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 = 34
sizeStates = 15
sizeConstants = 59
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_algebraic[0] = "L_iso in component beta_1_adrenergic_parameters (uM)"
legend_constants[0] = "K_H in component beta_1_adrenergic_parameters (uM)"
legend_constants[1] = "K_L in component beta_1_adrenergic_parameters (uM)"
legend_constants[2] = "K_C in component beta_1_adrenergic_parameters (uM)"
legend_algebraic[1] = "L_ach in component muscarinic_parameters (uM)"
legend_constants[3] = "K_H in component muscarinic_parameters (uM)"
legend_constants[4] = "K_L in component muscarinic_parameters (uM)"
legend_constants[5] = "K_C in component muscarinic_parameters (uM)"
legend_constants[6] = "k_PDE2 in component PDE_parameters (per_sec)"
legend_constants[7] = "Km_PDE2 in component PDE_parameters (uM)"
legend_constants[8] = "k_PDE3 in component PDE_parameters (per_sec)"
legend_constants[9] = "Km_PDE3 in component PDE_parameters (uM)"
legend_constants[10] = "k_PDE4 in component PDE_parameters (per_sec)"
legend_constants[11] = "Km_PDE4 in component PDE_parameters (uM)"
legend_constants[12] = "k_act1 in component G_s_parameters (per_sec)"
legend_constants[13] = "k_act2 in component G_s_parameters (per_sec)"
legend_constants[14] = "k_hydr in component G_s_parameters (per_sec)"
legend_constants[15] = "k_reas in component G_s_parameters (per_uM_per_sec)"
legend_constants[16] = "k_act1 in component G_i_parameters (per_sec)"
legend_constants[17] = "k_act2 in component G_i_parameters (per_sec)"
legend_constants[18] = "k_hydr in component G_i_parameters (per_sec)"
legend_constants[19] = "k_reas in component G_i_parameters (per_uM_per_sec)"
legend_algebraic[12] = "R in component caveolar_beta_1_adrenergic_receptor_module (uM)"
legend_algebraic[13] = "LR in component caveolar_beta_1_adrenergic_receptor_module (uM)"
legend_algebraic[14] = "LRG in component caveolar_beta_1_adrenergic_receptor_module (uM)"
legend_algebraic[15] = "RG in component caveolar_beta_1_adrenergic_receptor_module (uM)"
legend_constants[20] = "R_Total in component caveolar_beta_1_adrenergic_receptor_module (uM)"
legend_algebraic[5] = "Gs_alpha_beta_gamma in component caveolar_G_s_protein_activation_module (uM)"
legend_algebraic[16] = "R in component caveolar_muscarinic_receptor_module (uM)"
legend_algebraic[17] = "LR in component caveolar_muscarinic_receptor_module (uM)"
legend_algebraic[18] = "LRG in component caveolar_muscarinic_receptor_module (uM)"
legend_algebraic[19] = "RG in component caveolar_muscarinic_receptor_module (uM)"
legend_constants[21] = "R_Total in component caveolar_muscarinic_receptor_module (uM)"
legend_algebraic[6] = "Gi_alpha_beta_gamma in component caveolar_G_i_protein_activation_module (uM)"
legend_states[0] = "Gs_alpha_GTP in component caveolar_G_s_protein_activation_module (uM)"
legend_states[1] = "Gs_beta_gamma in component caveolar_G_s_protein_activation_module (uM)"
legend_states[2] = "Gs_alpha_GDP in component caveolar_G_s_protein_activation_module (uM)"
legend_constants[22] = "Gs_Total in component caveolar_G_s_protein_activation_module (uM)"
legend_states[3] = "Gi_alpha_GTP in component caveolar_G_i_protein_activation_module (uM)"
