CO2 Equilibria

CO2 Equilibria.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# CO2 Equilibria"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Atmospheric pressure (altitude)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$dp = -\\rho g dz$\n",
    "\n",
    "${{dp}\\over{dz}} = -\\rho g = -{{\\rho_0}\\over{p_0}} g p \n",
    "\\text{  ..    Boyle-Mariotte i.g. }p/p_0 = \\rho/\\rho_0$\n",
    "\n",
    "${{1}\\over{p}}{{dp}\\over{dz}} = -{{1}\\over{p_0/(\\rho_0\\times g)}} \n",
    "\\equiv -{{1}\\over{H}} [=] 1/m \\text{...(Skalenhöhe)}$\n",
    "\n",
    "$\\int{{{1}\\over{p}}dp} = \\int{-{{1}\\over{H}}dz}$\n",
    "\n",
    "$ln(p) + c1 = -z/H$\n",
    "\n",
    "$p(z) = e^{c1} e^{-z/H}$\n",
    "\n",
    "$p(0) = p_0 \\rightarrow p(0) = e^{c1}e^0 = e^{c1} = p_0$\n",
    "\n",
    "$p(z) = p_0 e^{-z/H}$\n",
    "\n",
    "=============================================\n",
    "\n",
    "Hg: $p=\\rho g z$\n",
    "\n",
    "$z=760mm=0.760m, \\rho=13,595.098kg/m^3, g=9.80665m/s^2 \\rightarrow p=p_0=101325Pa$\n",
    "\n",
    "\n",
    "N2/O2/Ar: $p=p_0 e^{-z/H}$\n",
    "\n",
    "$p/p_0 = 1 \\rightarrow 0 = -z/H$\n",
    "\n",
    "$\\lim_{p\\rightarrow 0}{p/p_0} = +\\inf$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "delta_z=8.8 km\n",
      "p_0=101325 Pa\n",
      "H = 8.8 km\n",
      "99.9999% of atmosphere weight: 122.2 km\n"
     ]
    },
    {
     "data": {
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72JmS682AJ4D/BbZLrrWJ+OdUCjwJlCTf75CCTDOBI5LHPwLm5PK/nbunqlAc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\nM/oWqJZLAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x6a5bb00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from scipy.constants import *\n",
    "def interp_1(x3, x_1_2, y_1_2):\n",
    "    x1, x2, y1, y2 = x_1_2[0], x_1_2[1], y_1_2[0], y_1_2[0]\n",
    "    return (y2-y1)/(x2-x1)*(x3-x2) + y2\n",
    "\n",
    "comps = np.array(['N2', 'O2', 'Ar'])\n",
    "mol_pct = np.array([0.7812, 0.2096, 0.0092])\n",
    "mm = np.array([28.013, 31.999, 39.948])\n",
    "w_pct = np.multiply(mol_pct, mm)/sum(np.multiply(mol_pct, mm))\n",
    "# 1dm^3 = 1dm^3*(1m/10dm)^3*(100cm/m)^3*(1mL/cm^3) = 10^3mL = 1L\n",
    "# 0.1MPa, 300K\n",
    "dens_moldm3 = 1/np.array([24.854, 24.928, 24.928]) # mol/dm^3\n",
    "dens_gml = np.multiply(mm, dens_moldm3)/1000.0 # g/mL, kg/L\n",
    "dens_kgm3 = 1000.0*dens_gml # kg/m^3\n",
    "rho_hg = 13.596*interp_1(293.15, [294, 292], [997.983, 998.392]) # kg/m3\n",
    "rho_a = sum(w_pct*dens_kgm3) # kg/m^3\n",
    "delta_z = rho_hg/rho_a*760.0/1000.0\n",
    "print 'delta_z=' + '%.1f' %  (delta_z/1000.0) + ' km'\n",
    "print 'p_0=' + '%g' % (rho_hg*g*761.4855/1000.0) + ' Pa' # kg/m^3*m/s^2*m [=] (kg m/s^2)/m^2 [=] Pa\n",
    "z = np.array(range(0,16500))\n",
    "p_0 = 101325.0 \n",
    "H = p_0/(g*rho_a)\n",
    "print 'H = ' + '%.1f' % (H/1000.0) + ' km'\n",
    "a = plt.plot(z,1.0*np.exp(-z/H))\n",
    "plt.xlabel('z, m')\n",
    "plt.yticks([1/float(x) for x in range(1,7,1)], ['$p_0$'] + ['$1/' + str(x) + 'p_0$' for x in range(2,7,1)]);\n",
    "print '99.9999% of atmosphere weight: ' + '%.1f' % (np.log(0.1/101325.0)*-H/1000.0) + ' km'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Henley 3.10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "air pressure at the top:\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x3fbf860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p to lift water:\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMAAAABHCAYAAABRaUhnAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x3fd5860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAacAAABHCAYAAACj3IiuAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nCCFE4/gfR8su4/6DB+UAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Henry's law application:\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAKwAAABHCAYAAACasqyZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x81babe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAATIAAABHCAYAAACEXssDAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7b33b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x8145860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7361240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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kIs3hwzB9ujNWNGkS1KrldM/d1GIR7f7YiRKlbCc94z1LTB6yxGQiQerP21nzqrOR3iOH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\ndj+/vvgNJack0nbrt2yq1Ib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      "text/plain": [
       "<matplotlib.figure.Figure at 0x734bda0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMUAAABHCAYAAAC3QIMjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAB1tJREFUeJztm3usHVUVxn+rt6W1pQ1oRUIlKL22kACh1dikiY8IKok2\nRElAg1pFeSgqjYLPxki0JYi1FVMsTbQWSPgDY1INii/6ikojAaEQNfiogNKC0gq20OfnH3tfOOzO\nOWfmPnp6c79fMplz9qxZa+195pu9Z+85IQljzIuM63UCxhxtWBTGFFgUxhRYFMYUWBTGFFgUxhRY\nFMYUWBTGFFgUxhRYFMYUWBTGFFgUxhRYFMYUWBTGFFgUxhRYFMYUWBTGFFgUxhRYFMYUWBTGFFgU\nxhSM73UCY5GImA0sBbblounANZKeHClfDeyuA9YBfwL2AqcCC4BbJP0r25wHrAIeAJ7Ldoda3GyR\ntKquXd38GvqbB1wO7AEmAy8Dlkh66PBWLJDk7QhuwDTgMeD9LWVfBLYC40fCV5OY+SJr3fYDXy5s\nPgMcbLMdAN7e0K5uPer6O5sk7GNazl0J/Bc4q2u79voiGWsbsATYDoxrKTse2AdcPhK+msQk3alX\nAT8CvgGcURH3JuAkoK8onw8sH4Rd3XrU9fetLOgLWsrelctWdG3XXl8kY20D/gysqyh/EPjVSPhq\nEhO4u0bcGyvKjgXuBCYOwq5uPer6+yCwEzi3pex9WRRLu9av1xfJWNryD3gI+E7FsbuAncPtq2nM\nOqJok89KYG5Tu6G2SYO4N+Se58xutj1/0I6IucAHAAGnAJeSHpCOA2YAX5H0995lOKyckvfPVBzb\nDUyLiAmS9g+Xr0HEnBgRnwdeSbpYZwJfkPRIu0QiYj4Qku7rlHAbu0G3SYO4M4GFwCclbe1kCz2e\nfYqIfmChpKvy9zXAPaQKjAM2A/cBy3uWZMrre8BcknC7mme7RZI2Fcem5f2+ivN25/1xwFM14tT1\n1TTmCcBtkv4JEBEXA5sj4iy1nx27EXhvjZyr7IbSJh3jRsT5wDnAO4BlklbXyLHnPcUi4JqW71OA\npyXdExGvBpYBP6jrLCL6JB0c3hRB0keHydVAblXimpD3fcPsq2nMWcrjjcztwGrgS6Tf6yVExDnA\nJEmPdkq2g92g2qROXEnrgHURMR74RUQsABZI2tkp116L4npJz7V8nw+sAZD0OPC58oRcwQ+T7txP\nAs+S5qt/A7wb+Fq2mwRcAkzNdtOBl+eYu0amOl3p1ANMyftnh9lXo5iFIJB0KCKeAs6nQhTAx0m9\nezfa2Q22TerGRdKBiLgWWE+aWbuok31PV7QlPTbwOSJOI023rW9nHxGvIzXEIUmfkPRVScuAO4C7\ngS3Zrh/4JfBHSddLWiPpBuDnwE9GrELd2UG6Ix5fcWwKsEvS7opjQ/FVO2ZEbIqIcsgH6U79qrIw\n36DeCTzRKdEudo3bpFvciJgdEWcWxQPPHRdExORO+fa6p2jlXNId/7cDBRHx2oGH7IiYQbrwF0ta\n23qipB0R8TtgY0RMJ138iyStL+w25AZ7i6SNdROLiNXAHJo9U3xW0uYi/p6IuB84ueK8fuAPdXOq\n66thzLOBqgfq6by40tzKG0kX7r+7pNvWbpBt0tZfREzN5/RFxOyWSZqBYVrQZYjaM1Hk4c21pNcH\nHiaJ4kFJz+fjAVwNXJlPWQFsKwXRwnJJeyPiu8Djktr1CBOAE7L/K0nL/+SepBJJlzWrXUfuJA3r\nXiDPjpwMXFeU95Pq8vwQfdW1uwu4orCbA0wEbq2I35/37fKra1e7TWr420e66P9GWqsY4PS8/72k\nzkPUwcxJD8dGmjU4CFwIzCYt1GxqOb4YmJc/v4L0usGHuvicSuptKu1ywxwEziA9f8zI5T8E5hyh\nep8IPA1c3FK2gsNfaXhTzvVnw+Crrt0bgFt46esRa0mzgBMq4l9Nmrb9SJc6d7Srm18Df18HPl2U\n3Uqa9u36O/dy+LSR9FD9+rzNA27Kd/p9wI8lbcm2M0nPP/dWOYqIU4F/ALNIvV+7l74+Rnpp7KE8\ne3Ea8E3gr6S70v3DUK+OSNoeEW8FluQ1mmmk8fR5kg60mO4gTRD8Zai+GtjdGxE3A7dFxJ5stxW4\nVNVrJ48Au0gv6HWio12DNqnrb3FELIyI20k30xOB/5AW+dq25wCRVXRUExEnAY+SVH7Y4ktEXCXp\n2xHxGtIFPlfSA4XN6cAG4G2SHs4LW8dI2h0RPwUukbR9hKtiRgGj4v8USq8sryVNw71ARPRFxBWk\n4Q+StpFmly4q7GYB3wfeo/T8gqT9WRDzgQ0WhBlgVPQUkARAWreYSRpS/I/0Tv0dkp5psZtMGlPu\nJQ2pjgUmAStVLNrkmYpPSVp6RCphRgWjRhQjQURcRupBAnizpF/3OCVzFDAqhk8jQURcSPq/wBOk\nd/k7LkCZscOY7imMqWLM9hTGtMOiMKbAojCmwKIwpsCiMKbAojCmwKIwpsCiMKbAojCmwKIwpsCi\nMKbAojCmwKIwpsCiMKbAojCmwKIwpsCiMKbAojCmwKIwpsCiMKbAojCmwKIwpsCiMKbAojCmwKIw\npsCiMKbAojCmwKIwpsCiMKbg/wwQq0MoM1WVAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x85bef28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7b02d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAN4AAABHCAYAAABoDvk8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nwH8ARAp+ZJvhvGsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x3fbfcf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAANcAAABHCAYAAACUG9L2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7b33d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total CO2 to absorb\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ed4d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ed4da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "water to absorb calc.kg of CO2 \n"
     ]
    },
    {
     "data": {
      "image/png": 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T3Y1fK8hTCDHI2WAMmrs/RKxbODPnfyGxd1qeTwNzzWw4sQ/bz1L8lcRmmBsK3fi+2Zgm\nMut+38zd/xvW+RbZ8flMC8Ja+b5ZH5nuvghYZGYnEt83m5b0KIQQ77Ahdjk2JU1fnUvM5nqeOqvj\nNyAWA39SO0jjhWOJt8t20y0mFkH2CTOzqcByi218IN6inHWn+x5G3y7ERmFl6tAnnZlNNbPnzWxC\n8lpI7PV2aEHeQohBTCUNmrt/391Hu/t4dx/n7k/0ukz9QN83a+P7ZkKIwccG0+U4WHF936yt75sJ\nIQYf5u69LoMQQgjRbyrZ5SiEEGLwIYMmhBCiEsigCSGEqAQyaEIIISqBDJoQQohKIIMmhBCiEsig\nCSGEqAQyaEIIISqBDJoQQohKIIMmhBCiEsigCSGEqAQyaEIIISqBDJoQQohKIIMmhBCiEsigCSGE\nqAQyaEIIISqBDJoQQohKIIMmhBCiEsigCSGEqAQyaEIIISqBDJoQQohKIIMmhBCiEsigCSGEqAQy\naEIIISqBDJoQQohKIIMmhBCiEsigCSGEqAT/D7WJjQwC/wvdAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7b02d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x718c4a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Actual balance: \n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAVAAAABHCAYAAABRTB9OAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRCSRAqiISCIFUBGRRP8Ht4kNFL8B6wIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x87010f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMEAAABHCAYAAAC+qyNZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nzmIAwqp/BqgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x836e358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x8144d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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GDBePRIwxxjRmlZ0TMcYYs/JYiRhjjGmMlYgxxpjGWIkYY4xpjJWIMcaYxliJGGOMaYyV\niDHGmMZYiRhjjGmMlYgxxpjGWIkYY4xpjJWIMcaYxliJGGOMaYyViDHGmMZYiRhjjGmMlYgxxpjG\nWIkYY4xpjJWIMcaYxliJGGOMaYyViDHGmMZYiRhjjGmMlYgxxpjGWIkYY4xpjJWIMcaYxliJGGOM\naYyViDHGmMZYiRhjjGmMlYgxxpjG/D9NZLeS8qMsNQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x8145e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7dac9e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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3y7kfSZgjmA9MyLgPBR5K/28N/JjY+XlTLv5jwNE9VId9iOODvkx8ic4CfkAPzEwS56W+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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x8452c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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e4LhO51s387zlutrst4ijWgduqXkLOKpM/E6bDdtFfjgKyzaGXOrSKWmxpDfMV4fPkPQ3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\ncoTyCoIgCCrH/wMFW0FKOqyKZwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x819a4a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def print_latex(str_x):\n",
    "    ax = plt.axes([0,0,0.1,0.2])\n",
    "    plt.cla()\n",
    "    plt.text(0.5, 0.5, '$%s$'%str_x, size=20)\n",
    "    ax.set_xticks([])\n",
    "    ax.set_yticks([])\n",
    "    ax.set_frame_on(0)\n",
    "    plt.show()\n",
    "\n",
    "z = 91.44 # m\n",
    "p_at_top = 101.325*np.exp(-z/H) # kPa\n",
    "rho_w = interp_1(293.15, [294, 292], [997.983, 998.392]) # kg/m^3\n",
    "delta_p = rho_w * g * z # kg/m^3*m/s^2*m [=] (kg m/s^2)/m^2 [=] Pa\n",
    "\n",
    "print 'air pressure at the top:'\n",
    "print_latex('p = 101.325kPa\\\\times e^{\\\\frac{-91.44}{%g' % H + \\\n",
    "            '}} = %g' % p_at_top + 'kPa')\n",
    "print 'p to lift water:'\n",
    "print_latex('\\\\rho g z = ' + '%g' % (delta_p/1000.0) + ' kPa')\n",
    "print_latex('p_{CO2} = '    + '%g' % (delta_p/1000.0)  + 'kPa + 68.8kPa = ' \\\n",
    "                            + '%g' % (delta_p/1000.0 + 68.8) + 'kPa')\n",
    "print \"Henry's law application:\"\n",
    "print_latex('\\\\mu_{id.\\ soln.}=\\\\mu_{id.\\ g.}')\n",
    "print_latex('\\\\mu_i^* + RTln(x_i) = \\mu_i^{\\\\circ} + RTln(p_i)')\n",
    "print_latex('p_i/x_i = exp \\\\left(\\\\frac{\\\\mu_i^*-\\\\mu_i^{\\\\circ}}{RT} \\\\right) \\\\equiv K_i = \\\\mathcal{H}_i')\n",
    "print_latex('CO_2, 298.15K: \\ \\\\mathcal{H}_{CO_2} = 1670bar = 167000kPa')\n",
    "p_co2 = delta_p/1000.0 + 68.8 # kPa\n",
    "h_co2 = 167000.0 # 1670.0bar = 167000.0 kPa\n",
    "#h_co2 = 1666.6666666666667*100 # correct for exercise\n",
    "x_co2_max = p_co2/h_co2\n",
    "x_co2 = np.arange(0.0,x_co2_max*(1+1/20.0),x_co2_max/20.0)\n",
    "n_co2 = 101325.0*1000.0*(1/3.280839895013123)**3/(8.314*273.15) # 28.31m^3 (STP)\n",
    "mm_co2 = 12+2*16\n",
    "mm_h2o = 2*1 + 16\n",
    "n_h2o = n_co2*(1-x_co2[-1])/x_co2[-1]\n",
    "#n_h2o = n_co2*(1-0.0057)/0.0057\n",
    "m_co2 = n_co2 * mm_co2 / 1000.0 # kg\n",
    "m_h2o = n_h2o * mm_h2o / 1000.0 # kg\n",
    "x1_co2 = p_at_top/100.0/1670.0\n",
    "y1_co2 = 1.0\n",
    "n_s0 = (1.0 - x1_co2)/(x_co2_max - x1_co2) * n_co2\n",
    "m_h2o_0 = n_s0 * (1 - x_co2_max) * mm_h2o / 1000.0 # kg\n",
    "ax = plt.axes([0.0,0.0,1.0,1.0])\n",
    "plt.cla()\n",
    "plt.subplot(211)\n",
    "plt.plot(x_co2, h_co2 * x_co2)\n",
    "plt.plot([x_co2[-1], x1_co2],\n",
    "         [p_co2, p_at_top], \n",
    "         marker='<', color='r', linestyle='--' )\n",
    "plt.xlabel('$x_{CO_2}$', size=20)\n",
    "plt.ylabel('$p_{CO_2}, kPa$', size=20)\n",
    "plt.subplot(212)\n",
    "plt.plot(x_co2, h_co2 * x_co2 / 101.325)\n",
    "plt.plot([x_co2[-1], x1_co2],\n",
    "         [p_co2/101.325, p_at_top/101.325], \n",
    "         marker='<', color='r', linestyle='--' )\n",
    "plt.xlabel('$x_{CO_2}$', size=20)\n",
    "plt.ylabel('$p_{CO_2}, atm$', size=20)\n",
    "plt.show()\n",
    "print_latex('x_{CO_2} = ' + '%g' % x_co2[-1])\n",
    "print_latex('n \\\\times x_{CO_2} = n_{CO_2}')\n",
    "print_latex('n \\\\times (1-x_{CO_2}) = n_{H_2O}')\n",
    "print_latex('n_{CO_2} \\\\times \\\\frac{1-x_{CO_2}}{x_{CO_2}} = n_{H_2O}')\n",
    "print 'total CO2 to absorb'\n",
    "print_latex('n_{CO_2} = \\\\frac{101325 Pa\\\\times 28.31m^3}' + \\\n",
    "            '{8.314\\\\frac{Pa \\\\times m^3}{mol K}\\\\times 273.15K} = ' + \\\n",
    "            '%g' % n_co2 + 'gmol') # n = PV/RT\n",
    "print_latex('m_{CO_2} = n_{CO_2}/M_{CO_2} = ' + '%g' % m_co2 + 'kg')\n",
    "print 'water to absorb calc.kg of CO2 '\n",
    "print_latex('n_{H_2O} = \\\\frac{1-' + '%g' % x_co2[-1] + '}' + \\\n",
    "            '{' + '%g' % x_co2[-1] + '} \\\\times ' + '%g' % n_co2 + 'mol = '+ \\\n",
    "            '%g' % n_h2o + ' mol')\n",
    "print_latex('m_{H_2O} = n_{H_2O}/M_{H_2O} = ' + '%g' % m_h2o + 'kg')\n",
    "print 'Actual balance: '\n",
    "print_latex('(1)\\\\ x_{CO_2 1} n_{s 1} + y_{CO_2 1} n_{g 1}  = x_{CO_2, 0} n_{s 0}')\n",
    "print_latex('(2)\\\\ n_{s 1} + n_{g 1}  = n_{s 0}')\n",
    "print_latex('y_{CO_2 1} = p_{CO_2 1}/P = 1.01325/1.01325 = 1.0')\n",
    "print_latex('x_{CO_2 1} = p_{CO_2 1}/ \\\\mathcal{H}_{CO_2} ' + \\\n",
    "            '= \\\\frac{1.01325}{1670} = ' + '%g' % x1_co2)\n",
    "print ''\n",
    "print_latex('x_{CO_2 1} (n_{s 0}-n_{g 1}) + n_{g 1}  = x_{CO_2, 0} n_{s 0}')\n",
    "print_latex('n_{s 0} = \\\\frac{1-x_{CO_2 1}}{x_{CO_2, 0}-x_{CO_2 1}}\\\\times n_{g 1}' + \\\n",
    "            '= \\\\frac{1-%g' % x1_co2 + '}{ %g' % x_co2_max + \\\n",
    "            '-%g' % x1_co2 + '}\\\\times %g' % n_co2 + 'mol' + '=%g' % n_s0 + 'mol')\n",
    "print_latex('m_{H_2O, 0} = n_{s 0}(1-x_{CO_2 0})/MM_{H_2O} = %g' % m_h2o_0 + 'kg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution with the remaining equilibria"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Eq.\n",
    "\n",
    "$\n",
    "\\begin{array}{ccccccc}\n",
    "(1) &\\ CO_2(ac) & + H_2O & \\rightleftharpoons & CO_2(g) & & \\mathcal{H_1} = 1670bar  \\\\\n",
    "(2) &\\ CO_2(ac) & + H_2O & \\rightleftharpoons & H_2CO_3  & &  pK_2 = 2.821023053\\\\\n",
    "(3) &\\ H_2CO_3 & + H_2O & \\rightleftharpoons & HCO_3^{-} & + H_3O^{+} & pK_3 = 3.539912399\\\\\n",
    "(4) &\\ HCO_3^{-} & + H_2O & \\rightleftharpoons & CO_3^{2-} & + H_3O^{+} & pK_4 = 10.32991986\\\\\n",
    "(5) &\\ 2 H_2O & & \\rightleftharpoons & H_3O^{+} & + HO^{-} & pK_w = 13.99602524\\\\\n",
    "(6) &\\ NaHCO_3 & & \\rightarrow & HCO_3^{-} & + Na^{+} & \\\\\n",
    "\\end{array}\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### Model\n",
    "\n",
    "Material Balances (n)\n",
    "\n",
    "$n_i = n_{0,i} + \\sum_j{(\\nu_{ij}\\times \\xi_i)}$\n",
    "\n",
    "Equilibrium constant expressions ($n_r$)\n",
    "\n",
    "$K_j(T) = \\left [ \\prod_i{(x_i)^{\\nu_{ij}}} \\right ]_{eq.}$\n",
    "\n",
    "Equation of state (gas ph)\n",
    "\n",
    "V = const. $p = \\sum_i{\\frac{n_{i,g} RT}{V}} = \\frac{RT}{V} \\sum_i{n_{i,g}}$\n",
    "\n",
