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santiago-salas-v/test_Debye_Hueckel.ipynb

Created August 21, 2016 08:05
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test_Debye_Hueckel.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# ref. Mortimer S. 271\n",
"$$\n",
"\\begin{align}\n",
"HA + H2O & \\rightleftharpoons H3O(+) + A(-) & K= & 1.75\\times 10^{-5} \\\\\n",
"2 H2O & \\rightleftharpoons H3O(+) + OH(-) & K= & 10^{-14}\n",
"\\end{align} \\\\\n",
"$$\n",
"<pre>\n",
"\n",
"| i | comp. | m0, mol/g |\n",
"| --- | ------- | ----------- |\n",
"|0|H2O\t|\t0.05555\n",
"|1|HA\t|\t0.000100\n",
"|2|A(-)\t|\t0.0\n",
"|3|H3O(+)|\t1.0E-10\n",
"|4|HO(-)|\t1.0E-10\n",
"\n",
"</pre>\n",
"$$x = [n_0 m_1 m_2 m_3 m_4 \\xi_1 \\xi_2 \\gamma_0 \\gamma_1 \\gamma_3 \\gamma_4]$$"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"f(x):\n",
"Matrix([[-n0 - xi1 - 2*xi2 + 55.55, -18.01528*m1*n0 - xi1 + 0.1000748804, -18.01528*m2*n0 + xi1, -18.01528*m3*n0 + xi1 + xi2 + 1.000748804e-7, -18.01528*m4*n0 + xi2 + 1.000748804e-7, -3.1621604814443e-7 + 18.01528*g2*g3*m2*m3/(g0*g1*m1), -3.26506413401086e-18 + 324.5503134784*g3*g4*m3*m4/g0**2, -g0 + exp(-18.01528*m1 - 18.01528*m2 - 18.01528*m3 - 18.01528*m4), 10**(100.0*i) - g1, -g2 + 10**(-16.1376887331227*sqrt(i)), -g3 + 10**(-16.1376887331227*sqrt(i)), -g4 + 10**(-16.1376887331227*sqrt(i)), -i + 0.5*m2 + 0.5*m3 + 0.5*m4]])\n",
"J(x):\n",
"Matrix([[-1, 0, 0, 0, 0, -1, -2, 0, 0, 0, 0, 0, 0], [-18.01528*m1, -18.01528*n0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0], [-18.01528*m2, 0, -18.01528*n0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [-18.01528*m3, 0, 0, -18.01528*n0, 0, 1, 1, 0, 0, 0, 0, 0, 0], [-18.01528*m4, 0, 0, 0, -18.01528*n0, 0, 1, 0, 0, 0, 0, 0, 0], [0, -18.01528*g2*g3*m2*m3/(g0*g1*m1**2), 18.01528*g2*g3*m3/(g0*g1*m1), 18.01528*g2*g3*m2/(g0*g1*m1), 0, 0, 0, -18.01528*g2*g3*m2*m3/(g0**2*g1*m1), -18.01528*g2*g3*m2*m3/(g0*g1**2*m1), 18.01528*g3*m2*m3/(g0*g1*m1), 18.01528*g2*m2*m3/(g0*g1*m1), 0, 0], [0, 0, 0, 324.5503134784*g3*g4*m4/g0**2, 324.5503134784*g3*g4*m3/g0**2, 0, 0, -649.1006269568*g3*g4*m3*m4/g0**3, 0, 0, 324.5503134784*g4*m3*m4/g0**2, 324.5503134784*g3*m3*m4/g0**2, 0], [0, -18.01528*exp(-18.01528*m1 - 18.01528*m2 - 18.01528*m3 - 18.01528*m4), -18.01528*exp(-18.01528*m1 - 18.01528*m2 - 18.01528*m3 - 18.01528*m4), -18.01528*exp(-18.01528*m1 - 18.01528*m2 - 18.01528*m3 - 18.01528*m4), -18.01528*exp(-18.01528*m1 - 18.01528*m2 - 18.01528*m3 - 18.01528*m4), 0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 100.0*10**(100.0*i)*log(10)], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -8.06884436656137*10**(-16.1376887331227*sqrt(i))*log(10)/sqrt(i)], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -8.06884436656137*10**(-16.1376887331227*sqrt(i))*log(10)/sqrt(i)], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -8.06884436656137*10**(-16.1376887331227*sqrt(i))*log(10)/sqrt(i)], [0, 0, 0.500000000000000, 0.500000000000000, 0.500000000000000, 0, 0, 0, 0, 0, 0, 0, -1]])\n",
"Jx:\n",
"[ -1.0 0.0 0.0 0.0 0.0 -1.0 -2.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ -0.00177549410848078655105 -1000.72405927429351199 0.0 0.0 0.0 -1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ -0.000024730422252795597438 0.0 -1000.72405927429351199 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[-0.0000247304223963773795398 0.0 0.0 -1000.72405927429351199 0.0 1.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ -1.4351267604990245186e-13 0.0 0.0 0.0 -1000.72405927429351199 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ 0.0 -0.00320852692481873824553 0.230352745039509860095 0.230352743702110234861 0.0 0.0 0.0 -3.16793655309088560399e-7 -3.16116112483328442868e-7 3.3028702661135703323e-7 3.3028702661135703323e-7 0.0 0.0]\n",
"[ 0.0 0.0 0.0 2.3784892813070466316e-12 0.000409866544273245785387 0.0 0.0 -6.54205633871808464933e-18 0.0 0.0 3.41035292189007831541e-18 3.41035292189007831541e-18 0.0]\n",
"[ 0.0 -17.9824329068783671524 -17.9824329068783671524 -17.9824329068783671524 -17.9824329068783671524 0.0 0.0 -1.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 0.0 0.0 0.0 230.331302452946354779]\n",
"[ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 0.0 0.0 -15181.8312729953955909]\n",
"[ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 0.0 -15181.8312729953955909]\n",
"[ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 -15181.8312729953955909]\n",
"[ 0.0 0.0 0.5 0.5 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0]\n",
"s: [ -5.28317031426552658291e-7]\n",
"[ 7.42990780789801653422e-8]\n",
"[ 5.28093654317834991841e-10]\n",
"[ 5.28093647529086825151e-10]\n",
"[ -2.95277941069934590148e-18]\n",
"[ 5.28462953806621189825e-7]\n",
"[ -7.48833549591879146828e-11]\n",
"[-0.00000135507051470299875807]\n",
"[ 1.2163553302709887778e-7]\n",
"[-0.00000801742895931672100377]\n",
"[-0.00000801742895931672100377]\n",
"[-0.00000801742895931672100377]\n",
"[ 5.28093647529086806971e-10]\n",
"x: [ 55.5486259306829661972]\n",
"[ 0.0000986291985012789797943]\n",
"[0.00000137327513132431777827]\n",
"[0.00000137327513928752905795]\n",
"[ 7.96321127964930121307e-15]\n",
"[ 0.00137426945085380652065]\n",
"[ -1.00066911422959186773e-7]\n",
"[ 0.998175354193485336391]\n",
"[ 1.00031625828553299226]\n",
"[ 0.957389709077040651895]\n",
"[ 0.957389709077040651895]\n",
"[ 0.957389709077040651895]\n",
"[0.00000137327513928752905794]\n",
"error: 8.04487973687909316354e-10\n",
"Jx:\n",
"[ -1.0 0.0 0.0 0.0 0.0 -1.0 -2.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ -0.00177683262717612124089 -1000.72404975651426207 0.0 0.0 0.0 -1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[-0.0000247399360078443564447 0.0 -1000.72404975651426207 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[-0.0000247399361513038373474 0.0 0.0 -1000.72404975651426207 0.0 1.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ -1.43459480902040468146e-13 0.0 0.0 0.0 -1000.72404975651426207 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ 0.0 -0.00320611031982736609002 0.23026419392471584367 0.23026419258948274004 0.0 0.0 0.0 -3.1679412822885357243e-7 -3.16116116810120610285e-7 3.30289837203385462512e-7 3.30289837203385462512e-7 0.0 0.0]\n",
"[ 0.0 0.0 0.0 2.37757429264127111337e-12 0.000410018465319079533494 0.0 0.0 -6.54206428595209175521e-18 0.0 0.0 3.41038099421502345282e-18 3.41038099421502345282e-18 0.0]\n",
"[ 0.0 -17.9824084949113833266 -17.9824084949113833266 -17.9824084949113833266 -17.9824084949113833266 0.0 0.0 -1.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 0.0 0.0 0.0 230.331330460786683494]\n",
"[ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 0.0 0.0 -15178.7848035610576996]\n",
"[ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 0.0 -15178.7848035610576996]\n",
"[ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 -15178.7848035610576996]\n",
"[ 0.0 0.0 0.5 0.5 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0]\n",
"s: [ 9.60428974550814917462e-11]\n",
"[ 9.65095331349219506067e-14]\n",
"[-9.59707629778136707795e-14]\n",
"[-9.59707613220973487882e-14]\n",
"[ 1.65575267544810455793e-21]\n",
"[-9.60429007690683016301e-11]\n",
"[ 1.65699340494194613575e-18]\n",
"[ 2.63588235215603188557e-12]\n",
"[-2.20976777593022918838e-11]\n",
"[ 2.26120750722966691082e-9]\n",
"[ 2.26120750722966691082e-9]\n",
"[ 2.26120750722966691082e-9]\n",
"[-9.59707613220789701114e-14]\n",
"x: [ 55.5486259307790090947]\n",
"[ 0.0000986291985977885129292]\n",
"[0.00000137327503535355480046]\n",
"[0.00000137327504331676773586]\n",
"[ 7.96321293540197666117e-15]\n",
"[ 0.00137426935481090575158]\n",
"[ -1.00066911421302193368e-7]\n",
"[ 0.998175354196121218743]\n",
"[ 1.0003162582634353145]\n",
"[ 0.957389711338248159125]\n",
"[ 0.957389711338248159125]\n",
"[ 0.957389711338248159125]\n",
"[0.00000137327504331676773586]\n",
"error: 2.6558823940276993919e-17\n",
"Jx:\n",
"[ -1.0 0.0 0.0 0.0 0.0 -1.0 -2.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ -0.00177683262891476750299 -1000.72404975824450176 0.0 0.0 0.0 -1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[-0.0000247399342789041895858 0.0 -1000.72404975824450176 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[-0.0000247399344223637003167 0.0 0.0 -1000.72404975824450176 0.0 1.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ -1.43459510730888527093e-13 0.0 0.0 0.0 -1000.72404975824450176 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ 0.0 -0.00320610988064463132125 0.230264178699658923244 0.230264177364425536965 0.0 0.0 0.0 -3.16794085142580394737e-7 -3.16116073823879838143e-7 3.30289791502377503726e-7 3.30289791502377503726e-7 0.0 0.0]\n",
"[ 0.0 0.0 0.0 2.37757479821737046537e-12 0.000410018438599745529959 0.0 0.0 -6.54206521987377346694e-18 0.0 0.0 3.41038147302301589043e-18 3.41038147302301589043e-18 0.0]\n",
"[ 0.0 -17.9824084949422992949 -17.9824084949422992949 -17.9824084949422992949 -17.9824084949422992949 0.0 0.0 -1.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 0.0 0.0 0.0 230.331330455696802305]\n",
"[ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 0.0 0.0 -15178.7853570379458258]\n",
"[ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 0.0 -15178.7853570379458258]\n",
"[ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 -15178.7853570379458258]\n",
"[ 0.0 0.0 0.5 0.5 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0]\n",
"s: [ 3.07999084949050480692e-18]\n",
"[ 3.07212205285850202962e-21]\n",
"[-3.07767306451377882478e-21]\n",
"[-3.07767280996651033784e-21]\n",
"[ 1.27109130658176133557e-28]\n",
"[-3.07999110389371650188e-18]\n",
"[ 1.27201605847480178295e-25]\n",
"[ 5.54437879560117744967e-20]\n",
"[-7.08672775981635335053e-19]\n",
"[ 7.3274162954459851102e-17]\n",
"[ 7.3274162954459851102e-17]\n",
"[ 7.3274162954459851102e-17]\n",
"[ -3.0776730756339709888e-21]\n",
"x: [ 55.5486259307790090978]\n",
"[ 0.0000986291985977885160014]\n",
"[0.00000137327503535355172278]\n",
"[0.00000137327504331676465818]\n",
"[ 7.9632129354021037703e-15]\n",
"[ 0.00137426935481090267159]\n",
"[ -1.00066911421302193241e-7]\n",
"[ 0.998175354196121218799]\n",
"[ 1.00031625826343531379]\n",
"[ 0.957389711338248232399]\n",
"[ 0.957389711338248232399]\n",
"[ 0.957389711338248232399]\n",
"[0.00000137327504331676465818]\n",
"error: 1.32348898008484427979e-23\n"
]
}
],
"source": [
"from sympy import *\n",
"import numpy as np\n",
"init_printing(use_unicode = True)\n",
"eps = np.finfo(float).eps\n",
"mm0 = 2*1.00794+15.9994\n",
"m0_ref = 1/1000.0\n",
"a_m = 0.51031852567504976\n",
"x, n0, m1, m2, m3, m4 = symbols('x n0 m1 m2 m3 m4')\n",
"xi1, xi2 = symbols('xi1 xi2')\n",
"g0, g1, g2, g3, g4 = symbols('g0 g1 g2 g3 g4')\n",
"i = symbols('i')\n",
"# X0 = (55.5486293302,0.0000985577634614,0.00000136987783435,0.0000013698778423,7.94928842737e-15,\n",
"# 0.00137086977796, -9.99920449554e-08,\n",
"# 0.998176760953, 1.00031547577, 0.959416637324, 0.959416637324, 0.959416637324, \n",
"# 0.0000013698778423) #1/2.0*(0.0 + 10e-10*(+1)**2 + 10e-10*(-1)**2)\n",
"X0 = (55.55,\n",
" 9.99251756288e-05,\n",
" 2.21878461446e-26,\n",
" 9.99251756288e-11,\n",
" 9.99251756288e-11,\n",
" 0.0,\n",
" 0.0,\n",
" 0.99820143574,\n",
" 1.00000000002,\n",
" 0.9999882541,\n",
" 0.9999882541,\n",
" 0.9999882541,\n",
" 9.99251756288e-11)\n",
"X0 = (55.548626459,\n",
" 9.85548994232e-05,\n",
" 1.37274703767e-06,\n",
" 1.37274704564e-06,\n",
" 7.96616405906e-15,\n",
" 0.0013737409879,\n",
" -9.9992028068e-08,\n",
" 0.998176709264,\n",
" 1.00031613665,\n",
" 0.957397726506,\n",
" 0.957397726506,\n",
" 0.957397726506,\n",
" 1.37274704564e-06)\n",
"X = (n0, m1, m2, m3, m4,\n",
" xi1, xi2,\n",
" g0, g1, g2, g3, g4, i)\n",
"Q1 = 1 * g0**-1 * g1**-1 * g2**1 * g3**1 * g4**0 * \\\n",
" (1/mm0)**-1 * m1**-1 * m2**1 * m3**1 * m4**0 * \\\n",
" (1/m0_ref)**(-1-1+1+1+0)\n",
"Q2 = 1 * g0**-2 * g1**0 * g2**0 * g3**1 * g4**1 * \\\n",
" (1/mm0)**-2 * m1**0 * m2**0 * m3**1 * m4**1 * \\\n",
" (1/m0_ref)**(-2+0+0+1+1)\n",
"f_0 = (\n",
" -n0 + 0.05555*1000 - 2*xi2 - 1*xi1,\n",
" -m1*n0*mm0 + 0.0001*(0.05555*1000)*mm0 -xi1,\n",
" -m2*n0*mm0 + 0*(0.05555*1000)*mm0 +xi1,\n",
" -m3*n0*mm0 + 1.0E-10*(0.05555*1000)*mm0 +xi1 + xi2,\n",
" -m4*n0*mm0 + 1.0E-10*(0.05555*1000)*mm0 + xi2,\n",
" -10**-4.75696195131371/(997/mm0) + Q1,\n",
" -10**-14/(997/mm0)**2 + Q2,\n",
" -g0 + exp(-1.0*mm0*(m1+ m2 + m3 + m4)),\n",
