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 = 31
sizeStates = 16
sizeConstants = 72
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 (millisecond)"
legend_states[0] = "V in component membrane (millivolt)"
legend_constants[0] = "C in component membrane (uF)"
legend_algebraic[0] = "i_Na in component sodium_current (nanoA)"
legend_algebraic[15] = "i_NaP in component persistent_sodium_current (nanoA)"
legend_algebraic[22] = "i_K in component delayed_rectifier_current (nanoA)"
legend_algebraic[23] = "i_leak in component leak_current (nanoA)"
legend_algebraic[24] = "i_T in component LVA_calcium_current (nanoA)"
legend_algebraic[25] = "i_N in component N_HVA_calcium_current (nanoA)"
legend_algebraic[26] = "i_P in component P_HVA_calcium_current (nanoA)"
legend_algebraic[27] = "i_SK in component calcium_dependent_potassium_current (nanoA)"
legend_algebraic[28] = "i_A in component fast_transient_potassium_current (nanoA)"
legend_algebraic[29] = "i_H in component hyperpolarization_activated_current (nanoA)"
legend_algebraic[30] = "i_app in component stimulus_protocol (nanoA)"
legend_constants[1] = "g_Na in component sodium_current (uS)"
legend_constants[2] = "E_Na in component sodium_current (millivolt)"
legend_states[1] = "m in component sodium_current_m_gate (dimensionless)"
legend_states[2] = "h in component sodium_current_h_gate (dimensionless)"
legend_constants[3] = "theta_h in component sodium_current_h_gate (millivolt)"
legend_constants[4] = "sigma_h in component sodium_current_h_gate (millivolt)"
legend_constants[5] = "theta_1 in component sodium_current_h_gate (millivolt)"
legend_constants[6] = "sigma_1 in component sodium_current_h_gate (millivolt)"
legend_constants[7] = "sigma_2 in component sodium_current_h_gate (millivolt)"
legend_algebraic[1] = "tau_h in component sodium_current_h_gate (millisecond)"
legend_algebraic[16] = "h_infinity in component sodium_current_h_gate (dimensionless)"
legend_constants[8] = "theta_m in component sodium_current_m_gate (millivolt)"
legend_constants[9] = "sigma_m in component sodium_current_m_gate (millivolt)"
legend_constants[10] = "tau_m in component sodium_current_m_gate (millisecond)"
legend_algebraic[2] = "m_infinity in component sodium_current_m_gate (dimensionless)"
legend_constants[11] = "g_NaP in component persistent_sodium_current (uS)"
legend_states[3] = "m in component persistent_sodium_current_m_gate (dimensionless)"
legend_states[4] = "h in component persistent_sodium_current_h_gate (dimensionless)"
legend_constants[12] = "theta_h in component persistent_sodium_current_h_gate (millivolt)"
legend_constants[13] = "sigma_h in component persistent_sodium_current_h_gate (millivolt)"
legend_constants[14] = "tau_h in component persistent_sodium_current_h_gate (millisecond)"
legend_algebraic[3] = "h_infinity in component persistent_sodium_current_h_gate (dimensionless)"
legend_constants[15] = "theta_m in component persistent_sodium_current_m_gate (millivolt)"
legend_constants[16] = "sigma_m in component persistent_sodium_current_m_gate (millivolt)"
legend_constants[17] = "tau_m in component persistent_sodium_current_m_gate (millisecond)"
legend_algebraic[4] = "m_infinity in component persistent_sodium_current_m_gate (dimensionless)"
legend_constants[18] = "g_K in component delayed_rectifier_current (uS)"
