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 = 70
sizeStates = 7
sizeConstants = 43
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_algebraic[1] = "IK in component membrane (femtoA)"
legend_algebraic[4] = "ICa in component membrane (femtoA)"
legend_algebraic[2] = "IKCa in component membrane (femtoA)"
legend_algebraic[29] = "IKATP in component KATP (femtoA)"
legend_constants[0] = "Cm in component membrane (femtoF)"
legend_constants[1] = "gK in component membrane (picoS)"
legend_constants[2] = "VK in component KATP (millivolt)"
legend_states[1] = "n in component membrane (dimensionless)"
legend_constants[3] = "gKCa in component membrane (picoS)"
legend_constants[4] = "kd in component membrane (micromolar)"
legend_states[2] = "c in component calcium_handling (micromolar)"
legend_constants[5] = "gCa in component membrane (picoS)"
legend_algebraic[3] = "minf in component membrane (dimensionless)"
legend_constants[6] = "VCa in component membrane (millivolt)"
legend_constants[7] = "taun in component membrane (millisecond)"
legend_algebraic[0] = "ninf in component membrane (dimensionless)"
legend_states[3] = "cer in component calcium_handling (micromolar)"
legend_constants[8] = "fcyt in component calcium_handling (dimensionless)"
legend_algebraic[11] = "Jmem in component calcium_handling (flux)"
legend_algebraic[9] = "Jer in component calcium_handling (flux)"
legend_constants[9] = "fer in component calcium_handling (dimensionless)"
legend_constants[10] = "sigmaV in component calcium_handling (dimensionless)"
legend_constants[11] = "pleak in component calcium_handling (first_order_rate_constant)"
legend_constants[12] = "Kserca in component calcium_handling (first_order_rate_constant)"
legend_constants[13] = "lambdaer in component calcium_handling (dimensionless)"
legend_constants[14] = "epser in component calcium_handling (dimensionless)"
legend_constants[15] = "alpha in component calcium_handling (micromolar_per_femtoA_millisecond)"
legend_constants[16] = "kpmca in component calcium_handling (first_order_rate_constant)"
legend_algebraic[5] = "Jserca in component calcium_handling (flux)"
legend_algebraic[7] = "Jleak in component calcium_handling (flux)"
legend_algebraic[8] = "rgpdh in component glycolysis (flux)"
legend_constants[17] = "Rgk in component glycolysis (per_second)"
legend_constants[18] = "atot in component glycolysis (micromolar)"
legend_constants[19] = "pfkbas in component glycolysis (dimensionless)"
legend_algebraic[6] = "f6p in component glycolysis (micromolar)"
legend_constants[20] = "lambda in component glycolysis (dimensionless)"
legend_algebraic[69] = "pfk in component pfk (micromolar)"
legend_states[4] = "g6p in component glycolysis (micromolar)"
legend_states[5] = "fbp in component glycolysis (micromolar)"
legend_constants[21] = "bottom1 in component pfk (dimensionless)"
legend_constants[22] = "topa1 in component pfk (dimensionless)"
legend_constants[23] = "k1 in component pfk (micromolar)"
legend_constants[24] = "k2 in component pfk (micromolar)"
legend_constants[25] = "k3 in component pfk (micromolar)"
legend_constants[26] = "k4 in component pfk (micromolar)"
legend_constants[27] = "cat in component pfk (dimensionless)"
legend_algebraic[21] = "atp in component nucleotides (micromolar)"