" -g1 + 10**(0.1*i/m0_ref),\n",
" -g2 + 10**(-a_m*(-1.0)**2*sqrt(i/m0_ref)),\n",
" -g3 + 10**(-a_m*(-1.0)**2*sqrt(i/m0_ref)),\n",
" -g4 + 10**(-a_m*(-1.0)**2*sqrt(i/m0_ref)),\n",
" -i + 1/2.0*(m2*(-1)**2 + m3*(+1)**2 + m4*(-1)**2)\n",
" )\n",
"solution = nsolve(f_0, X, X0, verbose=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<pre>\n",
"\n",
"| i | comp. | m0, mol/g |\n",
"| --- | ------- | ----------- |\n",
"|0|H2O\t\t|\t55.5084350618\n",
"|1|H2SO3\t|\t0.0\n",
"|2|HSO3(-)\t|\t0.0\n",
"|3|SO3(2-)\t|\t0.0\n",
"|4|H3O(+)\t|\t1.00300902708e-10\n",
"|5|HO(-)\t|\t1.01303910853e-10\n",
"|6|Na(+)\t|\t5.11620737613\n",
"\n",
"</pre>\n",
"$$x = [n_0 m_1 m_2 m_3 m_4 m_5 m_6 \\xi_1 \\xi_2 \\xi_3 \\gamma_0 \\gamma_1 \\gamma_3 \\gamma_4 \\gamma_5 \\gamma_6]$$"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"f(x):\n",
"Matrix([[-n0 - xi1 - xi2 - 2*xi3 + 55.3418794136, -18.01528*m1*n0 - xi1 + 2.22044483181836e-23, -18.01528*m2*n0 + xi1 - xi2 + 5.10085595728786, -18.01528*m3*n0 + xi2 + 2.22044483181836e-23, -18.01528*m4*n0 + xi1 + xi2 + xi3 + 9.99999451717388e-8, -18.01528*m5*n0 + xi3 + 1.00999943743761e-7, -18.01528*m6*n0 + 5.10085595728786, -0.771567246907483 + 18.01528*g2*g4*m2*m4/(g0*g1*m1), -3.73571767773199e-6 + 18.01528*g3*g4*m3*m4/(g0*g2*m2), -3.11199819953421e-11 + 324.5503134784*g4*g5*m4*m5/g0**2, -g0 + exp(-18.01528*m1 - 18.01528*m2 - 18.01528*m3 - 18.01528*m4 - 18.01528*m5 - 18.01528*m6), 10**(100.0*i) - g1, -g2 + 10**(-16.1376887331227*sqrt(i)), -g3 + 10**(-64.5507549324909*sqrt(i)), -g4 + 10**(-16.1376887331227*sqrt(i)), -g5 + 10**(-16.1376887331227*sqrt(i)), -g6 + 10**(-16.1376887331227*sqrt(i)), -i + 0.5*m2 + 2.0*m3 + 0.5*m4 + 0.5*m5 + 0.5*m6]])\n",
"J(x):\n",
"Matrix([[-1, 0, 0, 0, 0, 0, 0, -1, -1, -2, 0, 0, 0, 0, 0, 0, 0, 0], [-18.01528*m1, -18.01528*n0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-18.01528*m2, 0, -18.01528*n0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-18.01528*m3, 0, 0, -18.01528*n0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-18.01528*m4, 0, 0, 0, -18.01528*n0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [-18.01528*m5, 0, 0, 0, 0, -18.01528*n0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [-18.01528*m6, 0, 0, 0, 0, 0, -18.01528*n0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -18.01528*g2*g4*m2*m4/(g0*g1*m1**2), 18.01528*g2*g4*m4/(g0*g1*m1), 0, 18.01528*g2*g4*m2/(g0*g1*m1), 0, 0, 0, 0, 0, -18.01528*g2*g4*m2*m4/(g0**2*g1*m1), -18.01528*g2*g4*m2*m4/(g0*g1**2*m1), 18.01528*g4*m2*m4/(g0*g1*m1), 0, 18.01528*g2*m2*m4/(g0*g1*m1), 0, 0, 0], [0, 0, -18.01528*g3*g4*m3*m4/(g0*g2*m2**2), 18.01528*g3*g4*m4/(g0*g2*m2), 18.01528*g3*g4*m3/(g0*g2*m2), 0, 0, 0, 0, 0, -18.01528*g3*g4*m3*m4/(g0**2*g2*m2), 0, -18.01528*g3*g4*m3*m4/(g0*g2**2*m2), 18.01528*g4*m3*m4/(g0*g2*m2), 18.01528*g3*m3*m4/(g0*g2*m2), 0, 0, 0], [0, 0, 0, 0, 324.5503134784*g4*g5*m5/g0**2, 324.5503134784*g4*g5*m4/g0**2, 0, 0, 0, 0, -649.1006269568*g4*g5*m4*m5/g0**3, 0, 0, 0, 324.5503134784*g5*m4*m5/g0**2, 324.5503134784*g4*m4*m5/g0**2, 0, 0], [0, -18.01528*exp(-18.01528*m1 - 18.01528*m2 - 18.01528*m3 - 18.01528*m4 - 18.01528*m5 - 18.01528*m6), -18.01528*exp(-18.01528*m1 - 18.01528*m2 - 18.01528*m3 - 18.01528*m4 - 18.01528*m5 - 18.01528*m6), -18.01528*exp(-18.01528*m1 - 18.01528*m2 - 18.01528*m3 - 18.01528*m4 - 18.01528*m5 - 18.01528*m6), -18.01528*exp(-18.01528*m1 - 18.01528*m2 - 18.01528*m3 - 18.01528*m4 - 18.01528*m5 - 18.01528*m6), -18.01528*exp(-18.01528*m1 - 18.01528*m2 - 18.01528*m3 - 18.01528*m4 - 18.01528*m5 - 18.01528*m6), -18.01528*exp(-18.01528*m1 - 18.01528*m2 - 18.01528*m3 - 18.01528*m4 - 18.01528*m5 - 18.01528*m6), 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 100.0*10**(100.0*i)*log(10)], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -8.06884436656137*10**(-16.1376887331227*sqrt(i))*log(10)/sqrt(i)], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -32.2753774662455*10**(-64.5507549324909*sqrt(i))*log(10)/sqrt(i)], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -8.06884436656137*10**(-16.1376887331227*sqrt(i))*log(10)/sqrt(i)], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -8.06884436656137*10**(-16.1376887331227*sqrt(i))*log(10)/sqrt(i)], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -8.06884436656137*10**(-16.1376887331227*sqrt(i))*log(10)/sqrt(i)], [0, 0, 0.500000000000000, 2.00000000000000, 0.500000000000000, 0.500000000000000, 0.500000000000000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1]])\n",
"Jx:\n",
"[ -1.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 -1.0 -2.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[-0.000943434680036289850282 -995.231627290865910517 0.0 0.0 0.0 0.0 0.0 -1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ -0.0886699617083889458499 0.0 -995.231627290865910517 0.0 0.0 0.0 0.0 1.0 -1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ -0.00272028370558577731079 0.0 0.0 -995.231627290865910517 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ -0.00177684900774498078512 0.0 0.0 0.0 -995.231627290865910517 0.0 0.0 1.0 1.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[-2.97065817045393432386e-13 0.0 0.0 0.0 0.0 -995.231627290865910517 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
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"[ 0.0 0.0 0.0 0.0 6.64304343266513576554e-12 0.0397342422266449590281 0.0 0.0 0.0 0.0 -1.57898602562131521606e-15 0.0 0.0 0.0 7.08617043294323347023e-16 7.08617043294323347023e-16 0.0 0.0]\n",
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"[ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 0.0 0.0 0.0 0.0 0.0 793.795033261611324417]\n",
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"[ 0.0 0.0 0.5 2.0 0.5 0.5 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0]\n",
"s: [ -0.138981509550485999017]\n",
"[ -0.000326553664705585077349]\n",
"[ 0.000526135199693145233166]\n",
"[ -0.000186690186702075038587]\n",
"[ 0.000139864261194738067164]\n",
"[ 7.83193755688938738015e-10]\n",
"[ 0.0000128913482854910653385]\n",
"[ 0.325127655109952089017]\n",
"[ -0.186178047484465248925]\n",
"[ 7.79459210048239092049e-7]\n",
"[ -0.00247659415009687741323]\n",
"[ 2.4192325394005865462]\n",
"[ -0.858462669272593815761]\n",
"[ -0.730884317968520652099]\n",
"[ -0.858462669272593815761]\n",
"[ -0.858462669272593815761]\n",
"[ -0.858462669272593815761]\n",
"[-0.0000339345772205861405155]\n",
"x: [ 55.1047686453661112402]\n",
"[ -0.000274185082033748180144]\n",
"[ 0.00544806601111483519672]\n",
"[-0.0000356914952809160437673]\n",
"[ 0.000238494368955759862181]\n",
"[ 7.83210245347553280415e-10]\n",
"[ 0.00513818943380017095781]\n",
"[ 0.27300878534732048709]\n",
"[ -0.0358993740646782367144]\n",
"[ 6.78475621957707098379e-7]\n",
"[ 0.827428267569112086442]\n",
"[ 3.42047092822372652597]\n",
"[ 0.0661609985112081899546]\n",
"[ 0.0000191522972573026513287]\n",
"[ 0.0661609985112081899546]\n",
"[ 0.0661609985112081899546]\n",
"[ 0.0661609985112081899546]\n",
"[ 0.0053409923079786735946]\n",
"error: 0.771699286911824909663\n",
"Jx:\n",
"[ -1.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 -1.0 -2.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
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"[ 0.0 0.0 0.0 0.0 1.62518867591586510547e-9 0.000494884164244560615654 0.0 0.0 0.0 0.0 -9.36874803263175893899e-13 0.0 0.0 0.0 5.8584113967224812462e-12 5.8584113967224812462e-12 0.0 0.0]\n",
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"[ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 0.0 0.0 0.0 0.0 0.0 787.616706343424135811]\n",
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"[ 0.0 0.0 0.5 2.0 0.5 0.5 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0]\n",
"s: [ 28797.1473509295632486]\n",
"[ 26.3833978002947267589]\n",
"[ -26.3190575082311260844]\n",
"[ -2.74950166898041602687]\n",
"[ -29.1328165276562244599]\n",
"[0.0000829410925051978706471]\n",
"[ -2.6851613769168153445]\n",
"[ -26049.2901201490076413]\n",
"[ -2748.02271928047719528]\n",
"[ 0.0827442499607940097793]\n",
"[ 514.316998481669761234]\n",
"[ -27225.9243035570963828]\n",
"[ 581.443742286711409792]\n",
"[ 0.673658035020609878727]\n",
"[ 581.443742286711409792]\n",
"[ 581.443742286711409792]\n",
"[ 581.443742286711409792]\n",
"[ -34.5674795738166623992]\n",
"x: [ 55.3244734438808936746]\n",
"[-0.0000728957311403863121719]\n",
"[ 0.00524726753769388239151]\n",
"[-0.0000566685282778979775661]\n",
"[ 0.0000162286178597498489068]\n",
"[ 1.41600056292261027693e-9]\n",
"[ 0.00511770327827559808683]\n",
"[ 0.0742684737617109927557]\n",
"[ -0.056865123570907463363]\n",
"[ 0.0000013097641501009719435]\n",
"[ 0.831352194864657052271]\n",
"[ 3.21275361023394154991]\n",
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"[ 0.0000242919001856215133185]\n",
"[ 0.070597062218839960354]\n",
"[ 0.070597062218839960354]\n",
"[ 0.070597062218839960354]\n",
"[ 0.0050772633683591006698]\n",
"error: 0.771606517228533018488\n",
"Jx:\n",
"[ -1.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 -1.0 -2.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
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"s: [ 533.063927405469582299]\n",
"[ 0.985059428373232741189]\n",
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"[ -0.0493101252744615784645]\n",
"[ -981.096398216487557077]\n",
"[ 447.937888717068202466]\n",
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"[ 9.48979296492765402266]\n",
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"[ 2.48131828678937251346]\n",
"[ 2.48131828678937251346]\n",
"[ 2.48131828678937251346]\n",
"[ -0.134376172156296623685]\n",
"x: [ 57.4067544103085092305]\n",
"[ 0.0037749926609425540831]\n",
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"[ 0.00170103839913279125212]\n",
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"[ 1.86707611075823307387e-7]\n",
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"[ 0.0802897117766109467347]\n",
"[ 0.0802897117766109467347]\n",
"[ 0.0802897117766109467347]\n",
"[ 0.00455235644587356698353]\n",
"error: 0.77155291307123912266\n",
"Jx:\n",
"[ -1.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 -1.0 -2.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
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"s: [ 19492.4239801244693108]\n",
"[ 17.6052956546587139584]\n",
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"[ 456.571059944041904009]\n",
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"[ 456.571059944041904009]\n",
"[ 456.571059944041904009]\n",
"[ 456.571059944041904009]\n",
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"x: [ 59.7862006969447969882]\n",
"[ 0.00592407660316163537685]\n",
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"[ 0.00163619818038561912998]\n",
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"[ 0.13602348374243637447]\n",
"[ 0.13602348374243637447]\n",
"[ 0.13602348374243637447]\n",
"[ 0.00206901266232914452652]\n",
"error: 0.770935650794258300701\n",
"Jx:\n",
"[ -1.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 -1.0 -2.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
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"[ 0.0 0.0 0.0 0.0 -0.00000184555810281228484034 -0.031129546578615972425 0.0 0.0 0.0 0.0 -1.74029675900292366947e-8 0.0 0.0 0.0 5.81811150786711767408e-8 5.81811150786711767408e-8 0.0 0.0]\n",
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"[ 0.140011661297505107124]\n",
"[ 0.140011661297505107124]\n",
"[ 0.00201734204886709902856]\n",
"error: 0.769566630619763079635\n",
"Jx:\n",
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"x: [ 63.482294746856594963]\n",
"[ 0.0123498947015118382365]\n",
"[ -0.0128836007530311843508]\n",
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"[ 5.4847598386558495098]\n",
"[-0.000128608440005971519004]\n",
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"[ 0.139418916729179354082]\n",
"[ 0.139418916729179354082]\n",
"[ 0.139418916729179354082]\n",
"[ 0.0020252495915710281799]\n",
"error: 0.769207408930624352184\n",
"Jx:\n",
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"[ 0.0 0.0 0.5 2.0 0.5 0.5 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0]\n",
"s: [ 2311.71594790030501333]\n",
"[ 3.68331699648501687253]\n",
"[ -5.77578808562826093162]\n",
"[ 1.9309596046819954986]\n",
"[ -1.75234038367643596017]\n",
