebraic[2] = constants[2]*constants[3]*log(constants[13]*states[0])
    algebraic[17] = algebraic[15]+algebraic[2]
    algebraic[18] = custom_piecewise([equal(constants[26] , 0.00000), constants[7]*(exp(algebraic[16]/(constants[2]*constants[3]))-exp(algebraic[17]/(constants[2]*constants[3]))) , True, (((constants[7]*constants[26])/(constants[2]*constants[3]))/(exp(constants[26]/(constants[2]*constants[3]))-1.00000))*(exp(algebraic[16]/(constants[2]*constants[3]))-exp(algebraic[17]/(constants[2]*constants[3])))])
    algebraic[11] = algebraic[10]+constants[19]*constants[4]*constants[25]
    algebraic[19] = algebraic[15]+constants[21]*constants[4]*constants[25]
    algebraic[21] = constants[9]*(exp(algebraic[11]/(constants[2]*constants[3]))-exp(algebraic[19]/(constants[2]*constants[3])))
    algebraic[22] = algebraic[13]-algebraic[21]
    algebraic[8] = algebraic[6]+constants[20]*constants[4]*constants[25]
    algebraic[20] = algebraic[15]+constants[22]*constants[4]*constants[25]
    algebraic[23] = constants[11]*(exp(algebraic[8]/(constants[2]*constants[3]))-exp(algebraic[20]/(constants[2]*constants[3])))
    algebraic[25] = algebraic[9]-algebraic[23]
    algebraic[26] = algebraic[21]+algebraic[23]
    algebraic[0] = voi-floor(voi/constants[5])*constants[5]
    algebraic[24] = constants[4]*(-constants[18]*algebraic[18]+algebraic[9]*(constants[21]-constants[19])+algebraic[21]*(constants[21]-constants[19])+algebraic[13]*(constants[22]-constants[20])+algebraic[23]*(constants[22]-constants[20]))
    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):
        constants[23] = fsolve(residualSN_0, initialGuess0, args=(algebraic, voi, constants, rates, states), xtol=1E-6)
        initialGuess0 = constants[23]
    else:
        for (i,t) in enumerate(voi):
            constants[23][i] = fsolve(residualSN_0, initialGuess0, args=(algebraic[:,i], voi[i], constants, rates, states[:,i]), xtol=1E-6)
            initialGuess0 = constants[23][i]

def residualSN_0(algebraicCandidate, algebraic, voi, constants, rates, states):
    constants[23] = algebraicCandidate
    return (constants[1]) - (constants[23]*constants[0])

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)