Generated Code
The following is python code generated by the CellML API from this CellML file. (Back to language selection)
The raw code is available.
# Size of variable arrays:
sizeAlgebraic = 21
sizeStates = 3
sizeConstants = 19
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_constants[1] = "q_K_o in component environment (fmol)"
legend_constants[2] = "q_K_i in component environment (fmol)"
legend_states[0] = "q_S_Ks0 in component environment (fmol)"
legend_states[1] = "q_S_Ks1 in component environment (fmol)"
legend_states[2] = "q_S_Ks2 in component environment (fmol)"
legend_algebraic[1] = "q_mem in component environment (fC)"
legend_algebraic[0] = "Vmem in component environment (volt)"
legend_constants[3] = "R in component environment (J_per_K_per_mol)"
legend_constants[4] = "T in component environment (kelvin)"
legend_constants[5] = "F in component environment (C_per_mol)"
legend_algebraic[14] = "v_Ks in component Ks (fmol_per_sec)"
legend_algebraic[18] = "I_mem_Ks in component Ks (fA)"
legend_algebraic[15] = "i_Ks in component environment (uA_per_uF)"
legend_constants[6] = "kappa_Ks in component Ks_parameters (fmol_per_sec)"
legend_constants[7] = "kappa_xs1 in component Ks_parameters (fmol_per_sec)"
legend_constants[8] = "kappa_xs2 in component Ks_parameters (fmol_per_sec)"
legend_constants[9] = "K_K_i in component Ks_parameters (per_fmol)"
legend_constants[10] = "K_K_o in component Ks_parameters (per_fmol)"
legend_constants[11] = "K_S_Ks0 in component Ks_parameters (per_fmol)"
legend_constants[12] = "K_S_Ks1 in component Ks_parameters (per_fmol)"
legend_constants[13] = "K_S_Ks2 in component Ks_parameters (per_fmol)"
legend_constants[14] = "zK in component Ks_parameters (dimensionless)"
legend_constants[15] = "z_xs_f in component Ks_parameters (dimensionless)"
legend_constants[16] = "z_xs_r in component Ks_parameters (dimensionless)"
legend_constants[17] = "u_K_i in component Ks (J_per_mol)"
legend_constants[18] = "u_K_o in component Ks (J_per_mol)"
legend_algebraic[2] = "V_mem in component Ks (J_per_C)"
legend_algebraic[3] = "Am_Ks in component Ks (J_per_mol)"
legend_algebraic[12] = "Af_Ks in component Ks (J_per_mol)"
legend_algebraic[13] = "Ar_Ks in component Ks (J_per_mol)"
legend_algebraic[10] = "v_S_Ks0 in component Ks (fmol_per_sec)"
legend_algebraic[19] = "v_S_Ks1 in component Ks (fmol_per_sec)"
legend_algebraic[20] = "v_S_Ks2 in component Ks (fmol_per_sec)"
legend_algebraic[9] = "v_xs1 in component Ks (fmol_per_sec)"
legend_algebraic[17] = "v_xs2 in component Ks (fmol_per_sec)"
legend_algebraic[4] = "mu_S_Ks0 in component Ks (J_per_mol)"
legend_algebraic[6] = "mu_S_Ks1 in component Ks (J_per_mol)"
legend_algebraic[11] = "mu_S_Ks2 in component Ks (J_per_mol)"
legend_algebraic[5] = "Af_xs1 in component Ks (J_per_mol)"
legend_algebraic[7] = "Ar_xs1 in component Ks (J_per_mol)"
legend_algebraic[8] = "Af_xs2 in component Ks (J_per_mol)"
legend_algebraic[16] = "Ar_xs2 in component Ks (J_per_mol)"
legend_rates[0] = "d/dt q_S_Ks0 in component environment (fmol)"
legend_rates[1] = "d/dt q_S_Ks1 in component environment (fmol)"
legend_rates[2] = "d/dt q_S_Ks2 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] = 60000
constants[1] = 20.0448
constants[2] = 388.832
states[0] = 9.742056902468725e-06
states[1] = 9.742056902468725e-06
states[2] = 9.742056902468725e-06
constants[3] = 8.31
constants[4] = 310
constants[5] = 96500
constants[6] = 27.8683
constants[7] = 0.00829152
constants[8] = 0.0295644
constants[9] = 1.42292
constants[10] = 10.4348
constants[11] = 0.281155
constants[12] = 0.0394258
constants[13] = 0.0221145