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"[ -4727.25569083763792035]\n",
"[ 2415.51061659364524716]\n",
"[ 0.01456317184382993062]\n",
"[ 36.3998553058336235773]\n",
"[ 6.69640765442647538359]\n",
"[ -1.27819005724587436327]\n",
"[ -0.0341601666541475114704]\n",
"[ -1.27819005724587436327]\n",
"[ -1.27819005724587436327]\n",
"[ -1.27819005724587436327]\n",
"[ 0.0171077365284791986548]\n",
"x: [ 64.0466785231994428666]\n",
"[ 0.0132491420151068130589]\n",
"[ -0.0142937052661240214923]\n",
"[ 0.0054410815462784701256]\n",
"[ -0.0078081735569112636494]\n",
"[ -1.13087221004196581626e-7]\n",
"[ 0.00439651829526126167945]\n",
"[ -14.7790331139283428192]\n",
"[ 6.07448411028515743147]\n",
"[-0.000125052978130036477348]\n",
"[ 0.979284932831504314404]\n",
"[ 1.17897934873503446792]\n",
"[ 0.139106858609734560536]\n",
"[ 0.00023414428842791457716]\n",
"[ 0.139106858609734560536]\n",
"[ 0.139106858609734560536]\n",
"[ 0.139106858609734560536]\n",
"[ 0.00202942628505942642176]\n",
"error: 0.769023760869078159496\n",
"Jx:\n",
"[ -1.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 -1.0 -2.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
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"[ 0.0 0.0 0.0 0.0 -7.40584308893467399937e-7 -0.0511340783336676652418 0.0 0.0 0.0 0.0 -1.1809863755680453992e-8 0.0 0.0 0.0 4.1569559367223852622e-8 4.1569559367223852622e-8 0.0 0.0]\n",
"[ 0.0 -17.6984973530568841869 -17.6984973530568841869 -17.6984973530568841869 -17.6984973530568841869 -17.6984973530568841869 -17.6984973530568841869 0.0 0.0 0.0 -1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 0.0 0.0 0.0 0.0 0.0 367.416213567581753444]\n",
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"[ 0.0 0.0 0.5 2.0 0.5 0.5 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0]\n",
"s: [ 2453.54541840466609442]\n",
"[ 3.83963869554036431881]\n",
"[ -6.02057962394448575358]\n",
"[ 2.0125403269806290924]\n",
"[ -1.82708270579808679086]\n",
"[0.0000156627286342978802543]\n",
"[ -0.168400601423492341865]\n",
"[ -5016.38497098621963654]\n",
"[ 2562.81341694506035702]\n",
"[ 0.0130678182465925505988]\n",
"[ 38.3003473808978574542]\n",
"[ 6.68371460095943698236]\n",
"[ -1.27063166099544458364]\n",
"[ -0.0337794393929693207295]\n",
"[ -1.27063166099544458364]\n",
"[ -1.27063166099544458364]\n",
"[ -1.27063166099544458364]\n",
"[ 0.0170570197425428905931]\n",
"x: [ 64.6456886351146445499]\n",
"[ 0.0141865538060102223165]\n",
"[ -0.0157635733383760932095]\n",
"[ 0.00593242439954522527511]\n",
"[ -0.00825423867063149968232]\n",
"[ -1.09263312646213700704e-7]\n",
"[ 0.00435540486717935436943]\n",
"[ -16.0037364759855253476]\n",
"[ 6.7001709796565100577]\n",
"[-0.000121862592815926967925]\n",
"[ 0.988635603578793830384]\n",
"[ 1.18061111499503433047]\n",
"[ 0.138796645801874344573]\n",
"[ 0.000225897354982365426591]\n",
"[ 0.138796645801874344573]\n",
"[ 0.138796645801874344573]\n",
"[ 0.138796645801874344573]\n",
"[ 0.00203359059652000818216]\n",
"error: 0.768840086843422883115\n",
"Jx:\n",
"[ -1.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 -1.0 -2.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
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"[ 0.148702420838254248768 0.0 0.0 0.0 -1164.61018155440819416 0.0 0.0 1.0 1.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
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"[ -0.0784638381955988819127 0.0 0.0 0.0 0.0 0.0 -1164.61018155440819416 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
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"[ 0.0 0.0 0.0 0.0 -6.98943137276417836288e-7 -0.0528012864753595810579 0.0 0.0 0.0 0.0 -1.16711222039652201153e-8 0.0 0.0 0.0 4.15661591744431020511e-8 4.15661591744431020511e-8 0.0 0.0]\n",
"[ 0.0 -17.8677426320573252615 -17.8677426320573252615 -17.8677426320573252615 -17.8677426320573252615 -17.8677426320573252615 -17.8677426320573252615 0.0 0.0 0.0 -1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 0.0 0.0 0.0 0.0 0.0 367.768686232660970986]\n",
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"[ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 0.0 0.0 -77.118849605494245964]\n",
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"[ 0.0 0.0 0.5 2.0 0.5 0.5 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0]\n",
"s: [ 2602.06737334111541836]\n",
"[ 3.99565591921118719735]\n",
"[ -6.26480009353424976184]\n",
"[ 2.09385832375696211431]\n",
"[ -1.90178317097987680147]\n",
"[0.0000144244399843235322973]\n",
"[ -0.175285850566100449666]\n",
"[ -5318.92232396220870592]\n",
"[ 2716.83160776346511657]\n",
"[ 0.0116714288140854899209]\n",
"[ 40.2474142667913164713]\n",
"[ 6.59116760605951576841]\n",
"[ -1.2463858019618049611]\n",
"[ -0.0329646457285785338113]\n",
"[ -1.2463858019618049611]\n",
"[ -1.2463858019618049611]\n",
"[ -1.2463858019618049611]\n",
"[ 0.0167893021938028838919]\n",
"x: [ 64.9633238125244486781]\n",
"[ 0.0146743047727108066911]\n",
"[ -0.0165283194435438483074]\n",
"[ 0.00618802233945696381445]\n",
"[ -0.00848638993662025417469]\n",
"[ -1.07502516749689832016e-7]\n",
"[ 0.00433400766862392218563]\n",
"[ -16.6530189862348184026]\n",
"[ 7.03181546302607367056]\n",
"[-0.000120437857853270047769]\n",
"[ 0.993548618015658004758]\n",
"[ 1.18141570088444589245]\n",
"[ 0.138644499097533303928]\n",
"[ 0.000221873350376826054788]\n",
"[ 0.138644499097533303928]\n",
"[ 0.138644499097533303928]\n",
"[ 0.138644499097533303928]\n",
"[ 0.00203564007188546263576]\n",
"error: 0.768747250293392950894\n",
"Jx:\n",
"[ -1.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 -1.0 -2.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ -0.264361709285721550759 -1170.33246821329549048 0.0 0.0 0.0 0.0 0.0 -1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ 0.297762302704886629889 0.0 -1170.33246821329549048 0.0 0.0 0.0 0.0 1.0 -1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ -0.111478955091572254944 0.0 0.0 -1170.33246821329549048 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ 0.152884690897396137944 0.0 0.0 0.0 -1170.33246821329549048 0.0 0.0 1.0 1.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[0.00000193668793995035230426 0.0 0.0 0.0 0.0 -1170.33246821329549048 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ -0.0780783616724071755872 0.0 0.0 0.0 0.0 0.0 -1170.33246821329549048 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
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"[ 0.0 0.0 0.000773347159093244514783 0.00206562423098362308277 -0.00150619155868541385216 0.0 0.0 0.0 0.0 0.0 -0.0000128651267330823552024 0.0 -0.0000921935523547770138726 0.0576100233062750136887 0.0000921935523547770138726 0.0 0.0 0.0]\n",
"[ 0.0 0.0 0.0 0.0 -6.7940338059454906259e-7 -0.0536329956386811463415 0.0 0.0 0.0 0.0 -1.16062403136320327735e-8 0.0 0.0 0.0 4.1586085632776049161e-8 4.1586085632776049161e-8 0.0 0.0]\n",
"[ 0.0 -17.956464527791374748 -17.956464527791374748 -17.956464527791374748 -17.956464527791374748 -17.956464527791374748 -17.956464527791374748 0.0 0.0 0.0 -1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 0.0 0.0 0.0 0.0 0.0 367.942280595179466477]\n",
"[ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 0.0 0.0 0.0 0.0 -77.0149773504126819349]\n",
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"[ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 -77.0149773504126819349]\n",
"[ 0.0 0.0 0.5 2.0 0.5 0.5 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0]\n",
"s: [ 2679.9689239155798611]\n",
"[ 4.07452357666437036685]\n",
"[ -6.38823094609468675945]\n",
"[ 2.13493854729681812307]\n",
"[ -1.93957118673605102324]\n",
"[0.0000138425964544424772875]\n",
"[ -0.178768822133498268999]\n",
"[ -5477.54919616754178665]\n",
"[ 2797.55826285245640161]\n",
"[ 0.0110046997527619712401]\n",
"[ 41.2508913034549494213]\n",
"[ 6.52384139735781906989]\n",
"[ -1.22995599077336504641]\n",
"[ -0.0324487762640437492498]\n",
"[ -1.22995599077336504641]\n",
"[ -1.22995599077336504641]\n",
"[ -1.22995599077336504641]\n",
"[ 0.0165985384097454415356]\n",
"x: [ 65.2904684565571122353]\n",
"[ 0.0151716831390028440894]\n",
"[ -0.0173081327914557973747]\n",
"[ 0.00644863495509378243299]\n",
"[ -0.00872315399750111977811]\n",
"[ -1.058127466746846468e-7]\n",
"[ 0.00431218530264082913522]\n",
"[ -17.3216651283451140308]\n",
"[ 7.3733142744094301649]\n",
"[-0.000119094510715481721201]\n",
"[ 0.998584127207974282764]\n",
"[ 1.1822120682425217981]\n",
"[ 0.13849435798537835214]\n",
"[ 0.000217912318118031651803]\n",
"[ 0.13849435798537835214]\n",
"[ 0.13849435798537835214]\n",
"[ 0.13849435798537835214]\n",
"[ 0.00203766626065618351486]\n",
"error: 0.768654416990551130288\n"
]
},
{
"ename": "ValueError",
"evalue": "Could not find root within given tolerance. (0.59083 > 2.1684e-19)\nTry another starting point or tweak arguments.",
"output_type": "error",
"traceback": [
"\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[1;31mValueError\u001b[0m Traceback (most recent call last)",
"\u001b[1;32m<ipython-input-19-782c9b032992>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m 109\u001b[0m \u001b[1;33m-\u001b[0m\u001b[0mi\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m/\u001b[0m\u001b[1;36m2.0\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mm2\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;36m2\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mm3\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m2.0\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;36m2\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mm4\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1.0\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;36m2\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mm5\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1.0\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;36m2\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mm6\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1.0\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 110\u001b[0m )\n\u001b[1;32m--> 111\u001b[1;33m \u001b[0msolution\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnsolve\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mf_0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mX\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mX0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mverbose\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mTrue\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
"\u001b[1;32mc:\\users\\public\\apps\\anaconda\\lib\\site-packages\\sympy\\solvers\\solvers.pyc\u001b[0m in \u001b[0;36mnsolve\u001b[1;34m(*args, **kwargs)\u001b[0m\n\u001b[0;32m 2770\u001b[0m \u001b[0mJ\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mlambdify\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfargs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mJ\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmodules\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 2771\u001b[0m \u001b[1;31m# solve the system numerically\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 2772\u001b[1;33m \u001b[0mx\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfindroot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mf\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mx0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mJ\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mJ\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 2773\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 2774\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
"\u001b[1;32mc:\\users\\public\\apps\\anaconda\\lib\\site-packages\\mpmath\\calculus\\optimization.pyc\u001b[0m in \u001b[0;36mfindroot\u001b[1;34m(ctx, f, x0, solver, tol, verbose, verify, **kwargs)\u001b[0m\n\u001b[0;32m 973\u001b[0m \u001b[1;34m'(%g > %g)\\n'\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 974\u001b[0m \u001b[1;34m'Try another starting point or tweak arguments.'\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 975\u001b[1;33m % (norm(f(*xl))**2, tol))\n\u001b[0m\u001b[0;32m 976\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 977\u001b[0m \u001b[1;32mfinally\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
"\u001b[1;31mValueError\u001b[0m: Could not find root within given tolerance. (0.59083 > 2.1684e-19)\nTry another starting point or tweak arguments."