legend_algebraic[22] = "weight2 in component pfk (dimensionless)"
legend_constants[42] = "topa2 in component pfk (dimensionless)"
legend_algebraic[25] = "bottom2 in component pfk (dimensionless)"
legend_algebraic[12] = "topa3 in component pfk (dimensionless)"
legend_algebraic[10] = "weight3 in component pfk (dimensionless)"
legend_algebraic[28] = "bottom3 in component pfk (dimensionless)"
legend_constants[28] = "famp in component pfk (dimensionless)"
legend_constants[29] = "fatp in component pfk (dimensionless)"
legend_constants[30] = "ffbp in component pfk (dimensionless)"
legend_constants[31] = "fbt in component pfk (dimensionless)"
legend_constants[32] = "fmt in component pfk (dimensionless)"
legend_algebraic[30] = "weight4 in component pfk (dimensionless)"
legend_algebraic[31] = "topa4 in component pfk (dimensionless)"
legend_algebraic[32] = "bottom4 in component pfk (dimensionless)"
legend_algebraic[13] = "weight5 in component pfk (dimensionless)"
legend_algebraic[33] = "topa5 in component pfk (dimensionless)"
legend_algebraic[34] = "bottom5 in component pfk (dimensionless)"
legend_algebraic[35] = "weight6 in component pfk (dimensionless)"
legend_algebraic[36] = "topa6 in component pfk (dimensionless)"
legend_algebraic[37] = "bottom6 in component pfk (dimensionless)"
legend_algebraic[14] = "weight7 in component pfk (dimensionless)"
legend_algebraic[38] = "topa7 in component pfk (dimensionless)"
legend_algebraic[39] = "bottom7 in component pfk (dimensionless)"
legend_algebraic[40] = "weight8 in component pfk (dimensionless)"
legend_algebraic[41] = "topa8 in component pfk (dimensionless)"
legend_algebraic[42] = "bottom8 in component pfk (dimensionless)"
legend_algebraic[46] = "weight9 in component pfk (dimensionless)"
legend_algebraic[43] = "topa9 in component pfk (dimensionless)"
legend_algebraic[47] = "bottom9 in component pfk (dimensionless)"
legend_algebraic[48] = "weight10 in component pfk (dimensionless)"
legend_algebraic[44] = "topa10 in component pfk (dimensionless)"
legend_algebraic[49] = "bottom10 in component pfk (dimensionless)"
legend_algebraic[50] = "weight11 in component pfk (dimensionless)"
legend_algebraic[51] = "topa11 in component pfk (dimensionless)"
legend_algebraic[52] = "bottom11 in component pfk (dimensionless)"
legend_algebraic[53] = "weight12 in component pfk (dimensionless)"
legend_algebraic[54] = "topa12 in component pfk (dimensionless)"
legend_algebraic[55] = "bottom12 in component pfk (dimensionless)"
legend_algebraic[56] = "weight13 in component pfk (dimensionless)"
legend_algebraic[57] = "topa13 in component pfk (dimensionless)"
legend_algebraic[58] = "bottom13 in component pfk (dimensionless)"
legend_algebraic[59] = "weight14 in component pfk (dimensionless)"
legend_algebraic[60] = "topa14 in component pfk (dimensionless)"
legend_algebraic[61] = "bottom14 in component pfk (dimensionless)"
legend_algebraic[62] = "weight15 in component pfk (dimensionless)"
legend_algebraic[63] = "topa15 in component pfk (dimensionless)"
legend_algebraic[64] = "bottom15 in component pfk (dimensionless)"
legend_algebraic[66] = "weight16 in component pfk (dimensionless)"
legend_algebraic[67] = "topa16 in component pfk (dimensionless)"
legend_algebraic[68] = "bottom16 in component pfk (dimensionless)"
