User guides/Advanced/Gaussian_bump/Gauusian bump potential 3 - direct simulations.ipynb

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   "cell_type": "markdown",
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   "source": [
    "# Gaussian bump potential 3 - direct simulations\n",
    "\n",
    "This is the third in a series of notebooks which will run importance sampling for the Gaussian bump potential. Familiarity with stochastic simulations is assumed.\n",
    "\n",
    "In this notebook we show how to run stochastic simulations and compare the different noise models.\n",
    "\n",
    "We start as we did before by defining everything we need and loading in the required data\n",
    "\n",
    "Throughout natural units with $c = 8\\pi M_{\\rm PL} = \\hbar =1$ are used."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import mystyle\n",
    "plt.style.use(mystyle.paper_style)\n",
    "\n",
    "# Need to make sure you have pyfpt installed\n",
    "import pyfpt as fpt\n",
    "import multiprocessing as mp\n",
    "from multiprocessing import Process, Queue\n",
    "from timeit import default_timer as timer\n",
    "\n",
    "from scipy.optimize import root\n",
    "from scipy.integrate import trapezoid\n",
    "from scipy.interpolate import CubicSpline\n",
    "\n",
    "# Let us define the different colours used\n",
    "color = ['#377eb8', '#ff7f00', '#984ea3','#4daf4a', '#a65628', '#f781bf','#999999', '#e41a1c', '#dede00']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The potential\n",
    "This is the [Gaussian bump potential](https://arxiv.org/abs/1911.00057)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def potential(phi):\n",
    "    expo = np.exp(-0.5*((phi-phi_0)/sigma_tilde)**2)\n",
    "    fraction = (phi**2)/(m_squared + phi**2)\n",
    "    return V_0*fraction*(1 + K*expo)\n",
    "\n",
    "def potential_functional_form(phi):\n",
    "    expo = np.exp(-0.5*((phi-phi_0)/sigma_tilde)**2)\n",
    "    fraction = (phi**2)/(m_squared + phi**2)\n",
    "    return fraction*(1 + K*expo)\n",
    "\n",
    "def potential_dif(phi):\n",
    "    expo = np.exp(-0.5*((phi-phi_0)/sigma_tilde)**2)\n",
    "    fraction1 = (phi**2)/(m_squared + phi**2)\n",
    "    fraction2 = (phi)/(m_squared + phi**2) - (phi**3)/((m_squared + phi**2)**2)\n",
    "    \n",
    "    term1 = 2*V_0*fraction2*(1 + K*expo)\n",
    "    term2 = V_0*fraction1*(-K*expo*(phi-phi_0)/(sigma_tilde**2))\n",
    "    return term1 + term2\n",
    "\n",
    "# I tested this against an interpolation of my previous derivative\n",
    "def potential_ddif(phi):\n",
    "    expo = np.exp(-0.5*((phi-phi_0)/sigma_tilde)**2)\n",
    "    square_brackets = 1 + K*expo\n",
    "    overall_factor = 2*V_0/(m_squared + phi**2)\n",
    "    \n",
    "    term1 = -2*potential_dif(phi)*phi/(m_squared + phi**2)\n",
    "    term2 = overall_factor*(1 - 3*(phi**2)/(m_squared + phi**2) + 2*(phi**4)/((m_squared + phi**2)**2))*\\\n",
    "        (1 + K*expo)\n",
    "    term3 = overall_factor*(phi - (phi**3)/(m_squared + phi**2))*(-K*(phi-phi_0)*expo/(sigma_tilde**2))\n",
    "    term4 = -overall_factor*0.5*phi*K*(3*phi - 2*phi_0)*expo/(sigma_tilde**2)\n",
    "    term5 = overall_factor*0.5*K*expo*(phi*(phi-phi_0)/(sigma_tilde**2))**2\n",
    "    \n",
    "    return term1 + term2 + term3 + term4 + term5\n",
    "\n",
    "def V_prime_by_V(phi):\n",
    "    expo = np.exp(-0.5*((phi-phi_0)/sigma_tilde)**2)\n",
    "    fraction3 = 1/phi - (phi)/(m_squared + phi**2)\n",
    "    fraction4 = -(phi-phi_0)/(sigma_tilde**2)\n",
    "    \n",
    "    term1 = 2*fraction3\n",
    "    term2 = fraction4*K*expo/(1 + K*expo)\n",
    "    return term1 + term2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The parameters are shown such that the power spectrum peaks at $5 \\times 10^{-3}$ in the astroid mass gap."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "K = 1.17*(10**-3)  # This needs all 3 sig fig\n",
    "cmb_power = 2*10**-9\n",
    "cmb_phi = 3.0\n",
    "phi_0 = 2.18812\n",
    "m = 0.5\n",
    "m_squared = m**2\n",
    "sigma_tilde = 1.59*(10**-2)\n",
    "\n",
    "V_0 = 12*(np.pi**2)*(cmb_power/potential_functional_form(cmb_phi))*(V_prime_by_V(cmb_phi)**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Loading in background\n",
    "We have already simulated the background, now we can just load it in."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "background_data = pd.read_csv(\"gaussian_bump_dynamics_dynamics\"+\".csv\", index_col=0)\n",
    "\n",
    "N_values = np.array(background_data[\"N\"])\n",
    "phi_values = np.array(background_data[\"phi\"])\n",
    "phi_diff_values = np.array(background_data[\"phi_N_diff\"])\n",
    "hubble_param_values = np.array(background_data[\"H\"])\n",
    "epsilon1_values = np.array(background_data[\"epsilon1\"])\n",
    "epsilon2_values = np.array(background_data[\"epsilon2\"])\n",
    "nu_squared_values = np.array(background_data[\"nu_squared\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's interpolate over this data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "hubble_param_interpolation = CubicSpline(N_values, hubble_param_values)\n",
    "epsilon1_interpolation = CubicSpline(N_values, epsilon1_values)\n",
    "epsilon2_interpolation = CubicSpline(N_values, epsilon2_values)\n",
    "nu_squared_interpolation = CubicSpline(N_values, nu_squared_values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are also a few constants and functions we need."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "N_end = N_values[-1]\n",
    "\n",
    "N_usr_start = 29.84178346243688\n",
    "N_end_start = 32.25059795813168\n",
    "\n",
    "N_sim_start = 31.13831633\n",
    "N_sim_end = 39.1497714\n",
    "\n",
    "a_in = 1.\n",
    "\n",
    "dN = 0.00023659513392999544"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def find_cg_time(k, sigma, N_exit):\n",
    "    def exit_time_func(N_cg_exit):\n",
    "        return k - sigma*aH_interpolation(N_cg_exit)\n",
    "    N_guess = N_exit + np.log(sigma**-1)\n",
    "    sol_cg_time = root(exit_time_func, N_guess)\n",
    "    N_cg_exit = sol_cg_time.x\n",
    "    return float(N_cg_exit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Direct simulations\n",
    "## 2D noise\n",
    "We will first investigate a 2D noise model. The simulations are run using Cython compiled locally for efficiency."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext cython"
   ]
  },
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   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
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      "Content of stderr:\n",
      "/home/joe/.cache/ipython/cython/_cython_magic_a340241e5d4139803139c24d6920cbd683898caa.c:17490:15: warning: ‘__pyx_f_54_cython_magic_a340241e5d4139803139c24d6920cbd683898caa_V’ defined but not used [-Wunused-function]\n",
      "17490 | static double __pyx_f_54_cython_magic_a340241e5d4139803139c24d6920cbd683898caa_V(double __pyx_v_phi) {\n",
      "      |               ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~"
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       "<pre class='cython code score-16 '>  __pyx_t_7 = <span class='pyx_c_api'>__Pyx_ImportDottedModule</span>(__pyx_n_s_numpy, NULL);<span class='error_goto'> if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 2, __pyx_L1_error)</span>\n",
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       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">003</span>: </pre>\n",
       "<pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">004</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">V_0</span> <span class=\"o\">=</span> <span class=\"mf\">7.903587107979402e-11</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_54_cython_magic_a340241e5d4139803139c24d6920cbd683898caa_V_0 = 7.903587107979402e-11;\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">005</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">e</span> <span class=\"o\">=</span> <span class=\"mf\">2.718281828459045</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_54_cython_magic_a340241e5d4139803139c24d6920cbd683898caa_e = 2.718281828459045;\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">006</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">pi_num</span> <span class=\"o\">=</span> <span class=\"mf\">3.141592653589793</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_54_cython_magic_a340241e5d4139803139c24d6920cbd683898caa_pi_num = 3.141592653589793;\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">007</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">sigma_tilde</span> <span class=\"o\">=</span> <span class=\"mf\">1.59</span><span class=\"o\">*</span><span class=\"p\">(</span><span class=\"mf\">10</span><span class=\"o\">**-</span><span class=\"mf\">2</span><span class=\"p\">)</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_54_cython_magic_a340241e5d4139803139c24d6920cbd683898caa_sigma_tilde = (1.59 * pow(10.0, -2.0));\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">008</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">phi_0</span> <span class=\"o\">=</span> <span class=\"mf\">2.18812</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_54_cython_magic_a340241e5d4139803139c24d6920cbd683898caa_phi_0 = 2.18812;\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">009</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">m_squared</span> <span class=\"o\">=</span> <span class=\"mf\">0.25</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_54_cython_magic_a340241e5d4139803139c24d6920cbd683898caa_m_squared = 0.25;\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">010</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">K</span> <span class=\"o\">=</span> <span class=\"mf\">1.17</span><span class=\"o\">*</span><span class=\"p\">(</span><span class=\"mf\">10</span><span class=\"o\">**-</span><span class=\"mf\">3</span><span class=\"p\">)</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_54_cython_magic_a340241e5d4139803139c24d6920cbd683898caa_K = (1.17 * pow(10.0, -3.0));\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">011</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">diff_const_squared</span> <span class=\"o\">=</span> <span class=\"mf\">6.351213422073874e-13</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_54_cython_magic_a340241e5d4139803139c24d6920cbd683898caa_diff_const_squared = 6.351213422073874e-13;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">012</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">phi_end</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">013</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">expo</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">014</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">fraction</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">015</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">fraction3</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">016</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">fraction4</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">017</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">noise_value</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">018</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">term1</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">019</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">term2</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">020</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">phi_old</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">021</span>: </pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">022</span>: </pre>\n",
       "<pre class=\"cython line score-2\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">023</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">V</span><span class=\"p\">(</span><span class=\"n\">double</span> <span class=\"n\">phi</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-2 '>static double __pyx_f_54_cython_magic_a340241e5d4139803139c24d6920cbd683898caa_V(double __pyx_v_phi) {\n",
       "  __pyx_t_double_complex __pyx_v_expo;\n",
       "  double __pyx_v_fraction;\n",
       "  double __pyx_r;\n",
       "/* … */\n",
       "  /* function exit code */\n",
       "  __pyx_L1_error:;\n",
       "  <span class='pyx_c_api'>__Pyx_AddTraceback</span>(\"_cython_magic_a340241e5d4139803139c24d6920cbd683898caa.V\", __pyx_clineno, __pyx_lineno, __pyx_filename);\n",
       "  __pyx_r = -1;\n",
       "  __pyx_L0:;\n",
       "  return __pyx_r;\n",
       "}\n",
       "</pre><pre class=\"cython line score-5\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">024</span>:     <span class=\"n\">expo</span> <span class=\"o\">=</span> <span class=\"n\">e</span><span class=\"o\">**</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"p\">((</span><span class=\"n\">phi</span><span class=\"o\">-</span><span class=\"n\">phi_0</span><span class=\"p\">)</span><span class=\"o\">/</span><span class=\"n\">sigma_tilde</span><span class=\"p\">)</span><span class=\"o\">**</span><span class=\"mf\">2</span><span class=\"p\">)</span></pre>\n",
       "<pre class='cython code score-5 '>  __pyx_t_1 = (__pyx_v_phi - __pyx_v_54_cython_magic_a340241e5d4139803139c24d6920cbd683898caa_phi_0);\n",
       "  if (unlikely(__pyx_v_54_cython_magic_a340241e5d4139803139c24d6920cbd683898caa_sigma_tilde == 0)) {\n",
       "    <span class='py_c_api'>PyErr_SetString</span>(PyExc_ZeroDivisionError, \"float division\");\n",
       "    <span class='error_goto'>__PYX_ERR(0, 24, __pyx_L1_error)</span>\n",
       "  }\n",
       "  __pyx_v_expo = __Pyx_c_pow_double(__pyx_t_double_complex_from_parts(__pyx_v_54_cython_magic_a340241e5d4139803139c24d6920cbd683898caa_e, 0), __pyx_t_double_complex_from_parts((-0.5 * pow((__pyx_t_1 / __pyx_v_54_cython_magic_a340241e5d4139803139c24d6920cbd683898caa_sigma_tilde), 2.0)), 0));\n",
       "</pre><pre class=\"cython line score-5\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">025</span>:     <span class=\"n\">fraction</span> <span class=\"o\">=</span> <span class=\"p\">(</span><span class=\"n\">phi</span><span class=\"o\">**</span><span class=\"mf\">2</span><span class=\"p\">)</span><span class=\"o\">/</span><span class=\"p\">(</span><span class=\"n\">m_squared</span> <span class=\"o\">+</span> <span class=\"n\">phi</span><span class=\"o\">**</span><span class=\"mf\">2</span><span class=\"p\">)</span></pre>\n",
       "<pre class='cython code score-5 '>  __pyx_t_1 = pow(__pyx_v_phi, 2.0);\n",
       "  __pyx_t_2 = (__pyx_v_54_cython_magic_a340241e5d4139803139c24d6920cbd683898caa_m_squared + pow(__pyx_v_phi, 2.0));\n",
       "  if (unlikely(__pyx_t_2 == 0)) {\n",
       "    <span class='py_c_api'>PyErr_SetString</span>(PyExc_ZeroDivisionError, \"float division\");\n",
       "    <span class='error_goto'>__PYX_ERR(0, 25, __pyx_L1_error)</span>\n",
       "  }\n",
       "  __pyx_v_fraction = (__pyx_t_1 / __pyx_t_2);\n",