legend_constants[19] = "E_K in component delayed_rectifier_current (millivolt)"
legend_states[5] = "n in component delayed_rectifier_current_n_gate (dimensionless)"
legend_constants[20] = "theta_n in component delayed_rectifier_current_n_gate (millivolt)"
legend_constants[21] = "sigma_n in component delayed_rectifier_current_n_gate (millivolt)"
legend_constants[22] = "theta_1 in component delayed_rectifier_current_n_gate (millivolt)"
legend_constants[23] = "sigma_1 in component delayed_rectifier_current_n_gate (millivolt)"
legend_constants[24] = "sigma_2 in component delayed_rectifier_current_n_gate (millivolt)"
legend_algebraic[5] = "tau_n in component delayed_rectifier_current_n_gate (millisecond)"
legend_algebraic[17] = "n_infinity in component delayed_rectifier_current_n_gate (dimensionless)"
legend_constants[25] = "g_leak in component leak_current (uS)"
legend_constants[26] = "E_leak in component leak_current (millivolt)"
legend_constants[27] = "g_T in component LVA_calcium_current (uS)"
legend_constants[28] = "E_Ca in component LVA_calcium_current (millivolt)"
legend_states[6] = "m in component LVA_calcium_current_m_gate (dimensionless)"
legend_states[7] = "h in component LVA_calcium_current_h_gate (dimensionless)"
legend_constants[29] = "theta_m in component LVA_calcium_current_m_gate (millivolt)"
legend_constants[30] = "sigma_m in component LVA_calcium_current_m_gate (millivolt)"
legend_constants[31] = "theta_1 in component LVA_calcium_current_m_gate (millivolt)"
legend_constants[32] = "sigma_1 in component LVA_calcium_current_m_gate (millivolt)"
legend_constants[33] = "sigma_2 in component LVA_calcium_current_m_gate (millivolt)"
legend_algebraic[6] = "tau_m in component LVA_calcium_current_m_gate (millisecond)"
legend_algebraic[18] = "m_infinity in component LVA_calcium_current_m_gate (dimensionless)"
legend_constants[34] = "theta_h in component LVA_calcium_current_h_gate (millivolt)"
legend_constants[35] = "sigma_h in component LVA_calcium_current_h_gate (millivolt)"
legend_constants[36] = "theta_1 in component LVA_calcium_current_h_gate (millivolt)"
legend_constants[37] = "sigma_1 in component LVA_calcium_current_h_gate (millivolt)"
legend_algebraic[7] = "tau_h in component LVA_calcium_current_h_gate (millisecond)"
legend_algebraic[19] = "h_infinity in component LVA_calcium_current_h_gate (dimensionless)"
legend_constants[38] = "g_N in component N_HVA_calcium_current (uS)"
legend_states[8] = "m in component N_HVA_calcium_current_m_gate (dimensionless)"
legend_states[9] = "h in component N_HVA_calcium_current_h_gate (dimensionless)"
legend_constants[39] = "theta_m in component N_HVA_calcium_current_m_gate (millivolt)"
legend_constants[40] = "sigma_m in component N_HVA_calcium_current_m_gate (millivolt)"
legend_constants[41] = "tau_m in component N_HVA_calcium_current_m_gate (millisecond)"
legend_algebraic[8] = "m_infinity in component N_HVA_calcium_current_m_gate (dimensionless)"
legend_constants[42] = "theta_h in component N_HVA_calcium_current_h_gate (millivolt)"
legend_constants[43] = "sigma_h in component N_HVA_calcium_current_h_gate (millivolt)"
legend_constants[44] = "tau_h in component N_HVA_calcium_current_h_gate (millisecond)"
legend_algebraic[9] = "h_infinity in component N_HVA_calcium_current_h_gate (dimensionless)"
legend_constants[45] = "g_P in component P_HVA_calcium_current (uS)"
