Generated Code

# Size of variable arrays:
sizeAlgebraic = 11
sizeStates = 6
sizeConstants = 16
from math import *
from numpy import *

def createLegends():
    legend_states = [""] * sizeStates
    legend_rates = [""] * sizeStates
    legend_algebraic = [""] * sizeAlgebraic
    legend_voi = ""
    legend_constants = [""] * sizeConstants
    legend_algebraic[0] = "N_x in component N_x (dimensionless)"
    legend_constants[0] = "N_0 in component model_parameters (dimensionless)"
    legend_voi = "x in component model_parameters (mm)"
    legend_constants[1] = "ksh in component model_parameters (per_mm)"
    legend_states[0] = "F_DVR_v in component F_DVR_v (nl_min)"
    legend_algebraic[8] = "Jv in component model_parameters (nl_min_mm)"
    legend_states[1] = "F_DVR_GLU in component F_DVR_GLU (pmol_min)"
    legend_algebraic[9] = "JGLU in component JGLU (pmol_min_mm)"
    legend_states[2] = "F_DVR_LAC in component F_DVR_LAC (pmol_min)"
    legend_algebraic[10] = "JLAC in component JLAC (pmol_min_mm)"
    legend_states[3] = "F_AVR_v in component F_AVR_v (nl_min)"
    legend_algebraic[7] = "J_ABS_V in component J_ABS_V (nl_min_mm)"
    legend_states[4] = "F_AVR_GLU in component F_AVR_GLU (pmol_min)"
    legend_algebraic[6] = "JGLY in component JGLY (pmol_min_mm)"
    legend_states[5] = "F_AVR_LAC in component F_AVR_LAC (pmol_min)"
    legend_constants[2] = "PGLU in component JGLU (nl_min_mm)"
    legend_constants[3] = "sigma_GLU in component JGLU (dimensionless)"
    legend_algebraic[3] = "c_DVR_GLU in component c_DVR_GLU (millimolar)"
    legend_algebraic[4] = "c_AVR_GLU in component c_AVR_GLU (millimolar)"
    legend_constants[4] = "PLAC in component JLAC (nl_min_mm)"
    legend_constants[5] = "sigma_LAC in component JLAC (dimensionless)"
    legend_algebraic[5] = "c_AVR_LAC in component c_AVR_LAC (millimolar)"
    legend_algebraic[1] = "c_DVR_LAC in component c_DVR_LAC (millimolar)"
    legend_constants[15] = "Vmax in component JGLY (pmol_min_mm)"
    legend_constants[6] = "Km in component JGLY (millimolar)"
    legend_constants[7] = "GlyFract in component JGLY (dimensionless)"
    legend_constants[14] = "F_DVR_G_0 in component model_parameters (pmol_min)"
    legend_constants[8] = "L in component model_parameters (mm)"
    legend_constants[13] = "kv in component kv (nl_min_mm)"
    legend_constants[9] = "VolFract in component kv (dimensionless)"
    legend_constants[12] = "F_DVR_V_0 in component model_parameters (nl_min)"
    legend_constants[10] = "c_DVR_GLU_0 in component model_parameters (millimolar)"
    legend_algebraic[2] = "x_L in component model_parameters (dimensionless)"
    legend_constants[11] = "b in component model_parameters (dimensionless)"
    legend_rates[0] = "d/dt F_DVR_v in component F_DVR_v (nl_min)"
    legend_rates[1] = "d/dt F_DVR_GLU in component F_DVR_GLU (pmol_min)"
    legend_rates[2] = "d/dt F_DVR_LAC in component F_DVR_LAC (pmol_min)"
    legend_rates[3] = "d/dt F_AVR_v in component F_AVR_v (nl_min)"
    legend_rates[4] = "d/dt F_AVR_GLU in component F_AVR_GLU (pmol_min)"
    legend_rates[5] = "d/dt F_AVR_LAC in component F_AVR_LAC (pmol_min)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    constants[0] = 128.0
    constants[1] = 1.213
    states[0] = 3.75
    states[1] = 0.01
    states[2] = 0.01
    states[3] = 0.01
    states[4] = 0.01
    states[5] = 0.01
    constants[2] = 1.2
    constants[3] = 0.5
    constants[4] = 33.93
    constants[5] = 0.5
    constants[6] = 0.1
    constants[7] = 0.2
    constants[8] = 4.0
    constants[9] = 0.3
    constants[10] = 10.0
    constants[11] = 4.0
    constants[12] = 3.75000*constants[0]
    constants[13] = (constants[1]/(constants[0]*(1.00000-exp(-(constants[1]*constants[8])))))*constants[9]*constants[12]
    constants[14] = constants[12]*constants[10]
    constants[15] = (constants[1]/(constants[0]*(1.00000-exp(-(constants[1]*constants[8])))))*(constants[7]*constants[14])
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    algebraic[0] = constants[0]*exp(-(constants[1]*voi))
    algebraic[8] = 0.300000*(states[0]/(constants[0]*constants[11]))*algebraic[0]
    rates[0] = -(algebraic[8]+constants[1]*states[0])
    algebraic[7] = constants[13]*algebraic[0]
    rates[3] = algebraic[8]+constants[1]*states[0]+algebraic[7]
    algebraic[3] = states[1]/states[0]
    algebraic[4] = states[4]/states[3]
    algebraic[9] = algebraic[0]*constants[2]*(algebraic[3]-algebraic[4])+(1.00000-constants[3])*algebraic[8]*((algebraic[3]+algebraic[4])/2.00000)
    rates[1] = -(algebraic[9]+constants[1]*states[1])
    algebraic[5] = states[5]/states[3]
    algebraic[10] = algebraic[0]*constants[4]*(algebraic[3]-algebraic[5])+(1.00000-constants[5])*algebraic[8]*((algebraic[3]+algebraic[5])/2.00000)
    rates[2] = -(algebraic[10]+constants[1]*states[2])
    algebraic[6] = algebraic[0]*((constants[15]*algebraic[4])/(constants[6]+algebraic[4]))
    rates[4] = (algebraic[9]+constants[1]*states[1])-algebraic[6]
    rates[5] = algebraic[10]+constants[1]*states[2]+2.00000*algebraic[6]
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[0] = constants[0]*exp(-(constants[1]*voi))
    algebraic[8] = 0.300000*(states[0]/(constants[0]*constants[11]))*algebraic[0]
    algebraic[7] = constants[13]*algebraic[0]
    algebraic[3] = states[1]/states[0]
    algebraic[4] = states[4]/states[3]
    algebraic[9] = algebraic[0]*constants[2]*(algebraic[3]-algebraic[4])+(1.00000-constants[3])*algebraic[8]*((algebraic[3]+algebraic[4])/2.00000)
    algebraic[5] = states[5]/states[3]
    algebraic[10] = algebraic[0]*constants[4]*(algebraic[3]-algebraic[5])+(1.00000-constants[5])*algebraic[8]*((algebraic[3]+algebraic[5])/2.00000)
    algebraic[6] = algebraic[0]*((constants[15]*algebraic[4])/(constants[6]+algebraic[4]))
    algebraic[1] = states[2]/states[0]
    algebraic[2] = voi/constants[8]
    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)