    "p = const. $V = \\sum_i{\\frac{n_{i,g} RT}{p}} = \\frac{RT}{p} \\sum_i{n_{i,g}}$\n",
    "\n",
    "### Input \n",
    "\n",
    "$xw_{Na^{(+)},0} + xw_{HCO3^{(-)},0} = 0.1\\%$\n",
    "\n",
    "$\\frac{xw_{Na^{(+)},0}}{M_{Na^{(+)}}} = \\frac{xw_{HCO3^{(-)},0}}{M_{HCO3^{(-)}}}$\n",
    "\n",
    "$\\Rightarrow xw_{Na^{(+)}, 0} = \\frac{0.1\\%}{1+44/23}=0.034328\\%$\n",
    "\n",
    "$\\Rightarrow xw_{HCO3^{(-)}, 0} = \\frac{0.1\\%}{1+23/44}=0.065672\\%$\n",
    "\n",
    "$x_{Na^{(+)}, 0} = \\frac{0.00034324/23}{0.000343284/23+0.000656716/44+0.999/18} = 0.000268778$\n",
    "\n",
    "$x_{HCO3^{(-)}, 0} = \\frac{0.000656716/44}{0.000343284/23+0.000656716/44+0.999/18} = 0.000268778$\n",
    "\n",
    "$pH_0 = 13.99568/2 = 6.99784$\n",
    "\n",
    "$x_i/c_i = x_0 M_0 / \\rho_0$ ($x_0, M_0, \\rho_0$, solvent)\n",
    "\n",
    "Initial pH=-13.99568/2 = 6.99784, mole fraction:\n",
    "\n",
    "$x_{H_3O^{(+)},0} = \\frac{c_{H_3O^{(+)},0}}{M_0 \\rho_0}\\times\\left(1 - \\sum_{i\\neq 0}{x_i}\\right) = \\frac{c_{H_3O^{(+)},0}}{M_0 \\rho_0}\\times\\left(1 -x_{H_3O^{(+)},0} - x_{HO^{(-)},0} - x_{Na^{(+)}, 0} - x_{HCO3^{(-)}, 0} \\right)$\n",
    "\n",
    "$x_{HO^{(-)},0} = \\frac{10^{-13.99568}/c_{H_3O^{(+)},0}}{M_0 \\rho_0}\\times\\left(1 - \\sum_{i\\neq 0}{x_i}\\right) = \\frac{10^{-13.99568}}{c_{H_3O^{(+)},0}M_0 \\rho_0}\\times\\left(1 -x_{H_3O^{(+)},0} - x_{HO^{(-)},0} - x_{Na^{(+)}, 0} - x_{HCO3^{(-)}, 0} \\right)$\n",
    "\n",
    "System:\n",
    "\n",
    "$\n",
    "\\begin{align}\n",
    "\\left(1 + \\frac{M_0}{\\rho_0} 10^{-pH_0} \\right) & x_{H_3O^{(+)},0} + & \\left(\\frac{M_0}{\\rho_0} 10^{-pH_0} \\right) & x_{HO^{(-)},0}  = & \\frac{M_0}{\\rho_0} \\left(1-x_{Na^{(+)},0}-x_{H_3O^{(+)},0} \\right) \\\\\n",
    "\\left(\\frac{M_0}{\\rho_0} 10^{pH_0-13.99568} \\right) & x_{H_3O^{(+)},0}  + & \\left(1 + \\frac{M_0}{\\rho_0} 10^{pH_0-13.99568} \\right) & x_{HO^{(-)},0} = & \\frac{M_0}{\\rho_0} \\frac{10^{-13.99568}}{c_{H_3O^{(+)},0}} \\left(1-x_{Na^{(+)},0}-x_{H_3O^{(+)},0} \\right) \\\\\n",
    "\\end{align}\n",
    "$\n",
    "\n",
    "$\\Rightarrow x_{H_3O^{(+)},0} = 1.8082E-09; x_{HO^{(-)},0} = 1.8082E-09$\n",
    "\n",
    "\n",
    "| # | Var | alias | val |\n",
    "| - | - | - | - |\n",
    "| - | $p$ |  | 1.01325bar = const. |\n",
    "| - | $T$ |  | 298.15K |\n",
    "| 0 | $x_{H2O,0}$ | x00 | 9.99571E-01 |\n",
    "| 1 | $x_{H_3O^{(+)},0}$ | x10 | 1.80820E-09 |\n",
    "| 2 | $x_{HO^{(-)},0}$ | x20 | 1.80820E-09 |\n",
    "| 3 | $x_{HCO3^{(-)},0}$ | x30 | 2.14408E-04 |\n",
    "| 4 | $x_{Na^{(+)},0}$ | x40 | 2.14408E-04 |\n",
    "| 5 | $x_{CO3^{(2-)},0}$ | x50 | 0 |\n",
    "| 6 | $x_{CO_2(ac),0}$ | x60 | 0 |\n",
    "| 7 | $x_{H_2CO_3,0}$ | x70 | 0 |\n",
    "| 8 | $p_{CO_2(g),0}$ | x80 | 0 |\n",
    "\n",
    "### Solution\n",
    "$\n",
    "x_{CO_2} = {{C_{CO_2}}\\over{C_{H_2O}+C_{H_3O^{(+)}}+C_{HO^{(-)}}+C_{HCO_3^{(-)}}+C_{Na^{(+)}}+C_{CO_3^{(2-)}}+C_{CO_2}+C_{H_2CO_3} }} \n",
    "$\n",
    "\n",
    "$V_l/V_g = \\phi = 1.0$\n",
    "\n",
    "---\n",
    "\n",
    "$\n",
    "\\begin{array}{ccccccccccc}\n",
    "0 = & 1670\\times 100kPa & - & {{p_{CO_2}}\\over{x_{CO_2}}} &&&&&&\\\\\n",
    "0 = & 10^{-2.821023053} & - & {{C_{H_2CO_3}}\\over{C_{CO_2}}} &&&&&&\\\\\n",
    "0 = & 10^{-3.539912399} & - & {{C_{H_3O^{(+)}} \\times C_{HO^{(-)}}}\\over{C_{H_2CO_3}}} &&&&&&\\\\\n",
    "0 = & 10^{-10.32991986} & - & {{C_{H_3O^{(+)}} \\times C_{CO_3^{(2-)}}}\\over{C_{HCO_3^{(-)}}}} &&&&&&\\\\\n",
    "0 = & 10^{-13.99602524} & - & C_{H_3O^{(+)}} C_{HO^{(-)}} &&&&&&\\\\\n",
    "0 = & -C_{0,H_2O} & + & C_{H_2O} & - &(&- \\xi_0 & -\\xi_1& -\\xi_2& -\\xi_3 & -2\\xi_4 &)\\\\\n",
    "0 = & -C_{0,H_3O^{(+)}} & + & C_{H_3O^{(+)}} & - & (&&&+\\xi_2&+\\xi_3&+\\xi_4&)\\\\\n",
    "0 = & -C_{0,HO^{(-)}} & + & C_{HO^{(-)}} & - & (&&&&&+\\xi_4&)\\\\\n",
    "0 = & -C_{0,HCO_3^{(-)}} & + & C_{HCO_3^{(-)}} & - & (&&&+\\xi_2&-\\xi_3&&)\\\\\n",
    "0 = & -C_{0,Na^{(+)}} & + & C_{Na^{(+)}} & - & (&&&0&&&)\\\\\n",
    "0 = & -C_{0,CO_3^{(2-)}} & + & C_{CO_3^{(2-)}} & - & (&&&&+\\xi_3&&)\\\\\n",
    "0 = & -C_{0,CO_2(ac)} & + & C_{CO_2(ac)} & - &(&-\\xi_0&-\\xi_1&&&&)\\\\\n",
    "0 = & -C_{0,H2_CO_3} & + & C_{H2_CO_3} & - &(&&+\\xi_1&-\\xi_2&&&)\\\\\n",
    "0 = & -{p_{0,CO_2(g)}\\over{RT \\left({{V_l}\\over{V_g}}\\right)}} & + & {p_{CO_2(g)}\\over{RT \\left({{V_l}\\over{V_g}}\\right)}} & - &(&\\xi_0&&&&&)\\\\\n",
    "\\end{array}\n",
    "$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mole frac.\n",
      "[  9.99571180e-01   1.80748046e-09   1.80748046e-09   2.14408233e-04\n",
      "   2.14408233e-04   2.22044605e-16   2.22044605e-16   2.22044605e-16\n",
      "   2.22044605e-16]\n",
      "mass frac.\n",
      "[  9.98999996e-01   1.90680581e-09   1.70608941e-09   7.26190476e-04\n",
      "   2.73809524e-04   7.39725741e-16   5.42465543e-16   7.64383266e-16\n",
      "   5.42465543e-16]\n",
      "status: 5\n",
      "success: False\n",
      "nfev: 986\n",
      "fun: [  0.00000000e+00   0.00000000e+00  -6.59159551e-25  -9.28962602e-27\n",
      "  -1.76704843e-28   6.87099574e-16  -1.20305148e-20  -4.23516474e-22\n",
      "  -3.25260652e-19   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "   2.15993402e-20  -5.55111512e-17]\n",
      "x: [  5.55556289e+01   3.26903554e-09   3.08713142e-06   1.15820992e-02\n",
      "   1.19166786e-02   1.65747801e-04   8.69245345e-05   1.31256047e-07\n",
      "   2.61183128e-01   9.24397224e-05  -1.68700408e-04  -1.68831664e-04\n",
      "   1.65747801e-04   2.98667276e-06]\n",
      "message: The iteration is not making good progress, as measured by the \n",
      "  improvement from the last ten iterations.\n",
      "fjac: [[ -7.63820294e-01  -2.51044075e-17  -3.66996541e-18  -5.62722554e-14\n",
      "   -7.33732542e-19  -6.45235972e-01  -1.52460529e-04  -4.30031766e-18\n",
      "   -3.12760669e-03   5.53700196e-18   2.92525295e-16   1.95663871e-04\n",
      "   -7.31096002e-05   1.54677352e-02]\n",
      " [  1.16016605e-04   3.81335906e-21   1.15813217e-02   1.65736675e-04\n",
      "    3.08692420e-06   9.88733008e-05  -9.99932909e-01   6.53725271e-22\n",
      "    4.75064401e-07  -8.41213770e-22  -4.44338450e-20  -2.97201626e-08\n",
      "    1.11044284e-08  -2.35071166e-06]\n",
      " [  2.00868811e-03  -1.31070560e-18  -6.49025510e-09  -9.28802184e-11\n",
      "    3.26728978e-09  -2.37642959e-03  -2.13922180e-09  -9.99995157e-01\n",
      "   -1.15393933e-05   2.04281044e-20   1.07927577e-18   7.21907371e-07\n",
      "   -2.69742140e-07   5.70630568e-05]\n",
      " [  4.72895794e-03   1.02039634e-22   3.33896442e-09  -4.57803573e-11\n",
      "   -5.59596283e-14  -7.50892170e-04  -6.25963349e-10   2.28228176e-05\n",
      "   -9.99988536e-01  -6.62145071e-23  -9.64055940e-21  -6.78670481e-09\n",
      "    2.81871338e-09   3.67832431e-08]\n",
      " [  1.95744263e-03  -9.01866745e-20  -6.31391647e-09  -9.03546080e-11\n",
      "   -1.71378765e-12  -2.31591226e-03  -2.08462643e-09   9.43858158e-06\n",
      "    1.09960078e-05  -9.99995401e-01   1.04995375e-18   7.02291458e-07\n",
      "   -2.62410474e-07   5.55179440e-05]\n",
      " [ -2.05838653e-03   9.18110868e-20   6.12786720e-09  -3.18132682e-09\n",
      "    1.66576922e-12   2.43544259e-03   2.18574173e-09  -9.92532200e-06\n",
      "   -1.15631392e-05  -9.67271945e-06   9.99994914e-01  -6.81893310e-07\n",
      "    2.54677914e-07  -5.41930261e-05]\n",
      " [ -6.45375279e-01  -1.01709823e-06   3.17641550e-06   4.54663478e-08\n",
      "    8.56817349e-10   7.63345342e-01   6.99811870e-07  -3.11193229e-03\n",
      "   -3.62525617e-03  -3.03273167e-03  -3.18912013e-03  -1.02629740e-03\n",
      "    1.31990392e-04  -2.74111800e-02]\n",
      " [ -2.05134425e-05   7.07107053e-01  -2.03931120e-04   5.99970635e-10\n",
      "    1.11750675e-11   1.01493558e-04  -2.36186178e-06  -9.85881012e-08\n",
      "   -1.75220385e-07  -9.63962655e-08  -1.15906596e-07  -1.04001473e-05\n",
      "   -7.07106462e-01  -1.21312705e-04]\n",
      " [ -5.87984572e-03   6.21591320e-06  -3.74951679e-06  -5.36372573e-08\n",
      "   -9.98932662e-10   3.09214390e-02  -1.78983645e-08  -2.82572468e-05\n",
      "   -5.09886831e-05  -2.76304267e-05  -3.32446506e-05   1.27565083e-03\n",
      "   -1.60669896e-04   9.99503694e-01]\n",
      " [ -5.05567214e-04  -4.79908053e-02  -2.31454264e-03  -3.33237006e-05\n",
      "   -6.20672019e-07   8.75063241e-04  -2.68120251e-05  -2.43662500e-06\n",
      "   -3.05493712e-06  -2.37574905e-06  -2.55039355e-06   9.97689507e-01\n",
      "   -4.80044867e-02  -1.31080851e-03]\n",
      " [ -1.47074430e-05   7.05470244e-01  -4.01965428e-03  -5.46165251e-05\n",
      "   -1.01726245e-06  -4.13668925e-05  -4.65651237e-05  -7.11654774e-08\n",
      "   -3.69754635e-08  -6.91128551e-08  -6.16150727e-08   6.78694224e-02\n",
      "    7.05470986e-01   2.35743861e-05]\n",
      " [  5.49227983e-07  -2.86932910e-03  -9.99819735e-01  -1.43077527e-02\n",
      "   -2.66488495e-04   1.57438304e-06  -1.15823830e-02   2.65678644e-09\n",
      "   -1.90511576e-09   2.58091866e-09   2.25045394e-09  -2.58247837e-03\n",
      "   -2.58090418e-03  -8.98211783e-07]\n",
      " [  8.50952356e-13  -4.12398388e-06  -1.43108981e-02   9.99839349e-01\n",
      "    1.07923688e-02  -8.16975129e-13   4.24958535e-09   3.52847445e-11\n",
      "   -9.35529659e-11   4.00028262e-15   3.26851453e-09   4.15766570e-09\n",
      "    4.15684882e-09   1.60288045e-12]\n",
      " [  6.01318330e-15  -3.22835747e-08  -1.12039772e-04  -1.07950775e-02\n",
      "    9.99941725e-01  -8.13503478e-15   3.54201124e-11   3.26884507e-09\n",
      "    1.38790903e-13   1.97002319e-16  -3.52894634e-11   3.55750485e-11\n",
      "    3.55670328e-11   1.35969284e-14]]\n",
      "||f||: 6.89338392446e-16\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMwAAABHCAYAAABLVajpAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAB6lJREFUeJztmn/MVmUZxz+X/AYhMRE3p5SAb6uJEGYLsv6oVqzA0a/l\nKJhWw37MrawIHZkZOUrT1dqwmoA/RrQyyxb9sFZWy1YDQ9ZYtWCKINkyLRALufrjvp+4PZznec/1\nPO+7532372c7e55zXde5r/u+z/mec9/3OebuCCGacUq/KyDEaEKCESKABCNEAAlGiAASjBABJBgh\nAkgwQgSQYIQIIMEIEUCCESKABCNEAAlGiAASjBABJBghAkgwQgSQYIQIIMEIEUCCESKABCNEAAlG\niAASjBABxva7Ak0ws2XAeuBMYEY2PwY8CVwOfAh4BXA+MC77dwOPufuSLnOeDawFjgMTgUnABnff\n3WUzyrKvBsa6+4ZucprZjcB3gT3As8B5wFLgDnc/0EVc07wDwOeAfdl0BvBxd/9bJe6VwGrgCDA5\nl7e+m3aY2ZuAjcAfgGdy3PGimN+6+0ZqaNfPhX8y8Bt3v7DOX4u7j5oNuC531nPAe2r8e1v+HvOc\nDnwHmFnYXpRP7Owey54F/Bv4VLc5cxvL7b/AtTW5Bo1rmheYBjwKXFbY1gIP54uyZZtPEsH4wvYV\n4ClgXhf1+2g+33XbMeANkX4u/BcBv4teK6N5SGbDWPYVwP3ufqhlcPd9wBbgfT2WfQ3pjttLzkeA\nrwL3AjcBC9x9fU2ZTeKa5l1DenpvK2wbgQHgvYVtJekpsbSw/QCYmnNF6zcHOIckwDGtDbgE+LK7\n/6Sm3dCmn83sJWb2feCDJMGFGBVDsj5wHjCTdGcsOQq8sNtCzWw58DPg/T3m/Ku7X9kgZZO4pnnf\nThr+/H845O5Pmtke4B3Abdm8k/Q0eao4dmr+PdJF/Y55MXwEMLNTgWuBt9Yd0Kmf3X0P8JYctwm4\neJD8z2M0P2GGk4eA5WZ2t5mdBmBmE4B3A5u7KdDMpgBL3H1bm5Ahz9mQQfPmC3Qu6YlQ5QCwsLXj\n7ne6+3R3v7+IWUi6m2+NVs7dr6oxbwDWufuzVUeDfu6JvgnGzLaY2REzO25mB83sC2a2w8z2m9lu\nM1s9jLnnmtkBM7u5Tchm0vj2MuCPZrYC+Dqw1ruf9K8Fbuzgj+ScYGZrzOwmM/u8mX3bzObWlNkk\nrkneWfn36Zoch4FpZjauxoeZzQZWAR9294e7bEdZ3iLA3H1Hm5DB+rk3epnA9rqRxrStSfybs20S\n8Kdsv6YSX0769wE7im0nJ1ZQOk7kSOPfY8CPOsScCmzPuY4D3wPO7LKdFwJrKpPdkyajTXMCfwbO\nLvZXAI9XYwNxHfMCr8r262rqckc+bkbFfinwJdLiwZrqcZH6VY75PXBuL/1c+DcNdq2cdEyfBbOq\n7gIHbsj2w8Bphb0UzMqa8hqvkgEvBiZ28H+SNC5fAvwll3sAeFmwjUa6i5crSe0E0ygn6Q5b7p+S\n++rWLuM65iWN89vVeWs+H2e1af9Y0nziV8D0bupX+F8H7O61nwt/WDAjdQ7zUP6dCLx2OBK4+153\nP1rnM7OPAIvdfbW7bwcuAG4hvQe6K5hqNbDJ3TuuyERyej7bxf5x4AnSXT0U1zDvEx2qPiX//qvO\nmdt9PbCItKoWbkfBB4AH2/ga9XOvjFTBlCssM9pGDR/rgE+0dtz9GXe/mvSCdF5+gTcoZjYTeKm7\n/2KocprZA2b2QM3xY0irXUTiGuY9BDgwvaa8KcA/3f1wzjtgZhdUYlrzjbfll4WR+rXaMxZ4I3Cw\nxhfp554YqcvK5XLmSR00nJjZDOAFpKHJ83D328xsA+nJ14TXAwNmdk9hG59/32Vm80lzgF8Hcs4n\njf2rnMGJN/CN4pq21d2PmNlO0vuQKnPIIwIzm5r/jzGzAXffm2Oey79GEkSkHS0uJonz7zW+Rv3s\n7vfWHBsjMn4b6o32c5hbsv1pYHJhH8o5zDnAuDa+A8CiGvtU0tLquMI2hw5zoZoyZuU6rusmJ/BN\n4PRKzAIqiySBuKZ5rwcercTMzuVdmfcnAP8hTfTLuefCHPdgtH6Fb2X2re6lnysxo3fST1p2hDR2\nPphtV1TiPz0UggEWk1bJ7mvjfyfpk49zC9u0fJKXF7ZLcl22B9o8N9fxhi5zXkR6KpWfnmwBflkR\nctO4pnnPAv4BrChst3LypzGfBa6qtO1O0s1vQbR+he9jud8u76WfKzHfyOdv0mgUzBdJS4b7gZ+T\nXj614pblE/M4J74jegTYRbp73Z79Rwv/rnYXMulzjoOkTyva1e3VpG+stuZtG/CaSsz5g5VTxE4l\nrRbtz/U7QhqKLYvkzHGL8wW9GbiHdPcf30Nc07zzgPuAm4GvAd+iWBaunNetWRA/zv/ndFu/HHsp\nSbAv76WfSXPiH+brpXWtHAJ+SvGdXLvNciF9wcxWkR6L7un7ICFGNCN1lUyIEUm/BTOcXxwLMeT0\n81uy24HPkNb3MbNdZra081FC9Je+zmGEGG30e0gmxKhCghEigAQjRAAJRogAEowQASQYIQJIMEIE\nkGCECCDBCBFAghEigAQjRAAJRogAEowQASQYIQJIMEIEkGCECCDBCBFAghEigAQjRAAJRogAEowQ\nASQYIQJIMEIEkGCECCDBCBFAghEigAQjRAAJRogAEowQASQYIQL8Dyucs9giPM4bAAAAAElFTkSu\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x887a4a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ea7978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQcAAABHCAYAAAAKhIJ/AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nx0nyf5H3FPppTaFQAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x8904cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAUAAAABHCAYAAAB24p6mAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x892de10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy import linalg\n",
    "from scipy.optimize import root, fsolve\n",
    "eps = np.finfo(float).eps\n",
    "\n",
    "comps = np.array([\n",
    "        'H2O', 'H3O(+)', 'HO(-)', 'HCO3(-)', 'Na(+)', \n",
    "        'CO3(2-)', 'CO2', 'H2CO3', 'CO2'\n",
    "    ])\n",
    "\n",
    "mm = np.array([\n",
    "        18, 19, 17, 61, 23, 60, 44, 62, 44\n",
    "    ], dtype=float)\n",
    "\n",
    "pkw = 13.99602524\n",
    "mm0 = mm[0]\n",
    "rho0 = 1.0\n",
    "ph0 = pkw/2\n",
    "xw0nahco3 = 0.001\n",
    "\n",
    "x = np.ones_like(mm)*eps\n",
    "x[3] = xw0nahco3/(mm[3]+mm[4])/(xw0nahco3/(mm[3]+mm[4])+xw0nahco3/(mm[3]+mm[4])+(1-xw0nahco3)/mm[0])\n",
    "x[4] = xw0nahco3/(mm[3]+mm[4])/(xw0nahco3/(mm[3]+mm[4])+xw0nahco3/(mm[3]+mm[4])+(1-xw0nahco3)/mm[0])\n",
    "\n",
    "\n",
    "a = np.array([\n",
    "        [1 + mm0/rho0*10**(-ph0)/1000.0, mm0/rho0*10**(-ph0)/1000.0],\n",
    "        [mm0/rho0*10**(ph0-pkw)/1000.0,1 + mm0/rho0*10**(ph0-pkw)/1000.0]\n",
    "    ])\n",
    "b = np.array([\n",
    "        [mm0/rho0*10**(-ph0)/1000.0*(1 - x[3] - x[4])],\n",
    "        [mm0/rho0*10**(ph0-pkw)/1000.0*(1 - x[3] - x[4])]\n",
    "    ])\n",
    "\n",
    "x[1:2+1] = linalg.inv(a).dot(b).flatten()\n",
    "x[0] = 1 - sum(x[1:])\n",
    "\n",
    "print 'mole frac.'\n",
    "print x\n",
    "print 'mass frac.'\n",
    "print np.multiply(x, mm)/sum(np.multiply(x, mm))\n",
    "\n",
    "c0 = np.ones([len(mm)-1,])*eps\n",
    "c0 = x[:8]/x[0]*rho0/mm0*1000.0\n",
    "# v_g = const. = 50mL, nco2 = pco2 v_g / (RT)\n",
    "# pco2 = x[7]*8.314/1000.0*298.15/(50.0/1000/1000) # pco2 [=] kPa\n",
    "p0co2 = 10**-3.5*101.325 # 10^-3.5atm = 10^-3.5*101.325 kPa\n",
    "c0[6] = p0co2 / (1670.0 *100) * (sum(c0)-c0[6]) / (1 - p0co2 / (1670.0 *100))\n",
    "xi = np.ones(5)*eps\n",
    "\n",
    "x0 = np.append(np.append(c0, p0co2), xi)\n",
    "\n",
    "def eq_set(x):\n",
    "    # x, [nh2o, nh30, nho, nhco3, nna, nco3, nco2, nh2co3, pco2,\n",
    "    #     xi1, xi2, xi3, xi4, xi5]\n",
    "    c = x[:8]\n",
    "    xco2 = c[6] / sum(c)\n",
    "    pco2 = x[8]\n",
    "    xi = x[9:]\n",
    "    return np.array([\n",
    "            1670.0*100*xco2 - pco2, # Hco2 = pco2/xco2\n",
    "            10**-2.821023053*c[6] - c[7], # 10^-pK2 = ch2co3/cco2\n",
    "            10**-3.539912399*c[7] - c[1]*c[3], # 10^-pK3 = chco3*ch3o/ch2co3\n",
    "            10**-10.32991986*c[3] - c[1]*c[5], # 10^-pK4 = cco3*ch3o/chco3\n",
    "            10**-13.99602524 - c[1]*c[2], # 10^-pKw = ch3o*cho   \n",
    "            c[0] - c0[0] - (- xi[0] - xi[1] - xi[2] - xi[3] - 2*xi[4]),\n",
    "            c[1] - c0[1] - (+ xi[2] + xi[3] + xi[4]),\n",
    "            c[2] - c0[2] - (+ xi[4]),\n",
    "            c[3] - c0[3] - (+ xi[2] - xi[3]),\n",
    "            c[4] - c0[4] - (+ 0),\n",
    "            c[5] - c0[5] - (+ xi[3]),\n",
    "            c[6] - c0[6] - (- xi[0] - xi[1]),\n",
    "            c[7] - c0[7] - (+ xi[1] - xi[2]),\n",
    "            pco2 - p0co2 - (+ xi[0])*8.314*298.15\n",
    "        ]).T\n",
    "\n",
    "def jac_eq_set(x):\n",
    "    j = np.zeros([len(x), len(x)])\n",
    "    \n",
    "    c = x[:8]\n",
    "    xco2 = c[6] / sum(c)\n",
    "    pco2 = x[8]\n",
    "    xi = x[9:]\n",
    "    \n",
    "    d_f1_dc = np.zeros([9, ])\n",
    "    \n",
    "    d_f1_dc[0:6] = 1670.0*100*(-1.0/sum(c)**2)*c[6]\n",