legend_states[10] = "m in component P_HVA_calcium_current_m_gate (dimensionless)"
legend_constants[46] = "theta_m in component P_HVA_calcium_current_m_gate (millivolt)"
legend_constants[47] = "sigma_m in component P_HVA_calcium_current_m_gate (millivolt)"
legend_constants[48] = "tau_m in component P_HVA_calcium_current_m_gate (millisecond)"
legend_algebraic[10] = "m_infinity in component P_HVA_calcium_current_m_gate (dimensionless)"
legend_constants[49] = "g_SK in component calcium_dependent_potassium_current (uS)"
legend_states[11] = "z in component calcium_dependent_potassium_current_z_gate (dimensionless)"
legend_constants[50] = "K1 in component calcium_dependent_potassium_current_z_gate (uM_per_nanocoulomb)"
legend_constants[51] = "K2 in component calcium_dependent_potassium_current_z_gate (per_ms)"
legend_states[12] = "Ca_conc in component calcium_dependent_potassium_current_z_gate (uM)"
legend_constants[52] = "tau_z in component calcium_dependent_potassium_current_z_gate (millisecond)"
legend_algebraic[11] = "z_infinity in component calcium_dependent_potassium_current_z_gate (dimensionless)"
legend_constants[53] = "g_A in component fast_transient_potassium_current (uS)"
legend_states[13] = "m in component fast_transient_potassium_current_m_gate (dimensionless)"
legend_states[14] = "h in component fast_transient_potassium_current_h_gate (dimensionless)"
legend_constants[54] = "theta_m in component fast_transient_potassium_current_m_gate (millivolt)"
legend_constants[55] = "sigma_m in component fast_transient_potassium_current_m_gate (millivolt)"
legend_constants[56] = "theta_1 in component fast_transient_potassium_current_m_gate (millivolt)"
legend_constants[57] = "theta_2 in component fast_transient_potassium_current_m_gate (millivolt)"
legend_constants[58] = "sigma_1 in component fast_transient_potassium_current_m_gate (millivolt)"
legend_constants[59] = "sigma_2 in component fast_transient_potassium_current_m_gate (millivolt)"
legend_algebraic[12] = "tau_m in component fast_transient_potassium_current_m_gate (millisecond)"
legend_algebraic[20] = "m_infinity in component fast_transient_potassium_current_m_gate (dimensionless)"
legend_constants[60] = "theta_h in component fast_transient_potassium_current_h_gate (millivolt)"
legend_constants[61] = "sigma_h in component fast_transient_potassium_current_h_gate (millivolt)"
legend_constants[62] = "tau_h in component fast_transient_potassium_current_h_gate (millisecond)"
legend_algebraic[13] = "h_infinity in component fast_transient_potassium_current_h_gate (dimensionless)"
legend_constants[63] = "g_H in component hyperpolarization_activated_current (uS)"
legend_constants[64] = "E_H in component hyperpolarization_activated_current (millivolt)"
legend_states[15] = "m in component hyperpolarization_activated_current_m_gate (dimensionless)"
legend_constants[65] = "theta_m in component hyperpolarization_activated_current_m_gate (millivolt)"
legend_constants[66] = "sigma_m in component hyperpolarization_activated_current_m_gate (millivolt)"
legend_constants[67] = "theta_1 in component hyperpolarization_activated_current_m_gate (millivolt)"
legend_constants[68] = "sigma_1 in component hyperpolarization_activated_current_m_gate (millivolt)"
legend_algebraic[14] = "tau_m in component hyperpolarization_activated_current_m_gate (millisecond)"
