Generated Code

# Size of variable arrays:
sizeAlgebraic = 32
sizeStates = 7
sizeConstants = 22
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 environment (second)"
    legend_constants[0] = "C_m in component environment (fF)"
    legend_states[0] = "q_K_o in component environment (fmol)"
    legend_states[1] = "q_K_i in component environment (fmol)"
    legend_states[2] = "q_Sa in component environment (fmol)"
    legend_states[3] = "q_Sb in component environment (fmol)"
    legend_states[4] = "q_Sc in component environment (fmol)"
    legend_states[5] = "q_Sd in component environment (fmol)"
    legend_states[6] = "q_mem in component environment (fC)"
    legend_algebraic[0] = "Vmem in component environment (volt)"
    legend_constants[1] = "R in component environment (J_per_K_per_mol)"
    legend_constants[2] = "T in component environment (kelvin)"
    legend_constants[3] = "F in component environment (C_per_mol)"
    legend_algebraic[22] = "v_Kr in component Kr (fmol_per_sec)"
    legend_algebraic[29] = "I_mem_Kr in component Kr (fA)"
    legend_algebraic[2] = "I_stim in component environment (fA)"
    legend_constants[4] = "stimPeriod in component environment (second)"
    legend_constants[5] = "stimDuration in component environment (second)"
    legend_algebraic[1] = "tPeriod in component environment (second)"
    legend_algebraic[24] = "i_Kr in component environment (uA_per_uF)"
    legend_constants[6] = "kappa_Kr in component Kr_parameters (fmol_per_sec)"
    legend_constants[7] = "kappa_xr10 in component Kr_parameters (fmol_per_sec)"
    legend_constants[8] = "kappa_xr11 in component Kr_parameters (fmol_per_sec)"
    legend_constants[9] = "kappa_xr20 in component Kr_parameters (fmol_per_sec)"
    legend_constants[10] = "kappa_xr21 in component Kr_parameters (fmol_per_sec)"
    legend_constants[11] = "K_K_i in component Kr_parameters (per_fmol)"
    legend_constants[12] = "K_K_o in component Kr_parameters (per_fmol)"
    legend_constants[13] = "K_Sa_Kr in component Kr_parameters (per_fmol)"
    legend_constants[14] = "K_Sb_Kr in component Kr_parameters (per_fmol)"
    legend_constants[15] = "K_Sc_Kr in component Kr_parameters (per_fmol)"
    legend_constants[16] = "K_Sd_Kr in component Kr_parameters (per_fmol)"
    legend_constants[17] = "zK in component Kr_parameters (dimensionless)"
    legend_constants[18] = "z_xr1_f in component Kr_parameters (dimensionless)"
    legend_constants[19] = "z_xr1_r in component Kr_parameters (dimensionless)"
    legend_constants[20] = "z_xr2_f in component Kr_parameters (dimensionless)"
    legend_constants[21] = "z_xr2_r in component Kr_parameters (dimensionless)"
    legend_algebraic[3] = "u_K_i in component Kr (J_per_mol)"
    legend_algebraic[4] = "u_K_o in component Kr (J_per_mol)"
    legend_algebraic[5] = "V_mem in component Kr (J_per_C)"
    legend_algebraic[6] = "Am_Kr in component Kr (J_per_mol)"
    legend_algebraic[20] = "Af_Kr in component Kr (J_per_mol)"
    legend_algebraic[21] = "Ar_Kr in component Kr (J_per_mol)"
    legend_algebraic[18] = "v_Sa in component Kr (fmol_per_sec)"
    legend_algebraic[30] = "v_Sb in component Kr (fmol_per_sec)"
    legend_algebraic[28] = "v_Sc in component Kr (fmol_per_sec)"
    legend_algebraic[31] = "v_Sd in component Kr (fmol_per_sec)"
    legend_algebraic[13] = "v_x10 in component Kr (fmol_per_sec)"
    legend_algebraic[26] = "v_x11 in component Kr (fmol_per_sec)"
    legend_algebraic[17] = "v_x20 in component Kr (fmol_per_sec)"
    legend_algebraic[27] = "v_x21 in component Kr (fmol_per_sec)"
    legend_algebraic[7] = "mu_Sa in component Kr (J_per_mol)"
    legend_algebraic[10] = "mu_Sb in component Kr (J_per_mol)"
    legend_algebraic[14] = "mu_Sc in component Kr (J_per_mol)"
    legend_algebraic[19] = "mu_Sd in component Kr (J_per_mol)"
    legend_algebraic[8] = "Af_x10 in component Kr (J_per_mol)"
    legend_algebraic[11] = "Ar_x10 in component Kr (J_per_mol)"
    legend_algebraic[15] = "Af_x11 in component Kr (J_per_mol)"
    legend_algebraic[23] = "Ar_x11 in component Kr (J_per_mol)"
    legend_algebraic[9] = "Af_x20 in component Kr (J_per_mol)"
