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Bsm1Model_Scaled_No_p.py
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Bsm1Model_Scaled_No_p.py
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from __future__ import division
import numpy as np
"""
This is the scaled model without P
Q0 and Z0 are set as constant in the model
The model is scaled by x_scale = (x-xmin)/(xmax-xmin)
xmin and xmax value are got from 100 steps simulation result for EMPC with Nt=3
"""
# Bsm1 model
def ode_bsm1model(x_scale,u):
# min_x_empc = np.loadtxt('empc_x_min.txt')
# delta_x_empc = np.loadtxt('empc_x_delta.txt')
min_x_empc = np.zeros(145)
delta_x_empc = np.ones(145)
x = x_scale*delta_x_empc + min_x_empc
# Inputs:
KLa5 = u[0]
Qa = u[1]
Q0 = u[2]
Z0 = u[3:16]
# Q0 = 18446
# Z0 = np.array([30, 69.5, 51.2, 202.32, 28.17, 0, 0, 0, 0, 31.56, 6.95, 10.59, 7])
x1 = x[0]
x2 = x[1]
x3 = x[2]
x4 = x[3]
x5 = x[4]
x6 = x[5]
x7 = x[6]
x8 = x[7]
x9 = x[8]
x10 = x[9]
x11 = x[10]
x12 = x[11]
x13 = x[12]
x14 = x[13]
x15 = x[14]
x16 = x[15]
x17 = x[16]
x18 = x[17]
x19 = x[18]
x20 = x[19]
x21 = x[20]
x22 = x[21]
x23 = x[22]
x24 = x[23]
x25 = x[24]
x26 = x[25]
x27 = x[26]
x28 = x[27]
x29 = x[28]
x30 = x[29]
x31 = x[30]
x32 = x[31]
x33 = x[32]
x34 = x[33]
x35 = x[34]
x36 = x[35]
x37 = x[36]
x38 = x[37]
x39 = x[38]
x40 = x[39]
x41 = x[40]
x42 = x[41]
x43 = x[42]
x44 = x[43]
x45 = x[44]
x46 = x[45]
x47 = x[46]
x48 = x[47]
x49 = x[48]
x50 = x[49]
x51 = x[50]
x52 = x[51]
x53 = x[52]
x54 = x[53]
x55 = x[54]
x56 = x[55]
x57 = x[56]
x58 = x[57]
x59 = x[58]
x60 = x[59]
x61 = x[60]
x62 = x[61]
x63 = x[62]
x64 = x[63]
x65 = x[64]
x66 = x[65]
x67 = x[66]
x68 = x[67]
x69 = x[68]
x70 = x[69]
x71 = x[70]
x72 = x[71]
x73 = x[72]
x74 = x[73]
x75 = x[74]
x76 = x[75]
x77 = x[76]
x78 = x[77]
x79 = x[78]
x80 = x[79]
x81 = x[80]
x82 = x[81]
x83 = x[82]
x84 = x[83]
x85 = x[84]
x86 = x[85]
x87 = x[86]
x88 = x[87]
x89 = x[88]
x90 = x[89]
x91 = x[90]
x92 = x[91]
x93 = x[92]
x94 = x[93]
x95 = x[94]
x96 = x[95]
x97 = x[96]
x98 = x[97]
x99 = x[98]
x100 = x[99]
x101 = x[100]
x102 = x[101]
x103 = x[102]
x104 = x[103]
x105 = x[104]
x106 = x[105]
x107 = x[106]
x108 = x[107]
x109 = x[108]
x110 = x[109]
x111 = x[110]
x112 = x[111]
x113 = x[112]
x114 = x[113]
x115 = x[114]
x116 = x[115]
x117 = x[116]
x118 = x[117]
x119 = x[118]
x120 = x[119]
x121 = x[120]
x122 = x[121]
x123 = x[122]
x124 = x[123]
x125 = x[124]
x126 = x[125]
x127 = x[126]
x128 = x[127]
x129 = x[128]
x130 = x[129]
x131 = x[130]
x132 = x[131]
x133 = x[132]
x134 = x[133]
x135 = x[134]
x136 = x[135]
x137 = x[136]
x138 = x[137]
x139 = x[138]
x140 = x[139]
x141 = x[140]
x142 = x[141]
x143 = x[142]
x144 = x[143]
x145 = x[144]
Z01 = Z0[0]
Z02 = Z0[1]
Z03 = Z0[2]
Z04 = Z0[3]
Z05 = Z0[4]
Z06 = Z0[5]
Z07 = Z0[6]
Z08 = Z0[7]
Z09 = Z0[8]
Z010 = Z0[9]
Z011 = Z0[10]
Z012 = Z0[11]
Z013 = Z0[12]
dxdt = [
1/96*((9223*x76)/500 + (Q0*Z01)/1000 + (Qa*x53)/1000 - (x1*(Q0 + Qa + 18446))/1000),
1/96*((9223*x86)/500 + (Q0*Z02)/1000 + (Qa*x54)/1000 - (x2*(Q0 + Qa + 18446))/1000 + (3*x4*(x8/(x8 + 1/5) + (4*x9)/(25*(x9 + 1/2)*(x8 + 1/5))))/(x4/x5 + 1/10) - (400*x2*x5*x8)/(67*(x2 + 10)*(x8 + 1/5)) - (64*x2*x5*x9)/(67*(x2 + 10)*(x9 + 1/2)*(x8 + 1/5))),
1/96*((Q0*Z03)/1000 + (Qa*x55)/1000 - (x3*(Q0 + Qa + 18446))/1000 + (9223*x55*x66)/(500*((3*x55)/4 + (3*x56)/4 + (3*x57)/4 + (3*x58)/4 + (3*x59)/4))),
1/96*((69*x5)/250 + (23*x6)/500 + (Q0*Z04)/1000 + (Qa*x56)/1000 - (x4*(Q0 + Qa + 18446))/1000 + (9223*x56*x66)/(500*((3*x55)/4 + (3*x56)/4 + (3*x57)/4 + (3*x58)/4 + (3*x59)/4)) - (3*x4*(x8/(x8 + 1/5) + (4*x9)/(25*(x9 + 1/2)*(x8 + 1/5))))/(x4/x5 + 1/10)),
1/96*((Q0*Z05)/1000 - (3*x5)/10 + (Qa*x57)/1000 - (x5*(Q0 + Qa + 18446))/1000 + (9223*x57*x66)/(500*((3*x55)/4 + (3*x56)/4 + (3*x57)/4 + (3*x58)/4 + (3*x59)/4)) + (4*x2*x5*x8)/((x2 + 10)*(x8 + 1/5)) + (16*x2*x5*x9)/(25*(x2 + 10)*(x9 + 1/2)*(x8 + 1/5))),
1/96*((Q0*Z06)/1000 - x6/20 + (Qa*x58)/1000 - (x6*(Q0 + Qa + 18446))/1000 + (9223*x58*x66)/(500*((3*x55)/4 + (3*x56)/4 + (3*x57)/4 + (3*x58)/4 + (3*x59)/4)) + (x6*x8*x10)/(2*(x10 + 1)*(x8 + 2/5))),
1/96*((3*x5)/125 + x6/250 + (Q0*Z07)/1000 + (Qa*x59)/1000 - (x7*(Q0 + Qa + 18446))/1000 + (9223*x59*x66)/(500*((3*x55)/4 + (3*x56)/4 + (3*x57)/4 + (3*x58)/4 + (3*x59)/4))),
1/96*((9223*x96)/500 + (Q0*Z08)/1000 + (Qa*x60)/1000 - (x8*(Q0 + Qa + 18446))/1000 - (132*x2*x5*x8)/(67*(x2 + 10)*(x8 + 1/5)) - (433*x6*x8*x10)/(48*(x10 + 1)*(x8 + 2/5))),
1/96*((9223*x106)/500 + (Q0*Z09)/1000 + (Qa*x61)/1000 - (x9*(Q0 + Qa + 18446))/1000 + (25*x6*x8*x10)/(12*(x10 + 1)*(x8 + 2/5)) - (96*x2*x5*x9)/(871*(x2 + 10)*(x9 + 1/2)*(x8 + 1/5))),
1/96*((9223*x116)/500 + (Q0*Z010)/1000 + (Qa*x62)/1000 + (x5*x11)/20 - (x10*(Q0 + Qa + 18446))/1000 - (8*x2*x5*x8)/(25*(x2 + 10)*(x8 + 1/5)) - (637*x6*x8*x10)/(300*(x10 + 1)*(x8 + 2/5)) - (32*x2*x5*x9)/(625*(x2 + 10)*(x9 + 1/2)*(x8 + 1/5))),
1/96*((9223*x126)/500 + (Q0*Z011)/1000 + (Qa*x63)/1000 - (x5*x11)/20 - (x11*(Q0 + Qa + 18446))/1000 + (3*x12*(x8/(x8 + 1/5) + (4*x9)/(25*(x9 + 1/2)*(x8 + 1/5))))/(x4/x5 + 1/10)),
1/96*((141*x5)/6250 + (47*x6)/12500 + (Q0*Z012)/1000 + (Qa*x64)/1000 - (x12*(Q0 + Qa + 18446))/1000 + (9223*x64*x66)/(500*((3*x55)/4 + (3*x56)/4 + (3*x57)/4 + (3*x58)/4 + (3*x59)/4)) - (3*x12*(x8/(x8 + 1/5) + (4*x9)/(25*(x9 + 1/2)*(x8 + 1/5))))/(x4/x5 + 1/10)),
1/96*((9223*x136)/500 + (Q0*Z013)/1000 + (Qa*x65)/1000 + (x5*x11)/280 - (x13*(Q0 + Qa + 18446))/1000 - (4*x2*x5*x8)/(175*(x2 + 10)*(x8 + 1/5)) - (631*x6*x8*x10)/(2100*(x10 + 1)*(x8 + 2/5)) + (1518823277841921*x2*x5*x9)/(360287970189639680*(x2 + 10)*(x9 + 1/2)*(x8 + 1/5))),