legend_states[4] = "Gi_beta_gamma in component caveolar_G_i_protein_activation_module (uM)"
legend_states[5] = "Gi_alpha_GDP in component caveolar_G_i_protein_activation_module (uM)"
legend_constants[23] = "Gi_Total in component caveolar_G_i_protein_activation_module (uM)"
legend_algebraic[20] = "R in component extracaveolar_beta_1_adrenergic_receptor_module (uM)"
legend_algebraic[21] = "LR in component extracaveolar_beta_1_adrenergic_receptor_module (uM)"
legend_algebraic[22] = "LRG in component extracaveolar_beta_1_adrenergic_receptor_module (uM)"
legend_algebraic[23] = "RG in component extracaveolar_beta_1_adrenergic_receptor_module (uM)"
legend_constants[24] = "R_Total in component extracaveolar_beta_1_adrenergic_receptor_module (uM)"
legend_algebraic[7] = "Gs_alpha_beta_gamma in component extracaveolar_G_s_protein_activation_module (uM)"
legend_algebraic[24] = "R in component extracaveolar_muscarinic_receptor_module (uM)"
legend_algebraic[25] = "LR in component extracaveolar_muscarinic_receptor_module (uM)"
legend_algebraic[26] = "LRG in component extracaveolar_muscarinic_receptor_module (uM)"
legend_algebraic[27] = "RG in component extracaveolar_muscarinic_receptor_module (uM)"
legend_constants[25] = "R_Total in component extracaveolar_muscarinic_receptor_module (uM)"
legend_algebraic[8] = "Gi_alpha_beta_gamma in component extracaveolar_G_i_protein_activation_module (uM)"
legend_states[6] = "Gs_alpha_GTP in component extracaveolar_G_s_protein_activation_module (uM)"
legend_states[7] = "Gs_beta_gamma in component extracaveolar_G_s_protein_activation_module (uM)"
legend_states[8] = "Gs_alpha_GDP in component extracaveolar_G_s_protein_activation_module (uM)"
legend_constants[26] = "Gs_Total in component extracaveolar_G_s_protein_activation_module (uM)"
legend_states[9] = "Gi_alpha_GTP in component extracaveolar_G_i_protein_activation_module (uM)"
legend_states[10] = "Gi_beta_gamma in component extracaveolar_G_i_protein_activation_module (uM)"
legend_states[11] = "Gi_alpha_GDP in component extracaveolar_G_i_protein_activation_module (uM)"
legend_constants[27] = "Gi_Total in component extracaveolar_G_i_protein_activation_module (uM)"
legend_algebraic[9] = "dcAMP_AC_56_dt in component AC56_module (uM_per_sec)"
legend_algebraic[2] = "k_AC56 in component AC56_module (per_sec)"
legend_constants[28] = "AC_56 in component AC56_module (uM)"
legend_constants[29] = "AF56 in component AC56_module (dimensionless)"
legend_constants[30] = "MW_AC56 in component AC56_module (kDa)"
legend_constants[31] = "ATP in component AC56_module (uM)"
legend_constants[32] = "Km_ATP in component AC56_module (uM)"
legend_algebraic[10] = "dcAMP_AC_47_ecav_dt in component AC47_ecav_module (uM_per_sec)"
legend_algebraic[3] = "k_AC47_ecav in component AC47_ecav_module (per_sec)"
legend_constants[33] = "AC_47_ecav in component AC47_ecav_module (uM)"
legend_constants[34] = "AF47 in component AC47_ecav_module (dimensionless)"
legend_constants[35] = "MW_AC47 in component AC47_ecav_module (kDa)"
legend_constants[36] = "ATP in component AC47_ecav_module (uM)"
legend_constants[37] = "Km_ATP in component AC47_ecav_module (uM)"
legend_constants[55] = "dcAMP_AC_47_cyt_dt in component AC47_cyt_module (uM_per_sec)"
legend_constants[38] = "k_AC47_cyt in component AC47_cyt_module (per_sec)"
