Generated Code
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The raw code is available.
# Size of variable arrays:
sizeAlgebraic = 24
sizeStates = 7
sizeConstants = 58
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_algebraic[10] = "Pi in component TempCDa (UnitP)"
legend_states[0] = "Pi in component TempRLC (UnitP)"
legend_algebraic[18] = "Qo in component TempRC (UnitQ)"
legend_algebraic[21] = "Qvi in component TempIPump (UnitQ)"
legend_algebraic[5] = "Qo in component TempCDv (UnitQ)"
legend_algebraic[6] = "Pi in component TJoint (UnitP)"
legend_algebraic[19] = "Qvo in component TempIPump (UnitQ)"
legend_algebraic[14] = "Pi in component TJoint (UnitP)"
legend_algebraic[3] = "Pi in component TempCDv (UnitP)"
legend_algebraic[23] = "Qo in component TJoint (UnitQ)"
legend_constants[0] = "CVao in component ParaHeartP (UnitCV)"
legend_algebraic[2] = "E in component EVentricle (UnitE)"
legend_states[1] = "V in component TempCDv (UnitV)"
legend_constants[1] = "PlvIni in component ParaHeartP (UnitP)"
legend_constants[2] = "VlvIni in component ParaHeartP (UnitV)"
legend_algebraic[4] = "Tao in component TempCDv (dimensionless)"
legend_constants[3] = "Vlv0 in component ParaHeartP (UnitV)"
legend_algebraic[12] = "Qo in component TempCDa (UnitQ)"
legend_constants[4] = "CVmi in component ParaHeartP (UnitCV)"
legend_algebraic[9] = "E in component EAtrium (UnitE)"
legend_states[2] = "V in component TempCDa (UnitV)"
legend_constants[5] = "PlaIni in component ParaHeartP (UnitP)"
legend_constants[6] = "VlaIni in component ParaHeartP (UnitV)"
legend_algebraic[11] = "Tao in component TempCDa (dimensionless)"
legend_constants[7] = "Vla0 in component ParaHeartP (UnitV)"
legend_constants[8] = "ElvMax in component ParaHeartP (UnitE)"
legend_constants[9] = "ElvMin in component ParaHeartP (UnitE)"
legend_constants[10] = "T in component ParaHeartP (second)"
legend_constants[11] = "Ts1 in component ParaHeartP (dimensionless)"
legend_constants[12] = "Ts2 in component ParaHeartP (dimensionless)"
legend_algebraic[0] = "mt in component EVentricle (second)"
legend_algebraic[1] = "et in component EVentricle (dimensionless)"
legend_constants[13] = "ElaMax in component ParaHeartP (UnitE)"
legend_constants[14] = "ElaMin in component ParaHeartP (UnitE)"
legend_constants[15] = "Tpwb in component ParaHeartP (dimensionless)"
legend_constants[16] = "Tpww in component ParaHeartP (dimensionless)"
legend_algebraic[7] = "mt in component EAtrium (second)"
legend_algebraic[8] = "et in component EAtrium (dimensionless)"
legend_states[3] = "Qo in component TempRLC (UnitQ)"
legend_constants[17] = "Rsas in component ParaSys (UnitR)"
legend_constants[18] = "Csas in component ParaSys (UnitC)"
legend_constants[19] = "Lsas in component ParaSys (UnitL)"
legend_constants[20] = "P0sas in component ParaSys (UnitP)"
legend_constants[21] = "Q0sas in component ParaSys (UnitQ)"
legend_states[4] = "Pi in component TempRLC (UnitP)"
legend_algebraic[22] = "Qo in component TJoint (UnitQ)"
legend_algebraic[20] = "Pi in component TempR (UnitP)"
legend_states[5] = "Qo in component TempRLC (UnitQ)"
legend_constants[22] = "Rsat in component ParaSys (UnitR)"
legend_constants[23] = "Csat in component ParaSys (UnitC)"
legend_constants[24] = "Lsat in component ParaSys (UnitL)"
legend_constants[25] = "P0sat in component ParaSys (UnitP)"
legend_constants[26] = "Q0sat in component ParaSys (UnitQ)"
legend_algebraic[17] = "Pi in component TempR (UnitP)"
legend_algebraic[13] = "Qo in component TempR (UnitQ)"
legend_constants[27] = "Rsar in component ParaSys (UnitR)"
legend_states[6] = "Pi in component TempRC (UnitP)"
