lie_trotter_sample.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "# Imports"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "## Numpy imports "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T10:51:33.719173Z",
     "start_time": "2018-12-30T10:51:33.715321Z"
    },
    "hidden": true
   },
   "outputs": [],
   "source": [
    "from numpy import sin, cos, tan, real, imag,  log, conj\n",
    "from numpy import array, append, linspace, arange\n",
    "from numpy import add, sqrt, abs, dot\n",
    "from numpy.random import random, random_sample, rand, seed\n",
    "from numpy import concatenate, trace, diag\n",
    "from numpy import ones, zeros, ones_like, zeros_like\n",
    "# from numpy import pi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "## Scipy imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T10:49:28.097670Z",
     "start_time": "2018-12-30T10:49:28.093644Z"
    },
    "hidden": true
   },
   "outputs": [],
   "source": [
    "from scipy.integrate import ode, odeint, complex_ode\n",
    "from scipy.optimize import minimize\n",
    "from scipy.linalg import eigh, inv, norm, expm\n",
    "# from scipy.linalg import \n",
    "# from scipy import"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "## Matplotlib imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T12:40:18.509947Z",
     "start_time": "2018-12-30T12:40:18.491987Z"
    },
    "hidden": true
   },
   "outputs": [],
   "source": [
    "from matplotlib.pyplot import plot, figure, show, savefig, axes\n",
    "from matplotlib.pyplot import xlabel, ylabel, title, legend\n",
    "from matplotlib import rcParams\n",
    "from matplotlib.pyplot import style \n",
    "from matplotlib.pyplot import xlim, ylim, axis \n",
    "# beware not same as axes\n",
    "from matplotlib.pyplot import subplot, subplots, text\n",
    "from matplotlib.pyplot import GridSpec\n",
    "from matplotlib.pyplot import scatter, colorbar\n",
    "\n",
    "\n",
    "pgf_with_rc_fonts = {\"pgf.texsystem\": \"pdflatex\"}\n",
    "rcParams.update(pgf_with_rc_fonts)\n",
    "style.use('seaborn-whitegrid')\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "## Math imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T10:49:31.035525Z",
     "start_time": "2018-12-30T10:49:31.028537Z"
    },
    "hidden": true
   },
   "outputs": [],
   "source": [
    "from math import pi\n",
    "from math import exp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "## Cmath imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "## Date and datetime imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T10:49:32.944829Z",
     "start_time": "2018-12-30T10:49:32.940813Z"
    },
    "hidden": true
   },
   "outputs": [],
   "source": [
    "from datetime import date\n",
    "from datetime import datetime# now\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "## Os imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T10:49:34.096029Z",
     "start_time": "2018-12-30T10:49:34.092636Z"
    },
    "hidden": true
   },
   "outputs": [],
   "source": [
    "from os import getcwd, mkdir, chdir\n",
    "from os.path import abspath, join \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "## Sympy imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T10:49:34.968835Z",
     "start_time": "2018-12-30T10:49:34.964610Z"
    },
    "hidden": true
   },
   "outputs": [],
   "source": [
    "from sympy import Function, dsolve, Eq, Derivative, symbols\n",
    "# x, y, z, t = symbols('x y z t')\n",
    "# k, m, n = symbols('k m n', integer=True)\n",
    "# f, g, h = symbols('f g h', cls=Function)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "## Miscellaneous imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "## Extra useful functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T10:49:37.380514Z",
     "start_time": "2018-12-30T10:49:37.376716Z"
    },
    "hidden": true
   },
   "outputs": [],
   "source": [
    "def rint(x):\n",
    "    print(\"x = \", x)\n",
    "    return None"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "# Lie_trotter code"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "## parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T10:49:39.364050Z",
     "start_time": "2018-12-30T10:49:39.360261Z"
    },
    "hidden": true
   },
   "outputs": [],
   "source": [
    "d = 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "## code functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T10:57:02.171821Z",
     "start_time": "2018-12-30T10:57:01.931503Z"
    },
    "hidden": true
   },
   "outputs": [],
   "source": [
    "#import numpy as np\n",
    "#import math\n",
    "#from scipy import linalg\n",
    "\n",
    "def calc_exp(X, h):\n",
    "    rx, Ux = eigh(X)\n",
    "    Ux_inv = inv(Ux)\n",
    "    tx = diag(array([exp(h * i) for i in rx]))\n",
    "    eX = Ux.dot(tx.dot(Ux_inv))\n",
    "    return eX\n",
    "\n",
    "def trotter(X,Y,Z,h,n):\n",
    "    eZ = calc_exp(Z,h)\n",
    "    eX = calc_exp(X,h/n)\n",
    "    eY = calc_exp(Y,h/n)\n",
    "    S = diag(ones(d))\n",
    "    eXeY = eX.dot(eY)\n",
    "    for i in range(n):\n",
    "        S = S.dot(eXeY)\n",
    "    return norm(eZ - S)/norm(eZ)\n",
    "\n",
    "def trotter2nd(X,Y,Z,h,n):\n",
    "    eZ = calc_exp(Z,h)\n",
    "    eX = calc_exp(X,h/n*0.5)\n",
    "    eY = calc_exp(Y,h/n)\n",
    "    S = diag(ones(d))\n",
    "    eXeYeX = eX.dot(eY.dot(eX))\n",
    "    for i in range(n):\n",
    "        S = S.dot(eXeYeX)\n",
    "    return norm(eZ - S)/norm(eZ)\n",
    "\n",
    "\n",
    "seed(1)\n",
    "x1 = random_sample((d,d))\n",
    "x2 = random_sample((d,d))\n",
    "X = x1.dot(x1.T)\n",
    "Y = x2.dot(x2.T)\n",
    "Z = X + Y\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T10:57:17.945144Z",
     "start_time": "2018-12-30T10:57:17.936639Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.17022005e-01, 7.20324493e-01],\n",
       "       [1.14374817e-04, 3.02332573e-01]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T10:57:44.055698Z",
     "start_time": "2018-12-30T10:57:44.050785Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.14675589, 0.09233859],\n",
       "       [0.18626021, 0.34556073]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T10:57:53.423265Z",
     "start_time": "2018-12-30T10:57:53.418507Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.69277473, 0.21782525],\n",
       "       [0.21782525, 0.091405  ]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T10:57:56.580695Z",
     "start_time": "2018-12-30T10:57:56.576241Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.03006371, 0.05924338],\n",
       "       [0.05924338, 0.15410508]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T10:58:00.748559Z",
     "start_time": "2018-12-30T10:58:00.742643Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.72283844, 0.27706863],\n",
       "       [0.27706863, 0.24551008]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "# Plots of error "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "## n dependence plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T11:26:57.581071Z",
     "start_time": "2018-12-30T11:26:57.576072Z"
    },
    "hidden": true
   },
   "outputs": [],
   "source": [
    "n_vec = arange(100) + 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T11:26:58.099824Z",
     "start_time": "2018-12-30T11:26:58.095212Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  1,   2,   3,   4,   5,   6,   7,   8,   9,  10,  11,  12,  13,\n",
       "        14,  15,  16,  17,  18,  19,  20,  21,  22,  23,  24,  25,  26,\n",
       "        27,  28,  29,  30,  31,  32,  33,  34,  35,  36,  37,  38,  39,\n",
       "        40,  41,  42,  43,  44,  45,  46,  47,  48,  49,  50,  51,  52,\n",
       "        53,  54,  55,  56,  57,  58,  59,  60,  61,  62,  63,  64,  65,\n",
       "        66,  67,  68,  69,  70,  71,  72,  73,  74,  75,  76,  77,  78,\n",
       "        79,  80,  81,  82,  83,  84,  85,  86,  87,  88,  89,  90,  91,\n",
       "        92,  93,  94,  95,  96,  97,  98,  99, 100])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_vec"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T11:26:59.568667Z",
     "start_time": "2018-12-30T11:26:59.524131Z"
    },
    "hidden": true
   },
   "outputs": [],
   "source": [
    "n_error_1 = array([ trotter(X, Y, Z, 1.0, n_i) for n_i in n_vec])\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T11:27:02.464182Z",
     "start_time": "2018-12-30T11:27:02.457583Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.02860811, 0.01419363, 0.00944849, 0.00708269, 0.00566479,\n",
       "       0.00472004, 0.00404543, 0.00353957, 0.00314618, 0.00283149,\n",
       "       0.00257403, 0.00235949, 0.00217797, 0.00202238, 0.00188755,\n",
       "       0.00176956, 0.00166546, 0.00157293, 0.00149014, 0.00141563,\n",
       "       0.00134822, 0.00128693, 0.00123097, 0.00117968, 0.00113249,\n",
       "       0.00108893, 0.0010486 , 0.00101115, 0.00097628, 0.00094374,\n",
       "       0.0009133 , 0.00088475, 0.00085794, 0.00083271, 0.00080892,\n",
       "       0.00078645, 0.00076519, 0.00074505, 0.00072595, 0.0007078 ,\n",
       "       0.00069054, 0.0006741 , 0.00065842, 0.00064345, 0.00062916,\n",
       "       0.00061548, 0.00060238, 0.00058983, 0.0005778 , 0.00056624,\n",
       "       0.00055514, 0.00054446, 0.00053419, 0.0005243 , 0.00051476,\n",
       "       0.00050557, 0.0004967 , 0.00048814, 0.00047986, 0.00047187,\n",
       "       0.00046413, 0.00045664, 0.0004494 , 0.00044237, 0.00043557,\n",
       "       0.00042897, 0.00042257, 0.00041635, 0.00041032, 0.00040446,\n",
       "       0.00039876, 0.00039322, 0.00038783, 0.00038259, 0.00037749,\n",
       "       0.00037252, 0.00036769, 0.00036297, 0.00035838, 0.0003539 ,\n",
       "       0.00034953, 0.00034527, 0.00034111, 0.00033705, 0.00033308,\n",
       "       0.00032921, 0.00032542, 0.00032173, 0.00031811, 0.00031458,\n",
       "       0.00031112, 0.00030774, 0.00030443, 0.00030119, 0.00029802,\n",
       "       0.00029492, 0.00029187, 0.0002889 , 0.00028598, 0.00028312])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_error_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T14:34:48.481171Z",
     "start_time": "2018-12-30T14:34:48.088809Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x122274eb8>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = axes()\n",
    "ax.loglog(n_vec, n_error_1,\n",
    "          color='white', markeredgecolor='purple', marker='o',  markersize=10 )\n",