    "    d_f1_dc[6] = sum([c_ for i, c_ in enumerate(c) if i!=6])/sum(c)**2\n",
    "    d_f1_dc[7] = 1670.0*100*(-1.0/sum(c)**2)*c[6]\n",
    "    d_f1_dc[8] = -1.0\n",
    "    \n",
    "    j[0, :8+1] = d_f1_dc\n",
    "\n",
    "    j[1, 6], j[1, 7] = 10**-2.821023053, -1\n",
    "    j[2, 1], j[2, 3], j[2, 7] = -c[3], -c[1], 10**-3.539912399\n",
    "    j[3, 1], j[3, 3], j[3, 5] = -c[5], 10**-10.32991986, -c[1]\n",
    "    j[4, 1], j[4, 2] = -c[2], -c[1]\n",
    "    for ind in  range(8+1):\n",
    "        j[ind + 5, ind] = +1\n",
    "    j[5, 9:14] = np.array([+1, +1, +1, +1, +2])\n",
    "    j[6, 11:14] = np.array([-1, -1, -1])\n",
    "    j[7, 13] = -1\n",
    "    j[8, 11:13] = np.array([-1, +1])\n",
    "    j[10, 12] = -1\n",
    "    j[11, 9:11] = +1\n",
    "    j[12, 10:12] = np.array([-1, +1])\n",
    "    j[13, 9] = -1*8.314*298.15\n",
    "    \n",
    "    return j\n",
    "\n",
    "#res = root(eq_set, x0, jac=jac_eq_set, tol=1e-10)\n",
    "res = root(eq_set, x0, jac=False, tol=1e-10)\n",
    "#res = root(eq_set, x0, method='broyden1', jac=jac_eq_set, tol=1e-10, options={'line_search': 'wolfe'})\n",
    "#res = root(eq_set, res.x, jac=False, tol=1e-12, method='broyden1')\n",
    "for item in res.keys():\n",
    "    if item not in ['qtf', 'r']:\n",
    "        print str(item) + ': ' + str(getattr(res, str(item)))\n",
    "print '||f||: ' + str(np.sqrt(res.fun.T.dot(res.fun)))\n",
    "print ''\n",
    "print_latex('\\\\bf{pH}: ' + str(-np.log10(res.x[1])))\n",
    "print_latex('\\\\bf{pOH}: ' + str(-np.log10(res.x[2])) + \\\n",
    "            ', pH+pOH=' + str(-np.log10(res.x[1])+-np.log10(res.x[2])))\n",
    "print_latex('\\\\bf{p_{CO2}}:' + str(res.x[8]) + ' kPa')\n",
    "print_latex('\\\\Sigma{c_i\\\\times z_i}:' + \\\n",
    "            str(res.x[1]-res.x[2]-res.x[3]+res.x[4]-2*res.x[5]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
       "         0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
       "         0.00000000e+00,   0.00000000e+00,   1.00000000e+00,\n",
       "        -2.47881910e+03,   0.00000000e+00,   0.00000000e+00,\n",
       "         0.00000000e+00,   0.00000000e+00])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jac_eq_set(res.x)[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x0\n",
      "C0=5.55555555555555500291e+01,\n",
      "C1=1.00458659795015562355e-07,\n",
      "C2=1.00458659795015575590e-07,\n",
      "C3=1.19166786264420683505e-02,\n",
      "C4=1.19166786264420683505e-02,\n",
      "C5=1.23411034977318318904e-14,\n",
      "C6=1.06638491665527950045e-05,\n",
      "C7=1.23411034977318318904e-14,\n",
      "pco2=3.20417783916561033086e-02,\n",
      "x0=2.22044604925031308085e-16,\n",
      "x1=2.22044604925031308085e-16,\n",
      "x2=2.22044604925031308085e-16,\n",
      "x3=2.22044604925031308085e-16,\n",
      "x4=2.22044604925031308085e-16,\n"
     ]
    }
   ],
   "source": [
    "print 'x0'\n",
    "for index, num in enumerate(x0):\n",
    "    if index < 8:\n",
    "        print 'C' + str(index) + '=' + '%.20e' % num + ','\n",
    "    elif index == 8:\n",
    "        print 'pco2' + '=' + '%.20e' % num + ','\n",
    "    else:\n",
    "        print 'x' + str(index-9) + '=' + '%.20e' % num + ','"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x:\n",
      "C0=5.55556289267577199098e+01,\n",
      "C1=3.26903554347567655169e-09,\n",
      "C2=3.08713141646693843776e-06,\n",
      "C3=1.15820991613138461751e-02,\n",
      "C4=1.19166786264420683505e-02,\n",
      "C5=1.65747801385990306934e-04,\n",
      "C6=8.69245344681667691557e-05,\n",
      "C7=1.31256046958327811330e-07,\n",
      "pco2=2.61183127920939117672e-01,\n",
      "x0=9.24397224183414839517e-05,\n",
      "x1=-1.68700407719955461491e-04,\n",
      "x2=-1.68831663754572664209e-04,\n",
      "x3=1.65747801373649213076e-04,\n",
      "x4=2.98667275667192327245e-06,\n"
     ]
    }
   ],
   "source": [
    "print 'x:'\n",
    "for index, num in enumerate(res.x):\n",
    "    if index < 8:\n",
    "        print 'C' + str(index) + '=' + '%.20e' % num + ','\n",
    "    elif index == 8:\n",
    "        print 'pco2' + '=' + '%.20e' % num + ','\n",
    "    else:\n",
    "        print 'x' + str(index-9) + '=' + '%.20e' % num + ','"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "\n",
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      "\n",
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      "\n",
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      "\n",
      ";k=3;backtrack=1;lambda_ls=0.5;accum_step=2.5;stop=False;X=[55.5558035458,9.86761966997e-09,9.17278949492e-06,0.0107199145484,0.0119166786264,0.000593800578106,0.000267635864546,4.04130155192e-07,0.888690313311,0.000345587354446,-0.000602559369826,-0.000602963499969,0.000593800578094,9.07233083513e-06];||X(k)-X(k-1)||=0.704684651213;f(X)=[-0.0845207681222,-5.29395592034e-23,1.07958822488e-11,-5.35789765702e-12,-8.04216557208e-14,-2.61097567178e-15,-3.70576914424e-20,0.0,8.67361737988e-19,0.0,0.0,5.42101086243e-20,5.73335426173e-20,-1.11022302463e-16];||f(X)||=0.0845207681222;j(X)=[[-0.014468864913452851, -0.014468864913452851, -0.014468864913452851, -0.014468864913452851, -0.014468864913452851, -0.014468864913452851, 0.017992219833285056, -0.014468864913452851, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001509999998980679, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.01071991454837942, 0.0, -9.867619669966469e-09, 0.0, 0.0, 0.0, 0.0002884613296209884, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.0005938005781060392, 0.0, 4.678214600282143e-11, 0.0, -9.867619669966469e-09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -9.172789494922738e-06, -9.867619669966469e-09, 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, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0], [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, -1.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 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, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 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, 0.0, 1.0, 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, 0.0, 1.0, -2478.8190999999997, 0.0, 0.0, 0.0, 0.0]];Y=[-0.000308021096668,-1.12405826702e-08,5.20444413872e-07,-6.08180210088e-05,0.0,3.01431680061e-05,-0.000307511892836,-4.64342957869e-07,0.839454787145,0.000338651088797,-3.11391959605e-05,-3.06748530027e-05,3.01431680061e-05,5.20444413872e-07];||Y||=0.839454972713;g=nan;|g-g1|=nan\n",
      "\n",
      ";k=4;backtrack=0;lambda_ls=1.0;accum_step=3.5;stop=False;X=[55.5556469793,4.04747064703e-09,6.43305541431e-06,0.0111044829734,0.0119166786264,0.000402883322543,0.000108323802572,1.63568941774e-07,0.804166185444,0.00031148880814,-0.000409148761545,-0.000409312330475,0.000402883322531,6.33259675452e-06];||X(k)-X(k-1)||=0.00714467496298;f(X)=[-0.478683278115,-2.64697796017e-23,2.23824554335e-12,-1.11116687842e-12,-1.59456606324e-14,1.10865093148e-15,3.55489140051e-20,0.0,-6.50521303491e-19,0.0,5.42101086243e-20,-1.35525271561e-20,-2.32404664903e-20,0.0];||f(X)||=0.478683278115;j(X)=[[-0.005856201413773767, -0.005856201413773767, -0.005856201413773767, -0.005856201413773767, -0.005856201413773767, -0.005856201413773767, 0.017992311940718184, -0.005856201413773767, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001509999998980679, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.011104482973436114, 0.0, -4.04747064703097e-09, 0.0, 0.0, 0.0, 0.0002884613296209884, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.00040288332254348426, 0.0, 4.678214600282143e-11, 0.0, -4.04747064703097e-09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -6.433055414314924e-06, -4.04747064703097e-09, 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, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0], [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, -1.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 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, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 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, 0.0, 1.0, 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, 0.0, 1.0, -2478.8190999999997, 0.0, 0.0, 0.0, 0.0]];Y=[-0.000156566507742,-5.82014902294e-09,-2.73973408061e-06,0.000384568425057,0.0,-0.000190917255563,-0.000159312061974,-2.40561213419e-07,-0.0845241278671,-3.40985463066e-05,0.000193410608281,0.000193651169494,-0.000190917255563,-2.73973408061e-06];||Y||=0.0845261791576;g=nan;|g-g1|=nan\n",
      "\n",
      ";k=5;backtrack=0;lambda_ls=1.0;accum_step=4.5;stop=False;X=[55.5556327119,3.42158412683e-09,3.48817971186e-06,0.0115222365219,0.0119166786264,0.000195478673234,9.11108797541e-05,1.37577428336e-07,0.325481466738,0.000118378823346,-0.000198825853934,-0.00019896343135,0.000195478673222,3.38772105206e-06];||X(k)-X(k-1)||=0.229139446765;f(X)=[-0.0517194728318,2.64697796017e-23,2.61466314729e-13,-1.29811774229e-13,-1.84315800582e-15,1.93016447009e-15,1.60274515488e-20,-4.23516473627e-22,-8.67361737988e-19,0.0,0.0,0.0,5.88952596138e-20,5.55111512313e-17];||f(X)||=0.0517194728318;j(X)=[[-0.004925605203345656, -0.004925605203345656, -0.004925605203345656, -0.004925605203345656, -0.004925605203345656, -0.004925605203345656, 0.01799226057113341, -0.004925605203345656, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001509999998980679, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.011522236521870047, 0.0, -3.4215841268343927e-09, 0.0, 0.0, 0.0, 0.0002884613296209884, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.00019547867323448646, 0.0, 4.678214600282143e-11, 0.0, -3.4215841268343927e-09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -3.488179711856462e-06, -3.4215841268343927e-09, 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, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0], [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, -1.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 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, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 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, 0.0, 1.0, 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, 0.0, 1.0, -2478.8190999999997, 0.0, 0.0, 0.0, 0.0]];Y=[-1.42674212304e-05,-6.25886520197e-10,-2.94487570246e-06,0.000417753548434,0.0,-0.000207404649309,-1.72129228183e-05,-2.5991513438e-08,-0.478684718706,-0.000193109984793,0.000210322907611,0.000210348899125,-0.000207404649309,-2.94487570246e-06];||Y||=0.478685122774;g=nan;|g-g1|=nan\n",
      "\n",
      ";k=6;backtrack=0;lambda_ls=1.0;accum_step=5.5;stop=False;X=[55.5556276378,3.22418492354e-09,3.15073539748e-06,0.0115744683985,0.0119166786264,0.000169531358394,8.56991316844e-05,1.29405688756e-07,0.273761793766,9.75141813995e-05,-0.000172549463917,-0.000172678869594,0.000169531358381,3.05027673769e-06];||X(k)-X(k-1)||=0.00267493051899;f(X)=[-0.0162606182056,-2.64697796017e-23,1.0310530827e-14,-5.12197927729e-15,-6.66112388142e-17,3.37986474745e-15,-2.30287082535e-20,0.0,-5.42101086243e-20,0.0,0.0,-1.35525271561e-20,1.33142991397e-20,2.77555756156e-17];||f(X)||=0.0162606182056;j(X)=[[-0.004633034554817508, -0.004633034554817508, -0.004633034554817508, -0.004633034554817508, -0.004633034554817508, -0.004633034554817508, 0.01799225732060538, -0.004633034554817508, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001509999998980679, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.01157446839846698, 0.0, -3.224184923537078e-09, 0.0, 0.0, 0.0, 0.0002884613296209884, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.00016953135839360424, 0.0, 4.678214600282143e-11, 0.0, -3.224184923537078e-09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -3.1507353974847232e-06, -3.224184923537078e-09, 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, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0], [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, -1.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 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, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 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, 0.0, 1.0, 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, 0.0, 1.0, -2478.8190999999997, 0.0, 0.0, 0.0, 0.0]];Y=[-5.07410635802e-06,-1.97399203297e-10,-3.37444314372e-07,5.22318765969e-05,0.0,-2.59473148409e-05,-5.41174806967e-06,-8.17173957968e-09,-0.0517196729724,-2.08646419468e-05,2.62763900165e-05,2.62845617561e-05,-2.59473148409e-05,-3.37444314372e-07];||Y||=0.0517197304613;g=nan;|g-g1|=nan\n",
      "\n",
      ";k=7;backtrack=0;lambda_ls=1.0;accum_step=6.5;stop=False;X=[55.5556294385,3.28707888198e-09,3.0686143448e-06,0.0115840634369,0.0119166786264,0.000164774931153,8.74177496475e-05,1.32000801879e-07,0.25750117609,9.09543571365e-05,-0.000167708257617,-0.000167840258407,0.000164774931141,2.96815568501e-06];||X(k)-X(k-1)||=0.000264407920598;f(X)=[0.00516391168574,0.0,-6.0346994804e-16,2.99150537162e-16,5.16491807426e-18,-1.73190455033e-15,2.40610296579e-20,0.0,-1.62630325873e-19,0.0,0.0,-1.35525271561e-20,-3.22931311141e-21,2.77555756156e-17];||f(X)||=0.00516391168574;j(X)=[[-0.004725944431523252, -0.004725944431523252, -0.004725944431523252, -0.004725944431523252, -0.004725944431523252, -0.004725944431523252, 0.01799225408434268, -0.004725944431523252, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001509999998980679, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.011584063436893957, 0.0, -3.2870788819763e-09, 0.0, 0.0, 0.0, 0.0002884613296209884, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.00016477493115343535, 0.0, 4.678214600282143e-11, 0.0, -3.2870788819763e-09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -3.0686143448044967e-06, -3.2870788819763e-09, 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, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0], [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, -1.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 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, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 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, 0.0, 1.0, 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, 0.0, 1.0, -2478.8190999999997, 0.0, 0.0, 0.0, 0.0]];Y=[1.80067611839e-06,6.28939584392e-11,-8.21210526802e-08,9.59503842698e-06,0.0,-4.75642724017e-06,1.71861796305e-06,2.59511312245e-09,-0.0162606176757,-6.55982426298e-06,4.84120629993e-06,4.83861118681e-06,-4.75642724017e-06,-8.21210526802e-08];||Y||=0.0162606248526;g=nan;|g-g1|=nan\n",
      "\n",
      ";k=8;backtrack=0;lambda_ls=1.0;accum_step=7.5;stop=False;X=[55.5556287055,3.26120673249e-09,3.09433826874e-06,0.0115813393677,0.0119166786264,0.000166124090861,8.67105138224e-05,1.30932875783e-07,0.262665084896,9.30375703916e-05,-0.000169084235048,-0.000169215167911,0.000166124090849,2.99387960894e-06];||X(k)-X(k-1)||=2.66659743811e-05;f(X)=[-0.00212502341451,0.0,-7.04775258633e-17,3.49056616437e-17,6.65533205386e-19,-2.02587241687e-15,5.90276085118e-21,0.0,7.5894152074e-19,0.0,0.0,0.0,-5.21454658153e-21,-2.77555756156e-17];||f(X)||=0.00212502341451;j(X)=[[-0.004687710593720973, -0.004687710593720973, -0.004687710593720973, -0.004687710593720973, -0.004687710593720973, -0.004687710593720973, 0.01799225521661825, -0.004687710593720973, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001509999998980679, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.011581339367682164, 0.0, -3.261206732489176e-09, 0.0, 0.0, 0.0, 0.0002884613296209884, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.00016612409086129133, 0.0, 4.678214600282143e-11, 0.0, -3.261206732489176e-09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -3.0943382687373876e-06, -3.261206732489176e-09, 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, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0], [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, -1.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 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, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 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, 0.0, 1.0, 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, 0.0, 1.0, -2478.8190999999997, 0.0, 0.0, 0.0, 0.0]];Y=[-7.3293387512e-07,-2.58721494871e-11,2.57239239329e-08,-2.72406921179e-06,0.0,1.34915970786e-06,-7.07235825068e-07,-1.06792609513e-09,0.00516390880612,2.0832132551e-06,-1.37597743003e-06,-1.37490950394e-06,1.34915970786e-06,2.57239239329e-08];||Y||=0.00516391076425;g=nan;|g-g1|=nan\n",