    legend_algebraic[16] = "Ar_x20 in component Kr (J_per_mol)"
    legend_algebraic[12] = "Af_x21 in component Kr (J_per_mol)"
    legend_algebraic[25] = "Ar_x21 in component Kr (J_per_mol)"
    legend_rates[1] = "d/dt q_K_i in component environment (fmol)"
    legend_rates[0] = "d/dt q_K_o in component environment (fmol)"
    legend_rates[6] = "d/dt q_mem in component environment (fC)"
    legend_rates[2] = "d/dt q_Sa in component environment (fmol)"
    legend_rates[3] = "d/dt q_Sb in component environment (fmol)"
    legend_rates[4] = "d/dt q_Sc in component environment (fmol)"
    legend_rates[5] = "d/dt q_Sd 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] = 27.9828
    states[1] = 5510
    states[2] = 1.598306E-07
    states[3] = 1.598306E-07
    states[4] = 1.598306E-07
    states[5] = 1.598306E-07
    states[6] = -13039
    constants[1] = 8.31
    constants[2] = 310
    constants[3] = 96500
    constants[4] = 1
    constants[5] = 0.0001
    constants[6] = 271.854
    constants[7] = 2.51352
    constants[8] = 0.0672974
    constants[9] = 8.45146
    constants[10] = 68.9799
    constants[11] = 1.94622
    constants[12] = 12.9197
    constants[13] = 1.47312
    constants[14] = 0.180487
    constants[15] = 55.02
    constants[16] = 6.74109
    constants[17] = 1
    constants[18] = 1.6149028778859738
    constants[19] = -1.3218634652232777
    constants[20] = -1.0273976425216251
    constants[21] = -0.18153135376657775
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    algebraic[5] = states[6]/constants[0]
    algebraic[7] = constants[1]*constants[2]*log(constants[13]*states[2])
    algebraic[8] = algebraic[7]+constants[18]*constants[3]*algebraic[5]
    algebraic[10] = constants[1]*constants[2]*log(constants[14]*states[3])
    algebraic[11] = algebraic[10]+constants[19]*constants[3]*algebraic[5]
    algebraic[13] = constants[7]*(exp(algebraic[8]/(constants[1]*constants[2]))-exp(algebraic[11]/(constants[1]*constants[2])))
    algebraic[9] = algebraic[7]+constants[20]*constants[3]*algebraic[5]
    algebraic[14] = constants[1]*constants[2]*log(constants[15]*states[4])
    algebraic[16] = algebraic[14]+constants[21]*constants[3]*algebraic[5]
    algebraic[17] = constants[9]*(exp(algebraic[9]/(constants[1]*constants[2]))-exp(algebraic[16]/(constants[1]*constants[2])))
    algebraic[18] = -algebraic[13]-algebraic[17]
    rates[2] = algebraic[18]
    algebraic[6] = constants[17]*constants[3]*algebraic[5]
    algebraic[3] = constants[1]*constants[2]*log(constants[11]*states[1])
    algebraic[19] = constants[1]*constants[2]*log(constants[16]*states[5])
    algebraic[20] = algebraic[19]+algebraic[3]+algebraic[6]
    algebraic[4] = constants[1]*constants[2]*log(constants[12]*states[0])
    algebraic[21] = algebraic[19]+algebraic[4]
    algebraic[22] = custom_piecewise([equal(algebraic[6] , 0.00000), 1.00000*constants[6]*(exp(algebraic[20]/(constants[1]*constants[2]))-exp(algebraic[21]/(constants[1]*constants[2]))) , True, (((1.00000*constants[6]*algebraic[6])/(constants[1]*constants[2]))/(exp(algebraic[6]/(constants[1]*constants[2]))-1.00000))*(exp(algebraic[20]/(constants[1]*constants[2]))-exp(algebraic[21]/(constants[1]*constants[2])))])
    rates[1] = -algebraic[22]
    rates[0] = algebraic[22]
    algebraic[15] = algebraic[14]+constants[18]*constants[3]*algebraic[5]
    algebraic[23] = algebraic[19]+constants[19]*constants[3]*algebraic[5]
    algebraic[26] = constants[8]*(exp(algebraic[15]/(constants[1]*constants[2]))-exp(algebraic[23]/(constants[1]*constants[2])))
    algebraic[28] = algebraic[17]-algebraic[26]
    rates[4] = algebraic[28]
    algebraic[12] = algebraic[10]+constants[20]*constants[3]*algebraic[5]
    algebraic[25] = algebraic[19]+constants[21]*constants[3]*algebraic[5]
    algebraic[27] = constants[10]*(exp(algebraic[12]/(constants[1]*constants[2]))-exp(algebraic[25]/(constants[1]*constants[2])))
    algebraic[29] = constants[3]*(-constants[17]*algebraic[22]+algebraic[13]*(constants[19]-constants[18])+algebraic[26]*(constants[19]-constants[19])+algebraic[17]*(constants[21]-constants[20])+algebraic[27]*(constants[21]-constants[20]))