]
}
],
"source": [
"from sympy import *\n",
"import numpy as np\n",
"from IPython.display import display\n",
"init_printing(use_latex='mathjax')\n",
"eps = np.finfo(float).eps\n",
"mm0 = 2*1.00794+15.9994\n",
"m0_ref = 1/1000.0\n",
"a_m = 0.51031852567504976\n",
"x, n0, m1, m2, m3, m4, m5, m6 = symbols('x n0 m1 m2 m3 m4 m5 m6')\n",
"xi1, xi2, xi3 = symbols('xi1 xi2 xi3')\n",
"g0, g1, g2, g3, g4, g5, g6 = symbols('g0 g1 g2 g3 g4 g5 g6')\n",
"i = symbols('i')\n",
"# X0 = ( 55.3418794136,\n",
"# 1.1193032265e-05,\n",
"# 0.00509379348046,\n",
"# 1.12236685315e-05,\n",
"# 3.06355951606e-08,\n",
"# 3.31668819804e-13,\n",
"# 0.00511621018126,\n",
"# -0.0111594470496,\n",
"# 0.0111899913906,\n",
"# -1.00669325488e-07,\n",
"# 0.306009594112,\n",
"# 0.92620164755,\n",
"# 0.735905750795,\n",
"# 0.92620164755,\n",
"# 0.92620164755,\n",
"# 1.00118133956,\n",
"# 0.92620164755,\n",
"# 0.00512746448589)\n",
"X0 = (5.53419097566066e+01,\n",
" 2.22712743154495e-26,\n",
" 5.11620737612838e-03,\n",
" 2.22712743154495e-26,\n",
" 1.00300902708124e-10,\n",
" 1.01303910852863e-10,\n",
" 5.11620737612838e-03,\n",
" 0.00000000000000e+00,\n",
" 0.00000000000000e+00,\n",
" 0.00000000000000e+00,\n",
" 8.31653143040483e-01,\n",
" 1.00117874448073e+00,\n",
" 9.26272473142106e-01,\n",
" 7.36130872136064e-01,\n",
" 9.26272473142106e-01,\n",
" 9.26272473142106e-01,\n",
" 9.26272473142106e-01,\n",
" 5.11620747693079e-03)\n",
"X0 = (5.53418170913875e+01,\n",
" 7.80299247170542e-05,\n",
" 4.96006292351771e-03,\n",
" 7.81230945389717e-05,\n",
" 9.31572412327876e-08,\n",
" -1.15776748879335e-11,\n",
" 5.11621594277374e-03,\n",
" -7.77958281342660e-02,\n",
" 7.78887184392494e-02,\n",
" -1.12542941204768e-07,\n",
" 8.31651493810607e-01,\n",
" 3.30656950264337e+00,\n",
" 6.86753527413611e-02,\n",
" 2.36124465951004e-05,\n",
" 6.86753527413611e-02,\n",
" 6.86753527413611e-02,\n",
" 6.86753527413611e-02,\n",
" 5.19443219505545e-03)\n",
"X0 = (5.52437501549166e+01,\n",
" 5.23685826718369e-05,\n",
" 4.92193081142169e-03,\n",
" 1.50998691421159e-04,\n",
" 9.86301077610218e-05,\n",
" 1.64896586145424e-14,\n",
" 5.12529808551468e-03,\n",
" -5.21188697626316e-02,\n",
" 1.50278673419787e-01,\n",
" -1.00983588090532e-07,\n",
" 8.29904861719209e-01,\n",
" 1.00123838882314e+00,\n",
" 9.24623667783802e-01,\n",
" 7.30903470265778e-01,\n",
" 9.24623667783802e-01,\n",
" 9.24623667783802e-01,\n",
" 9.24623667783802e-01,\n",
" 5.37492688519926e-03)\n",
"X = (n0, m1, m2, m3, m4, m5, m6,\n",
" xi1, xi2, xi3,\n",
" g0, g1, g2, g3, g4, g5, g6, i)\n",
"Q1 = 1 * g0**-1 * g1**-1 * g2**1 * g3**0 * g4**1 * g5**0 * g6**0 *\\\n",
" (1/mm0)**-1 * m1**-1 * m2**1 * m3**0 * m4**1 * m5**0 * m6**0 *\\\n",
" (1/m0_ref)**(-1-1+1+0+1+0+0)\n",
"Q2 = 1 * g0**-1 * g1**0 * g2**-1 * g3**1 * g4**1 * g5**0 * g6**0 *\\\n",
" (1/mm0)**-1 * m1**0 * m2**-1 * m3**1 * m4**1 * m5**0 * m6**0 *\\\n",
" (1/m0_ref)**(-1+0-1+1+1+0+0)\n",
"Q3 = 1 * g0**-2 * g1**0 * g2**0 * g3**0 * g4**1 * g5**1 * g6**0 *\\\n",
" (1/mm0)**-2 * m1**0 * m2**0 * m3**0 * m4**1 * m5**1 * m6**0 *\\\n",
" (1/m0_ref)**(-2+0+0+0+1+1+0)\n",
"f_0 = (\n",
" -n0 + 55.3418794136 - 1*xi1 - 1*xi2 -2*xi3,\n",
" -m1*n0*mm0 + 2.22712743154495e-23/1000.0*(55.3418794136)*mm0 - xi1,\n",
" -m2*n0*mm0 + 5.11620737612839e+00/1000.0*(55.3418794136)*mm0 + xi1 - xi2,\n",
" -m3*n0*mm0 + 2.22712743154495e-23/1000.0*(55.3418794136)*mm0 + xi2,\n",
" -m4*n0*mm0 + 1.00300902708124e-07/1000.0*(55.3418794136)*mm0 + xi1 + xi2 + xi3,\n",
" -m5*n0*mm0 + 1.01303910852863e-07/1000.0*(55.3418794136)*mm0 + xi3,\n",
" -m6*n0*mm0 + 5.11620737612839e+00/1000.0*(55.3418794136)*mm0,\n",
" -10**-1.8569852/(1/(mm0 * m0_ref))**-1 + Q1,\n",
" -10**-7.171984936/(1/(mm0 * m0_ref))**-1 + Q2,\n",
" -10**-13.99567863/(1/(mm0 * m0_ref))**-2 + Q3,\n",
" -g0 + exp(-1.0*mm0*(m1+ m2 + m3 + m4 + m5 + m6)),\n",
" -g1 + 10**(0.1*i/m0_ref),\n",
" -g2 + 10**(-a_m*(-1.0)**2*(sqrt(i/m0_ref))),\n",
" -g3 + 10**(-a_m*(-2.0)**2*(sqrt(i/m0_ref))),\n",
" -g4 + 10**(-a_m*(+1.0)**2*(sqrt(i/m0_ref))),\n",
" -g5 + 10**(-a_m*(-1.0)**2*(sqrt(i/m0_ref))),\n",
" -g6 + 10**(-a_m*(+1.0)**2*(sqrt(i/m0_ref))),\n",
" -i + 1/2.0*(m2*(-1)**2 + m3*(-2.0)**2 + m4*(+1.0)**2 + m5*(-1.0)**2 + m6*(+1.0)**2)\n",
" )\n",
"solution = nsolve(f_0, X, X0, verbose=True)"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"f(x):\n",
"Matrix([[-n0 - xi1 - xi2 - 2*xi3 + 55.3418794136, -18.01528*m1*n0 - xi1 + 2.22044483181836e-23, -18.01528*m2*n0 + xi1 - xi2 + 5.10085595728786, -18.01528*m3*n0 + xi2 + 2.22044483181836e-23, -3.73571767773199e-6 + 18.01528*g3*g4*m3*m4/(g0*g2*m2), -3.11199819953421e-11 + 324.5503134784*g4*g5*m4*m5/g0**2, -18.01528*m6*n0 + 5.10085595728786, -18.01528*m4*n0 + xi1 + xi2 + xi3 + 9.99999451717388e-8, -i + 0.5*m2 + 2.0*m3 + 0.5*m4 + 0.5*m5 + 0.5*m6, -18.01528*m5*n0 + xi3 + 1.00999943743761e-7, -g0 + exp(-18.01528*m1 - 18.01528*m2 - 18.01528*m3 - 18.01528*m4 - 18.01528*m5 - 18.01528*m6), 10**(100.0*i) - g1, -g2 + 10**(-16.1376887331227*sqrt(i)), -g3 + 10**(-64.5507549324909*sqrt(i)), -g4 + 10**(-16.1376887331227*sqrt(i)), -g5 + 10**(-16.1376887331227*sqrt(i)), -g6 + 10**(-16.1376887331227*sqrt(i)), -0.771567246907483 + 18.01528*g2*g4*m2*m4/(g0*g1*m1)]])\n",
"J(x):\n",
"Matrix([[-1, 0, 0, 0, 0, 0, 0, -1, -1, -2, 0, 0, 0, 0, 0, 0, 0, 0], [-18.01528*m1, -18.01528*n0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-18.01528*m2, 0, -18.01528*n0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-18.01528*m3, 0, 0, -18.01528*n0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -18.01528*g3*g4*m3*m4/(g0*g2*m2**2), 18.01528*g3*g4*m4/(g0*g2*m2), 18.01528*g3*g4*m3/(g0*g2*m2), 0, 0, 0, 0, 0, -18.01528*g3*g4*m3*m4/(g0**2*g2*m2), 0, -18.01528*g3*g4*m3*m4/(g0*g2**2*m2), 18.01528*g4*m3*m4/(g0*g2*m2), 18.01528*g3*m3*m4/(g0*g2*m2), 0, 0, 0], [0, 0, 0, 0, 324.5503134784*g4*g5*m5/g0**2, 324.5503134784*g4*g5*m4/g0**2, 0, 0, 0, 0, -649.1006269568*g4*g5*m4*m5/g0**3, 0, 0, 0, 324.5503134784*g5*m4*m5/g0**2, 324.5503134784*g4*m4*m5/g0**2, 0, 0], [-18.01528*m6, 0, 0, 0, 0, 0, -18.01528*n0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-18.01528*m4, 0, 0, 0, -18.01528*n0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0.500000000000000, 2.00000000000000, 0.500000000000000, 0.500000000000000, 0.500000000000000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1], [-18.01528*m5, 0, 0, 0, 0, -18.01528*n0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, -18.01528*exp(-18.01528*m1 - 18.01528*m2 - 18.01528*m3 - 18.01528*m4 - 18.01528*m5 - 18.01528*m6), -18.01528*exp(-18.01528*m1 - 18.01528*m2 - 18.01528*m3 - 18.01528*m4 - 18.01528*m5 - 18.01528*m6), -18.01528*exp(-18.01528*m1 - 18.01528*m2 - 18.01528*m3 - 18.01528*m4 - 18.01528*m5 - 18.01528*m6), -18.01528*exp(-18.01528*m1 - 18.01528*m2 - 18.01528*m3 - 18.01528*m4 - 18.01528*m5 - 18.01528*m6), -18.01528*exp(-18.01528*m1 - 18.01528*m2 - 18.01528*m3 - 18.01528*m4 - 18.01528*m5 - 18.01528*m6), -18.01528*exp(-18.01528*m1 - 18.01528*m2 - 18.01528*m3 - 18.01528*m4 - 18.01528*m5 - 18.01528*m6), 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 100.0*10**(100.0*i)*log(10)], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -8.06884436656137*10**(-16.1376887331227*sqrt(i))*log(10)/sqrt(i)], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -32.2753774662455*10**(-64.5507549324909*sqrt(i))*log(10)/sqrt(i)], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -8.06884436656137*10**(-16.1376887331227*sqrt(i))*log(10)/sqrt(i)], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -8.06884436656137*10**(-16.1376887331227*sqrt(i))*log(10)/sqrt(i)], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -8.06884436656137*10**(-16.1376887331227*sqrt(i))*log(10)/sqrt(i)], [0, -18.01528*g2*g4*m2*m4/(g0*g1*m1**2), 18.01528*g2*g4*m4/(g0*g1*m1), 0, 18.01528*g2*g4*m2/(g0*g1*m1), 0, 0, 0, 0, 0, -18.01528*g2*g4*m2*m4/(g0**2*g1*m1), -18.01528*g2*g4*m2*m4/(g0*g1**2*m1), 18.01528*g4*m2*m4/(g0*g1*m1), 0, 18.01528*g2*m2*m4/(g0*g1*m1), 0, 0, 0]])\n",
"Jx:\n",
"[ -1.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 -1.0 -2.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[-0.000943402938507507121573 -995.231702898908208062 0.0 0.0 0.0 0.0 0.0 -1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ -0.088670094281669418191 0.0 -995.231702898908208062 0.0 0.0 0.0 0.0 1.0 -1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ -0.00272017585926201872186 0.0 0.0 -995.231702898908208062 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ 0.0 0.0 -0.00975320556792320889789 0.317927112804713410197 0.486735055346903275072 0.0 0.0 0.0 0.0 0.0 -0.0000578435826268138672367 0.0 -0.000051918064700514930903 0.0000656785242909755296578 0.000051918064700514930903 0.0 0.0 0.0]\n",
"[ 0.0 0.0 0.0 0.0 6.64329419285796845751e-12 0.0397325387567517355978 0.0 0.0 0.0 0.0 -1.57897785391658853356e-15 0.0 0.0 0.0 7.08613390263281562744e-16 7.08613390263281562744e-16 0.0 0.0]\n",
"[ -0.0923336730794389783379 0.0 0.0 0.0 0.0 0.0 -995.231702898908208062 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ -0.00177677290295001603383 0.0 0.0 0.0 -995.231702898908208062 0.0 0.0 1.0 1.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