legend_algebraic[21] = "m_infinity in component hyperpolarization_activated_current_m_gate (dimensionless)"
legend_constants[69] = "i_stimStart in component stimulus_protocol (millisecond)"
legend_constants[70] = "i_stimEnd in component stimulus_protocol (millisecond)"
legend_constants[71] = "i_stimAmplitude in component stimulus_protocol (nanoA)"
legend_rates[0] = "d/dt V in component membrane (millivolt)"
legend_rates[2] = "d/dt h in component sodium_current_h_gate (dimensionless)"
legend_rates[1] = "d/dt m in component sodium_current_m_gate (dimensionless)"
legend_rates[4] = "d/dt h in component persistent_sodium_current_h_gate (dimensionless)"
legend_rates[3] = "d/dt m in component persistent_sodium_current_m_gate (dimensionless)"
legend_rates[5] = "d/dt n in component delayed_rectifier_current_n_gate (dimensionless)"
legend_rates[6] = "d/dt m in component LVA_calcium_current_m_gate (dimensionless)"
legend_rates[7] = "d/dt h in component LVA_calcium_current_h_gate (dimensionless)"
legend_rates[8] = "d/dt m in component N_HVA_calcium_current_m_gate (dimensionless)"
legend_rates[9] = "d/dt h in component N_HVA_calcium_current_h_gate (dimensionless)"
legend_rates[10] = "d/dt m in component P_HVA_calcium_current_m_gate (dimensionless)"
legend_rates[12] = "d/dt Ca_conc in component calcium_dependent_potassium_current_z_gate (uM)"
legend_rates[11] = "d/dt z in component calcium_dependent_potassium_current_z_gate (dimensionless)"
legend_rates[13] = "d/dt m in component fast_transient_potassium_current_m_gate (dimensionless)"
legend_rates[14] = "d/dt h in component fast_transient_potassium_current_h_gate (dimensionless)"
legend_rates[15] = "d/dt m in component hyperpolarization_activated_current_m_gate (dimensionless)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
states[0] = -71.847
constants[0] = 0.04
constants[1] = 0.7
constants[2] = 60
states[1] = 0.015
states[2] = 0.981
constants[3] = 44.1
constants[4] = 7
constants[5] = 35
constants[6] = 4
constants[7] = 25
constants[8] = 36
constants[9] = 8.5
constants[10] = 0.1
constants[11] = 0.05
states[3] = 0.002
states[4] = 0.797
constants[12] = 65
constants[13] = 5
constants[14] = 150
constants[15] = 47.1
constants[16] = 4.1
constants[17] = 0.1
constants[18] = 1.3
constants[19] = -80
states[5] = 0.158
constants[20] = 30
constants[21] = 25
constants[22] = 30
constants[23] = 40
constants[24] = 50
constants[25] = 0.005
constants[26] = -50
constants[27] = 0.1
constants[28] = 40
states[6] = 0.001
states[7] = 0.562
constants[29] = 38
constants[30] = 5
constants[31] = 28
constants[32] = 25
constants[33] = 70
constants[34] = 70.1
constants[35] = 7
constants[36] = 70
constants[37] = 65
constants[38] = 0.05
states[8] = 0.001
states[9] = 0.649
constants[39] = 30
constants[40] = 6
constants[41] = 5
constants[42] = 70
constants[43] = 3
constants[44] = 25
constants[45] = 0.05
states[10] = 0
constants[46] = 17
constants[47] = 3
constants[48] = 10
constants[49] = 0.3
states[11] = 0
constants[50] = -500
constants[51] = 0.04
states[12] = 0.0604
constants[52] = 1
constants[53] = 1
states[13] = 0.057
states[14] = 0.287
constants[54] = 27
constants[55] = 16
constants[56] = 40
constants[57] = 74
constants[58] = 5
constants[59] = 7.5
constants[60] = 80
constants[61] = 11
constants[62] = 20
constants[63] = 0.005
constants[64] = -38.8
states[15] = 0.182
constants[65] = 79.8
constants[66] = 5.3
constants[67] = 70