legend_algebraic[15] = "Qo in component TempR (UnitQ)"
legend_constants[28] = "Rscp in component ParaSys (UnitR)"
legend_constants[29] = "Rsvn in component ParaSys (UnitR)"
legend_constants[30] = "Csvn in component ParaSys (UnitC)"
legend_constants[31] = "P0svn in component ParaSys (UnitP)"
legend_constants[57] = "Wn in component TempIPump (UnitRPM)"
legend_constants[32] = "Ts2 in component ParaHeartP (dimensionless)"
legend_constants[33] = "T in component ParaHeartP (second)"
legend_constants[34] = "Kp0 in component ParaIPump (UnitKp0)"
legend_constants[35] = "Kp1 in component ParaIPump (UnitKp1)"
legend_constants[36] = "Kp2 in component ParaIPump (UnitKp2)"
legend_constants[37] = "Kp3 in component ParaIPump (UnitKp3)"
legend_constants[38] = "Kp4 in component ParaIPump (UnitKp4)"
legend_constants[39] = "Kp5 in component ParaIPump (UnitKp5)"
legend_constants[40] = "Kp6 in component ParaIPump (UnitKp6)"
legend_constants[41] = "W in component ParaIPump (UnitRPM)"
legend_algebraic[16] = "dPv in component TempIPump (UnitP)"
legend_constants[42] = "ElaMax in component ParaHeartP (UnitE)"
legend_constants[43] = "ElaMin in component ParaHeartP (UnitE)"
legend_constants[44] = "PlaIni in component ParaHeartP (UnitP)"
legend_constants[45] = "VlaIni in component ParaHeartP (UnitV)"
legend_constants[46] = "ElvMax in component ParaHeartP (UnitE)"
legend_constants[47] = "ElvMin in component ParaHeartP (UnitE)"
legend_constants[48] = "PlvIni in component ParaHeartP (UnitP)"
legend_constants[49] = "VlvIni in component ParaHeartP (UnitV)"
legend_constants[50] = "Tpwb in component ParaHeartP (dimensionless)"
legend_constants[51] = "Tpww in component ParaHeartP (dimensionless)"
legend_constants[52] = "Ts1 in component ParaHeartP (dimensionless)"
legend_constants[53] = "CVao in component ParaHeartP (UnitCV)"
legend_constants[54] = "CVmi in component ParaHeartP (UnitCV)"
legend_constants[55] = "Vlv0 in component ParaHeartP (UnitV)"
legend_constants[56] = "Vla0 in component ParaHeartP (UnitV)"
legend_rates[1] = "d/dt V in component TempCDv (UnitV)"
legend_rates[2] = "d/dt V in component TempCDa (UnitV)"
legend_rates[0] = "d/dt Pi in component TempRLC (UnitP)"
legend_rates[3] = "d/dt Qo in component TempRLC (UnitQ)"
legend_rates[4] = "d/dt Pi in component TempRLC (UnitP)"
legend_rates[5] = "d/dt Qo in component TempRLC (UnitQ)"
legend_rates[6] = "d/dt Pi in component TempRC (UnitP)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
constants[0] = 350.
constants[1] = 1.0
constants[2] = 5.0
constants[3] = 500
constants[4] = 400.
constants[5] = 1.0
constants[6] = 4.0
constants[7] = 20
constants[8] = 0.5
constants[9] = 0.1
constants[10] = 1.0
constants[11] = 0.3
constants[12] = 0.45
constants[13] = 0.25
constants[14] = 0.15
constants[15] = 0.92
constants[16] = 0.09
constants[17] = 0.003
constants[18] = 0.08
constants[19] = 0.000062
constants[20] = 100.
constants[21] = 0.
constants[22] = 0.05
constants[23] = 1.6
constants[24] = 0.0017
constants[25] = 100.
constants[26] = 0.
constants[27] = 0.5
constants[28] = 0.52
constants[29] = 0.075
constants[30] = 20.5
constants[31] = 0.
constants[32] = 0.45
constants[33] = 1.0
constants[34] = 19.51840
constants[35] = -3.03610e-3
constants[36] = -1.23045
constants[37] = 5.78974e-4
constants[38] = -5.8777e-8
constants[39] = -1.27539e-6
constants[40] = 2.04834e-10
constants[41] = 3600
constants[42] = 0.25
constants[43] = 0.15
constants[44] = 1.0
constants[45] = 4.0
constants[46] = 0.5
constants[47] = 0.1
constants[48] = 1.0
constants[49] = 5.0
constants[50] = 0.92
constants[51] = 0.09
constants[52] = 0.3
constants[53] = 350.
constants[54] = 400.