       "</pre><pre class=\"cython line score-7\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">026</span>:     <span class=\"k\">return</span> <span class=\"n\">V_0</span><span class=\"o\">*</span><span class=\"n\">fraction</span><span class=\"o\">*</span><span class=\"p\">(</span><span class=\"mf\">1</span> <span class=\"o\">+</span> <span class=\"n\">K</span><span class=\"o\">*</span><span class=\"n\">expo</span><span class=\"p\">)</span></pre>\n",
       "<pre class='cython code score-7 '>  __pyx_t_2 = <span class='pyx_c_api'>__Pyx_SoftComplexToDouble</span>(__Pyx_c_prod_double(__pyx_t_double_complex_from_parts((__pyx_v_54_cython_magic_a340241e5d4139803139c24d6920cbd683898caa_V_0 * __pyx_v_fraction), 0), __Pyx_c_sum_double(__pyx_t_double_complex_from_parts(1, 0), __Pyx_c_prod_double(__pyx_t_double_complex_from_parts(__pyx_v_54_cython_magic_a340241e5d4139803139c24d6920cbd683898caa_K, 0), __pyx_v_expo))), 1); if (unlikely(__pyx_t_2 == ((double)-1) &amp;&amp; <span class='py_c_api'>PyErr_Occurred</span>())) <span class='error_goto'>__PYX_ERR(0, 26, __pyx_L1_error)</span>\n",
       "  __pyx_r = __pyx_t_2;\n",
       "  goto __pyx_L0;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">027</span>: </pre>\n",
       "<pre class=\"cython line score-2\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">028</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">V_prime_by_V_cython</span><span class=\"p\">(</span><span class=\"n\">double</span> <span class=\"n\">phi</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-2 '>static double __pyx_f_54_cython_magic_a340241e5d4139803139c24d6920cbd683898caa_V_prime_by_V_cython(double __pyx_v_phi) {\n",
       "  __pyx_t_double_complex __pyx_v_expo;\n",
       "  double __pyx_v_fraction3;\n",
       "  double __pyx_v_fraction4;\n",
       "  double __pyx_v_term1;\n",
       "  __pyx_t_double_complex __pyx_v_term2;\n",
       "  double __pyx_r;\n",
       "/* … */\n",
       "  /* function exit code */\n",
       "  __pyx_L1_error:;\n",
       "  <span class='pyx_c_api'>__Pyx_AddTraceback</span>(\"_cython_magic_a340241e5d4139803139c24d6920cbd683898caa.V_prime_by_V_cython\", __pyx_clineno, __pyx_lineno, __pyx_filename);\n",
       "  __pyx_r = -1;\n",
       "  __pyx_L0:;\n",
       "  return __pyx_r;\n",
       "}\n",
       "</pre><pre class=\"cython line score-5\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">029</span>:     <span class=\"n\">expo</span> <span class=\"o\">=</span> <span class=\"n\">e</span><span class=\"o\">**</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"p\">((</span><span class=\"n\">phi</span><span class=\"o\">-</span><span class=\"n\">phi_0</span><span class=\"p\">)</span><span class=\"o\">/</span><span class=\"n\">sigma_tilde</span><span class=\"p\">)</span><span class=\"o\">**</span><span class=\"mf\">2</span><span class=\"p\">)</span></pre>\n",
       "<pre class='cython code score-5 '>  __pyx_t_1 = (__pyx_v_phi - __pyx_v_54_cython_magic_a340241e5d4139803139c24d6920cbd683898caa_phi_0);\n",
       "  if (unlikely(__pyx_v_54_cython_magic_a340241e5d4139803139c24d6920cbd683898caa_sigma_tilde == 0)) {\n",
       "    <span class='py_c_api'>PyErr_SetString</span>(PyExc_ZeroDivisionError, \"float division\");\n",
       "    <span class='error_goto'>__PYX_ERR(0, 29, __pyx_L1_error)</span>\n",
       "  }\n",
       "  __pyx_v_expo = __Pyx_c_pow_double(__pyx_t_double_complex_from_parts(__pyx_v_54_cython_magic_a340241e5d4139803139c24d6920cbd683898caa_e, 0), __pyx_t_double_complex_from_parts((-0.5 * pow((__pyx_t_1 / __pyx_v_54_cython_magic_a340241e5d4139803139c24d6920cbd683898caa_sigma_tilde), 2.0)), 0));\n",
       "</pre><pre class=\"cython line score-10\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">030</span>:     <span class=\"n\">fraction3</span> <span class=\"o\">=</span> <span class=\"mf\">1</span><span class=\"o\">/</span><span class=\"n\">phi</span> <span class=\"o\">-</span> <span class=\"p\">(</span><span class=\"n\">phi</span><span class=\"p\">)</span><span class=\"o\">/</span><span class=\"p\">(</span><span class=\"n\">m_squared</span> <span class=\"o\">+</span> <span class=\"n\">phi</span><span class=\"o\">**</span><span class=\"mf\">2</span><span class=\"p\">)</span></pre>\n",
       "<pre class='cython code score-10 '>  if (unlikely(__pyx_v_phi == 0)) {\n",
       "    <span class='py_c_api'>PyErr_SetString</span>(PyExc_ZeroDivisionError, \"float division\");\n",
       "    <span class='error_goto'>__PYX_ERR(0, 30, __pyx_L1_error)</span>\n",
       "  }\n",
       "  __pyx_t_1 = (__pyx_v_54_cython_magic_a340241e5d4139803139c24d6920cbd683898caa_m_squared + pow(__pyx_v_phi, 2.0));\n",
       "  if (unlikely(__pyx_t_1 == 0)) {\n",
       "    <span class='py_c_api'>PyErr_SetString</span>(PyExc_ZeroDivisionError, \"float division\");\n",
       "    <span class='error_goto'>__PYX_ERR(0, 30, __pyx_L1_error)</span>\n",
       "  }\n",
       "  __pyx_v_fraction3 = ((1.0 / __pyx_v_phi) - (__pyx_v_phi / __pyx_t_1));\n",
       "</pre><pre class=\"cython line score-5\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">031</span>:     <span class=\"n\">fraction4</span> <span class=\"o\">=</span> <span class=\"o\">-</span><span class=\"p\">(</span><span class=\"n\">phi</span><span class=\"o\">-</span><span class=\"n\">phi_0</span><span class=\"p\">)</span><span class=\"o\">/</span><span class=\"p\">(</span><span class=\"n\">sigma_tilde</span><span class=\"o\">**</span><span class=\"mf\">2</span><span class=\"p\">)</span></pre>\n",
       "<pre class='cython code score-5 '>  __pyx_t_1 = (-(__pyx_v_phi - __pyx_v_54_cython_magic_a340241e5d4139803139c24d6920cbd683898caa_phi_0));\n",
       "  __pyx_t_2 = pow(__pyx_v_54_cython_magic_a340241e5d4139803139c24d6920cbd683898caa_sigma_tilde, 2.0);\n",
       "  if (unlikely(__pyx_t_2 == 0)) {\n",
       "    <span class='py_c_api'>PyErr_SetString</span>(PyExc_ZeroDivisionError, \"float division\");\n",
       "    <span class='error_goto'>__PYX_ERR(0, 31, __pyx_L1_error)</span>\n",
       "  }\n",
       "  __pyx_v_fraction4 = (__pyx_t_1 / __pyx_t_2);\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">032</span>: </pre>\n",
       "<pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">033</span>:     <span class=\"n\">term1</span> <span class=\"o\">=</span> <span class=\"mf\">2</span><span class=\"o\">*</span><span class=\"n\">fraction3</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_term1 = (2.0 * __pyx_v_fraction3);\n",
       "</pre><pre class=\"cython line score-5\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">034</span>:     <span class=\"n\">term2</span> <span class=\"o\">=</span> <span class=\"n\">fraction4</span><span class=\"o\">*</span><span class=\"n\">K</span><span class=\"o\">*</span><span class=\"n\">expo</span><span class=\"o\">/</span><span class=\"p\">(</span><span class=\"mf\">1</span> <span class=\"o\">+</span> <span class=\"n\">K</span><span class=\"o\">*</span><span class=\"n\">expo</span><span class=\"p\">)</span></pre>\n",
       "<pre class='cython code score-5 '>  __pyx_t_3 = __Pyx_c_prod_double(__pyx_t_double_complex_from_parts((__pyx_v_fraction4 * __pyx_v_54_cython_magic_a340241e5d4139803139c24d6920cbd683898caa_K), 0), __pyx_v_expo);\n",
       "  __pyx_t_4 = __Pyx_c_sum_double(__pyx_t_double_complex_from_parts(1, 0), __Pyx_c_prod_double(__pyx_t_double_complex_from_parts(__pyx_v_54_cython_magic_a340241e5d4139803139c24d6920cbd683898caa_K, 0), __pyx_v_expo));\n",
       "  if (unlikely(__Pyx_c_is_zero_double(__pyx_t_4))) {\n",
       "    <span class='py_c_api'>PyErr_SetString</span>(PyExc_ZeroDivisionError, \"float division\");\n",
       "    <span class='error_goto'>__PYX_ERR(0, 34, __pyx_L1_error)</span>\n",
       "  }\n",
       "  __pyx_v_term2 = __Pyx_c_quot_double(__pyx_t_3, __pyx_t_4);\n",
       "</pre><pre class=\"cython line score-7\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">035</span>:     <span class=\"k\">return</span> <span class=\"n\">term1</span> <span class=\"o\">+</span> <span class=\"n\">term2</span></pre>\n",
       "<pre class='cython code score-7 '>  __pyx_t_2 = <span class='pyx_c_api'>__Pyx_SoftComplexToDouble</span>(__Pyx_c_sum_double(__pyx_t_double_complex_from_parts(__pyx_v_term1, 0), __pyx_v_term2), 1); if (unlikely(__pyx_t_2 == ((double)-1) &amp;&amp; <span class='py_c_api'>PyErr_Occurred</span>())) <span class='error_goto'>__PYX_ERR(0, 35, __pyx_L1_error)</span>\n",
       "  __pyx_r = __pyx_t_2;\n",
       "  goto __pyx_L0;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">036</span>: </pre>\n",
       "<pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">037</span>: <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">end_cond</span><span class=\"p\">(</span><span class=\"n\">double</span> <span class=\"n\">phi</span><span class=\"p\">,</span> <span class=\"n\">double</span> <span class=\"n\">pi</span><span class=\"p\">,</span> <span class=\"n\">double</span> <span class=\"n\">N</span><span class=\"p\">,</span> <span class=\"n\">double</span> <span class=\"n\">phi_end</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-0 '>static int __pyx_f_54_cython_magic_a340241e5d4139803139c24d6920cbd683898caa_end_cond(double __pyx_v_phi, CYTHON_UNUSED double __pyx_v_pi, CYTHON_UNUSED double __pyx_v_N, double __pyx_v_phi_end) {\n",
       "  int __pyx_r;\n",
       "/* … */\n",
       "  /* function exit code */\n",
       "  __pyx_L0:;\n",
       "  return __pyx_r;\n",
       "}\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">038</span>:     <span class=\"k\">if</span> <span class=\"n\">phi</span><span class=\"o\">&lt;</span><span class=\"n\">phi_end</span><span class=\"p\">:</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_t_1 = (__pyx_v_phi &lt; __pyx_v_phi_end);\n",
       "  if (__pyx_t_1) {\n",
       "/* … */\n",
       "  }\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">039</span>:         <span class=\"k\">return</span> <span class=\"mf\">1</span></pre>\n",
       "<pre class='cython code score-0 '>    __pyx_r = 1;\n",
       "    goto __pyx_L0;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">040</span>:     <span class=\"k\">else</span><span class=\"p\">:</span></pre>\n",
       "<pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">041</span>:         <span class=\"k\">return</span> <span class=\"mf\">0</span></pre>\n",
       "<pre class='cython code score-0 '>  /*else*/ {\n",
       "    __pyx_r = 0;\n",
       "    goto __pyx_L0;\n",
       "  }\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">042</span>: </pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">043</span>: </pre>\n",
       "<pre class=\"cython line score-6\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">044</span>: <span class=\"k\">cdef</span> <span class=\"kt\">list</span> <span class=\"nf\">update</span><span class=\"p\">(</span><span class=\"n\">double</span> <span class=\"n\">phi</span><span class=\"p\">,</span> <span class=\"n\">double</span> <span class=\"n\">pi</span><span class=\"p\">,</span> <span class=\"n\">double</span> <span class=\"n\">A</span><span class=\"p\">,</span> <span class=\"n\">double</span> <span class=\"n\">N</span><span class=\"p\">,</span> <span class=\"n\">double</span> <span class=\"n\">dN</span><span class=\"p\">,</span> <span class=\"n\">double</span> <span class=\"p\">[:]</span> <span class=\"n\">dW</span><span class=\"p\">,</span> <span class=\"n\">double</span> <span class=\"p\">[:]</span> <span class=\"n\">noise</span><span class=\"p\">,</span></pre>\n",
       "<pre class='cython code score-6 '>static PyObject *__pyx_f_54_cython_magic_a340241e5d4139803139c24d6920cbd683898caa_update(double __pyx_v_phi, double __pyx_v_pi, double __pyx_v_A, CYTHON_UNUSED double __pyx_v_N, double __pyx_v_dN, __Pyx_memviewslice __pyx_v_dW, __Pyx_memviewslice __pyx_v_noise, CYTHON_UNUSED double __pyx_v_bias_amp) {\n",
       "  double __pyx_v_phi_old;\n",
       "  PyObject *__pyx_r = NULL;\n",
       "/* … */\n",
       "  /* function exit code */\n",
       "  __pyx_L1_error:;\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_7);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_8);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_9);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_10);\n",
       "  <span class='pyx_c_api'>__Pyx_AddTraceback</span>(\"_cython_magic_a340241e5d4139803139c24d6920cbd683898caa.update\", __pyx_clineno, __pyx_lineno, __pyx_filename);\n",
       "  __pyx_r = 0;\n",
       "  __pyx_L0:;\n",
       "  <span class='refnanny'>__Pyx_XGIVEREF</span>(__pyx_r);\n",
       "  <span class='refnanny'>__Pyx_RefNannyFinishContext</span>();\n",
       "  return __pyx_r;\n",
       "}\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">045</span>:                  <span class=\"n\">double</span> <span class=\"n\">bias_amp</span><span class=\"p\">):</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">046</span>:     <span class=\"c\"># Store old phi value to be used in calculating velocity</span></pre>\n",
       "<pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">047</span>:     <span class=\"n\">phi_old</span> <span class=\"o\">=</span> <span class=\"n\">phi</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_phi_old = __pyx_v_phi;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">048</span>:     <span class=\"c\"># Update field position</span></pre>\n",
       "<pre class=\"cython line score-8\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">049</span>:     <span class=\"n\">phi</span> <span class=\"o\">=</span> <span class=\"n\">phi</span> <span class=\"o\">+</span> <span class=\"n\">pi</span><span class=\"o\">*</span><span class=\"n\">dN</span> <span class=\"o\">+</span> <span class=\"n\">noise</span><span class=\"p\">[</span><span class=\"mf\">0</span><span class=\"p\">]</span><span class=\"o\">*</span><span class=\"n\">dW</span><span class=\"p\">[</span><span class=\"mf\">0</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"n\">noise</span><span class=\"p\">[</span><span class=\"mf\">1</span><span class=\"p\">]</span><span class=\"o\">*</span><span class=\"n\">dW</span><span class=\"p\">[</span><span class=\"mf\">1</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-8 '>  __pyx_t_1 = 0;\n",
       "  __pyx_t_2 = -1;\n",
       "  if (__pyx_t_1 &lt; 0) {\n",
       "    __pyx_t_1 += __pyx_v_noise.shape[0];\n",
       "    if (unlikely(__pyx_t_1 &lt; 0)) __pyx_t_2 = 0;\n",
       "  } else if (unlikely(__pyx_t_1 &gt;= __pyx_v_noise.shape[0])) __pyx_t_2 = 0;\n",
       "  if (unlikely(__pyx_t_2 != -1)) {\n",
       "    <span class='pyx_c_api'>__Pyx_RaiseBufferIndexError</span>(__pyx_t_2);\n",
       "    <span class='error_goto'>__PYX_ERR(0, 49, __pyx_L1_error)</span>\n",
       "  }\n",
       "  __pyx_t_3 = 0;\n",
       "  __pyx_t_2 = -1;\n",
       "  if (__pyx_t_3 &lt; 0) {\n",
       "    __pyx_t_3 += __pyx_v_dW.shape[0];\n",
       "    if (unlikely(__pyx_t_3 &lt; 0)) __pyx_t_2 = 0;\n",
       "  } else if (unlikely(__pyx_t_3 &gt;= __pyx_v_dW.shape[0])) __pyx_t_2 = 0;\n",