1/96*((x1*(Q0 + Qa + 18446))/1000 - (x14*(Q0 + Qa + 18446))/1000),
1/96*((x2*(Q0 + Qa + 18446))/1000 - (x15*(Q0 + Qa + 18446))/1000 + (3*x17*(x21/(x21 + 1/5) + (4*x22)/(25*(x22 + 1/2)*(x21 + 1/5))))/(x17/x18 + 1/10) - (400*x15*x18*x21)/(67*(x15 + 10)*(x21 + 1/5)) - (64*x15*x18*x22)/(67*(x15 + 10)*(x22 + 1/2)*(x21 + 1/5))),
1/96*((x3*(Q0 + Qa + 18446))/1000 - (x16*(Q0 + Qa + 18446))/1000),
1/96*((69*x18)/250 + (23*x19)/500 + (x4*(Q0 + Qa + 18446))/1000 - (x17*(Q0 + Qa + 18446))/1000 - (3*x17*(x21/(x21 + 1/5) + (4*x22)/(25*(x22 + 1/2)*(x21 + 1/5))))/(x17/x18 + 1/10)),
1/96*((x5*(Q0 + Qa + 18446))/1000 - (3*x18)/10 - (x18*(Q0 + Qa + 18446))/1000 + (4*x15*x18*x21)/((x15 + 10)*(x21 + 1/5)) + (16*x15*x18*x22)/(25*(x15 + 10)*(x22 + 1/2)*(x21 + 1/5))),
1/96*((x6*(Q0 + Qa + 18446))/1000 - x19/20 - (x19*(Q0 + Qa + 18446))/1000 + (x19*x21*x23)/(2*(x23 + 1)*(x21 + 2/5))),
1/96*((3*x18)/125 + x19/250 + (x7*(Q0 + Qa + 18446))/1000 - (x20*(Q0 + Qa + 18446))/1000),
1/96*((x8*(Q0 + Qa + 18446))/1000 - (x21*(Q0 + Qa + 18446))/1000 - (132*x15*x18*x21)/(67*(x15 + 10)*(x21 + 1/5)) - (433*x19*x21*x23)/(48*(x23 + 1)*(x21 + 2/5))),
1/96*((x9*(Q0 + Qa + 18446))/1000 - (x22*(Q0 + Qa + 18446))/1000 + (25*x19*x21*x23)/(12*(x23 + 1)*(x21 + 2/5)) - (96*x15*x18*x22)/(871*(x15 + 10)*(x22 + 1/2)*(x21 + 1/5))),
1/96*((x18*x24)/20 + (x10*(Q0 + Qa + 18446))/1000 - (x23*(Q0 + Qa + 18446))/1000 - (8*x15*x18*x21)/(25*(x15 + 10)*(x21 + 1/5)) - (637*x19*x21*x23)/(300*(x23 + 1)*(x21 + 2/5)) - (32*x15*x18*x22)/(625*(x15 + 10)*(x22 + 1/2)*(x21 + 1/5))),
1/96*((x11*(Q0 + Qa + 18446))/1000 - (x18*x24)/20 - (x24*(Q0 + Qa + 18446))/1000 + (3*x25*(x21/(x21 + 1/5) + (4*x22)/(25*(x22 + 1/2)*(x21 + 1/5))))/(x17/x18 + 1/10)),
1/96*((141*x18)/6250 + (47*x19)/12500 + (x12*(Q0 + Qa + 18446))/1000 - (x25*(Q0 + Qa + 18446))/1000 - (3*x25*(x21/(x21 + 1/5) + (4*x22)/(25*(x22 + 1/2)*(x21 + 1/5))))/(x17/x18 + 1/10)),
1/96*((x18*x24)/280 + (x13*(Q0 + Qa + 18446))/1000 - (x26*(Q0 + Qa + 18446))/1000 - (4*x15*x18*x21)/(175*(x15 + 10)*(x21 + 1/5)) - (631*x19*x21*x23)/(2100*(x23 + 1)*(x21 + 2/5)) + (1518823277841921*x15*x18*x22)/(360287970189639680*(x15 + 10)*(x22 + 1/2)*(x21 + 1/5))),
1/96*((x14*(Q0 + Qa + 18446))/1333 - (x27*(Q0 + Qa + 18446))/1333),
1/96*((x15*(Q0 + Qa + 18446))/1333 - (x28*(Q0 + Qa + 18446))/1333 + (3*x30*(x34/(x34 + 1/5) + (4*x35)/(25*(x35 + 1/2)*(x34 + 1/5))))/(x30/x31 + 1/10) - (400*x28*x31*x34)/(67*(x28 + 10)*(x34 + 1/5)) - (64*x28*x31*x35)/(67*(x28 + 10)*(x35 + 1/2)*(x34 + 1/5))),
1/96*((x16*(Q0 + Qa + 18446))/1333 - (x29*(Q0 + Qa + 18446))/1333),
1/96*((69*x31)/250 + (23*x32)/500 + (x17*(Q0 + Qa + 18446))/1333 - (x30*(Q0 + Qa + 18446))/1333 - (3*x30*(x34/(x34 + 1/5) + (4*x35)/(25*(x35 + 1/2)*(x34 + 1/5))))/(x30/x31 + 1/10)),
1/96*((x18*(Q0 + Qa + 18446))/1333 - (3*x31)/10 - (x31*(Q0 + Qa + 18446))/1333 + (4*x28*x31*x34)/((x28 + 10)*(x34 + 1/5)) + (16*x28*x31*x35)/(25*(x28 + 10)*(x35 + 1/2)*(x34 + 1/5))),
1/96*((x19*(Q0 + Qa + 18446))/1333 - x32/20 - (x32*(Q0 + Qa + 18446))/1333 + (x32*x34*x36)/(2*(x36 + 1)*(x34 + 2/5))),
1/96*((3*x31)/125 + x32/250 + (x20*(Q0 + Qa + 18446))/1333 - (x33*(Q0 + Qa + 18446))/1333),
1/96*((x21*(Q0 + Qa + 18446))/1333 - 240*x34 - (x34*(Q0 + Qa + 18446))/1333 - (132*x28*x31*x34)/(67*(x28 + 10)*(x34 + 1/5)) - (433*x32*x34*x36)/(48*(x36 + 1)*(x34 + 2/5)) + 1920),
1/96*((x22*(Q0 + Qa + 18446))/1333 - (x35*(Q0 + Qa + 18446))/1333 + (25*x32*x34*x36)/(12*(x36 + 1)*(x34 + 2/5)) - (96*x28*x31*x35)/(871*(x28 + 10)*(x35 + 1/2)*(x34 + 1/5))),
1/96*((x31*x37)/20 + (x23*(Q0 + Qa + 18446))/1333 - (x36*(Q0 + Qa + 18446))/1333 - (8*x28*x31*x34)/(25*(x28 + 10)*(x34 + 1/5)) - (637*x32*x34*x36)/(300*(x36 + 1)*(x34 + 2/5)) - (32*x28*x31*x35)/(625*(x28 + 10)*(x35 + 1/2)*(x34 + 1/5))),
1/96*((x24*(Q0 + Qa + 18446))/1333 - (x31*x37)/20 - (x37*(Q0 + Qa + 18446))/1333 + (3*x38*(x34/(x34 + 1/5) + (4*x35)/(25*(x35 + 1/2)*(x34 + 1/5))))/(x30/x31 + 1/10)),
1/96*((141*x31)/6250 + (47*x32)/12500 + (x25*(Q0 + Qa + 18446))/1333 - (x38*(Q0 + Qa + 18446))/1333 - (3*x38*(x34/(x34 + 1/5) + (4*x35)/(25*(x35 + 1/2)*(x34 + 1/5))))/(x30/x31 + 1/10)),
1/96*((x31*x37)/280 + (x26*(Q0 + Qa + 18446))/1333 - (x39*(Q0 + Qa + 18446))/1333 - (4*x28*x31*x34)/(175*(x28 + 10)*(x34 + 1/5)) - (631*x32*x34*x36)/(2100*(x36 + 1)*(x34 + 2/5)) + (1518823277841921*x28*x31*x35)/(360287970189639680*(x28 + 10)*(x35 + 1/2)*(x34 + 1/5))),
1/96*((x27*(Q0 + Qa + 18446))/1333 - (x40*(Q0 + Qa + 18446))/1333),
1/96*((x28*(Q0 + Qa + 18446))/1333 - (x41*(Q0 + Qa + 18446))/1333 + (3*x43*(x47/(x47 + 1/5) + (4*x48)/(25*(x48 + 1/2)*(x47 + 1/5))))/(x43/x44 + 1/10) - (400*x41*x44*x47)/(67*(x41 + 10)*(x47 + 1/5)) - (64*x41*x44*x48)/(67*(x41 + 10)*(x48 + 1/2)*(x47 + 1/5))),
1/96*((x29*(Q0 + Qa + 18446))/1333 - (x42*(Q0 + Qa + 18446))/1333),
1/96*((69*x44)/250 + (23*x45)/500 + (x30*(Q0 + Qa + 18446))/1333 - (x43*(Q0 + Qa + 18446))/1333 - (3*x43*(x47/(x47 + 1/5) + (4*x48)/(25*(x48 + 1/2)*(x47 + 1/5))))/(x43/x44 + 1/10)),
1/96*((x31*(Q0 + Qa + 18446))/1333 - (3*x44)/10 - (x44*(Q0 + Qa + 18446))/1333 + (4*x41*x44*x47)/((x41 + 10)*(x47 + 1/5)) + (16*x41*x44*x48)/(25*(x41 + 10)*(x48 + 1/2)*(x47 + 1/5))),
1/96*((x32*(Q0 + Qa + 18446))/1333 - x45/20 - (x45*(Q0 + Qa + 18446))/1333 + (x45*x47*x49)/(2*(x49 + 1)*(x47 + 2/5))),
1/96*((3*x44)/125 + x45/250 + (x33*(Q0 + Qa + 18446))/1333 - (x46*(Q0 + Qa + 18446))/1333),
1/96*((x34*(Q0 + Qa + 18446))/1333 - 240*x47 - (x47*(Q0 + Qa + 18446))/1333 - (132*x41*x44*x47)/(67*(x41 + 10)*(x47 + 1/5)) - (433*x45*x47*x49)/(48*(x49 + 1)*(x47 + 2/5)) + 1920),