constants[14] = 1
constants[15] = 0.000400323747581994
constants[16] = -1.41544821457997
constants[17] = constants[3]*constants[4]*log(constants[9]*constants[2])
constants[18] = constants[3]*constants[4]*log(constants[10]*constants[1])
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
algebraic[0] = custom_piecewise([greater_equal(voi , 0.00000) & less(voi , 4.00000), -0.0900000 , greater(voi , 10.1000) & less(voi , 13.1000), -0.0600000 , greater(voi , 14.1000) & less(voi , 15.1000), -0.0400000 , greater(voi , 17.0000), 0.0900000 , True, -0.0800000])
algebraic[1] = algebraic[0]*constants[0]
algebraic[2] = algebraic[1]/constants[0]
algebraic[4] = constants[3]*constants[4]*log(constants[11]*states[0])
algebraic[5] = algebraic[4]+constants[15]*constants[5]*algebraic[2]
algebraic[6] = constants[3]*constants[4]*log(constants[12]*states[1])
algebraic[7] = algebraic[6]+constants[16]*constants[5]*algebraic[2]
algebraic[9] = constants[7]*(exp(algebraic[5]/(constants[3]*constants[4]))-exp(algebraic[7]/(constants[3]*constants[4])))
algebraic[10] = -algebraic[9]
rates[0] = algebraic[10]
algebraic[8] = algebraic[6]+constants[15]*constants[5]*algebraic[2]
algebraic[11] = constants[3]*constants[4]*log(constants[13]*states[2])
algebraic[16] = algebraic[11]+constants[16]*constants[5]*algebraic[2]
algebraic[17] = constants[8]*(exp(algebraic[8]/(constants[3]*constants[4]))-exp(algebraic[16]/(constants[3]*constants[4])))
algebraic[19] = algebraic[9]-algebraic[17]
rates[1] = algebraic[19]
algebraic[20] = algebraic[17]
rates[2] = algebraic[20]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[0] = custom_piecewise([greater_equal(voi , 0.00000) & less(voi , 4.00000), -0.0900000 , greater(voi , 10.1000) & less(voi , 13.1000), -0.0600000 , greater(voi , 14.1000) & less(voi , 15.1000), -0.0400000 , greater(voi , 17.0000), 0.0900000 , True, -0.0800000])
algebraic[1] = algebraic[0]*constants[0]
algebraic[2] = algebraic[1]/constants[0]
algebraic[4] = constants[3]*constants[4]*log(constants[11]*states[0])
algebraic[5] = algebraic[4]+constants[15]*constants[5]*algebraic[2]
algebraic[6] = constants[3]*constants[4]*log(constants[12]*states[1])
algebraic[7] = algebraic[6]+constants[16]*constants[5]*algebraic[2]
algebraic[9] = constants[7]*(exp(algebraic[5]/(constants[3]*constants[4]))-exp(algebraic[7]/(constants[3]*constants[4])))
algebraic[10] = -algebraic[9]
algebraic[8] = algebraic[6]+constants[15]*constants[5]*algebraic[2]
algebraic[11] = constants[3]*constants[4]*log(constants[13]*states[2])
algebraic[16] = algebraic[11]+constants[16]*constants[5]*algebraic[2]
algebraic[17] = constants[8]*(exp(algebraic[8]/(constants[3]*constants[4]))-exp(algebraic[16]/(constants[3]*constants[4])))
algebraic[19] = algebraic[9]-algebraic[17]
algebraic[20] = algebraic[17]
algebraic[3] = constants[14]*constants[5]*algebraic[2]
algebraic[12] = algebraic[11]+constants[17]+algebraic[3]
algebraic[13] = algebraic[11]+constants[18]
algebraic[14] = custom_piecewise([equal(algebraic[3] , 0.00000), 1.00000*constants[6]*(exp(algebraic[12]/(constants[3]*constants[4]))-exp(algebraic[13]/(constants[3]*constants[4]))) , True, (((1.00000*constants[6]*algebraic[3])/(constants[3]*constants[4]))/(exp(algebraic[3]/(constants[3]*constants[4]))-1.00000))*(exp(algebraic[12]/(constants[3]*constants[4]))-exp(algebraic[13]/(constants[3]*constants[4])))])
algebraic[15] = ((1.00000e-09*constants[5])/constants[0])*algebraic[14]
algebraic[18] = constants[5]*(-constants[14]*algebraic[14]+(algebraic[9]+algebraic[17])*(constants[16]-constants[15]))
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)