constants[55] = 500
constants[56] = 20
constants[57] = 1.00000*constants[41]
states[0] = constants[20]
states[1] = constants[3]
states[2] = constants[7]
states[3] = constants[21]
states[4] = constants[25]
states[5] = constants[26]
states[6] = constants[31]
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
algebraic[0] = voi-constants[10]*floor(voi/constants[10])
algebraic[1] = custom_piecewise([greater_equal(algebraic[0] , 0.00000) & less_equal(algebraic[0] , constants[11]*constants[10]), 1.00000-cos((3.14159*algebraic[0])/(constants[11]*constants[10])) , greater(algebraic[0] , constants[11]*constants[10]) & less_equal(algebraic[0] , constants[12]*constants[10]), 1.00000+cos((3.14159*(algebraic[0]-constants[11]*constants[10]))/((constants[12]-constants[11])*constants[10])) , greater(algebraic[0] , constants[12]*constants[10]) & less(algebraic[0] , constants[10]), 0.00000 , True, float('nan')])
algebraic[2] = constants[9]+(algebraic[1]*(constants[8]-constants[9]))/2.00000
algebraic[3] = constants[1]+algebraic[2]*(states[1]-constants[2])
algebraic[4] = custom_piecewise([greater_equal(algebraic[3] , states[0]), 1.00000 , less(algebraic[3] , states[0]), 0.00000 , True, float('nan')])
algebraic[5] = custom_piecewise([greater_equal(algebraic[3] , states[0]), constants[0]*algebraic[4]*(power(fabs(algebraic[3]-states[0]), 0.500000)) , less(algebraic[3] , states[0]), -1.00000*constants[0]*algebraic[4]*(power(fabs(states[0]-algebraic[3]), 0.500000)) , True, float('nan')])
rates[0] = (algebraic[5]-states[3])/constants[18]
algebraic[14] = states[4]
rates[3] = ((states[0]-algebraic[14])-constants[17]*states[3])/constants[19]
algebraic[7] = voi-constants[10]*floor(voi/constants[10])
algebraic[8] = custom_piecewise([greater_equal(algebraic[7] , 0.00000) & less_equal(algebraic[7] , ((constants[15]+constants[16])-1.00000)*constants[10]), 1.00000-cos((2.00000*3.14159*(algebraic[7]-(constants[15]-1.00000)*constants[10]))/(constants[16]*constants[10])) , greater(algebraic[7] , ((constants[15]+constants[16])-1.00000)*constants[10]) & less_equal(algebraic[7] , constants[15]*constants[10]), 0.00000 , greater(algebraic[7] , constants[15]*constants[10]) & less_equal(algebraic[7] , constants[10]), 1.00000-cos((2.00000*3.14159*(algebraic[7]-constants[15]*constants[10]))/(constants[16]*constants[10])) , True, float('nan')])
algebraic[9] = constants[14]+(algebraic[8]*(constants[13]-constants[14]))/2.00000
algebraic[10] = constants[5]+algebraic[9]*(states[2]-constants[6])
algebraic[18] = (states[6]-algebraic[10])/constants[29]
algebraic[6] = algebraic[3]
algebraic[11] = custom_piecewise([greater_equal(algebraic[10] , algebraic[6]), 1.00000 , less(algebraic[10] , algebraic[6]), 0.00000 , True, float('nan')])
algebraic[12] = custom_piecewise([greater_equal(algebraic[10] , algebraic[6]), constants[4]*algebraic[11]*(power(fabs(algebraic[10]-algebraic[6]), 0.500000)) , less(algebraic[10] , algebraic[6]), -1.00000*constants[4]*algebraic[11]*(power(fabs(algebraic[6]-algebraic[10]), 0.500000)) , True, float('nan')])
rates[2] = algebraic[18]-algebraic[12]
algebraic[13] = states[5]
algebraic[17] = states[6]+constants[28]*algebraic[13]
algebraic[20] = algebraic[17]+constants[27]*states[5]
rates[5] = ((states[4]-algebraic[20])-constants[22]*states[5])/constants[24]
algebraic[15] = algebraic[13]
rates[6] = (algebraic[15]-algebraic[18])/constants[30]
algebraic[16] = algebraic[14]-algebraic[6]
algebraic[19] = (constants[34]+constants[35]*constants[57]+constants[36]*algebraic[16]+constants[37]*constants[57]*algebraic[16]+constants[38]*(power(constants[57], 2.00000))*algebraic[16]+constants[39]*constants[57]*(power(algebraic[16], 2.00000))+constants[40]*(power(constants[57], 2.00000))*(power(algebraic[16], 2.00000)))*16.6667