1/96*((x35*(Q0 + Qa + 18446))/1333 - (x48*(Q0 + Qa + 18446))/1333 + (25*x45*x47*x49)/(12*(x49 + 1)*(x47 + 2/5)) - (96*x41*x44*x48)/(871*(x41 + 10)*(x48 + 1/2)*(x47 + 1/5))),
1/96*((x44*x50)/20 + (x36*(Q0 + Qa + 18446))/1333 - (x49*(Q0 + Qa + 18446))/1333 - (8*x41*x44*x47)/(25*(x41 + 10)*(x47 + 1/5)) - (637*x45*x47*x49)/(300*(x49 + 1)*(x47 + 2/5)) - (32*x41*x44*x48)/(625*(x41 + 10)*(x48 + 1/2)*(x47 + 1/5))),
1/96*((x37*(Q0 + Qa + 18446))/1333 - (x44*x50)/20 - (x50*(Q0 + Qa + 18446))/1333 + (3*x51*(x47/(x47 + 1/5) + (4*x48)/(25*(x48 + 1/2)*(x47 + 1/5))))/(x43/x44 + 1/10)),
1/96*((141*x44)/6250 + (47*x45)/12500 + (x38*(Q0 + Qa + 18446))/1333 - (x51*(Q0 + Qa + 18446))/1333 - (3*x51*(x47/(x47 + 1/5) + (4*x48)/(25*(x48 + 1/2)*(x47 + 1/5))))/(x43/x44 + 1/10)),
1/96*((x44*x50)/280 + (x39*(Q0 + Qa + 18446))/1333 - (x52*(Q0 + Qa + 18446))/1333 - (4*x41*x44*x47)/(175*(x41 + 10)*(x47 + 1/5)) - (631*x45*x47*x49)/(2100*(x49 + 1)*(x47 + 2/5)) + (1518823277841921*x41*x44*x48)/(360287970189639680*(x41 + 10)*(x48 + 1/2)*(x47 + 1/5))),
1/96*((x40*(Q0 + Qa + 18446))/1333 - (x53*(Q0 + Qa + 18446))/1333),
1/96*((x41*(Q0 + Qa + 18446))/1333 - (x54*(Q0 + Qa + 18446))/1333 + (3*x56*(x60/(x60 + 1/5) + (4*x61)/(25*(x61 + 1/2)*(x60 + 1/5))))/(x56/x57 + 1/10) - (400*x54*x57*x60)/(67*(x54 + 10)*(x60 + 1/5)) - (64*x54*x57*x61)/(67*(x54 + 10)*(x61 + 1/2)*(x60 + 1/5))),
1/96*((x42*(Q0 + Qa + 18446))/1333 - (x55*(Q0 + Qa + 18446))/1333),
1/96*((69*x57)/250 + (23*x58)/500 + (x43*(Q0 + Qa + 18446))/1333 - (x56*(Q0 + Qa + 18446))/1333 - (3*x56*(x60/(x60 + 1/5) + (4*x61)/(25*(x61 + 1/2)*(x60 + 1/5))))/(x56/x57 + 1/10)),
1/96*((x44*(Q0 + Qa + 18446))/1333 - (3*x57)/10 - (x57*(Q0 + Qa + 18446))/1333 + (4*x54*x57*x60)/((x54 + 10)*(x60 + 1/5)) + (16*x54*x57*x61)/(25*(x54 + 10)*(x61 + 1/2)*(x60 + 1/5))),
1/96*((x45*(Q0 + Qa + 18446))/1333 - x58/20 - (x58*(Q0 + Qa + 18446))/1333 + (x58*x60*x62)/(2*(x62 + 1)*(x60 + 2/5))),
1/96*((3*x57)/125 + x58/250 + (x46*(Q0 + Qa + 18446))/1333 - (x59*(Q0 + Qa + 18446))/1333),
1/96*((x47*(Q0 + Qa + 18446))/1333 - KLa5*(x60 - 8) - (x60*(Q0 + Qa + 18446))/1333 - (132*x54*x57*x60)/(67*(x54 + 10)*(x60 + 1/5)) - (433*x58*x60*x62)/(48*(x62 + 1)*(x60 + 2/5))),
1/96*((x48*(Q0 + Qa + 18446))/1333 - (x61*(Q0 + Qa + 18446))/1333 + (25*x58*x60*x62)/(12*(x62 + 1)*(x60 + 2/5)) - (96*x54*x57*x61)/(871*(x54 + 10)*(x61 + 1/2)*(x60 + 1/5))),
1/96*((x57*x63)/20 + (x49*(Q0 + Qa + 18446))/1333 - (x62*(Q0 + Qa + 18446))/1333 - (8*x54*x57*x60)/(25*(x54 + 10)*(x60 + 1/5)) - (637*x58*x60*x62)/(300*(x62 + 1)*(x60 + 2/5)) - (32*x54*x57*x61)/(625*(x54 + 10)*(x61 + 1/2)*(x60 + 1/5))),
1/96*((x50*(Q0 + Qa + 18446))/1333 - (x57*x63)/20 - (x63*(Q0 + Qa + 18446))/1333 + (3*x64*(x60/(x60 + 1/5) + (4*x61)/(25*(x61 + 1/2)*(x60 + 1/5))))/(x56/x57 + 1/10)),
1/96*((141*x57)/6250 + (47*x58)/12500 + (x51*(Q0 + Qa + 18446))/1333 - (x64*(Q0 + Qa + 18446))/1333 - (3*x64*(x60/(x60 + 1/5) + (4*x61)/(25*(x61 + 1/2)*(x60 + 1/5))))/(x56/x57 + 1/10)),
1/96*((x57*x63)/280 + (x52*(Q0 + Qa + 18446))/1333 - (x65*(Q0 + Qa + 18446))/1333 - (4*x54*x57*x60)/(175*(x54 + 10)*(x60 + 1/5)) - (631*x58*x60*x62)/(2100*(x62 + 1)*(x60 + 2/5)) + (1518823277841921*x54*x57*x61)/(360287970189639680*(x54 + 10)*(x61 + 1/2)*(x60 + 1/5))),
1/96*((6277*x67)/200 - (6277*x66)/200 + (5*x67*(474* np.exp((1539*x55)/1562500000 + (1539*x56)/1562500000 + (1539*x57)/1562500000 + (1539*x58)/1562500000 + (1539*x59)/1562500000 - (9*x67)/15625) - 474* np.exp((24453*x55)/5000000000 + (24453*x56)/5000000000 + (24453*x57)/5000000000 + (24453*x58)/5000000000 + (24453*x59)/5000000000 - (143*x67)/50000)))/2),
1/96*((6277*x68)/200 - (6277*x67)/200 - (5*x67*(474* np.exp((1539*x55)/1562500000 + (1539*x56)/1562500000 + (1539*x57)/1562500000 + (1539*x58)/1562500000 + (1539*x59)/1562500000 - (9*x67)/15625) - 474* np.exp((24453*x55)/5000000000 + (24453*x56)/5000000000 + (24453*x57)/5000000000 + (24453*x58)/5000000000 + (24453*x59)/5000000000 - (143*x67)/50000)))/2 + (5*x68*(474* np.exp((1539*x55)/1562500000 + (1539*x56)/1562500000 + (1539*x57)/1562500000 + (1539*x58)/1562500000 + (1539*x59)/1562500000 - (9*x68)/15625) - 474* np.exp((24453*x55)/5000000000 + (24453*x56)/5000000000 + (24453*x57)/5000000000 + (24453*x58)/5000000000 + (24453*x59)/5000000000 - (143*x68)/50000)))/2),
1/96*((6277*x69)/200 - (6277*x68)/200),
1/96*((6277*x70)/200 - (6277*x69)/200 - (5*x68*(474* np.exp((1539*x55)/1562500000 + (1539*x56)/1562500000 + (1539*x57)/1562500000 + (1539*x58)/1562500000 + (1539*x59)/1562500000 - (9*x68)/15625) - 474* np.exp((24453*x55)/5000000000 + (24453*x56)/5000000000 + (24453*x57)/5000000000 + (24453*x58)/5000000000 + (24453*x59)/5000000000 - (143*x68)/50000)))/2 + (5*x70*(474* np.exp((1539*x55)/1562500000 + (1539*x56)/1562500000 + (1539*x57)/1562500000 + (1539*x58)/1562500000 + (1539*x59)/1562500000 - (9*x70)/15625) - 474* np.exp((24453*x55)/5000000000 + (24453*x56)/5000000000 + (24453*x57)/5000000000 + (24453*x58)/5000000000 + (24453*x59)/5000000000 - (143*x70)/50000)))/2),
1/96*((6277*x71)/200 - (6277*x70)/200),
1/96*((5*x72*(474* np.exp((1539*x55)/1562500000 + (1539*x56)/1562500000 + (1539*x57)/1562500000 + (1539*x58)/1562500000 + (1539*x59)/1562500000 - (9*x72)/15625) - 474* np.exp((24453*x55)/5000000000 + (24453*x56)/5000000000 + (24453*x57)/5000000000 + (24453*x58)/5000000000 + (24453*x59)/5000000000 - (143*x72)/50000)))/2 - (5*x70*(474* np.exp((1539*x55)/1562500000 + (1539*x56)/1562500000 + (1539*x57)/1562500000 + (1539*x58)/1562500000 + (1539*x59)/1562500000 - (9*x70)/15625) - 474* np.exp((24453*x55)/5000000000 + (24453*x56)/5000000000 + (24453*x57)/5000000000 + (24453*x58)/5000000000 + (24453*x59)/5000000000 - (143*x70)/50000)))/2 + ((Q0 + 18446)*((3*x55)/4 + (3*x56)/4 + (3*x57)/4 + (3*x58)/4 + (3*x59)/4))/600 - (5*x71*(Q0/1500 + 9223/750))/2),