    "ax.loglog(n_vec, 1/n_vec*(n_error_1[0]/n_vec[0]), label = '1/n')\n",
    "ax.set(xlim=(1, 1e2), ylim=(1e-4, 1e0),\n",
    "       xlabel='n', ylabel='Error',\n",
    "       title='Error in n using first order trotter');\n",
    "ax.legend()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T11:28:15.502321Z",
     "start_time": "2018-12-30T11:28:15.458290Z"
    },
    "hidden": true
   },
   "outputs": [],
   "source": [
    "n_error_2 = array([ trotter2nd(X, Y, Z, 1.0, n_i) for n_i in n_vec])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T11:28:26.248371Z",
     "start_time": "2018-12-30T11:28:26.242166Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.77891558e-03, 4.49175646e-04, 2.00003128e-04, 1.12574654e-04,\n",
       "       7.20693884e-05, 5.00563413e-05, 3.67797009e-05, 2.81612543e-05,\n",
       "       2.22518405e-05, 1.80245545e-05, 1.48966707e-05, 1.25175617e-05,\n",
       "       1.06659975e-05, 9.19680186e-06, 8.01150654e-06, 7.04141370e-06,\n",
       "       6.23741393e-06, 5.56364695e-06, 4.99343273e-06, 4.50658927e-06,\n",
       "       4.08762198e-06, 3.72447549e-06, 3.40765663e-06, 3.12960776e-06,\n",
       "       2.88425174e-06, 2.66665717e-06, 2.47278851e-06, 2.29931778e-06,\n",
       "       2.14348064e-06, 2.00296566e-06, 1.87582808e-06, 1.76042219e-06,\n",
       "       1.65534777e-06, 1.55940744e-06, 1.47157239e-06, 1.39095467e-06,\n",
       "       1.31678468e-06, 1.24839277e-06, 1.18519395e-06, 1.12667550e-06,\n",
       "       1.07238639e-06, 1.02192867e-06, 9.74950137e-07, 9.31138115e-07,\n",
       "       8.90214288e-07, 8.51930269e-07, 8.16063797e-07, 7.82415527e-07,\n",
       "       7.50806248e-07, 7.21074474e-07, 6.93074423e-07, 6.66674158e-07,\n",
       "       6.41754102e-07, 6.18205607e-07, 5.95929866e-07, 5.74836780e-07,\n",
       "       5.54844076e-07, 5.35876517e-07, 5.17865244e-07, 5.00746970e-07,\n",
       "       4.84463682e-07, 4.68961888e-07, 4.54192430e-07, 4.40109854e-07,\n",
       "       4.26672199e-07, 4.13840758e-07, 4.01579513e-07, 3.89855238e-07,\n",
       "       3.78636994e-07, 3.67896093e-07, 3.57605835e-07, 3.47741351e-07,\n",
       "       3.38279479e-07, 3.29198578e-07, 3.20478499e-07, 3.12100356e-07,\n",
       "       3.04046525e-07, 2.96300446e-07, 2.88846651e-07, 2.81670606e-07,\n",
       "       2.74758740e-07, 2.68098188e-07, 2.61676926e-07, 2.55483609e-07,\n",
       "       2.49507612e-07, 2.43738841e-07, 2.38167871e-07, 2.32785713e-07,\n",
       "       2.27583982e-07, 2.22554659e-07, 2.17690245e-07, 2.12983583e-07,\n",
       "       2.08427918e-07, 2.04016913e-07, 1.99744393e-07, 1.95604723e-07,\n",
       "       1.91592436e-07, 1.87702336e-07, 1.83929518e-07, 1.80269308e-07])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_error_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T14:35:37.605825Z",
     "start_time": "2018-12-30T14:35:37.182589Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1224b9fd0>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = axes()\n",
    "ax.loglog(n_vec, n_error_2,\n",
    "          color='white', markeredgecolor='purple', marker='o',  markersize=10 )\n",
    "ax.loglog(n_vec, 1/(n_vec**2)*(n_error_2[0]/n_vec[0]), label = '1/n**2')\n",
    "ax.set(xlim=(1, 1e2), ylim=(1e-7, 1e-2),\n",
    "       xlabel='n', ylabel='Error',\n",
    "       title='Error in n using second order trotter');\n",
    "ax.legend()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "## h dependence plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T13:17:25.142296Z",
     "start_time": "2018-12-30T13:17:25.136431Z"
    },
    "hidden": true
   },
   "outputs": [],
   "source": [
    "h_vec = (arange(100) + 1)/100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T13:17:33.389572Z",
     "start_time": "2018-12-30T13:17:33.383340Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.1 , 0.11,\n",
       "       0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18, 0.19, 0.2 , 0.21, 0.22,\n",
       "       0.23, 0.24, 0.25, 0.26, 0.27, 0.28, 0.29, 0.3 , 0.31, 0.32, 0.33,\n",
       "       0.34, 0.35, 0.36, 0.37, 0.38, 0.39, 0.4 , 0.41, 0.42, 0.43, 0.44,\n",
       "       0.45, 0.46, 0.47, 0.48, 0.49, 0.5 , 0.51, 0.52, 0.53, 0.54, 0.55,\n",
       "       0.56, 0.57, 0.58, 0.59, 0.6 , 0.61, 0.62, 0.63, 0.64, 0.65, 0.66,\n",
       "       0.67, 0.68, 0.69, 0.7 , 0.71, 0.72, 0.73, 0.74, 0.75, 0.76, 0.77,\n",
       "       0.78, 0.79, 0.8 , 0.81, 0.82, 0.83, 0.84, 0.85, 0.86, 0.87, 0.88,\n",
       "       0.89, 0.9 , 0.91, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97, 0.98, 0.99,\n",
       "       1.  ])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h_vec"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T13:23:19.814275Z",
     "start_time": "2018-12-30T13:23:19.771574Z"
    },
    "hidden": true
   },
   "outputs": [],
   "source": [
    "h_error_n1_1 = array([ trotter(X, Y, Z, h_i, 1) for h_i in h_vec])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T13:23:38.959620Z",
     "start_time": "2018-12-30T13:23:38.953604Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3.13229425e-06, 1.25287981e-05, 2.81883749e-05, 5.01091309e-05,\n",
       "       7.82884165e-05, 1.12722827e-04, 1.53408204e-04, 2.00339639e-04,\n",
       "       2.53511474e-04, 3.12917306e-04, 3.78549988e-04, 4.50401636e-04,\n",
       "       5.28463628e-04, 6.12726612e-04, 7.03180510e-04, 7.99814523e-04,\n",
       "       9.02617134e-04, 1.01157612e-03, 1.12667854e-03, 1.24791077e-03,\n",
       "       1.37525848e-03, 1.50870668e-03, 1.64823967e-03, 1.79384110e-03,\n",
       "       1.94549395e-03, 2.10318054e-03, 2.26688257e-03, 2.43658107e-03,\n",
       "       2.61225645e-03, 2.79388851e-03, 2.98145644e-03, 3.17493881e-03,\n",
       "       3.37431363e-03, 3.57955829e-03, 3.79064965e-03, 4.00756398e-03,\n",
       "       4.23027702e-03, 4.45876395e-03, 4.69299944e-03, 4.93295763e-03,\n",
       "       5.17861217e-03, 5.42993621e-03, 5.68690240e-03, 5.94948295e-03,\n",
       "       6.21764958e-03, 6.49137358e-03, 6.77062581e-03, 7.05537668e-03,\n",
       "       7.34559623e-03, 7.64125407e-03, 7.94231942e-03, 8.24876115e-03,\n",
       "       8.56054774e-03, 8.87764735e-03, 9.20002778e-03, 9.52765651e-03,\n",
       "       9.86050072e-03, 1.01985273e-02, 1.05417027e-02, 1.08899934e-02,\n",
       "       1.12433654e-02, 1.16017844e-02, 1.19652161e-02, 1.23336257e-02,\n",
       "       1.27069783e-02, 1.30852389e-02, 1.34683722e-02, 1.38563427e-02,\n",
       "       1.42491147e-02, 1.46466526e-02, 1.50489204e-02, 1.54558820e-02,\n",
       "       1.58675012e-02, 1.62837418e-02, 1.67045674e-02, 1.71299414e-02,\n",
       "       1.75598274e-02, 1.79941887e-02, 1.84329887e-02, 1.88761906e-02,\n",
       "       1.93237577e-02, 1.97756532e-02, 2.02318403e-02, 2.06922822e-02,\n",
       "       2.11569421e-02, 2.16257833e-02, 2.20987690e-02, 2.25758624e-02,\n",
       "       2.30570270e-02, 2.35422260e-02, 2.40314229e-02, 2.45245813e-02,\n",
       "       2.50216646e-02, 2.55226365e-02, 2.60274608e-02, 2.65361013e-02,\n",
       "       2.70485220e-02, 2.75646870e-02, 2.80845604e-02, 2.86081065e-02])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h_error_n1_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T13:41:38.426186Z",
     "start_time": "2018-12-30T13:41:38.383480Z"
    },
    "hidden": true
   },
   "outputs": [],
   "source": [
    "h_error_n2_1 = array([ trotter(X, Y, Z, h_i, 2) for h_i in h_vec])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T13:41:38.426186Z",
     "start_time": "2018-12-30T13:41:38.383480Z"
    },
    "hidden": true
   },
   "outputs": [],
   "source": [
    "h_error_n4_1 = array([ trotter(X, Y, Z, h_i, 4) for h_i in h_vec])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T14:40:25.325635Z",
     "start_time": "2018-12-30T14:40:24.801847Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1227fdef0>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = axes()\n",
    "ax.loglog(h_vec, h_error_n1_1, label = 'n=1', color='white',\n",
    "          markeredgecolor='purple', marker='+',  markersize=7 )\n",
    "\n",
    "ax.loglog(h_vec, h_error_n2_1, label = 'n=2', color='white',\n",
    "          markeredgecolor='green', marker='x',  markersize=7 )\n",
    "\n",
    "ax.loglog(h_vec, h_error_n4_1, label = 'n=4', color='white',\n",
    "          markeredgecolor='lightblue', marker='*',  markersize=7 )\n",
    "ax.loglog(h_vec, ((h_vec**2)*(h_error_n4_1[0]/(h_vec[0]**2))), \n",
    "          label = 'h**2', color='black')\n",
    "ax.set(xlim=(1e-2, 1e0), ylim=(1e-7, 1e-1),\n",
    "       xlabel='h', ylabel='Error',\n",
    "       title='Error in h using first order trotter');\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T14:40:25.325635Z",
     "start_time": "2018-12-30T14:40:24.801847Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.000e-04, 4.000e-04, 9.000e-04, 1.600e-03, 2.500e-03, 3.600e-03,\n",
       "       4.900e-03, 6.400e-03, 8.100e-03, 1.000e-02, 1.210e-02, 1.440e-02,\n",
       "       1.690e-02, 1.960e-02, 2.250e-02, 2.560e-02, 2.890e-02, 3.240e-02,\n",
       "       3.610e-02, 4.000e-02, 4.410e-02, 4.840e-02, 5.290e-02, 5.760e-02,\n",
       "       6.250e-02, 6.760e-02, 7.290e-02, 7.840e-02, 8.410e-02, 9.000e-02,\n",
       "       9.610e-02, 1.024e-01, 1.089e-01, 1.156e-01, 1.225e-01, 1.296e-01,\n",
       "       1.369e-01, 1.444e-01, 1.521e-01, 1.600e-01, 1.681e-01, 1.764e-01,\n",
       "       1.849e-01, 1.936e-01, 2.025e-01, 2.116e-01, 2.209e-01, 2.304e-01,\n",
       "       2.401e-01, 2.500e-01, 2.601e-01, 2.704e-01, 2.809e-01, 2.916e-01,\n",
       "       3.025e-01, 3.136e-01, 3.249e-01, 3.364e-01, 3.481e-01, 3.600e-01,\n",
       "       3.721e-01, 3.844e-01, 3.969e-01, 4.096e-01, 4.225e-01, 4.356e-01,\n",
       "       4.489e-01, 4.624e-01, 4.761e-01, 4.900e-01, 5.041e-01, 5.184e-01,\n",
       "       5.329e-01, 5.476e-01, 5.625e-01, 5.776e-01, 5.929e-01, 6.084e-01,\n",
       "       6.241e-01, 6.400e-01, 6.561e-01, 6.724e-01, 6.889e-01, 7.056e-01,\n",
       "       7.225e-01, 7.396e-01, 7.569e-01, 7.744e-01, 7.921e-01, 8.100e-01,\n",
       "       8.281e-01, 8.464e-01, 8.649e-01, 8.836e-01, 9.025e-01, 9.216e-01,\n",
       "       9.409e-01, 9.604e-01, 9.801e-01, 1.000e+00])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h_vec**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T13:41:38.426186Z",
     "start_time": "2018-12-30T13:41:38.383480Z"
    },
    "hidden": true
   },
   "outputs": [],
   "source": [