legend_algebraic[65] = "topb in component pfk (dimensionless)"
legend_algebraic[45] = "amp in component nucleotides (micromolar)"
legend_algebraic[15] = "mgadp in component KATP (micromolar)"
legend_algebraic[16] = "adp3m in component KATP (micromolar)"
legend_algebraic[23] = "atp4m in component KATP (micromolar)"
legend_algebraic[17] = "topo in component KATP (dimensionless)"
legend_algebraic[26] = "bottomo in component KATP (dimensionless)"
legend_algebraic[27] = "katpo in component KATP (dimensionless)"
legend_constants[33] = "gkatpbar in component KATP (picoS)"
legend_states[6] = "adp in component nucleotides (micromolar)"
legend_constants[34] = "kdd in component KATP (dimensionless)"
legend_constants[35] = "ktd in component KATP (dimensionless)"
legend_constants[36] = "ktt in component KATP (dimensionless)"
legend_algebraic[19] = "fback in component nucleotides (dimensionless)"
legend_constants[37] = "taua in component nucleotides (dimensionless)"
legend_constants[38] = "r1 in component nucleotides (micromolar)"
legend_constants[39] = "r in component nucleotides (dimensionless)"
legend_algebraic[18] = "y in component nucleotides (dimensionless)"
legend_constants[40] = "vg in component nucleotides (dimensionless)"
legend_constants[41] = "kg in component nucleotides (flux)"
legend_algebraic[20] = "rad in component nucleotides (dimensionless)"
legend_algebraic[24] = "ratio in component nucleotides (dimensionless)"
legend_rates[0] = "d/dt V in component membrane (millivolt)"
legend_rates[1] = "d/dt n in component membrane (dimensionless)"
legend_rates[2] = "d/dt c in component calcium_handling (micromolar)"
legend_rates[3] = "d/dt cer in component calcium_handling (micromolar)"
legend_rates[5] = "d/dt fbp in component glycolysis (micromolar)"
legend_rates[4] = "d/dt g6p in component glycolysis (micromolar)"
legend_rates[6] = "d/dt adp in component nucleotides (micromolar)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
states[0] = -60
constants[0] = 5300
constants[1] = 2700
constants[2] = -75
states[1] = 0
constants[3] = 100
constants[4] = 0.5
states[2] = 0.1
constants[5] = 1000
constants[6] = 25
constants[7] = 20
states[3] = 185
constants[8] = 0.01
constants[9] = 0.01
constants[10] = 31
constants[11] = 0.0002
constants[12] = 0.4
constants[13] = 1
constants[14] = 1
constants[15] = 0.00000450
constants[16] = 0.2
constants[17] = 0.2
constants[18] = 3000
constants[19] = 0.06
constants[20] = 0.005
states[4] = 200
states[5] = 40
constants[21] = 1
constants[22] = 0
constants[23] = 30
constants[24] = 1
constants[25] = 50000
constants[26] = 1000
constants[27] = 2
constants[28] = 0.02
constants[29] = 20
constants[30] = 0.2
constants[31] = 20
constants[32] = 20
constants[33] = 27000
states[6] = 780
constants[34] = 17
constants[35] = 26
constants[36] = 1
constants[37] = 300000
constants[38] = 0.35
constants[39] = 1
constants[40] = 2.2
constants[41] = 10
constants[42] = constants[22]
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
algebraic[0] = 1.00000/(1.00000+exp(-(16.0000+states[0])/5.00000))
rates[1] = (algebraic[0]-states[1])/constants[7]
algebraic[5] = constants[12]*states[2]
algebraic[7] = constants[11]*(states[3]-states[2])
algebraic[9] = (constants[14]*(algebraic[7]-algebraic[5]))/constants[13]
rates[3] = -constants[9]*constants[10]*algebraic[9]