      "\n",
      ";k=9;backtrack=0;lambda_ls=1.0;accum_step=8.5;stop=False;X=[55.5556290207,3.27235710692e-09,3.08396250913e-06,0.0115824329607,0.0119166786264,0.000165582487808,8.70153354738e-05,1.31393156477e-07,0.260540062947,9.2180298496e-05,-0.000168531784803,-0.000168663177947,0.000165582487795,2.98350384933e-06];||X(k)-X(k-1)||=4.51572160244e-06;f(X)=[0.000915894130457,0.0,-1.21939716052e-17,6.03907683884e-18,1.15693604632e-19,2.72338033201e-16,-3.26901778081e-21,0.0,1.08420217249e-19,0.0,0.0,0.0,2.49345323848e-20,0.0];||f(X)||=0.000915894130457;j(X)=[[-0.004704189548391102, -0.004704189548391102, -0.004704189548391102, -0.004704189548391102, -0.004704189548391102, -0.004704189548391102, 0.017992254741746327, -0.004704189548391102, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001509999998980679, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.011582432960699338, 0.0, -3.272357106916855e-09, 0.0, 0.0, 0.0, 0.0002884613296209884, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.00016558248780769645, 0.0, 4.678214600282143e-11, 0.0, -3.272357106916855e-09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -3.0839625091267406e-06, -3.272357106916855e-09, 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, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0], [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, -1.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 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, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 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, 0.0, 1.0, 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, 0.0, 1.0, -2478.8190999999997, 0.0, 0.0, 0.0, 0.0]];Y=[3.15186262595e-07,1.11503744277e-11,-1.03757596106e-08,1.09359301717e-06,0.0,-5.41603053595e-07,3.04821651333e-07,4.60280693201e-10,-0.00212502194872,-8.57271895606e-07,5.52450244273e-07,5.5198996358e-07,-5.41603053595e-07,-1.03757596106e-08];||Y||=0.00212502272986;g=nan;|g-g1|=nan\n",
      "\n",
      ";k=10;backtrack=0;lambda_ls=1.0;accum_step=9.5;stop=False;X=[55.5556288865,3.26761326441e-09,3.0884685962e-06,0.0115819582515,0.0119166786264,0.000165817586968,8.68856534367e-05,1.31197336601e-07,0.261455956483,9.25497863442e-05,-0.000168771590614,-0.000168902787939,0.000165817586956,2.9880099364e-06];||X(k)-X(k-1)||=8.38861590248e-07;f(X)=[-0.000389654135203,0.0,-2.25194545094e-18,1.11527339082e-18,2.13761673928e-20,-3.37403716077e-16,2.40742645477e-20,0.0,-1.62630325873e-19,0.0,0.0,0.0,-9.92616735064e-21,-2.77555756156e-17];||f(X)||=0.000389654135203;j(X)=[[-0.004697178812431813, -0.004697178812431813, -0.004697178812431813, -0.004697178812431813, -0.004697178812431813, -0.004697178812431813, 0.01799225494531918, -0.004697178812431813, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001509999998980679, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.011581958251547637, 0.0, -3.2676132644082073e-09, 0.0, 0.0, 0.0, 0.0002884613296209884, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.00016581758696809025, 0.0, 4.678214600282143e-11, 0.0, -3.2676132644082073e-09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -3.088468596197536e-06, -3.2676132644082073e-09, 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, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0], [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, -1.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 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, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 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, 0.0, 1.0, 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, 0.0, 1.0, -2478.8190999999997, 0.0, 0.0, 0.0, 0.0]];Y=[-1.34183380514e-07,-4.74384250865e-12,4.5060870708e-09,-4.74709151701e-07,0.0,2.35099160394e-07,-1.29682037013e-07,-1.95819875757e-10,0.000915893535326,3.69487848196e-07,-2.39805811183e-07,-2.39609991307e-07,2.35099160394e-07,4.5060870708e-09];||Y||=0.000915893874992;g=nan;|g-g1|=nan\n",
      "\n",
      ";k=11;backtrack=0;lambda_ls=1.0;accum_step=10.5;stop=False;X=[55.5556289439,3.26964214585e-09,3.08655748863e-06,0.0115821596302,0.0119166786264,0.000165717854227,8.6941117158e-05,1.3128108682e-07,0.261066302607,9.23925929953e-05,-0.000168669860987,-0.000168801142061,0.000165717854215,2.98609882883e-06];||X(k)-X(k-1)||=1.51830255022e-07;f(X)=[0.000166651209359,0.0,-4.08573346001e-19,2.02345907153e-19,3.87741068171e-21,1.36018583549e-15,2.06464280893e-21,0.0,-4.87890977618e-19,0.0,0.0,-1.35525271561e-20,-2.40874994375e-21,0.0];||f(X)||=0.000166651209359;j(X)=[[-0.0047001772348511, -0.0047001772348511, -0.0047001772348511, -0.0047001772348511, -0.0047001772348511, -0.0047001772348511, 0.01799225485852273, -0.0047001772348511, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001509999998980679, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.011582159630166082, 0.0, -3.26964214584865e-09, 0.0, 0.0, 0.0, 0.0002884613296209884, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.0001657178542270932, 0.0, 4.678214600282143e-11, 0.0, -3.26964214584865e-09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -3.0865574886271137e-06, -3.26964214584865e-09, 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, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0], [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, -1.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 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, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 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, 0.0, 1.0, 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, 0.0, 1.0, -2478.8190999999997, 0.0, 0.0, 0.0, 0.0]];Y=[5.73728002605e-08,2.02888144044e-12,-1.91110757042e-09,2.01378618446e-07,0.0,-9.9732740997e-08,5.54637212341e-08,8.3750219007e-11,-0.000389653875651,-1.57193348902e-07,1.01729627668e-07,1.01645877449e-07,-9.9732740997e-08,-1.91110757042e-09];||Y||=0.000389654019641;g=nan;|g-g1|=nan\n",
      "\n",
      ";k=12;backtrack=0;lambda_ls=1.0;accum_step=11.5;stop=False;X=[55.5556289194,3.26877639043e-09,3.08737595167e-06,0.0115820733952,0.0119166786264,0.000165760562026,8.69174499866e-05,1.31245349391e-07,0.261232953707,9.24598230322e-05,-0.000168713423852,-0.000168844669189,0.000165760562014,2.98691729188e-06];||X(k)-X(k-1)||=2.7772609531e-08;f(X)=[-7.11124792921e-05,-2.64697796017e-23,-7.46583558711e-20,3.69745085969e-20,7.0858881291e-22,2.19334099494e-16,-3.123433993e-21,0.0,8.13151629364e-19,0.0,0.0,0.0,3.97046694025e-22,0.0];||f(X)||=7.11124792921e-05;j(X)=[[-0.004698897764707276, -0.004698897764707276, -0.004698897764707276, -0.004698897764707276, -0.004698897764707276, -0.004698897764707276, 0.01799225489560968, -0.004698897764707276, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001509999998980679, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.011582073395238642, 0.0, -3.268776390433573e-09, 0.0, 0.0, 0.0, 0.0002884613296209884, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.0001657605620264132, 0.0, 4.678214600282143e-11, 0.0, -3.268776390433573e-09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -3.0873759516732315e-06, -3.268776390433573e-09, 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, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0], [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, -1.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 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, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 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, 0.0, 1.0, 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, 0.0, 1.0, -2478.8190999999997, 0.0, 0.0, 0.0, 0.0]];Y=[-2.44847699866e-08,-8.65755415077e-13,8.18463046118e-10,-8.6234927441e-08,0.0,4.270779932e-08,-2.36671713357e-08,-3.57374286928e-11,0.000166651099527,6.72300368859e-08,-4.35628655502e-08,-4.35271281215e-08,4.270779932e-08,8.18463046118e-10];||Y||=0.000166651161205;g=nan;|g-g1|=nan\n",
      "\n",
      ";k=13;backtrack=0;lambda_ls=1.0;accum_step=12.5;stop=False;X=[55.5556289299,3.26914617911e-09,3.08702690116e-06,0.0115821101735,0.0119166786264,0.000165742347615,8.69275589182e-05,1.31260613878e-07,0.261161841274,9.2431135004e-05,-0.000168694844756,-0.000168826105357,0.000165742347602,2.98656824136e-06];||X(k)-X(k-1)||=5.05698175584e-09;f(X)=[3.03741911792e-05,2.64697796017e-23,-1.36001740518e-20,6.73548323052e-21,1.29074928037e-22,-4.12308533669e-16,-2.52786395196e-21,0.0,-7.5894152074e-19,0.0,0.0,1.35525271561e-20,-6.53803556162e-21,-2.77555756156e-17];||f(X)||=3.03741911792e-05;j(X)=[[-0.004699444263318518, -0.004699444263318518, -0.004699444263318518, -0.004699444263318518, -0.004699444263318518, -0.004699444263318518, 0.01799225487977779, -0.004699444263318518, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001509999998980679, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.011582110173482596, 0.0, -3.2691461791111696e-09, 0.0, 0.0, 0.0, 0.0002884613296209884, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.0001657423476145872, 0.0, 4.678214600282143e-11, 0.0, -3.2691461791111696e-09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -3.0870269011585073e-06, -3.2691461791111696e-09, 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, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0], [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, -1.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 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, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 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, 0.0, 1.0, 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, 0.0, 1.0, -2478.8190999999997, 0.0, 0.0, 0.0, 0.0]];Y=[1.04576120779e-08,3.69788677597e-13,-3.49050514724e-10,3.67782439546e-08,0.0,-1.8214411826e-08,1.01089315711e-08,1.52644866621e-11,-7.11124322117e-05,-2.86880281872e-08,1.8579096616e-08,1.85638321294e-08,-1.8214411826e-08,-3.49050514724e-10];||Y||=7.11124585135e-05;g=nan;|g-g1|=nan\n",
      "\n",
      ";k=14;backtrack=0;lambda_ls=1.0;accum_step=13.5;stop=False;X=[55.5556289254,3.26898829721e-09,3.08717602718e-06,0.0115820944609,0.0119166786264,0.000165750129274,8.69232428948e-05,1.31254096683e-07,0.261192215445,9.24433884884e-05,-0.000168702782217,-0.000168834036301,0.000165750129262,2.98671736738e-06];||X(k)-X(k-1)||=9.225909532e-10;f(X)=[-1.29683061013e-05,0.0,-2.48074050644e-21,1.22858333339e-21,2.35443015565e-23,-2.61149066781e-15,-1.66362564797e-20,0.0,6.50521303491e-19,0.0,0.0,1.35525271561e-20,-5.00278834472e-21,-2.77555756156e-17];||f(X)||=1.29683061013e-05;j(X)=[[-0.0046992109349246825, -0.0046992109349246825, -0.0046992109349246825, -0.0046992109349246825, -0.0046992109349246825, -0.0046992109349246825, 0.017992254886538887, -0.0046992109349246825, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001509999998980679, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.011582094460878881, 0.0, -3.268988297206125e-09, 0.0, 0.0, 0.0, 0.0002884613296209884, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.0001657501292744936, 0.0, 4.678214600282143e-11, 0.0, -3.268988297206125e-09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -3.0871760271798893e-06, -3.268988297206125e-09, 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, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0], [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, -1.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 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, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 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, 0.0, 1.0, 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, 0.0, 1.0, -2478.8190999999997, 0.0, 0.0, 0.0, 0.0]];Y=[-4.46499109658e-09,-1.57881905045e-13,1.49126021382e-10,-1.57126037153e-08,0.0,7.78165990639e-09,-4.31602336943e-09,-6.51719528341e-12,3.03741711088e-05,1.22534843744e-08,-7.93746100497e-09,-7.93094380968e-09,7.78165990639e-09,1.49126021382e-10];||Y||=3.03741823462e-05;g=nan;|g-g1|=nan\n",
      "\n",
      ";k=15;backtrack=0;lambda_ls=1.0;accum_step=14.5;stop=False;X=[55.5556289273,3.26905571705e-09,3.08711236425e-06,0.0115821011688,0.0119166786264,0.000165746807204,8.6925085954e-05,1.31256879702e-07,0.261179247148,9.2438156845e-05,-0.000168699393632,-0.0001688306505,0.000165746807191,2.98665370445e-06];||X(k)-X(k-1)||=1.68176865124e-10;f(X)=[5.53781874191e-06,0.0,-4.52248075216e-22,2.23973489185e-22,4.29214485365e-24,-1.10016704948e-15,5.75717706337e-21,0.0,1.08420217249e-19,0.0,0.0,0.0,1.15672936859e-20,0.0];||f(X)||=5.53781874191e-06;j(X)=[[-0.004699310572482959, -0.004699310572482959, -0.004699310572482959, -0.004699310572482959, -0.004699310572482959, -0.004699310572482959, 0.01799225488365202, -0.004699310572482959, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001509999998980679, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.011582101168750959, 0.0, -3.2690557170510095e-09, 0.0, 0.0, 0.0, 0.0002884613296209884, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.00016574680720363136, 0.0, 4.678214600282143e-11, 0.0, -3.2690557170510095e-09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -3.0871123642463875e-06, -3.2690557170510095e-09, 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, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0], [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, -1.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 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, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 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, 0.0, 1.0, 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, 0.0, 1.0, -2478.8190999999997, 0.0, 0.0, 0.0, 0.0]];Y=[1.90665726645e-09,6.74198448848e-14,-6.36629335018e-11,6.70787207714e-09,0.0,-3.32207086223e-09,1.84305914127e-09,2.78301930144e-12,-1.29682975251e-05,-5.23164337614e-09,3.38858423485e-09,3.38580121556e-09,-3.32207086223e-09,-6.36629335018e-11];||Y||=1.29683023224e-05;g=nan;|g-g1|=nan\n",
      "\n",
      ";k=16;backtrack=0;lambda_ls=1.0;accum_step=15.5;stop=False;X=[55.5556289265,3.26902692912e-09,3.08713955126e-06,0.0115820983042,0.0119166786264,0.000165748225877,8.69242989773e-05,1.31255691367e-07,0.261184784963,9.24403908988e-05,-0.000168700840709,-0.000168832096389,0.000165748225864,2.98668089146e-06];||X(k)-X(k-1)||=3.0667418561e-11;f(X)=[-2.36461994912e-06,2.64697796017e-23,-8.24660296624e-23,4.08406291061e-23,7.82657303062e-25,1.0803668073e-15,6.35274710441e-22,0.0,-5.42101086243e-20,0.0,0.0,1.35525271561e-20,-2.64433098221e-20,2.77555756156e-17];||f(X)||=2.36461994912e-06;j(X)=[[-0.004699268027761154, -0.004699268027761154, -0.004699268027761154, -0.004699268027761154, -0.004699268027761154, -0.004699268027761154, 0.01799225488488475, -0.004699268027761154, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001509999998980679, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.011582098304189383, 0.0, -3.2690269291234566e-09, 0.0, 0.0, 0.0, 0.0002884613296209884, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.0001657482258765189, 0.0, 4.678214600282143e-11, 0.0, -3.2690269291234566e-09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -3.087139551259069e-06, -3.2690269291234566e-09, 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, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0], [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, -1.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 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, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 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, 0.0, 1.0, 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, 0.0, 1.0, -2478.8190999999997, 0.0, 0.0, 0.0, 0.0]];Y=[-8.14133841561e-10,-2.87879275531e-14,2.71870126812e-11,-2.86456157574e-09,0.0,1.41867288751e-09,-7.86976716969e-10,-1.18833484182e-12,5.53781508093e-06,2.23405373992e-09,-1.44707702295e-09,-1.44588868812e-09,1.41867288751e-09,2.71870126812e-11];||Y||=5.53781712959e-06;g=nan;|g-g1|=nan\n",
      "\n",