    "h_error_n1_2 = array([ trotter2nd(X, Y, Z, h_i, 1) for h_i in h_vec])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T13:41:38.426186Z",
     "start_time": "2018-12-30T13:41:38.383480Z"
    },
    "hidden": true
   },
   "outputs": [],
   "source": [
    "h_error_n2_2 = array([ trotter2nd(X, Y, Z, h_i, 2) for h_i in h_vec])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T13:41:38.426186Z",
     "start_time": "2018-12-30T13:41:38.383480Z"
    },
    "hidden": true
   },
   "outputs": [],
   "source": [
    "h_error_n4_2 = array([ trotter2nd(X, Y, Z, h_i, 4) for h_i in h_vec])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T14:40:25.325635Z",
     "start_time": "2018-12-30T14:40:24.801847Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x122921320>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = axes()\n",
    "ax.loglog(h_vec, h_error_n1_2, label = 'n=1', color='white',\n",
    "          markeredgecolor='purple', marker='+',  markersize=7 )\n",
    "\n",
    "ax.loglog(h_vec, h_error_n2_2, label = 'n=2', color='white',\n",
    "          markeredgecolor='green', marker='x',  markersize=7 )\n",
    "\n",
    "ax.loglog(h_vec, h_error_n4_2, label = 'n=4', color='white',\n",
    "          markeredgecolor='lightblue', marker='*',  markersize=7 )\n",
    "ax.loglog(h_vec, ((h_vec**3)*(h_error_n4_2[0]/(h_vec[0]**3))), \n",
    "          label = 'h**3', color='black')\n",
    "ax.set(xlim=(1e-2, 1e0), ylim=(1e-10, 1e-2),\n",
    "       xlabel='h', ylabel='Error',\n",
    "       title='Error in h using second order trotter');\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T14:40:25.325635Z",
     "start_time": "2018-12-30T14:40:24.801847Z"
    },
    "hidden": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "# Actual original code which uses gnuplot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "### sub sub topic 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "def n_dependence(X,Y,Z,h,order):\n",
    "    filename = \"n_%x.dat\" % order\n",
    "    t = trotter if order == 1 else trotter2nd\n",
    "    print(filename)\n",
    "    f = open(filename,'w')\n",
    "    for i in range(100):\n",
    "        n = i+1\n",
    "        f.write(str(n) + \" \" +  str(t(X,Y,Z,h,n)))\n",
    "        f.write(\"\\n\")\n",
    "    f.close()\n",
    "\n",
    "def h_dependence(X,Y,Z,n, order):\n",
    "    t = trotter if order == 1 else trotter2nd\n",
    "    filename = \"h%x_%x.dat\" %(n, order)\n",
    "    print(filename)\n",
    "    f = open(filename,'w')\n",
    "    for i in range(100):\n",
    "        h = (i+1)/100.0\n",
    "        f.write(str(h) + \" \" +  str(t(X,Y,Z,h,n)))\n",
    "        f.write(\"\\n\")\n",
    "    f.close()\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n_1.dat\n",
      "n_2.dat\n",
      "h1_1.dat\n",
      "h2_1.dat\n",
      "h4_1.dat\n",
      "h1_2.dat\n",
      "h2_2.dat\n",
      "h4_2.dat\n"
     ]
    }
   ],
   "source": [
    "n_dependence(X,Y,Z,1.0,1)\n",
    "n_dependence(X,Y,Z,1.0,2)\n",
    "\n",
    "h_dependence(X,Y,Z,1,1)\n",
    "h_dependence(X,Y,Z,2,1)\n",
    "h_dependence(X,Y,Z,4,1)\n",
    "\n",
    "h_dependence(X,Y,Z,1,2)\n",
    "h_dependence(X,Y,Z,2,2)\n",
    "h_dependence(X,Y,Z,4,2)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "# My various errors while preparing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T12:53:14.454984Z",
     "start_time": "2018-12-30T12:53:13.997955Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x11e210e80>"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = axes()\n",
    "ax.loglog(n_vec, n_error_1, )\n",
    "ax.loglog(n_vec, 1/n_vec, label = '1/n')\n",
    "ax.set(xlim=(1, 1e2), ylim=(1e-4, 1e0),\n",
    "       xlabel='n', ylabel='Error',\n",
    "       title='Error in n using first order trotter');\n",
    "ax.legend()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T12:53:35.735831Z",
     "start_time": "2018-12-30T12:53:35.368219Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x122932d30>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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U6NPKGDPEWruyvsM0FQ6Hg15dO9Kr63RcrhcpOnKcQ+tnEH14IQOOziD0o79yyRnD6VaPkDRgKnE9hkGgBjoUEf9V06+2PwRUFrXgcDjo0bEtPTq+gMv1PPuOn2bfujwiD84n89h8Io/P4GpeJMUtBpOQOZWEPiMhSAMdioh/qWlZuIwxeYAFqgCstd+ut1RNlMPhwLRtiXniS8CXOHDiLEXrZxN2YD6ZJ1cQM3ceN+aFcSLpQWIyppCUPhaCI3wdW0SkxmXxh3pN0Ux1aZ1El9xngWc5cvoia9fPI8jOJeN0AYkLl1C6MIQTCQOJSH+Mlv0nQmiMryOLSDNV07L4C/AFoAewD/hVfQUyxgwDHgfCgdettdvra13+pEOLODpMegp4iuPnLzN/3UKce+fS79xaWixbyc1lX+d4bBahaY+RMmASjogEX0cWkWakpmXxG6AEWAo8DPwe+HQ9ZQoHPg/0BUYAzaIsqmuTEE2bCdNgwjROlVxnQf4SqnbPpu/FNbRa/U0qV0/no+j+BPWeQOvsKTiiNNChiNSvmpZFV2vtQ57Hs4wx+XUVwBjzAvCIZ7LAWvtjY0wE8BzwUl2tp7FqGRvO6NETYfREzl0pZWHBSsp3zqLXpdW0Wf8dqtZ/l2ORaTh6jKd1Ti7OOA10KCJ1r6ZlEWqMCbfWXjfGhAEBdRXAWvsm8ObH08aYROB14BVr7Zm6Wk9TkBgVyqgRo2DEKEqulbF443pKt8+ke8kqzKYfwaYfcSy8B1Xdx9PmgccJSOjo68gi0kTUtCzeBLYbY3bhPm/x/ZrMZIzJAl6z1g42xjiBt4E0oAx41lp74Daz/RxIAv7VGDPLWvu3GmZsVmIjQnh06FAYOpTLpeUs27yJK1tm0PX8Snpt+Sls+SnFoV252W0srQdOI6hlqq8ji0gjVtOyOAlkAZ2Aw9ba895mMMZMB54CrnmemgiEWmtzjDHZwBvAhFvns9bW17mQJis6NIhHBj0Agx7gWlkFK7ZspWTLDDqcWU6/Hb+AHb/gVEgHbnQZQ+uB0whupYEOReTe1PimPM85iwv3sOyDwCTgXc/0IGARgLV2gzGm/z0s6x8UFRXdz+xNWkpsJClDP0NZxVP89fBHVB5cQdeSdWTsepuA3f/J6YCWnEp+mNDuw6lK6qniqEOlpaXaNqVJqreb8qy1M4wxHao9FQ1cqjZdaYwJtNZW3EPe/5OaqsMqNdG3d09gFDcrqijYbTm1cQYpxUsYUPw3gk6+x4XAZEraP0rLnMcJ76SBDu9XUVGRtk3xW4WFhbWet6Zl8SegstZrcbsMRFWbdta2KOTeBQc6GZSWCmnfpaLy22zee5jjG2eQfGwxWQf+SsjBdykJiOdC2+EkZ00jspsGOhSRv6vpp8Hj1toR97mu9cA44H3POYud97k8qaXAACfZPTtDz+lUVr3I1gPHOFIwk/iji8g+PIvwI+9xxRnN2VbDSMqaSlTqcA10KNLM1bQsLhpjJvDJw1D77nFdecBwzz0aDuCZe5xf6kGA00H/bu3o3+0FqqqeZ8eRkxzMn03U4QVkH1tE1PE8rjvCOdVyCPGZU4jtPQqCwnwdW0QamMPlcnl9kTFmJeDC/SEPnqua6jPY3RQWFroyMjJ8tfpmweVysefYWWz+XMIOzCe7fCNxjquUOkIpTnqQ2IzJxPcdCyFR3hfWjOichfizwsJCMjIyanVFy133LIwx71lrp1lrhxhjvmmt/ZnneQ1X3sQ5HA56tkumZ7vP4nL9M/tPXmRl/gKC980j63Q+8QuXcnNhECcSBxLVdxKJGRMhLNbXsUWknng7DJVc7fFo4Geex953R6TJcDgcdGsVT7cpTwJPcvjMZdblLyJg71z6n11H4rLVlC/7BsVxAwhLm0hy5mSISPR1bBGpQ/dyuYsuxhcAOiZH03FiLpDLsfNXmV2wHNeeOaSfX0PyqulUrnqZE9HpBPWeSMusKTiiW/k6sojcJ29l4brDYxEA2iZE0nbsBBg7gVMlN5izYTUVu2bRp2Q17dZ/j6r1r3A8sjfOnhNolT0VR1x7X0cWkVrwVhY9jTH/g3uvovrjHvWeTBqdlrFhjB85EkaO5NzVMuZvzKd0Rx6pF1fRY+OrsPFVToSnUtV9HK1zpuFM6uLryCJSQ97KIrfa41/f4bHIP0iMDGHMsCEwbAiXrpezcPMmrm3No9uFFfTZ8jpseZ1ToZ252W0crXJyCWzZQ8OOiPixu5aFtXZ1QwWRpismPIhRDz0ADz3AldJylmzZxqUtM+l4dgX9tv8S5443ORPcjutdxtA6ZxpBbfqqOET8jMZzkAYVFRrEiIGZMDCTGzcrWb19F2c359H21DIyd/+GwD2/4nxQClc6jiIlJ5eQ9lkar0rED6gsxGfCggMYkpkGmWmUVXyP/F37OLVpJinFS8myfyJ43x+4GJjIpXaP0iI7l7AuD4Kzzv7ulojcA5WF+IWQwAAe6psKfb9DeeW3+HDvYY5tyCP5+GJyDr5P6KG/cNkZy/m2w0nOziWi2xAICPJ1bJFmQ2UhficowMnAnp2h5zeprPoGhfuPcWTDbOKPLiDnyBwijn7AVWcUZ1sNJSlzKpE9hkNQqK9jizRpKgvxawFOBwNMOwaYf6Gq6qtsP3KKA/mziTq8kIHHlhJ5fDY3ZoVzqsVDxGdOJab3KAiO8HVskSZHZSGNhtPpIL1TCumdvojL9QX2HDvHnvx5hB+cT/bJ9cTMXUTZ3BBOJg0iJmMycX3HQWi0r2OLNAkqC2mU3AMdJtGz3TO4XE+z/1QJK9cvIGTfPAacySdu0XLKFz1HcUI2EX0nkZjxGITH+zq2SKOlspBGz+Fw0C0ljm5TPgV8isNnrzAzfzHOorn0P7eOxOVfp2L5ixTH9ic07TH3QIeRyV6XKyJ/p7KQJqdjUhQdJ0yBCVM4dv4aszasoGr3HPpeWEPy6pepXP1tiqPTCOw1gZZZU3HEtPF1ZBG/p7KQJq1tQgRtx4yDMeM4fekGczau4+aOWfQuWY3J/wHk/4ATEb2gx3ha5eTiiO/o68gifkllIc1Gi5gwxo8YDiOGc/5qGfM2beDGdvdAh70+/Al8+BNOhnWjovs4WuVMIyDZ+DqyiN9QWUizlBAZwtihD8PQh90DHRYWcmXrTLqcX0G/rW/A1jc4HdKBso8HOkzprfGqpFlTWUizFxMexKgHs+HBbK6WVbB0604uFs6kw5llZOz4DwJ2vsW54NZc6zyGlJxcgtv2V3FIs6OyEKkmMiSQ4dnpkJ3OjZs/YPWOvZzdPIM2J5cxYM9/EVT0Wy4EtuByh5GkDJxGSIccDXQozYLKQuQOwoIDGNq/J/TvSVnFd9iw+yDFG2fSsngJ2fv/QsiBP1ESkMDFdiNomZ1LWJeHfB1ZpN6oLERqICQwgAfTukHay5RXTmezPcpHG/JIPLaYgYdmEHb4f7nijKEqPodrlU8T0X0YBAb7OrZInXG4XI3vT2sXFha6MjIyfB1DhMoqF1sPFnOwYBZxRxaSU7mZKMcNrjkiONNqKAmZU4ju+SgEhfk6qgiFhYVkZGTU6oSbykKkjlRVuZi7eiM3i3cScWgBAys2Euu4RqkjlFMtHiI2YwqxfcZASKSvo0ozdT9locNQInXE6XTQrWUMqUM+h8v1LHtOnGdZ/gJC9s8n+2Q+sfOXUDY/mJNJDxDdbxLx6RMgNMbXsUVqRGUhUg8cDgc92yTSM/fTwKfZf7KENQWLCbRzGXBmPfGLV1K++GsUx2cR3vcxkjImQUSCr2OL3JHKQqQBdE2JpeukacA0jpy9wsyCZTiK5pJxbg1JK75J5YrpFMdkENxnIsmZk3FEp/g6ssgnqCxEGliHpCg6jH8Mxj/GiYvXmVWwiqrds0i7uIa2a79D1drvciKqNwE9J9IyeyqO2Ha+jiyishDxpdZx4bQePRpGj+bMpRvM2ZTPzZ159CxZTeqGH8GGH1EckYordTwp2dNwJnb2dWRpplQWIn4iOSaM8cOHwfBhXLh2kwUfbuLatpmYCyvps/k12Pwap8K6UN5trHugwxapGnZEGozKQsQPxUcEM3rwIBg8iEs3ylm0ZSuXtuTR5dxy0rf9Euf2NzkT0o7SLmNIyXmcoNZpKg6pVyoLET8XExbEyAcGwAMDuFZWwfJtuzhfOJMOp5fTf9dvCNz9K84HpXC102j3QIftBmi8KqlzKguRRiQiJJDhWX0hqy+l5d9n7U7LmQ/zaHVyKVl7/0iw/S9KAhMpaT+SlJzHCek0EJwBvo4tTYDKQqSRCg0KYEi/HtCvBzcrvsWmokMc35hHi+OLyTnwHiEH/8zlgDjOtx1Oi6xcwrsNhoAgX8eWRkplIdIEBAc6GdS7C/R+kYrKb7B53zGObphF/EeLGHh4NuFH3ueqM4qzrYeRlDmVyB7DITDE17GlEVFZiDQxgQFOslPbk536PFVVz7H10EkOFMwm5vBCBn60hMhjs7iRF87ploOJz5xCdK9REBzu69ji51QWIk2Y0+kgo0srMrp8CZfri+w8epa9BfOIODifnOI1RM9ZQOncEE4lPUhsxmRi08ZCaLSvY4sfUlmINBMOh4M+HZLp0+GfcbmeYW/xRZbnLyRk/zyyT+cTu3AZNxc+x8nEHCLTJ5PQbwKExfk6tvgJlYVIM+RwOEhtHU/q1E8Bn+LA6cuszV9MwN65ZJ5dR8LSNVQs/TrFcZmEpj1Gcv/JEJnk69jiQyoLEaFLi2i6PDYVmMpH566Rt2E5rj1zSD+/huRVL1G56lsUR/cluPdEkgdMwRHT2teRpYGpLETkE9olRtBu7HgYO56TJdeZtWENFbtm06dkNW3XvwLrX+F4ZG+cPcaTkpOLI66DryNLA/C7sjDGZAD/AjiA6dba0z6OJNJspcSGM3HkSBg5krNXypi7qYDSHXmkXlxFr00/hk0/5mS4obL7OFplT8OZ3M3XkaWe+F1ZAKHAC8AIIAeY5ds4IgKQFBXCuGGDYdhgSq7fZMGHm7m6bSbdzq+k75afwZafcTq0Ize7jiMlJ5fAlF4ar6oJ8XlZGGNeAB7xTBZYa39sjMkBvgnk+i6ZiNxJbHgwox8eCA8P5EppOYu37qBk80w6nVtOxo63cO78d84Gt+F65zG0Gvg4QW3SVRyNnMPlcvk6wycYYzKB7UAU8H1r7XO3vqawsNCVkZHR4NlEvCkqKiI1NdXXMXzm+s0KCrbv4ezmmbQ7tYwB7CbQUcX5oJZc6TiKlJxcQtpna6BDHyksLCQjI6NWrV2vexbGmCzgNWvtYGOME3gbSAPKgGettQduM1s08AfgJvDb+swnInUrPDiQYZl9ILMPpeXfY/2u/Zz8MI9WxUvIsu8Ssu8dSgISKWk/ghbZuYR1fhACfH6AQ2qg3n5LxpjpwFPANc9TE4FQa22OMSYbeAOYcOt81trlwPL6yiUiDSM0KICH07tD+rcor3yJTUVHOLYxj+Tji8k5+DfCDv0PV5wxnG/7CElZuUR0GwqBwb6OLXdQn5V+EJgEvOuZHgQsArDWbjDG9L+fhRcVFd1fOpF6UFpaqm3zDuIDIH7gaCqrRjH/5EUu2bW0PruaQUfmE3F0BlcdEXwUl0NAl0dwtcvBFaCBDv1JvZWFtXaGMaZDtaeigUvVpiuNMYHW2oraLL85HxcW/9Xcz1nUVK+ewCMPUFX1EtsOn+LAhrlEHVrAwPP5xFxYxo0Pwzjd4iHi+k8hpvdoCIn0deQmobCwsNbzNuTBwsu4T1p/zFnbohCRpsHpdNCvcwr9On8el+tz7D5+niX58wjbP5/skwXEzFvMzXnBFCc9QHS/ycSnj4fQGF/HbpYasizWA+OA9z3nLHY24LpFxM85HA56tU2k17Sncbk+w76Tl1iVv5CgffPIOrOe+MUrKV/8AsXx2USkP0ZixiQIj/d17GajIcsiDxhujMnHfXf2Mw24bhFpRBwOB6ZVLGbKE8ATHD57hZn5S3HsnUP/c+tIXP4NKpe/yInY/oR6xqsiqoWvYzdpfnefRU3oPgvxVzpnUf+OX7jGhwWrqNozm/Qra+jkPEkVDoqj0wjoOYGWWVNxxLb1dUy/5Lf3WYiI1LU28RG0GTMGxozhzKUbzNm4jpvR0u9oAAAIrElEQVQ7Z9OrZBXdC34IBT+kOKIHrtTxtMqZhiOhk68jNwkqCxFptJJjwhg/YjiMGM75q2XM37SRa9tn0f3iSvps/ils/imnwrpSbsbSKmcaAS2011dbKgsRaRISIkMYM/QhGPoQl66Xs3DLVq5smUHn8yvI2PYL2PYLzoR0oLTrGFJyphHUqo/Gq7oHKgsRaXJiwoMYNWgADBrA1bIKlm7dyYXCmbQ/s5zMnW8TsOs/OR/UiqudR5OSk0twuwEqDi9UFiLSpEWGBDI8Ox2y0ykt/wFrduzl9Id5tDm1lKyidwja+3suBiZzqcNIUrKnEdIpB5wBvo7td1QWItJshAYFMCSjJ2T05GbFt9lQdJATG2bS8sQScvb/LyEH/ptLAXFcbDeCFlm5hHUdrIEOPfQuiEizFBzo5MHeXaH3S1RUvsjmfR9xpCCPxGOLGXhoFmGH3+OqM4qzrYeTPGAKEamPQGDzHa9KZSEizV5ggJPs1A5kp36NyqoX2HaomAP5s4k9spCcjxYScWwm1x3hnEkZQkLmFKJ6jYKgMF/HblAqCxGRagKcDjK6tCajy5dxub7EjqNnsPlziTi0gIEnVhNVPJ/SOSGcSn6I2IzJxKaNhZAo7wtu5FQWIiJ34HA4SOvQgrQOz+JyfZaiExdZlj+f0P3zyD5VQOyCpdxcEERx4kCi0ieR0G8ChMX5Ona9UFmIiNSAw+GgR5t4euQ+BTzFgVMlrMlfQoCdy4Cz60hYupqKpV/nRNwAwtIeIzlzMkQk+jp2nVFZiIjUQpeWsXSZlAvkcvTcVWYWLIc9c+h3fi3Jq6ZTuepliqPTCeozkRYDpuCIbuXryPdFZSEicp/aJ0bSftwEGDeB4ovXmbVhDZW7ZtGnZA1t130P1n2P45F93AMdZk/BEdfB15HvmcpCRKQOtYoLZ+KokTBqJGeulDJnYwFlO/LoWbKKHhtfhY2vUhzeHVfqOFKyp+FM6urryDWishARqSfJUaGMf2QIPDKEi9duMn/zh1zbOhNzYSVphf8Ghf/GqdDOlHcbQ0p2LoEpvfx22BGVhYhIA4iLCGbMww/Aww9wubScxVu2U1I4g07nVpCx/S2cO/6ds8FtudFlDCkDpxHUOt2vikNlISLSwKJDg3h0YH8Y2J/rNytYsX0P5z6cQfvTy8jc/VsC9/ya80EtudpxFC1zcglpnw1Op08zqyxERHwoPDiQRzL7QGYfSstfYf2ufZzalEfLk0vJtu8Ssu8dSgISKWn/KC1zcgnt/KBPBjpUWYiI+InQoAAeTk+F9FTKK19mY9ERTmycQdKxJQw8+D6hh/7CZWcsF9oOJyk7l4huQyAgqEGyqSxERPxQUICTQb06Qa8Xqaj8BoX7j3Nkwyziji5i4JG5RBz9gGvOSM60GkZS5lQiewyHoNB6y6OyEBHxc4EBTrK6tyOr+3NUVf0L2w6fYn/BHKIPLWDgsaVEHp/NjVnhnG7xEHGZU4npPQqCI+o2Q50uTURE6pXT6aBf5xT6df4CLtfn2f3RORYXzCP8wAJyTq4nZu4iyuaGcDJ5EDEZk4lLGwuhMfe9XpWFiEgj5XA46NU+iV7tn8Hlehp78iIr1i8iZP88sk6vJ27hcsoXPkdxQjaR/Z+A4NRar0tlISLSBDgcDrq3iqf71H8C/olDZy4zI38pzr1zyDy3joTFX+HIuBW1Xr7KQkSkCeqUHE2niZOByRw7f40VHx0npupqrZfn27s8RESk3rVNiGBourmvZagsRETEK5WFiIh4pbIQERGvVBYiIuKVykJERLxSWYiIiFcqCxER8UplISIiXqksRETEK5WFiIh4pbIQERGvVBYiIuKVykJERLxSWYiIiFcqCxER8UplISIiXqksRETEK78sC2NMC2PMZl/nEBERN78rC2OMA5gOHPV1FhERcQv0dQBjzAvAI57JAuAC8GfgGz4LJSIin+DzsrDWvgm8+fG0MWYmkAYMMMZMtdZ+4LNwIiIC1HNZGGOygNestYONMU7gbdxFUAY8a609cOs81tpJnnn/rKIQEfEP9VYWxpjpwFPANc9TE4FQa22OMSYbeAOYcKf5rbVP3m35hYWFdRVVpE5p25SmqD73LA4Ck4B3PdODgEUA1toNxpj+tV1wRkaG4/7jiYhITdXb1VDW2hlAebWnooFL1aYrjTE+P2ciIiLeNeSls5eBqOrrttZWNOD6RUSklhqyLNYDowE85yx2NuC6RUTkPjTkYaA8YLgxJh9wAM/UxUKNMQOBL3gmn7fWltTFckXqijFmKPBP1tpnfZ1F5GPGmGHA40A48Lq1dvvdXl+vZWGtPQJkex5XAV+sh9V8HndZDACmAb+ph3WI1IoxpguQDoT6OovILcJxf372BUYAdy0LvxvuoxYCrLWlwEkgxddhRKqz1h6w1r7h6xwit7LWzsVdGM8Bf/L2+qZQFteNMSG4i+KUr8OIiDQGxphE4C3gFWvtGW+v9+tLV2t4B/hvcR96CuLv5y5E6l1tRigQaQg13DZ/DiQB/2qMmWWt/dvdlum3ZVHTO8CttYXA075JKc3VvY5Q4G1EApG6cg+fnZ++l+X682Goj+8A/9gn7gAHan0HuEgd0PYp/qpetk2/LQvdAS7+TNun+Kv62jb9tixuQ3eAiz/T9in+qk62zcZUFroDXPyZtk/xV3WybTam3eR6uQNcpI5o+xR/VSfbpsPlctVpKhERaXoa02EoERHxEZWFiIh4pbIQERGvVBYiIuKVykJERLxSWYiIiFcqCxER8UplISIiXqksRETEq8Y03IeI3zLGPI17/J1woDPuPzzzR19mEqlL2rMQqTsx1tqxwHjgZV+HEalLKguRurPN8/9jQKgvg4jUNZWFSN3RqJzSZKksRETEKw1RLiIiXmnPQkREvFJZiIiIVyoLERHxSmUhIiJeqSxERMQrlYWIiHilshAREa9UFiIi4tX/B2BM2BP1O2saAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = axes()\n",
    "ax.loglog(n_vec, n_error_1, )\n",
    "ax.loglog(n_vec, 1/n_vec*n_error_1[0], label = '1/n')\n",
    "ax.set(xlim=(1, 1e2), ylim=(1e-4, 1e0),\n",
    "       xlabel='n', ylabel='Error',\n",
    "       title='Error in n using first order trotter');\n",
    "ax.legend()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T13:03:48.065365Z",
     "start_time": "2018-12-30T13:03:47.683227Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x122e65ac8>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = axes()\n",
    "ax.loglog(n_vec, n_error_1, color='purple', marker='o',  markersize=12 )\n",
    "ax.loglog(n_vec, 1/n_vec*n_error_1[0], label = '1/n')\n",
    "ax.set(xlim=(1, 1e2), ylim=(1e-4, 1e0),\n",
    "       xlabel='n', ylabel='Error',\n",
    "       title='Error in n using first order trotter');\n",
    "ax.legend()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T13:03:55.669795Z",
     "start_time": "2018-12-30T13:03:55.113643Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x123085eb8>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = axes()\n",
    "ax.loglog(n_vec, n_error_1, color='purple', marker='o',  markersize=10 )\n",
    "ax.loglog(n_vec, 1/n_vec*n_error_1[0], label = '1/n')\n",
    "ax.set(xlim=(1, 1e2), ylim=(1e-4, 1e0),\n",
    "       xlabel='n', ylabel='Error',\n",
    "       title='Error in n using first order trotter');\n",
    "ax.legend()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T13:41:48.732868Z",
     "start_time": "2018-12-30T13:41:48.293839Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x122fc79b0>"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = axes()\n",
    "ax.loglog(h_vec, h_error_n1_1, label = 'n=1',\n",
    "          color='purple', marker='+',  markersize=7 )\n",
    "\n",
    "ax.loglog(h_vec, h_error_n2_1, label = 'n=2',\n",
    "          color='green', marker='x',  markersize=7 )\n",
    "\n",
    "ax.loglog(h_vec, h_error_n4_1, label = 'n=4',\n",
    "          color='blue', marker='*',  markersize=7 )\n",
    "ax.loglog(n_vec, (h_vec**2)*h_error_n4_1[0], label = 'h**2')\n",
    "ax.set(xlim=(1e-2, 1e0), ylim=(1e-7, 1e-2),\n",
    "       xlabel='h', ylabel='Error',\n",
    "       title='Error in h using second order trotter');\n",
    "ax.legend()\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T13:48:49.670574Z",
     "start_time": "2018-12-30T13:48:49.135568Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1233e9390>"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = axes()\n",
    "ax.loglog(h_vec, h_error_n1_1, label = 'n=1',\n",
    "          color='purple', marker='+',  markersize=7 )\n",
    "\n",
    "ax.loglog(h_vec, h_error_n2_1, label = 'n=2',\n",
    "          color='green', marker='x',  markersize=7 )\n",
    "\n",
    "ax.loglog(h_vec, h_error_n4_1, label = 'n=4',\n",
    "          color='lightblue', marker='*',  markersize=7 )\n",
    "ax.loglog(n_vec, (h_vec**2)*h_error_n4_1[0], label = 'h**2')\n",
    "ax.set(xlim=(1e-2, 1e0), ylim=(1e-7, 1e-2),\n",
    "       xlabel='h', ylabel='Error',\n",
    "       title='Error in h using second order trotter');\n",
    "ax.legend()\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T13:51:01.848181Z",
     "start_time": "2018-12-30T13:51:01.410760Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1236bae10>"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = axes()\n",
    "ax.loglog(h_vec, h_error_n1_1, label = 'n=1',\n",
    "          markerfacecolor='purple', marker='+',  markersize=7 )\n",
    "\n",
    "ax.loglog(h_vec, h_error_n2_1, label = 'n=2',\n",
    "          color='green', marker='x',  markersize=7 )\n",
    "\n",
    "ax.loglog(h_vec, h_error_n4_1, label = 'n=4',\n",
    "          color='lightblue', marker='*',  markersize=7 )\n",
    "ax.loglog(n_vec, (h_vec**2)*h_error_n4_1[0], label = 'h**2')\n",
    "ax.set(xlim=(1e-2, 1e0), ylim=(1e-7, 1e-2),\n",
    "       xlabel='h', ylabel='Error',\n",
    "       title='Error in h using second order trotter');\n",
    "ax.legend()\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T13:55:28.743626Z",
     "start_time": "2018-12-30T13:55:27.920585Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1237e7c18>"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = axes()\n",
    "ax.loglog(h_vec, h_error_n1_1, label = 'n=1',\n",
    "          markeredgecolor='purple', marker='+',  markersize=7 )\n",
    "\n",
    "ax.loglog(h_vec, h_error_n2_1, label = 'n=2',\n",
    "          markeredgecolor='green', marker='x',  markersize=7 )\n",
    "\n",
    "ax.loglog(h_vec, h_error_n4_1, label = 'n=4',\n",
    "          markeredgecolor='lightblue', marker='*',  markersize=7 )\n",
    "ax.loglog(n_vec, (h_vec**2)*h_error_n4_1[0], label = 'h**2')\n",
    "ax.set(xlim=(1e-2, 1e0), ylim=(1e-7, 1e-2),\n",
    "       xlabel='h', ylabel='Error',\n",
    "       title='Error in h using second order trotter');\n",
    "ax.legend()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T13:57:31.928963Z",
     "start_time": "2018-12-30T13:57:31.488002Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x123985a58>"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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/k4g4DhCIVzlFYtkJx4FDa6oYEgr2O0C0tLRk3e5j0JfOKlCIVAZvCaxf23BvHrI/O67XvLOGU8adEp8RXPDYBdzxyh1MGjkp6a7rqUdMpSpYRXWomu82fpc5T8wBepfApip/feHdnTyTUAJbFdsn4TgQjO2T6HEOlr8eUl3FmLpq6qurOO3IhoLOJBIN+pmFSD5pZpF/hZxJuMtNcHA24Db5+87q7+A4Dh09HX2Oy2Um8evNO9nnaReeLHEdrXJy4hVPw6pCRByH0XU1OQUIzSxEZMAq1EzCnUV4ZwPdkW7Ofvhsbl5zMzj0CRTZzCQgGiRW2K38YuO2eKAYU1sd33Ht3UyXbCYxsraaz310TFFnEokULESk7Hgb/UH+ggT0bs0BsPzC5cx5Yg6P/+lxOns66ezpZH/X/vjua4jOJGqravneZ7/Hs//0bLwtx/zp81m/ZT2NExp9d1zDwaWmuqoQR42oSRoknBIvN6WiYCEiZcMbHBYGFuYlSLizCO9swm3Jce7/OZc3/voGHzv0Yyx9fWmfVuFTj5jKF479ArVVtf3KSbz43i7+3t7Zqy1HkGigcBzoijj8YVsbASBS5kHCpWAhIiWXbAbR5DTFg0LivyG7Bn/uL/uLJl3E0teX8tkJn2Xec/N67bquCdXEl5pad7Qyb9o8Vl28Kp709ptJ/HrzTrbt72D15p3AwdlEOBSI77bu6onQHQsS9dVVnH5kQ9kGCdeg3GfhJrUSe7CseWdNvD9LIb3yyivceeedhMNhDjvsMBYtWsTQoUMLek2RcuNNQCdrv+Ntw+PtDt3fHddznpjTq8Hf2Q+fTWdPJ+cdd16vTrA1oRpCwRDdkW5uP+N2Jo+dzPmPnc8Fj13AyotXxvdJpMpJuEtNrmSb6XocBze7fEj1wfLXUbXVjKqt9vmJldagnFm4H6A176yJv7bmnTXMeWJOvDKikBYsWMDdd9/Nww8/zPjx43n88ccLfk2RcuMGiHR5CW9gyDZxvfzC5TSva44vNXX2RJeFvIFi6hFTozcaamzmF5f/gttevA04uNzkziZSLTk9EwsUQWBoKMgx9bWEA0kS187BfRLlPItIZlDOLBonNMaTWu6mG/dxso6PmehP19mHHnqIkSNHAtDd3U11dXn/RSGSL4nlrOnahSf2bOvPTGL5hctZfuHy+I7rrkhX0gZ/U4+YykUnXMRtL97G9z77vfhGPO8sItMusEFim+mALR8eiE4tPL2bHAcastxMVw4GZbCAgwFj1oOzAFg9d3XWgcKVadfZ0aNHA/Dcc8/x2muvcf311+d0XZFyl0m7cHcPhbtXwpVrkEjs3VQTqqG9pz3e4G/y2MnxPx7dnES6INGydQ/b93fE8w9jaqvZ2d4Z32nd1RMhFNuBHQ4EiETgkAoOEq5BuQxVKMm6zl5xxRXxf77+9a/H37ts2TJ+8pOf8MADD2hmIQNeusS1+zixwV86qZab3B3XbpDY37U/fsx5x51HfXU9Dg7XTLmGl99/mfnT5/c6Pt0+CbcEdlssUASB2nDvElg3J+E4DnXhEEcMH8rpRzVU3JJTMoN2ZuHmKFbPXQ3kvgwFmXedXbp0KW+++SbLli2jpqYm6+uJlDN3NuHmJFIlrpMFiUwa/GU6k6gKVnHlp67kZ7//Gd9t/C6Tx06OzyK8Df6SzSb8ZhI9TkIJbOx+1/XV0ZyEGxzKPXmdiUE5s3ADhRscvDkMb9K7EHbs2MHdd9/Ntm3b+OpXv8oVV1zBI488UtBrihSLt2op3V6JxKCQ6V6J/swk6qrq+MKxX2Bo1VAumnQRT136VDxx7Z1FJEtcw8EKp3Qzic6eSHwzXX11FZ85qoHRsRLYSp5FJDMoe0OVunRWBq7B3hvKezOxZI+9r/W3d5O3IMWdSazetLpXgIBokJh5zExeePcFVl28qs+x6f4fT5a49s4kAgRw3KomHHpiM4lDaqoqIkDk0htqUAYLkUIZjMHC+0s/XXWTN4GdKe8qABBfPrp5zc15DxItW/dQWxVk054DQDQI1IRDTBo5jDf+1kYwAN0RJ5rIJrpP4oRRw/nLrn0Vk7hWI0ERKRl3uSlZoJjRNKNXAtsvce1yl528S8QQ3Xk977l5SZebQsFQfLe1d6kq1R4J6L1PYtv+jnigGDeshlAg0Ccn4XaBPSSWkxhVW13xietMKViISL948xIuvwqn/myog74bZ2cfP5tZD85i6etL4+/PJUhA35yE2wW2rirEuGHVEBhcOQk/g7YaSkQyl6w1R7IWHYnvdfV3r0TjhEbmT5/POY+cw5DQEC7/+OXx93uXm+ZNm8e8afN6VUal2ycBfVtzjBtWw64DnRw1ooYdBzrjTf56HIfDhlaxu72r10xiIFQ2ZUMzCxHxlVjRNHPBzIxnE6mkq3A695FzWbhuIaFAiLaONpa+vjTn5Sbv3engYHXTuGHVRCC+3NQdiTb5cxyoCgU57ciGQTmTSKRgISJJJS43efMS7uPEPIU3QPhVOiUGiTlPzOGNv74RL4Nt62hj7klz4+9vbmzmqcueyion0brjQ3Ye6GT7gU4c+uYkunoiVIWCODgc4ukCWxOKNvkb7IECBvkylFsBMeXwemrCoaJf/95778Vay/e///2iX1vEj19rjmQVUJmWwibub5o/fT5Tj5jKvOfm9Xr/T9/4KUvOWhLfSDd57OT4cf1tywEHl5zGDatm+/4OOnsiBGO1QSOqw3xqbD3vt7UP6uWmVMpuZmGMOdkYs8wY8zNjzJhCXusvu/axu72Tt3btK+Rlklq3bh1r164t+nVFUskmcQ2ZLzdB78S1u69p/vT5zHtuXq+d19dMuYb66nqGhIf0ChDusZlWNyVLXEeAP2w/mJOAaBdYzSLSK8eZRQ1wPXAWMA1Yle8LrHprK5HYnxuzxo9k9eYdvL17H8EAnH/c4Vmdsz9dZzdv3sxjjz3Gddddp/bkUjaySVxD/1pzJCaum2Y0sXDdwWvUVdXR3NjMzWtu7tWawz3Wu+zklWwmkSpx3RVxqBsSorunJ56TeL+tXUHCR8mDhTHmeuCM2NNXrLW3GmOmAf8KzCnENT/3kdG07tjL9v0dHFJTRV1ViNG11UwcOSyn82bSdXbfvn00NzezaNEiNm7cmNP1RHKRqmrJu7zk3YGdaeLaldi/yV1u8iau5z03j7qqOuqr65l+9HReePcFJo+dzFOXPtWnwslduvIGinRBYtywanYc6OQP2w8mrl3Dh4SZPEZLTv1R8mBhrb0TuNN9bow5BWgBPg80Adfl+5pDwyFGDq1i6952nn9nO92R6HQ017xFsq6ziTOL8847j+3bt/PNb36TtrY2tm3bxv33389VV12V07VF+stvJuGVaeI605zEkrOWxB/PPGYm86bNo3FCY68d2/1t8JcsSHT1RGcRByI9vXZcu0tOChKZK2iwMMacCiyy1s40xgSBe4CTgA7gSmvt20kOGwH8BOgE7i/U2N7/sJ3uSIRjG+po3fEhH+xt5+j62pzOmWnX2bPOOguA1157jUcffVSBQoqiPzMJ97n3fal4A4R3NgH0ykl4Na9r5qpPXYUZaeLN/QDf5HV/g0R3T49mEXlSsGBhjLkBuAJws8fnAzXW2mnGmKnAEuCLicdZa38F/Mrv/K2trTmNryNYyxGRTnr+9neOIMzevZ20tv4t6/Nt2bKFnTt30traSmdnJ52dnb5j3Lx5M21tbTl/L1I+2tvby/a/57qF6zhw4AC/Wfyb+GuJMwnv2CddOymj72V092i+9NiXuGPaHZw6+lSWzlrKBY9dgIPDt6d9m3976d/i7734oxfz3+/+Nz2RHqaNmMaph5xKw6cbeh0/lrGc23Bu0mu3BushdhfrPkEilo8YQgQIEuzq4MhIO3v3drKj7W/UAK27t/TvhyZxhZxZbARmAw/Fnk8HngGw1r5qjJmSy8lzbdaW71ZvieN58cUXMzpmzpyCpGWkRMqlkWCqZPTnF32ezy/6PJB8JuEd+8S7U38f3tnExIkTGX/0+Phyk91hcXBo62jjprU3xXMSt8y4JWni+sszvsz4o8ezfsv6lD87b1FK2plEZw8Nw4bysUPrYknro7L46Q1cLS0tWR9bsNJZa+3PgS7PSyOAPZ7nPcaYkudMRAYiNw+xdsHajDbTQeaJa+jbu8mtcpr33Dzu/+39NM04GIRmHjOTlRev5FvTvtXnnhLrt6yPH5+uFDa6iQ6GhoO9yl+7eiIMCQUJEE1an35Ug0pgC6SYv6zbgOGe50FrbXcRry8y6GSak3Dfm0riPWDc3MIFj13AxSdczCUnXtKrBDbbnAT03iz7zMZt8dzExMOGsfHv+/qUvyonURzFDBYvAecCy2M5iw1FvLbIgOZuqEtV2ZRs1pDJZrp0ietTxp2Cg8P9v72f+397P/XV9Sw5awnN65pxcLjkxEtonNDYZ69EYvmry3tPiW37O3g61sPJXXba3d5FV49DdThIIOIoSBRZMYPFSuBMY8zLRDNUXynitUUGNPemQqlmEe57vDLt3eTdEOcmrptmNDHniTk0zWiKVzrdMuMWuiPdrLx4JUBGm+kgeYXT6Uc08MoHuxgSCsZzE7sOdBIOBjhx5HCGVoUUJIqsoMHCWrsJmBp7HAGuLuT1RCS1THIS6fZJeBPX856bx5KzlnDbi7f1Wm5ygwOQdjOdl3epyZ1FjBlWTSgQwAE2xBLYRwyvYevedj7Y2860IxoUJIpMt1UVyaNiVEO5lU5rF6xN2egP6NftS13eTXHuL/c7Xrkj6Wa6+up6Vl68Mv6+ZMemkuqeEieOGs4ftn9IVTAQv/HQodXRe0qMGVbtqXJS8jobuq1qGVixYgX/8R//EX/uOA7vv/8+3/72t3nvvfc4cOAAW7Zs4eabb+b9998HYNmyZVx00UVcdNFF3HXXXaUaulQYN0CkuqdEk9PU79uXurzLTV/7r6+x5p01fRLXq+eu5qpPXYVD7z80vctNybiVTe3dPfxl1z7CAaivDvdp8NfVE+HQmioiTrRd+IzxI1XlVAYULApk//79LFu2jNWrV/Pkk0/S1tbGD37wA371q1/x0ksv8d577/Hkk0/y6KOPsnz5cl588UX+/Oc/l3rYUkaSdYHNlF8+wpVYAutyE9ezHpxFgABLzlpCfXV9PEDcd+598ftKJAabxBJY7z0l3MT127v38Q9Hj2RPRzddkUj8nhJuGWyP48RvOgQoSJSBAbnP4ect77P89ffyes45U47iSycfmfY9v//97/nnf/5ndu3axaWXXsoRRxzB7bffzocffsiYMWMYN24cN910EyNHjmTs2LE88MADhELRflTd3d1UV2sNVg5at3Bd/Jd+4pKTX6VTKpmUwOYrce3y5iS8ietDaqoYEgrQHXGoHxJmT0e3KpzK2IAMFqUSDof58Y9/zAcffMBVV13F008/3evr113XuydiQ0MDjuOwePFiJk2axIQJE4o5XKkg6fZL9EdihZPLWwKbj8R1qpyEN3H9/DvbcBz42CF1nDh6BNv3dyhIlLEBGSy+dPKRvrOAQpg0aRKBQIBRo0bR3t7u+/6Ojg5uuukm6urqaGrK7n9+qXze1hx+M4hUy0t+95Toz0yieV1zr8R1f/dJTDm8Pp6TqBsSpjvixMtfn/2fbRCArkiEYxuG07rjQz7siu7NVZAob8pZ5FFi19l0HMfh2muvxRhDc3NzfDlKBh9vcEiXtM40D+GVSU5i/vT53PbibVknrl1/2bXPNyfhTVwf1zCM046MJq6l/A3ImUUl+OUvf8lvfvMbOjs7eeGFFwD41re+xeTJk0s8Mil3/clRePdKuLuv080kGic0xmcb3qWnTJeb/HISbuL6/bbozFuzicqhYJEns2fPjj+urq5m9erVad9/5plnsmGDOp4MVtkuN0HmS05es4+fzawHZwHEcxKr567m0T8+yqNvPtrrvZkmroE+y01jhlUTDiknMRApWIgUiTc3kUnCuj8zCEievHY3ys2fPj/+vlxnEi1b97DjQEef+9gPCQV4ZuPfcBzodpSTGGiUsxApknS7rZPxy1FksqHODRS55CQSN9Ptbu/k6BFDOaa+lrqqUK/lpqNHDFVOYoBSsBCpUP1JXrswuU1fAAATdElEQVSzhv5spnMlJq4/c9RhbNpzgE179tMVifD8O9vjy02TRo3QZroBSstQInn0x7v+2OsOc5nkJvq73OTKJHltd9g+eyoyyUn4Ja7rqkIEYu8b3zBUy02DgIKFSB796Z4/wd0Hn2eSm8ikJDab5DVEg8clJ17S55h0XWDBP3HdHXEYUR1m8th6RtVWc2hNVbzCSQYmLUOJVIBkS05uTsKMNPHXmtc199o85848EpeqErl5iVVvbWWF3dpnn4SbuO6KRBhfX0t3JEI4GIjPILTcNPBpZiGSo1zKYBP5zSASl5y8yetcymC9iWsIsH1/R6/E9UcOreUvu/fFE9eaSQw+up+FSD94y1+TSde3ye9YSH5PCO9rQJ8lp1TvTRcc0pXAAgwJBagOhWjv7mFCfW2vfRKaQVQu3c9CpEj6W/7qlckMI3HpKN0vf7/kdTqpSmDrqkIMqwrRE3EYXx8tg/UmrhUoBi8tQ4mUQKrlpjXvrGH9lvUsv3B5fAaxeu5qGic0xgNHNsnrTGYSz7+zXYlrSUnBQsRHf3ISk66dlNE50+22dpebvJLNMLxls5m05UiWk0hWApuYuFYZrIByFiL94ncvif7cgzsxOKR7PPv42Vxy4iUpZyKpNtStemtr2pxEZ0+EEdVhjj9sGKNqq5WXGOCUsxDJk1xuZdpfbn5h1oOzmPXgrD6Bwlv+uuLPK1KeI9VtTNu7e/jcR0anzUmoBFYypWAh4pFLAjuZxP5NrjXvrGHxS4v7vO7mK7JJWrvcJae3du1jaDjEyKFVdEeceE5iaFWI045sUO8m6RflLET6Id+dYBMT1qnyD+l2XKdLXr+9ex/hYADHcTi2oU45CcmagoUMev1JYPf3bnWp+jclNviD/iWsvdIlr0fXVtPtRDimvlbVTZITJbhFPPwS2Ml4y2C9CW5v8nnNO2t6lcKu37I+belsqoS1VybJ64+PGs7R9bX9+n5k4FKCW8RHIRPX6fo2nTLulKTH3HD6DSmXm9IFiv4mrz/Yq1mE5IeChQwK+U5ce3mXmt5x3umzJ8K7mW713NUZNfZLRclrKRXlLEQ8cr23RKpd17nmJpItOSl5LcWkYCEDVjbdYJO95teaI92ykV8prF+F05TD66kJh/jcR0bTumOvktdSMkpwy6CQTeLa5dcJ1juD+PdP/zvjjx6fVVWT1x+2tbF5z37G19fyidEjAHh3z342bP+QIaGgkteSlVwS3GU5szDGjAH+21o7pdRjEUlV/poYKJZfuJyx7WOZOGFi1mWwqZabggGiM4lIJL7k9MHedgULKZqyS3AbYwLADcDmUo9FylupW3O4QSCXXdfe6iYgaYXThPpazv7IaIaGlbyW0in5zMIYcz1wRuzpK8Au4D+BeSUblFSEdQvXZbxJLtvEdSZS5Sz87nMNvaubPjF6RLzCaeve9niF02FDq6gJh3r1bFLyWoqt5MHCWnsncKf73BizAjgJ+LQx5iJr7eMlG5wMGOmCSiYJ7GT3ksglJ6HlJqk0BQ0WxphTgUXW2pnGmCBwD9FA0AFcaa19O/EYa+3s2LH/qUAhifJ5v2uX370l8lH+mml108SRw2jdsZfTjmxQhZOUlYIFC2PMDcAVwL7YS+cDNdbaacaYqcAS4IupjrfW/lOhxiaVa+aCmfGAkEuFk5dfAnvxS4uzKn/10nKTVLpCziw2ArOBh2LPpwPPAFhrXzXG5FTp1NramtvopKwFAgEOPfRQDjvsMMLhMG1tbezYsYOOjo5e78v1czBixAhGjhxJ44RGHjr3ofimup/O/Clj28fS2trKuQ3nQnvfa41lLOc2nNvr9fb29l7P/xysxyFaqehdbgrgMDzQQ5cTpr5rH/uCQ3nrbzvZt0V1HVKeChYsrLU/N8Yc43lpBLDH87zHGBO21nZnc/5M70YmlWHtgrVpl5BGjBjBiBEj+ryez89BdfXBv+DHHz2eiRP6d+4D3T28sHEL//DRcdSEo5VKx3T3pF1uOmlETa871E0ce1Tevh+RRC0tLVkfW8zS2TZguPfa2QYKGXiy6d3kV+HUnxsP5aN/01927aMjWMVbu/bFX0vWv8m73KQ71EmlKGaweAk4ByCWs9hQxGvLAOSXzM60G2xiAtubw8gkYKx6aysr7Fbe3r2Pzxx1GG/v3scKu5VVb20F4P0P2+mORNQJVipaMUtnVwJnGmNeBgLAV4p4bSlDhahs8vJLXLuy7d/kSlfZBMQ306m6SSqZekNJWchXZVMyiTceynZvRGL5q5fbtykcgG4H9W2SsqSbH4kUgbf8NZG71FTXuU9LTTIglXwHt0gh5WPndbrd1ucfdzhwcKlpx+b/wRx5hJaaZMDRzELKQqa9m7KpcMo2ce1K19zPpcomGegULKQsZJrM7s/9rnPpBuuVrvxVZLBQsJC8KFa78MTZQbK+Ta4bTr8h6XJT44TGpJ1iE9uFe6n8VQY7BQvJi2w21WUr3b0lcpEuga17Schgl1GC2xjTaK3t33ZWkQqRSQJbzf1ksMu0GmohoGAhvRR6U10q+b63hN+mOhHJPFg4xpiVgAUiANbamwo2KqkIubYLz+SmQ4nycW+JROnahYtIVKY5i58Aq4BWogHDFmxEMmj0p7LJlU2FU7rEtUsJbJH0Mp1ZPAx8DZgEvAUsLdiIZNDItHeTVzb3u0688VAy6t8kkl6mweI+4O/A88AM4AFgbqEGJZUn0011ibyVTZBb76ZEmSSuXUpgi6SXabA41lr7D7HHq2KdY0XiCpXMzoUS1yL5k2nOosYYUwtgjBkKKPMneZGPmw6lop3XIvmTabC4E/h9rCLqd8D3CzckGSzy1bspHSWuRfIj02CxFTgVuBU4zVr7aOGGJIVWrNYcfnLp3ZRJhRNo57VIvmS8KS+Ws9hVyMFIcaxbuK4scgzZVDa5MqlwAiWuRfJFm/Ika9lsqstVfyqcRCR/Mg0WPwPSz/elrBWiNYe7qc67lOTNQxSCKpxESiPTYHGJtfasgo5ECirX1hzJZLOpLldqzSFSGpkGi93GmC/SexnqrYKNSipGITfVpeJWOB3bUEfrjg/5YG87R9fXFvSaIoNdpsFiNPANIBB7XgNMK8iIRHyoNYdI8aUtnTXGPAZgrW0EnrbWNsYe6//OCpZta45k8rGpLtMyWJfudy1SfH77LEZ7Hp/jeewUYCxSJPkqm83Xprp0d6gTkfKQ6TIUHFyCEgH8N9X55S5UBitSOfyChZPisUhOm+pAZbAilcQvWJxgjHmE6KzC+3hSwUcmA57KYEUqh1+wmON5fG+KxyJZUxmsSGVIGyystevSfV0qRylac2RCZbAilSHTrrNS4bK533UxqAxWpDIoWJRQMVuFJ5a1Jpa95qK/+yREpPIoWJSQt7FfMXhbc8x6cFbeejhpn4TIwNeffRZFYYw5Cfgh8D/Az6y1+bllmuSd9kmIDB5lFyyI3pHvr0Rbor9Z4rHkXSFahWfK25oDcu8Qq30SIoNHyYOFMeZ64IzY01eAlcBjwBjgX4HSlOkUSCFahWciWY7C2148m4ChfRIig0fJg4W19k7gTve5MeYyovf83k0ZjG+gyLU1RyraJyEyOBT0l7Ex5lRgkbV2pjEmCNwDnAR0AFdaa99OctgmojmLLqC5kOMbTHJtzZGK9kmIDA4FCxbGmBuAKwC3ROZ8oMZaO80YMxVYAnwx8Thr7cvAy37nb21tzeNo82f48OGMGjWK6upqDhw4wPbt29m3L3mV0KRrJ2X1fQwdOpRRo0ZRV1dHV1cX27dvZ8+ePbkOvZchQ4YwcuRIRowYQSQSYefOnezevZtIJNLrfTXAjt2ww/O8dfeWvI6lkrS3t5ftZ1MkF4WcWWwEZgMPxZ5PB54BsNa+aoyZksvJJ06cmNvoimDo0KEcffTRKb8+8e7cv4eqqirGjRvHuHHjcj5XKqFQiNGjRzN69Gj/Nw9yra2tFfHZlMGppaUl62MLts/CWvtzoktJrhGA98/fHmOMchIiIhWgmJvy2oDh3mtba7uLeH0REclSMYPFS8TuthfLWWwo4rUlRq05RCQbxQwWK4F2Y8zLwPeBbxbx2hKj1hwiko2C5gystZuAqbHHEeDqQl6vEpSqVbhac4hILtRIsMhK1Sr8cx8ZzTH1tdRVheKtOSbU13L2R1ThJCL+VI1UZN5W4csvXA7k3qMpE2rNISK5ULAoAW+rcIDVc1cXNFC41JpDRLKlYDGIqDWHiGRLwaIE8t0qPFPeW5aOqq2O385URMSPEtxFltgqPPF2pyIi5UjBosj8WoWLiJQjLUMVWaFahYuIFJJmFiIi4kvBQkREfClYiIiILwULERHxpWBRImoVLiKVRMGiRNQqXEQqiUpni0ytwkWkElVssFgYWBh/PKNpBjMXzCzdYPrhcx8ZTeuOvWzf3xFvFT66tpqJI4eVemgiIilVbLBocppKPYSsqFW4iFQi5SxKwG0VPr5+KN2RCB/sVfdXESlvFTuzqGRqFS4ilUbBogTUKlxEKo2WoURExJeChYiI+FKwEBERXwoWIiLiS8FCRER8VXywWPPOGha/tLjUwxARGdAqOliseWcNc56YwynjTin1UEREBrSKDRZuoFh+4XLdu1pEpMAqdlPerAdnsXruagUKEZEiqNiZhYiIFE/FBovVc1cz54k5rHlnTamHIiIy4JVdsDDGTDLG3GeMWWaMOTHV+xonNLL8wuUKGCIiRVB2wQK4EvgA6AA2pXujGzDWb1lfjHGJiAxaJU9wG2OuB86IPX0F+BjwZeBTwFzgnnTHN05oVJJbRKTASh4srLV3Ane6z40xDwD7gF2U58xHRGTQKWiwMMacCiyy1s40xgSJzhJOIrrEdKW19u0kh90L/IhooPhGIccnIiKZKViwMMbcAFxBdJYAcD5QY62dZoyZCiwBvph4nLX2daLLTyIiUiYKObPYCMwGHoo9nw48A2CtfdUYMyWXk7e2tsYfB4NBGhoaaGhoIBgM0tbWxvbt2+nq6srlEiL91t7e3uuzKTJQFCxYWGt/bow5xvPSCGCP53mPMSZsre3O5vwTjj2OmnAo6dfq6+upr69P+jWRQmptbWXixImlHoZIUi0tLVkfW8wEchsw3HvtbAMFwFu79vm/SURE8qKYweIl4ByAWM5iQy4ne3v3PlbYrax6a2s+xiYiImkUs3R2JXCmMeZlIAB8JZeT1VWFGF1bzcSRw/IyOBERSa2gwcJauwmYGnscAa7O17m7Iw6HDa1KmbcQEZH8qdhNb92RCB/sbS/1MEREBoWKDRanHdlATUizChGRYih5u49sjaqtZlRtdamHISIyKFTszEJERIpHwUJERHwpWIiIiC8FCxER8aVgISIivhQsRETEl4KFiIj4UrAQERFfChYiIuJLwUJERHwpWIiIiC8FCxER8aVgISIivhQsRETEl4KFiIj4UrAQERFfChYiIuJLwUJERHwpWIiIiC8FCxER8aVgISIivhQsRETEl4KFiIj4UrAQERFfChYiIuJLwUJERHwpWIiIiC8FCxER8aVgISIivsKlHkAiY8z1wCeBY4GHrbX3lHhIIiKDXtnNLKy1dwJXAW8C95Z4OCIiQhnMLGIziTNiT1+x1t4KXAqssNZGSjcyERFxlTxYxGYSdya8/A/AlSUYjoiIJFHQYGGMORVYZK2daYwJAvcAJwEdwJXW2rdTHFprrXUKOTYREclcwYKFMeYG4ApgX+yl84Eaa+00Y8xUYAnwxWTHWmsv9Tt/S0tLvoYqklf6bMpAVMiZxUZgNvBQ7Pl04BkAa+2rxpgp2Z745JNPDuQ+PBERyVTBqqGstT8HujwvjQD2eJ73GGNKnjMRERF/xSydbQOGe69tre0u4vVFRCRLxQwWLwHnAMRyFhuKeG0REclBMZeBVgJnGmNeBgLAV/J5cmPMZ4FLgFpgsbX29/k8v0iujDGzgMustSoLl5IzxpwGfC329BvW2r+ne39Bg4W1dhMwNfY4AlxdwMvVEt35/UngLEDBQsqGMeZjwGSgptRjEYm5imiw+DRwMXBfujdXbII52c5vY0wdcB1wY+lGJpKyM8ESY8x/lnBYIl4ha227MWYrMMvvzRUbLBJ3fhtjRgKLgVustdtKNjARUnYmECkn+40x1cDhwF/93lyWwSLLnd93AKOA24wxq6y1TxRvxDKY5NCZQKQoMvyM3k906amKg7mLlMouWGS789taO7d4o5TBKpfOBADW2n8q/ChlMMv0M2qtbQG+nOl5y65FOQd3frt67fwGst75LZIH+nxKuSvIZ7TsgoV2fks50+dTyl2hPqNlFyyS0M5vKWf6fEq5y8tntBKChXZ+SznT51PKXV4+o5UwXS7ozm+RHOnzKeUuL5/RgOPoHkMiIpJeJSxDiYhIiSlYiIiILwULERHxpWAhIiK+FCxERMSXgoWIiPhSsBAREV8KFiJ5YIz5sjHm9lKPQ6RQFCxERMRXJbT7EKkUU40xzxG9CddSa+39pR6QSL5oZiGSP13A54ALgOtLPBaRvFKwEMmf31prHaL3M64t9WBE8knBQiR/1JVTBiwFCxER8aUW5SIi4kszCxER8aVgISIivhQsRETEl4KFiIj4UrAQERFfChYiIuJLwUJERHwpWIiIiK//H/yX7UFH7apMAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = axes()\n",
    "ax.loglog(h_vec, h_error_n1_1, label = 'n=1', color='white',\n",
    "          markeredgecolor='purple', marker='+',  markersize=7 )\n",
    "\n",
    "ax.loglog(h_vec, h_error_n2_1, label = 'n=2', color='white',\n",
    "          markeredgecolor='green', marker='x',  markersize=7 )\n",
    "\n",
    "ax.loglog(h_vec, h_error_n4_1, label = 'n=4', color='white',\n",
    "          markeredgecolor='lightblue', marker='*',  markersize=7 )\n",
    "ax.loglog(n_vec, (h_vec**2)*h_error_n4_1[0], label = 'h**2')\n",