1/96*((5*(Q0/1500 - 77/300)*(x71 - x72))/2 - (5*x72*(474* np.exp((1539*x55)/1562500000 + (1539*x56)/1562500000 + (1539*x57)/1562500000 + (1539*x58)/1562500000 + (1539*x59)/1562500000 - (9*x72)/15625) - 474* np.exp((24453*x55)/5000000000 + (24453*x56)/5000000000 + (24453*x57)/5000000000 + (24453*x58)/5000000000 + (24453*x59)/5000000000 - (143*x72)/50000)))/2 + (5*x73*(474* np.exp((1539*x55)/1562500000 + (1539*x56)/1562500000 + (1539*x57)/1562500000 + (1539*x58)/1562500000 + (1539*x59)/1562500000 - (9*x73)/15625) - 474* np.exp((24453*x55)/5000000000 + (24453*x56)/5000000000 + (24453*x57)/5000000000 + (24453*x58)/5000000000 + (24453*x59)/5000000000 - (143*x73)/50000)))/2),
1/96*((5*(Q0/1500 - 77/300)*(x72 - x73))/2 - (5*x73*(474* np.exp((1539*x55)/1562500000 + (1539*x56)/1562500000 + (1539*x57)/1562500000 + (1539*x58)/1562500000 + (1539*x59)/1562500000 - (9*x73)/15625) - 474* np.exp((24453*x55)/5000000000 + (24453*x56)/5000000000 + (24453*x57)/5000000000 + (24453*x58)/5000000000 + (24453*x59)/5000000000 - (143*x73)/50000)))/2 + (5*x74*(474* np.exp((1539*x55)/1562500000 + (1539*x56)/1562500000 + (1539*x57)/1562500000 + (1539*x58)/1562500000 + (1539*x59)/1562500000 - (9*x74)/15625) - 474* np.exp((24453*x55)/5000000000 + (24453*x56)/5000000000 + (24453*x57)/5000000000 + (24453*x58)/5000000000 + (24453*x59)/5000000000 - (143*x74)/50000)))/2),
1/96*((5*(Q0/1500 - 77/300)*(x73 - x74))/2 - (5*x74*(474* np.exp((1539*x55)/1562500000 + (1539*x56)/1562500000 + (1539*x57)/1562500000 + (1539*x58)/1562500000 + (1539*x59)/1562500000 - (9*x74)/15625) - 474* np.exp((24453*x55)/5000000000 + (24453*x56)/5000000000 + (24453*x57)/5000000000 + (24453*x58)/5000000000 + (24453*x59)/5000000000 - (143*x74)/50000)))/2 + (5*x75*(474* np.exp((1539*x55)/1562500000 + (1539*x56)/1562500000 + (1539*x57)/1562500000 + (1539*x58)/1562500000 + (1539*x59)/1562500000 - (9*x75)/15625) - 474* np.exp((24453*x55)/5000000000 + (24453*x56)/5000000000 + (24453*x57)/5000000000 + (24453*x58)/5000000000 + (24453*x59)/5000000000 - (143*x75)/50000)))/2),
1/96*((5*(Q0/1500 - 77/300)*(x74 - x75))/2 - (5*x75*(474* np.exp((1539*x55)/1562500000 + (1539*x56)/1562500000 + (1539*x57)/1562500000 + (1539*x58)/1562500000 + (1539*x59)/1562500000 - (9*x75)/15625) - 474* np.exp((24453*x55)/5000000000 + (24453*x56)/5000000000 + (24453*x57)/5000000000 + (24453*x58)/5000000000 + (24453*x59)/5000000000 - (143*x75)/50000)))/2),
1/96*((6277*x77)/200 - (6277*x76)/200),
1/96*((6277*x78)/200 - (6277*x77)/200),
1/96*((6277*x79)/200 - (6277*x78)/200),
1/96*((6277*x80)/200 - (6277*x79)/200),
1/96*((6277*x81)/200 - (6277*x80)/200),
1/96*((x53*(Q0 + 18446))/600 - (5*x81*(Q0/1500 + 9223/750))/2),
1/96*((5*(Q0/1500 - 77/300)*(x81 - x82))/2),
1/96*((5*(Q0/1500 - 77/300)*(x82 - x83))/2),
1/96*((5*(Q0/1500 - 77/300)*(x83 - x84))/2),
1/96*((5*(Q0/1500 - 77/300)*(x84 - x85))/2),
1/96*((6277*x87)/200 - (6277*x86)/200),
1/96*((6277*x88)/200 - (6277*x87)/200),
1/96*((6277*x89)/200 - (6277*x88)/200),
1/96*((6277*x90)/200 - (6277*x89)/200),
1/96*((6277*x91)/200 - (6277*x90)/200),
1/96*((x54*(Q0 + 18446))/600 - (5*x91*(Q0/1500 + 9223/750))/2),
1/96*((5*(Q0/1500 - 77/300)*(x91 - x92))/2),
1/96*((5*(Q0/1500 - 77/300)*(x92 - x93))/2),
1/96*((5*(Q0/1500 - 77/300)*(x93 - x94))/2),
1/96*((5*(Q0/1500 - 77/300)*(x94 - x95))/2),
1/96*((6277*x97)/200 - (6277*x96)/200),
1/96*((6277*x98)/200 - (6277*x97)/200),
1/96*((6277*x99)/200 - (6277*x98)/200),
1/96*((6277*x100)/200 - (6277*x99)/200),
1/96*((6277*x101)/200 - (6277*x100)/200),
1/96*((x60*(Q0 + 18446))/600 - (5*x101*(Q0/1500 + 9223/750))/2),
1/96*((5*(Q0/1500 - 77/300)*(x101 - x102))/2),
1/96*((5*(Q0/1500 - 77/300)*(x102 - x103))/2),
1/96*((5*(Q0/1500 - 77/300)*(x103 - x104))/2),
1/96*((5*(Q0/1500 - 77/300)*(x104 - x105))/2),
1/96*((6277*x107)/200 - (6277*x106)/200),
1/96*((6277*x108)/200 - (6277*x107)/200),
1/96*((6277*x109)/200 - (6277*x108)/200),
1/96*((6277*x110)/200 - (6277*x109)/200),
1/96*((6277*x111)/200 - (6277*x110)/200),
1/96*((x61*(Q0 + 18446))/600 - (5*x111*(Q0/1500 + 9223/750))/2),
1/96*((5*(Q0/1500 - 77/300)*(x111 - x112))/2),
1/96*((5*(Q0/1500 - 77/300)*(x112 - x113))/2),
1/96*((5*(Q0/1500 - 77/300)*(x113 - x114))/2),
1/96*((5*(Q0/1500 - 77/300)*(x114 - x115))/2),
1/96*((6277*x117)/200 - (6277*x116)/200),
1/96*((6277*x118)/200 - (6277*x117)/200),
1/96*((6277*x119)/200 - (6277*x118)/200),
1/96*((6277*x120)/200 - (6277*x119)/200),
1/96*((6277*x121)/200 - (6277*x120)/200),
1/96*((x62*(Q0 + 18446))/600 - (5*x121*(Q0/1500 + 9223/750))/2),
1/96*((5*(Q0/1500 - 77/300)*(x121 - x122))/2),
1/96*((5*(Q0/1500 - 77/300)*(x122 - x123))/2),
1/96*((5*(Q0/1500 - 77/300)*(x123 - x124))/2),
1/96*((5*(Q0/1500 - 77/300)*(x124 - x125))/2),
1/96*((6277*x127)/200 - (6277*x126)/200),
1/96*((6277*x128)/200 - (6277*x127)/200),
1/96*((6277*x129)/200 - (6277*x128)/200),
1/96*((6277*x130)/200 - (6277*x129)/200),
1/96*((6277*x131)/200 - (6277*x130)/200),
1/96*((x63*(Q0 + 18446))/600 - (5*x131*(Q0/1500 + 9223/750))/2),
1/96*((5*(Q0/1500 - 77/300)*(x131 - x132))/2),
1/96*((5*(Q0/1500 - 77/300)*(x132 - x133))/2),
1/96*((5*(Q0/1500 - 77/300)*(x133 - x134))/2),
1/96*((5*(Q0/1500 - 77/300)*(x134 - x135))/2),
1/96*((6277*x137)/200 - (6277*x136)/200),
1/96*((6277*x138)/200 - (6277*x137)/200),
1/96*((6277*x139)/200 - (6277*x138)/200),
1/96*((6277*x140)/200 - (6277*x139)/200),
1/96*((6277*x141)/200 - (6277*x140)/200),
1/96*((x65*(Q0 + 18446))/600 - (5*x141*(Q0/1500 + 9223/750))/2),