      ";k=17;backtrack=0;lambda_ls=1.0;accum_step=16.5;stop=False;X=[55.5556289269,3.26903922182e-09,3.08712794277e-06,0.0115820995273,0.0119166786264,0.000165747620121,8.69246350231e-05,1.31256198796e-07,0.261182420345,9.24394369694e-05,-0.000168700222826,-0.000168831479012,0.000165747620109,2.98666928297e-06];||X(k)-X(k-1)||=5.59142424666e-12;f(X)=[1.00971311112e-06,-2.64697796017e-23,-1.50314226937e-23,7.4464430485e-24,1.42700204589e-25,-8.2604008269e-16,-4.28810429547e-21,0.0,-7.5894152074e-19,0.0,0.0,0.0,4.20869495667e-21,0.0];||f(X)||=1.00971311112e-06;j(X)=[[-0.004699286194724284, -0.004699286194724284, -0.004699286194724284, -0.004699286194724284, -0.004699286194724284, -0.004699286194724284, 0.017992254884358374, -0.004699286194724284, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001509999998980679, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.011582099527320823, 0.0, -3.2690392218163145e-09, 0.0, 0.0, 0.0, 0.0002884613296209884, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.00016574762012119135, 0.0, 4.678214600282143e-11, 0.0, -3.2690392218163145e-09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -3.0871279427662425e-06, -3.2690392218163145e-09, 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, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0], [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, -1.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 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, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 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, 0.0, 1.0, 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, 0.0, 1.0, -2478.8190999999997, 0.0, 0.0, 0.0, 0.0]];Y=[3.47640964947e-10,1.2292692858e-14,-1.16084928264e-11,1.22313144065e-09,0.0,-6.0575532754e-10,3.36045845167e-10,5.07429225887e-13,-2.36461838567e-06,-9.53929387441e-10,6.1788354226e-10,6.1737611306e-10,-6.0575532754e-10,-1.16084928264e-11];||Y||=2.36461926042e-06;g=nan;|g-g1|=nan\n",
      "\n",
      ";k=18;backtrack=0;lambda_ls=1.0;accum_step=17.5;stop=False;X=[55.5556289267,3.2690339728e-09,3.08713289973e-06,0.011582099005,0.0119166786264,0.000165747878786,8.69244915306e-05,1.31255982123e-07,0.261183430057,9.24398443055e-05,-0.00016870048667,-0.000168831742639,0.000165747878774,2.98667423994e-06];||X(k)-X(k-1)||=1.01951997296e-12;f(X)=[-4.31150256774e-07,2.64697796017e-23,-2.74003577908e-24,1.35769903765e-24,2.60197880978e-26,-3.20269255994e-15,7.25271961086e-21,0.0,0.0,0.0,0.0,1.35525271561e-20,-4.31457407508e-21,-2.77555756156e-17];||f(X)||=4.31150256774e-07;j(X)=[[-0.0046992784373814005, -0.0046992784373814005, -0.0046992784373814005, -0.0046992784373814005, -0.0046992784373814005, -0.0046992784373814005, 0.017992254884583135, -0.0046992784373814005, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001509999998980679, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.011582099005029224, 0.0, -3.2690339728027964e-09, 0.0, 0.0, 0.0, 0.0002884613296209884, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.00016574787878588325, 0.0, 4.678214600282143e-11, 0.0, -3.2690339728027964e-09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -3.087132899733077e-06, -3.2690339728027964e-09, 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, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0], [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, -1.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 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, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 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, 0.0, 1.0, 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, 0.0, 1.0, -2478.8190999999997, 0.0, 0.0, 0.0, 0.0]];Y=[-1.48443385636e-10,-5.2490135179e-15,4.95696683451e-12,-5.22291598931e-10,0.0,2.58664691919e-10,-1.4349249386e-10,-2.16673665608e-13,1.00971244355e-06,4.07336075292e-10,-2.63843581432e-10,-2.63626907771e-10,2.58664691919e-10,4.95696683451e-12];||Y||=1.00971281708e-06;g=nan;|g-g1|=nan\n",
      "\n",
      ";k=19;backtrack=0;lambda_ls=1.0;accum_step=18.5;stop=False;X=[55.5556289268,3.26903621416e-09,3.0871307831e-06,0.011582099228,0.0119166786264,0.000165747768336,8.69245528027e-05,1.31256074643e-07,0.261182998907,9.24396703718e-05,-0.000168700374008,-0.00016883163007,0.000165747768323,2.98667212331e-06];||X(k)-X(k-1)||=1.85890435653e-13;f(X)=[1.84103422285e-07,0.0,-5.04063185775e-25,2.47588728269e-25,4.744209484e-27,-2.1228543012e-15,-7.59682674569e-21,0.0,5.42101086243e-19,0.0,0.0,-1.35525271561e-20,1.60936259978e-20,0.0];||f(X)||=1.84103422285e-07;j(X)=[[-0.004699281749807521, -0.004699281749807521, -0.004699281749807521, -0.004699281749807521, -0.004699281749807521, -0.004699281749807521, 0.017992254884487163, -0.004699281749807521, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001509999998980679, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.011582099228048448, 0.0, -3.2690362141590984e-09, 0.0, 0.0, 0.0, 0.0002884613296209884, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.00016574776833570742, 0.0, 4.678214600282143e-11, 0.0, -3.2690362141590984e-09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -3.087130783102042e-06, -3.2690362141590984e-09, 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, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0], [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, -1.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 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, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 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, 0.0, 1.0, 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, 0.0, 1.0, -2478.8190999999997, 0.0, 0.0, 0.0, 0.0]];Y=[6.33896402672e-11,2.24135630222e-15,-2.11663103486e-12,2.23019224062e-10,0.0,-1.10450175832e-10,6.12720478898e-11,9.25207922776e-14,-4.3114997173e-07,-1.73933616922e-10,1.12661569018e-10,1.1256904823e-10,-1.10450175832e-10,-2.11663103486e-12];||Y||=4.31150131227e-07;g=nan;|g-g1|=nan\n",
      "\n",
      ";k=20;backtrack=0;lambda_ls=1.0;accum_step=19.5;stop=False;X=[55.5556289267,3.26903525709e-09,3.08713168692e-06,0.0115820991328,0.0119166786264,0.000165747815499,8.69245266392e-05,1.31256035137e-07,0.26118318301,9.24397446424e-05,-0.000168700422115,-0.000168831678138,0.000165747815486,2.98667302712e-06];||X(k)-X(k-1)||=3.38940503501e-14;f(X)=[-7.86129296659e-08,0.0,-9.69352280336e-26,4.5236439749e-26,8.64591552122e-28,-4.18651116378e-16,2.03155558443e-20,0.0,8.67361737988e-19,0.0,0.0,1.35525271561e-20,-2.03817302933e-20,2.77555756156e-17];||f(X)||=7.86129296659e-08;j(X)=[[-0.004699280335387743, -0.004699280335387743, -0.004699280335387743, -0.004699280335387743, -0.004699280335387743, -0.004699280335387743, 0.017992254884528144, -0.004699280335387743, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001509999998980679, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.01158209913281794, 0.0, -3.2690352570906003e-09, 0.0, 0.0, 0.0, 0.0002884613296209884, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.0001657478154985767, 0.0, 4.678214600282143e-11, 0.0, -3.2690352570906003e-09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -3.087131686915941e-06, -3.2690352570906003e-09, 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, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0], [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, -1.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 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, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 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, 0.0, 1.0, 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, 0.0, 1.0, -2478.8190999999997, 0.0, 0.0, 0.0, 0.0]];Y=[-2.70641541536e-11,-9.57068498265e-16,9.03813899015e-13,-9.52305101094e-11,0.0,4.71628692961e-11,-2.61634201714e-11,-3.95067644321e-14,1.84103300554e-07,7.42705672045e-11,-4.81071470196e-11,-4.80676402712e-11,4.71628692961e-11,9.03813899015e-13];||Y||=1.8410336866e-07;g=nan;|g-g1|=nan\n",
      "\n",
      ";k=21;backtrack=0;lambda_ls=1.0;accum_step=20.5;stop=False;X=[55.5556289268,3.26903566576e-09,3.08713130098e-06,0.0115820991735,0.0119166786264,0.00016574779536,8.69245378111e-05,1.31256052006e-07,0.261183104397,9.24397129286e-05,-0.000168700401573,-0.000168831657613,0.000165747795348,2.98667264119e-06];||X(k)-X(k-1)||=6.17998911391e-15;f(X)=[3.35680851449e-08,0.0,-1.93870456067e-26,8.17890986533e-27,1.57772181044e-28,2.686693641e-15,2.56756862136e-21,0.0,1.08420217249e-19,0.0,0.0,-1.35525271561e-20,1.5749518863e-20,-5.55111512313e-17];||f(X)||=3.35680851449e-08;j(X)=[[-0.004699280939351539, -0.004699280939351539, -0.004699280939351539, -0.004699280939351539, -0.004699280939351539, -0.004699280939351539, 0.017992254884510644, -0.004699280939351539, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001509999998980679, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.01158209917348174, 0.0, -3.269035665763282e-09, 0.0, 0.0, 0.0, 0.0002884613296209884, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.00016574779535984648, 0.0, 4.678214600282143e-11, 0.0, -3.269035665763282e-09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -3.0871313009838784e-06, -3.269035665763282e-09, 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, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0], [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, -1.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 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, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 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, 0.0, 1.0, 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, 0.0, 1.0, -2478.8190999999997, 0.0, 0.0, 0.0, 0.0]];Y=[1.15578436475e-11,4.08672681443e-16,-3.85932062718e-13,4.06638003286e-11,0.0,-2.01387302201e-11,1.11719016131e-11,1.68695714245e-14,-7.86128776924e-08,-3.17138421536e-11,2.05419405269e-11,2.05250709758e-11,-2.01387302201e-11,-3.85932062718e-13];||Y||=7.86129067741e-08;g=nan;|g-g1|=nan\n",
      "\n",
      ";k=22;backtrack=0;lambda_ls=1.0;accum_step=21.5;stop=False;X=[55.5556289268,3.26903549126e-09,3.08713146578e-06,0.0115820991561,0.0119166786264,0.000165747803959,8.69245330407e-05,1.31256044803e-07,0.261183137966,9.24397264705e-05,-0.000168700410345,-0.000168831666377,0.000165747803947,2.98667280598e-06];||X(k)-X(k-1)||=1.1268156833e-15;f(X)=[-1.4333721321e-08,0.0,-1.29246970711e-26,1.51461293802e-27,2.8398992588e-29,-5.13478148889e-16,3.66606447484e-21,0.0,-6.50521303491e-19,0.0,0.0,0.0,-8.17916189692e-21,0.0];||f(X)||=1.4333721321e-08;j(X)=[[-0.004699280681456319, -0.004699280681456319, -0.004699280681456319, -0.004699280681456319, -0.004699280681456319, -0.004699280681456319, 0.017992254884518118, -0.004699280681456319, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001509999998980679, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.011582099156118103, 0.0, -3.2690354912582336e-09, 0.0, 0.0, 0.0, 0.0002884613296209884, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.00016574780395917972, 0.0, 4.678214600282143e-11, 0.0, -3.2690354912582336e-09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -3.0871314657787017e-06, -3.2690354912582336e-09, 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, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0], [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, -1.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 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, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 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, 0.0, 1.0, 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, 0.0, 1.0, -2478.8190999999997, 0.0, 0.0, 0.0, 0.0]];Y=[-4.93775857948e-12,-1.74505048411e-16,1.64794823301e-13,-1.73636359252e-11,0.0,8.59933324549e-12,-4.77045155147e-12,-7.20338183785e-15,3.35680629638e-08,1.35419575024e-11,-8.77150593736e-12,-8.76430257127e-12,8.59933324549e-12,1.64794823301e-13];||Y||=3.35680753822e-08;g=nan;|g-g1|=nan\n",
      "\n",
      ";k=23;backtrack=0;lambda_ls=1.0;accum_step=22.5;stop=False;X=[55.5556289268,3.26903556577e-09,3.08713139541e-06,0.0115820991635,0.0119166786264,0.000165747800287,8.69245350777e-05,1.31256047879e-07,0.261183123632,9.2439720688e-05,-0.000168700406599,-0.000168831662635,0.000165747800275,2.98667273562e-06];||X(k)-X(k-1)||=2.05455446807e-16;f(X)=[6.12056383353e-09,2.64697796017e-23,0.0,2.01948391737e-28,4.73316543133e-30,2.5004954704e-15,-1.74038800881e-20,0.0,-7.04731412116e-19,0.0,0.0,0.0,1.40025134093e-20,0.0];||f(X)||=6.12056383353e-09;j(X)=[[-0.0046992807915787445, -0.0046992807915787445, -0.0046992807915787445, -0.0046992807915787445, -0.0046992807915787445, -0.0046992807915787445, 0.017992254884514926, -0.0046992807915787445, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001509999998980679, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.011582099163532452, 0.0, -3.269035565772678e-09, 0.0, 0.0, 0.0, 0.0002884613296209884, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.00016574780028722668, 0.0, 4.678214600282143e-11, 0.0, -3.269035565772678e-09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -3.087131395410589e-06, -3.269035565772678e-09, 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, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0], [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, -1.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 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, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 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, 0.0, 1.0, 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, 0.0, 1.0, -2478.8190999999997, 0.0, 0.0, 0.0, 0.0]];Y=[2.10781147922e-12,7.4514444478e-17,-7.03681126801e-14,7.41434938304e-12,0.0,-3.67195305086e-12,2.0370044065e-12,3.07587665174e-15,-1.43337118466e-08,-5.78247595662e-12,3.74547155013e-12,3.74239568165e-12,-3.67195305086e-12,-7.03681126801e-14];||Y||=1.43337171492e-08;g=nan;|g-g1|=nan\n",
      "\n",
      ";k=24;backtrack=0;lambda_ls=1.0;accum_step=23.5;stop=False;X=[55.5556289268,3.26903553395e-09,3.08713142546e-06,0.0115820991604,0.0119166786264,0.000165747801855,8.69245342079e-05,1.31256046565e-07,0.261183129752,9.24397231572e-05,-0.000168700408199,-0.000168831664233,0.000165747801843,2.98667276566e-06];||X(k)-X(k-1)||=3.74612797566e-17;f(X)=[-2.61350818764e-09,-2.64697796017e-23,6.46234853557e-27,1.00974195868e-28,1.57772181044e-30,-6.31141189658e-17,7.10713582306e-21,0.0,-6.50521303491e-19,0.0,0.0,-1.35525271561e-20,3.41460156862e-21,-2.77555756156e-17];||f(X)||=2.61350818764e-09;j(X)=[[-0.004699280744555974, -0.004699280744555974, -0.004699280744555974, -0.004699280744555974, -0.004699280744555974, -0.004699280744555974, 0.01799225488451629, -0.004699280744555974, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001509999998980679, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.011582099160366491, 0.0, -3.269035533954676e-09, 0.0, 0.0, 0.0, 0.0002884613296209884, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.0001657478018551673, 0.0, 4.678214600282143e-11, 0.0, -3.269035533954676e-09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -3.087131425458093e-06, -3.269035533954676e-09, 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, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0], [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, -1.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 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, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 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, 0.0, 1.0, 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, 0.0, 1.0, -2478.8190999999997, 0.0, 0.0, 0.0, 0.0]];Y=[-9.0232618868e-13,-3.18180021984e-17,3.00475037003e-14,-3.16595989043e-12,0.0,1.56794062803e-12,-8.69810024916e-13,-1.31341311027e-15,6.12055979864e-09,2.46914339116e-12,-1.59933336624e-12,-1.59801996713e-12,1.56794062803e-12,3.00475037003e-14];||Y||=6.12056206321e-09;g=nan;|g-g1|=nan\n",
      "\n",