constants[68] = 11
constants[69] = 10
constants[70] = 11
constants[71] = 10
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
algebraic[2] = 1.00000/(1.00000+exp((states[0]+constants[8])/-constants[9]))
rates[1] = (algebraic[2]-states[1])/constants[10]
algebraic[3] = 1.00000/(1.00000+exp((states[0]+constants[12])/constants[13]))
rates[4] = (algebraic[3]-states[4])/constants[14]
algebraic[4] = 1.00000/(1.00000+exp(-(states[0]+constants[15])/constants[16]))
rates[3] = (algebraic[4]-states[3])/constants[17]
algebraic[8] = 1.00000/(1.00000+exp(-(states[0]+constants[39])/constants[40]))
rates[8] = (algebraic[8]-states[8])/constants[41]
algebraic[9] = 1.00000/(1.00000+exp((states[0]+constants[42])/constants[43]))
rates[9] = (algebraic[9]-states[9])/constants[44]
algebraic[10] = 1.00000/(1.00000+exp(-(states[0]+constants[46])/constants[47]))
rates[10] = (algebraic[10]-states[10])/constants[48]
algebraic[11] = 1.00000/(1.00000+power(0.00300000/states[12], 2.00000))
rates[11] = (algebraic[11]-states[11])/constants[52]
algebraic[13] = 1.00000/(1.00000+exp((states[0]+constants[60])/constants[61]))
rates[14] = (algebraic[13]-states[14])/constants[62]
algebraic[1] = 3.50000/(exp((states[0]+constants[5])/constants[6])+exp(-(states[0]+constants[5])/constants[7]))+1.00000
algebraic[16] = 1.00000/(1.00000+exp((states[0]+constants[3])/constants[4]))
rates[2] = (algebraic[16]-states[2])/algebraic[1]
algebraic[5] = 2.50000/(exp((states[0]+constants[22])/constants[23])+exp(-(states[0]+constants[22])/constants[24]))+0.0100000
algebraic[17] = 1.00000/(1.00000+exp(-(states[0]+constants[20])/constants[21]))
rates[5] = (algebraic[17]-states[5])/algebraic[5]
algebraic[6] = 5.00000/(exp((states[0]+constants[31])/constants[32])+exp(-(states[0]+constants[31])/constants[33]))+2.00000
algebraic[18] = 1.00000/(1.00000+exp(-(states[0]+constants[29])/constants[30]))
rates[6] = (algebraic[18]-states[6])/algebraic[6]
algebraic[7] = 20.0000/(exp((states[0]+constants[36])/constants[37])+exp(-(states[0]+constants[36])/constants[37]))+1.00000
algebraic[19] = 1.00000/(1.00000+exp((states[0]+constants[34])/constants[35]))
rates[7] = (algebraic[19]-states[7])/algebraic[7]
algebraic[12] = 1.00000/(exp((states[0]+constants[56])/constants[58])+exp(-(states[0]+constants[57])/constants[59]))+0.370000
algebraic[20] = 1.00000/(1.00000+exp(-(states[0]+constants[54])/constants[55]))
rates[13] = (algebraic[20]-states[13])/algebraic[12]
algebraic[14] = 1.00000/(exp((states[0]+constants[67])/constants[68])+exp(-(states[0]+constants[67])/constants[68]))+50.0000
algebraic[21] = 1.00000/(1.00000+exp((states[0]+constants[65])/constants[66]))
rates[15] = (algebraic[21]-states[15])/algebraic[14]
algebraic[24] = constants[27]*states[6]*states[7]*(states[0]-constants[28])
algebraic[25] = constants[38]*states[8]*states[9]*(states[0]-constants[28])
algebraic[26] = constants[45]*states[10]*(states[0]-constants[28])
rates[12] = (1.00000/1000.00)*constants[50]*(algebraic[24]+algebraic[25]+algebraic[26])-constants[51]*states[12]
algebraic[0] = constants[1]*(power(states[1], 3.00000))*states[2]*(states[0]-constants[2])
algebraic[15] = constants[11]*states[3]*states[4]*(states[0]-constants[2])
algebraic[22] = constants[18]*(power(states[5], 4.00000))*(states[0]-constants[19])
algebraic[23] = constants[25]*(states[0]-constants[26])
