Generated Code
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The raw code is available.
# Size of variable arrays:
sizeAlgebraic = 7
sizeStates = 1
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 = "time in component environment (second)"
legend_constants[0] = "L_1 in component contraction (mm)"
legend_constants[1] = "L_2 in component contraction (mm)"
legend_constants[2] = "L_3 in component contraction (mm)"
legend_constants[3] = "L_4 in component contraction (mm)"
legend_constants[4] = "f_c in component contraction (newton)"
legend_constants[5] = "v_max in component contraction (mm_per_second)"
legend_constants[6] = "curv in component contraction (dimensionless)"
legend_constants[7] = "k_1 in component contraction (newton)"
legend_constants[8] = "k_2 in component contraction (per_mm)"
legend_constants[9] = "F_1 in component contraction (newton)"
legend_constants[10] = "d_LSEC1 in component contraction (mm)"
legend_constants[11] = "k_sh in component contraction (dimensionless)"
legend_constants[12] = "L_m in component contraction (mm)"
legend_constants[13] = "F_im in component contraction (newton)"
legend_constants[14] = "tau in component contraction (second)"
legend_algebraic[5] = "v_cc in component contraction (mm_per_second)"
legend_algebraic[6] = "f_v in component contraction (dimensionless)"
legend_algebraic[1] = "f_L in component contraction (newton)"
legend_algebraic[4] = "f_sec in component contraction (newton)"
legend_algebraic[0] = "f_pec in component contraction (newton)"
legend_algebraic[3] = "delta_L_sec in component contraction (mm)"
legend_constants[15] = "delta_L_sec1 in component contraction (mm)"
legend_states[0] = "delta_L_pec in component contraction (mm)"
legend_constants[16] = "k in component contraction (newton_per_mm)"
legend_algebraic[2] = "L_mtc in component contraction (mm)"
legend_constants[17] = "A in component contraction (dimensionless)"
legend_constants[18] = "L_mslack in component contraction (mm)"
legend_rates[0] = "d/dt delta_L_pec in component contraction (mm)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
constants[0] = -23
constants[1] = -14
constants[2] = 2
constants[3] = 19
constants[4] = 0.49
constants[5] = -141
constants[6] = 5.8
constants[7] = 0.012
constants[8] = 0.317
constants[9] = 4.1
constants[10] = 4.1
constants[11] = 3.3
constants[12] = 0.3
constants[13] = 18.1
constants[14] = 0.006
constants[15] = 4.1
states[0] = 0.2
constants[16] = 3.5
constants[17] = 1
constants[18] = 0.3
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
algebraic[1] = custom_piecewise([greater_equal(states[0] , constants[0]) & less_equal(states[0] , constants[1]), (constants[4]/(constants[1]-constants[0]))*(states[0]-constants[0]) , greater(states[0] , constants[1]) & less_equal(states[0] , 0.00000), ((1.00000-constants[4])/-constants[1])*(states[0]-constants[1]) , greater(states[0] , 0.00000) & less_equal(states[0] , constants[2]), 1.00000 , greater(states[0] , constants[2]) & less_equal(states[0] , constants[3]), (-1.00000/(constants[3]-constants[2]))*(states[0]-constants[2]) , True, float('nan')])
algebraic[2] = custom_piecewise([less_equal(voi , 1.00000), 0.290000 , greater(voi , 1.00000) & less(voi , 5.00000), 0.220000 , True, 0.190000])
algebraic[3] = (algebraic[2]-states[0])-constants[18]
algebraic[4] = custom_piecewise([greater(algebraic[3] , 0.00000) & less(algebraic[3] , constants[15]), (constants[9]/(exp(constants[11])-1.00000))*(exp((constants[11]*algebraic[3])/constants[15])-1.00000) , less_equal(algebraic[3] , constants[15]), constants[9]+constants[16]*(algebraic[3]-constants[15]) , True, float('nan')])
algebraic[0] = custom_piecewise([greater(states[0] , 0.00000), constants[7]*(exp(constants[8]*states[0])-1.00000) , less_equal(states[0] , 0.00000), 0.00000 , True, float('nan')])
rootfind_0(voi, constants, rates, states, algebraic)
rates[0] = algebraic[5]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[1] = custom_piecewise([greater_equal(states[0] , constants[0]) & less_equal(states[0] , constants[1]), (constants[4]/(constants[1]-constants[0]))*(states[0]-constants[0]) , greater(states[0] , constants[1]) & less_equal(states[0] , 0.00000), ((1.00000-constants[4])/-constants[1])*(states[0]-constants[1]) , greater(states[0] , 0.00000) & less_equal(states[0] , constants[2]), 1.00000 , greater(states[0] , constants[2]) & less_equal(states[0] , constants[3]), (-1.00000/(constants[3]-constants[2]))*(states[0]-constants[2]) , True, float('nan')])
algebraic[2] = custom_piecewise([less_equal(voi , 1.00000), 0.290000 , greater(voi , 1.00000) & less(voi , 5.00000), 0.220000 , True, 0.190000])
algebraic[3] = (algebraic[2]-states[0])-constants[18]
algebraic[4] = custom_piecewise([greater(algebraic[3] , 0.00000) & less(algebraic[3] , constants[15]), (constants[9]/(exp(constants[11])-1.00000))*(exp((constants[11]*algebraic[3])/constants[15])-1.00000) , less_equal(algebraic[3] , constants[15]), constants[9]+constants[16]*(algebraic[3]-constants[15]) , True, float('nan')])
algebraic[0] = custom_piecewise([greater(states[0] , 0.00000), constants[7]*(exp(constants[8]*states[0])-1.00000) , less_equal(states[0] , 0.00000), 0.00000 , True, float('nan')])
return algebraic
initialGuess0 = None
def rootfind_0(voi, constants, rates, states, algebraic):
"""Calculate values of algebraic variables for DAE"""
from scipy.optimize import fsolve
global initialGuess0
if initialGuess0 is None: initialGuess0 = ones(2)*0.1
if not iterable(voi):
soln = fsolve(residualSN_0, initialGuess0, args=(algebraic, voi, constants, rates, states), xtol=1E-6)
initialGuess0 = soln
algebraic[5] = soln[0]
algebraic[6] = soln[1]
else:
for (i,t) in enumerate(voi):
soln = fsolve(residualSN_0, initialGuess0, args=(algebraic[:,i], voi[i], constants, rates[:i], states[:,i]), xtol=1E-6)
initialGuess0 = soln
algebraic[5][i] = soln[0]
algebraic[6][i] = soln[1]
def residualSN_0(algebraicCandidate, algebraic, voi, constants, rates, states):
resid = array([0.0] * 2)
algebraic[5] = algebraicCandidate[0]
algebraic[6] = algebraicCandidate[1]
resid[0] = (algebraic[5]-(1.00000/algebraic[6])*((algebraic[4]-algebraic[0])/(constants[17]*algebraic[1]*constants[13])))
resid[1] = (algebraic[6]-(constants[5]-algebraic[5])/(constants[5]+algebraic[5]*constants[6]))
return resid
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)