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 = 10
sizeStates = 3
sizeConstants = 7
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] = "u_in_e in component Environment (J_per_C)"
legend_voi = "t in component Environment (second)"
legend_states[0] = "v_1_e in component Voice_coil_equations (C_per_s)"
legend_algebraic[8] = "a_1_e in component Voice_coil_equations (C_per_s2)"
legend_states[1] = "q_C_m in component Voice_coil_equations (metre)"
legend_states[2] = "v_2_m in component Voice_coil_equations (m_per_s)"
legend_algebraic[9] = "a_2_m in component Voice_coil_equations (m_per_s2)"
legend_algebraic[2] = "u_R_e in component Voice_coil_equations (J_per_C)"
legend_algebraic[6] = "u_L_e in component Voice_coil_equations (J_per_C)"
legend_algebraic[4] = "u_1_e in component Voice_coil_equations (J_per_C)"
legend_algebraic[1] = "u_2_m in component Voice_coil_equations (J_per_m)"
legend_algebraic[3] = "u_C_m in component Voice_coil_equations (J_per_m)"
legend_algebraic[5] = "u_R_m in component Voice_coil_equations (J_per_m)"
legend_algebraic[7] = "u_L_m in component Voice_coil_equations (J_per_m)"
legend_constants[0] = "E_1 in component Voice_coil_equations (J_per_C2)"
legend_constants[1] = "E_2 in component Voice_coil_equations (J_per_m2)"
legend_constants[2] = "R_1_e in component Voice_coil_equations (Js_per_C2)"
legend_constants[3] = "R_2_m in component Voice_coil_equations (Js_per_m2)"
legend_constants[4] = "L_1_e in component Voice_coil_equations (Js2_per_C2)"
legend_constants[5] = "L_2_m in component Voice_coil_equations (Js2_per_m2)"
legend_constants[6] = "Bl in component Voice_coil_equations (Js_per_C_m)"
legend_rates[0] = "d/dt v_1_e in component Voice_coil_equations (C_per_s)"
legend_rates[1] = "d/dt q_C_m in component Voice_coil_equations (metre)"
legend_rates[2] = "d/dt v_2_m in component Voice_coil_equations (m_per_s)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
states[0] = 0
states[1] = 0
states[2] = 0
constants[0] = 1
constants[1] = 100
constants[2] = 5
constants[3] = 0.4
constants[4] = 0.2
constants[5] = 0.01
constants[6] = 6
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
rates[1] = states[2]
algebraic[0] = 50.0000*sin(50.0000*2.00000* pi*voi)
algebraic[2] = constants[2]*states[0]
algebraic[4] = constants[6]*states[2]
rootfind_0(voi, constants, rates, states, algebraic)
rootfind_1(voi, constants, rates, states, algebraic)
rates[0] = algebraic[8]
algebraic[1] = constants[6]*states[0]
algebraic[3] = constants[1]*states[1]
algebraic[5] = constants[3]*states[2]
rootfind_2(voi, constants, rates, states, algebraic)
rootfind_3(voi, constants, rates, states, algebraic)
rates[2] = algebraic[9]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[0] = 50.0000*sin(50.0000*2.00000* pi*voi)
algebraic[2] = constants[2]*states[0]
algebraic[4] = constants[6]*states[2]
algebraic[1] = constants[6]*states[0]
algebraic[3] = constants[1]*states[1]
algebraic[5] = constants[3]*states[2]
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[6] = fsolve(residualSN_0, initialGuess0, args=(algebraic, voi, constants, rates, states), xtol=1E-6)
initialGuess0 = algebraic[6]
else:
for (i,t) in enumerate(voi):
algebraic[6][i] = fsolve(residualSN_0, initialGuess0, args=(algebraic[:,i], voi[i], constants, rates, states[:,i]), xtol=1E-6)
initialGuess0 = algebraic[6][i]
def residualSN_0(algebraicCandidate, algebraic, voi, constants, rates, states):
algebraic[6] = algebraicCandidate
return (algebraic[0]) - (algebraic[2]+algebraic[6]+algebraic[4])
initialGuess1 = None
def rootfind_1(voi, constants, states, algebraic):
"""Calculate value of algebraic variable for DAE"""
from scipy.optimize import fsolve
global initialGuess1
if initialGuess1 is None: initialGuess1 = 0.1
if not iterable(voi):
algebraic[8] = fsolve(residualSN_1, initialGuess1, args=(algebraic, voi, constants, rates, states), xtol=1E-6)
initialGuess1 = algebraic[8]
else:
for (i,t) in enumerate(voi):
algebraic[8][i] = fsolve(residualSN_1, initialGuess1, args=(algebraic[:,i], voi[i], constants, rates, states[:,i]), xtol=1E-6)
initialGuess1 = algebraic[8][i]
def residualSN_1(algebraicCandidate, algebraic, voi, constants, rates, states):
algebraic[8] = algebraicCandidate
return (algebraic[6]) - (constants[4]*algebraic[8])
initialGuess2 = None
def rootfind_2(voi, constants, states, algebraic):
"""Calculate value of algebraic variable for DAE"""
from scipy.optimize import fsolve
global initialGuess2
if initialGuess2 is None: initialGuess2 = 0.1
if not iterable(voi):
algebraic[7] = fsolve(residualSN_2, initialGuess2, args=(algebraic, voi, constants, rates, states), xtol=1E-6)
initialGuess2 = algebraic[7]
else:
for (i,t) in enumerate(voi):
algebraic[7][i] = fsolve(residualSN_2, initialGuess2, args=(algebraic[:,i], voi[i], constants, rates, states[:,i]), xtol=1E-6)
initialGuess2 = algebraic[7][i]
def residualSN_2(algebraicCandidate, algebraic, voi, constants, rates, states):
algebraic[7] = algebraicCandidate
return (algebraic[1]) - (algebraic[3]+algebraic[5]+algebraic[7])
initialGuess3 = None
def rootfind_3(voi, constants, states, algebraic):
"""Calculate value of algebraic variable for DAE"""
from scipy.optimize import fsolve
global initialGuess3
if initialGuess3 is None: initialGuess3 = 0.1
if not iterable(voi):
algebraic[9] = fsolve(residualSN_3, initialGuess3, args=(algebraic, voi, constants, rates, states), xtol=1E-6)
initialGuess3 = algebraic[9]
else:
for (i,t) in enumerate(voi):
algebraic[9][i] = fsolve(residualSN_3, initialGuess3, args=(algebraic[:,i], voi[i], constants, rates, states[:,i]), xtol=1E-6)
initialGuess3 = algebraic[9][i]
def residualSN_3(algebraicCandidate, algebraic, voi, constants, rates, states):
algebraic[9] = algebraicCandidate
return (algebraic[7]) - (constants[5]*algebraic[9])
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)