    "ax.set(xlim=(1e-2, 1e0), ylim=(1e-7, 1e-2),\n",
    "       xlabel='h', ylabel='Error',\n",
    "       title='Error in h using second order trotter');\n",
    "ax.legend()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T13:59:14.867847Z",
     "start_time": "2018-12-30T13:59:14.437776Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x123c7b5c0>"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = axes()\n",
    "ax.loglog(h_vec, h_error_n1_1, label = 'n=1', color='white',\n",
    "          markeredgecolor='purple', marker='+',  markersize=7 )\n",
    "\n",
    "ax.loglog(h_vec, h_error_n2_1, label = 'n=2', color='white',\n",
    "          markeredgecolor='green', marker='x',  markersize=7 )\n",
    "\n",
    "ax.loglog(h_vec, h_error_n4_1, label = 'n=4', color='white',\n",
    "          markeredgecolor='lightblue', marker='*',  markersize=7 )\n",
    "ax.loglog(n_vec, (h_vec**2)*h_error_n4_1[0], label = 'h**2', color='black')\n",
    "ax.set(xlim=(1e-2, 1e0), ylim=(1e-7, 1e-2),\n",
    "       xlabel='h', ylabel='Error',\n",
    "       title='Error in h using second order trotter');\n",
    "ax.legend()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T14:01:54.493642Z",
     "start_time": "2018-12-30T14:01:54.006708Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x12384ccc0>"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = axes()\n",
    "ax.loglog(h_vec, h_error_n1_1, label = 'n=1', color='white',\n",
    "          markeredgecolor='purple', marker='+',  markersize=7 )\n",
    "\n",
    "ax.loglog(h_vec, h_error_n2_1, label = 'n=2', color='white',\n",
    "          markeredgecolor='green', marker='x',  markersize=7 )\n",
    "\n",
    "ax.loglog(h_vec, h_error_n4_1, label = 'n=4', color='white',\n",
    "          markeredgecolor='lightblue', marker='*',  markersize=7 )\n",
    "ax.loglog(n_vec, (h_vec**2)*h_error_n4_1[0], label = 'h**2', color='black')\n",
    "ax.set(xlim=(1e-1, 1e0), ylim=(1e-7, 1e-2),\n",
    "       xlabel='h', ylabel='Error',\n",
    "       title='Error in h using second order trotter');\n",
    "ax.legend()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T14:03:47.624367Z",
     "start_time": "2018-12-30T14:03:47.175956Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x123f28128>"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = axes()\n",
    "ax.loglog(h_vec, h_error_n1_1, label = 'n=1', color='white',\n",
    "          markeredgecolor='purple', marker='+',  markersize=7 )\n",
    "\n",
    "ax.loglog(h_vec, h_error_n2_1, label = 'n=2', color='white',\n",
    "          markeredgecolor='green', marker='x',  markersize=7 )\n",
    "\n",
    "ax.loglog(h_vec, h_error_n4_1, label = 'n=4', color='white',\n",
    "          markeredgecolor='lightblue', marker='*',  markersize=7 )\n",
    "ax.loglog(n_vec, (h_vec**2)*h_error_n4_1[0], label = 'h**2', color='black')\n",
    "ax.set(xlim=(1e-2, 1e0), ylim=(1e-7, 1e-1),\n",
    "       xlabel='h', ylabel='Error',\n",
    "       title='Error in h using second order trotter');\n",
    "ax.legend()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "color='white',"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T14:11:25.324678Z",
     "start_time": "2018-12-30T14:11:24.877265Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x124233d68>"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = axes()\n",
    "ax.loglog(h_vec, h_error_n1_1, label = 'n=1', color='white',\n",
    "          markeredgecolor='purple', marker='+',  markersize=7 )\n",
    "\n",
    "ax.loglog(h_vec, h_error_n2_1, label = 'n=2', color='white',\n",
    "          markeredgecolor='green', marker='x',  markersize=7 )\n",
    "\n",
    "ax.loglog(h_vec, h_error_n4_1, label = 'n=4', color='red',\n",
    "          markeredgecolor='lightblue', marker='*',  markersize=7 )\n",
    "ax.loglog(n_vec, h_vec**2/h_error_n4_1[0], label = 'h**2', color='black')\n",
    "ax.set(xlim=(1e-2, 1e0), ylim=(1e-7, 1e-1),\n",
    "       xlabel='h', ylabel='Error',\n",
    "       title='Error in h using second order trotter');\n",
    "ax.legend()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T14:12:37.251717Z",
     "start_time": "2018-12-30T14:12:36.794759Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x12401cc18>"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = axes()\n",
    "ax.loglog(h_vec, h_error_n1_1, label = 'n=1', color='white',\n",
    "          markeredgecolor='purple', marker='+',  markersize=7 )\n",
    "\n",
    "ax.loglog(h_vec, h_error_n2_1, label = 'n=2', color='white',\n",
    "          markeredgecolor='green', marker='x',  markersize=7 )\n",
    "\n",
    "ax.loglog(h_vec, h_error_n4_1, label = 'n=4', color='red',\n",
    "          markeredgecolor='lightblue', marker='*',  markersize=7 )\n",
    "ax.loglog(h_vec, h_vec**2/h_error_n4_1[0], label = 'h**2', color='black')\n",
    "ax.set(xlim=(1e-2, 1e0), ylim=(1e-7, 1e-1),\n",
    "       xlabel='h', ylabel='Error',\n",
    "       title='Error in h using second order trotter');\n",
    "ax.legend()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T14:13:23.636314Z",
     "start_time": "2018-12-30T14:13:23.011071Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x124457390>"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = axes()\n",
    "ax.loglog(h_vec, h_error_n1_1, label = 'n=1', color='white',\n",
    "          markeredgecolor='purple', marker='+',  markersize=7 )\n",
    "\n",
    "ax.loglog(h_vec, h_error_n2_1, label = 'n=2', color='white',\n",
    "          markeredgecolor='green', marker='x',  markersize=7 )\n",
    "\n",
    "ax.loglog(h_vec, h_error_n4_1, label = 'n=4', color='red',\n",
    "          markeredgecolor='lightblue', marker='*',  markersize=7 )\n",
    "ax.loglog(h_vec, h_vec**2, label = 'h**2', color='black')\n",
    "ax.set(xlim=(1e-2, 1e0), ylim=(1e-7, 1e-1),\n",
    "       xlabel='h', ylabel='Error',\n",
    "       title='Error in h using second order trotter');\n",
    "ax.legend()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T14:14:51.463782Z",
     "start_time": "2018-12-30T14:14:51.020457Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1246bda58>"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = axes()\n",
    "ax.loglog(h_vec, h_error_n1_1, label = 'n=1', color='white',\n",
    "          markeredgecolor='purple', marker='+',  markersize=7 )\n",
    "\n",
    "ax.loglog(h_vec, h_error_n2_1, label = 'n=2', color='white',\n",
    "          markeredgecolor='green', marker='x',  markersize=7 )\n",
    "\n",
    "ax.loglog(h_vec, h_error_n4_1, label = 'n=4', color='white',\n",
    "          markeredgecolor='lightblue', marker='*',  markersize=7 )\n",
    "ax.loglog(h_vec, h_vec**2, label = 'h**2', color='black')\n",
    "ax.set(xlim=(1e-2, 1e0), ylim=(1e-7, 1e-1),\n",
    "       xlabel='h', ylabel='Error',\n",
    "       title='Error in h using second order trotter');\n",
    "ax.legend()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.000e-04, 4.000e-04, 9.000e-04, 1.600e-03, 2.500e-03, 3.600e-03,\n",
       "       4.900e-03, 6.400e-03, 8.100e-03, 1.000e-02, 1.210e-02, 1.440e-02,\n",
       "       1.690e-02, 1.960e-02, 2.250e-02, 2.560e-02, 2.890e-02, 3.240e-02,\n",
       "       3.610e-02, 4.000e-02, 4.410e-02, 4.840e-02, 5.290e-02, 5.760e-02,\n",
       "       6.250e-02, 6.760e-02, 7.290e-02, 7.840e-02, 8.410e-02, 9.000e-02,\n",
       "       9.610e-02, 1.024e-01, 1.089e-01, 1.156e-01, 1.225e-01, 1.296e-01,\n",
       "       1.369e-01, 1.444e-01, 1.521e-01, 1.600e-01, 1.681e-01, 1.764e-01,\n",
       "       1.849e-01, 1.936e-01, 2.025e-01, 2.116e-01, 2.209e-01, 2.304e-01,\n",
       "       2.401e-01, 2.500e-01, 2.601e-01, 2.704e-01, 2.809e-01, 2.916e-01,\n",
       "       3.025e-01, 3.136e-01, 3.249e-01, 3.364e-01, 3.481e-01, 3.600e-01,\n",
       "       3.721e-01, 3.844e-01, 3.969e-01, 4.096e-01, 4.225e-01, 4.356e-01,\n",
       "       4.489e-01, 4.624e-01, 4.761e-01, 4.900e-01, 5.041e-01, 5.184e-01,\n",
       "       5.329e-01, 5.476e-01, 5.625e-01, 5.776e-01, 5.929e-01, 6.084e-01,\n",
       "       6.241e-01, 6.400e-01, 6.561e-01, 6.724e-01, 6.889e-01, 7.056e-01,\n",
       "       7.225e-01, 7.396e-01, 7.569e-01, 7.744e-01, 7.921e-01, 8.100e-01,\n",
       "       8.281e-01, 8.464e-01, 8.649e-01, 8.836e-01, 9.025e-01, 9.216e-01,\n",
       "       9.409e-01, 9.604e-01, 9.801e-01, 1.000e+00])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h_vec**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T14:22:13.865655Z",
     "start_time": "2018-12-30T14:22:13.400081Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x124970748>"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = axes()\n",
    "ax.loglog(h_vec, h_error_n1_1, label = 'n=1', color='white',\n",
    "          markeredgecolor='purple', marker='+',  markersize=7 )\n",
    "\n",
    "ax.loglog(h_vec, h_error_n2_1, label = 'n=2', color='white',\n",
    "          markeredgecolor='green', marker='x',  markersize=7 )\n",
    "\n",
    "ax.loglog(h_vec, h_error_n4_1, label = 'n=4', color='white',\n",
    "          markeredgecolor='lightblue', marker='*',  markersize=7 )\n",
    "ax.loglog(h_vec, ((h_vec**2)/h_error_n4_1[0]), label = 'h**2', color='black')\n",
    "ax.set(xlim=(1e-2, 1e0), ylim=(1e-7, 1e-1),\n",
    "       xlabel='h', ylabel='Error',\n",
    "       title='Error in h using second order trotter');\n",
    "ax.legend()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T14:29:31.202392Z",