legend_constants[39] = "AC_47_cyt in component AC47_cyt_module (uM)"
legend_constants[40] = "AF47 in component AC47_cyt_module (dimensionless)"
legend_constants[41] = "ATP in component AC47_cyt_module (uM)"
legend_constants[42] = "Km_ATP in component AC47_cyt_module (uM)"
legend_algebraic[28] = "dcAMP_cav_PDE2_dt in component caveolar_PDE_module (uM_per_sec)"
legend_algebraic[31] = "dcAMP_cav_PDE3_dt in component caveolar_PDE_module (uM_per_sec)"
legend_algebraic[33] = "dcAMP_cav_PDE4_dt in component caveolar_PDE_module (uM_per_sec)"
legend_states[12] = "cAMP_cav in component cAMP_flux_module (uM)"
legend_constants[43] = "PDE2 in component caveolar_PDE_module (uM)"
legend_constants[44] = "PDE3 in component caveolar_PDE_module (uM)"
legend_constants[45] = "PDE4 in component caveolar_PDE_module (uM)"
legend_algebraic[29] = "dcAMP_ecav_PDE2_dt in component extracaveolar_PDE_module (uM_per_sec)"
legend_algebraic[32] = "dcAMP_ecav_PDE4_dt in component extracaveolar_PDE_module (uM_per_sec)"
legend_states[13] = "cAMP_ecav in component cAMP_flux_module (uM)"
legend_constants[46] = "PDE2 in component extracaveolar_PDE_module (uM)"
legend_constants[47] = "PDE4 in component extracaveolar_PDE_module (uM)"
legend_algebraic[4] = "dcAMP_cyt_PDE2_dt in component bulk_cytoplasmic_PDE_module (uM_per_sec)"
legend_algebraic[11] = "dcAMP_cyt_PDE3_dt in component bulk_cytoplasmic_PDE_module (uM_per_sec)"
legend_algebraic[30] = "dcAMP_cyt_PDE4_dt in component bulk_cytoplasmic_PDE_module (uM_per_sec)"
legend_states[14] = "cAMP_cyt in component cAMP_flux_module (uM)"
legend_constants[48] = "PDE2 in component bulk_cytoplasmic_PDE_module (uM)"
legend_constants[49] = "PDE3 in component bulk_cytoplasmic_PDE_module (uM)"
legend_constants[50] = "PDE4 in component bulk_cytoplasmic_PDE_module (uM)"
legend_constants[56] = "V_cav in component cAMP_flux_module (liter)"
legend_constants[57] = "V_ecav in component cAMP_flux_module (liter)"
legend_constants[58] = "V_cyt in component cAMP_flux_module (liter)"
legend_constants[51] = "V_cell in component cAMP_flux_module (liter)"
legend_constants[52] = "J_cav_ecav in component cAMP_flux_module (liters_per_second)"
legend_constants[53] = "J_cav_cyt in component cAMP_flux_module (liters_per_second)"
legend_constants[54] = "J_ecav_cyt in component cAMP_flux_module (liters_per_second)"
legend_rates[0] = "d/dt Gs_alpha_GTP in component caveolar_G_s_protein_activation_module (uM)"
legend_rates[1] = "d/dt Gs_beta_gamma in component caveolar_G_s_protein_activation_module (uM)"
legend_rates[2] = "d/dt Gs_alpha_GDP in component caveolar_G_s_protein_activation_module (uM)"
legend_rates[3] = "d/dt Gi_alpha_GTP in component caveolar_G_i_protein_activation_module (uM)"
legend_rates[4] = "d/dt Gi_beta_gamma in component caveolar_G_i_protein_activation_module (uM)"
legend_rates[5] = "d/dt Gi_alpha_GDP in component caveolar_G_i_protein_activation_module (uM)"
legend_rates[6] = "d/dt Gs_alpha_GTP in component extracaveolar_G_s_protein_activation_module (uM)"
legend_rates[7] = "d/dt Gs_beta_gamma in component extracaveolar_G_s_protein_activation_module (uM)"
legend_rates[8] = "d/dt Gs_alpha_GDP in component extracaveolar_G_s_protein_activation_module (uM)"
legend_rates[9] = "d/dt Gi_alpha_GTP in component extracaveolar_G_i_protein_activation_module (uM)"
legend_rates[10] = "d/dt Gi_beta_gamma in component extracaveolar_G_i_protein_activation_module (uM)"
legend_rates[11] = "d/dt Gi_alpha_GDP in component extracaveolar_G_i_protein_activation_module (uM)"
legend_rates[12] = "d/dt cAMP_cav in component cAMP_flux_module (uM)"
legend_rates[13] = "d/dt cAMP_ecav in component cAMP_flux_module (uM)"
legend_rates[14] = "d/dt cAMP_cyt in component cAMP_flux_module (uM)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
constants[0] = 0.035
constants[1] = 0.386
constants[2] = 8.809
constants[3] = 0.16
constants[4] = 11
constants[5] = 30
constants[6] = 20
constants[7] = 50
constants[8] = 1.25
constants[9] = 0.08
constants[10] = 2.5
constants[11] = 2.2
constants[12] = 5
constants[13] = 0.1
constants[14] = 0.8
constants[15] = 1.21e3
constants[16] = 2.5
constants[17] = 0.05
constants[18] = 0.8
constants[19] = 1.21e3
constants[20] = 0.633
constants[21] = 0.633
states[0] = 0.041983438
states[1] = 0.042634499
states[2] = 0.000651061
constants[22] = 10
states[3] = 0.012644961
states[4] = 0.013274751
states[5] = 0.00062979
constants[23] = 20
constants[24] = 0.633
constants[25] = 0.633
states[6] = 0.083866891
states[7] = 0.084522918
states[8] = 0.000656025
constants[26] = 10
states[9] = 0.001018705
states[10] = 0.001475253
states[11] = 0.000456548
constants[27] = 1
constants[28] = 3.379
constants[29] = 500
constants[30] = 130
constants[31] = 5000
constants[32] = 315
constants[33] = 0.2
constants[34] = 130
constants[35] = 130
constants[36] = 5000
constants[37] = 315
constants[38] = 1.08e-3
constants[39] = 0.136
constants[40] = 130
constants[41] = 5000
constants[42] = 315
states[12] = 0.11750433
constants[43] = 4.5
constants[44] = 5.6
constants[45] = 2
states[13] = 1.092200547
constants[46] = 0.02
constants[47] = 0.16
states[14] = 0.992583576
constants[48] = 5e-3
constants[49] = 7.5e-3
constants[50] = 5e-3
constants[51] = 38e-12
constants[52] = 7.5e-15
constants[53] = 7.5e-14
constants[54] = 1.5e-17
constants[55] = (constants[38]*constants[39]*constants[40]*constants[41])/(constants[42]+constants[41])
constants[56] = 0.0100000*constants[51]
constants[57] = 0.0200000*constants[51]
constants[58] = 0.500000*constants[51]
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
rates[2] = states[0]*constants[14]-states[2]*states[1]*constants[15]
rates[5] = states[3]*constants[18]-states[5]*states[4]*constants[19]
rates[8] = states[6]*constants[14]-states[8]*states[7]*constants[15]
rates[11] = states[9]*constants[18]-states[11]*states[10]*constants[19]
algebraic[0] = custom_piecewise([greater(voi , 120.000) & less_equal(voi , 720.000), 1.00000 , True, 1.00000])
algebraic[5] = (constants[22]-states[0])-states[2]
rootfind_0(voi, constants, rates, states, algebraic)
rates[0] = (algebraic[15]*constants[13]+algebraic[14]*constants[12])-states[0]*constants[14]
rates[1] = (algebraic[15]*constants[13]+algebraic[14]*constants[12])-states[2]*states[1]*constants[15]
algebraic[1] = custom_piecewise([greater(voi , 240.000) & less_equal(voi , 540.000), 0.00000 , True, 0.00000])
algebraic[6] = (constants[23]-states[3])-states[5]
rootfind_1(voi, constants, rates, states, algebraic)
rates[3] = (algebraic[19]*constants[17]+algebraic[18]*constants[16])-states[3]*constants[18]