      ";k=25;backtrack=0;lambda_ls=1.0;accum_step=24.5;stop=False;X=[55.5556289268,3.26903554754e-09,3.08713141263e-06,0.0115820991617,0.0119166786264,0.000165747801186,8.69245345793e-05,1.31256047126e-07,0.261183127139,9.24397221029e-05,-0.000168700407516,-0.00016883166355,0.000165747801173,2.98667275283e-06];||X(k)-X(k-1)||=6.8304211052e-18;f(X)=[1.11597986407e-09,2.64697796017e-23,-6.46234853557e-27,0.0,0.0,-5.9963156402e-16,1.13687703389e-20,0.0,4.33680868994e-19,0.0,0.0,1.35525271561e-20,-2.1069944563e-20,0.0];||f(X)||=1.11597986407e-09;j(X)=[[-0.004699280764634911, -0.004699280764634911, -0.004699280764634911, -0.004699280764634911, -0.004699280764634911, -0.004699280764634911, 0.01799225488451571, -0.004699280764634911, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001509999998980679, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.011582099161718372, 0.0, -3.2690355475411063e-09, 0.0, 0.0, 0.0, 0.0002884613296209884, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.00016574780118564964, 0.0, 4.678214600282143e-11, 0.0, -3.2690355475411063e-09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -3.087131412627674e-06, -3.2690355475411063e-09, 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, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0], [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, -1.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 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, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 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, 0.0, 1.0, 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, 0.0, 1.0, -2478.8190999999997, 0.0, 0.0, 0.0, 0.0]];Y=[3.84292730468e-13,1.35864304349e-17,-1.28304187404e-14,1.35187998922e-12,0.0,-6.69517663208e-13,3.71412804699e-13,5.60833308247e-16,-2.61350646001e-09,-1.05433530336e-12,6.82922512209e-13,6.82361675486e-13,-6.69517663208e-13,-1.28304187404e-14];||Y||=2.61350742684e-09;g=nan;|g-g1|=nan\n",
      "\n",
      ";k=26;backtrack=0;lambda_ls=1.0;accum_step=25.5;stop=False;X=[55.5556289268,3.26903554174e-09,3.08713141811e-06,0.0115820991611,0.0119166786264,0.000165747801472,8.69245344207e-05,1.31256046887e-07,0.261183128255,9.24397225531e-05,-0.000168700407807,-0.000168831663842,0.000165747801459,2.98667275831e-06];||X(k)-X(k-1)||=1.24541036757e-18;f(X)=[-4.7652848334e-10,-2.64697796017e-23,0.0,-1.00974195868e-28,-1.57772181044e-30,4.3327429318e-17,-6.35274710441e-22,0.0,3.25260651746e-19,0.0,0.0,-1.35525271561e-20,8.47032947254e-22,2.77555756156e-17];||f(X)||=4.7652848334e-10;j(X)=[[-0.004699280756061114, -0.004699280756061114, -0.004699280756061114, -0.004699280756061114, -0.004699280756061114, -0.004699280756061114, 0.017992254884515956, -0.004699280756061114, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001509999998980679, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.011582099161141113, 0.0, -3.269035541739639e-09, 0.0, 0.0, 0.0, 0.0002884613296209884, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.00016574780147153673, 0.0, 4.678214600282143e-11, 0.0, -3.269035541739639e-09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -3.087131418106321e-06, -3.269035541739639e-09, 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, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0], [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, -1.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 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, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 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, 0.0, 1.0, 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, 0.0, 1.0, -2478.8190999999997, 0.0, 0.0, 0.0, 0.0]];Y=[-1.63468163554e-13,-5.80146730009e-18,5.47864704466e-15,-5.77259033962e-13,0.0,2.85887081569e-13,-1.58594951725e-13,-2.39478350473e-16,1.11597912342e-09,4.50205956305e-13,-2.91611018133e-13,-2.91371518712e-13,2.85887081569e-13,5.47864704466e-15];||Y||=1.11597953617e-09;g=nan;|g-g1|=nan\n",
      "\n",
      ";k=27;backtrack=0;lambda_ls=1.0;accum_step=26.5;stop=False;X=[55.5556289268,3.26903554422e-09,3.08713141577e-06,0.0115820991614,0.0119166786264,0.000165747801349,8.69245344884e-05,1.31256046989e-07,0.261183127778,9.24397223608e-05,-0.000168700407683,-0.000168831663717,0.000165747801337,2.98667275597e-06];||X(k)-X(k-1)||=2.27079246152e-19;f(X)=[2.03479788574e-10,2.64697796017e-23,-6.46234853557e-27,1.00974195868e-28,0.0,1.03992606627e-15,7.09390093325e-21,0.0,3.25260651746e-19,0.0,0.0,0.0,-8.20563167653e-21,0.0];||f(X)||=2.03479788577e-10;j(X)=[[-0.004699280759722165, -0.004699280759722165, -0.004699280759722165, -0.004699280759722165, -0.004699280759722165, -0.004699280759722165, 0.017992254884515852, -0.004699280759722165, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001509999998980679, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.011582099161387605, 0.0, -3.2690355442168916e-09, 0.0, 0.0, 0.0, 0.0002884613296209884, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.00016574780134946164, 0.0, 4.678214600282143e-11, 0.0, -3.2690355442168916e-09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -3.087131415766914e-06, -3.2690355442168916e-09, 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, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0], [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, -1.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 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, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 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, 0.0, 1.0, 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, 0.0, 1.0, -2478.8190999999997, 0.0, 0.0, 0.0, 0.0]];Y=[7.00143514791e-14,2.47725230575e-18,-2.33940711373e-15,2.46491740774e-13,0.0,-1.22075091152e-13,6.77207619642e-14,1.02258324027e-16,-4.76528168075e-10,-1.92239982466e-13,1.24519234054e-13,1.24416974883e-13,-1.22075091152e-13,-2.33940711373e-15];||Y||=4.76528344353e-10;g=nan;|g-g1|=nan\n",
      "\n",
      ";k=28;backtrack=0;lambda_ls=1.0;accum_step=27.5;stop=False;X=[55.5556289268,3.26903554316e-09,3.08713141677e-06,0.0115820991613,0.0119166786264,0.000165747801402,8.69245344595e-05,1.31256046945e-07,0.261183127982,9.24397224429e-05,-0.000168700407736,-0.00016883166377,0.000165747801389,2.98667275697e-06];||X(k)-X(k-1)||=4.14040097233e-20;f(X)=[-8.68868310633e-11,-2.64697796017e-23,6.46234853557e-27,-1.00974195868e-28,1.57772181044e-30,2.5331299558e-15,-8.07328277852e-22,0.0,-7.5894152074e-19,0.0,0.0,-1.35525271561e-20,-6.69685423923e-21,5.55111512313e-17];||f(X)||=8.68868311002e-11;j(X)=[[-0.004699280758158879, -0.004699280758158879, -0.004699280758158879, -0.004699280758158879, -0.004699280758158879, -0.004699280758158879, 0.017992254884515894, -0.004699280758158879, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001509999998980679, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.01158209916128235, 0.0, -3.269035543159094e-09, 0.0, 0.0, 0.0, 0.0002884613296209884, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.00016574780140158826, 0.0, 4.678214600282143e-11, 0.0, -3.269035543159094e-09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -3.087131416765851e-06, -3.269035543159094e-09, 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, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0], [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, -1.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 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, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 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, 0.0, 1.0, 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, 0.0, 1.0, -2478.8190999999997, 0.0, 0.0, 0.0, 0.0]];Y=[-3.09548753357e-14,-1.05779766693e-18,9.98936954014e-16,-1.05253539762e-13,0.0,5.21266134219e-14,-2.89170630192e-14,-4.36647386598e-17,2.03479658931e-10,8.20873370432e-14,-5.3170274024e-14,-5.31266010797e-14,5.21266134219e-14,9.98936954014e-16];||Y||=2.03479734361e-10;g=nan;|g-g1|=nan\n",
      "\n",
      ";k=29;backtrack=0;lambda_ls=1.0;accum_step=28.5;stop=False;X=[55.5556289268,3.26903554361e-09,3.08713141634e-06,0.0115820991613,0.0119166786264,0.000165747801379,8.69245344719e-05,1.31256046964e-07,0.261183127895,9.24397224079e-05,-0.000168700407713,-0.000168831663748,0.000165747801367,2.98667275654e-06];||X(k)-X(k-1)||=7.54931723879e-21;f(X)=[3.71010444589e-11,0.0,0.0,0.0,-1.57772181044e-30,-3.13526873734e-15,1.50745394832e-20,0.0,5.42101086243e-19,0.0,0.0,1.35525271561e-20,-9.95263713024e-21,-5.55111512313e-17];||f(X)||=3.71010445914e-11;j(X)=[[-0.004699280758826408, -0.004699280758826408, -0.004699280758826408, -0.004699280758826408, -0.004699280758826408, -0.004699280758826408, 0.017992254884515876, -0.004699280758826408, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001509999998980679, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.011582099161327295, 0.0, -3.2690355436107783e-09, 0.0, 0.0, 0.0, 0.0002884613296209884, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.00016574780137932994, 0.0, 4.678214600282143e-11, 0.0, -3.2690355436107783e-09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -3.0871314163393007e-06, -3.2690355436107783e-09, 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, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0], [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, -1.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 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, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 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, 0.0, 1.0, 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, 0.0, 1.0, -2478.8190999999997, 0.0, 0.0, 0.0, 0.0]];Y=[1.02406771715e-14,4.51684331701e-19,-4.26550061853e-16,4.4944370851e-14,0.0,-2.22583054853e-14,1.23477214949e-14,1.8645032975e-17,-8.68867617172e-11,-3.50516527027e-14,2.27039447603e-14,2.26853064242e-14,-2.22583054853e-14,-4.26550061853e-16];||Y||=8.68867935245e-11;g=nan;|g-g1|=nan\n",
      "\n",
      ";k=30;backtrack=0;lambda_ls=1.0;accum_step=29.5;stop=False;X=[55.5556289268,3.26903554342e-09,3.08713141652e-06,0.0115820991613,0.0119166786264,0.000165747801389,8.69245344666e-05,1.31256046956e-07,0.261183127932,9.24397224228e-05,-0.000168700407723,-0.000168831663757,0.000165747801376,2.98667275673e-06];||X(k)-X(k-1)||=1.37648436957e-21;f(X)=[-1.58422719387e-11,2.64697796017e-23,-6.46234853557e-27,0.0,1.57772181044e-30,2.31923041969e-15,-7.54388718648e-21,0.0,3.7947076037e-19,0.0,0.0,0.0,-2.59403840097e-21,0.0];||f(X)||=1.58422721085e-11;j(X)=[[-0.0046992807585413705, -0.0046992807585413705, -0.0046992807585413705, -0.0046992807585413705, -0.0046992807585413705, -0.0046992807585413705, 0.017992254884515883, -0.0046992807585413705, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001509999998980679, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.011582099161308104, 0.0, -3.269035543417907e-09, 0.0, 0.0, 0.0, 0.0002884613296209884, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.00016574780138883433, 0.0, 4.678214600282143e-11, 0.0, -3.269035543417907e-09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -3.087131416521439e-06, -3.269035543417907e-09, 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, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0], [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, -1.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 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, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 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, 0.0, 1.0, 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, 0.0, 1.0, -2478.8190999999997, 0.0, 0.0, 0.0, 0.0]];Y=[-2.31921095801e-15,-1.92871233144e-19,1.82138510726e-16,-1.91916194247e-14,0.0,9.50438050809e-15,-5.27253253385e-15,-7.96152412074e-18,3.71010051982e-11,1.49671872736e-14,-9.69466829227e-15,-9.68669681551e-15,9.50438050809e-15,1.82138510726e-16];||Y||=3.71010185949e-11;g=nan;|g-g1|=nan\n",
      "\n",
      ";k=31;backtrack=0;lambda_ls=1.0;accum_step=30.5;stop=False;X=[55.5556289268,3.2690355435e-09,3.08713141644e-06,0.0115820991613,0.0119166786264,0.000165747801385,8.69245344688e-05,1.31256046959e-07,0.261183127916,9.24397224164e-05,-0.000168700407719,-0.000168831663753,0.000165747801372,2.98667275665e-06];||X(k)-X(k-1)||=2.50977760449e-22;f(X)=[6.76469991134e-12,0.0,0.0,0.0,0.0,-9.83913471531e-18,2.81903152758e-21,0.0,5.42101086243e-19,0.0,0.0,1.35525271561e-20,-1.8211208366e-20,0.0];||f(X)||=6.76469991135e-12;j(X)=[[-0.004699280758663083, -0.004699280758663083, -0.004699280758663083, -0.004699280758663083, -0.004699280758663083, -0.004699280758663083, 0.01799225488451588, -0.004699280758663083, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001509999998980679, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.011582099161316299, 0.0, -3.2690355435002637e-09, 0.0, 0.0, 0.0, 0.0002884613296209884, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.00016574780138477592, 0.0, 4.678214600282143e-11, 0.0, -3.2690355435002637e-09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -3.0871314164436654e-06, -3.2690355435002637e-09, 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, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0], [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, -1.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 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, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 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, 0.0, 1.0, 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, 0.0, 1.0, -2478.8190999999997, 0.0, 0.0, 0.0, 0.0]];Y=[9.85357969282e-18,8.23567843311e-20,-7.77735926005e-17,8.19430259752e-15,0.0,-4.05841683139e-15,2.25138521968e-15,3.3996181492e-18,-1.58422505641e-11,-6.39104748068e-15,4.139662261e-15,4.13626523689e-15,-4.05841683139e-15,-7.77735926005e-17];||Y||=1.58422562533e-11;g=nan;|g-g1|=nan\n",
      "\n",
      ";k=32;backtrack=0;lambda_ls=1.0;accum_step=31.5;stop=False;X=[55.5556289268,3.26903554347e-09,3.08713141648e-06,0.0115820991613,0.0119166786264,0.000165747801387,8.69245344679e-05,1.31256046958e-07,0.261183127923,9.24397224192e-05,-0.00016870040772,-0.000168831663755,0.000165747801374,2.98667275668e-06];||X(k)-X(k-1)||=4.57611977571e-23;f(X)=[-2.88857826547e-12,2.64697796017e-23,0.0,2.01948391737e-28,1.57772181044e-30,9.84658860524e-16,1.59348073202e-20,0.0,7.5894152074e-19,0.0,0.0,1.35525271561e-20,-6.1939284268e-21,-2.77555756156e-17];||f(X)||=2.88857843343e-12;j(X)=[[-0.004699280758611111, -0.004699280758611111, -0.004699280758611111, -0.004699280758611111, -0.004699280758611111, -0.004699280758611111, 0.017992254884515883, -0.004699280758611111, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001509999998980679, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.0115820991613128, 0.0, -3.269035543465097e-09, 0.0, 0.0, 0.0, 0.0002884613296209884, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.00016574780138650885, 0.0, 4.678214600282143e-11, 0.0, -3.269035543465097e-09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -3.087131416476875e-06, -3.269035543465097e-09, 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, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0], [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, -1.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 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, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 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, 0.0, 1.0, 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, 0.0, 1.0, -2478.8190999999997, 0.0, 0.0, 0.0, 0.0]];Y=[-9.8467923245e-16,-3.51665928763e-20,3.32097624003e-17,-3.49967681713e-15,0.0,1.73294630304e-15,-9.61354504853e-16,-1.45164530135e-18,6.76469539498e-12,2.72899922184e-15,-1.76765826951e-15,-1.766188413e-15,1.73294630304e-15,3.32097624003e-17];||Y||=6.76469789631e-12;g=nan;|g-g1|=nan\n",
      "\n",
      ";k=33;backtrack=0;lambda_ls=1.0;accum_step=32.5;stop=False;X=[55.5556289268,3.26903554348e-09,3.08713141646e-06,0.0115820991613,0.0119166786264,0.000165747801386,8.69245344683e-05,1.31256046959e-07,0.26118312792,9.2439722418e-05,-0.00016870040772,-0.000168831663754,0.000165747801373,2.98667275667e-06];||X(k)-X(k-1)||=8.34389038704e-24;f(X)=[1.23345778036e-12,-2.64697796017e-23,0.0,0.0,0.0,5.59963317034e-16,8.93355061557e-21,0.0,2.16840434497e-19,0.0,0.0,0.0,-9.71440911382e-21,0.0];||f(X)||=1.23345790746e-12;j(X)=[[-0.004699280758633304, -0.004699280758633304, -0.004699280758633304, -0.004699280758633304, -0.004699280758633304, -0.004699280758633304, 0.01799225488451588, -0.004699280758633304, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001509999998980679, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.011582099161314294, 0.0, -3.269035543480114e-09, 0.0, 0.0, 0.0, 0.0002884613296209884, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.00016574780138576889, 0.0, 4.678214600282143e-11, 0.0, -3.269035543480114e-09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -3.087131416462694e-06, -3.269035543480114e-09, 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, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0], [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, -1.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 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, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 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, 0.0, 1.0, 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, 0.0, 1.0, -2478.8190999999997, 0.0, 0.0, 0.0, 0.0]];Y=[-5.59994142471e-16,1.5017167425e-20,-1.41810607459e-17,1.49339793146e-15,0.0,-7.39972430132e-16,4.10501056755e-16,6.19883065061e-19,-2.88857172496e-12,-1.16531274127e-15,7.54798131989e-16,7.54184442853e-16,-7.39972430132e-16,-1.41810607459e-17];||Y||=2.88857281621e-12;g=nan;|g-g1|=nan\n",
      "\n",
      ";k=34;backtrack=0;lambda_ls=1.0;accum_step=33.5;stop=False;X=[55.5556289268,3.26903554347e-09,3.08713141647e-06,0.0115820991613,0.0119166786264,0.000165747801386,8.69245344681e-05,1.31256046958e-07,0.261183127921,9.24397224185e-05,-0.00016870040772,-0.000168831663755,0.000165747801374,2.98667275667e-06];||X(k)-X(k-1)||=1.52141918914e-24;f(X)=[-5.2657878058e-13,2.64697796017e-23,0.0,-1.00974195868e-28,0.0,7.41377445546e-16,-8.49679925214e-21,0.0,-1.62630325873e-19,0.0,0.0,1.35525271561e-20,-3.36166200942e-21,2.77555756156e-17];||f(X)||=5.26579303209e-13;j(X)=[[-0.004699280758623829, -0.004699280758623829, -0.004699280758623829, -0.004699280758623829, -0.004699280758623829, -0.004699280758623829, 0.017992254884515883, -0.004699280758623829, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001509999998980679, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.011582099161313655, 0.0, -3.2690355434737017e-09, 0.0, 0.0, 0.0, 0.0002884613296209884, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.00016574780138608488, 0.0, 4.678214600282143e-11, 0.0, -3.2690355434737017e-09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -3.0871314164687494e-06, -3.2690355434737017e-09, 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, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0], [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, -1.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 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, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 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, 0.0, 1.0, 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, 0.0, 1.0, -2478.8190999999997, 0.0, 0.0, 0.0, 0.0]];Y=[-7.41302246864e-16,-6.41242824871e-21,6.0556113383e-18,-6.3825269098e-16,0.0,3.15991380165e-16,-1.75280797369e-16,-2.64700473628e-19,1.23345959746e-12,4.97599682632e-16,-3.22318885263e-16,-3.22044470381e-16,3.15991380165e-16,6.0556113383e-18];||Y||=1.23346026331e-12;g=nan;|g-g1|=nan\n",
      "\n",
      ";k=35;backtrack=0;lambda_ls=1.0;accum_step=34.5;stop=False;X=[55.5556289268,3.26903554348e-09,3.08713141647e-06,0.0115820991613,0.0119166786264,0.000165747801386,8.69245344682e-05,1.31256046958e-07,0.261183127921,9.24397224183e-05,-0.00016870040772,-0.000168831663755,0.000165747801374,2.98667275667e-06];||X(k)-X(k-1)||=2.77285411292e-25;f(X)=[2.24709140184e-13,-2.64697796017e-23,6.46234853557e-27,1.00974195868e-28,0.0,6.63911200321e-16,3.98370183006e-21,0.0,-2.16840434497e-19,0.0,0.0,-1.35525271561e-20,1.21760986168e-21,0.0];||f(X)||=2.24710120957e-13;j(X)=[[-0.0046992807586278725, -0.0046992807586278725, -0.0046992807586278725, -0.0046992807586278725, -0.0046992807586278725, -0.0046992807586278725, 0.01799225488451588, -0.0046992807586278725, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001509999998980679, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.011582099161313928, 0.0, -3.269035543476439e-09, 0.0, 0.0, 0.0, 0.0002884613296209884, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.00016574780138594997, 0.0, 4.678214600282143e-11, 0.0, -3.269035543476439e-09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -3.0871314164661647e-06, -3.269035543476439e-09, 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, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0], [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, -1.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 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, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 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, 0.0, 1.0, 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, 0.0, 1.0, -2478.8190999999997, 0.0, 0.0, 0.0, 0.0]];Y=[-6.63964980825e-16,2.73710347734e-21,-2.58479848954e-18,2.72557656011e-16,0.0,-1.34907993446e-16,7.48083540083e-17,1.12987084256e-19,-5.26574949702e-13,-2.12418564197e-16,1.37596657662e-16,1.3748703224e-16,-1.34907993446e-16,-2.58479848954e-18];||Y||=5.26575557502e-13;g=nan;|g-g1|=nan\n",
      "\n",
      ";k=36;backtrack=0;lambda_ls=1.0;accum_step=35.5;stop=False;X=[55.5556289268,3.26903554348e-09,3.08713141647e-06,0.0115820991613,0.0119166786264,0.000165747801386,8.69245344682e-05,1.31256046958e-07,0.261183127921,9.24397224184e-05,-0.00016870040772,-0.000168831663755,0.000165747801374,2.98667275667e-06];||X(k)-X(k-1)||=5.04942339492e-26;f(X)=[-9.58677581764e-14,2.64697796017e-23,-6.46234853557e-27,-1.00974195868e-28,0.0,6.96965814055e-16,1.12893610001e-20,0.0,-1.62630325873e-19,0.0,0.0,1.35525271561e-20,-1.99052742605e-20,0.0];||f(X)||=9.587029164e-14;j(X)=[[-0.004699280758626147, -0.004699280758626147, -0.004699280758626147, -0.004699280758626147, -0.004699280758626147, -0.004699280758626147, 0.01799225488451588, -0.004699280758626147, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001509999998980679, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.011582099161313811, 0.0, -3.2690355434752712e-09, 0.0, 0.0, 0.0, 0.0002884613296209884, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.00016574780138600755, 0.0, 4.678214600282143e-11, 0.0, -3.2690355434752712e-09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -3.0871314164672675e-06, -3.2690355434752712e-09, 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, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0], [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, -1.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 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, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 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, 0.0, 1.0, 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, 0.0, 1.0, -2478.8190999999997, 0.0, 0.0, 0.0, 0.0]];Y=[-6.96947651017e-16,-1.16769116267e-21,1.10271547222e-18,-1.16033189987e-16,0.0,5.75750654799e-17,-3.19173666851e-17,-4.82216934415e-20,2.24712110833e-13,9.06528882373e-17,-5.8721969025e-17,-5.86749649415e-17,5.75750654799e-17,1.10271547222e-18];||Y||=2.24713272226e-13;g=nan;|g-g1|=nan\n",
      "\n",
      ";k=37;backtrack=0;lambda_ls=1.0;accum_step=36.5;stop=False;X=[55.5556289268,3.26903554348e-09,3.08713141647e-06,0.0115820991613,0.0119166786264,0.000165747801386,8.69245344682e-05,1.31256046958e-07,0.261183127921,9.24397224183e-05,-0.00016870040772,-0.000168831663755,0.000165747801374,2.98667275667e-06];||X(k)-X(k-1)||=9.19063373082e-27;f(X)=[4.09117184574e-14,0.0,-6.46234853557e-27,0.0,-1.57772181044e-30,6.82857633286e-16,-6.00863996959e-21,0.0,5.42101086243e-19,0.0,0.0,-1.35525271561e-20,6.61744490042e-22,0.0];||f(X)||=4.09174168537e-14;j(X)=[[-0.004699280758626883, -0.004699280758626883, -0.004699280758626883, -0.004699280758626883, -0.004699280758626883, -0.004699280758626883, 0.01799225488451588, -0.004699280758626883, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001509999998980679, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.011582099161313862, 0.0, -3.269035543475769e-09, 0.0, 0.0, 0.0, 0.0002884613296209884, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.000165747801385983, 0.0, 4.678214600282143e-11, 0.0, -3.269035543475769e-09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -3.0871314164667974e-06, -3.269035543475769e-09, 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, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0], [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, -1.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 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, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 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, 0.0, 1.0, 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, 0.0, 1.0, -2478.8190999999997, 0.0, 0.0, 0.0, 0.0]];Y=[-6.82882349533e-16,4.9794829965e-22,-4.70240173036e-19,4.97760773244e-17,0.0,-2.45657097581e-17,1.36114591309e-17,2.05797730534e-20,-9.58644205795e-14,-3.86734233973e-17,2.50484117392e-17,2.50477372404e-17,-2.45657097581e-17,-4.70240173036e-19];||Y||=9.58668873079e-14;g=nan;|g-g1|=nan\n",
      "\n",
      ";k=38;backtrack=0;lambda_ls=1.0;accum_step=37.5;stop=False;X=[55.5556289268,3.26903554348e-09,3.08713141647e-06,0.0115820991613,0.0119166786264,0.000165747801386,8.69245344682e-05,1.31256046958e-07,0.261183127921,9.24397224183e-05,-0.00016870040772,-0.000168831663755,0.000165747801374,2.98667275667e-06];||X(k)-X(k-1)||=1.67376996894e-27;f(X)=[-1.74305014866e-14,0.0,6.46234853557e-27,0.0,0.0,6.8888850787e-16,1.02967442651e-20,0.0,-8.67361737988e-19,0.0,0.0,1.35525271561e-20,-8.09975255812e-21,0.0];||f(X)||=1.74441093268e-14;j(X)=[[-0.004699280758626569, -0.004699280758626569, -0.004699280758626569, -0.004699280758626569, -0.004699280758626569, -0.004699280758626569, 0.01799225488451588, -0.004699280758626569, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001509999998980679, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.01158209916131384, 0.0, -3.2690355434755566e-09, 0.0, 0.0, 0.0, 0.0002884613296209884, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.00016574780138599345, 0.0, 4.678214600282143e-11, 0.0, -3.2690355434755566e-09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -3.0871314164669977e-06, -3.2690355434755566e-09, 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, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0], [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, -1.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 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, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 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, 0.0, 1.0, 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, 0.0, 1.0, -2478.8190999999997, 0.0, 0.0, 0.0, 0.0]];Y=[-6.88869057568e-16,-2.12698709942e-22,2.00380552362e-19,-2.16963740185e-17,0.0,1.04738355206e-17,-5.80371254145e-18,-8.76360593167e-21,4.09149030631e-14,1.65058043417e-17,-1.06885392731e-17,-1.06804374117e-17,1.04738355206e-17,2.00380552362e-19];||Y||=4.09207167324e-14;g=nan;|g-g1|=nan\n",
      "\n",
      ";k=39;backtrack=0;lambda_ls=1.0;accum_step=38.5;stop=True;X=[55.5556289268,3.26903554348e-09,3.08713141647e-06,0.0115820991613,0.0119166786264,0.000165747801386,8.69245344682e-05,1.31256046958e-07,0.261183127921,9.24397224183e-05,-0.00016870040772,-0.000168831663755,0.000165747801374,2.98667275667e-06];||X(k)-X(k-1)||=3.03822626972e-28;f(X)=[7.38298311376e-15,0.0,0.0,-1.00974195868e-28,0.0,6.86340632765e-16,-1.24805010822e-20,0.0,5.42101086243e-19,0.0,0.0,0.0,-4.36751363428e-21,0.0];||f(X)||=7.41481647893e-15;j(X)=[[-0.004699280758626702, -0.004699280758626702, -0.004699280758626702, -0.004699280758626702, -0.004699280758626702, -0.004699280758626702, 0.01799225488451588, -0.004699280758626702, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001509999998980679, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.01158209916131385, 0.0, -3.269035543475647e-09, 0.0, 0.0, 0.0, 0.0002884613296209884, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -0.000165747801385989, 0.0, 4.678214600282143e-11, 0.0, -3.269035543475647e-09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, -3.087131416466912e-06, -3.269035543475647e-09, 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, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0], [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, -1.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 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, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 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, 0.0, 1.0, 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, 0.0, 1.0, -2478.8190999999997, 0.0, 0.0, 0.0, 0.0]];Y=[-6.86329795518e-16,9.0659596155e-23,-8.56148805273e-20,9.87406480979e-18,0.0,-4.45535039371e-18,2.46993234833e-18,3.72959784347e-21,-1.74272568702e-14,-7.03046739887e-18,4.54698252338e-18,4.55135267809e-18,-4.45535039371e-18,-8.56148805273e-20];||Y||=1.74407730545e-14;g=nan;|g-g1|=nan\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from numerik import nr_ls\n",
    "\n",
    "def notify_status_func(progress_k, stop_value, k,\n",
    "                       j_it_backtrack, lambda_ls, accum_step,\n",
    "                       x, diff, f_val, j_val, lambda_ls_y,\n",
    "                       method_loops):\n",
    "    g_min = np.nan\n",
    "    g1 = np.nan\n",
    "    y = lambda_ls_y\n",
    "    pr_str =';k=' + str(k) + \\\n",
    "            ';backtrack=' + str(j_it_backtrack) + \\\n",
    "            ';lambda_ls=' + str(lambda_ls) + \\\n",
    "            ';accum_step=' + str(accum_step) + \\\n",
    "            ';stop=' + str(stop_value) + \\\n",
    "            ';X=' + '[' + ','.join(map(str, x.T.A1)) + ']' + \\\n",
    "            ';||X(k)-X(k-1)||=' + str((diff.T * diff).item()) + \\\n",
    "            ';f(X)=' + '[' + ','.join(map(str, f_val.T.A1)) + ']' + \\\n",
    "            ';||f(X)||=' + str(np.sqrt((f_val.T * f_val).item())) + \\\n",
    "            ';j(X)=' + str(j_val.tolist()) + \\\n",
    "            ';Y=' + '[' + ','.join(map(str, y.T.A1)) + ']' + \\\n",
    "            ';||Y||=' + str(np.sqrt((y.T * y).item())) + \\\n",
    "            ';g=' + str(g_min) + \\\n",
    "            ';|g-g1|=' + str(abs(g_min - g1))\n",
    "    print pr_str + '\\n'\n",
    "\n",
    "progress_k, stop, outer_it_k, outer_it_j, \\\n",
    "        lambda_ls, accum_step, x, \\\n",
    "        diff, f_val, lambda_ls_y, \\\n",
    "        method_loops = \\\n",
    "        nr_ls(x0=np.matrix(x0).T,\n",
    "              f=lambda x: np.matrix(eq_set(x)).T,\n",
    "              j=lambda x: np.matrix(jac_eq_set(x)),\n",
    "              tol=1e-14,\n",
    "              max_it=1000,\n",
    "              inner_loop_condition=lambda x_vec:\n",
    "              all([item >= 0 for item in\n",
    "                   x_vec[0:9]]),\n",
    "              notify_status_func=notify_status_func,\n",
    "              method_loops=[0, 0],\n",
    "              process_func_handle=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 8.48558036]\n",
      " [ 5.51044488]]\n",
      "[[ 13.99602524]]\n"
     ]
    }
   ],
   "source": [
    "pHOH = -np.log10(x[1:3])\n",
    "print pHOH\n",
    "print sum(pHOH)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[  5.55556289e+01],\n",
       "        [  3.26903554e-09],\n",
       "        [  3.08713142e-06],\n",
       "        [  1.15820992e-02],\n",
       "        [  1.19166786e-02],\n",
       "        [  1.65747801e-04],\n",
       "        [  8.69245345e-05],\n",
       "        [  1.31256047e-07],\n",
       "        [  2.61183128e-01],\n",
       "        [  9.24397224e-05],\n",
       "        [ -1.68700408e-04],\n",
       "        [ -1.68831664e-04],\n",
       "        [  1.65747801e-04],\n",
       "        [  2.98667276e-06]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[  7.41481648e-15]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(np.matrix(eq_set(x)) * np.matrix(eq_set(x)).T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x:\n",
      "C0=5.55556289267577199098e+01,\n",
      "C1=3.26903554347567655169e-09,\n",
      "C2=3.08713141646693843776e-06,\n",
      "C3=1.15820991613138461751e-02,\n",
      "C4=1.19166786264420683505e-02,\n",
      "C5=1.65747801385990306934e-04,\n",
      "C6=8.69245344681667691557e-05,\n",
      "C7=1.31256046958327811330e-07,\n",
      "pco2=2.61183127920939117672e-01,\n",
      "x0=9.24397224183414839517e-05,\n",
      "x1=-1.68700407719955461491e-04,\n",