algebraic[3] = 1.00000/(1.00000+exp(-(20.0000+states[0])/12.0000))
algebraic[4] = constants[5]*algebraic[3]*(states[0]-constants[6])
algebraic[11] = -(constants[15]*algebraic[4]+constants[16]*states[2])
rates[2] = constants[8]*(algebraic[11]+algebraic[9])
algebraic[20] = (power(power(states[6]-constants[18], 2.00000)-4.00000*(power(states[6], 2.00000)), 1.0/2))/1.00000
algebraic[21] = 0.500000*((constants[18]-states[6])+algebraic[20]*1.00000)
algebraic[8] = 0.200000*(power(states[5]/1.00000, 1.0/2))
algebraic[18] = constants[40]*(algebraic[8]/(constants[41]+algebraic[8]))
algebraic[19] = constants[39]+algebraic[18]
rates[6] = (algebraic[21]-states[6]*exp(algebraic[19]*(1.00000-states[2]/constants[38])))/(constants[37]*1.00000)
algebraic[1] = constants[1]*states[1]*(states[0]-constants[2])
algebraic[2] = (constants[3]/(1.00000+power(constants[4]/states[2], 2.00000)))*(states[0]-constants[2])
algebraic[15] = 0.165000*states[6]
algebraic[17] = 0.0800000*(1.00000+(2.00000*algebraic[15])/(constants[34]*1.00000))+0.890000*(power(algebraic[15]/(constants[34]*1.00000), 2.00000))
algebraic[16] = 0.135000*states[6]
algebraic[23] = 0.0500000*algebraic[21]
algebraic[26] = (power(1.00000+algebraic[15]/(constants[34]*1.00000), 2.00000))*(1.00000+algebraic[16]/(constants[35]*1.00000)+algebraic[23]/(constants[36]*1.00000))
algebraic[27] = algebraic[17]/algebraic[26]
algebraic[29] = constants[33]*algebraic[27]*(states[0]-constants[2])
rates[0] = -(algebraic[1]+algebraic[4]+algebraic[2]+algebraic[29])/constants[0]
algebraic[6] = 0.300000*states[4]
algebraic[10] = (power(algebraic[6], 2.00000))/(constants[25]*1.00000)
algebraic[12] = constants[42]+algebraic[10]
algebraic[30] = (power(algebraic[6]*algebraic[21], 2.00000))/(constants[29]*constants[25]*constants[26]*(power(1.00000, 2.00000)))
algebraic[31] = algebraic[12]+algebraic[30]
algebraic[33] = algebraic[31]
algebraic[36] = algebraic[33]
algebraic[14] = (states[5]*(power(algebraic[6], 2.00000)))/(constants[24]*constants[25]*constants[30]*1.00000)
algebraic[38] = algebraic[36]+algebraic[14]
algebraic[40] = (states[5]*(power(algebraic[6], 2.00000))*(power(algebraic[21], 2.00000)))/(constants[24]*constants[25]*constants[26]*constants[30]*constants[31]*constants[29]*(power(1.00000, 2.00000)))
algebraic[41] = algebraic[38]+algebraic[40]
algebraic[43] = algebraic[41]
algebraic[44] = algebraic[43]
algebraic[45] = (states[6]*states[6])/algebraic[21]
algebraic[50] = (algebraic[45]*(power(algebraic[6], 2.00000)))/(constants[23]*constants[25]*constants[28]*1.00000)
algebraic[51] = algebraic[44]+algebraic[50]
algebraic[53] = (algebraic[45]*(power(algebraic[6], 2.00000))*(power(algebraic[21], 2.00000)))/(constants[23]*constants[25]*constants[26]*constants[28]*constants[32]*constants[29]*(power(1.00000, 2.00000)))
algebraic[54] = algebraic[51]+algebraic[53]
algebraic[57] = algebraic[54]
algebraic[60] = algebraic[57]
algebraic[63] = algebraic[60]
algebraic[66] = (algebraic[45]*states[5]*(power(algebraic[6], 2.00000))*(power(algebraic[21], 2.00000)))/(constants[23]*constants[24]*constants[25]*constants[26]*constants[30]*constants[28]*constants[31]*constants[32]*constants[29]*(power(1.00000, 2.00000)))
algebraic[67] = algebraic[63]+algebraic[66]
algebraic[22] = (power(algebraic[21], 2.00000))/(constants[26]*1.00000)