rates[4] = (algebraic[19]*constants[17]+algebraic[18]*constants[16])-states[5]*states[4]*constants[19]
algebraic[7] = (constants[26]-states[6])-states[8]
rootfind_2(voi, constants, rates, states, algebraic)
rates[6] = (algebraic[23]*constants[13]+algebraic[22]*constants[12])-states[6]*constants[14]
rates[7] = (algebraic[23]*constants[13]+algebraic[22]*constants[12])-states[8]*states[7]*constants[15]
algebraic[8] = (constants[27]-states[9])-states[11]
rootfind_3(voi, constants, rates, states, algebraic)
rates[9] = (algebraic[27]*constants[17]+algebraic[26]*constants[16])-states[9]*constants[18]
rates[10] = (algebraic[27]*constants[17]+algebraic[26]*constants[16])-states[11]*states[10]*constants[19]
algebraic[4] = (constants[6]*constants[48]*states[14])/(constants[7]+states[14])
algebraic[11] = (constants[8]*constants[49]*states[14])/(constants[9]+states[14])
algebraic[30] = (constants[10]*constants[50]*states[14])/(constants[11]+states[14])
rates[14] = (constants[55]-(algebraic[4]+algebraic[11]+algebraic[30]))+(constants[53]*(states[12]-states[14]))/constants[58]+(constants[54]*(states[13]-states[14]))/constants[58]
algebraic[3] = (((0.0630000+(2.01000*(power(states[6]*1000.00, 1.00430)))/(31.5440+power(states[6]*1000.00, 1.00430)))*(1.00000+((1.00000/3.01000)*49.1000*(power(states[10]*1000.00, 0.892100)))/(25.4400+power(states[10]*1000.00, 0.892100)))*constants[35])/60.0000)*0.00100000
algebraic[10] = (algebraic[3]*constants[33]*constants[34]*constants[36])/(constants[37]+constants[36])
algebraic[29] = (constants[6]*constants[46]*states[13])/(constants[7]+states[13])
algebraic[32] = (constants[10]*constants[47]*states[13])/(constants[11]+states[13])
rates[13] = ((algebraic[10]-(algebraic[29]+algebraic[32]))+(constants[52]*(states[12]-states[13]))/constants[57])-(constants[54]*(states[13]-states[14]))/constants[57]
algebraic[2] = (((0.700000+(3.82340*(power(states[0]/1.00000, 0.978700)))/(0.198600+power(states[0]/1.00000, 0.978700)))*(1.00000+((1.00000/1.44320)*-1.00610*(power(states[3]/1.00000, 0.835600)))/(0.191800+power(states[3]/1.00000, 0.835600)))*constants[30])/60.0000)*0.00100000
algebraic[9] = (algebraic[2]*constants[28]*constants[29]*constants[31])/(constants[32]+constants[31])
algebraic[28] = (constants[6]*constants[43]*states[12])/(constants[7]+states[12])
algebraic[31] = (constants[8]*constants[44]*states[12])/(constants[9]+states[12])
algebraic[33] = (constants[10]*constants[45]*states[12])/(constants[11]+states[12])
rates[12] = ((algebraic[9]-(algebraic[28]+algebraic[31]+algebraic[33]))-(constants[52]*(states[12]-states[13]))/constants[56])-(constants[53]*(states[12]-states[14]))/constants[56]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[0] = custom_piecewise([greater(voi , 120.000) & less_equal(voi , 720.000), 1.00000 , True, 1.00000])
algebraic[5] = (constants[22]-states[0])-states[2]
algebraic[1] = custom_piecewise([greater(voi , 240.000) & less_equal(voi , 540.000), 0.00000 , True, 0.00000])
algebraic[6] = (constants[23]-states[3])-states[5]
algebraic[7] = (constants[26]-states[6])-states[8]
algebraic[8] = (constants[27]-states[9])-states[11]
algebraic[4] = (constants[6]*constants[48]*states[14])/(constants[7]+states[14])