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"[ -0.00247651396528507705385]\n",
"[ 2.41922474746046656832]\n",
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"[ -0.730884522437086848326]\n",
"[ -0.858462567321047386274]\n",
"[ -0.858462567321047386274]\n",
"[ -0.858462567321047386274]\n",
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"x: [ 55.104777332464056564]\n",
"[ -0.000274176645033262926155]\n",
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"[-0.0000356918238293559373779]\n",
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"[ 0.0661611651892235818246]\n",
"[ 0.0661611651892235818246]\n",
"[ 0.0661611651892235818246]\n",
"[ 0.00534098240600123840115]\n",
"error: 0.771699286847232011704\n",
"Jx:\n",
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"s: [ 28788.2442624472168006]\n",
"[ 26.3751178711073898372]\n",
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"[ 581.267729967245571731]\n",
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"[ 581.267729967245571731]\n",
"[ 581.267729967245571731]\n",
"[ 581.267729967245571731]\n",
"[ -34.556896420403602314]\n",
"x: [ 55.3244142058042605496]\n",
"[-0.0000729504649863620637495]\n",
"[ 0.0052473225160967011483]\n",
"[-0.0000566632406841848480967]\n",
"[ 0.0000162886391908178194653]\n",
"[ 1.41589194309688112651e-9]\n",
"[ 0.00511770881042615424122]\n",
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"[ 0.0705958860294277869312]\n",
"[ 0.0705958860294277869312]\n",
"[ 0.0705958860294277869312]\n",
"[ 0.00507733420943443845674]\n",
"error: 0.771606631356869839574\n",
"Jx:\n",
"[ -1.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 -1.0 -2.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
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"s: [ 533.506119629195980509]\n",
"[ 0.982842338578278446088]\n",
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"[ 445.284081783525781457]\n",
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"[ 9.49767331245989832187]\n",
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"[ 0.00360710298822805624548]\n",
"[ 2.53936971221704450868]\n",
"[ 2.53936971221704450868]\n",
"[ 2.53936971221704450868]\n",
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"x: [ 57.4084224856058073485]\n",
"[ 0.00376627742008503811628]\n",
"[-0.000531992708413969319956]\n",
"[ 0.00169064622448941381922]\n",
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"[ 1.86151958756038899979e-7]\n",
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"[ -3.74944517771447797467]\n",
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"[ 0.000038380822515652139348]\n",
"[ 0.0805152989677756170432]\n",
"[ 0.0805152989677756170432]\n",
"[ 0.0805152989677756170432]\n",
"[ 0.00454013211653027352545]\n",
"error: 0.77155324030260260465\n",
"Jx:\n",
"[ -1.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 -1.0 -2.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
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"[ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 0.0 0.0 0.0 0.0 0.0 654.981299214857739423]\n",
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"s: [ 19736.7003784802957908]\n",
"[ 17.5853728892055165952]\n",
"[ -18.5012955135822045717]\n",
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"[ -18.3662813911514648554]\n",
"[-0.00367402448353728831615]\n",
"[ -1.69315710217103435392]\n",
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"[ -3.73358641954775209322]\n",
"[ 340.720712121999145011]\n",
"[ -13647.6012340791579121]\n",
"[ 469.847314039686849402]\n",
"[ 1.02783055772611748748]\n",
"[ 469.847314039686849402]\n",
"[ 469.847314039686849402]\n",
"[ 469.847314039686849402]\n",
"[ -20.8366729712828132864]\n",
"x: [ 59.8176876685257653308]\n",
"[ 0.00591292938409938340379]\n",
"[ -0.00279045163341179702647]\n",
"[ 0.00159576896889928364639]\n",
"[ -0.00431742275348317161478]\n",
"[ -2.62337358082008990176e-7]\n",
"[ 0.00471824671958687002809]\n",
"[ -6.13306221473662068567]\n",
"[ 1.6577945070363078802]\n",
"[-0.000270273612727559652459]\n",
"[ 0.910043306387755933268]\n",
"[ 1.14868072569964331798]\n",
"[ 0.137869707419885828152]\n",
"[ 0.000163848419894328590456]\n",
"[ 0.137869707419885828152]\n",
"[ 0.137869707419885828152]\n",
"[ 0.137869707419885828152]\n",
"[ 0.00199659293546547698171]\n",
"error: 0.770899804628067265331\n",
"Jx:\n",
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"[ 1.83030876704076987848]\n",
"[ 1.83030876704076987848]\n",
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"[ 0.141444529230512331821]\n",
"[ 0.141444529230512331821]\n",
"[ 0.00195264988408086540028]\n",
"error: 0.769536533324800954814\n",
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"s: [ 1883.8704381735523886]\n",
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"[ 0.140941993643369834845]\n",
"[ 0.140941993643369834845]\n",
"[ 0.00195913658743769232029]\n",
"error: 0.769176247524049396868\n",
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"[ 0.140402356098859161556]\n",
"[ 0.140402356098859161556]\n",
"[ 0.00196610945578835942996]\n",
"error: 0.768815654506030511087\n",
"Jx:\n",
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"[ 0.0141869416340810057723]\n",
"x: [ 64.8525714090783026677]\n",
"[ 0.0144294477590652489846]\n",
"[ -0.0161161932002191782762]\n",
"[ 0.0060286282124727507576]\n",
"[ -0.00840093791963143248001]\n",
"[ -1.1837218772876818457e-7]\n",
"[ 0.00434188277131882147004]\n",
"[ -16.3540738480838616313]\n",
"[ 6.84364533119103202782]\n",
"[-0.000131739292737829145563]\n",
"[ 0.99179737815016555395]\n",
"[ 1.14015285092266449244]\n",
"[ 0.140135697602749430884]\n",
"[ 0.000223297283533315959591]\n",
"[ 0.140135697602749430884]\n",
"[ 0.140135697602749430884]\n",
"[ 0.140135697602749430884]\n",
"[ 0.00196957306458574248802]\n",
"error: 0.768631672634406894602\n",
"Jx:\n",
"[ -1.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 -1.0 -2.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ -0.259950541624933007766 -1168.33723265454020511 0.0 0.0 0.0 0.0 0.0 -1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ 0.290337733036044568111 0.0 -1168.33723265454020511 0.0 0.0 0.0 0.0 1.0 -1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ -0.108607425263596101045 0.0 0.0 -1168.33723265454020511 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ 0.0 0.0 0.000790902316044006621543 0.00211430097837097830836 -0.00151725136524104068061 0.0 0.0 0.0 0.0 0.0 -0.0000128517525945063836149 0.0 -0.0000909570847821999838758 0.0570823537401621172456 0.0000909570847821999838758 0.0 0.0 0.0]\n",
"[ 0.0 0.0 0.0 0.0 -7.66978791509247492261e-7 -0.0544328979363552994704 0.0 0.0 0.0 0.0 -1.29932612347913621564e-8 0.0 0.0 0.0 4.5979299517303797339e-8 4.5979299517303797339e-8 0.0 0.0]\n",
"[ -0.0782202338524845407725 0.0 0.0 0.0 0.0 0.0 -1168.33723265454020511 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ 0.151345248884777758191 0.0 0.0 0.0 -1168.33723265454020511 0.0 0.0 1.0 1.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ 0.0 0.0 0.5 2.0 0.5 0.5 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0]\n",
"[0.00000213250810614632297427 0.0 0.0 0.0 0.0 -1168.33723265454020511 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ 0.0 -17.9237598817866002626 -17.9237598817866002626 -17.9237598817866002626 -17.9237598817866002626 -17.9237598817866002626 -17.9237598817866002626 0.0 0.0 0.0 -1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 0.0 0.0 0.0 0.0 0.0 362.387321612477273439]\n",
"[ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 0.0 0.0 0.0 0.0 -80.4734117902245190365]\n",
"[ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 0.0 0.0 0.0 -2.28637103947915792116]\n",
"[ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 0.0 0.0 -80.4734117902245190365]\n",
"[ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 0.0 -80.4734117902245190365]\n",
"[ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 -80.4734117902245190365]\n",
"[ 0.0 -0.203443286402409883638 -0.182150600740887089939 0.0 -0.349434110948044358265 0.0 0.0 0.0 0.0 0.0 -0.00295985282654342225556 -0.00257471993399877943948 0.0209480833455994986121 0.0 0.0209480833455994986121 0.0 0.0 0.0]\n",
"s: [ 2482.0828552991517498]\n",
"[ 3.78544228912015733957]\n",
"[ -5.93434118596545048375]\n",
"[ 1.9827473583156586343]\n",
"[ -1.8026803514822670577]\n",
"[0.0000145792896584279886178]\n",
"[ -0.166151538529634510047]\n",
"[ -5068.39633825256292032]\n",
"[ 2586.29001534384496201]\n",
"[ 0.0117338047831042536702]\n",
"[ 38.2697914923960469239]\n",
"[ 5.47646457163709941496]\n",
"[ -1.06773521449649189264]\n",
"[ -0.0306738654903803334845]\n",
"[ -1.06773521449649189264]\n",
"[ -1.06773521449649189264]\n",
"[ -1.06773521449649189264]\n",
"[ 0.0139154682874704568389]\n",
"x: [ 65.4585486686728221379]\n",
"[ 0.0153536280054324748976]\n",