1/96*((5*(Q0/1500 - 77/300)*(x141 - x142))/2),
1/96*((5*(Q0/1500 - 77/300)*(x142 - x143))/2),
1/96*((5*(Q0/1500 - 77/300)*(x143 - x144))/2),
1/96*((5*(Q0/1500 - 77/300)*(x144 - x145))/2),
]
return np.array(1./delta_x_empc * dxdt)
def ode_bsm1model_constant_distur(x_scale,u):
# min_x_empc = np.loadtxt('empc_x_min.txt')
# delta_x_empc = np.loadtxt('empc_x_delta.txt')
min_x_empc = np.zeros(145)
delta_x_empc = np.ones(145)
x = x_scale*delta_x_empc + min_x_empc
# Inputs:
KLa5 = u[0]
Qa = u[1]
# Q0 = u[2]
# Z0 = u[3:16]
Q0 = 18446
Z0 = np.array([30, 69.5, 51.2, 202.32, 28.17, 0, 0, 0, 0, 31.56, 6.95, 10.59, 7])
x1 = x[0]
x2 = x[1]
x3 = x[2]
x4 = x[3]
x5 = x[4]
x6 = x[5]
x7 = x[6]
x8 = x[7]
x9 = x[8]
x10 = x[9]
x11 = x[10]
x12 = x[11]
x13 = x[12]
x14 = x[13]
x15 = x[14]
x16 = x[15]
x17 = x[16]
x18 = x[17]
x19 = x[18]
x20 = x[19]
x21 = x[20]
x22 = x[21]
x23 = x[22]
x24 = x[23]
x25 = x[24]
x26 = x[25]
x27 = x[26]
x28 = x[27]
x29 = x[28]
x30 = x[29]
x31 = x[30]
x32 = x[31]
x33 = x[32]
x34 = x[33]
x35 = x[34]
x36 = x[35]
x37 = x[36]
x38 = x[37]
x39 = x[38]
x40 = x[39]
x41 = x[40]
x42 = x[41]
x43 = x[42]
x44 = x[43]
x45 = x[44]
x46 = x[45]
x47 = x[46]
x48 = x[47]
x49 = x[48]
x50 = x[49]
x51 = x[50]
x52 = x[51]
x53 = x[52]
x54 = x[53]
x55 = x[54]
x56 = x[55]
x57 = x[56]
x58 = x[57]
x59 = x[58]
x60 = x[59]
x61 = x[60]
x62 = x[61]
x63 = x[62]
x64 = x[63]
x65 = x[64]
x66 = x[65]
x67 = x[66]
x68 = x[67]
x69 = x[68]
x70 = x[69]
x71 = x[70]
x72 = x[71]
x73 = x[72]
x74 = x[73]
x75 = x[74]
x76 = x[75]
x77 = x[76]
x78 = x[77]
x79 = x[78]
x80 = x[79]
x81 = x[80]
x82 = x[81]
x83 = x[82]
x84 = x[83]
x85 = x[84]
x86 = x[85]
x87 = x[86]
x88 = x[87]
x89 = x[88]
x90 = x[89]
x91 = x[90]
x92 = x[91]
x93 = x[92]
x94 = x[93]
x95 = x[94]
x96 = x[95]
x97 = x[96]
x98 = x[97]
x99 = x[98]
x100 = x[99]
x101 = x[100]
x102 = x[101]
x103 = x[102]
x104 = x[103]
x105 = x[104]
x106 = x[105]
x107 = x[106]
x108 = x[107]
x109 = x[108]
x110 = x[109]
x111 = x[110]
x112 = x[111]
x113 = x[112]
x114 = x[113]
x115 = x[114]
x116 = x[115]
x117 = x[116]
x118 = x[117]
x119 = x[118]
x120 = x[119]
x121 = x[120]
x122 = x[121]
x123 = x[122]
x124 = x[123]
x125 = x[124]
x126 = x[125]
x127 = x[126]
x128 = x[127]
x129 = x[128]
x130 = x[129]
x131 = x[130]
x132 = x[131]
x133 = x[132]
x134 = x[133]
x135 = x[134]
x136 = x[135]
x137 = x[136]
x138 = x[137]
x139 = x[138]
x140 = x[139]
x141 = x[140]
x142 = x[141]
x143 = x[142]
x144 = x[143]
x145 = x[144]
Z01 = Z0[0]
Z02 = Z0[1]
Z03 = Z0[2]
Z04 = Z0[3]
Z05 = Z0[4]
Z06 = Z0[5]
Z07 = Z0[6]
Z08 = Z0[7]
Z09 = Z0[8]
Z010 = Z0[9]
Z011 = Z0[10]
Z012 = Z0[11]
Z013 = Z0[12]
dxdt = [
1/96*((9223*x76)/500 + (Q0*Z01)/1000 + (Qa*x53)/1000 - (x1*(Q0 + Qa + 18446))/1000),
1/96*((9223*x86)/500 + (Q0*Z02)/1000 + (Qa*x54)/1000 - (x2*(Q0 + Qa + 18446))/1000 + (3*x4*(x8/(x8 + 1/5) + (4*x9)/(25*(x9 + 1/2)*(x8 + 1/5))))/(x4/x5 + 1/10) - (400*x2*x5*x8)/(67*(x2 + 10)*(x8 + 1/5)) - (64*x2*x5*x9)/(67*(x2 + 10)*(x9 + 1/2)*(x8 + 1/5))),
1/96*((Q0*Z03)/1000 + (Qa*x55)/1000 - (x3*(Q0 + Qa + 18446))/1000 + (9223*x55*x66)/(500*((3*x55)/4 + (3*x56)/4 + (3*x57)/4 + (3*x58)/4 + (3*x59)/4))),
1/96*((69*x5)/250 + (23*x6)/500 + (Q0*Z04)/1000 + (Qa*x56)/1000 - (x4*(Q0 + Qa + 18446))/1000 + (9223*x56*x66)/(500*((3*x55)/4 + (3*x56)/4 + (3*x57)/4 + (3*x58)/4 + (3*x59)/4)) - (3*x4*(x8/(x8 + 1/5) + (4*x9)/(25*(x9 + 1/2)*(x8 + 1/5))))/(x4/x5 + 1/10)),
1/96*((Q0*Z05)/1000 - (3*x5)/10 + (Qa*x57)/1000 - (x5*(Q0 + Qa + 18446))/1000 + (9223*x57*x66)/(500*((3*x55)/4 + (3*x56)/4 + (3*x57)/4 + (3*x58)/4 + (3*x59)/4)) + (4*x2*x5*x8)/((x2 + 10)*(x8 + 1/5)) + (16*x2*x5*x9)/(25*(x2 + 10)*(x9 + 1/2)*(x8 + 1/5))),
1/96*((Q0*Z06)/1000 - x6/20 + (Qa*x58)/1000 - (x6*(Q0 + Qa + 18446))/1000 + (9223*x58*x66)/(500*((3*x55)/4 + (3*x56)/4 + (3*x57)/4 + (3*x58)/4 + (3*x59)/4)) + (x6*x8*x10)/(2*(x10 + 1)*(x8 + 2/5))),
1/96*((3*x5)/125 + x6/250 + (Q0*Z07)/1000 + (Qa*x59)/1000 - (x7*(Q0 + Qa + 18446))/1000 + (9223*x59*x66)/(500*((3*x55)/4 + (3*x56)/4 + (3*x57)/4 + (3*x58)/4 + (3*x59)/4))),
1/96*((9223*x96)/500 + (Q0*Z08)/1000 + (Qa*x60)/1000 - (x8*(Q0 + Qa + 18446))/1000 - (132*x2*x5*x8)/(67*(x2 + 10)*(x8 + 1/5)) - (433*x6*x8*x10)/(48*(x10 + 1)*(x8 + 2/5))),
1/96*((9223*x106)/500 + (Q0*Z09)/1000 + (Qa*x61)/1000 - (x9*(Q0 + Qa + 18446))/1000 + (25*x6*x8*x10)/(12*(x10 + 1)*(x8 + 2/5)) - (96*x2*x5*x9)/(871*(x2 + 10)*(x9 + 1/2)*(x8 + 1/5))),
1/96*((9223*x116)/500 + (Q0*Z010)/1000 + (Qa*x62)/1000 + (x5*x11)/20 - (x10*(Q0 + Qa + 18446))/1000 - (8*x2*x5*x8)/(25*(x2 + 10)*(x8 + 1/5)) - (637*x6*x8*x10)/(300*(x10 + 1)*(x8 + 2/5)) - (32*x2*x5*x9)/(625*(x2 + 10)*(x9 + 1/2)*(x8 + 1/5))),
1/96*((9223*x126)/500 + (Q0*Z011)/1000 + (Qa*x63)/1000 - (x5*x11)/20 - (x11*(Q0 + Qa + 18446))/1000 + (3*x12*(x8/(x8 + 1/5) + (4*x9)/(25*(x9 + 1/2)*(x8 + 1/5))))/(x4/x5 + 1/10)),
1/96*((141*x5)/6250 + (47*x6)/12500 + (Q0*Z012)/1000 + (Qa*x64)/1000 - (x12*(Q0 + Qa + 18446))/1000 + (9223*x64*x66)/(500*((3*x55)/4 + (3*x56)/4 + (3*x57)/4 + (3*x58)/4 + (3*x59)/4)) - (3*x12*(x8/(x8 + 1/5) + (4*x9)/(25*(x9 + 1/2)*(x8 + 1/5))))/(x4/x5 + 1/10)),
1/96*((9223*x136)/500 + (Q0*Z013)/1000 + (Qa*x65)/1000 + (x5*x11)/280 - (x13*(Q0 + Qa + 18446))/1000 - (4*x2*x5*x8)/(175*(x2 + 10)*(x8 + 1/5)) - (631*x6*x8*x10)/(2100*(x10 + 1)*(x8 + 2/5)) + (1518823277841921*x2*x5*x9)/(360287970189639680*(x2 + 10)*(x9 + 1/2)*(x8 + 1/5))),
1/96*((x1*(Q0 + Qa + 18446))/1000 - (x14*(Q0 + Qa + 18446))/1000),
1/96*((x2*(Q0 + Qa + 18446))/1000 - (x15*(Q0 + Qa + 18446))/1000 + (3*x17*(x21/(x21 + 1/5) + (4*x22)/(25*(x22 + 1/2)*(x21 + 1/5))))/(x17/x18 + 1/10) - (400*x15*x18*x21)/(67*(x15 + 10)*(x21 + 1/5)) - (64*x15*x18*x22)/(67*(x15 + 10)*(x22 + 1/2)*(x21 + 1/5))),