       "  if (unlikely(__pyx_t_2 != -1)) {\n",
       "    <span class='pyx_c_api'>__Pyx_RaiseBufferIndexError</span>(__pyx_t_2);\n",
       "    <span class='error_goto'>__PYX_ERR(0, 49, __pyx_L1_error)</span>\n",
       "  }\n",
       "  __pyx_t_4 = 1;\n",
       "  __pyx_t_2 = -1;\n",
       "  if (__pyx_t_4 &lt; 0) {\n",
       "    __pyx_t_4 += __pyx_v_noise.shape[0];\n",
       "    if (unlikely(__pyx_t_4 &lt; 0)) __pyx_t_2 = 0;\n",
       "  } else if (unlikely(__pyx_t_4 &gt;= __pyx_v_noise.shape[0])) __pyx_t_2 = 0;\n",
       "  if (unlikely(__pyx_t_2 != -1)) {\n",
       "    <span class='pyx_c_api'>__Pyx_RaiseBufferIndexError</span>(__pyx_t_2);\n",
       "    <span class='error_goto'>__PYX_ERR(0, 49, __pyx_L1_error)</span>\n",
       "  }\n",
       "  __pyx_t_5 = 1;\n",
       "  __pyx_t_2 = -1;\n",
       "  if (__pyx_t_5 &lt; 0) {\n",
       "    __pyx_t_5 += __pyx_v_dW.shape[0];\n",
       "    if (unlikely(__pyx_t_5 &lt; 0)) __pyx_t_2 = 0;\n",
       "  } else if (unlikely(__pyx_t_5 &gt;= __pyx_v_dW.shape[0])) __pyx_t_2 = 0;\n",
       "  if (unlikely(__pyx_t_2 != -1)) {\n",
       "    <span class='pyx_c_api'>__Pyx_RaiseBufferIndexError</span>(__pyx_t_2);\n",
       "    <span class='error_goto'>__PYX_ERR(0, 49, __pyx_L1_error)</span>\n",
       "  }\n",
       "  __pyx_v_phi = (((__pyx_v_phi + (__pyx_v_pi * __pyx_v_dN)) + ((*((double *) ( /* dim=0 */ (__pyx_v_noise.data + __pyx_t_1 * __pyx_v_noise.strides[0]) ))) * (*((double *) ( /* dim=0 */ (__pyx_v_dW.data + __pyx_t_3 * __pyx_v_dW.strides[0]) ))))) + ((*((double *) ( /* dim=0 */ (__pyx_v_noise.data + __pyx_t_4 * __pyx_v_noise.strides[0]) ))) * (*((double *) ( /* dim=0 */ (__pyx_v_dW.data + __pyx_t_5 * __pyx_v_dW.strides[0]) )))));\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">050</span>: </pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">051</span>:     <span class=\"c\"># Update the velocity</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">052</span>:     <span class=\"n\">pi</span> <span class=\"o\">=</span>\\</pre>\n",
       "<pre class=\"cython line score-5\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">053</span>:         <span class=\"n\">pi</span> <span class=\"o\">-</span> <span class=\"p\">(</span><span class=\"mf\">3</span> <span class=\"o\">-</span> <span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"n\">pi</span><span class=\"o\">**</span><span class=\"mf\">2</span><span class=\"p\">)</span><span class=\"o\">*</span><span class=\"p\">(</span><span class=\"n\">pi</span> <span class=\"o\">+</span> <span class=\"n\">V_prime_by_V_cython</span><span class=\"p\">(</span><span class=\"n\">phi_old</span><span class=\"p\">))</span><span class=\"o\">*</span><span class=\"n\">dN</span> <span class=\"o\">+</span>\\</pre>\n",
       "<pre class='cython code score-5 '>  __pyx_t_6 = __pyx_f_54_cython_magic_a340241e5d4139803139c24d6920cbd683898caa_V_prime_by_V_cython(__pyx_v_phi_old); if (unlikely(__pyx_t_6 == ((double)-1) &amp;&amp; <span class='py_c_api'>PyErr_Occurred</span>())) <span class='error_goto'>__PYX_ERR(0, 53, __pyx_L1_error)</span>\n",
       "</pre><pre class=\"cython line score-8\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">054</span>:         <span class=\"n\">noise</span><span class=\"p\">[</span><span class=\"mf\">2</span><span class=\"p\">]</span><span class=\"o\">*</span><span class=\"n\">dW</span><span class=\"p\">[</span><span class=\"mf\">1</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"n\">noise</span><span class=\"p\">[</span><span class=\"mf\">1</span><span class=\"p\">]</span><span class=\"o\">*</span><span class=\"n\">dW</span><span class=\"p\">[</span><span class=\"mf\">0</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-8 '>  __pyx_t_5 = 2;\n",
       "  __pyx_t_2 = -1;\n",
       "  if (__pyx_t_5 &lt; 0) {\n",
       "    __pyx_t_5 += __pyx_v_noise.shape[0];\n",
       "    if (unlikely(__pyx_t_5 &lt; 0)) __pyx_t_2 = 0;\n",
       "  } else if (unlikely(__pyx_t_5 &gt;= __pyx_v_noise.shape[0])) __pyx_t_2 = 0;\n",
       "  if (unlikely(__pyx_t_2 != -1)) {\n",
       "    <span class='pyx_c_api'>__Pyx_RaiseBufferIndexError</span>(__pyx_t_2);\n",
       "    <span class='error_goto'>__PYX_ERR(0, 54, __pyx_L1_error)</span>\n",
       "  }\n",
       "  __pyx_t_4 = 1;\n",
       "  __pyx_t_2 = -1;\n",
       "  if (__pyx_t_4 &lt; 0) {\n",
       "    __pyx_t_4 += __pyx_v_dW.shape[0];\n",
       "    if (unlikely(__pyx_t_4 &lt; 0)) __pyx_t_2 = 0;\n",
       "  } else if (unlikely(__pyx_t_4 &gt;= __pyx_v_dW.shape[0])) __pyx_t_2 = 0;\n",
       "  if (unlikely(__pyx_t_2 != -1)) {\n",
       "    <span class='pyx_c_api'>__Pyx_RaiseBufferIndexError</span>(__pyx_t_2);\n",
       "    <span class='error_goto'>__PYX_ERR(0, 54, __pyx_L1_error)</span>\n",
       "  }\n",
       "/* … */\n",
       "  __pyx_t_3 = 1;\n",
       "  __pyx_t_2 = -1;\n",
       "  if (__pyx_t_3 &lt; 0) {\n",
       "    __pyx_t_3 += __pyx_v_noise.shape[0];\n",
       "    if (unlikely(__pyx_t_3 &lt; 0)) __pyx_t_2 = 0;\n",
       "  } else if (unlikely(__pyx_t_3 &gt;= __pyx_v_noise.shape[0])) __pyx_t_2 = 0;\n",
       "  if (unlikely(__pyx_t_2 != -1)) {\n",
       "    <span class='pyx_c_api'>__Pyx_RaiseBufferIndexError</span>(__pyx_t_2);\n",
       "    <span class='error_goto'>__PYX_ERR(0, 54, __pyx_L1_error)</span>\n",
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       "/* … */\n",
       "  __pyx_t_1 = 0;\n",
       "  __pyx_t_2 = -1;\n",
       "  if (__pyx_t_1 &lt; 0) {\n",
       "    __pyx_t_1 += __pyx_v_dW.shape[0];\n",
       "    if (unlikely(__pyx_t_1 &lt; 0)) __pyx_t_2 = 0;\n",
       "  } else if (unlikely(__pyx_t_1 &gt;= __pyx_v_dW.shape[0])) __pyx_t_2 = 0;\n",
       "  if (unlikely(__pyx_t_2 != -1)) {\n",
       "    <span class='pyx_c_api'>__Pyx_RaiseBufferIndexError</span>(__pyx_t_2);\n",
       "    <span class='error_goto'>__PYX_ERR(0, 54, __pyx_L1_error)</span>\n",
       "  }\n",
       "  __pyx_v_pi = (((__pyx_v_pi - (((3.0 - (0.5 * pow(__pyx_v_pi, 2.0))) * (__pyx_v_pi + __pyx_t_6)) * __pyx_v_dN)) + ((*((double *) ( /* dim=0 */ (__pyx_v_noise.data + __pyx_t_5 * __pyx_v_noise.strides[0]) ))) * (*((double *) ( /* dim=0 */ (__pyx_v_dW.data + __pyx_t_4 * __pyx_v_dW.strides[0]) ))))) + ((*((double *) ( /* dim=0 */ (__pyx_v_noise.data + __pyx_t_3 * __pyx_v_noise.strides[0]) ))) * (*((double *) ( /* dim=0 */ (__pyx_v_dW.data + __pyx_t_1 * __pyx_v_dW.strides[0]) )))));\n",
       "</pre><pre class=\"cython line score-27\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">055</span>:     <span class=\"k\">return</span> <span class=\"p\">[</span><span class=\"n\">phi</span><span class=\"p\">,</span> <span class=\"n\">pi</span><span class=\"p\">,</span> <span class=\"n\">A</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-27 '>  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_r);\n",
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       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_8);\n",
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       "  <span class='refnanny'>__Pyx_GIVEREF</span>(__pyx_t_9);\n",
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       "  __pyx_t_7 = 0;\n",
       "  __pyx_t_8 = 0;\n",
       "  __pyx_t_9 = 0;\n",
       "  __pyx_r = ((PyObject*)__pyx_t_10);\n",
       "  __pyx_t_10 = 0;\n",
       "  goto __pyx_L0;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">056</span>: </pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">057</span>: </pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">058</span>: <span class=\"c\">#A let&#39;s us calculate the bias w=e^-A is the bias, which propagated along with </span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">059</span>: <span class=\"c\">#the importance sample path.</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">060</span>: <span class=\"c\">#See Eq. (33) of arXiv:nucl-th/9809075v1 for more info</span></pre>\n",
       "<pre class=\"cython line score-6\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">061</span>: <span class=\"k\">cdef</span> <span class=\"kt\">list</span> <span class=\"nf\">simulation_diff_general_end</span><span class=\"p\">(</span><span class=\"n\">double</span> <span class=\"n\">x_in</span><span class=\"p\">,</span> <span class=\"n\">double</span> <span class=\"n\">y_in</span><span class=\"p\">,</span> <span class=\"n\">double</span> <span class=\"n\">t_in</span><span class=\"p\">,</span>\\</pre>\n",
       "<pre class='cython code score-6 '>static PyObject *__pyx_f_54_cython_magic_a340241e5d4139803139c24d6920cbd683898caa_simulation_diff_general_end(double __pyx_v_x_in, double __pyx_v_y_in, double __pyx_v_t_in, double __pyx_v_t_f, double __pyx_v_dt, double __pyx_v_bias_amp, double __pyx_v_phi_end_in, PyObject *__pyx_v_noise_list, PyObject *__pyx_v_rng) {\n",
       "  double __pyx_v_t;\n",
       "  double __pyx_v_sqrt_dt;\n",
       "  double __pyx_v_x;\n",
       "  double __pyx_v_y;\n",
       "  double __pyx_v_A;\n",
       "  int __pyx_v_i;\n",
       "  int __pyx_v_end_cond_value;\n",
       "  int __pyx_v_len_rand_nums;\n",
       "  int __pyx_v_reduced_step;\n",
       "  int __pyx_v_num_steps;\n",
       "  __Pyx_memviewslice __pyx_v_rand_nums = { 0, 0, { 0 }, { 0 }, { 0 } };\n",
       "  __Pyx_memviewslice __pyx_v_dW = { 0, 0, { 0 }, { 0 }, { 0 } };\n",
       "  __Pyx_memviewslice __pyx_v_noise = { 0, 0, { 0 }, { 0 }, { 0 } };\n",
       "  PyObject *__pyx_r = NULL;\n",
       "/* … */\n",
       "  /* function exit code */\n",
       "  __pyx_L1_error:;\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_1);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_2);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_3);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_4);\n",
       "  __PYX_XCLEAR_MEMVIEW(&amp;__pyx_t_5, 1);\n",
       "  __PYX_XCLEAR_MEMVIEW(&amp;__pyx_t_6, 1);\n",
       "  <span class='pyx_c_api'>__Pyx_AddTraceback</span>(\"_cython_magic_a340241e5d4139803139c24d6920cbd683898caa.simulation_diff_general_end\", __pyx_clineno, __pyx_lineno, __pyx_filename);\n",
       "  __pyx_r = 0;\n",
       "  __pyx_L0:;\n",
       "  __PYX_XCLEAR_MEMVIEW(&amp;__pyx_v_rand_nums, 1);\n",
       "  __PYX_XCLEAR_MEMVIEW(&amp;__pyx_v_dW, 1);\n",
       "  __PYX_XCLEAR_MEMVIEW(&amp;__pyx_v_noise, 1);\n",
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       "  <span class='refnanny'>__Pyx_RefNannyFinishContext</span>();\n",
       "  return __pyx_r;\n",
       "}\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">062</span>:                           <span class=\"n\">double</span> <span class=\"n\">t_f</span><span class=\"p\">,</span> <span class=\"n\">double</span> <span class=\"n\">dt</span><span class=\"p\">,</span> <span class=\"n\">double</span> <span class=\"n\">bias_amp</span><span class=\"p\">,</span> <span class=\"n\">double</span> <span class=\"n\">phi_end_in</span><span class=\"p\">,</span> <span class=\"n\">noise_list</span><span class=\"p\">,</span> <span class=\"n\">rng</span><span class=\"p\">):</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">063</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">t</span><span class=\"p\">,</span> <span class=\"nf\">sqrt_dt</span><span class=\"p\">,</span> <span class=\"nf\">x</span><span class=\"p\">,</span> <span class=\"nf\">y</span><span class=\"p\">,</span> <span class=\"nf\">z</span><span class=\"p\">,</span> <span class=\"nf\">A</span></pre>\n",
       "<pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">064</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">i</span> <span class=\"o\">=</span> <span class=\"mf\">0</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_i = 0;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">065</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">end_cond_value</span></pre>\n",
       "<pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">066</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">len_rand_nums</span> <span class=\"o\">=</span> <span class=\"mf\">1000</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_len_rand_nums = 0x3E8;\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">067</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">reduced_step</span> <span class=\"o\">=</span> <span class=\"mf\">0</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_reduced_step = 0;\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">068</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">num_steps</span> <span class=\"o\">=</span> <span class=\"mf\">0</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_num_steps = 0;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">069</span>: </pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">070</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">double</span> [<span class=\"p\">:,</span> <span class=\"p\">:]</span> <span class=\"n\">rand_nums</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">071</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">double</span> [<span class=\"p\">:]</span> <span class=\"n\">dW</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">072</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">double</span> [<span class=\"p\">:]</span> <span class=\"n\">noise</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">073</span>: </pre>\n",
       "<pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">074</span>:     <span class=\"n\">t</span> <span class=\"o\">=</span> <span class=\"n\">t_in</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_t = __pyx_v_t_in;\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">075</span>:     <span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">x_in</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_x = __pyx_v_x_in;\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">076</span>:     <span class=\"n\">y</span> <span class=\"o\">=</span> <span class=\"n\">y_in</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_y = __pyx_v_y_in;\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">077</span>:     <span class=\"n\">sqrt_dt</span> <span class=\"o\">=</span> <span class=\"n\">dt</span><span class=\"o\">**</span><span class=\"mf\">0.5</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_sqrt_dt = pow(__pyx_v_dt, 0.5);\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">078</span>:     <span class=\"n\">A</span> <span class=\"o\">=</span> <span class=\"mf\">0.0</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_A = 0.0;\n",
       "</pre><pre class=\"cython line score-34\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">079</span>:     <span class=\"n\">rand_nums</span> <span class=\"o\">=</span> <span class=\"n\">rng</span><span class=\"o\">.</span><span class=\"n\">normal</span><span class=\"p\">(</span><span class=\"mf\">0</span><span class=\"p\">,</span> <span class=\"mf\">1</span><span class=\"p\">,</span> <span class=\"n\">size</span><span class=\"o\">=</span><span class=\"p\">(</span><span class=\"mf\">2</span><span class=\"p\">,</span> <span class=\"n\">len_rand_nums</span><span class=\"p\">))</span></pre>\n",