algebraic[11] = (constants[8]*constants[49]*states[14])/(constants[9]+states[14])
algebraic[30] = (constants[10]*constants[50]*states[14])/(constants[11]+states[14])
algebraic[3] = (((0.0630000+(2.01000*(power(states[6]*1000.00, 1.00430)))/(31.5440+power(states[6]*1000.00, 1.00430)))*(1.00000+((1.00000/3.01000)*49.1000*(power(states[10]*1000.00, 0.892100)))/(25.4400+power(states[10]*1000.00, 0.892100)))*constants[35])/60.0000)*0.00100000
algebraic[10] = (algebraic[3]*constants[33]*constants[34]*constants[36])/(constants[37]+constants[36])
algebraic[29] = (constants[6]*constants[46]*states[13])/(constants[7]+states[13])
algebraic[32] = (constants[10]*constants[47]*states[13])/(constants[11]+states[13])
algebraic[2] = (((0.700000+(3.82340*(power(states[0]/1.00000, 0.978700)))/(0.198600+power(states[0]/1.00000, 0.978700)))*(1.00000+((1.00000/1.44320)*-1.00610*(power(states[3]/1.00000, 0.835600)))/(0.191800+power(states[3]/1.00000, 0.835600)))*constants[30])/60.0000)*0.00100000
algebraic[9] = (algebraic[2]*constants[28]*constants[29]*constants[31])/(constants[32]+constants[31])
algebraic[28] = (constants[6]*constants[43]*states[12])/(constants[7]+states[12])
algebraic[31] = (constants[8]*constants[44]*states[12])/(constants[9]+states[12])
algebraic[33] = (constants[10]*constants[45]*states[12])/(constants[11]+states[12])
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(4)*0.1
if not iterable(voi):
soln = fsolve(residualSN_0, initialGuess0, args=(algebraic, voi, constants, rates, states), xtol=1E-6)
initialGuess0 = soln
algebraic[12] = soln[0]
algebraic[13] = soln[1]
algebraic[14] = soln[2]
algebraic[15] = soln[3]
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[12][i] = soln[0]
algebraic[13][i] = soln[1]
algebraic[14][i] = soln[2]
algebraic[15][i] = soln[3]
def residualSN_0(algebraicCandidate, algebraic, voi, constants, rates, states):
resid = array([0.0] * 4)
algebraic[12] = algebraicCandidate[0]
algebraic[13] = algebraicCandidate[1]
algebraic[14] = algebraicCandidate[2]
algebraic[15] = algebraicCandidate[3]
resid[0] = (algebraic[12]-(((constants[20]-algebraic[13])-algebraic[14])-algebraic[15]))
resid[1] = (algebraic[13]-(algebraic[0]*algebraic[12])/constants[1])
resid[2] = (algebraic[14]-(algebraic[0]*algebraic[12]*algebraic[5])/(constants[0]*constants[2]))
resid[3] = (algebraic[15]-(algebraic[12]*algebraic[5])/constants[2])
return resid
initialGuess1 = None
def rootfind_1(voi, constants, rates, states, algebraic):
"""Calculate values of algebraic variables for DAE"""
from scipy.optimize import fsolve
global initialGuess1
if initialGuess1 is None: initialGuess1 = ones(4)*0.1
if not iterable(voi):
soln = fsolve(residualSN_1, initialGuess1, args=(algebraic, voi, constants, rates, states), xtol=1E-6)
initialGuess1 = soln
algebraic[16] = soln[0]
algebraic[17] = soln[1]
algebraic[18] = soln[2]
algebraic[19] = soln[3]
else:
for (i,t) in enumerate(voi):
soln = fsolve(residualSN_1, initialGuess1, args=(algebraic[:,i], voi[i], constants, rates[:i], states[:,i]), xtol=1E-6)
initialGuess1 = soln
algebraic[16][i] = soln[0]
algebraic[17][i] = soln[1]
algebraic[18][i] = soln[2]
algebraic[19][i] = soln[3]
def residualSN_1(algebraicCandidate, algebraic, voi, constants, rates, states):
resid = array([0.0] * 4)