1/96*((x3*(Q0 + Qa + 18446))/1000 - (x16*(Q0 + Qa + 18446))/1000),
1/96*((69*x18)/250 + (23*x19)/500 + (x4*(Q0 + Qa + 18446))/1000 - (x17*(Q0 + Qa + 18446))/1000 - (3*x17*(x21/(x21 + 1/5) + (4*x22)/(25*(x22 + 1/2)*(x21 + 1/5))))/(x17/x18 + 1/10)),
1/96*((x5*(Q0 + Qa + 18446))/1000 - (3*x18)/10 - (x18*(Q0 + Qa + 18446))/1000 + (4*x15*x18*x21)/((x15 + 10)*(x21 + 1/5)) + (16*x15*x18*x22)/(25*(x15 + 10)*(x22 + 1/2)*(x21 + 1/5))),
1/96*((x6*(Q0 + Qa + 18446))/1000 - x19/20 - (x19*(Q0 + Qa + 18446))/1000 + (x19*x21*x23)/(2*(x23 + 1)*(x21 + 2/5))),
1/96*((3*x18)/125 + x19/250 + (x7*(Q0 + Qa + 18446))/1000 - (x20*(Q0 + Qa + 18446))/1000),
1/96*((x8*(Q0 + Qa + 18446))/1000 - (x21*(Q0 + Qa + 18446))/1000 - (132*x15*x18*x21)/(67*(x15 + 10)*(x21 + 1/5)) - (433*x19*x21*x23)/(48*(x23 + 1)*(x21 + 2/5))),
1/96*((x9*(Q0 + Qa + 18446))/1000 - (x22*(Q0 + Qa + 18446))/1000 + (25*x19*x21*x23)/(12*(x23 + 1)*(x21 + 2/5)) - (96*x15*x18*x22)/(871*(x15 + 10)*(x22 + 1/2)*(x21 + 1/5))),
1/96*((x18*x24)/20 + (x10*(Q0 + Qa + 18446))/1000 - (x23*(Q0 + Qa + 18446))/1000 - (8*x15*x18*x21)/(25*(x15 + 10)*(x21 + 1/5)) - (637*x19*x21*x23)/(300*(x23 + 1)*(x21 + 2/5)) - (32*x15*x18*x22)/(625*(x15 + 10)*(x22 + 1/2)*(x21 + 1/5))),
1/96*((x11*(Q0 + Qa + 18446))/1000 - (x18*x24)/20 - (x24*(Q0 + Qa + 18446))/1000 + (3*x25*(x21/(x21 + 1/5) + (4*x22)/(25*(x22 + 1/2)*(x21 + 1/5))))/(x17/x18 + 1/10)),
1/96*((141*x18)/6250 + (47*x19)/12500 + (x12*(Q0 + Qa + 18446))/1000 - (x25*(Q0 + Qa + 18446))/1000 - (3*x25*(x21/(x21 + 1/5) + (4*x22)/(25*(x22 + 1/2)*(x21 + 1/5))))/(x17/x18 + 1/10)),
1/96*((x18*x24)/280 + (x13*(Q0 + Qa + 18446))/1000 - (x26*(Q0 + Qa + 18446))/1000 - (4*x15*x18*x21)/(175*(x15 + 10)*(x21 + 1/5)) - (631*x19*x21*x23)/(2100*(x23 + 1)*(x21 + 2/5)) + (1518823277841921*x15*x18*x22)/(360287970189639680*(x15 + 10)*(x22 + 1/2)*(x21 + 1/5))),
1/96*((x14*(Q0 + Qa + 18446))/1333 - (x27*(Q0 + Qa + 18446))/1333),
1/96*((x15*(Q0 + Qa + 18446))/1333 - (x28*(Q0 + Qa + 18446))/1333 + (3*x30*(x34/(x34 + 1/5) + (4*x35)/(25*(x35 + 1/2)*(x34 + 1/5))))/(x30/x31 + 1/10) - (400*x28*x31*x34)/(67*(x28 + 10)*(x34 + 1/5)) - (64*x28*x31*x35)/(67*(x28 + 10)*(x35 + 1/2)*(x34 + 1/5))),
1/96*((x16*(Q0 + Qa + 18446))/1333 - (x29*(Q0 + Qa + 18446))/1333),
1/96*((69*x31)/250 + (23*x32)/500 + (x17*(Q0 + Qa + 18446))/1333 - (x30*(Q0 + Qa + 18446))/1333 - (3*x30*(x34/(x34 + 1/5) + (4*x35)/(25*(x35 + 1/2)*(x34 + 1/5))))/(x30/x31 + 1/10)),
1/96*((x18*(Q0 + Qa + 18446))/1333 - (3*x31)/10 - (x31*(Q0 + Qa + 18446))/1333 + (4*x28*x31*x34)/((x28 + 10)*(x34 + 1/5)) + (16*x28*x31*x35)/(25*(x28 + 10)*(x35 + 1/2)*(x34 + 1/5))),
1/96*((x19*(Q0 + Qa + 18446))/1333 - x32/20 - (x32*(Q0 + Qa + 18446))/1333 + (x32*x34*x36)/(2*(x36 + 1)*(x34 + 2/5))),
1/96*((3*x31)/125 + x32/250 + (x20*(Q0 + Qa + 18446))/1333 - (x33*(Q0 + Qa + 18446))/1333),
1/96*((x21*(Q0 + Qa + 18446))/1333 - 240*x34 - (x34*(Q0 + Qa + 18446))/1333 - (132*x28*x31*x34)/(67*(x28 + 10)*(x34 + 1/5)) - (433*x32*x34*x36)/(48*(x36 + 1)*(x34 + 2/5)) + 1920),
1/96*((x22*(Q0 + Qa + 18446))/1333 - (x35*(Q0 + Qa + 18446))/1333 + (25*x32*x34*x36)/(12*(x36 + 1)*(x34 + 2/5)) - (96*x28*x31*x35)/(871*(x28 + 10)*(x35 + 1/2)*(x34 + 1/5))),
1/96*((x31*x37)/20 + (x23*(Q0 + Qa + 18446))/1333 - (x36*(Q0 + Qa + 18446))/1333 - (8*x28*x31*x34)/(25*(x28 + 10)*(x34 + 1/5)) - (637*x32*x34*x36)/(300*(x36 + 1)*(x34 + 2/5)) - (32*x28*x31*x35)/(625*(x28 + 10)*(x35 + 1/2)*(x34 + 1/5))),
1/96*((x24*(Q0 + Qa + 18446))/1333 - (x31*x37)/20 - (x37*(Q0 + Qa + 18446))/1333 + (3*x38*(x34/(x34 + 1/5) + (4*x35)/(25*(x35 + 1/2)*(x34 + 1/5))))/(x30/x31 + 1/10)),
1/96*((141*x31)/6250 + (47*x32)/12500 + (x25*(Q0 + Qa + 18446))/1333 - (x38*(Q0 + Qa + 18446))/1333 - (3*x38*(x34/(x34 + 1/5) + (4*x35)/(25*(x35 + 1/2)*(x34 + 1/5))))/(x30/x31 + 1/10)),
1/96*((x31*x37)/280 + (x26*(Q0 + Qa + 18446))/1333 - (x39*(Q0 + Qa + 18446))/1333 - (4*x28*x31*x34)/(175*(x28 + 10)*(x34 + 1/5)) - (631*x32*x34*x36)/(2100*(x36 + 1)*(x34 + 2/5)) + (1518823277841921*x28*x31*x35)/(360287970189639680*(x28 + 10)*(x35 + 1/2)*(x34 + 1/5))),
1/96*((x27*(Q0 + Qa + 18446))/1333 - (x40*(Q0 + Qa + 18446))/1333),
1/96*((x28*(Q0 + Qa + 18446))/1333 - (x41*(Q0 + Qa + 18446))/1333 + (3*x43*(x47/(x47 + 1/5) + (4*x48)/(25*(x48 + 1/2)*(x47 + 1/5))))/(x43/x44 + 1/10) - (400*x41*x44*x47)/(67*(x41 + 10)*(x47 + 1/5)) - (64*x41*x44*x48)/(67*(x41 + 10)*(x48 + 1/2)*(x47 + 1/5))),
1/96*((x29*(Q0 + Qa + 18446))/1333 - (x42*(Q0 + Qa + 18446))/1333),
1/96*((69*x44)/250 + (23*x45)/500 + (x30*(Q0 + Qa + 18446))/1333 - (x43*(Q0 + Qa + 18446))/1333 - (3*x43*(x47/(x47 + 1/5) + (4*x48)/(25*(x48 + 1/2)*(x47 + 1/5))))/(x43/x44 + 1/10)),
1/96*((x31*(Q0 + Qa + 18446))/1333 - (3*x44)/10 - (x44*(Q0 + Qa + 18446))/1333 + (4*x41*x44*x47)/((x41 + 10)*(x47 + 1/5)) + (16*x41*x44*x48)/(25*(x41 + 10)*(x48 + 1/2)*(x47 + 1/5))),
1/96*((x32*(Q0 + Qa + 18446))/1333 - x45/20 - (x45*(Q0 + Qa + 18446))/1333 + (x45*x47*x49)/(2*(x49 + 1)*(x47 + 2/5))),
1/96*((3*x44)/125 + x45/250 + (x33*(Q0 + Qa + 18446))/1333 - (x46*(Q0 + Qa + 18446))/1333),
1/96*((x34*(Q0 + Qa + 18446))/1333 - 240*x47 - (x47*(Q0 + Qa + 18446))/1333 - (132*x41*x44*x47)/(67*(x41 + 10)*(x47 + 1/5)) - (433*x45*x47*x49)/(48*(x49 + 1)*(x47 + 2/5)) + 1920),
1/96*((x35*(Q0 + Qa + 18446))/1333 - (x48*(Q0 + Qa + 18446))/1333 + (25*x45*x47*x49)/(12*(x49 + 1)*(x47 + 2/5)) - (96*x41*x44*x48)/(871*(x41 + 10)*(x48 + 1/2)*(x47 + 1/5))),
1/96*((x44*x50)/20 + (x36*(Q0 + Qa + 18446))/1333 - (x49*(Q0 + Qa + 18446))/1333 - (8*x41*x44*x47)/(25*(x41 + 10)*(x47 + 1/5)) - (637*x45*x47*x49)/(300*(x49 + 1)*(x47 + 2/5)) - (32*x41*x44*x48)/(625*(x41 + 10)*(x48 + 1/2)*(x47 + 1/5))),