       "<pre class='cython code score-34 '>  __pyx_t_1 = <span class='pyx_c_api'>__Pyx_PyObject_GetAttrStr</span>(__pyx_v_rng, __pyx_n_s_normal);<span class='error_goto'> if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 79, __pyx_L1_error)</span>\n",
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       "<pre class='cython code score-5 '>  __pyx_t_6.data = __pyx_v_rand_nums.data;\n",
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       "</pre><pre class=\"cython line score-10\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">081</span>:     <span class=\"n\">noise</span> <span class=\"o\">=</span> <span class=\"n\">noise_list</span><span class=\"p\">[:,</span> <span class=\"mf\">2</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-10 '>  __pyx_t_4 = <span class='pyx_c_api'>__Pyx_PyObject_GetItem</span>(__pyx_v_noise_list, __pyx_tuple__10);<span class='error_goto'> if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 81, __pyx_L1_error)</span>\n",
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       "<pre class='cython code score-4 '>    __pyx_t_8 = 0;\n",
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       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">091</span>:         <span class=\"c\"># Define the Wiener step, using the pre-drawn random numbers.</span></pre>\n",
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       "<pre class=\"cython line score-33\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">093</span>:         <span class=\"p\">[</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">y</span><span class=\"p\">,</span> <span class=\"n\">A</span><span class=\"p\">]</span> <span class=\"o\">=</span>\\</pre>\n",
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       "<pre class='cython code score-18 '>    __pyx_t_4 = __pyx_f_54_cython_magic_a340241e5d4139803139c24d6920cbd683898caa_update(__pyx_v_x, __pyx_v_y, __pyx_v_A, __pyx_v_t, __pyx_v_dt, __pyx_v_dW, __pyx_v_noise, __pyx_v_bias_amp);<span class='error_goto'> if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 94, __pyx_L1_error)</span>\n",
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       "<pre class='cython code score-0 '>    __pyx_v_t = (__pyx_v_t + __pyx_v_dt);\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">096</span>:         <span class=\"n\">i</span> <span class=\"o\">+=</span> <span class=\"mf\">1</span></pre>\n",
       "<pre class='cython code score-0 '>    __pyx_v_i = (__pyx_v_i + 1);\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">097</span>:         <span class=\"n\">num_steps</span> <span class=\"o\">+=</span> <span class=\"mf\">1</span></pre>\n",
       "<pre class='cython code score-0 '>    __pyx_v_num_steps = (__pyx_v_num_steps + 1);\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">098</span>:         <span class=\"c\"># Using 1/0 for True/False</span></pre>\n",
       "<pre class=\"cython line score-5\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">099</span>:         <span class=\"n\">end_cond_value</span> <span class=\"o\">=</span> <span class=\"n\">end_cond</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">y</span><span class=\"p\">,</span> <span class=\"n\">t</span><span class=\"p\">,</span> <span class=\"n\">phi_end_in</span><span class=\"p\">)</span></pre>\n",
       "<pre class='cython code score-5 '>    __pyx_t_10 = __pyx_f_54_cython_magic_a340241e5d4139803139c24d6920cbd683898caa_end_cond(__pyx_v_x, __pyx_v_y, __pyx_v_t, __pyx_v_phi_end_in); if (unlikely(__pyx_t_10 == ((int)-1) &amp;&amp; <span class='py_c_api'>PyErr_Occurred</span>())) <span class='error_goto'>__PYX_ERR(0, 99, __pyx_L1_error)</span>\n",
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       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">100</span>:         <span class=\"k\">if</span> <span class=\"n\">end_cond_value</span> <span class=\"o\">==</span> <span class=\"mf\">1</span><span class=\"p\">:</span></pre>\n",
       "<pre class='cython code score-0 '>    __pyx_t_7 = (__pyx_v_end_cond_value == 1);\n",
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       "<pre class='cython code score-0 '>      goto __pyx_L4_break;\n",
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       "<pre class='cython code score-0 '>    __pyx_t_15 = (__pyx_v_end_cond_value == -1L);\n",
       "    if (__pyx_t_15) {\n",
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       "      goto __pyx_L6_bool_binop_done;\n",
       "    }\n",
       "    __pyx_t_15 = (__pyx_v_reduced_step == 0);\n",
       "    __pyx_t_7 = __pyx_t_15;\n",
       "    __pyx_L6_bool_binop_done:;\n",
       "    if (__pyx_t_7) {\n",
       "/* … */\n",
       "      goto __pyx_L5;\n",
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       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">103</span>:             <span class=\"n\">dt</span> <span class=\"o\">=</span> <span class=\"n\">dt</span><span class=\"o\">/</span><span class=\"mf\">100</span></pre>\n",
       "<pre class='cython code score-0 '>      __pyx_v_dt = (__pyx_v_dt / 100.0);\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">104</span>:             <span class=\"n\">sqrt_dt</span> <span class=\"o\">=</span> <span class=\"n\">dt</span><span class=\"o\">**</span><span class=\"mf\">0.5</span></pre>\n",
       "<pre class='cython code score-0 '>      __pyx_v_sqrt_dt = pow(__pyx_v_dt, 0.5);\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">105</span>:             <span class=\"n\">reduced_step</span> <span class=\"o\">=</span> <span class=\"mf\">1</span></pre>\n",
       "<pre class='cython code score-0 '>      __pyx_v_reduced_step = 1;\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">106</span>:         <span class=\"k\">elif</span> <span class=\"n\">end_cond_value</span> <span class=\"o\">==</span> <span class=\"mf\">0</span> <span class=\"ow\">and</span> <span class=\"n\">reduced_step</span> <span class=\"o\">==</span> <span class=\"mf\">1</span><span class=\"p\">:</span></pre>\n",
       "<pre class='cython code score-0 '>    __pyx_t_15 = (__pyx_v_end_cond_value == 0);\n",
       "    if (__pyx_t_15) {\n",
       "    } else {\n",
       "      __pyx_t_7 = __pyx_t_15;\n",
       "      goto __pyx_L8_bool_binop_done;\n",
       "    }\n",
       "    __pyx_t_15 = (__pyx_v_reduced_step == 1);\n",
       "    __pyx_t_7 = __pyx_t_15;\n",
       "    __pyx_L8_bool_binop_done:;\n",
       "    if (__pyx_t_7) {\n",
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       "    __pyx_L5:;\n",
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       "<pre class='cython code score-0 '>      __pyx_v_dt = (100.0 * __pyx_v_dt);\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">108</span>:             <span class=\"n\">sqrt_dt</span> <span class=\"o\">=</span> <span class=\"n\">dt</span><span class=\"o\">**</span><span class=\"mf\">0.5</span></pre>\n",
       "<pre class='cython code score-0 '>      __pyx_v_sqrt_dt = pow(__pyx_v_dt, 0.5);\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">109</span>:             <span class=\"n\">reduced_step</span> <span class=\"o\">=</span> <span class=\"mf\">0</span></pre>\n",
       "<pre class='cython code score-0 '>      __pyx_v_reduced_step = 0;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">110</span>:         <span class=\"c\"># If all of the random numbers have been used up, need to update them.</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">111</span>:         <span class=\"c\"># This should still be more efficient than drawing a new random number</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">112</span>:         <span class=\"c\"># each time.</span></pre>\n",
       "<pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">113</span>:         <span class=\"k\">if</span> <span class=\"n\">i</span> <span class=\"o\">==</span> <span class=\"n\">len_rand_nums</span><span class=\"p\">:</span></pre>\n",
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       "<pre class='cython code score-257 '>static PyObject *__pyx_pw_54_cython_magic_a340241e5d4139803139c24d6920cbd683898caa_1importance_sampling_simulations_2dim_full(PyObject *__pyx_self, \n",
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       "static PyObject *__pyx_pw_54_cython_magic_a340241e5d4139803139c24d6920cbd683898caa_1importance_sampling_simulations_2dim_full(PyObject *__pyx_self, \n",
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       "          (void)<span class='pyx_c_api'>__Pyx_Arg_NewRef_FASTCALL</span>(values[1]);\n",
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       "          (void)<span class='pyx_c_api'>__Pyx_Arg_NewRef_FASTCALL</span>(values[2]);\n",
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       "        case  3:\n",
       "        if (likely((values[3] = <span class='pyx_c_api'>__Pyx_GetKwValue_FASTCALL</span>(__pyx_kwds, __pyx_kwvalues, __pyx_n_s_t_f)) != 0)) {\n",
       "          (void)<span class='pyx_c_api'>__Pyx_Arg_NewRef_FASTCALL</span>(values[3]);\n",
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       "        CYTHON_FALLTHROUGH;\n",
       "        case  4:\n",
       "        if (likely((values[4] = <span class='pyx_c_api'>__Pyx_GetKwValue_FASTCALL</span>(__pyx_kwds, __pyx_kwvalues, __pyx_n_s_dt)) != 0)) {\n",
       "          (void)<span class='pyx_c_api'>__Pyx_Arg_NewRef_FASTCALL</span>(values[4]);\n",
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       "        if (likely((values[5] = <span class='pyx_c_api'>__Pyx_GetKwValue_FASTCALL</span>(__pyx_kwds, __pyx_kwvalues, __pyx_n_s_num_runs)) != 0)) {\n",
       "          (void)<span class='pyx_c_api'>__Pyx_Arg_NewRef_FASTCALL</span>(values[5]);\n",
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       "          (void)<span class='pyx_c_api'>__Pyx_Arg_NewRef_FASTCALL</span>(values[6]);\n",
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       "        if (likely((values[7] = <span class='pyx_c_api'>__Pyx_GetKwValue_FASTCALL</span>(__pyx_kwds, __pyx_kwvalues, __pyx_n_s_phi_end_in)) != 0)) {\n",
       "          (void)<span class='pyx_c_api'>__Pyx_Arg_NewRef_FASTCALL</span>(values[7]);\n",
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       "        CYTHON_FALLTHROUGH;\n",
       "        case  8:\n",
       "        if (likely((values[8] = <span class='pyx_c_api'>__Pyx_GetKwValue_FASTCALL</span>(__pyx_kwds, __pyx_kwvalues, __pyx_n_s_noise_list)) != 0)) {\n",
       "          (void)<span class='pyx_c_api'>__Pyx_Arg_NewRef_FASTCALL</span>(values[8]);\n",
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       "      values[2] = <span class='pyx_c_api'>__Pyx_Arg_FASTCALL</span>(__pyx_args, 2);\n",
       "      values[3] = <span class='pyx_c_api'>__Pyx_Arg_FASTCALL</span>(__pyx_args, 3);\n",
       "      values[4] = <span class='pyx_c_api'>__Pyx_Arg_FASTCALL</span>(__pyx_args, 4);\n",
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       "      values[6] = <span class='pyx_c_api'>__Pyx_Arg_FASTCALL</span>(__pyx_args, 6);\n",
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       "      values[8] = <span class='pyx_c_api'>__Pyx_Arg_FASTCALL</span>(__pyx_args, 8);\n",
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     "execution_count": 9,
     "metadata": {},
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   "source": [
    "%%cython -a\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "cdef double V_0 = 7.903587107979402e-11\n",
    "cdef double e = 2.718281828459045\n",
    "cdef double pi_num = 3.141592653589793\n",
    "cdef double sigma_tilde = 1.59*(10**-2)\n",
    "cdef double phi_0 = 2.18812\n",
    "cdef double m_squared = 0.25\n",
    "cdef double K = 1.17*(10**-3)\n",
    "cdef double diff_const_squared = 6.351213422073874e-13\n",
    "cdef double phi_end\n",
    "cdef double expo\n",
    "cdef double fraction\n",
    "cdef double fraction3\n",
    "cdef double fraction4\n",
    "cdef double noise_value\n",
    "cdef double term1\n",
    "cdef double term2\n",
    "cdef double phi_old\n",
    "\n",
    "\n",
    "cdef double V(double phi):\n",
    "    expo = e**(-0.5*((phi-phi_0)/sigma_tilde)**2)\n",
    "    fraction = (phi**2)/(m_squared + phi**2)\n",
    "    return V_0*fraction*(1 + K*expo)\n",
    "\n",
    "cdef double V_prime_by_V_cython(double phi):\n",
    "    expo = e**(-0.5*((phi-phi_0)/sigma_tilde)**2)\n",
    "    fraction3 = 1/phi - (phi)/(m_squared + phi**2)\n",
    "    fraction4 = -(phi-phi_0)/(sigma_tilde**2)\n",
    "    \n",
    "    term1 = 2*fraction3\n",
    "    term2 = fraction4*K*expo/(1 + K*expo)\n",
    "    return term1 + term2\n",
    "    \n",
    "cdef int end_cond(double phi, double pi, double N, double phi_end):\n",
    "    if phi<phi_end:\n",
    "        return 1\n",
    "    else:\n",
    "        return 0\n",
    "\n",
    "\n",
    "cdef list update(double phi, double pi, double A, double N, double dN, double [:] dW, double [:] noise,\n",
    "                 double bias_amp):\n",
    "    # Store old phi value to be used in calculating velocity\n",
    "    phi_old = phi\n",
    "    # Update field position\n",
    "    phi = phi + pi*dN + noise[0]*dW[0] + noise[1]*dW[1]\n",
    "\n",
    "    # Update the velocity\n",
    "    pi =\\\n",
    "        pi - (3 - 0.5*pi**2)*(pi + V_prime_by_V_cython(phi_old))*dN +\\\n",
    "        noise[2]*dW[1] + noise[1]*dW[0]\n",
    "    return [phi, pi, A]\n",
    "\n",
    "\n",
    "#A let's us calculate the bias w=e^-A is the bias, which propagated along with \n",
    "#the importance sample path.\n",
    "#See Eq. (33) of arXiv:nucl-th/9809075v1 for more info\n",
    "cdef list simulation_diff_general_end(double x_in, double y_in, double t_in,\\\n",
    "                          double t_f, double dt, double bias_amp, double phi_end_in, noise_list, rng):\n",
    "    cdef double t, sqrt_dt, x, y, z, A\n",
    "    cdef int i = 0\n",
    "    cdef int end_cond_value\n",
    "    cdef int len_rand_nums = 1000\n",
    "    cdef int reduced_step = 0\n",
    "    cdef int num_steps = 0\n",
    "    \n",
    "    cdef double [:, :] rand_nums\n",
    "    cdef double [:] dW\n",
    "    cdef double [:] noise\n",
    "\n",
    "    t = t_in\n",
    "    x = x_in\n",
    "    y = y_in\n",
    "    sqrt_dt = dt**0.5\n",
    "    A = 0.0\n",
    "    rand_nums = rng.normal(0, 1, size=(2, len_rand_nums))\n",
    "    dW = rand_nums[:, 0]\n",
    "    noise = noise_list[:, 2]\n",
    "\n",
    "    while t<t_f:\n",
    "        # Scale the step varaince to the dt used\n",
    "        dW[0] = sqrt_dt*rand_nums[0, i]\n",
    "        dW[1] = sqrt_dt*rand_nums[1, i]\n",
    "        # Find the noise from the list provided\n",
    "        noise[0] = noise_list[0, num_steps]\n",
    "        noise[1] = noise_list[1, num_steps]\n",
    "        noise[2] = noise_list[2, num_steps]\n",
    "        # Define the Wiener step, using the pre-drawn random numbers.\n",
    "        # Step in x and A simultanioues\n",
    "        [x, y, A] =\\\n",