"[ -0.0175650069663240245857]\n",
"[ 0.00651269739174903460386]\n",
"[ -0.0088410454273175328359]\n",
"[ -1.14812790839503538912e-7]\n",
"[ 0.00430131843085748491973]\n",
"[ -17.5914752978525537505]\n",
"[ 7.47506379196833792675]\n",
"[-0.000128874594304454083632]\n",
"[ 1.00114058896373880759]\n",
"[ 1.14148987840597433116]\n",
"[ 0.139875020060147748293]\n",
"[ 0.000215808546841328573487]\n",
"[ 0.139875020060147748293]\n",
"[ 0.139875020060147748293]\n",
"[ 0.139875020060147748293]\n",
"[ 0.00197297039571061320502]\n",
"error: 0.768447673997778632794\n",
"Jx:\n",
"[ -1.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 -1.0 -2.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ -0.276599907533707565991 -1179.25408265976816021 0.0 0.0 0.0 0.0 0.0 -1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ 0.316438518700277884641 0.0 -1179.25408265976816021 0.0 0.0 0.0 0.0 1.0 -1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ -0.117328067067628552198 0.0 0.0 -1179.25408265976816021 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ 0.0 0.0 0.000724740375119395030169 0.00195465395856964622063 -0.00143988285575531749837 0.0 0.0 0.0 0.0 0.0 -0.0000127155665029275344763 0.0 -0.0000910103157252409681452 0.0589877923004974294998 0.0000910103157252409681452 0.0 0.0 0.0]\n",
"[ 0.0 0.0 0.0 0.0 -7.27381903321063442235e-7 -0.0560113242021947799581 0.0 0.0 0.0 0.0 -1.28469797771891857639e-8 0.0 0.0 0.0 4.59754461340194420389e-8 4.59754461340194420389e-8 0.0 0.0]\n",
"[ -0.0774894559010582336191 0.0 0.0 0.0 0.0 0.0 -1179.25408265976816021 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ 0.159273908865845008486 0.0 0.0 0.0 -1179.25408265976816021 0.0 0.0 1.0 1.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ 0.0 0.0 0.5 2.0 0.5 0.5 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0]\n",
"[0.0000020683845745550913864 0.0 0.0 0.0 0.0 -1179.25408265976816021 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ 0.0 -18.09285939973476947 -18.09285939973476947 -18.09285939973476947 -18.09285939973476947 -18.09285939973476947 -18.09285939973476947 0.0 0.0 0.0 -1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n",
"[ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 0.0 0.0 0.0 0.0 0.0 362.670915221464802322]\n",
"[ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 0.0 0.0 0.0 0.0 -80.2898718470193960906]\n",
"[ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 0.0 0.0 0.0 -2.27144811434688054895]\n",
"[ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 0.0 0.0 -80.2898718470193960906]\n",
"[ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 0.0 -80.2898718470193960906]\n",
"[ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 -80.2898718470193960906]\n",
"[ 0.0 -0.203181483138747821436 -0.177601575432636663951 0.0 -0.352851134557612642559 0.0 0.0 0.0 0.0 0.0 -0.003116018813035434028 -0.00273289581337391341543 0.0223025734570971655151 0.0 0.0223025734570971655151 0.0 0.0 0.0]\n",
"s: [ 2620.13520334956923587]\n",
"[ 3.92115213375739595809]\n",
"[ -6.1467165209282869989]\n",
"[ 2.05341798916986167717]\n",
"[ -1.86772065626688752014]\n",
"[0.0000134882868982774842421]\n",
"[ -0.172146398001029363799]\n",
"[ -5349.27817064696647689]\n",
"[ 2729.12200719680315175]\n",
"[ 0.0104800502970446314166]\n",
"[ 40.0245700626541395354]\n",
"[ 5.34809985074387983087]\n",
"[ -1.03592523540538490061]\n",
"[ -0.0296384407314073622967]\n",
"[ -1.03592523540538490061]\n",
"[ -1.03592523540538490061]\n",
"[ -1.03592523540538490061]\n",
"[ 0.0135509348850705516666]\n",
"x: [ 66.0982301148030880646]\n",
"[ 0.0163109405380880891452]\n",
"[ -0.0190656701794412821538]\n",
"[ 0.00701402014301120786489]\n",
"[ -0.00929703191566394092187]\n",
"[ -1.11519752045978762485e-7]\n",
"[ 0.00425929050165801486021]\n",
"[ -18.8974514137331608005]\n",
"[ 8.14135334450661994622]\n",
"[-0.000126315988274902171665]\n",
"[ 1.01091221251419147838]\n",
"[ 1.1427955668460973487]\n",
"[ 0.139622108625722605495]\n",
"[ 0.000208572599397137322926]\n",
"[ 0.139622108625722605495]\n",
"[ 0.139622108625722605495]\n",
"[ 0.139622108625722605495]\n",
"[ 0.00197627872942278863267]\n",
"error: 0.768263667086415563701\n"
]
},
{
"ename": "ValueError",
"evalue": "Could not find root within given tolerance. (0.590229 > 2.1684e-19)\nTry another starting point or tweak arguments.",
"output_type": "error",
"traceback": [
"\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[1;31mValueError\u001b[0m Traceback (most recent call last)",
"\u001b[1;32m<ipython-input-20-718fa527724d>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m 129\u001b[0m \u001b[1;33m-\u001b[0m\u001b[1;36m10\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1.8569852\u001b[0m\u001b[1;33m/\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m/\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmm0\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mm0_ref\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mQ1\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 130\u001b[0m )\n\u001b[1;32m--> 131\u001b[1;33m \u001b[0msolution\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnsolve\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mf_0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mX\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mX0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mverbose\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mTrue\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
"\u001b[1;32mc:\\users\\public\\apps\\anaconda\\lib\\site-packages\\sympy\\solvers\\solvers.pyc\u001b[0m in \u001b[0;36mnsolve\u001b[1;34m(*args, **kwargs)\u001b[0m\n\u001b[0;32m 2770\u001b[0m \u001b[0mJ\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mlambdify\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfargs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mJ\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmodules\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 2771\u001b[0m \u001b[1;31m# solve the system numerically\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 2772\u001b[1;33m \u001b[0mx\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfindroot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mf\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mx0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mJ\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mJ\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 2773\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 2774\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
"\u001b[1;32mc:\\users\\public\\apps\\anaconda\\lib\\site-packages\\mpmath\\calculus\\optimization.pyc\u001b[0m in \u001b[0;36mfindroot\u001b[1;34m(ctx, f, x0, solver, tol, verbose, verify, **kwargs)\u001b[0m\n\u001b[0;32m 973\u001b[0m \u001b[1;34m'(%g > %g)\\n'\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 974\u001b[0m \u001b[1;34m'Try another starting point or tweak arguments.'\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 975\u001b[1;33m % (norm(f(*xl))**2, tol))\n\u001b[0m\u001b[0;32m 976\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 977\u001b[0m \u001b[1;32mfinally\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
"\u001b[1;31mValueError\u001b[0m: Could not find root within given tolerance. (0.590229 > 2.1684e-19)\nTry another starting point or tweak arguments."
]
}
],
"source": [
"from sympy import *\n",
"import numpy as np\n",
"from IPython.display import display\n",
"init_printing(use_latex='mathjax')\n",
"eps = np.finfo(float).eps\n",
"mm0 = 2*1.00794+15.9994\n",
"m0_ref = 1/1000.0\n",
"a_m = 0.51031852567504976\n",
"x, n0, m1, m2, m3, m4, m5, m6 = symbols('x n0 m1 m2 m3 m4 m5 m6')\n",
"xi1, xi2, xi3 = symbols('xi1 xi2 xi3')\n",
"g0, g1, g2, g3, g4, g5, g6 = symbols('g0 g1 g2 g3 g4 g5 g6')\n",
"i = symbols('i')\n",
"# X0 = ( 55.3418794136,\n",
"# 1.1193032265e-05,\n",
"# 0.00509379348046,\n",
"# 1.12236685315e-05,\n",
"# 3.06355951606e-08,\n",
"# 3.31668819804e-13,\n",
"# 0.00511621018126,\n",
"# -0.0111594470496,\n",
"# 0.0111899913906,\n",
"# -1.00669325488e-07,\n",
"# 0.306009594112,\n",
"# 0.92620164755,\n",
"# 0.735905750795,\n",
"# 0.92620164755,\n",
"# 0.92620164755,\n",
"# 1.00118133956,\n",
"# 0.92620164755,\n",
"# 0.00512746448589)\n",
"X0 = (5.53419097566066e+01,\n",
" 2.22712743154495e-26,\n",
" 5.11620737612838e-03,\n",
" 2.22712743154495e-26,\n",
" 1.00300902708124e-10,\n",
" 1.01303910852863e-10,\n",
" 5.11620737612838e-03,\n",
" 0.00000000000000e+00,\n",
" 0.00000000000000e+00,\n",
" 0.00000000000000e+00,\n",
" 8.31653143040483e-01,\n",
" 1.00117874448073e+00,\n",
" 9.26272473142106e-01,\n",
" 7.36130872136064e-01,\n",
" 9.26272473142106e-01,\n",
" 9.26272473142106e-01,\n",
" 9.26272473142106e-01,\n",
" 5.11620747693079e-03)\n",
"# p = [[ 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
"# [ 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
"# [ 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
"# [ 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