1/96*((x37*(Q0 + Qa + 18446))/1333 - (x44*x50)/20 - (x50*(Q0 + Qa + 18446))/1333 + (3*x51*(x47/(x47 + 1/5) + (4*x48)/(25*(x48 + 1/2)*(x47 + 1/5))))/(x43/x44 + 1/10)),
1/96*((141*x44)/6250 + (47*x45)/12500 + (x38*(Q0 + Qa + 18446))/1333 - (x51*(Q0 + Qa + 18446))/1333 - (3*x51*(x47/(x47 + 1/5) + (4*x48)/(25*(x48 + 1/2)*(x47 + 1/5))))/(x43/x44 + 1/10)),
1/96*((x44*x50)/280 + (x39*(Q0 + Qa + 18446))/1333 - (x52*(Q0 + Qa + 18446))/1333 - (4*x41*x44*x47)/(175*(x41 + 10)*(x47 + 1/5)) - (631*x45*x47*x49)/(2100*(x49 + 1)*(x47 + 2/5)) + (1518823277841921*x41*x44*x48)/(360287970189639680*(x41 + 10)*(x48 + 1/2)*(x47 + 1/5))),
1/96*((x40*(Q0 + Qa + 18446))/1333 - (x53*(Q0 + Qa + 18446))/1333),
1/96*((x41*(Q0 + Qa + 18446))/1333 - (x54*(Q0 + Qa + 18446))/1333 + (3*x56*(x60/(x60 + 1/5) + (4*x61)/(25*(x61 + 1/2)*(x60 + 1/5))))/(x56/x57 + 1/10) - (400*x54*x57*x60)/(67*(x54 + 10)*(x60 + 1/5)) - (64*x54*x57*x61)/(67*(x54 + 10)*(x61 + 1/2)*(x60 + 1/5))),
1/96*((x42*(Q0 + Qa + 18446))/1333 - (x55*(Q0 + Qa + 18446))/1333),
1/96*((69*x57)/250 + (23*x58)/500 + (x43*(Q0 + Qa + 18446))/1333 - (x56*(Q0 + Qa + 18446))/1333 - (3*x56*(x60/(x60 + 1/5) + (4*x61)/(25*(x61 + 1/2)*(x60 + 1/5))))/(x56/x57 + 1/10)),
1/96*((x44*(Q0 + Qa + 18446))/1333 - (3*x57)/10 - (x57*(Q0 + Qa + 18446))/1333 + (4*x54*x57*x60)/((x54 + 10)*(x60 + 1/5)) + (16*x54*x57*x61)/(25*(x54 + 10)*(x61 + 1/2)*(x60 + 1/5))),
1/96*((x45*(Q0 + Qa + 18446))/1333 - x58/20 - (x58*(Q0 + Qa + 18446))/1333 + (x58*x60*x62)/(2*(x62 + 1)*(x60 + 2/5))),
1/96*((3*x57)/125 + x58/250 + (x46*(Q0 + Qa + 18446))/1333 - (x59*(Q0 + Qa + 18446))/1333),
1/96*((x47*(Q0 + Qa + 18446))/1333 - KLa5*(x60 - 8) - (x60*(Q0 + Qa + 18446))/1333 - (132*x54*x57*x60)/(67*(x54 + 10)*(x60 + 1/5)) - (433*x58*x60*x62)/(48*(x62 + 1)*(x60 + 2/5))),
1/96*((x48*(Q0 + Qa + 18446))/1333 - (x61*(Q0 + Qa + 18446))/1333 + (25*x58*x60*x62)/(12*(x62 + 1)*(x60 + 2/5)) - (96*x54*x57*x61)/(871*(x54 + 10)*(x61 + 1/2)*(x60 + 1/5))),
1/96*((x57*x63)/20 + (x49*(Q0 + Qa + 18446))/1333 - (x62*(Q0 + Qa + 18446))/1333 - (8*x54*x57*x60)/(25*(x54 + 10)*(x60 + 1/5)) - (637*x58*x60*x62)/(300*(x62 + 1)*(x60 + 2/5)) - (32*x54*x57*x61)/(625*(x54 + 10)*(x61 + 1/2)*(x60 + 1/5))),
1/96*((x50*(Q0 + Qa + 18446))/1333 - (x57*x63)/20 - (x63*(Q0 + Qa + 18446))/1333 + (3*x64*(x60/(x60 + 1/5) + (4*x61)/(25*(x61 + 1/2)*(x60 + 1/5))))/(x56/x57 + 1/10)),
1/96*((141*x57)/6250 + (47*x58)/12500 + (x51*(Q0 + Qa + 18446))/1333 - (x64*(Q0 + Qa + 18446))/1333 - (3*x64*(x60/(x60 + 1/5) + (4*x61)/(25*(x61 + 1/2)*(x60 + 1/5))))/(x56/x57 + 1/10)),
1/96*((x57*x63)/280 + (x52*(Q0 + Qa + 18446))/1333 - (x65*(Q0 + Qa + 18446))/1333 - (4*x54*x57*x60)/(175*(x54 + 10)*(x60 + 1/5)) - (631*x58*x60*x62)/(2100*(x62 + 1)*(x60 + 2/5)) + (1518823277841921*x54*x57*x61)/(360287970189639680*(x54 + 10)*(x61 + 1/2)*(x60 + 1/5))),
1/96*((6277*x67)/200 - (6277*x66)/200 + (5*x67*(474* np.exp((1539*x55)/1562500000 + (1539*x56)/1562500000 + (1539*x57)/1562500000 + (1539*x58)/1562500000 + (1539*x59)/1562500000 - (9*x67)/15625) - 474* np.exp((24453*x55)/5000000000 + (24453*x56)/5000000000 + (24453*x57)/5000000000 + (24453*x58)/5000000000 + (24453*x59)/5000000000 - (143*x67)/50000)))/2),
1/96*((6277*x68)/200 - (6277*x67)/200 - (5*x67*(474* np.exp((1539*x55)/1562500000 + (1539*x56)/1562500000 + (1539*x57)/1562500000 + (1539*x58)/1562500000 + (1539*x59)/1562500000 - (9*x67)/15625) - 474* np.exp((24453*x55)/5000000000 + (24453*x56)/5000000000 + (24453*x57)/5000000000 + (24453*x58)/5000000000 + (24453*x59)/5000000000 - (143*x67)/50000)))/2 + (5*x68*(474* np.exp((1539*x55)/1562500000 + (1539*x56)/1562500000 + (1539*x57)/1562500000 + (1539*x58)/1562500000 + (1539*x59)/1562500000 - (9*x68)/15625) - 474* np.exp((24453*x55)/5000000000 + (24453*x56)/5000000000 + (24453*x57)/5000000000 + (24453*x58)/5000000000 + (24453*x59)/5000000000 - (143*x68)/50000)))/2),
1/96*((6277*x69)/200 - (6277*x68)/200),
1/96*((6277*x70)/200 - (6277*x69)/200 - (5*x68*(474* np.exp((1539*x55)/1562500000 + (1539*x56)/1562500000 + (1539*x57)/1562500000 + (1539*x58)/1562500000 + (1539*x59)/1562500000 - (9*x68)/15625) - 474* np.exp((24453*x55)/5000000000 + (24453*x56)/5000000000 + (24453*x57)/5000000000 + (24453*x58)/5000000000 + (24453*x59)/5000000000 - (143*x68)/50000)))/2 + (5*x70*(474* np.exp((1539*x55)/1562500000 + (1539*x56)/1562500000 + (1539*x57)/1562500000 + (1539*x58)/1562500000 + (1539*x59)/1562500000 - (9*x70)/15625) - 474* np.exp((24453*x55)/5000000000 + (24453*x56)/5000000000 + (24453*x57)/5000000000 + (24453*x58)/5000000000 + (24453*x59)/5000000000 - (143*x70)/50000)))/2),
1/96*((6277*x71)/200 - (6277*x70)/200),
1/96*((5*x72*(474* np.exp((1539*x55)/1562500000 + (1539*x56)/1562500000 + (1539*x57)/1562500000 + (1539*x58)/1562500000 + (1539*x59)/1562500000 - (9*x72)/15625) - 474* np.exp((24453*x55)/5000000000 + (24453*x56)/5000000000 + (24453*x57)/5000000000 + (24453*x58)/5000000000 + (24453*x59)/5000000000 - (143*x72)/50000)))/2 - (5*x70*(474* np.exp((1539*x55)/1562500000 + (1539*x56)/1562500000 + (1539*x57)/1562500000 + (1539*x58)/1562500000 + (1539*x59)/1562500000 - (9*x70)/15625) - 474* np.exp((24453*x55)/5000000000 + (24453*x56)/5000000000 + (24453*x57)/5000000000 + (24453*x58)/5000000000 + (24453*x59)/5000000000 - (143*x70)/50000)))/2 + ((Q0 + 18446)*((3*x55)/4 + (3*x56)/4 + (3*x57)/4 + (3*x58)/4 + (3*x59)/4))/600 - (5*x71*(Q0/1500 + 9223/750))/2),