    "            update(x, y, A, t, dt, dW, noise, bias_amp)\n",
    "        t += dt\n",
    "        i += 1\n",
    "        num_steps += 1\n",
    "        # Using 1/0 for True/False\n",
    "        end_cond_value = end_cond(x, y, t, phi_end_in)\n",
    "        if end_cond_value == 1:\n",
    "            break\n",
    "        elif end_cond_value == -1 and reduced_step == 0:\n",
    "            dt = dt/100\n",
    "            sqrt_dt = dt**0.5\n",
    "            reduced_step = 1\n",
    "        elif end_cond_value == 0 and reduced_step == 1:\n",
    "            dt = 100*dt\n",
    "            sqrt_dt = dt**0.5\n",
    "            reduced_step = 0\n",
    "        # If all of the random numbers have been used up, need to update them.\n",
    "        # This should still be more efficient than drawing a new random number\n",
    "        # each time.\n",
    "        if i == len_rand_nums:\n",
    "            rand_nums = rng.normal(0, 1, size=(2, len_rand_nums))\n",
    "            i = 0\n",
    "    return [t, e**(-A)]\n",
    "\n",
    "\n",
    "cpdef importance_sampling_simulations_2dim_full(double x_in, double y_in, double t_in, double t_f,\n",
    "                                           double dt, int num_runs, double bias_amp, double phi_end_in,\n",
    "                                                noise_list):\n",
    "    # As this variable is global, I can just redfine it hear\n",
    "    rng = np.random.default_rng()\n",
    "    results =\\\n",
    "        [simulation_diff_general_end(x_in, y_in, t_in, t_f, dt, bias_amp, phi_end_in, noise_list, rng)\\\n",
    "         for i in range(num_runs)]\n",
    "                \n",
    "    \n",
    "    ts, ws = [[results[i][j] for i in range(num_runs)] for j in range(2)]\n",
    "    return ts, ws"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Multiprocessing is also used. Below is a simple implementation of this. It also saves the data using the pyfpt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_func_full_2d(N_exit, N_start, bias_amp, num_runs, noise_matrix, sigma, phi_in_post,\n",
    "                                phi_deriv_in_post, phi_end, extra_label=None):\n",
    "\n",
    "    start = timer()\n",
    "    num_runs_per_core = int(num_runs/mp.cpu_count())\n",
    "\n",
    "    # Using multiprocessing\n",
    "    def multi_processing_func(x_in, y_in, t_i, t_f, dt, num_runs, bias_amp, phi_end, noise_matrix, queue_efolds,\n",
    "                              queue_ws, ):\n",
    "        results =\\\n",
    "            importance_sampling_simulations_2dim_full(x_in, y_in, t_i, t_f, dt, num_runs, bias_amp, phi_end,\n",
    "                                                      noise_matrix)\n",
    "        fpt_values = np.array(results[0][:])\n",
    "        ws = np.array(results[1][:])\n",
    "        queue_efolds.put(fpt_values)\n",
    "        queue_ws.put(ws)\n",
    "    queue_efolds = Queue()\n",
    "    queue_ws = Queue()\n",
    "    cores = int(mp.cpu_count()/1)\n",
    "\n",
    "    print('Number of cores used: '+str(cores))\n",
    "    processes = [Process(target=multi_processing_func,\n",
    "                         args=(phi_in_post, phi_deriv_in_post, N_start, 80., dN, num_runs_per_core, bias_amp,\n",
    "                               phi_end, noise_matrix, queue_efolds, queue_ws))\n",
    "                 for k in range(cores)]\n",
    "\n",
    "    for p in processes:\n",
    "        p.start()\n",
    "\n",
    "    # More efficient to work with numpy arrays\n",
    "    fpt_array = np.array([queue_efolds.get() for p in processes])\n",
    "    ws_array = np.array([queue_ws.get() for p in processes])\n",
    "\n",
    "    end = timer()\n",
    "    print(f'The simulations took: {end - start} seconds')\n",
    "\n",
    "    # Combine into columns into 1\n",
    "    fpt_values = fpt_array.flatten()\n",
    "    w_values = ws_array.flatten()\n",
    "\n",
    "    # Sort in order of increasing Ns\n",
    "    sort_idx = np.argsort(fpt_values)\n",
    "    Ns = fpt_values[sort_idx]\n",
    "    ws = w_values[sort_idx]\n",
    "    if extra_label != None:\n",
    "        extra_label = \"_Gaussian_bump_sigma_\"+str(sigma)+\"_scale_exited\"+str(round(N_exit, 5))\\\n",
    "            + \"_2D_noise_\" + extra_label\n",
    "    else:\n",
    "        extra_label = \"_Gaussian_bump_sigma_\"+str(sigma)+\"_scale_exited\"+str(round(N_exit, 5))\\\n",
    "        +\"_2D_noise\"\n",
    "\n",
    "    fpt.numerics.save_data_to_file(Ns, ws, round(phi_in_post, 5), num_runs, bias_amp,\n",
    "                      extra_label=extra_label)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Loading in the 2D noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "sigma = 0.01\n",
    "noise_data = pd.read_csv(\"gaussian_bump_noise_curves_Bessel_matched_sigma_\"+str(sigma)+\"_2D.csv\",\n",
    "                             index_col=0)\n",
    "\n",
    "N_cg_values = np.array(noise_data[\"N\"])\n",
    "\n",
    "noise_matrix_array = np.zeros((3, len(N_cg_values)))\n",
    "\n",
    "noise_matrix_array[0, :] = np.array(noise_data[\"phi-phi noise\"])\n",
    "noise_matrix_array[1, :] = np.array(noise_data[\"phi-pi noise\"])\n",
    "noise_matrix_array[2, :] = np.array(noise_data[\"pi-pi noise\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We also need to make sure the simulation is initiated with the correct position and velocity. This is the position and velocity when the starting scale left the **coarse-graining scale**, not Hubble exit\n",
    "\n",
    "Also need to find phi_end. In principle this should be the end of inflation value, but in practise it can just be sufficently long after the classical end field value to allow the for large fluctutations and the attractor solution to still be found (this has been tested to be correct)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "sigma = 0.01\n",
    "\n",
    "aH_interpolation = CubicSpline(N_values, hubble_param_values*a_in*np.exp(N_values-N_sim_start))\n",
    "# Interpolation over the phase spcae such that the position/velocity at any scale can be found\n",
    "phi_with_scale_interpolation = CubicSpline(aH_interpolation(N_values), phi_values)\n",
    "phi_diff_with_scale_interpolation = CubicSpline(aH_interpolation(N_values), phi_diff_values)\n",
    "\n",
    "N_start_sigma_exit = find_cg_time(aH_interpolation(N_sim_start), sigma, N_sim_start)\n",
    "N_end_sigma_exit = find_cg_time(aH_interpolation(N_sim_end), sigma, N_sim_end)\n",
    "\n",
    "# Scales at the start and end\n",
    "k_in_scale = aH_interpolation(N_sim_start)\n",
    "k_end_scale = aH_interpolation(N_sim_end)\n",
    "\n",
    "# This returns an array, so need to convert to a float\n",
    "phi_in = float(phi_with_scale_interpolation(k_in_scale/sigma))\n",
    "phi_deriv_in = float(phi_diff_with_scale_interpolation(k_in_scale/sigma))\n",
    "\n",
    "# end value\n",
    "N_sim_end_later = N_sim_end+2\n",
    "k_end_scale_later = aH_interpolation(N_sim_end_later)\n",
    "N_sim_end_later_sigma_exit = find_cg_time(aH_interpolation(N_sim_end_later), sigma, N_sim_end_later)\n",
    "phi_end = float(phi_with_scale_interpolation(k_end_scale_later/sigma))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We start by running a test to see if the noise-less simulation recovers the classical background, to check we have the correct initial and end field values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_runs = 1\n",
    "\n",
    "# Need enough zero noise for the whole simulation, as it ends at N_sim_end_later\n",
    "noise_matrix_array_test = np.zeros((3, len(noise_matrix_array[0,:])+int(2.2/dN)))\n",
    "\n",
    "bias_amp = 0.0\n",
    "\n",
    "N, w =\\\n",
    "    importance_sampling_simulations_2dim_full(phi_in, phi_deriv_in, N_start_sigma_exit, 100, dN,\n",
    "                                              num_runs, bias_amp, phi_end, noise_matrix_array_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "error in simulation time\n",
      "0.000958195723484323\n",
      "Step size\n",
      "0.00023659513392999544\n"
     ]
    }
   ],
   "source": [
    "print(\"error in simulation time\")\n",
    "print(np.abs(N_sim_end_later_sigma_exit - N[0]))\n",
    "\n",
    "print(\"Step size\")\n",
    "print(dN)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The final error is approximately the order of the step size, which for Euler steps is expected."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To run the simulations, we need enough noise, even if it is zero, until the end surface is crossed. Therefore we need to add a few e-folds woth of zero values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "noise_matrix_array_with_zeros = np.zeros((3, len(noise_matrix_array[0,:])+int(4/dN)))\n",
    "\n",
    "noise_matrix_array_with_zeros[:, :len(noise_matrix_array[0,:])] = noise_matrix_array"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can run many simulations, using multiprocessing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of cores used: 8\n",
      "The simulations took: 638.7569171520881 seconds\n",
      "Saved data to file IS_data_x_in_2.2_iterations_100000_bias_0.0_Gaussian_bump_sigma_0.01_scale_exited31.13832_2D_noise_bessel.csv\n"
     ]
    }
   ],
   "source": [
    "num_runs = 10**5\n",
    "\n",
    "run_func_full_2d(N_sim_start, N_start_sigma_exit, bias_amp, num_runs, noise_matrix_array_with_zeros, sigma,\n",
    "                              phi_in, phi_deriv_in, phi_end, extra_label=\"bessel\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's load this data in and plot it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "raw_data = pd.read_csv(\"IS_data_x_in_2.2_iterations_100000_bias_0.0_Gaussian_bump_sigma_0.01_scale_exited\"+\n",
    "                       \"31.13832_2D_noise_bessel.csv\", index_col=0)\n",
    "\n",
    "# Easier to work with NumPy arrays\n",
    "Ns = np.array(raw_data['FPTs'])\n",
    "ws = np.array(raw_data['ws'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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o7n8grPij56/8/Ri63xjpSSv+5s2bVVZW5np94oknVpmfnZ3tukoo1R5sN9Qy7t6Npbb1AV8hGAcCmPtNY6Zp+vQmyZdeesnVBzksLEyffPKJXnnlFU2dOlX9+vVTfHx8jRbWyv6dvlA5KEpjdO3aVQ8++KCys7P1ww8/6Pnnn9e0adNqBNSbNm3SyJEj6x2G25tlNcTfjrmveVJ3925Zjb15uTE8eV/5I384hvX56aefXM8bc29KJfch7ENDQ2u0fO/atavK6x49elR5nZWVJZvN5npdPRj/7rvvlJub63rti0GtgLoQjAMBrPoP0htvvOGzbX300Ueu55deeqlGjRrV4Drul5XrEx4e7nru3vpVn6ZeBejdu7dmz56txYsXKzs7W19//bUmTJjgmm+z2XTvvfe2eFm18eUx90e7d+9u9LLuwVddNyy25PvKX3j7GHqbe8Drfn4a8tJLL7meDx8+vEYaSfdWcUmKjIys8tq9VTwxMVFJSUlV5r/yyiuu5126dKmR/aY60zT1wgsvaNiwYWrbtq3i4uJ06qmnavHixY3bIcANwTgQwIYMGVIlN+6SJUtq/Ch5y88//+x6Xl8O40qmaeq///1vo8p2T/F2+PDhBpcvLS2t0sLWHMOGDdOKFSuqXGVoak50b5Yl+faY+6P169e7+hPXp7y8vMH+v5K17yurePsYeltY2K95I/bv39+odZYsWaIff/zR9fr666+vsUz1wL76zcv17esvv/yiBQsWuF5fddVV9f5RcDgcSk9P15VXXqmNGzfKMAwVFBRo7dq1mj59uv761782ar+ASgTjQIC77bbbXM+Li4v1hz/8wSfbaWzLYqWPPvpIOTk5jVrW/XL1li1bGlz+vffeqzX1WFOFhIToggsucL1ubJDg67J8ecz90f79+7Vq1aoGl/vggw+qtGCPHDmy1uWsfl9ZwdvH0NvcW+AbM3DU/v37q6QoHDBgQJXPVyX3NJBSxZ8Sd+79wat3UbnjjjtcXVg6duxYZUCk2jz99NNavXq1Fi1apKNHj+qXX35Rdna266rY3//+d8sz/CCwEIwDAW7y5MkaP3686/W7776r66+/vlGtY55wv6zb0I9oUVGRbrrppkaX7d5StXTp0nrrXlJS0uibFD3J+OHe19Y9S40vymosXx5zf3XHHXfU22+7rKysSstjz549NXr06FqX9dX7yt958xhKFfm1DcNwPZrDfeCon376Sf/617/qXPbgwYOaMGGCK3d4WFiYXnrppVrTGp5yyilVuqY8++yzVY5BXTdvLly4UE8//bTr9SOPPFIly0xt8vPzlZGRoenTp7sGA+vevbuWLFmijh07yul06s0336y3DMAdwTgQ4AzD0GuvvabU1FTXtCeffFJjx45t9A2dmzdvrvJjVRv3/ulLly7Ve++9V+tyhw8f1oQJE6pcVm7I5MmTXc+3b9+u++67r9blCgoKdNFFF7lyIzdkwIABWrRokQoLC+tdbseOHVV+kGsLTLxZVmP58pj7q8rBZ2proS4pKdG0adO0detW17Q77rijzgDRV+8rf+fNY+hts2fPrrKtK6+8Uq+++mqVwLmsrExvvPGGBg8e7GrRNgxDCxcurDULilSRRcY9PeumTZt09dVXq6SkRPv3769yheqUU07RL7/8optvvrnKQEfXXXedLr/88gb3Yfjw4bV+rmNiYnT22WdLUpXjCzSEQX+AIBAfH69Vq1YpPT3d9eO1atUqDRs2TIMHD9Zvf/tbDRw4UAkJCYqNjVVRUZEOHDig77//Xp988okyMzOrtPzWllnhyiuv1IMPPqiCggI5nU6df/75mjZtmiZOnKjExETl5+fryy+/1IsvvqhDhw6pbdu2+t3vfldvy1elsWPHVvnhvfPOO7Vu3Tpdeuml6t69u44ePaqvv/5aCxYs0P79+9W/f3+1adOmyqXn2mzbtk1XXHGFrrnmGp111lkaNmyY+vbt62qtzs3N1RdffKHFixe7BlVp06ZNla4/viirsXx5zP1Renq6PvzwQ7300kv6+uuvNXv2bPXv31+maWrLli167rnnqvTpHjdunGbNmlVneb56X/kzbx9Dbxs0aJCuvfZaPfnkk5Iq/ghNmzZNf/rTn9S7d2+VlZXp+++/1y+//OJaJyoqSs8++2yDgfJdd92lFStWuALvF154QUuXLlVKSkqV5S6++GJ98803VQb5ufbaa/X44483ah+GDRtW57zKgYYac48C4GICCBrFxcXmtddea7Zp08aU5PEjKirKvOOOO0y73V5r+cuWLTPDwsIaLCcmJsb84IMPzLvuuss1beTIkfXWfdu2bWZCQkKDZffs2dPcvXu3OXLkSNe0u+66q9YyPd3/yMhIc9myZT4vyzRNc/r06a5lp0+fXudyvjrmjTl+1XlyPhurej0WL17cqP097bTTzKNHjzZYvi/eV7XVuzHct7dq1aoGl1+1alWVdRpbF28fwz59+rjWGThwYKP2tT4Oh8O87rrrzJCQkAbrOHLkSHPbtm2NLnvjxo1mcnJyoz+nXbp0MV977bVGlV15nOs735WfEW99PtA60E0FCCKRkZF68skntXPnTt10003q1atXo9YZNWqUnn/+eeXm5uree++tMsqkuwsvvFCfffaZ+vXrV+v8kJAQjRs3Ths3bqzSj70xTjrpJH311Vd15veNiIjQFVdcoU2bNtXIIVyXp59+Wueee67i4uLqXS4yMlIXX3yxtm7dqgsvvNDnZXnCl8fcH02bNk2rVq3SySefXOv82NhYzZ07V6tWrWrwXEi+eV/5O28ewwMHDuiHH35wvb7zzjubXb+QkBA98cQTWr9+va677jpXzvzw8HB17txZaWlpuvnmm7VmzRqtXr1aJ510UqPLHjRokLZt26b77rtPgwcPVvv27avMDwsLU1JSks4++2w9/fTT2rlzpy699NJm7xPQHIZp+mBMYwB+Y+/evdq0aZMOHjyoQ4cOqby8XO3bt1d8fLz69Omjfv36VUk31himaWrjxo3KzMzUoUOHFBcXp65du+qMM85Qly5dml3nnTt36j//+Y/279+viIgIpaSkaPTo0TVyCzeWw+HQd999p+3bt2vv3r0qKChQaGio4uPj1bt3b6WlpdX5B8SXZXnC18fcH23dulXffPONcnNzFRUVpdTUVP32t7913TTnKW+/r/zFqFGj9MUXX0iq6Koxb94817zmHsOlS5dqypQpkipGzNy8eXOL9S/3lsTERFfK1xUrVui8885rUjmVx7n6MXY3b9483X333Ro5cqRWr17dxBqjtaHPOBDkunfvXuvQ7c1hGIYGDx7ss9zEqampVW5Iba7Q0FD179/fo+G3W6IsT/j6mPsjbx9nb7+vAkFzj2FlkC9VtIoHWiC+d+/eKmMv1HUDKGAluqkAAIBaVQbjJ510kiZNmmRxbTznniWqU6dOXm+YALyBYBwAANRw+PBhbdu2TZI0d+7cgGsVl+ofeRPwF3RTAQAANXTo0MHrg4e1tPpG3gT8BS3jAAAgKNU18ibgT2gZBwAAQefAgQPKzc11vW5uMN6Y7Cjz5s2rM9MKUBdSGwYQp9Mpm80mSYqOjg7I/nsAAADBzDRN10jMCQkJCgmpvyMKLeMBxGazKTEx0epqAAAAoBHy8vLUuXPnepehzzgAAABgEVrGA0h0dLTreV5enmJiYiysDQAAAKorLCx09WRwj93qQjAeQNz7iMfExBCMAwAA+LHG3N9HNxUAAADAIgTjAAAAgEUIxgEAAACLEIwDAAAAFiEYBwAAACxCMA4AAABYhGAcAAAAsAjBOAAAAGARgnEAAADAIgTjAAAAgEUIxgEAAACLEIwDAAAAFgmzugJomsLCwhrTYmJiLKgJAAAAmopgPEAlJibWmGaapgU1ARDsikrLtXRdlnLzi5UUH6XJQ1MUHdG4n4/mrAsArYFhEsEFjMLCQsXGxtY5n1MJoDqbvVQ2e6lKyhz6bNt+2ewlSoiL1Nh+XRQZHqqEuAglxEXUue7ew0X6W8ZW5R4pVogkp6Sk9lGam95f3TtE+2RdAAhk7vFaQUFBgz0XCMYDiPvJzcvLq3Fy6aYCBLemtDK/sGqHFq7eWef8WaNSNXt0L79aV2renwgAsJKnwTjXCgNUTEwMwTfQStTVyrxiw94GW5nT05L1S1GZlq3PknvTi2FIk4akKD0tuc7tjuzTWd/sydemnw/L6bZuiCENOq6DRvbp7JN1JSkjM7vWYH7puixJDQfzABAoyKYCAH4uIzNbc15cp5z8Ypmm5DAl05Ry8os158V1ysjMrnd9m72kxpd9yP+m1+eLHw5ow56qwbQkOU1pw57D+uKHAz5ZV6r4EzF5aIoMo+p0w5AmD63/TwQABBKCcQDwcyP7dNbgHh0UUi0wDTGkwT3qb2XOyMzW6u8PyFEtKHaY0urvD9QbyKenJevZmUPVLT5KhiGFGhXBcLf4KD07c2i9AXFz1q3U1D8RABBI6DMeQDztgwQgODSn/7U3bqS0IptKc/ucA4BVuIEziBGMA62T1QG1FZqbyYWbPwFYhWA8iBGMA61boAXU3tDSGWQAoLkIxoMYwTgANMxmL9Wif++qM4PMjDOPp2UcgM94Gq9xAycAIOhw8yeAQBHc1zcBwM+0xq4mLa0yg0x1lRlkUhPj6KYCwG/wCwAALaA5A/fAM+lpyRpyfMd6b/4EAH9Bn/EAQp9xIHBxU2HL4yoEACt4Gq/xrQQALaC5w8PDc9ERYbp8xPFWVwMA6kUwDgAtoHJ4+Orch4f/Tde2FtQMtaFVHUBL4ZsFADzQ1CCNfsyBo6i0XH9YsFZ7DhYoxDDkNE19tGWfFvxhGAE5AK+jz3gAoc84YB1vjIIp0eLq78hRDqC5GPQniBGMA9bhBszW4fGPftC/1vxc5/xLTjtON5zTpwVrBCDQMOgPAPjAyD6dNbhHB4UYVaeHGNLgHtyACQBoGoJxAGiEyhswndWuJbrfgInAd9nwnnp25lB1i4+SYUihRkUXlW7xUXp25lBdNryn1VUEEGTophJA6KYCWMdbfcYRGOjbD6Cp6DMexAjGAesRpKEhvEeA1o1gPIgRjAOA/+LqCQCJGzgBALBERma25ry4Tjn5xTJNyWFKpinl5BdrzovrlJGZbXUVAfghrpsFqMLCwhrTaCkHAOuM7NNZ3+zJ16afq97oG2JIg44j4w6A2hGMB6jExMQa0+hxBADWqcy4U517xp3fdG1rQc0A+DOCcQCtDjfYwRfS05I15PiO9fYZB4DquIEzgLjfEJCXl1ejWwrdVID6cYMdWgJ/9oDWjWwqQYxsKkDzMKQ9AMDXyKYCAHVIT0vWqL6dFVptSPtQQxrVt7PS05KtqRgAoNUiGAfQqiTERcpZbZrzf9MBAGhpBOMAWo2MzGwtXZel6p3zTFNaui6LPNAAgBbHHSUAWo30tGSN6N1ZJWUOfbZtv2z2EiXERWpsvy6KDA/l5k0AQIsjGAfQaiTERbgC7pOPi7e4NkBVNnupbPbSev8s8ocRCD4E4wAA+IGMzOxas/0sXZcliWw/QLCizzgAAH4gPS1Zk4emyKiW7ccwpMlDU8j2AwQpgnEAAPyEzV5S44c55H/TAQQngnEAAPxARma2Vn9/QI5q2X4cprT6+wNk+wGCFH3GAQQkhhxHsElPS9aQ4zvqbxlblXukWCGqyIGf1D5Kc9P7q3uHaKurCMAHDNOsnnEX/srT4VWBYGSzl2rv4aJ6AxYyTiCQ8UcTCGyexmsE4wGEYByQXli1o9aME5XIOAEAsJKn8Rp9xgEElJF9Omtwjw4KqZZxIsSQBvfooJF9OltTMQAAmoBgHEBA+eKHA9qw57Cc1a7pOU1pw57D+uKHA9ZUDACAJqATGoCAwk1uAIBgQp/xAEKfceBX3OQGAPBHnsZr/HIBCEjREWG6fMTxVlcDAIBmIRgHACBIcMUICDx8QgEACHB15d9fsWEv+fcBP0c2FQAAAlxGZrbmvLhOOfnFMk3JYUqmKeXkF2vOi+uUkZltdRUB1IFgHACAAJeelqxRfTsrtFr+/VBDGtW3s9LTkq2pGIAGEYwDABAEEuIi5aw2zfm/6QD8F8E4AAABLiMzW0vXZal6smLTlJauy6KbCuDHuIETAIAAl56WrBG9O6ukzKHPtu2XzV6ihLhIje3XRZHhody8CfgxgnEAAAJcQlyEK+A++bh4i2sDwBN0UwEAAAAsQjAOAAAAWIRgHAAAALAIwTgAAABgEYJxAAAAwCJkUwHQ4mz2UtnspfWmYSMVGwCgNSAYB9DiMjKztXD1zhrTl67LkiTNGpWq2aN7tXS1AABocXRTAdDi0tOSNXloigyj6nTDkCYPTVF6WrI1FQMAoIXRMh6gCgsLa0yLiYmxoCaA5xLiIlTucCrUMFTuNn53qGGo3OGkiwrQgug2BliLYDxAJSYm1phmugU1gD+z2UsVFhoiR7X3rMM0FRYaIpu9lB9/oIXQbQywFt1UALS4jMxsLV2Xper/H02zIgDIyMy2pmJAK0S3McBatIwHqLy8PLqlIGClpyVrRO/O9V4WB9BybPYShUhyuE0L+d90AL5FMB6gYmJiCMYRsNz7oJ58XLzFtQFat4zMbK3+/kCN6Q5TWv39AaUmxtFNBfAhgnEAAFqx9LRkDTm+o/6WsVW5R4oVIskpKal9lOam91f3DtFWVxEIaobJXX8Bo7CwULGxsZKkgoICWsYBAF5TVFqupeuylJtfrKT4KE0emqLoCNrsAE95Gq/xKQMAAIqOCNPlI463uhpAq0M2FQAAAMAiBOMAAACARQjGAQAAAIsQjAMAAAAW4QZOAB6z2Utls5fWO2gPA/cAANAwgnEAHsvIzNbC1TtrTF+6LkuSNGtUKoOEAADQCATjADyWnpasX4rKtGx9ltxHKjAMadKQFKWnJVtXOQAthqtkQPMRjAPwWEJchModToUahsrdovFQw1C5w8mPL9BKcJUMaD5u4ATgMZu9VGGhIXJUG8DXYZoKCw2RzV5qUc0AtKT0tGRNHpoiw6g63TCkyUO5SgY0BsE4AI9lZGZr6bqqXVQkyTQrWsQyMrOtqRiAFuV+lcwdV8mAxqObCgCPpacla0TvzvX2EwUQ/BpzlYzvA6B+BOMAPOZ+U9bJx8VbXBsAVqm8SlZd5VWydtHh9BkHGkAwDgAAmoSrZEDzEYwDAIAm4SoZ0HzcwAkAAABYhGAcAAAAsAjBOAAAAGARgnEAAADAIgTjAAAAgEUIxgEAAACLEIwDAAAAFiEYBwAAACzCoD9AK2Wzl8pmL6135DxGzwMAwLcIxoFWKiMzWwtX76wxfem6LEnSrFGpmj26V0tXCwCAVoVgHGil0tOS9UtRmZatz5Jp/jrdMKRJQ1KUnpZsXeUAtApcoQMIxoFWKyEuQuUOp0INQ+Vu0XioYajc4eQHEIDPcYUO4AZOoNWy2UsVFhoih3uzuCSHaSosNEQ2e6lFNQPQWqSnJWvy0BQZRtXphiFNHsoVOrQOBONAK5WRma2l66p2UZEk06xolcrIzLamYgBaDfcrdO64QofWhG4qQCuVnpasEb0719tXEwB8qTFX6PguQrAjGAdaKfcbo04+Lt7i2gBojSqv0FVXeYWuXXQ4fcYR9AjGAQCAJbhCBxCMAwAAi3CFDuAGTgAAAMAyBOMAAACARQjGAQAAAIsQjAMAAAAWIRgHAAAALEIwDgAAAFiEYBwAAACwCME4AAAAYBGCcQAAAMAiBOMAAACARQjGAQAAAIsQjAMAAAAWIRhvYQ6HQw8++KB69eqliIgIpaam6t5771V5ebnVVQMAAEALIxhvYdddd53+8pe/aPDgwXr66ad11lln6c4779RVV11lddUAAADQwgzTNE2rK9FabN26VQMHDtRFF12kJUuWuKbfeuuteuihh7R+/XqlpaXVuX5hYaFiY2MlSQUFBYqJifF5neHfbPZS2eylKilz6LNt+2WzlyghLlJj+3VRZHioEuIilBAXYXU1AcDr+P6Dv/I0XgtriUqhwpIlS2Sapq6//voq06+//no99NBDWrJkSb3BOFBdRma2Fq7eWWP60nVZkqRZo1I1e3Svlq4WAPgc338IFnRTaUGZmZkKCQmpEXB369ZN3bp1U2ZmpkU1Q6BKT0vW5KEpMoyq0w1Dmjw0RelpydZUDAB8jO8/BItWF4wXFRXpww8/1L333qsLL7xQxx13nAzDkGEYmjdvXqPKsNvtmjdvnvr376/Y2Fi1a9dOQ4YM0cMPP6xjx47VuV5ubq4SEhLUpk2bGvOSkpKUk5PT1N1CK5UQF6Fyh1Oh1X6NQg1D5Q4nl2gBBC2+/xAsWl03lXXr1uncc89t8vo///yzRo0apT179kiSoqOjVVpaqszMTGVmZuq1117TypUrFR8fX2PdoqIiRUTU/uUQGRmp4uLiJtcLrZPNXqqw0BA5qt364TBNhYWGyGYv5QcJQNBKio+Ss9r3n9M0lRQfZVGNAM+1upZxSYqPj9eYMWN0yy236F//+pe6dOnSqPUcDocmTpyoPXv2qGvXrvr0009VWFiooqIiLVmyRHFxcdq0aZMuu+yyWtePjIxUaWlprfNKSkoUGRnZ5H1C65SRma2l67JU/TZs06zoN5mRmW1NxQDAx2z2Ug1IiVfX9r8G3oYhdW0fpQEp8bLZa/+9BfxNq2sZHzFihA4fPlxl2l/+8pdGrbto0SJt3bpVkrRs2TKddtppkqSQkBBNnTpVTqdTl156qT788EOtXLlSY8aMqbJ+9+7d9cMPP+jYsWM1uqrk5uYqNTW1qbuFVio9LVkjeneuN5sAAASj2m7gNE0pJ79Yc15cxw2cCBitLhgPDQ1t8rovv/yyJGn06NGuQNzdxRdfrDvuuEO7d+/W4sWLawTjgwcP1ieffKLMzEydfvrpruk5OTnKycnR1KlTm1w3tE7uqbtOPq5m1ygACFaVjRF1oTECgaJVdlNpiqKiIn311VeSpPHjx9e6jGEYOueccyRJn3zySY35U6dOlWEYeuKJJ6pMr3xNMA4AQOMkxEWoT1LbOh8E4wgUra5lvKm+//57OZ1OSVK/fv3qXK5y3v79+3X48GF16NDBNW/gwIG68sor9dxzz8k0TY0bN06ZmZl67rnnNH36dA0dOtS3OwEAAAC/QjDeSLm5ua7n3bp1q3M593m5ublVgnFJeuqpp3TcccdpwYIFevvtt5WUlKR58+bptttu86g+hYWFdc5jZE4AAIDAQDDeSHa73fU8Ojq6zuXc57mvUyksLEy33Xabx8F3dYmJiXXOM6un1gAAAIBfos84AAAAYBFaxhspLi7O9byoqKjO5dznua/jbXl5eXRHAQAACHAE442UlJTkep6Tk6MBAwbUupz7kPbu63hbTEwMwTgAAECAo5tKI/Xt21chIRWHa9u2bXUuVzmvS5cuNW7eBAAAANwRjDdSdHS0hg8fLkn66KOPal3GNE19/PHHkqRx48a1WN0AAAAQmAjGPTB9+nRJ0qpVq7R27doa89966y3t2rVLknT55Ze3aN0AAAAQeFplMJ6fny+bzeZ6VA7mU1RUVGV6QUFBlfWmT5+u/v37yzRNTZo0SStXrpQkOZ1OvfXWW5o9e7akihE6x4wZ07I7BQAAgIBjmK0wKXWPHj30888/N7jc9OnTtWjRoirT9uzZo9GjR2vPnj2SKrqvOJ1OlZSUSJIGDRqklStXKj4+3tvVVmFhoWJjYyXVnk2FGzoBAACs5R6vFRQUNBifkU3FQz169NCWLVs0f/58LV++XLt371Z4eLhOOukkXXLJJbruuuvUpk0bn9ejtkF/WuH/KgAAPGazl8pmL1VJmUOfbdsvm71ECXGRGtuviyLDQ5UQF6GEuAirq4lWolW2jAcq939ateFUAgDQsBdW7dDC1TvrnD9rVKpmj+7VgjVCMKFlvJVg0B8AAJomPS1ZvxSVadn6LLm3YxmGNGlIitLTkq2rHFodgvEAxaA/AAA0TUJchModToUahsrdovFQw1C5w0kXFbQognHAYvRdBICWZbOXKiw0RI5q3Tsdpqmw0BDZ7KV876LFEIwDFsvIzK617+LSdVmS6LsIAN6WkZnt+o51Z5oV373tosP53kWLIRgHLEbfRQBoWelpyRrRu3O9VySBlkIwDliMvosA0LLcu/+dfJz3xwUBPNEqR+AE/E1SfJSc1fouOk1TSfFRFtUIAAC0BIJxwGI2e6kGpMSra/tfA2/DkLq2j9KAlHjZ7KUW1g4AAPgSwXiAKiwsrPFAYMrIzNacF9cpJ7/YNc00pZz8Ys15cZ0yMrMtrB0AAPAlRuAMIIzAGZwqUxvWhdSGAAAEDktH4Ny+fbvWrFmj3NxcHTx4UCUlJerYsaM6deqkvn37avjw4YqOjvbmJoGAR7ANAEDr1exgfM2aNXr++ef10Ucf6cCBA/VvLCxMp5xyii677DJNmzZN7dq1a+7mW628vDxG4AQAAAhwTe6m8uqrr+qhhx7St99+W6V7RGxsrDp27KgOHTooKipKhw8f1uHDh2Wz2eR0Ois2ahiKiorSJZdcojvvvFPJyeRRbgxPL3sAAACgZXkar3kcjK9evVo333yzNm3aJNM01aFDB02aNElnnnmmhg0bpl69ah+xqqCgQJmZmVq7dq3eeecdrVmzRpIUGRmpG264Qbfffrvi4uI8qUqrQzAOAADg33wejIeEhMgwDI0bN05z5szRueeeq/DwcI8rumfPHi1evFhPPvmkDh8+rHnz5mnu3Lkel9OaEIwDAAD4N58G48XFxYqLi9OYMWP0xhtvqH379s2qrCQVFRXpqaeeUkxMjK655ppmlxfMCMYBAAD8m6fxmkd5xqdNmyan06nPPvtMjz32WJMr6S46Olp//vOfCcQBAADQ6ngUjH/88ccyDEPt2rXT+PHjfVUnAAAAoFXwKBj/zW9+I0latmyZhg0b5pMKAQAAAK2FR3nGH3/8cY0bN05vvvmmRo0aJcMwfFUvAAAAv8OoyfA2j4LxM844Q1999ZVuuukm9e7dW5deeqkmTpyowYMH+6p+AAAAfiMjM1sLV++sc/6sUamaPbr2NM9AbZo86M/PP/+s5cuXKyMjQ3v27NH48eM1ceJEjR07VpGRkd6uJ1T17tzaRuAkuwoAAL5ls5dq7+Ei/S1jq3LyiyVJhiEltY/S3PT+6t4hmpbxVs7necZrY7PZ9M4772jFihX66quvdNppp2nixImaMGGCkpKSmls8/sf95NbGC6cSAAA0YPGXu/Tsyp/kdPvZDTGkOWNO0OUjjreuYvALPk1tWJeEhATNnDlTK1asUHZ2tmbPnq3169crLS1NaWlpuvvuu7VhwwZvbAoAAMBSufnFCql231yIYSj3fy3lgCc86jPeGFFRUTrvvPN03nnnyTRNrVu3TitWrNCMGTN0+PBhTZgwge4sXlBbNxUAAOBbNnupwkJD5Kh2NdphmgoLDZHNXko3FXjEK91UGqOwsFBTpkzRxx9/LEmKjIzU7bffrjvuuKMlNh8UGIETAABrvbBqBzdwol6exmtebxmvzdtvv60bb7xR2dnZrn7N6enpjLoJAAACSnpaskb07qySMoc+27ZfNnuJEuIiNbZfF0WGh9IqDo/5NBhfv369br31Vn3xxReSKm4w7Ny5s/75z38qPT3dl5sGAADwOvc84icfF29xbRAMvHIDZ3UffPCBxo4dq1NPPVVffPGFTNNUWFiYbrrpJm3fvp1AHAAAAJAXW8btdrtefvllPfnkk9qxY4ekipZwwzB0wQUX6IEHHtBvfvMbb20OAAAACHjNDsbXrl2rBQsWaMmSJSoqKnL1CTcMQ5MmTdLcuXM1YMCAZlcUAAAACDZNDsaffvppPffcc/r2228l/TrgTMeOHTVjxgxdddVV6tWLu4kBAACAujQ5GC8pKdEJJ5ygoqIi7d69W5LUtm1bXXPNNTrzzDMZeRMAAABogFfyjNvtdm3ZskWbNm3S+vXr9fXXX2vPnj1KS0vTuHHjNGHCBA0ePNgb9W3VyDPun2z2UtnspfWmuSLVFQAArYOn8ZrPBv05dOiQvvzyS3388cdasWKFYmNjddVVV2nmzJmKjycVUFMQjPsnBoAAAACVPI3XfJLaUKroO37BBRfon//8p/bu3aunnnpKGzZs0PHHH6+7775b5eXlvtp0q1BYWFjjAWukpyVr8tAUGUbV6YYhTR6aovS0ZGsqBgAA/F6LjMAZEhKicePGady4cdq6dasuvPBCrVmzRu+++67Cw8NbogpBJzExscY0H13kQAMS4iJU7nAq1DBU7nYOQg1D5Q4nXVQAAECdfNYyXpf+/fvr2Wef1SeffKL/+7//a+nNAz6RFB8lZ7U/Q07TVFJ8lEU1AgAAgaDFg/HCwkK98MILkqRXX321pTcfNPLy8lRQUFDlAWvY7KUakBKvru1/DbwNQ+raPkoDUuJls5daWDsAAODPWjwYf+yxx/Tmm2/KMAx17ty5pTcfNGJiYmo8YI2MzGzNeXGdcvKLXdNMU8rJL9acF9cpIzPbwtoBAAB/1iJ9xt0NHz5cHTt2VNu2bbVw4cKW3jzgdelpyRrRu+4/lvQZBwAAdfFZakN4H6kNAQAA/JvfpDYEAAAAUD+CcQAAAMAiTeozvmzZMj3wwAOaM2eOZs2aVWXel19+qYyMDB08eFAdOnRQ3759dfbZZ6tnz55eqTAAAAAQLJoUjL/00kvauHFjjQD75ptv1qOPPlrrOmPHjtXf//53nXLKKU3ZJAAAABB0mnQDZ/fu3bVv3z7Z7XZFR0dLkt555x1dcMEFkqSePXuqc+fOOnjwoHbv3u0aGTIsLEwPP/ywrrvuOu/tQSvCDZwAAAQ2m7203vEnEuIiyMIV4DyN15rUMm6z2RQXF+cKxCXp0UcfVfv27fXmm29q7Nixrun79u1TRkaGHnvsMe3YsUM33nijYmJiNHPmzKZsGgAAIGBlZGZr4eqddc6fNSpVs0f3asEawWpNahlv06aN4uPjlZeXJ0kqKipS+/bt9fLLL+uSSy6pdZ2ioiLdcMMNWrhwoaKjo/XTTz+pa9euzat9K0PLOAAAgc1mL9Xew0X6W8ZW12BxhiEltY/S3PT+6t4hmpbxANciqQ3bt2+vo0ePul6vXbtWISEhmjx5cp3rREdH64UXXtCUKVNUXFysp59+uimbBgAACFgJcRHakpWvfUeqjtq870ixtmTlE4i3Qk0Kxk844QQdO3ZM3333nSTp448/1gknnKDw8PAG173vvvtkmqY+/PDDpmwaAAAgoOXmFyvEMKpMCzEM5eYX17EGglmTgvGxY8fKNE3deOONev/99/X888/LbrerrKyswXV79eqldu3aaefOuvtLAQAABKuk+Cg5q/USdpqmkuKjLKoRrNSkYPzqq69Wu3bttHLlSp133nn65ZdfdPjw4UZlSXE4HCopKdGxY8easmn8T2FhYY0HAADwbzZ7qQakxKtr+18Db8OQuraP0oCU+HozrSA4NSkY79Kli95//3316tVLpmkqISFBn3zyiTZt2qSLLrrIdWNnbV555RWVlpYqKSmpyZWGlJiYqNjY2CoPAADg3zIyszXnxXWumzelij7jOfnFmvPiOmVkZltYO1ihSdlU3OXm5qpTp04KDw/Xzp07NWLECB05ckTnn3++zjrrLPXv318dO3aUzWbT22+/rUceeURlZWWaM2cON3F6yP3u3No081QCAAAfI8948PM0m0qzg/HqduzYofT0dH377bcyqt2cIFUEjB07dtTmzZtpHfeQ+8nNy8urcXJJdQgAAGCtFkltWJ9evXopMzNTDz30kKsbi/tj+PDh+ve//00g3kwxMTE1HgAAAAgsXm8Zr27fvn3atWuXHA6HUlNT1a1bN19uLqgx6A8AAIB/8zReC/N1hbp27cpImwAAAEAtPO6mMn/+fBUXezcp/fr16xkECAAAAK2Ox8H4n//8Zx1//PF69NFHdeTIkWZt/D//+Y8mTJigU089VevXr29WWQAAAECg8TgYv/3223X06FHdfPPN6tq1qyZPnqxly5bpwIEDDa5bVlam9evXa+7cuUpNTdXIkSP1wQcfaMiQIbrggguaUn8AAAAgYDXpBs6cnBzdfvvtev311+VwOFwpDJOTkzVw4EB16tRJHTp0UEREhPLz83X48GHt2rVLmzdvdo28aZqmUlNT9be//U0XX3yxd/cqSHEDJwAAgH9r0Tzjubm5ev755/Xiiy9q7969vxZaR35xSQoLC9Pvfvc7XXXVVTr77LNrXRa1IxgHAADwb5YN+rNt2zb9+9//1tq1a5Wbm6uDBw+qpKREHTt2VKdOnXTiiSfqzDPP1PDhwxUXF+eNTbY6BOMAAAD+zfIROOE7BOO+w/DEAADAGyzJM26aJt1NENAyMrO1cPXOOufPGpWq2aN7tWCNAABAa+BxNpVKOTk5mjFjhjp37qywsDC1a9dOo0eP1ssvvywa2xFo0tOS9ezMoeoWH+WaZhhSt/goPTtzqNLTki2sHQAACFZNCsZtNptOPfVUvfLKK7LZbDJNU3a7Xf/+9781c+ZMnX322SoqKvJ2XQGfSYiL0JasfO078uuAVqYp7TtSrC1Z+XRRAQAAPtGkYPyBBx5QTk6OTNPUSSedpBkzZujSSy9Vjx49ZJqmVq5cqTlz5ni7roBP5eYXK6Rad6sQw1BuvndHnAUAAKjUpGD8ww8/lGEYuvrqq7Vlyxa9+OKLevXVV7Vz504988wzMgxDr732mrZs2eLt+gI+kxQfJWe1LlZO01SSW9cVAAAAb2pSML5nzx5J0v3331/jxs05c+bohhtukGmaeu2115pdQaAl2OylGpASr67tq/YZ79o+SgNS4uvNtAIAANBUTUptGBISooSEBB04cKDW+d9995369eunM888U6tXr25uHfE/7qly8vLyaqTKIdVh072wagfZVAAAfo00vIGhxVIbhoXVveoJJ5wgSdq3b19Ti0cDEhMTa0wji03Tpacla0TvznXO58sNAGA10vAGJ6/kGa8uPDxcUsW/ASAQ0JoAAPB36WnJGnJ8R/0tY6ty/pdcwDCkpPZRmpveX907RFtcQzRFk/OMHzt2TNu2bVN5eXmdy9BS6zt5eXkqKCio8gAAAMGLNLzBqckt4/n5+Ro4cKDCw8N14oknauDAgRo4cKBOPvlkDRw40Jt1RC1iYmLoIw4AQCtTmYbXPfsXaXgDW5OC8e7du2vv3r2SKlrIv/nmG23evLnGcna7XY888ogGDx6sU045RXFxcc2rLQAAQCtGGt7g06RgPCsrS4cPH9aGDRu0YcMGbdy4URs2bNDu3burLFdUVKRbbrlFkmQYhlJTU5WWlqbBgwdr8ODBGjlyZPP3AAAAoBVwT8Pr3mfcPQ0vXVUCT5NSG9blyJEj2rhxoys437hxo3bs2FGl73hlXnLDMOrtb46aPE2VAwAAggdpeAODp/GaV4Px2tjtdm3atKlKgP7jjz/KNE05HA5fbjroEIwDANB6kWc8MPhdMF6boqIiffPNNzr99NNbetMBjWAcAADAv3karzU5tWFzREdHE4gDAACg1bMkGAcAAABAMA4AAABYhmAcAAAAsAjBOAAAAGARgnEAAADAIk0agRPwR+RfBQAAgYZgHEEjIzObkckAAEBAIRhH0EhPS9aI3p1VUubQDYszZZqmzhucrLH9uigyPJRWcQAA4HfoM46gkRAXoZSO0Xrove9UWu7UMYep5euz9NB73ymlYzTBOAAA8DsE4wgqS9dlac/BAtdrpyntOVigpeuyLKwVAABA7QjGEVRy84sVYhhVpoUYhnLziy2qEQAAQN0IxhFUkuKj5DTNKtOcpqmk+CiLagQAAFA3gnEElclDU9SjU6zrdYgh9egUq8lDUyysFQAAQO0IxhE0bPZSZR0q0p8nnKiIsBC1CTV04ZAU/XnCico6VFRvDnIAAAArGKZZ7Zo+/FZhYaFiYytafQsKChQTE2NxjfzLC6t2kGccAABYytN4jTzjCBqVecbrQmpDAADgbwjGA1RhYWGNaa29pZzh7gEAQKAhGA9QiYmJNabR4wgAANTGZi+t994pGrSsQzAOAAAQ5DIys7mvyk8RjAeovLy8Vt8tBQAANE7lfVUlZQ7dsDhTpmnqvMHJGtuviyLDQ2kVtxDBeICKiYkhGAcAAI2SEBeh6Dah+sOCtSotd0qSlq/P0sY9h7XgD8MUHUFIaBXyjAMAALQCS9dlac/BAtdrpyntOVigpeuyLKwVCMYBAABagdz8YoUYRpVpIYah3Pxii2oEiWAcAACgVUiKj5KzWuY1p2kqKT7KohpBIhgHAABoFSYPTVGPTrGu1yGG1KNTrCYPTbGwViAYBwAAaAWiI8IqbtZsE6qIsBDNGXMCN2/6AY4+AABAkHMf9Cc81FB4qKGhqQnKOlQkiUF/rEQwDgAAEORqG/RnxnNrXM8Z9Mc6BOMAAABBrnLQn7rQKm4dgnEAAIAgRzcU/8UNnAAAAIBFCMYBAAAAixCMAwAAABYhGAcAAAAsQjAOAAAAWIRgHAAAALAIwTgAAABgEYJxAAAAwCIE4wAAAIBFCMYBAAAAixCMAwAAABYhGAcAAAAsQjAOAAAAWIRgHAAAALAIwTgAAABgkTCrKwAAAAD/ZbOXymYvrXN+QlyEEuIiWrBGwYVgHAAAAHXKyMzWwtU765w/a1SqZo/u1YI1Ci4E4/Ar/PsGAMC/pKcla0TvzpKkGxavlyQ9fvkQ13x+l5uHYBx+hX/fAAD4l8qGsKLScpU5TDmcptbttGny0BRFRxBKNpdhmqZpdSXQOIWFhYqNjZUkFRQUKCYmxuIaeZ97y3hd/775Bw4AQMsqKi3XHxas1a4DBZKkEEPq0SlWC/4wjIC8Gk/jNY4e/Ip7sB0WWpHsp09SWyurBABAq7d0XZb2HCxwvXaa0p6DBVq6LkuXjzjewpoFPlIbwi8VlZar+JhDBSXlWvzlLhWVlltdJQAAWq3c/GKFGEaVaSGGodz8YotqFDwIxuF3Ki+FFR1zqLTcqWdX/lTxmoAcAABLJMVHyVmtZ7PTNJUUH2VRjYIHwXiAKiwsrPEIFvVdCgMAAC1v8tAU9egU63pd2Wd88tAUC2sVHOgzHqASExNrTAuWe3ErL4W5/wPnUhgAANaJjgjTgj8M04T5q+Vwmpo1KpVsKl7CEYTf4VIYAAD+wz3TWXioofBQQ0NTE5R1qEgSmc6ai2A8QOXl5QVlakOp4lLYR1v21UifxKUwAABaXm1jgMx4bo3rOWOANA95xgNIa8gzXqmotJxLYQAA+AFGx/YMecYRFKIjwhTVJlSSyF8KAICFCLZ9i2wqAAAAgEVoGYdfcb8UVu5wSpJ+yD3qms+/cwAAEEwIxuFXuEkEAAC0JgTj8Cvpacka0btznfNpFQcAAMGEYBx+hW4oAACgNeEGTgAAAMAiBOMAAACARQjGAQAAAIsQjAMAAAAWIRgHAAAALEIwDgAAAFiEYBwAAACwCME4AAAAYBGCcQAAAMAiBOMAAACARQjGAQAAAIuEWV0BAAAABCebvVQ2e2md8xPiIpQQF9GCNfI/BOMAAADwiYzMbC1cvbPO+bNGpWr26F4tWCP/QzAOAAAAn0hPS9aI3p0lSTcsXi9JevzyIa75rb1VXCIYBwAAgI9UdkMpKi1XmcOUw2lq3U6bJg9NUXQEYajEDZwAAADwoaLScv1hwVoVHXOotNypZ1f+VPG6tNzqqvkFgnEAAAD4zNJ1WdpzsMD12mlKew4WaOm6LAtr5T8IxgEAAOAzufnFCjGMKtNCDEO5+cUW1ci/EIwDAADAZ5Lio+Q0zSrTnKappPgoi2rkXwjGAQAA4DOTh6aoR6dY1+sQQ+rRKVaTh6ZYWCv/QTAOAAAAn4mOCNOCPwxTdJtQRYSFaM6YEypek01FEqkNAQAA4CPuI3CGhxoKDzU0NDVBWYeKJDECp0QwDgAAAB+pbQTOGc+tcT1nBE6CcQAAAPiI+wictWntreISwTgAAAB8hG4oDeMGTgAAAMAiBOMAAACARQjGAQAAAIsQjAMAAAAWIRgHAAAALEIwDgAAAFiEYBwAAACwCHnG4XXuQ9/WhpyjAAAAFQjG4XW1DX3rjqFvAQAAKhCMw+vch769YfF6SdLjlw9xzadVHAAAoALBOLzOvRtKWGjFbQl9ktpaWSUAAAC/xA2c8Jmi0nIVH3OooKRci7/cpaLScqurBAAA4FcIxuETRaXl+sOCtSo65lBpuVPPrvyp4jUBOQAAgAvBOHxi6bos7TlY4HrtNKU9Bwu0dF2WhbUCAADwLwTj8Inc/GKFGEaVaSGGodz8YotqBAAA4H+4gRM+kRQfJadpVpnmNE0lxUdZVCMEC9M0VVZWJqfTaXVVADQgJCRE4eHhMqo1zgD4FcE4fGLy0BR9tGWfdh2o6KoSYkg9OsVq8tAUi2uGQOVwOGSz2WS321VWVmZ1dQA0Unh4uOLi4pSQkKDQ0FCrqwP4HYLxFlRQUKD58+crMzNTmZmZysvL0/Tp07Vo0SKrq+Z10RFhWvCHYZowf7UcTlOzRqVq8tAURUfwloPnHA6HsrOzVVpaqnbt2ik2NlahoaG0tgF+zDRNORwOFRQU6MiRIyouLlZycjIBOVANkVELstlsuvvuu9W1a1elpaXp/ffft7pKPmGzl8pmL5UkhYcaCg81NDQ1QVmHiiRVzUMONIbNZlNpaalSUlIUFUVXJyCQxMbGql27dsrKypLNZlNiYqLVVUIAcY8pahMMMQXBeAvq2rWr9u7dq27duqmkpCRog4qMzGwtXL2zyrQZz61xPZ81KlWzR/dq6WohQJmmKbvdrnbt2gXtZwYIdlFRUWrbtq3sdrs6d+7MVS00Wm0xhbtgiCkIxltQRESEunXrZnU1fC49LVkjeneuc36g/4NFyyorK1NZWZliY2OtrgqAZoiLi9ORI0dUVlamNm3aWF0dBAj3mOKGxeslSY9fPsQ1PxhiCoJxeF0wXDKC/6jMmkI/UyCwVX6GyYQET7jHFGGhFRm5+yS1tbJKXhewecaLior04Ycf6t5779WFF16o4447ToZhyDAMzZs3r1Fl2O12zZs3T/3793f1aRsyZIgefvhhHTt2zLc7AMAjXNYGAhufYaB2Adsyvm7dOp177rlNXv/nn3/WqFGjtGfPHklSdHS0SktLXZlOXnvtNa1cuVLx8fE11j127Ji2bNnSqO1ERUXppJNOanI9AVirNdw8BACwTsAG45IUHx+vU045xfW46aabtH///gbXczgcmjhxovbs2aOuXbtq8eLFGjt2rJxOp9566y3Nnj1bmzZt0mWXXaYPPvigxvq5ubkaMmRILSXXdNJJJ2nbtm0e7xsA/9Aabh4CAH9XVFqu4mMOOZymFn+5K6jSJQfsXowYMUKHDx+uMu0vf/lLo9ZdtGiRtm7dKklatmyZTjvtNEkVI4VNnTpVTqdTl156qT788EOtXLlSY8aMqbJ+ly5dtGrVqkZtKyYmplHLAfBPreHmIQDwZ0Wl5frDgrUqOuaQJD278id9tGWfFvxhWFAE5AG7B825mevll1+WJI0ePdoViLu7+OKLdccdd2j37t1avHhxjWA8MjJSo0aNavL2AQSO1nDzEAD4s6XrsrTnYIHrtdOU9hws0NJ1Wbp8xPEW1sw7AjYYb6qioiJ99dVXkqTx48fXuoxhGDrnnHP0z3/+U5988klLVs8v0EcWAAD4i9z8YoUYhpym6ZoWYhjKzS+2sFbe0+qC8e+//96VVqlfv351Llc5b//+/Tp8+LA6dOjgle0/9dRTOnLkiMrLyyVJW7Zs0b333itJOvPMM3XmmWc2qpzCwsI65zW3awx9ZIHgdejQIb3zzjtauXKlNm7cqJ9//lnl5eXq1KmT0tLSNH36dKWnp9e67rx583T33XdXmWYYhmJjY9W2bVulpKRo0KBBGj16tM477zxySTfAbrfr4Ycf1rJly7R7926FhobqN7/5jS6++GJdd911zT5+TS2/qKhIX3zxhTZs2KCNGzdqw4YNysrKkiTdddddjc5YBnhLUnxUlUBckpymqaT44BgIrtUF47m5ua7n9Q3A4z4vNzfXa8H4/Pnz9fPPP7teb9q0SZs2bZJU8SXX2GC8vuGEzWpvWE/RRxYIXl26dHE1BkgV3e7Cw8OVk5OjnJwcrVixQuPHj9fSpUsVHR1dZznu30HFxcXKzc1VTk6O1qxZo2eeeUYdO3bU3/72N82ZM4eUdrVoTkYvX5ff3GxlgLdNHpqij7bs064DFV1VQgypR6dYTR6aYnHNvCNg84w3ld1udz2v74fGfZ77Os21Z88emaZZ68NfWhsS4iLUJ6mt+iS1VVhoiMJCQ1yv+yS1JRgHAlh5ebmGDh2qZ555Rjt37lRxcbEKCgq0e/duzZo1S5L04Ycf6qqrrqq3nP3797sev/zyi8rKyrRlyxY9/PDD6tmzpw4dOqQ//vGP+v3vf9/sBoJgUz2j16effqrCwkIVFRVpyZIliouLc2X0sqr8+Ph4jRkzRrfccov+9a9/qUuXLk3dXaDZoiPCKm7WbBOqiLAQzRlzQtDcvCm1wpbxYJGXl0emFgAe+/zzzzV69Oga03v06KEFCxYoLCxMzz33nF599VXdf//9Sk5OblS5oaGh6t+/v/r37685c+Zo1qxZWrJkiV5//XX169dPt912m7d3JWA1N6OXr8tvTrYywFeiI8IU1aYieUcw3LTprtW1jMfFxbmeFxUV1bmc+zz3dfxFTExMnQ8AqEttgbi7ytZxScrMzGzSNqKjo/Xyyy9r0KBBkqQHHnigRnDnbe+9956mTJmiHj16KDo62jUic22PhQsX+rQuDWlMRq+ePXtKkhYvXtzi5TcnWxkAz7W6YDwpKcn1PCcnp87l3Oe5r9OaVCbYLygp1+Ivd6motLzhlQAEtMjISNdzh8PR5HLatGmj22+/XZJ09OhRvf32282tWq2Ki4t1/vnna+LEiVq6dKmysrIUERGhsLC6L/wOHDjQJ3VpDE8yeknyOKOXr8sH4H2tLhjv27evQkIqdru+kTEr53Xp0sVrN28GEvcE+6XlTj278qeK1wTkaKVay5/T1atXu57379+/WWWdc845rlbWL774olll1eXSSy/VO++8o9DQUM2dO1f79+9Xfn6+7Ha7Hn30Uddyw4YN00svvaSXXnqp2fvVHE3N6OUv5QPwvlYXjEdHR2v48OGSpI8++qjWZUzT1McffyxJGjduXIvVzZ/Ul2AfaG1ay5/TI0eO6O9//7ukin7DvXv3blZ5sbGxOv74ir6dO3fWnS61qV555RVXi/tzzz2ne+65R507V2SCioyM1I033qipU6dKknbs2KEZM2ZoxowZioio/Sb0RYsW1du9paGH+x+ZujQ1o1dj+bp8oKXZ7KX6Ifeofsg9qnKHU+UOp+v1D7lH6x0XJVC0yhs4p0+fri+//FKrVq3S2rVrNWzYsCrz33rrLe3atUuSdPnll1tRRcsFe4J9wBPBPvqbJDmdTk2bNk379u1TRESEnnzySa+UW3ll0dutr6ZpusZouOCCC6r0dXc3ceJEvfHGGzp06JD27dunrl271llmVFRUvWljG9KYvOC+zuhldcYwwNtqG/tkxnNrXM/rG/skUAYxDOhgPD8/v0qfxspLc0VFRbLZbK7pkZGRio2Ndb2ePn26Hn/8cW3dulWTJk3Syy+/rDFjxsjpdGrZsmWaPXu2pIr+dp7exR4sgj3BPuCJ1vDn9IYbbtB7770nSXrmmWe81q/aV2kN16xZo+3bt0uSbr755jqX69ixo+t5WVlZvWVOnTrV1ZIOwD+4j31Sm/qC6UAZxDCgg/FBgwZVGUCn0j/+8Q/94x//cL2ePn26Fi1a5HodFhamd955R6NHj9aePXs0duxYRUdHy+l0qqSkxFX2a6+95vN9aKraRuD0ZiaVYE+wD3gi2P+c3nzzzXrqqackSY8++qhmzpzptbLz8/MlVQ2KvWHlypWSKu7rqS1jSKUDBw5Iqkjr5w+5sn2d0StYMoYBlZrTeh0ogxi2uj7jlXr06KEtW7bozjvvVL9+/WQYhsLDwzV48GDNnz9fX3/9dZNHPmsJiYmJio2NrfLwpmBPsA94YvLQFPXo9OtnLJj+nP75z3/Www8/LKmiIePGG2/0WtkFBQWuLn+pqaleK1eSK4/20KFDXTfl16byxtEBAwY0e3h5b/B1Ri8yhgG/CpRBDAM6sqoc5rep4uLidPfdd+vuu+/2ToWCTDAn2Ac8UfnndML81XI4Tc0alarJQ1MC/s/pLbfcovnz50uSHnrooXq7ezTFRx995OpKOGrUKK+WXRlMJiQk1LmMw+HQO++8I0mNGt79jTfe0A033NDkOi1fvlynn356vctUZvRyOp3atm1bnekHm5rRy9flA/C+wP4lacUYgRNoWcH25/Tmm292tYg/9NBDuuWWW7xa/rFjx3T//fdLktq1a6cLLrjAq+VX5hE/dOhQncs899xzstlsCg0Ndd0LVJ/i4mLl5eU1uU7Hjh1rcJnKjF5ffvmlPvroo1qPe3Myevm6fADe12q7qQQ6Rt4E0FTugfj8+fO9HogXFxdrxowZ2rRpkyTptttuU/v27b26jT59+kiSVq1apSNHjtSY/8MPP+jPf/6zJOn6669Xjx49GixzxowZMk2zyY/Gtv5Pnz7dVfe1a9fWmN/cjF6+Lh+AdxGMA0Arcuutt7oC8UceeUR/+tOfvFJuZbeIRx55RCeddJL+9a9/SZKmTZvmCoqr27NnjytH97x58zza3mWXXSapYnTPKVOmKCurYgyEkpISvfLKKxoxYoQKCws1fPhw3XfffU3fMR+YPn26+vfvL9M0NWnSJNfNqE6nU2+99VaDGb3c86HXltu8ueVLFTfe2mw216N6trLKR0FBQa3rA/7E3wdto5sKanDPy1nuqPgC/iH3qGu+v+TlBOCZrKwsPfTQQ5Iqsos8+OCDevDBB+tc/uabb66zH7l7ZpLS0lIdPXrUFbBJFX257733Xl111VVeqn1VZ555pq699lo99dRT+uyzz3Tcccepffv2KigoUHl5xQ9tenq6Fi1apKgo/8p64+uMXt4ov6nZygB/4z5omyQ9u/InfbRln18lpfCPWsCvNCfBPgD/5R4sO53OBvtH19fqWbmuYRiKiYlRly5dlJKSokGDBmnMmDGaOHFig9lL3DN6nHrqqY3ZhSqefPJJnXbaaXr++ee1efNmFRUVqUuXLjr99NM1a9Ysv+4PXZnRa/78+Vq+fLl2796t8PBwnXTSSbrkkkt03XXXNSv7i6/LBwJFIAzaZpi+GpEBXldYWOhKYVhQUOCzfuKBMmIVWoeSkhLt3r1bPXv2VGRkpKV1+d0/VkmS3r9ltKX1CBb33nuv5s6dqzPOOENffvml1dWBj/nTZxmtxwPvfKv3NuWo3PlruBsWYmjCoG76y3kn+WSbnsZrtIyjBoJtAC3h888/lyRX1hUA8LZAGLSNYBwA6sE9FL5RWlqqNWvW6JxzztGIESOsrg6AIBUII4oTjAeowsLCGtNIbwh4H/dQ+EZERISKi4utrgaAIBcIg7b5T03gkcTExBrT6P4PeF96WrJG9O5c53xaxQHAv/n7oG0E4wBQD7qhAAB8iWA8QOXl5dEtBQAAIMARjAeomJgYgnEAAIAARzAOAACAoBMo2bAIxgEAABB0AiUbFsE4gIBAtiAgsPEZRksLlGxYBOMA/FpISIgkyeFwWFwTAM1R+Rmu/EwDvuYv3VAawicCgF8LDw9XeHi4CgoKrK4KgGaw2+2uzzOAXxGMA/BrhmEoLi5Ov/zyCyM2AgGquLhYR48eVVxcnAzDsLo6gF+hmwoAv5eQkKDi4mJlZWWpbdu2iouLU2hoKD/qgB8zTVMOh0N2u11Hjx5VRESEEhISrK4W4HcIxgNUYWFhjWnkHUewCg0NVXJysmw2m+x2u44cOWJ1lQA0Unh4uNq3b6+EhASFhoZaXR3A7xCMB6jExMQa07hTHcEsNDRUiYmJ6ty5s8rKyuR0Oq2uEoAGhISEKDw8nKtYQD0IxgEEFMMw1KZNG6urAQCAVxCMB6i8vDy6pQAAAAQ4sqkEqJiYmBoP+E5hYaEMw5BhGLX210fL4Vz4F86H/+Bc+A/Ohf8IhHNBMA4AAABYhGAcAAAAsAjBOAAAAGARgnEAAADAIgTjAAAAgEVIbRhA3Af18dc7goOV+/Hm2FuLc+FfOB/+g3PhPzgX/sOKc+G+ncYMyGiYDNsYMA4cOFDryJsAAADwP3l5eercuXO9y9BNBQAAALAILeMBxOl0ymazSZKio6NlGIbFNQIAAIA70zRVVFQkSUpISFBISP1t3wTjAAAAgEXopgIAAABYhGAcAAAAsAjBOAAAAGARgnEAAADAIgTjAAAAgEUIxgEAAACLEIwDAAAAFiEYB2pht9s1b9489e/fX7GxsWrXrp2GDBmihx9+WMeOHWtyuTk5OXrmmWc0ZcoU9erVS1FRUYqKilLPnj11ySWX6PPPP/fiXgQPX52PI0eOaMWKFbrzzjs1YcIEde3aVYZhyDAMLVq0yHs7EAB8dYyliuGg//SnP6l3796KiopShw4dNGLECC1YsEAMdVE7X5wP3u9N44tzwW9B0/jiXHzxxRe64447dPbZZ+uEE05QfHy8wsPD1blzZ40ePVpPPPGEiouLvbwn1ZgAqtizZ4/Zo0cPU5IpyYyOjjYjIiJcrwcNGmQePnzY43KzsrJMwzBc5VSWHRUVVWXazJkzzfLych/sWWDy1fkwTdN86aWXqhx798dLL73k3R3xY748xpmZmWbHjh1dZcXGxpphYWGu1+PGjTNLSkq8vEeBzVfng/e753xxLvgtaBpffS5+97vfVTnuMTExZkxMTJVpPXv2NH/88Ucf7FUFgnHATXl5udm/f39Tktm1a1fz008/NU3TNB0Oh7lkyRIzLi7OlGSOHz/e47J3795tSjLHjBljvvzyy2ZOTo6r7G+//dY8//zzXR/8v/71r17dr0Dly/NhmhXBSZcuXczx48ebd9xxh7ls2bJWF5z48hgfOXLE7NKliynJ7NOnj7l+/XrTNE2ztLTUfOqpp8zw8HBTknn11Vd7dZ8CmS/PB+93z/jqXPBb4Dlffi4effRR84knnjA3btxoHj161DXdZrOZTzzxhOtP0oknnmg6HA6v7ZM7gnHAzYIFC1xfgv/9739rzH/99ddd8z/77DOPyj5y5Ii5YcOGOuc7nU7znHPOcbUeFhcXe1z/YOPL82GapllWVlZjWmsLTnx5jP/617+aksyoqChz165dNebff//9piQzNDTUp61OgcSX54P3u2d8dS74LfCcr38L6vPcc8+5yv7Pf/7j1bIrEYwDbkaMGGFKMkePHl3rfKfTafbs2dOUZF5++eVe3/6bb77p+tBv3LjR6+UHGivOR2sLTnx5jFNSUkxJ5hVXXFHrfLvdbsbGxpqSzDvvvNPjugejln7Pt7b3uyes/D3gt6AqK8/F5s2bXediyZIlXi27EjdwAv9TVFSkr776SpI0fvz4WpcxDEPnnHOOJOmTTz7xeh0iIyNdzx0Oh9fLDyT+cD6CnS+P8Y8//qisrKx6y46NjdWIESM8LjtY8Z73H1afC34LfmX1ufjyyy9dz1NTU71adiWCceB/vv/+ezmdTklSv3796lyuct7+/ft1+PBhr9Zh9erVkqQ2bdroN7/5jVfLDjT+cD6CnS+P8bZt22qsX1/Z3333XaPKDWa85/2H1eeC34JfWXEuiouL9dNPP+n+++/Xn/70J0nSmWeeqbS0tGaVW5cwn5QKBKDc3FzX827dutW5nPu83NxcdejQwSvb3717t5599llJ0tSpU9W2bVuvlBuorD4frYEvj7GnZR89elQFBQWKjY1tsOxgxXvef1h5LvgtqKqlzsX+/fvVtWvXWudNnDjRp+k/aRkH/sdut7ueR0dH17mc+zz3dZqjuLhYU6ZMUVFRkTp27Ki///3vXik3kFl5PloLXx5jzp/nOGb+w6pzwW9BTS11LkJDQ5WYmKjExMQq3YSmTJmihx56yKd/egnGEdAWLVrkGrSiKY+PPvrI6l1QeXm5Lr30Um3YsEHh4eF6/fXX6/3378+C4XwAgBWC6bcgEHXq1En79+/X/v37VVRUpOzsbN1xxx169913NWDAAD3//PM+2zbBOPA/cXFxrudFRUV1Luc+z32dpnA4HPr973+vt99+W2FhYXr99dc1bty4ZpUZLKw4H62NL48x589zHDP/0dLngt+CulnxuTAMQ927d9e9996r1157TWVlZbr66qu1efPmZpVbF/qMI6BdcsklmjBhQpPXb9eunet5UlKS63lOTo4GDBhQ6zo5OTm1ruOpyi/fN954Q6GhoXr11Vc1efLkJpfnDwL5fLRGvjzG1cuuq99rZdlt27Zt1f3FJd7z/qQlz0Uw/hZ4k9WfiwsvvFDHHXecfv75Zy1cuFBPPPGE18quRDCOgBYREaGIiAivlNW3b1+FhITI6XRq27ZtdaZQqswS0aVLlyb3IXM4HLrsssuqfPlOnTq1yXX3F4F6PlorXx5j96wH27ZtU9++fest+8QTT/Sk6kGJ97z/aKlzEay/Bd7kD5+LpKQk/fzzz9qxY4dXy61ENxXgf6KjozV8+HBJqrPvsmma+vjjjyWpyZcQa/vyvfjii5tW6SDWUuejNfPlMe7du7dSUlLqLbuwsNCVw5fzx3ven7TEueC3oHGs/lyYpqndu3dL8mG3MJ8MJQQEqMohdw3DML/++usa8994441mDblbXl5uXnTRRaYkMywszGejeQULX5+P2qiVjUjoy2P817/+1ZRkRkdHm7t3764x/8EHHzQlmaGhoeaPP/7Y1F0IKi39nm9t73dP+PJc8FvgGV+di7KysgaXWbhwoavsZ555xqN6NxbBOOCmrKzM7N+/vynJ7Natm+tD7XA4zDfffNNs27atKckcP358revfddddrg9t9eCjvLzcvOSSS1xfvm+++aavdyfg+fJ8VDp48GCVR+XyTz75ZJXphYWFvtpNSzXnGDd0fI8cOWJ26dLFlGSeeOKJZmZmpmmapllaWmo+88wzZps2bUxJ5tVXX+3TfQwkvjwfpsn73RO+Ohf8FnjOV+di1apV5ogRI8zFixeb2dnZVeZt377dvPXWW82wsDBTkpmammoWFRX5ZP8IxoFqdu/ebfbo0cP14Y2OjjYjIyNdrwcNGmQePny41nXr+9B/8cUXrnnh4eFmYmJivQ9aSir46nxUqpzf0OOuu+7y3U5arKnHuDHHNzMz0+zYsaNrubi4ODM8PNz1ety4cWZJSYmP9zCw+PJ88H73jC/OBb8FTeOLc7Fq1aoq7/vIyEgzISHBjIqKqjJ94MCBdX6mvIE+40A1PXr00JYtW3TnnXeqX79+MgxD4eHhGjx4sObPn6+vv/5a8fHxHpdbOZyvJJWVlSkvL6/eR3FxsTd3K2D56nzgV748xoMHD9a3336rm266SSeccILKysoUExOjM844Qy+88II+/PBDr930Gyx4z/sPX5wLfguaxhfnYvDgwVq8eLFmzpypgQMHql27djpy5IhCQkKUmpqqKVOmaMmSJdqwYYN69Ojhmx2TZJimafqsdAAAAAB1omUcAAAAsAjBOAAAAGARgnEAAADAIgTjAAAAgEUIxgEAAACLEIwDAAAAFiEYBwAAACxCMA4AAABYhGAcAAAAsAjBOAAg4P3nP//R4MGDFRsbq0mTJqmoqMjqKgFAoximaZpWVwIAgKbatGmTTj/9dJWUlLimPfTQQ7rlllssrBUANA4t4wCAZtu3b5/uuusunX766erUqZPCw8MVERGhbt266Xe/+52WLl3qs23feOONmjZtmj777DO1b99eknT06FGfbQ8AvImWcQBAs/z3v//Vueeeq19++UWS1KZNG7Vt21alpaWy2+2SpFNOOUUbNmxoVHnz589XZGSkrr322gaX3bNnj8aOHasff/xRoaGhWrNmjT788EPdeOON6tChQ9N3CgBaCME4AKBZevfure3bt+u3v/2tHnvsMfXr10+GYUiSCgoK9PXXX2v37t2aPXt2o8q78MILtX37dm3btq3BZR955BEdOXJE99xzT7P2AQCsQjAOAGiynJwcde/eXZL0zjvvaOLEic0uMzU1Vbt27dJ///tfnXbaafUuO2LECD3yyCMaMmRIs7cLAFagzzgAoMk6deqkhIQESdLll1+uW2+9VZ9//rkKCwubVN7Ro0e1e/duSdKCBQvqXfbgwYPavXu30tLSmrQtAPAHBOMAgCZr06aN3nnnHcXGxiouLk7vvfeezjnnHLVv316jRo3SihUrPCpvy5Ytqrxgu2TJElc/9Nq88847Gj9+vKtLDAAEIoJxAECT7dy5UzfccIMuvvhi/fTTT/r2229lt9u1aNEibd68WRdccIH+7//+r9Hlbdq0SW3btpUkFRUV6eWXX65z2RUrVnilWwwAWIk+4wCAJtmxY4dGjBih008/XcuWLasx/9NPP9W4ceMkSatXr9bIkSMbLPPyyy9Xjx499Mwzz+jQoUPq1auXtm/fXqP1u6ioSN27d9fevXsVHR3tnR0CAAvQMg4A8FhJSYnS09OVn5+vJ598stZlzjrrLPXs2VOSlJGR0ahyv/76a5155pmaMWOGpIqA//3336+x3KeffqrTTjuNQBxAwCMYBwB47KmnntK2bdt03nnnKSkpqc7lOnfuLKniZsuG2Gw27d69W6eeeqquuuoqV2v4I488UmPZd999ly4qAIICwTgAwGPPP/+8JLm6odSlMghvzAA8X375pdLS0hQbG6sTTjhBF154oSRp1apVWrt2rWs5p9Op999/XxMmTGhq9QHAbxCMAwA8kpubq59++kmS1L9//3qXq0xT2Ldv3wbL/fjjj6sE93PnznW1jt96662u6evWrVPXrl1d+c0BIJARjAMAPLJr1y7X844dO9a53Ntvv+1KU3j22WfXW6bD4dCKFSuqtHYPHDhQ559/viTpiy++0PLlyyWRRQVAcCEYBwB4xOFwuJ7bbLZalyksLNSjjz4qSRozZoxSU1PrLXPlypWKiYmpMZLmAw88oPDwcEnSjTfeqIKCAr377rt0UQEQNAjGAQAecQ+s33777VqXufHGG7Vjxw6Fhobq73//e4NlvvTSS7rqqqtqTO/du7euvfZaSVJ2dramTJmiQ4cOMeomgKBBMA4A8Ej37t01fPhwSRWZTl566SWVl5dLqkhFOHXqVNdQ9vPnz6/R2r1q1Srde++9KigokCRt3bpVH3zwgWbOnFnr9u666y5XVpaPPvpIEyZMYNRNAEGDQX8AAB777rvvNGLECB0+fFiSFBERocjISNfw9VFRUXr88cc1e/bsGut26tRJNptNU6ZM0ZVXXqk5c+bo0ksv1T333FPn9pYvX65JkyZJqugzft555/lgrwCg5RGMAwCaZO/evbrvvvv08ccfKzc3V23atFFqaqrOOeccXXvtterWrVut6x1//PGuLCuSNHbsWL3//vtq06ZNvdu77LLLtHz5ch06dIjBfgAEDYJxAECL+ve//61Zs2bpwIEDuuyyy/Too48qIiKiwfXy8/P11FNPae7cuS1QSwBoGQTjAAAAgEW4gRMAAACwCME4AAAAYBGCcQAAAMAiBOMAAACARQjGAQAAAIsQjAMAAAAWIRgHAAAALEIwDgAAAFiEYBwAAACwCME4AAAAYBGCcQAAAMAiBOMAAACARQjGAQAAAIv8P94Ih9CSeliTAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 800x520 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 800x520 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bin_centres, heights, errors = fpt.numerics.re_processing(Ns, estimator=\"naive\", min_bin_size=100)\n",
    "# Apply the delta N formula\n",
    "bin_centres = np.array(bin_centres) - find_cg_time(k_end_scale_later, sigma, N_sim_end_later)\n",
    "\n",
    "plt.errorbar(bin_centres, heights, yerr=errors, fmt=\".\", ms=7, label=\"2D, $\\sigma=$\"+str(sigma),\n",
    "            color=color[0])\n",
    "plt.yscale('log')\n",
    "plt.legend(fontsize=18)\n",
    "plt.xlabel(r'$\\delta \\mathcal{N}$')\n",
    "plt.ylabel(r'$P(\\delta \\mathcal{N})$')\n",
    "plt.title(r\"Gaussian bump, $\\delta \\phi_{\\mathrm{h}}$\")\n",
    "plt.show()\n",
    "plt.clf()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can already see some non-Gassianity!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we want to compare this with the Gaussian prediction. To do this we need to load the power spectrum data in and integrate to find the variance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "sigma_values = np.array([1.0, 0.5, 0.1, 0.01])\n",
    "\n",
    "matching_data = pd.read_csv(\"gaussian_bump_range_of_R_values_at_different_sigma\"+\".csv\",\n",
    "                             index_col=0)\n",
    "\n",
    "N_modes = np.array(matching_data[\"N exit\"])\n",
    "k_raw_values = np.array(matching_data[\"k\"])\n",
    "R_end_values = np.array(matching_data[\"R end\"],  dtype=np.complex64)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We also need a function to do the integration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def analytical_fpt_variance_func(power_spectrum, k_values):\n",
    "    ln_k_values = np.log(k_values)\n",
    "    return trapezoid(power_spectrum/k_values, x=k_values)\n",
    "\n",
    "def power_spectrum_func(k, R):\n",
    "    return (np.abs(R)**2)*(k**3)/(2*np.pi**2)\n",
    "\n",
    "def gaussian_pdf_generator(std, mean=0):\n",
    "    def pdf(x):\n",
    "        expo_term = np.exp(-0.5*((x-mean)/std)**2)\n",
    "        norm = 1/(std*(2*np.pi)**0.5)\n",
    "        return norm*expo_term\n",
    "    return pdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "a_in = 1.\n",
    "aH_interpolation = CubicSpline(N_values, hubble_param_values*a_in*np.exp(N_values-N_sim_start))\n",
    "a_interpolation = CubicSpline(N_values, a_in*np.exp(N_values-N_sim_start))\n",
    "k_values_normed = aH_interpolation(N_modes)/aH_interpolation(N_usr_start)\n",
    "\n",
    "ps_values = power_spectrum_func(k_raw_values, R_end_values)\n",
    "\n",
    "ps_log_interpolation = CubicSpline(N_modes, np.log(ps_values))\n",
    "\n",
    "N_values_integrated = np.linspace(N_sim_start, N_sim_end, 600)\n",
    "\n",
    "k_values_integrated_normed = aH_interpolation(N_values_integrated)/aH_interpolation(N_usr_start)\n",
    "ps_values = np.exp(ps_log_interpolation(N_values_integrated))\n",
    "\n",
    "analytical_fpt_variance = analytical_fpt_variance_func(ps_values, k_values_integrated_normed)\n",
    "analytical_fpt_std = analytical_fpt_variance**0.5\n",
    "gaussian_pdf = gaussian_pdf_generator(analytical_fpt_std, mean=0.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.10104472578966923"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "analytical_fpt_std"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x520 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 800x520 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.errorbar(bin_centres, heights, yerr=errors, fmt=\".\", ms=7, label=\"2D, $\\sigma=$\"+str(sigma),\n",
    "            color=color[0])\n",
    "plt.plot(bin_centres, gaussian_pdf(bin_centres), color=\"k\",\n",
    "         label=\"Gaussian\")\n",
    "plt.yscale('log')\n",
    "plt.legend(fontsize=18)\n",
    "plt.xlabel(r'$\\delta \\mathcal{N}$')\n",
    "plt.ylabel(r'$P(\\delta \\mathcal{N})$')\n",
    "plt.title(r\"Gaussian bump, $\\delta \\phi_{\\mathrm{h}}$\")\n",
    "plt.show()\n",
    "plt.clf()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The non-Gassuianity becomes very clear here!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1D noise\n",
    "Now let's investigate the effect of using a 2D noise. This is the same as the 2D case but the Cython code is changed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</head>\n",
       "<body class=\"cython\">\n",
       "<p><span style=\"border-bottom: solid 1px grey;\">Generated by Cython 3.0.7</span></p>\n",
       "<p>\n",
       "    <span style=\"background-color: #FFFF00\">Yellow lines</span> hint at Python interaction.<br />\n",
       "    Click on a line that starts with a \"<code>+</code>\" to see the C code that Cython generated for it.\n",
       "</p>\n",
       "<div class=\"cython\"><pre class=\"cython line score-0\">&#xA0;<span class=\"\">001</span>: </pre>\n",
       "<pre class=\"cython line score-16\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">002</span>: <span class=\"k\">import</span> <span class=\"nn\">numpy</span> <span class=\"k\">as</span> <span class=\"nn\">np</span></pre>\n",
       "<pre class='cython code score-16 '>  __pyx_t_7 = <span class='pyx_c_api'>__Pyx_ImportDottedModule</span>(__pyx_n_s_numpy, NULL);<span class='error_goto'> if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 2, __pyx_L1_error)</span>\n",