algebraic[25] = constants[21]+algebraic[22]
algebraic[28] = algebraic[25]+algebraic[10]
algebraic[32] = algebraic[28]+algebraic[30]
algebraic[13] = states[5]/constants[24]
algebraic[34] = algebraic[32]+algebraic[13]
algebraic[35] = (states[5]*(power(algebraic[21], 2.00000)))/(constants[24]*constants[26]*constants[31]*1.00000)
algebraic[37] = algebraic[34]+algebraic[35]
algebraic[39] = algebraic[37]+algebraic[14]
algebraic[42] = algebraic[39]+algebraic[40]
algebraic[46] = algebraic[45]/constants[23]
algebraic[47] = algebraic[42]+algebraic[46]
algebraic[48] = (algebraic[45]*(power(algebraic[21], 2.00000)))/(constants[23]*constants[26]*constants[32]*1.00000)
algebraic[49] = algebraic[47]+algebraic[48]
algebraic[52] = algebraic[49]+algebraic[50]
algebraic[55] = algebraic[52]+algebraic[53]
algebraic[56] = (algebraic[45]*states[5])/(constants[23]*constants[24])
algebraic[58] = algebraic[55]+algebraic[56]
algebraic[59] = (algebraic[45]*states[5]*(power(algebraic[21], 2.00000)))/(constants[23]*constants[24]*constants[26]*constants[31]*constants[32]*1.00000)
algebraic[61] = algebraic[58]+algebraic[59]
algebraic[62] = (algebraic[45]*states[5]*(power(algebraic[6], 2.00000)))/(constants[23]*constants[24]*constants[25]*constants[30]*constants[28]*1.00000)
algebraic[64] = algebraic[61]+algebraic[62]
algebraic[68] = algebraic[64]+algebraic[66]
algebraic[65] = algebraic[62]
algebraic[69] = 1.00000*((constants[19]*constants[27]*algebraic[67]+constants[27]*algebraic[65])/algebraic[68])
rates[5] = constants[20]*(algebraic[69]/1.00000-0.500000*algebraic[8])
rates[4] = constants[20]*(constants[17]*1.00000-algebraic[69]/1.00000)
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[0] = 1.00000/(1.00000+exp(-(16.0000+states[0])/5.00000))
algebraic[5] = constants[12]*states[2]
algebraic[7] = constants[11]*(states[3]-states[2])
algebraic[9] = (constants[14]*(algebraic[7]-algebraic[5]))/constants[13]
algebraic[3] = 1.00000/(1.00000+exp(-(20.0000+states[0])/12.0000))
algebraic[4] = constants[5]*algebraic[3]*(states[0]-constants[6])
algebraic[11] = -(constants[15]*algebraic[4]+constants[16]*states[2])
algebraic[20] = (power(power(states[6]-constants[18], 2.00000)-4.00000*(power(states[6], 2.00000)), 1.0/2))/1.00000
algebraic[21] = 0.500000*((constants[18]-states[6])+algebraic[20]*1.00000)
algebraic[8] = 0.200000*(power(states[5]/1.00000, 1.0/2))
algebraic[18] = constants[40]*(algebraic[8]/(constants[41]+algebraic[8]))
algebraic[19] = constants[39]+algebraic[18]
algebraic[1] = constants[1]*states[1]*(states[0]-constants[2])
algebraic[2] = (constants[3]/(1.00000+power(constants[4]/states[2], 2.00000)))*(states[0]-constants[2])
algebraic[15] = 0.165000*states[6]
algebraic[17] = 0.0800000*(1.00000+(2.00000*algebraic[15])/(constants[34]*1.00000))+0.890000*(power(algebraic[15]/(constants[34]*1.00000), 2.00000))
algebraic[16] = 0.135000*states[6]
algebraic[23] = 0.0500000*algebraic[21]
algebraic[26] = (power(1.00000+algebraic[15]/(constants[34]*1.00000), 2.00000))*(1.00000+algebraic[16]/(constants[35]*1.00000)+algebraic[23]/(constants[36]*1.00000))
algebraic[27] = algebraic[17]/algebraic[26]
algebraic[29] = constants[33]*algebraic[27]*(states[0]-constants[2])
algebraic[6] = 0.300000*states[4]
algebraic[10] = (power(algebraic[6], 2.00000))/(constants[25]*1.00000)
