Generated Code

# Size of variable arrays:
sizeAlgebraic = 12
sizeStates = 1
sizeConstants = 11
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 (minute)"
    legend_constants[0] = "VP in component red_cells_and_viscosity (litre)"
    legend_states[0] = "VRC in component RBC_volume (litre)"
    legend_algebraic[2] = "HM in component hematocrit_fraction (dimensionless)"
    legend_algebraic[1] = "HM1 in component hematocrit_fraction (dimensionless)"
    legend_algebraic[0] = "VB in component hematocrit_fraction (litre)"
    legend_algebraic[3] = "VIE in component viscosity_due_to_RBCs (dimensionless)"
    legend_constants[1] = "HMK in component parameter_values (dimensionless)"
    legend_constants[2] = "HKM in component parameter_values (dimensionless)"
    legend_algebraic[5] = "VIM in component blood_viscosity (dimensionless)"
    legend_algebraic[4] = "VIB in component blood_viscosity (dimensionless)"
    legend_algebraic[8] = "HM7 in component oxygen_stimulation (mmHg)"
    legend_constants[3] = "PO2AMB in component parameter_values (mmHg)"
    legend_constants[4] = "HM6 in component parameter_values (mmHg)"
    legend_constants[9] = "PO2AM1 in component oxygen_stimulation (mmHg)"
    legend_algebraic[6] = "HM3 in component oxygen_stimulation (mmHg)"
    legend_constants[10] = "HM4 in component oxygen_stimulation (mmHg)"
    legend_algebraic[7] = "HM5 in component oxygen_stimulation (mmHg)"
    legend_algebraic[9] = "RC1 in component RBC_production (L_per_minute)"
    legend_constants[5] = "HM8 in component parameter_values (L_per_minute_per_mmHg)"
    legend_constants[6] = "REK in component parameter_values (dimensionless)"
    legend_algebraic[10] = "RC2 in component RBC_destruction (L_per_minute)"
    legend_constants[7] = "RKC in component parameter_values (per_minute)"
    legend_constants[8] = "TRRBC in component parameter_values (L_per_minute)"
    legend_algebraic[11] = "RCD in component RBC_volume (L_per_minute)"
    legend_rates[0] = "d/dt VRC in component RBC_volume (litre)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    constants[0] = 3.00449
    states[0] = 2.00439
    constants[1] = 90
    constants[2] = 0.53333
    constants[3] = 150
    constants[4] = 1850
    constants[5] = 4.714e-08
    constants[6] = 1
    constants[7] = 5.8e-06
    constants[8] = 0
    constants[9] = custom_piecewise([greater(constants[3] , 80.0000), 80.0000 , True, constants[3]])
    constants[10] = constants[3]-40.0000
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    algebraic[0] = constants[0]+states[0]
    algebraic[1] = states[0]/algebraic[0]
    algebraic[2] = 100.000*algebraic[1]
    algebraic[6] = (constants[9]-40.0000)*algebraic[2]
    algebraic[7] = custom_piecewise([less(algebraic[6]+constants[10] , 0.00000), 0.00000 , True, algebraic[6]+constants[10]])
    algebraic[8] = constants[4]-algebraic[7]
    algebraic[9] = custom_piecewise([less(algebraic[8]*constants[5]*constants[6]+5.00000e-06 , 0.00000), 0.00000 , True, algebraic[8]*constants[5]*constants[6]+5.00000e-06])
    algebraic[3] = algebraic[2]/((constants[1]-algebraic[2])*constants[2])
    algebraic[4] = algebraic[3]+1.50000
    algebraic[5] = 0.333300*algebraic[4]
    algebraic[10] = states[0]*constants[7]*algebraic[5]
    algebraic[11] = (algebraic[9]-algebraic[10])+constants[8]
    rates[0] = algebraic[11]
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[0] = constants[0]+states[0]
    algebraic[1] = states[0]/algebraic[0]
    algebraic[2] = 100.000*algebraic[1]
    algebraic[6] = (constants[9]-40.0000)*algebraic[2]
    algebraic[7] = custom_piecewise([less(algebraic[6]+constants[10] , 0.00000), 0.00000 , True, algebraic[6]+constants[10]])
    algebraic[8] = constants[4]-algebraic[7]
    algebraic[9] = custom_piecewise([less(algebraic[8]*constants[5]*constants[6]+5.00000e-06 , 0.00000), 0.00000 , True, algebraic[8]*constants[5]*constants[6]+5.00000e-06])
    algebraic[3] = algebraic[2]/((constants[1]-algebraic[2])*constants[2])
    algebraic[4] = algebraic[3]+1.50000
    algebraic[5] = 0.333300*algebraic[4]
    algebraic[10] = states[0]*constants[7]*algebraic[5]
    algebraic[11] = (algebraic[9]-algebraic[10])+constants[8]
    return algebraic

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)