"# [ 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
"# [ 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
"# [ 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
"# [ 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
"# [ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n",
"# [ 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
"# [ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]\n",
"# [ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]\n",
"# [ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]\n",
"# [ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]\n",
"# [ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]\n",
"# [ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]\n",
"# [ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]\n",
"# [ 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]]\n",
"#\n",
"X0 = (5.53419076022840e+01,\n",
" 2.31834134006059e-06,\n",
" 5.11156853001899e-03,\n",
" 2.32070393053873e-06,\n",
" 2.31374172867891e-03,\n",
" -1.00590009831908e-07,\n",
" 5.11620757528959e-03,\n",
" 2.36199869292589e-09,\n",
" 5.11853064172033e-03,\n",
" 4.11222973276393e-13,\n",
" 8.31653104698448e-01,\n",
" 3.24977328473669e+00,\n",
" 2.68985722658317e+00,\n",
" 5.23500276945496e+01,\n",
" 2.68985722658317e+00,\n",
" 2.68985722658317e+00,\n",
" 2.68985722658317e+00,\n",
" -2.31138622606391e-03)\n",
"X0 = (5.52437543518007e+01,\n",
" 5.23668207492477e-05,\n",
" 4.92193817035702e-03,\n",
" 1.50992705040500e-04,\n",
" 9.86258833029526e-05,\n",
" 1.64902817266026e-14,\n",
" 5.12529769614677e-03,\n",
" -5.21171201896341e-02,\n",
" 1.50272726962743e-01,\n",
" -1.00983587469140e-07,\n",
" 8.29904936521807e-01,\n",
" 1.00123838637933e+00,\n",
" 9.24623732510271e-01,\n",
" 7.30903674927664e-01,\n",
" 9.24623732510271e-01,\n",
" 9.24623732510271e-01,\n",
" 9.24623732510271e-01,\n",
" 5.37491628499262e-03)\n",
"X = (n0, m1, m2, m3, m4, m5, m6,\n",
" xi1, xi2, xi3,\n",
" g0, g1, g2, g3, g4, g5, g6, i)\n",
"Q1 = 1 * g0**-1 * g1**-1 * g2**1 * g3**0 * g4**1 * g5**0 * g6**0 *\\\n",
" (1/mm0)**-1 * m1**-1 * m2**1 * m3**0 * m4**1 * m5**0 * m6**0 *\\\n",
" (1/m0_ref)**(-1-1+1+0+1+0+0)\n",
"Q2 = 1 * g0**-1 * g1**0 * g2**-1 * g3**1 * g4**1 * g5**0 * g6**0 *\\\n",
" (1/mm0)**-1 * m1**0 * m2**-1 * m3**1 * m4**1 * m5**0 * m6**0 *\\\n",
" (1/m0_ref)**(-1+0-1+1+1+0+0)\n",
"Q3 = 1 * g0**-2 * g1**0 * g2**0 * g3**0 * g4**1 * g5**1 * g6**0 *\\\n",
" (1/mm0)**-2 * m1**0 * m2**0 * m3**0 * m4**1 * m5**1 * m6**0 *\\\n",
" (1/m0_ref)**(-2+0+0+0+1+1+0)\n",
"# Or [1, 2, 3, 4, 9, 10, 7, 5, 18, 6, 11, 12, 13, 14, 15, 16, 17, 8]\n",
"f_0 = (\n",
" -n0 + 55.3418794136 - 1*xi1 - 1*xi2 -2*xi3,\n",
" -m1*n0*mm0 + 2.22712743154495e-23/1000.0*(55.3418794136)*mm0 - xi1,\n",
" -m2*n0*mm0 + 5.11620737612839e+00/1000.0*(55.3418794136)*mm0 + xi1 - xi2,\n",
" -m3*n0*mm0 + 2.22712743154495e-23/1000.0*(55.3418794136)*mm0 + xi2,\n",
" -10**-7.171984936/(1/(mm0 * m0_ref))**-1 + Q2,\n",
" -10**-13.99567863/(1/(mm0 * m0_ref))**-2 + Q3,\n",
" -m6*n0*mm0 + 5.11620737612839e+00/1000.0*(55.3418794136)*mm0,\n",
" -m4*n0*mm0 + 1.00300902708124e-07/1000.0*(55.3418794136)*mm0 + xi1 + xi2 + xi3,\n",
" -i + 1/2.0*(m2*(-1)**2 + m3*(-2.0)**2 + m4*(+1.0)**2 + m5*(-1.0)**2 + m6*(+1.0)**2),\n",
" -m5*n0*mm0 + 1.01303910852863e-07/1000.0*(55.3418794136)*mm0 + xi3,\n",
" -g0 + exp(-1.0*mm0*(m1+ m2 + m3 + m4 + m5 + m6)),\n",
" -g1 + 10**(0.1*i/m0_ref),\n",
" -g2 + 10**(-a_m*(-1.0)**2*(sqrt(i/m0_ref))),\n",
" -g3 + 10**(-a_m*(-2.0)**2*(sqrt(i/m0_ref))),\n",
" -g4 + 10**(-a_m*(+1.0)**2*(sqrt(i/m0_ref))),\n",
" -g5 + 10**(-a_m*(-1.0)**2*(sqrt(i/m0_ref))),\n",
" -g6 + 10**(-a_m*(+1.0)**2*(sqrt(i/m0_ref))),\n",
" -10**-1.8569852/(1/(mm0 * m0_ref))**-1 + Q1\n",
" )\n",
"solution = nsolve(f_0, X, X0, verbose=True)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/latex": [
"$$\\left[\\begin{array}{cccccccccccccccccc}-1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & -1 & -2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\- 18.01528 m_{1} & - 18.01528 n_{0} & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\- 18.01528 m_{2} & 0 & - 18.01528 n_{0} & 0 & 0 & 0 & 0 & 1 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\- 18.01528 m_{3} & 0 & 0 & - 18.01528 n_{0} & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & - \\frac{18.01528 g_{3} g_{4} m_{3} m_{4}}{g_{0} g_{2} m_{2}^{2}} & \\frac{18.01528 g_{3} g_{4} m_{4}}{g_{0} g_{2} m_{2}} & \\frac{18.01528 g_{3} g_{4} m_{3}}{g_{0} g_{2} m_{2}} & 0 & 0 & 0 & 0 & 0 & - \\frac{18.01528 g_{3} g_{4} m_{3} m_{4}}{g_{0}^{2} g_{2} m_{2}} & 0 & - \\frac{18.01528 g_{3} g_{4} m_{3} m_{4}}{g_{0} g_{2}^{2} m_{2}} & \\frac{18.01528 g_{4} m_{3} m_{4}}{g_{0} g_{2} m_{2}} & \\frac{18.01528 g_{3} m_{3} m_{4}}{g_{0} g_{2} m_{2}} & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & \\frac{324.5503134784 g_{4}}{g_{0}^{2}} g_{5} m_{5} & \\frac{324.5503134784 g_{4}}{g_{0}^{2}} g_{5} m_{4} & 0 & 0 & 0 & 0 & - \\frac{649.1006269568 g_{4}}{g_{0}^{3}} g_{5} m_{4} m_{5} & 0 & 0 & 0 & \\frac{324.5503134784 g_{5}}{g_{0}^{2}} m_{4} m_{5} & \\frac{324.5503134784 g_{4}}{g_{0}^{2}} m_{4} m_{5} & 0 & 0\\\\- 18.01528 m_{6} & 0 & 0 & 0 & 0 & 0 & - 18.01528 n_{0} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\- 18.01528 m_{4} & 0 & 0 & 0 & - 18.01528 n_{0} & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0.5 & 2.0 & 0.5 & 0.5 & 0.5 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1\\\\- 18.01528 m_{5} & 0 & 0 & 0 & 0 & - 18.01528 n_{0} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & - 18.01528 e^{- 18.01528 m_{1} - 18.01528 m_{2} - 18.01528 m_{3} - 18.01528 m_{4} - 18.01528 m_{5} - 18.01528 m_{6}} & - 18.01528 e^{- 18.01528 m_{1} - 18.01528 m_{2} - 18.01528 m_{3} - 18.01528 m_{4} - 18.01528 m_{5} - 18.01528 m_{6}} & - 18.01528 e^{- 18.01528 m_{1} - 18.01528 m_{2} - 18.01528 m_{3} - 18.01528 m_{4} - 18.01528 m_{5} - 18.01528 m_{6}} & - 18.01528 e^{- 18.01528 m_{1} - 18.01528 m_{2} - 18.01528 m_{3} - 18.01528 m_{4} - 18.01528 m_{5} - 18.01528 m_{6}} & - 18.01528 e^{- 18.01528 m_{1} - 18.01528 m_{2} - 18.01528 m_{3} - 18.01528 m_{4} - 18.01528 m_{5} - 18.01528 m_{6}} & - 18.01528 e^{- 18.01528 m_{1} - 18.01528 m_{2} - 18.01528 m_{3} - 18.01528 m_{4} - 18.01528 m_{5} - 18.01528 m_{6}} & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 100.0 \\cdot 10^{100.0 i} \\log{\\left (10 \\right )}\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & - \\frac{8.06884436656137}{\\sqrt{i}} 10^{- 16.1376887331227 \\sqrt{i}} \\log{\\left (10 \\right )}\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & - \\frac{32.2753774662455}{\\sqrt{i}} 10^{- 64.5507549324909 \\sqrt{i}} \\log{\\left (10 \\right )}\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & - \\frac{8.06884436656137}{\\sqrt{i}} 10^{- 16.1376887331227 \\sqrt{i}} \\log{\\left (10 \\right )}\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & - \\frac{8.06884436656137}{\\sqrt{i}} 10^{- 16.1376887331227 \\sqrt{i}} \\log{\\left (10 \\right )}\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & - \\frac{8.06884436656137}{\\sqrt{i}} 10^{- 16.1376887331227 \\sqrt{i}} \\log{\\left (10 \\right )}\\\\0 & - \\frac{18.01528 g_{2} g_{4} m_{2} m_{4}}{g_{0} g_{1} m_{1}^{2}} & \\frac{18.01528 g_{2} g_{4} m_{4}}{g_{0} g_{1} m_{1}} & 0 & \\frac{18.01528 g_{2} g_{4} m_{2}}{g_{0} g_{1} m_{1}} & 0 & 0 & 0 & 0 & 0 & - \\frac{18.01528 g_{2} g_{4} m_{2} m_{4}}{g_{0}^{2} g_{1} m_{1}} & - \\frac{18.01528 g_{2} g_{4} m_{2} m_{4}}{g_{0} g_{1}^{2} m_{1}} & \\frac{18.01528 g_{4} m_{2} m_{4}}{g_{0} g_{1} m_{1}} & 0 & \\frac{18.01528 g_{2} m_{2} m_{4}}{g_{0} g_{1} m_{1}} & 0 & 0 & 0\\end{array}\\right]$$"
],
"text/plain": [
"⎡ -1 0 \n",
"⎢ \n",
"⎢-18.01528⋅m₁ -18.01528⋅n₀ \n",
"⎢ \n",
"⎢-18.01528⋅m₂ 0 \n",
"⎢ \n",
"⎢-18.01528⋅m₃ 0 \n",
"⎢ \n",
"⎢ \n",
"⎢ 0 0 \n",
"⎢ \n",
"⎢ \n",
"⎢ \n",
"⎢ \n",
"⎢ 0 0 \n",
"⎢ \n",
"⎢ \n",
"⎢ \n",
"⎢-18.01528⋅m₆ 0 \n",
"⎢ \n",
"⎢-18.01528⋅m₄ 0 \n",
"⎢ \n",
"⎢ 0 0 \n",
"⎢ \n",
"⎢-18.01528⋅m₅ 0 \n",
"⎢ \n",
"⎢ -18.01528⋅m₁ - 18.01528⋅m₂ - 18.01528⋅m₃ - 18.01528⋅\n",
"⎢ 0 -18.01528⋅ℯ \n",
"⎢ \n",
"⎢ \n",
"⎢ 0 0 \n",
"⎢ \n",
"⎢ \n",
"⎢ \n",
"⎢ 0 0 \n",
"⎢ \n",
"⎢ \n",
"⎢ \n",
"⎢ \n",
"⎢ 0 0 \n",
"⎢ \n",
"⎢ \n",
"⎢ \n",
"⎢ \n",
"⎢ 0 0 \n",
"⎢ \n",
"⎢ \n",
"⎢ \n",
"⎢ \n",
"⎢ 0 0 \n",
"⎢ \n",
"⎢ \n",
"⎢ \n",
"⎢ \n",
"⎢ 0 0 \n",
"⎢ \n",
"⎢ \n",
"⎢ -18.01528⋅g₂⋅g₄⋅m₂⋅m₄ \n",
"⎢ 0 ────────────────────── \n",
"⎢ 2 \n",
"⎣ g₀⋅g₁⋅m₁ \n",
"\n",
" \n",
" \n",
" \n",
" \n",
" -18.01\n",
" \n",
" \n",
" \n",
" -18.01528⋅g\n",
" ───────────\n",
" \n",
" g₀⋅g₂\n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" 0\n",
" \n",
" \n",
" \n",
"m₄ - 18.01528⋅m₅ - 18.01528⋅m₆ -18.01528⋅m₁ - 18.01528⋅m₂ - 18.015\n",
" -18.01528⋅ℯ \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" 18.01528\n",
" ────────\n",
" g₀⋅\n",
" \n",
"\n",
"0 \n",
" \n",
"0 \n",
" \n",
"528⋅n₀ \n",
" \n",
"0 \n",
" \n",
"₃⋅g₄⋅m₃⋅m₄ \n",
"─────────── \n",
" 2 \n",
"⋅m₂ \n",
" \n",
" \n",
"0 \n",
" \n",
" \n",
" \n",
"0 \n",
" \n",
"0 \n",
" \n",
".5 \n",