1/96*((5*(Q0/1500 - 77/300)*(x71 - x72))/2 - (5*x72*(474* np.exp((1539*x55)/1562500000 + (1539*x56)/1562500000 + (1539*x57)/1562500000 + (1539*x58)/1562500000 + (1539*x59)/1562500000 - (9*x72)/15625) - 474* np.exp((24453*x55)/5000000000 + (24453*x56)/5000000000 + (24453*x57)/5000000000 + (24453*x58)/5000000000 + (24453*x59)/5000000000 - (143*x72)/50000)))/2 + (5*x73*(474* np.exp((1539*x55)/1562500000 + (1539*x56)/1562500000 + (1539*x57)/1562500000 + (1539*x58)/1562500000 + (1539*x59)/1562500000 - (9*x73)/15625) - 474* np.exp((24453*x55)/5000000000 + (24453*x56)/5000000000 + (24453*x57)/5000000000 + (24453*x58)/5000000000 + (24453*x59)/5000000000 - (143*x73)/50000)))/2),
1/96*((5*(Q0/1500 - 77/300)*(x72 - x73))/2 - (5*x73*(474* np.exp((1539*x55)/1562500000 + (1539*x56)/1562500000 + (1539*x57)/1562500000 + (1539*x58)/1562500000 + (1539*x59)/1562500000 - (9*x73)/15625) - 474* np.exp((24453*x55)/5000000000 + (24453*x56)/5000000000 + (24453*x57)/5000000000 + (24453*x58)/5000000000 + (24453*x59)/5000000000 - (143*x73)/50000)))/2 + (5*x74*(474* np.exp((1539*x55)/1562500000 + (1539*x56)/1562500000 + (1539*x57)/1562500000 + (1539*x58)/1562500000 + (1539*x59)/1562500000 - (9*x74)/15625) - 474* np.exp((24453*x55)/5000000000 + (24453*x56)/5000000000 + (24453*x57)/5000000000 + (24453*x58)/5000000000 + (24453*x59)/5000000000 - (143*x74)/50000)))/2),
1/96*((5*(Q0/1500 - 77/300)*(x73 - x74))/2 - (5*x74*(474* np.exp((1539*x55)/1562500000 + (1539*x56)/1562500000 + (1539*x57)/1562500000 + (1539*x58)/1562500000 + (1539*x59)/1562500000 - (9*x74)/15625) - 474* np.exp((24453*x55)/5000000000 + (24453*x56)/5000000000 + (24453*x57)/5000000000 + (24453*x58)/5000000000 + (24453*x59)/5000000000 - (143*x74)/50000)))/2 + (5*x75*(474* np.exp((1539*x55)/1562500000 + (1539*x56)/1562500000 + (1539*x57)/1562500000 + (1539*x58)/1562500000 + (1539*x59)/1562500000 - (9*x75)/15625) - 474* np.exp((24453*x55)/5000000000 + (24453*x56)/5000000000 + (24453*x57)/5000000000 + (24453*x58)/5000000000 + (24453*x59)/5000000000 - (143*x75)/50000)))/2),
1/96*((5*(Q0/1500 - 77/300)*(x74 - x75))/2 - (5*x75*(474* np.exp((1539*x55)/1562500000 + (1539*x56)/1562500000 + (1539*x57)/1562500000 + (1539*x58)/1562500000 + (1539*x59)/1562500000 - (9*x75)/15625) - 474* np.exp((24453*x55)/5000000000 + (24453*x56)/5000000000 + (24453*x57)/5000000000 + (24453*x58)/5000000000 + (24453*x59)/5000000000 - (143*x75)/50000)))/2),
1/96*((6277*x77)/200 - (6277*x76)/200),
1/96*((6277*x78)/200 - (6277*x77)/200),
1/96*((6277*x79)/200 - (6277*x78)/200),
1/96*((6277*x80)/200 - (6277*x79)/200),
1/96*((6277*x81)/200 - (6277*x80)/200),
1/96*((x53*(Q0 + 18446))/600 - (5*x81*(Q0/1500 + 9223/750))/2),
1/96*((5*(Q0/1500 - 77/300)*(x81 - x82))/2),
1/96*((5*(Q0/1500 - 77/300)*(x82 - x83))/2),
1/96*((5*(Q0/1500 - 77/300)*(x83 - x84))/2),
1/96*((5*(Q0/1500 - 77/300)*(x84 - x85))/2),
1/96*((6277*x87)/200 - (6277*x86)/200),
1/96*((6277*x88)/200 - (6277*x87)/200),
1/96*((6277*x89)/200 - (6277*x88)/200),
1/96*((6277*x90)/200 - (6277*x89)/200),
1/96*((6277*x91)/200 - (6277*x90)/200),
1/96*((x54*(Q0 + 18446))/600 - (5*x91*(Q0/1500 + 9223/750))/2),
1/96*((5*(Q0/1500 - 77/300)*(x91 - x92))/2),
1/96*((5*(Q0/1500 - 77/300)*(x92 - x93))/2),
1/96*((5*(Q0/1500 - 77/300)*(x93 - x94))/2),
1/96*((5*(Q0/1500 - 77/300)*(x94 - x95))/2),
1/96*((6277*x97)/200 - (6277*x96)/200),
1/96*((6277*x98)/200 - (6277*x97)/200),
1/96*((6277*x99)/200 - (6277*x98)/200),
1/96*((6277*x100)/200 - (6277*x99)/200),
1/96*((6277*x101)/200 - (6277*x100)/200),
1/96*((x60*(Q0 + 18446))/600 - (5*x101*(Q0/1500 + 9223/750))/2),
1/96*((5*(Q0/1500 - 77/300)*(x101 - x102))/2),
1/96*((5*(Q0/1500 - 77/300)*(x102 - x103))/2),
1/96*((5*(Q0/1500 - 77/300)*(x103 - x104))/2),
1/96*((5*(Q0/1500 - 77/300)*(x104 - x105))/2),
1/96*((6277*x107)/200 - (6277*x106)/200),
1/96*((6277*x108)/200 - (6277*x107)/200),
1/96*((6277*x109)/200 - (6277*x108)/200),
1/96*((6277*x110)/200 - (6277*x109)/200),
1/96*((6277*x111)/200 - (6277*x110)/200),
1/96*((x61*(Q0 + 18446))/600 - (5*x111*(Q0/1500 + 9223/750))/2),
1/96*((5*(Q0/1500 - 77/300)*(x111 - x112))/2),
1/96*((5*(Q0/1500 - 77/300)*(x112 - x113))/2),
1/96*((5*(Q0/1500 - 77/300)*(x113 - x114))/2),
1/96*((5*(Q0/1500 - 77/300)*(x114 - x115))/2),
1/96*((6277*x117)/200 - (6277*x116)/200),
1/96*((6277*x118)/200 - (6277*x117)/200),
1/96*((6277*x119)/200 - (6277*x118)/200),
1/96*((6277*x120)/200 - (6277*x119)/200),
1/96*((6277*x121)/200 - (6277*x120)/200),
1/96*((x62*(Q0 + 18446))/600 - (5*x121*(Q0/1500 + 9223/750))/2),
1/96*((5*(Q0/1500 - 77/300)*(x121 - x122))/2),
1/96*((5*(Q0/1500 - 77/300)*(x122 - x123))/2),
1/96*((5*(Q0/1500 - 77/300)*(x123 - x124))/2),
1/96*((5*(Q0/1500 - 77/300)*(x124 - x125))/2),
1/96*((6277*x127)/200 - (6277*x126)/200),
1/96*((6277*x128)/200 - (6277*x127)/200),
1/96*((6277*x129)/200 - (6277*x128)/200),
1/96*((6277*x130)/200 - (6277*x129)/200),
1/96*((6277*x131)/200 - (6277*x130)/200),
1/96*((x63*(Q0 + 18446))/600 - (5*x131*(Q0/1500 + 9223/750))/2),
1/96*((5*(Q0/1500 - 77/300)*(x131 - x132))/2),
1/96*((5*(Q0/1500 - 77/300)*(x132 - x133))/2),
1/96*((5*(Q0/1500 - 77/300)*(x133 - x134))/2),
1/96*((5*(Q0/1500 - 77/300)*(x134 - x135))/2),
1/96*((6277*x137)/200 - (6277*x136)/200),
1/96*((6277*x138)/200 - (6277*x137)/200),
1/96*((6277*x139)/200 - (6277*x138)/200),
1/96*((6277*x140)/200 - (6277*x139)/200),
1/96*((6277*x141)/200 - (6277*x140)/200),
1/96*((x65*(Q0 + 18446))/600 - (5*x141*(Q0/1500 + 9223/750))/2),
1/96*((5*(Q0/1500 - 77/300)*(x141 - x142))/2),
1/96*((5*(Q0/1500 - 77/300)*(x142 - x143))/2),
1/96*((5*(Q0/1500 - 77/300)*(x143 - x144))/2),
1/96*((5*(Q0/1500 - 77/300)*(x144 - x145))/2),
]
return np.array(1./delta_x_empc * dxdt)