algebraic[27] = constants[49]*(power(states[11], 2.00000))*(states[0]-constants[19])
algebraic[28] = constants[53]*states[13]*states[14]*(states[0]-constants[19])
algebraic[29] = constants[63]*states[15]*(states[0]-constants[64])
algebraic[30] = custom_piecewise([greater_equal(voi , constants[69]) & less_equal(voi , constants[70]), constants[71] , True, 0.00000])
rates[0] = (-(algebraic[0]+algebraic[15]+algebraic[22]+algebraic[23]+algebraic[24]+algebraic[25]+algebraic[26]+algebraic[27]+algebraic[28]+algebraic[29])+algebraic[30])/constants[0]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[2] = 1.00000/(1.00000+exp((states[0]+constants[8])/-constants[9]))
algebraic[3] = 1.00000/(1.00000+exp((states[0]+constants[12])/constants[13]))
algebraic[4] = 1.00000/(1.00000+exp(-(states[0]+constants[15])/constants[16]))
algebraic[8] = 1.00000/(1.00000+exp(-(states[0]+constants[39])/constants[40]))
algebraic[9] = 1.00000/(1.00000+exp((states[0]+constants[42])/constants[43]))
algebraic[10] = 1.00000/(1.00000+exp(-(states[0]+constants[46])/constants[47]))
algebraic[11] = 1.00000/(1.00000+power(0.00300000/states[12], 2.00000))
algebraic[13] = 1.00000/(1.00000+exp((states[0]+constants[60])/constants[61]))
algebraic[1] = 3.50000/(exp((states[0]+constants[5])/constants[6])+exp(-(states[0]+constants[5])/constants[7]))+1.00000
algebraic[16] = 1.00000/(1.00000+exp((states[0]+constants[3])/constants[4]))
algebraic[5] = 2.50000/(exp((states[0]+constants[22])/constants[23])+exp(-(states[0]+constants[22])/constants[24]))+0.0100000
algebraic[17] = 1.00000/(1.00000+exp(-(states[0]+constants[20])/constants[21]))
algebraic[6] = 5.00000/(exp((states[0]+constants[31])/constants[32])+exp(-(states[0]+constants[31])/constants[33]))+2.00000
algebraic[18] = 1.00000/(1.00000+exp(-(states[0]+constants[29])/constants[30]))
algebraic[7] = 20.0000/(exp((states[0]+constants[36])/constants[37])+exp(-(states[0]+constants[36])/constants[37]))+1.00000
algebraic[19] = 1.00000/(1.00000+exp((states[0]+constants[34])/constants[35]))
algebraic[12] = 1.00000/(exp((states[0]+constants[56])/constants[58])+exp(-(states[0]+constants[57])/constants[59]))+0.370000
algebraic[20] = 1.00000/(1.00000+exp(-(states[0]+constants[54])/constants[55]))
algebraic[14] = 1.00000/(exp((states[0]+constants[67])/constants[68])+exp(-(states[0]+constants[67])/constants[68]))+50.0000
algebraic[21] = 1.00000/(1.00000+exp((states[0]+constants[65])/constants[66]))
algebraic[24] = constants[27]*states[6]*states[7]*(states[0]-constants[28])
algebraic[25] = constants[38]*states[8]*states[9]*(states[0]-constants[28])
algebraic[26] = constants[45]*states[10]*(states[0]-constants[28])
algebraic[0] = constants[1]*(power(states[1], 3.00000))*states[2]*(states[0]-constants[2])
algebraic[15] = constants[11]*states[3]*states[4]*(states[0]-constants[2])
algebraic[22] = constants[18]*(power(states[5], 4.00000))*(states[0]-constants[19])
algebraic[23] = constants[25]*(states[0]-constants[26])
algebraic[27] = constants[49]*(power(states[11], 2.00000))*(states[0]-constants[19])
algebraic[28] = constants[53]*states[13]*states[14]*(states[0]-constants[19])
algebraic[29] = constants[63]*states[15]*(states[0]-constants[64])
algebraic[30] = custom_piecewise([greater_equal(voi , constants[69]) & less_equal(voi , constants[70]), constants[71] , True, 0.00000])
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)