" \n",
"0 \n",
" \n",
"28⋅m₃ - 18.01528⋅m₄ - 18.01528⋅m₅ - 18.01528⋅m₆ -18.01528⋅m₁ - 18.\n",
" -18.01528⋅ℯ \n",
" \n",
" \n",
"0 \n",
" \n",
" \n",
" \n",
"0 \n",
" \n",
" \n",
" \n",
" \n",
"0 \n",
" \n",
" \n",
" \n",
" \n",
"0 \n",
" \n",
" \n",
" \n",
" \n",
"0 \n",
" \n",
" \n",
" \n",
" \n",
"0 \n",
" \n",
" \n",
"⋅g₂⋅g₄⋅m₄ \n",
"───────── \n",
"g₁⋅m₁ \n",
" \n",
"\n",
" 0 \n",
" \n",
" 0 \n",
" \n",
" 0 \n",
" \n",
" -18.01528⋅n₀ \n",
" \n",
" 18.01528⋅g₃⋅g₄⋅m₄ \n",
" ───────────────── \n",
" g₀⋅g₂⋅m₂ \n",
" \n",
" \n",
" \n",
" 0 \n",
" \n",
" \n",
" \n",
" 0 \n",
" \n",
" 0 \n",
" \n",
" 2.0 \n",
" \n",
" 0 \n",
" \n",
"01528⋅m₂ - 18.01528⋅m₃ - 18.01528⋅m₄ - 18.01528⋅m₅ - 18.01528⋅m₆ -\n",
" -18.01528⋅ℯ \n",
" \n",
" \n",
" 0 \n",
" \n",
" \n",
" \n",
" 0 \n",
" \n",
" \n",
" \n",
" \n",
" 0 \n",
" \n",
" \n",
" \n",
" \n",
" 0 \n",
" \n",
" \n",
" \n",
" \n",
" 0 \n",
" \n",
" \n",
" \n",
" \n",
" 0 \n",
" \n",
" \n",
" \n",
" 0 \n",
" \n",
" \n",
"\n",
" 0 \n",
" \n",
" 0 \n",
" \n",
" 0 \n",
" \n",
" 0 \n",
" \n",
" 18.01528⋅g₃⋅g₄⋅m₃ \n",
" ───────────────── \n",
" g₀⋅g₂⋅m₂ \n",
" \n",
" \n",
" 324.5503134784⋅g₄⋅g₅⋅m₅ \n",
" ─────────────────────── \n",
" 2 \n",
" g₀ \n",
" \n",
" 0 \n",
" \n",
" -18.01528⋅n₀ \n",
" \n",
" 0.5 \n",
" \n",
" 0 \n",
" \n",
"18.01528⋅m₁ - 18.01528⋅m₂ - 18.01528⋅m₃ - 18.01528⋅m₄ - 18.01528⋅m₅ - 18.01528\n",
" \n",
" \n",
" \n",
" 0 \n",
" \n",
" \n",
" \n",
" 0 \n",
" \n",
" \n",
" \n",
" \n",
" 0 \n",
" \n",
" \n",
" \n",
" \n",
" 0 \n",
" \n",
" \n",
" \n",
" \n",
" 0 \n",
" \n",
" \n",
" \n",
" \n",
" 0 \n",
" \n",
" \n",
" 18.01528⋅g₂⋅g₄⋅m₂ \n",
" ───────────────── \n",
" g₀⋅g₁⋅m₁ \n",
" \n",
"\n",
" 0 \n",
" \n",
" 0 \n",
" \n",
" 0 \n",
" \n",
" 0 \n",
" \n",
" \n",
" 0 \n",
" \n",
" \n",
" \n",
" 324.5503134784⋅g₄⋅g₅⋅m₄ \n",
" ─────────────────────── \n",
" 2 \n",
" g₀ \n",
" \n",
" 0 \n",
" \n",
" 0 \n",
" \n",
" 0.5 \n",
" \n",
" -18.01528⋅n₀ \n",
" \n",
"⋅m₆ -18.01528⋅m₁ - 18.01528⋅m₂ - 18.01528⋅m₃ - 18.01528⋅m₄ - 18.01\n",
" -18.01528⋅ℯ \n",
" \n",
" \n",
" 0 \n",
" \n",
" \n",
" \n",
" 0 \n",
" \n",
" \n",
" \n",
" \n",
" 0 \n",
" \n",
" \n",
" \n",
" \n",
" 0 \n",
" \n",
" \n",
" \n",
" \n",
" 0 \n",
" \n",
" \n",
" \n",
" \n",
" 0 \n",
" \n",
" \n",
" \n",
" 0 \n",
" \n",
" \n",
"\n",
" 0 \n",
" \n",
" 0 \n",
" \n",
" 0 \n",
" \n",
" 0 \n",
" \n",
" \n",
" 0 \n",
" \n",
" \n",
" \n",
" \n",
" 0 \n",
" \n",
" \n",
" \n",
" -18.01528⋅n₀ \n",
" \n",
" 0 \n",
" \n",
" 0.5 \n",
" \n",
" 0 \n",
" \n",
"528⋅m₅ - 18.01528⋅m₆ -18.01528⋅m₁ - 18.01528⋅m₂ - 18.01528⋅m₃ - 18\n",
" -18.01528⋅ℯ \n",
" \n",
" \n",
" 0 \n",
" \n",
" \n",
" \n",
" 0 \n",
" \n",
" \n",
" \n",
" \n",
" 0 \n",
" \n",
" \n",
" \n",
" \n",
" 0 \n",
" \n",
" \n",
" \n",
" \n",
" 0 \n",
" \n",
" \n",
" \n",
" \n",
" 0 \n",
" \n",
" \n",
" \n",
" 0 \n",
" \n",
" \n",
"\n",
" -1 -1 -2 0 \n",
" \n",
" -1 0 0 0 \n",
" \n",
" 1 -1 0 0 \n",
" \n",
" 0 1 0 0 \n",
" \n",
" -18.01528⋅g₃⋅g₄⋅m₃⋅m₄ \n",
" 0 0 0 ────────────────────── \n",
" 2 \n",
" g₀ ⋅g₂⋅m₂ \n",
" \n",
" -649.1006269568⋅g₄⋅g₅⋅m₄⋅m₅\n",
" 0 0 0 ───────────────────────────\n",
" 3 \n",
" g₀ \n",
" \n",
" 0 0 0 0 \n",
" \n",
" 1 1 1 0 \n",
" \n",
" 0 0 0 0 \n",
" \n",
" 0 0 1 0 \n",
" \n",
".01528⋅m₄ - 18.01528⋅m₅ - 18.01528⋅m₆ \n",
" 0 0 0 -1 \n",
" \n",
" \n",
" 0 0 0 0 \n",
" \n",
" \n",
" \n",
" 0 0 0 0 \n",
" \n",
" \n",
" \n",
" \n",
" 0 0 0 0 \n",
" \n",
" \n",
" \n",
" \n",
" 0 0 0 0 \n",
" \n",
" \n",
" \n",
" \n",
" 0 0 0 0 \n",
" \n",
" \n",
" \n",
" \n",
" 0 0 0 0 \n",
" \n",
" \n",
" -18.01528⋅g₂⋅g₄⋅m₂⋅m₄ \n",
" 0 0 0 ────────────────────── \n",
" 2 \n",
" g₀ ⋅g₁⋅m₁ \n",
"\n",
" 0 0 0 \n",
" \n",
" 0 0 0 \n",
" \n",
" 0 0 0 \n",
" \n",
" 0 0 0 \n",
" \n",
" -18.01528⋅g₃⋅g₄⋅m₃⋅m₄ 18.01528⋅g₄⋅m₃⋅m₄ 18.01\n",
" 0 ────────────────────── ───────────────── ─────\n",
" 2 g₀⋅g₂⋅m₂ \n",
" g₀⋅g₂ ⋅m₂ \n",
" \n",
" 324.5503\n",
"─ 0 0 0 ────────\n",
" \n",
" \n",
" \n",
" 0 0 0 \n",
" \n",
" 0 0 0 \n",
" \n",
" 0 0 0 \n",
" \n",
" 0 0 0 \n",
" \n",
" \n",
" 0 0 0 \n",
" \n",
" \n",
" -1 0 0 \n",
" \n",
" \n",
" \n",
" 0 -1 0 \n",
" \n",
" \n",
" \n",
" \n",
" 0 0 -1 \n",
" \n",
" \n",
" \n",
" \n",
" 0 0 0 \n",
" \n",
" \n",
" \n",
" \n",
" 0 0 0 \n",
" \n",
" \n",
" \n",
" \n",
" 0 0 0 \n",
" \n",
" \n",
" -18.01528⋅g₂⋅g₄⋅m₂⋅m₄ 18.01528⋅g₄⋅m₂⋅m₄ 18.01\n",
" ────────────────────── ───────────────── 0 ─────\n",
" 2 g₀⋅g₁⋅m₁ \n",
" g₀⋅g₁ ⋅m₁ \n",
"\n",
" 0 0 0 0 \n",
" \n",
" 0 0 0 0 \n",
" \n",
" 0 0 0 0 \n",
" \n",
" 0 0 0 0 \n",
" \n",
"528⋅g₃⋅m₃⋅m₄ \n",
"──────────── 0 0 0 \n",
"g₀⋅g₂⋅m₂ \n",
" \n",
" \n",
"134784⋅g₅⋅m₄⋅m₅ 324.5503134784⋅g₄⋅m₄⋅m₅ \n",
"─────────────── ─────────────────────── 0 0 \n",
" 2 2 \n",
" g₀ g₀ \n",
" \n",
" 0 0 0 0 \n",
" \n",
" 0 0 0 0 \n",
" \n",
" 0 0 0 -1 \n",
" \n",
" 0 0 0 0 \n",
" \n",
" \n",
" 0 0 0 0 \n",
" \n",
" 100.0⋅i \n",
" 0 0 0 100.0⋅10 ⋅log\n",
" \n",
" -16.13768873\n",
" -8.06884436656137⋅10 \n",
" 0 0 0 ────────────────────────────────\n",
" √i \n",
" \n",
" -64.55075493\n",
" -32.2753774662455⋅10 \n",
" 0 0 0 ────────────────────────────────\n",
" √i \n",
" \n",
" -16.13768873\n",
" -8.06884436656137⋅10 \n",
" -1 0 0 ────────────────────────────────\n",
" √i \n",
" \n",
" -16.13768873\n",
" -8.06884436656137⋅10 \n",
" 0 -1 0 ────────────────────────────────\n",
" √i \n",
" \n",
" -16.13768873\n",
" -8.06884436656137⋅10 \n",
" 0 0 -1 ────────────────────────────────\n",
" √i \n",
" \n",
"528⋅g₂⋅m₂⋅m₄ \n",
"──────────── 0 0 0 \n",
"g₀⋅g₁⋅m₁ \n",
" \n",
"\n",
" ⎤\n",
" ⎥\n",
" ⎥\n",
" ⎥\n",
" ⎥\n",
" ⎥\n",
" ⎥\n",
" ⎥\n",
" ⎥\n",
" ⎥\n",
" ⎥\n",
" ⎥\n",
" ⎥\n",
" ⎥\n",
" ⎥\n",
" ⎥\n",
" ⎥\n",
" ⎥\n",
" ⎥\n",
" ⎥\n",
" ⎥\n",
" ⎥\n",
" ⎥\n",
" ⎥\n",
" ⎥\n",
" ⎥\n",
" ⎥\n",
" ⎥\n",
" ⎥\n",
" ⎥\n",
"(10) ⎥\n",
" ⎥\n",
"31227⋅√i ⎥\n",
" ⋅log(10) ⎥\n",
"─────────────────⎥\n",
" ⎥\n",
" ⎥\n",
"24909⋅√i ⎥\n",
" ⋅log(10) ⎥\n",
"─────────────────⎥\n",
" ⎥\n",
" ⎥\n",
"31227⋅√i ⎥\n",
" ⋅log(10) ⎥\n",
"─────────────────⎥\n",
" ⎥\n",
" ⎥\n",
"31227⋅√i ⎥\n",
" ⋅log(10) ⎥\n",
"─────────────────⎥\n",
" ⎥\n",
" ⎥\n",
"31227⋅√i ⎥\n",
" ⋅log(10) ⎥\n",
"─────────────────⎥\n",
" ⎥\n",
" ⎥\n",
" ⎥\n",
" ⎥\n",
" ⎥\n",
" ⎦"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Matrix([[-1, 0, 0, 0, 0, 0, 0, -1, -1, -2, 0, 0, 0, 0, 0, 0, 0, 0], [-18.01528*m1, -18.01528*n0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-18.01528*m2, 0, -18.01528*n0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-18.01528*m3, 0, 0, -18.01528*n0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -18.01528*g3*g4*m3*m4/(g0*g2*m2**2), 18.01528*g3*g4*m4/(g0*g2*m2), 18.01528*g3*g4*m3/(g0*g2*m2), 0, 0, 0, 0, 0, -18.01528*g3*g4*m3*m4/(g0**2*g2*m2), 0, -18.01528*g3*g4*m3*m4/(g0*g2**2*m2), 18.01528*g4*m3*m4/(g0*g2*m2), 18.01528*g3*m3*m4/(g0*g2*m2), 0, 0, 0], [0, 0, 0, 0, 324.5503134784*g4*g5*m5/g0**2, 324.5503134784*g4*g5*m4/g0**2, 0, 0, 0, 0, -649.1006269568*g4*g5*m4*m5/g0**3, 0, 0, 0, 324.5503134784*g5*m4*m5/g0**2, 324.5503134784*g4*m4*m5/g0**2, 0, 0], [-18.01528*m6, 0, 0, 0, 0, 0, -18.01528*n0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-18.01528*m4, 0, 0, 0, -18.01528*n0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0.500000000000000, 2.00000000000000, 0.500000000000000, 0.500000000000000, 0.500000000000000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1], [-18.01528*m5, 0, 0, 0, 0, -18.01528*n0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, -18.01528*exp(-18.01528*m1 - 18.01528*m2 - 18.01528*m3 - 18.01528*m4 - 18.01528*m5 - 18.01528*m6), -18.01528*exp(-18.01528*m1 - 18.01528*m2 - 18.01528*m3 - 18.01528*m4 - 18.01528*m5 - 18.01528*m6), -18.01528*exp(-18.01528*m1 - 18.01528*m2 - 18.01528*m3 - 18.01528*m4 - 18.01528*m5 - 18.01528*m6), -18.01528*exp(-18.01528*m1 - 18.01528*m2 - 18.01528*m3 - 18.01528*m4 - 18.01528*m5 - 18.01528*m6), -18.01528*exp(-18.01528*m1 - 18.01528*m2 - 18.01528*m3 - 18.01528*m4 - 18.01528*m5 - 18.01528*m6), -18.01528*exp(-18.01528*m1 - 18.01528*m2 - 18.01528*m3 - 18.01528*m4 - 18.01528*m5 - 18.01528*m6), 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 100.0*10**(100.0*i)*log(10)], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -8.06884436656137*10**(-16.1376887331227*sqrt(i))*log(10)/sqrt(i)], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -32.2753774662455*10**(-64.5507549324909*sqrt(i))*log(10)/sqrt(i)], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -8.06884436656137*10**(-16.1376887331227*sqrt(i))*log(10)/sqrt(i)], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -8.06884436656137*10**(-16.1376887331227*sqrt(i))*log(10)/sqrt(i)], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -8.06884436656137*10**(-16.1376887331227*sqrt(i))*log(10)/sqrt(i)], [0, -18.01528*g2*g4*m2*m4/(g0*g1*m1**2), 18.01528*g2*g4*m4/(g0*g1*m1), 0, 18.01528*g2*g4*m2/(g0*g1*m1), 0, 0, 0, 0, 0, -18.01528*g2*g4*m2*m4/(g0**2*g1*m1), -18.01528*g2*g4*m2*m4/(g0*g1**2*m1), 18.01528*g4*m2*m4/(g0*g1*m1), 0, 18.01528*g2*m2*m4/(g0*g1*m1), 0, 0, 0]])"
]
}
],
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