algebraic[12] = constants[42]+algebraic[10]
algebraic[30] = (power(algebraic[6]*algebraic[21], 2.00000))/(constants[29]*constants[25]*constants[26]*(power(1.00000, 2.00000)))
algebraic[31] = algebraic[12]+algebraic[30]
algebraic[33] = algebraic[31]
algebraic[36] = algebraic[33]
algebraic[14] = (states[5]*(power(algebraic[6], 2.00000)))/(constants[24]*constants[25]*constants[30]*1.00000)
algebraic[38] = algebraic[36]+algebraic[14]
algebraic[40] = (states[5]*(power(algebraic[6], 2.00000))*(power(algebraic[21], 2.00000)))/(constants[24]*constants[25]*constants[26]*constants[30]*constants[31]*constants[29]*(power(1.00000, 2.00000)))
algebraic[41] = algebraic[38]+algebraic[40]
algebraic[43] = algebraic[41]
algebraic[44] = algebraic[43]
algebraic[45] = (states[6]*states[6])/algebraic[21]
algebraic[50] = (algebraic[45]*(power(algebraic[6], 2.00000)))/(constants[23]*constants[25]*constants[28]*1.00000)
algebraic[51] = algebraic[44]+algebraic[50]
algebraic[53] = (algebraic[45]*(power(algebraic[6], 2.00000))*(power(algebraic[21], 2.00000)))/(constants[23]*constants[25]*constants[26]*constants[28]*constants[32]*constants[29]*(power(1.00000, 2.00000)))
algebraic[54] = algebraic[51]+algebraic[53]
algebraic[57] = algebraic[54]
algebraic[60] = algebraic[57]
algebraic[63] = algebraic[60]
algebraic[66] = (algebraic[45]*states[5]*(power(algebraic[6], 2.00000))*(power(algebraic[21], 2.00000)))/(constants[23]*constants[24]*constants[25]*constants[26]*constants[30]*constants[28]*constants[31]*constants[32]*constants[29]*(power(1.00000, 2.00000)))
algebraic[67] = algebraic[63]+algebraic[66]
algebraic[22] = (power(algebraic[21], 2.00000))/(constants[26]*1.00000)
algebraic[25] = constants[21]+algebraic[22]
algebraic[28] = algebraic[25]+algebraic[10]
algebraic[32] = algebraic[28]+algebraic[30]
algebraic[13] = states[5]/constants[24]
algebraic[34] = algebraic[32]+algebraic[13]
algebraic[35] = (states[5]*(power(algebraic[21], 2.00000)))/(constants[24]*constants[26]*constants[31]*1.00000)
algebraic[37] = algebraic[34]+algebraic[35]
algebraic[39] = algebraic[37]+algebraic[14]
algebraic[42] = algebraic[39]+algebraic[40]
algebraic[46] = algebraic[45]/constants[23]
algebraic[47] = algebraic[42]+algebraic[46]
algebraic[48] = (algebraic[45]*(power(algebraic[21], 2.00000)))/(constants[23]*constants[26]*constants[32]*1.00000)
algebraic[49] = algebraic[47]+algebraic[48]
algebraic[52] = algebraic[49]+algebraic[50]
algebraic[55] = algebraic[52]+algebraic[53]
algebraic[56] = (algebraic[45]*states[5])/(constants[23]*constants[24])
algebraic[58] = algebraic[55]+algebraic[56]
algebraic[59] = (algebraic[45]*states[5]*(power(algebraic[21], 2.00000)))/(constants[23]*constants[24]*constants[26]*constants[31]*constants[32]*1.00000)
algebraic[61] = algebraic[58]+algebraic[59]
algebraic[62] = (algebraic[45]*states[5]*(power(algebraic[6], 2.00000)))/(constants[23]*constants[24]*constants[25]*constants[30]*constants[28]*1.00000)
algebraic[64] = algebraic[61]+algebraic[62]
algebraic[68] = algebraic[64]+algebraic[66]
algebraic[65] = algebraic[62]
algebraic[69] = 1.00000*((constants[19]*constants[27]*algebraic[67]+constants[27]*algebraic[65])/algebraic[68])
algebraic[24] = algebraic[21]/states[6]
return algebraic
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)