      "x2=-1.68831663754572664209e-04,\n",
      "x3=1.65747801373649213076e-04,\n",
      "x4=2.98667275667192327245e-06,\n"
     ]
    }
   ],
   "source": [
    "print 'x:'\n",
    "for index, num in enumerate(res.x):\n",
    "    if index < 8:\n",
    "        print 'C' + str(index) + '=' + '%.20e' % num + ','\n",
    "    elif index == 8:\n",
    "        print 'pco2' + '=' + '%.20e' % num + ','\n",
    "    else:\n",
    "        print 'x' + str(index-9) + '=' + '%.20e' % num + ','"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}

CO2 Equilibria.mn.txt

0  H2O
1  H3O(+)
2  HO(-)
3  HCO3(-)
4  Na(+)
5  CO3(2-)
6  CO2(ac)
7  H2CO3
8  CO2(g)
eqs := {
0 = 1670.0*100*C6/(C0+C1+C2+C3+C4+C5+C6+C7+C8) - C8*8.314*298.15,
0 = 10^-0.005080863*C6 - C7,
0 = 10^-6.361590742*C7 - C1*C3,
0 = 10^-10.32991986*C3 - C1*C5,
0 = 10^-13.99602524 - C1*C2,
0 = C0 - 5.55555555555555500291e+01 - (- x0 - x1 - x2 - x3 - 2*x4),
0 = C1 - 1.00458659795015482946e-07 - (+ x2 + x3 + x4),
0 = C2 - 1.00458659795015496181e-07 - (+ x4),
0 = C3 - 1.19166786264420579422e-02 - (+ x2 - x3),
0 = C4 - 1.19166786264420579422e-02 - (0),
0 = C5 - 0.0            - (+ x3),
0 = C6 - 0.0            - (- x0 - x1),
0 = C7 - 0.0            - (+ x1 - x2),
0 = C8 - 0.0            - (+ x0)
};
numeric::solve(eqs, {C0,C1,C2,C3,C4,C5,C6,C7,C8,x0,x1,x2,x3,x4});
solve(eqs, {C0,C1,C2,C3,C5,C4,C6,C7,C8,x0,x1,x2,x3,x4})

{0 = C1 - x2 - x3 - x4 - 0.0000001004586598, 0 = (167000.0*C6)/(C0 + C1 + C2 + C3 + C4 + C5 + C6 + C7 + C8) - 2478.8191*C8, 0 = C0 + x0 + x1 + x2 + x3 + 2*x4 - 55.55555556, 0 = C7 - x1 + x2, 0 = C2 - x4 - 0.0000001004586598, 0 = 0.9883690492*C6 - C7, 0 = C4 - 0.01191667863, 0 = 1.009194233*10^(-14) - C1*C2, 0 = 0.0000004349198785*C7 - C1*C3, 0 = C5 - x3, 0 = C8 - x0, 0 = C3 - x2 + x3 - 0.01191667863, 0 = 4.6782146*10^(-11)*C3 - C1*C5, 0 = C6 + x0 + x1}
Warning: the solution [C0 = 55.55395508, C1 = 0.0000001266598701, C2 = 0.000003988812187, C3 = 0.01148800552, C4 = 0.01191667863, C5 = 0.0002124164193, C6 = -0.003662109375, C7 = -0.004150390625, C8 = 0.001953125, x0 = 0.001953125, x1 = -0.002197265625, x2 = -0.0002165958285, x3 = 0.0002124164193, x4 = 0.... [numeric::polysysroots::checkstability]
Warning: the solution [C0 = 55.57119751, C1 = -0.01191681297, C2 = -8.468658843e-13, C3 = -0.000000134576112, C4 = 0.01191667863, C5 = 5.272765538e-16, C6 = 0.003726959229, C7 = 0.003681182861, C8 = 0.004524230957, x0 = 0.004524230957, x1 = -0.008232116699, x2 = -0.01191681286, x3 = 5.272765538e-16, x4 = ... [numeric::polysysroots::checkstability]
Warning: the solution [C0 = 55.56347656, C1 = -0.0000002533197403, C2 = -0.000003991460732, C3 = 0.01237848401, C4 = 0.01191667863, C5 = -0.0002290414307, C6 = 0.006103515625, C7 = 0.0009765625, C8 = -0.00390625, x0 = -0.00390625, x1 = 0.005126953125, x2 = 0.0002328753471, x3 = -0.0002290414307, x4 = -0.0... [numeric::polysysroots::checkstability]
Warning: the solution [C0 = 0.0, C1 = 0.0, C2 = -0.0001078610401, C3 = 255213.0, C4 = 0.01191667863, C5 = -127606.4317, C6 = 4096.0, C7 = 2048.0, C8 = -131072.0, x0 = -131072.0, x1 = 129024.0, x2 = 127606.25, x3 = -127606.4317, x4 = -0.0001079614988] seems to be marred by some numerical instability. Inser... [numeric::polysysroots::checkstability]
Warning: the solution [C0 = 2.858730232e13, C1 = -654311424.0, C2 = -0.01213239807, C3 = -620756992.0, C4 = 0.01191667863, C5 = 0.006881952286, C6 = 2.913705814e13, C7 = 3.848290697e13, C8 = 2.199023256e12, x0 = 2.199023256e12, x1 = 3.95824186e13, x2 = -2785017856.0, x3 = 0.006881952286, x4 = -0.012132498... [numeric::polysysroots::checkstability]
{[C0 = 55.55395508, C1 = 0.0000001266598701, C2 = 0.000003988812187, C3 = 0.01148800552, C4 = 0.01191667863, C5 = 0.0002124164193, C6 = -0.003662109375, C7 = -0.004150390625, C8 = 0.001953125, x0 = 0.001953125, x1 = -0.002197265625, x2 = -0.0002165958285, x3 = 0.0002124164193, x4 = 0.000003888353527], [C0 = 55.56347656, C1 = -0.0000002533197403, C2 = -0.000003991460732, C3 = 0.01237848401, C4 = 0.01191667863, C5 = -0.0002290414307, C6 = 0.006103515625, C7 = 0.0009765625, C8 = -0.00390625, x0 = -0.00390625, x1 = 0.005126953125, x2 = 0.0002328753471, x3 = -0.0002290414307, x4 = -0.000004091919391], [C0 = 55.57119751, C1 = -0.01191681297, C2 = -8.468658843*10^(-13), C3 = -0.000000134576112, C4 = 0.01191667863, C5 = 5.272765538*10^(-16), C6 = 0.003726959229, C7 = 0.003681182861, C8 = 0.004524230957, x0 = 0.004524230957, x1 = -0.008232116699, x2 = -0.01191681286, x3 = 5.272765538*10^(-16), x4 = -0.0000001004595067], [C0 = - 33.89917755 + 0.002046041827*I, C1 = - 0.005958380178 + (- 0.001718687111*I), C2 = - 1.563640209*10^(-12) + 4.510300085*10^(-13)*I, C3 = 0.00595829857 + (- 0.001718687162*I), C4 = 0.01191667863, C5 = - 3.959471937*10^(-11) + 2.491529619*10^(-11)*I, C6 = - 89.46068954 + 0.0003273547199*I, C7 = - 88.42017746 + 0.0003235473005*I, C8 = 177.8868332 + 0.001067785085*I, x0 = 177.8868332 + 0.001067785085*I, x1 = - 88.4261322 + (- 0.001395139863*I), x2 = - 0.005958380178 + (- 0.001718687137*I), x3 = - 3.959471937*10^(-11) + 2.491529619*10^(-11)*I, x4 = - 0.0000001004602234 + 4.510300085*10^(-13)*I], [C0 = 0.0, C1 = 0.0, C2 = -0.0001078610401, C3 = 255213.0, C4 = 0.01191667863, C5 = -127606.4317, C6 = 4096.0, C7 = 2048.0, C8 = -131072.0, x0 = -131072.0, x1 = 129024.0, x2 = 127606.25, x3 = -127606.4317, x4 = -0.0001079614988], [C0 = 2.858730232*10^13, C1 = -654311424.0, C2 = -0.01213239807, C3 = -620756992.0, C4 = 0.01191667863, C5 = 0.006881952286, C6 = 2.913705814*10^13, C7 = 3.848290697*10^13, C8 = 2.199023256*10^12, x0 = 2.199023256*10^12, x1 = 3.95824186*10^13, x2 = -2785017856.0, x3 = 0.006881952286, x4 = -0.01213249853], [C0 = - 33.89917755 + (- 0.002046041827*I), C1 = - 0.005958380178 + 0.001718687111*I, C2 = - 1.563640209*10^(-12) + (- 4.510300085*10^(-13)*I), C3 = 0.00595829857 + 0.001718687162*I, C4 = 0.01191667863, C5 = - 3.959471937*10^(-11) + (- 2.491529619*10^(-11)*I), C6 = - 89.46068954 + (- 0.0003273547199*I), C7 = - 88.42017746 + (- 0.0003235473005*I), C8 = 177.8868332 + (- 0.001067785085*I), x0 = 177.8868332 + (- 0.001067785085*I), x1 = - 88.4261322 + 0.001395139863*I, x2 = - 0.005958380178 + 0.001718687137*I, x3 = - 3.959471937*10^(-11) + (- 2.491529619*10^(-11)*I), x4 = - 0.0000001004602234 + (- 4.510300085*10^(-13)*I)]}
matrix([[C0], [C1], [C2], [C3], [C4], [C5], [C6], [C7], [C8], [x0], [x1], [x2], [x3], [x4]]) in Dom::ImageSet(matrix([[- 5.987429602*10^42*z1^6 - 7.329131454*10^40*z1^5 - 7.872140498*10^36*z1^4 - 2.009851769*10^30*z1^3 + 1.24616353*10^26*z1^2 + 2.506693716*10^19*z1 + 1.259333237*10^12], [2.159683152*10^38*z1^6 + 2.643638886*10^36*z1^5 + 2.839503839*10^32*z1^4 + 7.249617408*10^25*z1^3 - 4.49494781*10^21*z1^2 - 9.041754741*10^14*z1 - 45424896.55], [z1 + 0.0000001004586598], [2.159683152*10^38*z1^6 + 2.643638886*10^36*z1^5 + 2.839503839*10^32*z1^4 + 7.249617408*10^25*z1^3 - 4.49494781*10^21*z1^2 - 9.041754741*10^14*z1 - 45424896.53], [0.01191667863], [7.279248332*10^26*z1^6 + 8.831914525*10^24*z1^5 + 4.447893031*10^18*z1^4 - 1.397067299*10^14*z1^3 - 42801383.95*z1^2 + 50.88461943*z1 + 0.000005401796013], [- 5.987213634*10^42*z1^6 - 7.32886709*10^40*z1^5 - 7.871856548*10^36*z1^4 - 2.009779273*10^30*z1^3 + 1.24611858*10^26*z1^2 + 2.506603298*10^19*z1 + 1.259287812*10^12], [- 5.917576646*10^42*z1^6 - 7.243625397*10^40*z1^5 - 7.780299372*10^36*z1^4 - 1.986403629*10^30*z1^3 + 1.231625036*10^26*z1^2 + 2.477449118*10^19*z1 + 1.244641098*10^12], [1.190457431*10^43*z1^6 + 1.457222812*10^41*z1^5 + 1.565187197*10^37*z1^4 + 3.996110405*10^30*z1^3 - 2.477698667*10^26*z1^2 - 4.983961999*10^19*z1 - 2.503883485*10^12], [1.190457431*10^43*z1^6 + 1.457222812*10^41*z1^5 + 1.565187197*10^37*z1^4 + 3.996110405*10^30*z1^3 - 2.477698667*10^26*z1^2 - 4.983961999*10^19*z1 - 2.503883485*10^12], [- 5.917360678*10^42*z1^6 - 7.243361033*10^40*z1^5 - 7.780015421*10^36*z1^4 - 1.986331133*10^30*z1^3 + 1.231580087*10^26*z1^2 + 2.477358701*10^19*z1 + 1.244595673*10^12], [2.159683152*10^38*z1^6 + 2.643638886*10^36*z1^5 + 2.839503839*10^32*z1^4 + 7.249617408*10^25*z1^3 - 4.49494781*10^21*z1^2 - 9.041754741*10^14*z1 - 45424896.55], [7.279248332*10^26*z1^6 + 8.831914525*10^24*z1^5 + 4.447893031*10^18*z1^4 - 1.397067299*10^14*z1^3 - 42801383.95*z1^2 + 50.88461943*z1 + 0.000005401796013], [z1]]), z1, RootOf(z^7 + (3288854257908087952623227863194376641217053483675868772953977*z^6)/268676061519215510599283100254114319489836879945000000000000000 + (2050134592226248730134824256713854736228400666906115319201897296308956154738386104552131437*z^5)/1557843948512929939169698043870198415364424558737555735391792292425000000000000000000000000000000 + (6023827913122314278109268292139954914316831247067391446756236788761598164895936283191047475179790509107195265489595577*z^4)/12878017264464141415647653185706324823133814701346600775997442666727707967291802614725000000000000000000000000000000000000000000000 - (1337979289618648321625397786703665133379116515552518649126090379866479124961511411714573635366139681808386840387385300578983431477*z^3)/64390086322320707078238265928531624115669073506733003879987213333638539836459013073625000000000000000000000000000000000000000000000000000000000000 - (10105150659376346296921576118615232529285931060237289209074775758508362339723127187001429846811738303273458103633738862619824685022919607869*z^2)/1609752158058017676955956648213290602891726837668325096999680333340963495911475326840625000000000000000000000000000000000000000000000000000000000000000000000000000 - (725437914676416108172794804095353677574908830094399178427691869302779102452150472371102437895997799952034908439047265878428016000550985113681527611*z)/1149822970041441197825683320152350430636947741191660783571200238100688211365339519171875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 - 17353785743537659610508901962077068706625995923427835674781174126323437441132917007276490488608203757911635354942744855996997797103239378808854711658699361/821302121458172284161202371537393164740676957994043416836571598643348722403813942265625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000, z) minus RootOf(z^6 + (1470930349923710945719980829141033235794033720994127290292853072865039583091607582948054745344027621521521042109959146040663895447282467433*z^5)/120165560888786716335676939886413629510322660569448141597223816369210085273463450836153904529429370349017781022381043618207222500000000000000 + (366426946763980973975369759844966511288043893144467031043608210352605348478727464787218043674194701505737448773522925224117938166682262075615854625679119481256060775591*z^4)/278698728560705889328577424933245864636130541947036502962048723997915799126001112574017033376018494242038069447845996989798195532231935916726985000000000000000000000000000000 + (966704321358337826679775393362083521875211638768065080864011679391930193294593701928623467992089549912339949537152535498839586470224592225152814351279153255444467193414555842230094362619286754611*z^3)/2879851221150077613444171302794542896486514506584218974806059389945280782564477547426710989615374327555375442404904194199947929718921508490874059813423420150446806250000000000000000000000000000000000000000000 - (1198766683356958588513758074308229090602888042249179788211820513910926757397662249790037278137376160912405439134503824119166122899325958347814739231183829712157447310734118830779060952737455600771940605829933*z^2)/57597024423001552268883426055890857929730290131684379496121187798905615651289550948534219792307486551107508848098083883998958594378430169817481196268468403008936125000000000000000000000000000000000000000000000000000000000000 - (274017454331546479027153473298348796037217508156117565744240081861403276457629426111079961869594805475138474496207812442122737067876120373495498061093809764099647728430013083276815386507349064055017359696840233293997*z)/65451164117047218487367529608966884011057147876914067609228622498756381421919944259697977036713052898985805509202368049998816584520943374792592268486895912510154687500000000000000000000000000000000000000000000000000000000000000000000000000 - 216327766279637425531785296940907490552624393498128115988956836195471884446342622820699789663981899215083167914168548727471566675647528811469265775096384894844224092740660492750276065595153971331698872550706819073484851098673/1028518293267884861944346893855193891602326609494363919573592639266171708058741981223825353434062259841205515144608640785695689185329110175312164219079792910873859375000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000, z))
subs(eqs,
{
C0=5.55556010750400801612e+01,
C1=3.46561148691701824919e-09,
C2=2.86202585956707773146e-06,
C3=1.16111088945490704277e-02,
C4=1.19166786267409195721e-02,
C5=1.51355586271531528889e-04,
C6=4.81840577796665813230e-05,
C7=4.76236316774989850635e-05,
C8=5.84064570612180726061e-05,
x0=5.84064568807210029500e-05,
x1=-1.06590514733496258336e-04,
x2=-1.54214146182733708021e-04,
x3=1.51355585977442909330e-04,
x4=2.76156690306190568131e-06
})
{0 = 2.282615354*10^(-13), 0 = 2.539207943*10^(-13), 0 = 2.671891029*10^(-13), 0 = 2.781108677*10^(-13), 0 = 2.940886196*10^(-13), 0 = 2.967101566*10^(-13), 0 = 2.988616299*10^(-13), 0 = 1.73272633*10^(-16), 0 = 1.804970697*10^(-13), 0 = 1.865293317*10^(-14), 0 = -1.952712826*10^(-11), 0 = -7.310867406*10^(-14), 0 = -3.033297159*10^(-13), 0 = -4.412648632*10^(-12)}
eqs[8];
subs(eqs[8], {
C0=5.55556010750400801612e+01,
C1=3.46561148691701824919e-09,
C2=2.86202585956707773146e-06,
C3=1.16111088945490704277e-02,
C4=1.19166786267409195721e-02,
C5=1.51355586271531528889e-04,
C6=4.81840577796665813230e-05,
C7=4.76236316774989850635e-05,
C8=5.84064570612180726061e-05,
x0=5.84064568807210029500e-05,
x1=-1.06590514733496258336e-04,
x2=-1.54214146182733708021e-04,
x3=1.51355585977442909330e-04,
x4=2.76156690306190568131e-06
})
0 = 4.6782146*10^(-11)*C3 - C1*C5
0 = 1.865293317*10^(-14)

{0 = C1 - x2 - x3 - x4 - 0.0000001004586598, 0 = (167000.0*C6)/(C0 + C1 + C2 + C3 + C4 + C5 + C6 + C7 + C8) - 2478.8191*C8, 0 = C0 + x0 + x1 + x2 + x3 + 2*x4 - 55.55555556, 0 = C7 - x1 + x2, 0 = C2 - x4 - 0.0000001004586598, 0 = 0.9883690492*C6 - C7, 0 = C4 - 0.01191667863, 0 = 1.009194233*10^(-14) - C1*C2, 0 = 0.0000004349198785*C7 - C1*C3, 0 = C5 - x3, 0 = C8 - x0, 0 = C3 - x2 + x3 - 0.01191667863, 0 = 4.6782146*10^(-11)*C3 - C1*C5, 0 = C6 + x0 + x1}
eqs2 := {
0 = 1670.0*100*C6/(C0+C1+C2+C3+C4+C5+C6+C7+C8) - C8*8.314*298.15,
0 = -0.005080863 + log10(C6) - log10(C7),
0 = -6.361590742 + log10(C7) - log10(C1) - log10(C3),
0 = -10.32991986 + log10(C3) - log10(C1) - log10(C5),
0 = -13.99602524 - log10(C1) - log10(C2),
0 = C0 - 5.55555555555555500291e+01 - (- x0 - x1 - x2 - x3 - 2*x4),
0 = C1 - 1.00458659795015482946e-07 - (+ x2 + x3 + x4),
0 = C2 - 1.00458659795015496181e-07 - (+ x4),
0 = C3 - 1.19166786264420579422e-02 - (+ x2 - x3),
0 = C4 - 1.19166786264420579422e-02 - (0),
0 = C5 - 0.0            - (+ x3),
0 = C6 - 0.0            - (- x0 - x1),
0 = C7 - 0.0            - (+ x1 - x2),
0 = C8 - 0.0            - (+ x0)
};
numeric::solve(eqs2, {C0,C1,C2,C3,C4,C5,C6,C7,C8,x0,x1,x2,x3,x4});
solve(eqs2, {C0,C1,C2,C3,C5,C4,C6,C7,C8,x0,x1,x2,x3,x4})
{0 = - ln(C1)/ln(10) - ln(C2)/ln(10) - 13.99602524, 0 = C1 - x2 - x3 - x4 - 0.0000001004586598, 0 = (167000.0*C6)/(C0 + C1 + C2 + C3 + C4 + C5 + C6 + C7 + C8) - 2478.8191*C8, 0 = C0 + x0 + x1 + x2 + x3 + 2*x4 - 55.55555556, 0 = C7 - x1 + x2, 0 = C2 - x4 - 0.0000001004586598, 0 = ln(C7)/ln(10) - ln(C3)/ln(10) - ln(C1)/ln(10) - 6.361590742, 0 = ln(C3)/ln(10) - ln(C1)/ln(10) - ln(C5)/ln(10) - 10.32991986, 0 = C4 - 0.01191667863, 0 = ln(C6)/ln(10) - ln(C7)/ln(10) - 0.005080863, 0 = C5 - x3, 0 = C8 - x0, 0 = C3 - x2 + x3 - 0.01191667863, 0 = C6 + x0 + x1}
{}
{}
simplify(subs(eqs2,
{
C0=5.55556010750400801612e+01,
C1=3.46561148691701824919e-09,
C2=2.86202585956707773146e-06,
C3=1.16111088945490704277e-02,
C4=1.19166786267409195721e-02,
C5=1.51355586271531528889e-04,
C6=4.81840577796665813230e-05,
C7=4.76236316774989850635e-05,
C8=5.84064570612180726061e-05,
x0=5.84064568807210029500e-05,
x1=-1.06590514733496258336e-04,
x2=-1.54214146182733708021e-04,
x3=1.51355585977442909330e-04,
x4=2.76156690306190568131e-06
}))
{0 = -0.000000002758601001, 0 = -0.2884218038, 0 = 2.282615354*10^(-13), 0 = 2.539207943*10^(-13), 0 = 2.671891029*10^(-13), 0 = 2.781108677*10^(-13), 0 = 2.940886196*10^(-13), 0 = 2.967101566*10^(-13), 0 = 2.988616299*10^(-13), 0 = 1.804970697*10^(-13), 0 = -7.310867406*10^(-14), 0 = -4.412648632*10^(-12), 0 = 0.007521332093, 0 = 0.01517550905}