algebraic[16] = algebraicCandidate[0]
algebraic[17] = algebraicCandidate[1]
algebraic[18] = algebraicCandidate[2]
algebraic[19] = algebraicCandidate[3]
resid[0] = (algebraic[16]-(((constants[21]-algebraic[17])-algebraic[18])-algebraic[19]))
resid[1] = (algebraic[17]-(algebraic[1]*algebraic[16])/constants[4])
resid[2] = (algebraic[18]-(algebraic[1]*algebraic[16]*algebraic[6])/(constants[3]*constants[5]))
resid[3] = (algebraic[19]-(algebraic[16]*algebraic[6])/constants[5])
return resid
initialGuess2 = None
def rootfind_2(voi, constants, rates, states, algebraic):
"""Calculate values of algebraic variables for DAE"""
from scipy.optimize import fsolve
global initialGuess2
if initialGuess2 is None: initialGuess2 = ones(4)*0.1
if not iterable(voi):
soln = fsolve(residualSN_2, initialGuess2, args=(algebraic, voi, constants, rates, states), xtol=1E-6)
initialGuess2 = soln
algebraic[20] = soln[0]
algebraic[21] = soln[1]
algebraic[22] = soln[2]
algebraic[23] = soln[3]
else:
for (i,t) in enumerate(voi):
soln = fsolve(residualSN_2, initialGuess2, args=(algebraic[:,i], voi[i], constants, rates[:i], states[:,i]), xtol=1E-6)
initialGuess2 = soln
algebraic[20][i] = soln[0]
algebraic[21][i] = soln[1]
algebraic[22][i] = soln[2]
algebraic[23][i] = soln[3]
def residualSN_2(algebraicCandidate, algebraic, voi, constants, rates, states):
resid = array([0.0] * 4)
algebraic[20] = algebraicCandidate[0]
algebraic[21] = algebraicCandidate[1]
algebraic[22] = algebraicCandidate[2]
algebraic[23] = algebraicCandidate[3]
resid[0] = (algebraic[20]-(((constants[24]-algebraic[21])-algebraic[22])-algebraic[23]))
resid[1] = (algebraic[21]-(algebraic[0]*algebraic[20])/constants[1])
resid[2] = (algebraic[22]-(algebraic[0]*algebraic[20]*algebraic[7])/(constants[0]*constants[2]))
resid[3] = (algebraic[23]-(algebraic[20]*algebraic[7])/constants[2])
return resid
initialGuess3 = None
def rootfind_3(voi, constants, rates, states, algebraic):
"""Calculate values of algebraic variables for DAE"""
from scipy.optimize import fsolve
global initialGuess3
if initialGuess3 is None: initialGuess3 = ones(4)*0.1
if not iterable(voi):
soln = fsolve(residualSN_3, initialGuess3, args=(algebraic, voi, constants, rates, states), xtol=1E-6)
initialGuess3 = soln
algebraic[24] = soln[0]
algebraic[25] = soln[1]
algebraic[26] = soln[2]
algebraic[27] = soln[3]
else:
for (i,t) in enumerate(voi):
soln = fsolve(residualSN_3, initialGuess3, args=(algebraic[:,i], voi[i], constants, rates[:i], states[:,i]), xtol=1E-6)
initialGuess3 = soln
algebraic[24][i] = soln[0]
algebraic[25][i] = soln[1]
algebraic[26][i] = soln[2]
algebraic[27][i] = soln[3]
def residualSN_3(algebraicCandidate, algebraic, voi, constants, rates, states):
resid = array([0.0] * 4)
algebraic[24] = algebraicCandidate[0]
algebraic[25] = algebraicCandidate[1]
algebraic[26] = algebraicCandidate[2]
algebraic[27] = algebraicCandidate[3]
resid[0] = (algebraic[24]-(((constants[25]-algebraic[25])-algebraic[26])-algebraic[27]))
resid[1] = (algebraic[25]-(algebraic[1]*algebraic[24])/constants[4])
resid[2] = (algebraic[26]-(algebraic[1]*algebraic[24]*algebraic[8])/(constants[3]*constants[5]))
resid[3] = (algebraic[27]-(algebraic[24]*algebraic[8])/constants[5])
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)