algebraic[22] = states[3]+algebraic[19]
rates[4] = (algebraic[22]-states[5])/constants[23]
algebraic[21] = -1.00000*algebraic[19]
algebraic[23] = algebraic[12]+algebraic[21]
rates[1] = algebraic[23]-algebraic[5]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[0] = voi-constants[10]*floor(voi/constants[10])
algebraic[1] = custom_piecewise([greater_equal(algebraic[0] , 0.00000) & less_equal(algebraic[0] , constants[11]*constants[10]), 1.00000-cos((3.14159*algebraic[0])/(constants[11]*constants[10])) , greater(algebraic[0] , constants[11]*constants[10]) & less_equal(algebraic[0] , constants[12]*constants[10]), 1.00000+cos((3.14159*(algebraic[0]-constants[11]*constants[10]))/((constants[12]-constants[11])*constants[10])) , greater(algebraic[0] , constants[12]*constants[10]) & less(algebraic[0] , constants[10]), 0.00000 , True, float('nan')])
algebraic[2] = constants[9]+(algebraic[1]*(constants[8]-constants[9]))/2.00000
algebraic[3] = constants[1]+algebraic[2]*(states[1]-constants[2])
algebraic[4] = custom_piecewise([greater_equal(algebraic[3] , states[0]), 1.00000 , less(algebraic[3] , states[0]), 0.00000 , True, float('nan')])
algebraic[5] = custom_piecewise([greater_equal(algebraic[3] , states[0]), constants[0]*algebraic[4]*(power(fabs(algebraic[3]-states[0]), 0.500000)) , less(algebraic[3] , states[0]), -1.00000*constants[0]*algebraic[4]*(power(fabs(states[0]-algebraic[3]), 0.500000)) , True, float('nan')])
algebraic[14] = states[4]
algebraic[7] = voi-constants[10]*floor(voi/constants[10])
algebraic[8] = custom_piecewise([greater_equal(algebraic[7] , 0.00000) & less_equal(algebraic[7] , ((constants[15]+constants[16])-1.00000)*constants[10]), 1.00000-cos((2.00000*3.14159*(algebraic[7]-(constants[15]-1.00000)*constants[10]))/(constants[16]*constants[10])) , greater(algebraic[7] , ((constants[15]+constants[16])-1.00000)*constants[10]) & less_equal(algebraic[7] , constants[15]*constants[10]), 0.00000 , greater(algebraic[7] , constants[15]*constants[10]) & less_equal(algebraic[7] , constants[10]), 1.00000-cos((2.00000*3.14159*(algebraic[7]-constants[15]*constants[10]))/(constants[16]*constants[10])) , True, float('nan')])
algebraic[9] = constants[14]+(algebraic[8]*(constants[13]-constants[14]))/2.00000
algebraic[10] = constants[5]+algebraic[9]*(states[2]-constants[6])
algebraic[18] = (states[6]-algebraic[10])/constants[29]
algebraic[6] = algebraic[3]
algebraic[11] = custom_piecewise([greater_equal(algebraic[10] , algebraic[6]), 1.00000 , less(algebraic[10] , algebraic[6]), 0.00000 , True, float('nan')])
algebraic[12] = custom_piecewise([greater_equal(algebraic[10] , algebraic[6]), constants[4]*algebraic[11]*(power(fabs(algebraic[10]-algebraic[6]), 0.500000)) , less(algebraic[10] , algebraic[6]), -1.00000*constants[4]*algebraic[11]*(power(fabs(algebraic[6]-algebraic[10]), 0.500000)) , True, float('nan')])
algebraic[13] = states[5]
algebraic[17] = states[6]+constants[28]*algebraic[13]
algebraic[20] = algebraic[17]+constants[27]*states[5]
algebraic[15] = algebraic[13]
algebraic[16] = algebraic[14]-algebraic[6]
algebraic[19] = (constants[34]+constants[35]*constants[57]+constants[36]*algebraic[16]+constants[37]*constants[57]*algebraic[16]+constants[38]*(power(constants[57], 2.00000))*algebraic[16]+constants[39]*constants[57]*(power(algebraic[16], 2.00000))+constants[40]*(power(constants[57], 2.00000))*(power(algebraic[16], 2.00000)))*16.6667
algebraic[22] = states[3]+algebraic[19]
algebraic[21] = -1.00000*algebraic[19]
algebraic[23] = algebraic[12]+algebraic[21]
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)