     "start_time": "2018-12-30T14:29:30.752536Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x124565940>"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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r9dzp6emsXr2ali1bVut5hRDBM5eaKlJyCrZhveTHJViwcOfFdzL3u7nFGtZlBQpPFvFAlwd4Y9MbfLT9I0Z0HeHtbbRr1I4ZN80AXH8cV0Z1NrizgAam+9ZwBYrl2w/gdFffrm7bhFV7j7IjMxurBW69oGJf3uXZdXbv3r0sXbqU5ORk3nnnnap4S0KIKuKvaR0oUPjLIjzH8PAEiCGdhtCtVTee//p575f6xc0uJuNABjM3zsRmsQUsN1mxcvMFN3uziMWbF/Nc0nOk7U5jz+97+PTOTwFXgEjfdwzDMMgtdNK0XL+J4qozWKwF+gGp7p7F5mo8dzHX/aEZW4+e4khOHo1io4iPstEsLoYOTepX6rjB7DqbnZ3NhAkTeOmll9i5c6efowghwsFTbqpoJhEoi/BkEEt/XMqywcsY23ssT375JIXOQr797VuirFEAFBklMwCbxUaRUUSHJh3Ye2IvFiyk701nbO+x6KMagEJnIR8N/QhwBYn/7v+dnPxCThdVzTTa6gwWy4BrlVLfABbgb9V47mLq2W00qRfFgVO5fLH7CIVOg7PqRVW6bxHMrrP9+/fnyJEj/P3vfycrK4vDhw8zZ84c7r///kqdWwhRfr5ZRLB7NXkyiWD2aTKXmcb2Hsuzac/S982+GIZRLDAUOAtKnMdTZoqxxzDs0mHM2jirWJmp0FnI7H6zAVeASNt7lOz8QvKdxScuWaHS328hDRZa6z1AD/dtJzAilOcrj19P5lLodHJ+Yjxbj57kt1O5nJNQuRlWwe4627dvXwDWr1/PkiVLJFAIUc18swgP8wI5s95je3uf6wkQvcf2Lrth7SdIPPnlkzidzjL7EHarnUJnIVHWKF685kXvXk+LNy9mRNcRZZaZckx9CQtgtYDNYgELFFVy5qu1Uq+uwerZbVzRJpELEutzRZtEYm3VPxtKCFF9Vo9bXeoqa38lJ39ZgzlA+PYjHvjoAdJ2p9GtVTeW/LiECekTuPPiO8kpyGHMV2O8m/r5BgpP+QlcM5ssWBjZdST1ouoxIX0CY3uP5c6L72TwRYNp16hdsUCxeu8xjp3O53hugTdQWAC7xRUowEKRAYYB+ZUsR9XJXWeFCBWZOht5PFmEuQEdTD/CXGryTJ0tq9Q0Pn08FiwsG7yM7w9+7+1HRFmj/JaYzI/3aN2DgRcN9GYRdqudZ3s/iz6qOTfxXO/mp55exLHT+SWOZwWsVgtWCziduKKG++vdiYHTgLan9kfkOgshhAgbc6nJ/CVfWhaRPj7d715NvpmEv1lN5mmv1791PRYsFDpdkz19A0W0LRrPH+k9Wvfgh8M/sPXoVjq36MzywctZsmUJcKYfUVqpybfMVFhkYBje+ACG4c1hnAbE2ipXSJJgIYSoVfz1I0rrRXiYn++v/OS5Bs6G/RuwW+3eWU3P9n6WIRcNYeGmhczcOJMoaxT5RSX/6gfXjCZwZRQTkiYwPn08W49u5bmk59BHtfdaOp7LJHga1ifzCyn0aVh7AoWnzGQFbFYLhlG8NxFvtxEf7fqar2e34TxBhdXZnoUQonbw9CHM/YiydoD1BIOxxli/j/cZ16dEP8JutTPo3UHYrXYmrpnI2N5jySvM47GVj3Hw1EFyi3IB/zOa7FY7NouNWHssk66dhM1q8/YiBl802JtBmEtN6fuO8dnOw2TmFngDhacXEW21EGWzYLW4dnuy4AoQTsPAiUG83UZCTBT1bFaaxMVwRZtErmiTSOcWCRX47ZreR6VeLYQQYeJbZjIHhrJ6EoGyCCiZSUxcM5ExvcYwIX0CV51zFU+vetobIMxbg3t4+hF2i52XrnmJzi06c+vSW71BQh/VJaa9/nf/7xiGwfHcMwHHAtgsYHWXmpxOvJmE4afM1Cg2inp2W6UDgz+SWQghahR/WUOga0kEk0VMWjuJtN1pJTKJCekT6NG6B8+mPUtOQQ4f//wxuYW5fs8Ta4/1zm4a2XUkcdFxTEifAMDywctLZBKeLCLdNKvJw2YBu8WVO3hmNIEpk8D1WKOYKFrEx9CyfmyVZBClkcxCCFEjlNWLKCtIBNqGA4qXmsb0GuPNJJ5Ne5b8ony+3P1lqQHCnEU8f/Xz3ixi8ebF3izC3I/wBAgrcPR0PuZuhAWwWy1Y3A1rVwpxJkB4+PYiQhUgzCSzqCLvv/8+L7/8sve+YRj8+uuv/OMf/+CXX37h9OnT7N+/n2eeeYZff/0VgAULFjBw4EAGDhzItGnTwjV0ISJasL0IOJNBmDOJQFmEZ23ExDUTGdhxIM+mPcvAjgMZ89UYsguyKXAWlBooerTugdVirVAWccQdKHx7EYY7i7BZLe4MwvXPBjSLi6FZXEyV9iKCJcEiRHJycliwYAGrVq3iww8/JCsri5SUFL766ivWrl3LL7/8wocffsiSJUtITU1lzZo1bNu2LdzDFiIieIIClC9ImJW1V5O5zDTo3UEADOw4kJkbZ/Ln9n9m5saZpc5qirJGEWWNYmTXkezI3MELf36Bd356x9uw3rB/A0ntk0oEic92HubY6Xzv1NfmcTHY3QHCt9TkbVi7y0wJMVHERdmrPUCY1coy1MKFC5k/f36VHvOee+5h2LBhZT5n06ZN3HPPPRw/fpw77riD1q1b8+KLL3Ly5EmaN29Oq1ateOqpp2jSpAktWrRg7ty52NwrxwsLC4mJianSMQtR0/g2rYMJEr7TYssKEt1adaNbq27Fyk0DOw7k+reuJ78on/4X9PfbsAaIscVwzR+u4et9XzO291hvqarQWUjq7als2L/B27AG/wvoPGWmaJuVsxvGFitDmUtNhgGNYqOItlmrrcwUSK0MFuFit9uZN28ev/32G/fffz+ffvppsZ8nJycXu5+YmIhhGEyaNImOHTvSvn376hyuEBHD3wK6stZG+OtF+AsSvgvoBr07iNTbUxnTawxPr3qay5pfxsyNM73P9w0UMbYYnIaTKFsUzyU95502aw4Unimvnn7Ef/f/XqIfYe5FOJ1Q4DT44XAWFsBpGN7nhaMXEaxaGSyGDRsWMAsIhY4dO2KxWGjatCm5uf5rnGZ5eXk89dRTxMfHM3ZsyTRaiNrMvH1GoAV0/lZY+wYHf1NfPSusPduCj+k1hhsX34jVYgWDYtey9uh/QX9W7lyJ1WolqV1SmZmE7zYcpwuKSmzmZw4SHgVFTjz7jjaKieKipg34+Xh2xAUIM+lZVCHfXWfLYhgGDz74IEopJkyY4C1HCVGb+fYizI+VtYDOHAgCXaLU07D29CKWD15OobOQ69+6nmfSngEDcgpyvOskAGJtruum97+gP1/u/pLn//w8H9/xMet/W8/Y3mO9AcKTSSS1T2JU98dI33eMr/cdY0UZ/QjDtxfhziMaxUTRLC6GhJgomrob1pEaKKCWZhY1wZdffsl///tf8vPz+frrrwF49NFH6dy5c5hHJkTo+O7TFKjU5HkNlF5m8iye8+1HDLhwALctvY2rzrkKA4P8ovwSTev+F/QnfW86uYW5jOw6knd+esdbbkq9PbVEBtHj7D+x5pfjdGpan/W//U62nyzCXz/C3ItoHGG9iGDJrrNCVCHZddY/351f/fEtNXmCRWm7vXZr1Q2gxNqItN1pfPLzJ4zoOoI3Nr1BTkFOiXNFWaO474/38camN3gu6Tk6t+jsPU6hs9AbgDxBAlylpv/sPVYsQIAriziWm+/d7dVqtbg28TPAwNWPiJQgkZGRUeFdZ6UMJYQICfOeTenj00vtRXiCgr9Sk+/j/spMqbenMiF9Auc1Po/HVz5O2p40RnQdwcyNM4sFilhbLPFR8URZo4i2RTOw40A+vuNjJq6Z6D2Ouczkmfa65pfjLN9+gM92HvYGCgsQZbUQH2Xj7IaxxUpNBUVOCt3lpoSYKK5sk0jzeFe5KdJLTWWRYCGEqDL+ehKeL3vzgjl/AQLKnvbqL0jctvQ2Xln3CgXOAr797VsMDLILsovNcPIECQODCUkT+Pyuz7FZbdy29DbvcTxrI8wB4vfcfP6z9xiHc/JwuhdT17NZaZcQh93i6kX4zmqqqf2IYEiwEEJUir8A4THeMt6bUZj/1/waqFyQ+Pjnj/2WmuKj4rnp/Ju8QeKzOz/zZhGeFdbmIAFnSk2Hc/JYZSo5WXH1I5zA/pOnXakFtTeL8Ed6FkJUobrYszD3F4LtSYD/XoSHb08i9fZUAG/DetWeVSUCxMiuI1m4aSE5BTl0b92dn47+xPLBy0scw3fKa8aBE3RqWp9Ve48VO54ViLFZaV4/lt+yXAGi0Glgs1pwGgZ2i4VCpxFxi+fKIj0LIUS18c0KoHgGYebbkwi0mV/a7jSAYpnEmF5j6Pd2P74/+L3fTCI+Kp6RXUcya+Ms+rTrw8t9X2ZH5g7G9h5bLBspLYvIzM33BgpzqclmKZ5JFBmG60qlhuuaEa0b1OPKsxNrZRbhjwQLIURA/vZqCjZAmAWzNiJtdxpJ7ZO8C+jGp49n2KXDeGzlYyWCxE3n34TNaqPIWcTLfV9m/W/r6dyis7dZbQ4So7o/5u1FvK/PNKwL3BcXalU/tkSAyC9y4sQVKGJsViwWSIiJoklcDJ1bJNDU/b91gQQLIURAvr2IPuP6FGtUl9W0huKzmzzK6kf0W9yP8enjsVlsZOVlFWtYm4PEYz0fY/ng5by/7X1vkDBnEOamdVlZRKzNSqv6MSUCRKzd6s0kWsS7rheREBNVZwKEmQQLIYRfvuUm32Z1aZmFR2nXsg621JSVl8WEpAneY/gLEmWVmcBVagomi3ACPxzJosgwOKteVIkAURczCV8R1+BWSnUBRuGab/CE1vqQ73OkwS0iVU1ucPs2nAMFAvOGf8EsoEtqn0Ta7rRizeYlW5aw9MelGBjcefGdxTIIcAUIu9VOr3N68fW+rwM2rD08jesjOXkYFG9WHzyVS6emDdh0OMvbsC5yGkTbLBQUGTSvH8N5jeP5NSu31gWG2tbgjgUeAT4BeoZ5LELUGf72Zgqm1BTsAjrfXsStS29FNVEYGCVKTSO7jiQhJoFCZyHP9n6Wj4d+XGYmYV4bseaX46zYeZjD7kARTBZRP8pGq/quhnWszVanM4jShD1YKKUeUUp97P73tNZ6LdABeBz4X5iHJ0St5W9Wk2/j2nzb3/PBf48CKNGLGPTuIF5Z90qxXsRjKx9jbO8zOy7HR8Uzue9k3tj0Bs/2fta7NsITaEoLEluPnvT2I8xBwl8voqDI6VomYUCUzSplpiBFYhmqG7AJaACM1Von+z5HylAiUtWkMtR4y3jv2ofSmNdPlGd9RFL7JABv2cmzZ9PHP38MwOS+k3ls5WNAxUpNvmUms1b1Yzl+Op9OTRvww5GTgEGh0yAxNorM3ALi7DaaxMXQpmFsrSw1laUyZaiQ7jqrlOoOvKS17qOUsgIzgEuBPOA+rfUOPy9rCMwH8oE5oRyfEHWJvy9583WpzQHBc98j0PoIT4AwX2AIXF/yY3qN8QYGjwnpE5jcdzIT0ieQW5jLhKQJPNrz0WI9DfOOr57g4y9ItKofy7GcPFo2qMfBU7m0qh/D0dP5/HAki4Iig/hoG4VFRd4swhwgmsbJ1SmDFbLMQin1BHA3kK217qGUGgD011r/VSnVAxijtb6lIsfOyMgw4uLiqnK4QlSJ3NxcYmNjwz0Mv1I7ptJzTE/WTVxX6nMG/TSo2PPN983mbZtHp8ROdG/WnfWH1/Poukd5pecr2O12vjjwBR/s+AADgzE9x/DC2hc4WXASgMHnDuaTfZ8AcMPZN3DjOTcCeF/vOd6W41u498J7vecrwMJBazynsOHZa6NEBmEYrh+592yKxkk+VhpYCmlUlMspazTNnSW3BalLcnJyIjKz2AkMABa57/cCVgBorb9VSnWtzMFrSqov6pZIKUOVVirq+0Jf+r7QF/CfSZjH3nts71Lfy02xN3kzgL/2/ittz2nLbUtvw8BgbO+xLN+xnKy8LMasHkN8VDwJMQk82/tZnkl7ptiW4CN7jSSpfRJtz2nLhv0b6NChQ7FzlpZJHD+dXyKDiIuykVNQRLTNggVIrF/PNKvp7Er/TmuDjIyMCr82ZA1urfV7QIHpoYbACdP9IqWUXHxJiBAwX4Uu2PXFWjfJAAAgAElEQVQRvgvn/M1s8vA0m29behsPfPQAgHdWk2/Tuk+7PiwbvIxHez5aYkvwDfs3eI9n3oZjzS/HyS0sKjGrydOw9sxoKihyEm2zevb1o1PTBjKrKUSqczZUFq6mtffcWuvCajy/ELVWWTOV/E1/NWcU5uea+VtAl7Y7jbTdaUxaOwlwBYg5383h6oVXFwsQE9IncP8f72dy38ms/22993F/M5o8zDObDufk8enOw0EFiQbRdq48O5FmcTGcn1hfZjWFSHX+Zb8W6AekunsWm6vx3ELUap5MwjyzqbQGdVmPmZmb1eZMwlNqGvTuIMb2HuttXpub1gYGQzoNIal9krfk5DmO55+Hv1LTla0TWffbcaLdQcJfw7pBtJ3OzRP4NSuXpnEx0qwOserMLJYBuUqpb4BXgb9X47mFqDUqkkX461+UtakfnMkCPOsjlmxZUqzU5LmU6eS+k0mIScDAQB/VLBu8zLuAznd9hEegUlPz+jHYLBYMYHMpmYSUmapXxK2zCIassxCRqjoa3J7GtOdypaXxLTUF2ooDiq+L8Fxi9JV1r3izB/P6iISYBJYNXsaG/RtKXHvCs7WHv2tHdG2ZwPbj2ezIzPaOw3dmU5TVQn6RkyLDoHGMa31Ebd6Go7rUtu0+hBCUnkF4lKcf4Xm+L3MvAvBux/H4ysexW+2k7U5jfPqZctaE9AmsGraK+/94P4a7aORZB+GbQfhbZe3pRezIzObK1olYwW8/onFsFE7DoFFMFL3bNpFMIgLIbCQhIlT6+HTvF7xvFlHRfoRvJmHuRQy+aDBDOg1h4pqJvNz35WIZhLkXATC732yGdBpSLJPwHM/cjwBY4W5UQ/FeRPP6Mdht5lLTmX5EkWF4F9AB0pOIABIshKgBylppDf6vN+GPb9PawzOrac53c1g1bFWx1zzb+1kKnYUsG7wMoETT2zOzyex0YRGf7Tzsve8pM5l7EV/sPoxhQKHhdJWaigqkaR3BpAwlRJiZy01lrYsoqyxVViZR1voIT4/CPO31+4PfM+jdQd6prxPXTPRmI6WVmqB40/rn49nYLZAQYyc+yuYtM32+6zBYoMDppG1CnJSaahDJLIQIM3O5KVAGUZrKZBKegLBq2Cq+P/g9j698nJf7vsyjPR8FKHPqq7lp/fPxbG9PAuDqtk1Ytfco0TYLPxzOosBp0CwulgOncmkUE8UFifVpHBslpaYaQjILIWqYYLMIONOw7vd2P++COt9MYkL6BG8gKHQW8nLfl73bgnuO4Tv11cMcIHyb1o1io4i2WSh0GsRH2bCAtxeREBMFIFlEDSKZhRDVxDx1NVDDurRMAcqXRaTtTmPimolMSJrA1QuvBiiWSSzZsoQlPy7xHsNTUurconOxXoQnm/BkEkdP5+G+QmmpTWtPT+K8RvF0ataQIzl50ouowWSdhRBVqKx1FqWVlUp7vKzrRkDJmU3gCg7mmU3m7cI9wcKzPsJ3bYVvqcrDd33E3hM5tG4QC1g4kpPHdX9oxsc7DmLBQrTNQm6ha31ExyYN2Hr0JM3iY+jZOrHU9yGqj6yzEKIWKitQQMk1Eh7m/Zo8gWLQu4NKrI/wKKvMBCVLTVedfRZ7Tpxmz4kcCpxOvth9BMMo2bS+ILE+V7RxNa1FzSdlKCGq0JZpW+gw/UxmUZlyk5m/LMLcj/jojo8ASuzX9P3B75m4ZmKx5nQw6yN8p76aS02NYqO8PYjThUW0TazH1qMnpWldy0mwEKIK/TTjJ5h+5n4ws5sCbegHFetHANz89s08l/RciSDjuz7CXGqKtdu8U1/jo+0UOo0SvYhCp0HDGLt3h1cJELWfBAshwsz3uhG+GYTHgAsHFOtBmG97TEifUKwf8fEdHzPo3UF0btG5RMAw3//5eDaZufl8ZlptbZ76umLnIe8CuvMTXb0Iu9XiDQoSIGo/CRZClIO/pnNVlZqg9AzC89iQTkO8WYQne/D0I3xnNoH/LALwO6vJExys4C03eaa+/qFxHD9nZvstNYk6wjCMGvdv48aNhhDhMI5xFf552ti0oM6xatcqo8mkJsaqXauK3fb8jHEYjMOY/M3kYj/zfW1ZNh06YXy4/YCRcSDTyDjwu7Fi5yHDMAxjxc5DRvreo8bHPx80Vu46bHy4/YCx+dAJwzAM43B2rvHdgd+Deg8iMrm/Oyv0vSuZhRDVJJhyk2db79TbU4tlEJ4tvz1ZBATfj4CyMwmAaJuFL3YfodBpUOR0Uuh0cn5iPFuPnuRkgeuCllJqqtskWAgRQFWWmTwClZt8+VsLEWw/As70JM5pWA/P+ojSZjXlOy1c0SaxRONa1G0SLIQw8deTKM9+TR0f7FjsfkUb1uYMYtC7gxhw4YASi+YCZRFdWyawYtfhgJmEv1lN0rgWvmRRnhAmZV15LhidHu5U7L6/hXOeLGFIpyHecpPvAjrzuojU21N5f9v7fs9n3vXVw5NFbD+ezXV/aEa7hDjio2zeTKJ+lI0ip0HbhHoUOp0lZjXJXk3CH8kshAgh83Ws/QUD39XXnn5FMBmER1n9iB2Z2VhwzW4qK5MQIhAJFqLOK09Pwt8CukDN6ieufCKohnVZ+zP560N4lNWPaBYXQ3ZBIcdO53sb1rI+QlREUMFCKZWktU4L/EwhIlNZm/KVpydR1nWsU29PpQUtgLKb1b4/9wQBcwZSWmAobz/irHqurcDVWfUlkxCVEmzPYnzgpwgRuSrbiyiLudSk83SJQGDOIFYNW8WgdwexZMuSMstNpSlvP+K3U7nekhNIT0JUXLBlKEMptQzQgBNAa/1UyEYlRA3j+aIvrdTkL4MY0mmI3+OYrxvh2atp+fYD0o8QYRVssJgf0lEIEQIVWR9R0Z5EaSrSsIbiGcQlzRpy3R+asfXoKelHiLAJ6uJHSik78ADQEdgOzNRa54dqUEqp5sAnWuuu/n4uFz8S5VWe61n78pcdlFZq+vfl/6btOW0D9h5K4y+DALBa4I/NE9h85CTRNiv5RU4ubtqAY6cLaNMwlqZxMd4r0UmZSZSmOi5+NBv4A/AF0A6YW5GTBUMpZQGeAPaG6hyidlg9bnW1nMfckzBfx9o3UKTenkr3Zt1LPL8spwuLWPPLcXILiwD89iHaJ8Rx/R+a8evJXAqdTulHiLAItgx1vtb6T+7by5VS31TVAJRSjwDXuO+uA44DbwKPVdU5RO2UPj69Qltt+AqmzFRaTwKKl5q2bt0KBFdqgpLlpnp2G03qRXHgVG6xGU2xdhv17DbZhkOETbDBIlYpFae1zlFK1QOq7DqJWuspwBTPfaXU+8ClwOVKqYFa63eq6lyi7irrAkPl3afJV2k9C/PaiGAb1lYLNIuLKbaR32+ncjknIa5Y1iD9CFHdgg0WU4BNSqktuPoWQRV/lVLdgZe01n2UUlZgBq5AkAfcp7Xe4fsarfUA92vflEAhfFV0U7+yMpBAq6yBci2g8yfYhnWHJvXZevSUZBAi4gQbLA4A3XH1LXZrrY8FeoFS6gngbiDb/dCtQKzWuqdSqgcwGbiltNdrre8KcmyiDinPArryKKvMVNEFdOC/Ye3JIP7YPMFvuUkyCBGJgg0W4909i+PlOPZOYACwyH2/F7ACQGv9rVLK70ynYHlqw6J22DJti3cTPrvdTuPGjWnUqBF2u53c3FyOHz9OVlYWvrP3Kvo5sFqtJCQkkJiYSHR0NAUFBWT+nun9+d59e9ma6zr2J9s+4d+X/5sWuS2852tBC/59+b/55H+f0CLXtWq7AAv7iaNw6zbs7ouTXhLfgKPWemTmF9EoNoo4u5V6znwSC7PZfqiQAsNOQkE22dZ6bD90jOz9Mq9DRKaQLcrTWr+nlGpneqghcMJ0v0gpZddaF5ZjvF4dOnSoyMtEhEqdkcrA6QP9/iw2NpZWrVrRqlWrEj8r63MQsHGtzvQa1vy6hge+fMBvmenlDi/7Pb7vuX84nEXBiRyMhMZ0aNbQ+7j9RA5Hjpzki91HKDKgfbOzOCfhbAoPnuBSn2mvHVqcXer7EaKyMjIyKvzaYKfOvgEsB7biChi6AufKAhqYz13RQCEElN20hrK3B+/WqluJx3y3BQ9m6iu4Sk3v6wPsyMzmqrPPYkdmNu/rAyzffgDA75RXQKa9imrz+++/89lnn1XqGMFmFkO01n0rdSZYC/QDUt09i82VPJ6o4Sp7BbpAPw+mcQ0VX2XtUVazGpApryJstm3bxtSpU1mwYAG5ubn897//rfCxgl3BvRRYTPEy1PYgXtcOWKK17mGaDXUJYAH+prXeVpFBywru2qcqm9W+0nan+W1cl5fv9FezfSdy2HzkJHYLFBpwcdMGnJMQV+mxC1FeTqeTzz//HIfDweeff050dDRDhw5l9OjRFBUVVXgFd7CZRTNgNK4veYBYoGegF2mt9wA93LedwIjyD1GIyOA7/dXMU2pKKDrNMVs979oIIarLyZMnWbhwIVOnTkVrTcuWLZkwYQIPPPAAzZo1A0LYs3BnFGitk4BPtdZJ7tuSR4uwmLR2kt8+QtruNCatneT3cd/twYPpQ5gF6knAmVLTWeRxRZtEYm1Vtm5ViDLt2rWLRx99lDZt2vDwww+TkJDAW2+9xZ49e3jmmWe8gaKyAjW4zWe50XQ7cO1K1CmV3acpULPaI9imtfnxYBvXvvs0eZS1X5OHNKtFdTIMg7S0NG699VbOO+88pk6dyo033si6detYv349Q4cOJTo6ukrPGexsKDhTghKihMpeXCjYPZ4CbepnFqhx7ctcZjLz7NdU6DRKLKATojqdPn2auXPncumll3L11VezZs0axowZw549e3j77bfp0aNHyM4dqGdhlHJbiLApa7W1WTB7NkHZq6xvvaAlcKYn4btfkxDV4ddff2XmzJnMnj2bY8eOcckllzBv3jzuuOMO6tWrVy1jCBQsLlJKLcaVVZhvdwz5yETEq+zU10gRaOoryPRXUf0Mw+Dbb7/F4XDw7rvvYhgG/fv3Z/To0fTu3RuLpXqLPYGCxSDT7Vml3BZ1VGX3aaroFegqu6mfr7K2BfeQ/ZpEdcnPzyc1NZWUlBQ2bNhAQkICjzzyCA899BDt27cP27jKDBZa69Bd5V7UeRXZGrwim/qVtT7CQ8pMItwOHTrE7NmzmTlzJgcPHkQpxYwZM7j77rupX79+4AOEWLDrLISocsGusDaryGrrstZHeEiZSYTL999/j8Ph4O233yY/P5/rr7+e0aNH07dvX6zW8sxBCi0JFqJKBDv11VewzWqPYJvWEFzj2kPKTKI6FRYW8sEHHzBlyhTWrFlDfHw8w4cPZ9SoUSilwj08vyRYiCoRic3sYBrXQlSn48ePM3fuXKZPn86+ffto3749kydP5p577qFRo0bhHl6ZIifHEdWmsgvoqlJFV1iXtoDOTNZHiEjx008/MWLECNq0acOTTz7Jueeey7Jly/j555959NFHIz5QgASLOqmyC+iqSmW2Bi9tAZ2v0rYHFyLUnE4nH3/8Mddeey0XXXQRb7zxBkOHDmXTpk2sWrWKW2+9FVsN2hZGylCiwio69dWjIs3q8vQhQBrXovplZWWxYMECpk6dyo4dO2jdujXPP/88999/P02aNAn38CpMgkUdEYoFdBWZ+mpWnma1R3n7ENK4FtVlx44dTJs2jfnz53Py5El69uzJv/71LwYMGEBUVFS4h1dpEizqiMouoPOnIlNfKyuYBXRCVBfDMPjqq69wOBx88skn2O12Bg0aRHJyMpdffnm4h1elJFiISinv1NeqIAvoRLjl5OTw5ptvkpKSwo8//kjTpk355z//yYgRI/xeK742kGAhwi6YFdZm0ocQ4bJv3z6mT5/Oa6+9RmZmJpdddhmvv/46Q4YMITY2NtzDCykJFnVQRRfQ+VMV+zQFs8LaTPoQojoZhsHatWtxOBwsW7YMwzC47bbbSE5O5qqrrqr2Df3CRYJFHVRVC+gqsk+TWXlnNglRnfLy8liyZAkpKSl89913NGrUiEcffZSHHnqItm3bhnt41U6Chaiwikx9NZMV1iISHTx4kJkzZzJr1iwOHz5Mhw4dmDVrFnfddRfx8fHhHl7YSLAQFVaRqa9mMrNJRJKNGzficDhYunQpBQUF3HTTTYwePZprrrmmzpSayiIruOuISWsn+V0VnbY7jUlrJ4VhRC6ywlqEU0FBAUuXLuWKK66gW7duLF++nJEjR7J9+3bv6msJFC4SLOoIzwI6c8Dw9By6teoWtnF5ZjZdkFifK9okEluDtj8QNdexY8eYOHEi7du3Z8iQIRw6dIhXX32V3377DYfDwfnnnx/uIUYcKUOF0epxq6ttt9ZQLqAr79RXM5nZJKrT5s2bSUlJ4c033yQ3N5c///nPzJw5kxtvvLFG7dMUDhEXLJRSlwJTgV3AG1rrwFuQ1lDp49OrdWvvUC2gK+/UVyGqU1FREZ988glTpkwhLS2NevXqMWzYMJKTk7nooovCPbwaI+KCBdAdOAgUAT+GeSyiDDL1VUSyEydOMH/+fKZNm8auXbs4++yzefHFFxk+fDiJiYnhHl6NE/ZgoZR6BLjGfXcdsAxYCjQHHgfK3rq0hgnFhn7BqooFdGYy9VVEou3btzN16lQWLFjAqVOnuPLKK3nxxRe57bbbsNvD/pVXY4X9N6e1ngJM8dxXSg0FDgCZRMD4qlooNvQLRmUX0PkjU19FpDAMg5UrV+JwOPjss8+Ijo5myJAhJCcn06VLl3APr1YI6ZexUqo78JLWuo9SygrMAC4F8oD7tNY7/LxsD66eRQEwIZTjq0squ4CuNLKpnwin7OxsFi5cSEpKCtu2baN58+aMGzeOESNG0Lx583APr1YJWbBQSj0B3A14LmV2KxCrte6plOoBTAZu8X2d1vob4JtQjauuquwCutLIpn4iHPbu3cu0adOYO3cuv//+O127dmXRokUMGjSI6OjocA+vVgplZrETGAAsct/vBawA0Fp/q5TqWpmDb926tXKjq2LR0dEkJiaSkJCA1WolOzubzMxMTp48WeprOj7YsVzvw26306hRIxo3bozdbicvL4/jx49z4sQJDMOoireBxWLxniMmJobCwkIyMzPJzMykqKjk9a5jgaOZcNR0f2vm/ioZS02Um5sbcZ/N2sIwDDZu3Mibb77JV199hcVi4dprr+Wuu+6ic+fOWCwWdu7cGe5h1lohCxZa6/eUUu1MDzUETpjuFyml7Frrwoocv0OHDpUZXsjFx8cH3Eemw/TKvYeYmBhatmxJy5ahm3lkt9tp2rQpTZs2Ddk5apOtW7dG/GezpsnNzeXtt9/G4XCwadMmEhMTeeKJJ3jwwQc5++yzwz28GiUjI6PCr63OBnIW0MB031rRQCEqrjIL6ISoTvv372fmzJnMnj2bI0eO0KlTJ+bMmcOdd95JXJz0xapbdQaLtUA/INXds9hcjecWbrKATkS69evX43A4eOeddygqKqJfv36MHj2apKQk2acpjKozWCwDrlVKfQNYgL9V47kjxqS1k+jWqluJpnLa7jQ27N9QaiO6smQBnYhkBQUFvPvuuzgcDtavX0/Dhg15+OGHefjhhzn33HPDPTxBiIOF1noP0MN92wmMCOX5agLPhn7maazmNRChIgvoRCQ6cuQIc+bMYcaMGezfv5/zzz+fqVOn8pe//IUGDRoEPoCoNrVu0VukC+WGfmWRBXQikmzatAmHw8HixYvJy8vjuuuuY+7cuVx33XVYrbIZdiSSYBEGodrQLxBZQCfCqaioiA8//BCHw0F6ejpxcXHcc889jBo1SmaQ1QASLOoQWUAnwiEzM5N58+Yxbdo09u7dS9u2bfn3v//NvffeS+PGjcM9PBEkCRZhUNUb+gVLrh0hqtO2bdtISUnhjTfeICcnh969e/PKK6/Qv39/2dCvBpL/YtUsFBv6CREpnE4nK1aswOFwsHLlSmJiYhg6dCjJyclcdtll4R6eqATpJFWzQBv6CVETnTx5kmnTptGhQwduuukmNm/ezHPPPccvv/zC/PnzJVDUApJZVLNQbegnRDjs2rWLadOmMW/ePLKysujevTuLFy/m//7v/2RDv1pGgoUQolwMwyAtLY2UlBQ+/PBDbDYbAwcOZPTo0XTv3j3cwxMhIsFCCBGU06dP89Zbb5GSksLmzZtp0qQJTz31FCNHjqR169bhHp4IMQkWYSIb+oma4tdff2XGjBnMmTOHY8eOcemllzJ//nzuuOMOYmNjwz08UU0kWISJbOgnIplhGKxbtw6Hw8F7772HYRjccsstjB49mj/96U+yoV8dJMGimsmGfiKS5efnk5qaisPhYOPGjTRq1Ii///3vPPTQQ7Rr1y7cwxNhVGODxXjLeO/t3mN702dcn/ANphxkQz8RiQ4dOsSsWbOYNWsWBw8e5MILL2TGjBncfffd1K8vn01Rg4PFWGNsuIdQIbKhn4gk3333HQ6HgyVLlpCfn88NN9zA6NGjufbaa2VDP1FMjQ0WNZls6CfCqbCwkOXLl+NwOFizZg3x8fEMHz6cUaNGoZQK9/BEhJJgEQayoZ8Ih+PHjzN37lymT5/Ovn37aN++PZMnT+aee+6hUaNG4R6eiHASLMJANvQT1enHH39k6tSpLFy4kNOnT5OUlERKSgo333wzNpuUP0VwJFgIUQs5nU4++eQTUlJS+PLLL4mNjeXOO+8kOTmZSy65JNzDEzWQBAshapGsrCxef/11pk6dys6dO2ndujUvvPACw4cPp0mTJuEenqjBJFgIUQv8/PPPTJ06lddff51Tp07Rs2dPnn/+eQYMGEBUVFS4hydqgRofLNJ2p7Fh/4ZSd3MVorYyDIMvv/wSh8PBp59+it1uZ9CgQYwePZpu3bqFe3iilqnRwcJ8ISEh6oqcnBwWLVpESkoKP/30E02bNuWf//wnI0eOpGVL2QVAhEaNDRb+rjgnRG22d+9eZsyYwWuvvUZmZiadO3dmwYIFDB48WDb0EyFXY4PF1QuvZtWwVRIoRK1mGAZr1qzB4XCwbNkyAG677TZGjx5Nr169ZEM/UW1qbLAQojbLy8tjyZIlOBwOvv/+exo3bszjjz/Ogw8+SNu2bcM9PFEHRVywUEp1BEYDMcDLWust/p63atgqKUOJWufAgQPMnDmT2bNnc/jwYTp27MisWbO46667iI+PD/fwRB0WiTuF3Qf8BuQBe0p7UlL7JFJvT2XQu4NI251WXWMTIiQ2bNjAXXfdRdu2bfnXv/7F5ZdfzsqVK9myZQsPPPCABAoRdmHPLJRSjwDXuO+uA84D/gr8ERgGzCjttZ6AsWH/BskuRI1TUFDA+++/j8PhYN26dTRo0ICRI0cyatQozjvvvHAPT4hiwh4stNZTgCme+0qpuUA2cJwgMp+k9kkSKESNcvToUebMmcOMGTP47bffOPfcc5kyZQp/+9vfaNhQrpooIlNIg4VSqjvwkta6j1LKiitLuBRXiek+rfUOPy+bBbyGK1CMDuX4hKhOmzdvxuFw8NZbb5Gbm8s111zDrFmzuOGGG2RDPxHxQhYslFJPAHfjyhIAbgVitdY9lVI9gMnALb6v01pvxFV+KtPWrVu9t202G40aNaJx48ZERUWRl5dHZmYmJ06cwOl0VsXbESIoubm5xT6bRUVFrF69mjfffJP169cTGxtLv379uOuuuzj//PMB2L59e7iGK0TQQplZ7AQGAIvc93sBKwC01t8qpbpW5uDtz7+g1KvLxcTE0KJFC1q0aFGZUwhRblu3bqVDhw6cOHGC+fPnM23aNHbt2sXZZ5/Niy++yPDhw0lMTAz3MEUdlZGRUeHXhmw2lNb6PaDA9FBD4ITpfpFSqsLBavvx7MBPEqKa7dmzh1GjRtGmTRseffRRWrVqxTvvvMOuXbt48sknJVCIGqs6G9xZQAPTfavWurCiB9uRmc2OzGysFrj1AtkPR4SPYRisXLkSh8PBZ599RnR0NHfccQfJycn88Y9/DPfwhKgS1Rks1gL9gFR3z2JzZQ4WH2WjWVwMHZrUr5LBCVFe2dnZLFy4kJSUFLZt20aLFi14+OGH+ec//0nz5s3DPTwhqlR1BotlwLVKqW8AC/C3yhys0GlwVr2oUvsWQoTKnj17mDZtGvPmzeP333+na9euLFq0iEGDBrFz504JFKJWCmmw0FrvAXq4bzuBEVV17EKnk99O5XJOQlxVHVKIUhmGwX/+8x8cDgcffPABFouF22+/neTkZHr27Ckb+olaL+yL8irqijaJ/JqVG+5hiFouNzeXxYsXk5KSwqZNm0hMTOTJJ5/kwQcfpE2bNuEenhDVpsYGi6ZxMTSNiwn3MEQttX//fmbMmMHs2bM5evQonTp14rXXXuPOO++kXr164R6eENWuxgYLIUJh/fr1OBwO3nnnHYqKiujfvz+jR4+mT58+UmoSdZoEC1Hn5efn89577+FwOFi/fj0NGzZk1KhRPPzww/zhD38I9/CEiAgSLESddeTIEWbPns2MGTM4cOAAF1xwAVOnTuUvf/kLDRo0CHwAIeoQCRaiztm0aRMOh4PFixeTl5fHddddx7x587juuuuwWiPxEi9ChJ8EC1EnFBUV8cEHH5CSkkJ6ejpxcXHce++9PPzww3To0CHcwxMi4kmwELVaZmYm8+bNY9q0aezdu5d27drx8ssvc++999KoUaNwD0+IGkOChaiVtm3bRkpKCm+88QY5OTn07t2bV199lf79+8u1I4SoAAkWotZwOp2sWLECh8PBypUriYmJYejQoSQnJ3PZZZeFe3hC1GgSLESNd/LkSd544w2mTp3K9u3badWqFf/617+4//77adq0abiHJ0StIMFC1Fi7du1i6tSpzJ8/n6ysLLp3787ixYu5/fbbiYqKCvfwhKhVJFiIGsUwDNLS0nA4HHz00UfYbDYGDRpEcnIy3bt3D/fwhKi1JFiIGuH06TO0iVIAAAWcSURBVNO8+eabpKSksGXLFpo2bcrTTz/NyJEjadWqVbiHJ0StJ8FCRLRffvmFGTNmMGfOHI4fP86ll17K/PnzueOOO4iNjQ338ISoMyRYiIhjGAbffPMNKSkpvPfeexiGwS233MIjjzzCVVddJRv6CREGEixExMjLyyM1NRWHw0FGRgaNGjXi73//Ow899BDt2rUL9/CEqNMkWIiwO3ToELNmzWLmzJkcOnSICy+8kBkzZnD33XdTv75cY12ISCDBQoRNRkYGDoeDpUuXkp+fzw033MDo0aO59tprZUM/ISKMBAtRrQoLC1m2bBkOh4O1a9cSHx/P8OHDGTVqFEqpcA9PCFEKCRaiWhw7dozXXnuN6dOn8+uvv9K+fXteeeUV7rnnHhISEsI9PCFEABIsREht2bKFlJQU3nzzTU6fPk1SUhLTpk3j5ptvlg39hKhBJFiIKldUVMSnn36Kw+Hgq6++IjY2lrvuuotRo0ZxySWXhHt4QogKkGAhqkxWVhbz589n6tSp7Nq1i9atW/PCCy8wfPhwmjRpEu7hCSEqIeKChVLqEeAy4HzgLa31jDAPSQTw888/M3XqVF5//XVOnTrFFVdcwQsvvMCAAQNkQz8haomICxZa6ylKqWhgGjAr3OMR/hmGwZdffonD4eDTTz/FbrczePBgkpOT6datW7iHJ4SoYmEPFu5M4hr33XVa6+eBO4D3tdbO8I1M+JOdnc2iRYtISUlh69atNGvWjGeeeYYRI0bQsmXLcA9PCBEiYQ8WWuspwBSfh/8E3BeG4YhS7N27l+nTpzN37lwyMzPp3LkzCxYsYMiQIcTExIR7eEKIEAtpsFBKdQde0lr3UUpZgRnApUAecJ/WekcpL43TWhuhHJsIzDAM1qxZg8PhYNmyZQAMGDCA0aNHc+WVV8qGfkLUIRbDCM13slLqCeBuIFtr3UMpNQDor7X+q1KqBzBGa31LRY6dkZEhgUQIISqgS5cuFforL5SZxU5gALDIfb8XsAJAa/2tUqprRQ9c0TcrhBCiYkK2W5vW+j2gwPRQQ+CE6X6RUirsPRMhhBCBVefWnllAA/O5tdaF1Xh+IYQQFVSdwWItcCOAu2exuRrPLYQQohKqswy0DLhWKfUNYAH+VpUHV0r9GRgCxAGTtNabqvL4QlSWUupqYKjWWqaFi7BTSl0BPOC+O1pr/XtZzw9psNBa7wF6uG87gREhPF0ccD+urUL6AhIsRMRQSp0HdAZiwz0WIdzuxxUsLgcGA7PLenKNbTD7W/mtlIoHkoEnwzcyIUrdmWCyUurNMA5LCDOb1jpXKXUAuDrQk2tssPBd+a2UagJMAp7VWh8O28CEoNSdCYSIJDlKqRigJXAw0JMjMlhUcOX3K0BTYKJSarnW+t3qG7GoSyqxM4EQ1SLIz+gcXKWnKM70LkoVccHCvPLb/dCtQKzWuqd7FtVkoMTKb631sOobpairKvr59NBa3xX6UYq6LNjPqNY6A/hrsMetzqmzwfKs/PYotvIbqPDKbyGqgHw+RaQLyWc04oKFrPwWkUw+nyLSheozGnHBwg9Z+S0imXw+RaSrks9oTQgWsvJbRDL5fIpIVyWf0ZqQLod05bcQlSSfTxHpquQzGrLrWQghhKg9akIZSgghRJhJsBBCCBGQBAshhBABSbAQQggRkAQLIYQQAUmwEEIIEZAECyGEEAFJsBCiCiil/qqUejHc4xAiVCRYCCGECKgmbPchRE3RQym1EtdFuGZqreeEe0BCVBXJLISoOgXAdcBtwCNhHosQVUqChRBV5zuttYHresZx4R6MEFVJgoUQVUd25RS1lgQLIYQQAckW5UIIIQKSzEIIIURAEiyEEEIEJMFCCCFEQBIshBBCBCTBQgghREASLIQQQgQkwUIIIURAEiyEEEIE9P/hqsdkRzM82AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = axes()\n",
    "ax.loglog(h_vec, h_error_n1_1, label = 'n=1', color='white',\n",
    "          markeredgecolor='purple', marker='+',  markersize=7 )\n",
    "\n",
    "ax.loglog(h_vec, h_error_n2_1, label = 'n=2', color='white',\n",
    "          markeredgecolor='green', marker='x',  markersize=7 )\n",
    "\n",
    "ax.loglog(h_vec, h_error_n4_1, label = 'n=4', color='white',\n",
    "          markeredgecolor='lightblue', marker='*',  markersize=7 )\n",
    "ax.loglog(h_vec, ((h_vec**2)*(h_error_n4_1[0]/(h_vec[0]))), \n",
    "          label = 'h**2', color='black')\n",
    "ax.set(xlim=(1e-2, 1e0), ylim=(1e-7, 1e-1),\n",
    "       xlabel='h', ylabel='Error',\n",
    "       title='Error in h using second order trotter');\n",
    "ax.legend()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T14:30:49.445830Z",
     "start_time": "2018-12-30T14:30:49.018802Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x124cfaf60>"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = axes()\n",
    "ax.loglog(n_vec, n_error_2,\n",
    "          color='white', markeredgecolor='purple', marker='o',  markersize=10 )\n",
    "ax.loglog(n_vec, 1/(n_vec**2)*n_error_2[0], label = '1/n**2')\n",
    "ax.set(xlim=(1, 1e2), ylim=(1e-7, 1e-2),\n",
    "       xlabel='n', ylabel='Error',\n",
    "       title='Error in n using second order trotter');\n",
    "ax.legend()\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T14:31:38.339953Z",
     "start_time": "2018-12-30T14:31:37.956469Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x124e87b00>"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = axes()\n",
    "ax.loglog(n_vec, n_error_1,\n",
    "          color='white', markeredgecolor='purple', marker='o',  markersize=10 )\n",
    "ax.loglog(n_vec, 1/n_vec*n_error_1[0], label = '1/n')\n",
    "ax.set(xlim=(1, 1e2), ylim=(1e-4, 1e0),\n",
    "       xlabel='n', ylabel='Error',\n",
    "       title='Error in n using first order trotter');\n",
    "ax.legend()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-30T14:38:53.041940Z",
     "start_time": "2018-12-30T14:38:52.588480Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x12503ab38>"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = axes()\n",
    "ax.loglog(h_vec, h_error_n1_1, label = 'n=1', color='white',\n",
    "          markeredgecolor='purple', marker='+',  markersize=7 )\n",
    "\n",
    "ax.loglog(h_vec, h_error_n2_1, label = 'n=2', color='white',\n",
    "          markeredgecolor='green', marker='x',  markersize=7 )\n",
    "\n",
    "ax.loglog(h_vec, h_error_n4_1, label = 'n=4', color='white',\n",
    "          markeredgecolor='lightblue', marker='*',  markersize=7 )\n",
    "ax.loglog(h_vec, ((h_vec**2)*(h_error_n4_1[0]/(h_vec[0]**2))), \n",
    "          label = 'h**2', color='black')\n",
    "ax.set(xlim=(1e-2, 1e0), ylim=(1e-7, 1e-1),\n",
    "       xlabel='h', ylabel='Error',\n",
    "       title='Error in h using second order trotter');\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.1"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}