    algebraic[1] = voi-floor(voi/constants[4])*constants[4]
    algebraic[2] = custom_piecewise([greater_equal(algebraic[1] , 0.300000) & less_equal(algebraic[1] , 0.300000+constants[5]), (0.00000*0.0750000*constants[0])/constants[5] , True, 0.00000])
    rates[6] = algebraic[29]+algebraic[2]
    algebraic[30] = algebraic[13]-algebraic[27]
    rates[3] = algebraic[30]
    algebraic[31] = algebraic[26]+algebraic[27]
    rates[5] = algebraic[31]
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[5] = states[6]/constants[0]
    algebraic[7] = constants[1]*constants[2]*log(constants[13]*states[2])
    algebraic[8] = algebraic[7]+constants[18]*constants[3]*algebraic[5]
    algebraic[10] = constants[1]*constants[2]*log(constants[14]*states[3])
    algebraic[11] = algebraic[10]+constants[19]*constants[3]*algebraic[5]
    algebraic[13] = constants[7]*(exp(algebraic[8]/(constants[1]*constants[2]))-exp(algebraic[11]/(constants[1]*constants[2])))
    algebraic[9] = algebraic[7]+constants[20]*constants[3]*algebraic[5]
    algebraic[14] = constants[1]*constants[2]*log(constants[15]*states[4])
    algebraic[16] = algebraic[14]+constants[21]*constants[3]*algebraic[5]
    algebraic[17] = constants[9]*(exp(algebraic[9]/(constants[1]*constants[2]))-exp(algebraic[16]/(constants[1]*constants[2])))
    algebraic[18] = -algebraic[13]-algebraic[17]
    algebraic[6] = constants[17]*constants[3]*algebraic[5]
    algebraic[3] = constants[1]*constants[2]*log(constants[11]*states[1])
    algebraic[19] = constants[1]*constants[2]*log(constants[16]*states[5])
    algebraic[20] = algebraic[19]+algebraic[3]+algebraic[6]
    algebraic[4] = constants[1]*constants[2]*log(constants[12]*states[0])
    algebraic[21] = algebraic[19]+algebraic[4]
    algebraic[22] = custom_piecewise([equal(algebraic[6] , 0.00000), 1.00000*constants[6]*(exp(algebraic[20]/(constants[1]*constants[2]))-exp(algebraic[21]/(constants[1]*constants[2]))) , True, (((1.00000*constants[6]*algebraic[6])/(constants[1]*constants[2]))/(exp(algebraic[6]/(constants[1]*constants[2]))-1.00000))*(exp(algebraic[20]/(constants[1]*constants[2]))-exp(algebraic[21]/(constants[1]*constants[2])))])
    algebraic[15] = algebraic[14]+constants[18]*constants[3]*algebraic[5]
    algebraic[23] = algebraic[19]+constants[19]*constants[3]*algebraic[5]
    algebraic[26] = constants[8]*(exp(algebraic[15]/(constants[1]*constants[2]))-exp(algebraic[23]/(constants[1]*constants[2])))
    algebraic[28] = algebraic[17]-algebraic[26]
    algebraic[12] = algebraic[10]+constants[20]*constants[3]*algebraic[5]
    algebraic[25] = algebraic[19]+constants[21]*constants[3]*algebraic[5]
    algebraic[27] = constants[10]*(exp(algebraic[12]/(constants[1]*constants[2]))-exp(algebraic[25]/(constants[1]*constants[2])))
    algebraic[29] = constants[3]*(-constants[17]*algebraic[22]+algebraic[13]*(constants[19]-constants[18])+algebraic[26]*(constants[19]-constants[19])+algebraic[17]*(constants[21]-constants[20])+algebraic[27]*(constants[21]-constants[20]))
    algebraic[1] = voi-floor(voi/constants[4])*constants[4]
    algebraic[2] = custom_piecewise([greater_equal(algebraic[1] , 0.300000) & less_equal(algebraic[1] , 0.300000+constants[5]), (0.00000*0.0750000*constants[0])/constants[5] , True, 0.00000])
    algebraic[30] = algebraic[13]-algebraic[27]
    algebraic[31] = algebraic[26]+algebraic[27]
    rootfind_0(voi, constants, rates, states, algebraic)
    algebraic[24] = ((1.00000e-09*constants[3])/constants[0])*algebraic[22]
    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[0] = fsolve(residualSN_0, initialGuess0, args=(algebraic, voi, constants, rates, states), xtol=1E-6)
        initialGuess0 = algebraic[0]
    else:
        for (i,t) in enumerate(voi):
            algebraic[0][i] = fsolve(residualSN_0, initialGuess0, args=(algebraic[:,i], voi[i], constants, rates, states[:,i]), xtol=1E-6)
            initialGuess0 = algebraic[0][i]

def residualSN_0(algebraicCandidate, algebraic, voi, constants, rates, states):
    algebraic[0] = algebraicCandidate
    return (states[6]) - (algebraic[0]*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)