       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_7);\n",
       "  if (<span class='py_c_api'>PyDict_SetItem</span>(__pyx_d, __pyx_n_s_np, __pyx_t_7) &lt; 0) <span class='error_goto'>__PYX_ERR(0, 2, __pyx_L1_error)</span>\n",
       "  <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_7); __pyx_t_7 = 0;\n",
       "/* … */\n",
       "  __pyx_t_7 = <span class='pyx_c_api'>__Pyx_PyDict_NewPresized</span>(0);<span class='error_goto'> if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 2, __pyx_L1_error)</span>\n",
       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_7);\n",
       "  if (<span class='py_c_api'>PyDict_SetItem</span>(__pyx_d, __pyx_n_s_test, __pyx_t_7) &lt; 0) <span class='error_goto'>__PYX_ERR(0, 2, __pyx_L1_error)</span>\n",
       "  <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_7); __pyx_t_7 = 0;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">003</span>: </pre>\n",
       "<pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">004</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">V_0</span> <span class=\"o\">=</span> <span class=\"mf\">7.903587107979402e-11</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_54_cython_magic_29b43f5a1a5ff71efdfd0feb317c267eaae2123d_V_0 = 7.903587107979402e-11;\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">005</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">e</span> <span class=\"o\">=</span> <span class=\"mf\">2.718281828459045</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_54_cython_magic_29b43f5a1a5ff71efdfd0feb317c267eaae2123d_e = 2.718281828459045;\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">006</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">pi_num</span> <span class=\"o\">=</span> <span class=\"mf\">3.141592653589793</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_54_cython_magic_29b43f5a1a5ff71efdfd0feb317c267eaae2123d_pi_num = 3.141592653589793;\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">007</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">sigma_tilde</span> <span class=\"o\">=</span> <span class=\"mf\">1.59</span><span class=\"o\">*</span><span class=\"p\">(</span><span class=\"mf\">10</span><span class=\"o\">**-</span><span class=\"mf\">2</span><span class=\"p\">)</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_54_cython_magic_29b43f5a1a5ff71efdfd0feb317c267eaae2123d_sigma_tilde = (1.59 * pow(10.0, -2.0));\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">008</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">phi_0</span> <span class=\"o\">=</span> <span class=\"mf\">2.18812</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_54_cython_magic_29b43f5a1a5ff71efdfd0feb317c267eaae2123d_phi_0 = 2.18812;\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">009</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">m_squared</span> <span class=\"o\">=</span> <span class=\"mf\">0.25</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_54_cython_magic_29b43f5a1a5ff71efdfd0feb317c267eaae2123d_m_squared = 0.25;\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">010</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">K</span> <span class=\"o\">=</span> <span class=\"mf\">1.17</span><span class=\"o\">*</span><span class=\"p\">(</span><span class=\"mf\">10</span><span class=\"o\">**-</span><span class=\"mf\">3</span><span class=\"p\">)</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_54_cython_magic_29b43f5a1a5ff71efdfd0feb317c267eaae2123d_K = (1.17 * pow(10.0, -3.0));\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">011</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">diff_const_squared</span> <span class=\"o\">=</span> <span class=\"mf\">6.351213422073874e-13</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_54_cython_magic_29b43f5a1a5ff71efdfd0feb317c267eaae2123d_diff_const_squared = 6.351213422073874e-13;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">012</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">phi_end</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">013</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">expo</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">014</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">fraction</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">015</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">fraction3</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">016</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">fraction4</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">017</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">noise_value</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">018</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">bias_value</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">019</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">term1</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">020</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">term2</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">021</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">phi_old</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">022</span>: </pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">023</span>: </pre>\n",
       "<pre class=\"cython line score-2\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">024</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">V</span><span class=\"p\">(</span><span class=\"n\">double</span> <span class=\"n\">phi</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-2 '>static double __pyx_f_54_cython_magic_29b43f5a1a5ff71efdfd0feb317c267eaae2123d_V(double __pyx_v_phi) {\n",
       "  __pyx_t_double_complex __pyx_v_expo;\n",
       "  double __pyx_v_fraction;\n",
       "  double __pyx_r;\n",
       "/* … */\n",
       "  /* function exit code */\n",
       "  __pyx_L1_error:;\n",
       "  <span class='pyx_c_api'>__Pyx_AddTraceback</span>(\"_cython_magic_29b43f5a1a5ff71efdfd0feb317c267eaae2123d.V\", __pyx_clineno, __pyx_lineno, __pyx_filename);\n",
       "  __pyx_r = -1;\n",
       "  __pyx_L0:;\n",
       "  return __pyx_r;\n",
       "}\n",
       "</pre><pre class=\"cython line score-5\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">025</span>:     <span class=\"n\">expo</span> <span class=\"o\">=</span> <span class=\"n\">e</span><span class=\"o\">**</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"p\">((</span><span class=\"n\">phi</span><span class=\"o\">-</span><span class=\"n\">phi_0</span><span class=\"p\">)</span><span class=\"o\">/</span><span class=\"n\">sigma_tilde</span><span class=\"p\">)</span><span class=\"o\">**</span><span class=\"mf\">2</span><span class=\"p\">)</span></pre>\n",
       "<pre class='cython code score-5 '>  __pyx_t_1 = (__pyx_v_phi - __pyx_v_54_cython_magic_29b43f5a1a5ff71efdfd0feb317c267eaae2123d_phi_0);\n",
       "  if (unlikely(__pyx_v_54_cython_magic_29b43f5a1a5ff71efdfd0feb317c267eaae2123d_sigma_tilde == 0)) {\n",
       "    <span class='py_c_api'>PyErr_SetString</span>(PyExc_ZeroDivisionError, \"float division\");\n",
       "    <span class='error_goto'>__PYX_ERR(0, 25, __pyx_L1_error)</span>\n",
       "  }\n",
       "  __pyx_v_expo = __Pyx_c_pow_double(__pyx_t_double_complex_from_parts(__pyx_v_54_cython_magic_29b43f5a1a5ff71efdfd0feb317c267eaae2123d_e, 0), __pyx_t_double_complex_from_parts((-0.5 * pow((__pyx_t_1 / __pyx_v_54_cython_magic_29b43f5a1a5ff71efdfd0feb317c267eaae2123d_sigma_tilde), 2.0)), 0));\n",
       "</pre><pre class=\"cython line score-5\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">026</span>:     <span class=\"n\">fraction</span> <span class=\"o\">=</span> <span class=\"p\">(</span><span class=\"n\">phi</span><span class=\"o\">**</span><span class=\"mf\">2</span><span class=\"p\">)</span><span class=\"o\">/</span><span class=\"p\">(</span><span class=\"n\">m_squared</span> <span class=\"o\">+</span> <span class=\"n\">phi</span><span class=\"o\">**</span><span class=\"mf\">2</span><span class=\"p\">)</span></pre>\n",
       "<pre class='cython code score-5 '>  __pyx_t_1 = pow(__pyx_v_phi, 2.0);\n",
       "  __pyx_t_2 = (__pyx_v_54_cython_magic_29b43f5a1a5ff71efdfd0feb317c267eaae2123d_m_squared + pow(__pyx_v_phi, 2.0));\n",
       "  if (unlikely(__pyx_t_2 == 0)) {\n",
       "    <span class='py_c_api'>PyErr_SetString</span>(PyExc_ZeroDivisionError, \"float division\");\n",
       "    <span class='error_goto'>__PYX_ERR(0, 26, __pyx_L1_error)</span>\n",
       "  }\n",
       "  __pyx_v_fraction = (__pyx_t_1 / __pyx_t_2);\n",
       "</pre><pre class=\"cython line score-7\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">027</span>:     <span class=\"k\">return</span> <span class=\"n\">V_0</span><span class=\"o\">*</span><span class=\"n\">fraction</span><span class=\"o\">*</span><span class=\"p\">(</span><span class=\"mf\">1</span> <span class=\"o\">+</span> <span class=\"n\">K</span><span class=\"o\">*</span><span class=\"n\">expo</span><span class=\"p\">)</span></pre>\n",
       "<pre class='cython code score-7 '>  __pyx_t_2 = <span class='pyx_c_api'>__Pyx_SoftComplexToDouble</span>(__Pyx_c_prod_double(__pyx_t_double_complex_from_parts((__pyx_v_54_cython_magic_29b43f5a1a5ff71efdfd0feb317c267eaae2123d_V_0 * __pyx_v_fraction), 0), __Pyx_c_sum_double(__pyx_t_double_complex_from_parts(1, 0), __Pyx_c_prod_double(__pyx_t_double_complex_from_parts(__pyx_v_54_cython_magic_29b43f5a1a5ff71efdfd0feb317c267eaae2123d_K, 0), __pyx_v_expo))), 1); if (unlikely(__pyx_t_2 == ((double)-1) &amp;&amp; <span class='py_c_api'>PyErr_Occurred</span>())) <span class='error_goto'>__PYX_ERR(0, 27, __pyx_L1_error)</span>\n",
       "  __pyx_r = __pyx_t_2;\n",
       "  goto __pyx_L0;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">028</span>: </pre>\n",
       "<pre class=\"cython line score-2\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">029</span>: <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">V_prime_by_V_cython</span><span class=\"p\">(</span><span class=\"n\">double</span> <span class=\"n\">phi</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-2 '>static double __pyx_f_54_cython_magic_29b43f5a1a5ff71efdfd0feb317c267eaae2123d_V_prime_by_V_cython(double __pyx_v_phi) {\n",
       "  __pyx_t_double_complex __pyx_v_expo;\n",
       "  double __pyx_v_fraction3;\n",
       "  double __pyx_v_fraction4;\n",
       "  double __pyx_v_term1;\n",
       "  __pyx_t_double_complex __pyx_v_term2;\n",
       "  double __pyx_r;\n",
       "/* … */\n",
       "  /* function exit code */\n",
       "  __pyx_L1_error:;\n",
       "  <span class='pyx_c_api'>__Pyx_AddTraceback</span>(\"_cython_magic_29b43f5a1a5ff71efdfd0feb317c267eaae2123d.V_prime_by_V_cython\", __pyx_clineno, __pyx_lineno, __pyx_filename);\n",
       "  __pyx_r = -1;\n",
       "  __pyx_L0:;\n",
       "  return __pyx_r;\n",
       "}\n",
       "</pre><pre class=\"cython line score-5\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">030</span>:     <span class=\"n\">expo</span> <span class=\"o\">=</span> <span class=\"n\">e</span><span class=\"o\">**</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"p\">((</span><span class=\"n\">phi</span><span class=\"o\">-</span><span class=\"n\">phi_0</span><span class=\"p\">)</span><span class=\"o\">/</span><span class=\"n\">sigma_tilde</span><span class=\"p\">)</span><span class=\"o\">**</span><span class=\"mf\">2</span><span class=\"p\">)</span></pre>\n",
       "<pre class='cython code score-5 '>  __pyx_t_1 = (__pyx_v_phi - __pyx_v_54_cython_magic_29b43f5a1a5ff71efdfd0feb317c267eaae2123d_phi_0);\n",
       "  if (unlikely(__pyx_v_54_cython_magic_29b43f5a1a5ff71efdfd0feb317c267eaae2123d_sigma_tilde == 0)) {\n",
       "    <span class='py_c_api'>PyErr_SetString</span>(PyExc_ZeroDivisionError, \"float division\");\n",
       "    <span class='error_goto'>__PYX_ERR(0, 30, __pyx_L1_error)</span>\n",
       "  }\n",
       "  __pyx_v_expo = __Pyx_c_pow_double(__pyx_t_double_complex_from_parts(__pyx_v_54_cython_magic_29b43f5a1a5ff71efdfd0feb317c267eaae2123d_e, 0), __pyx_t_double_complex_from_parts((-0.5 * pow((__pyx_t_1 / __pyx_v_54_cython_magic_29b43f5a1a5ff71efdfd0feb317c267eaae2123d_sigma_tilde), 2.0)), 0));\n",
       "</pre><pre class=\"cython line score-10\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">031</span>:     <span class=\"n\">fraction3</span> <span class=\"o\">=</span> <span class=\"mf\">1</span><span class=\"o\">/</span><span class=\"n\">phi</span> <span class=\"o\">-</span> <span class=\"p\">(</span><span class=\"n\">phi</span><span class=\"p\">)</span><span class=\"o\">/</span><span class=\"p\">(</span><span class=\"n\">m_squared</span> <span class=\"o\">+</span> <span class=\"n\">phi</span><span class=\"o\">**</span><span class=\"mf\">2</span><span class=\"p\">)</span></pre>\n",
       "<pre class='cython code score-10 '>  if (unlikely(__pyx_v_phi == 0)) {\n",
       "    <span class='py_c_api'>PyErr_SetString</span>(PyExc_ZeroDivisionError, \"float division\");\n",
       "    <span class='error_goto'>__PYX_ERR(0, 31, __pyx_L1_error)</span>\n",
       "  }\n",
       "  __pyx_t_1 = (__pyx_v_54_cython_magic_29b43f5a1a5ff71efdfd0feb317c267eaae2123d_m_squared + pow(__pyx_v_phi, 2.0));\n",
       "  if (unlikely(__pyx_t_1 == 0)) {\n",
       "    <span class='py_c_api'>PyErr_SetString</span>(PyExc_ZeroDivisionError, \"float division\");\n",
       "    <span class='error_goto'>__PYX_ERR(0, 31, __pyx_L1_error)</span>\n",
       "  }\n",
       "  __pyx_v_fraction3 = ((1.0 / __pyx_v_phi) - (__pyx_v_phi / __pyx_t_1));\n",
       "</pre><pre class=\"cython line score-5\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">032</span>:     <span class=\"n\">fraction4</span> <span class=\"o\">=</span> <span class=\"o\">-</span><span class=\"p\">(</span><span class=\"n\">phi</span><span class=\"o\">-</span><span class=\"n\">phi_0</span><span class=\"p\">)</span><span class=\"o\">/</span><span class=\"p\">(</span><span class=\"n\">sigma_tilde</span><span class=\"o\">**</span><span class=\"mf\">2</span><span class=\"p\">)</span></pre>\n",
       "<pre class='cython code score-5 '>  __pyx_t_1 = (-(__pyx_v_phi - __pyx_v_54_cython_magic_29b43f5a1a5ff71efdfd0feb317c267eaae2123d_phi_0));\n",
       "  __pyx_t_2 = pow(__pyx_v_54_cython_magic_29b43f5a1a5ff71efdfd0feb317c267eaae2123d_sigma_tilde, 2.0);\n",
       "  if (unlikely(__pyx_t_2 == 0)) {\n",
       "    <span class='py_c_api'>PyErr_SetString</span>(PyExc_ZeroDivisionError, \"float division\");\n",
       "    <span class='error_goto'>__PYX_ERR(0, 32, __pyx_L1_error)</span>\n",
       "  }\n",
       "  __pyx_v_fraction4 = (__pyx_t_1 / __pyx_t_2);\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">033</span>: </pre>\n",
       "<pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">034</span>:     <span class=\"n\">term1</span> <span class=\"o\">=</span> <span class=\"mf\">2</span><span class=\"o\">*</span><span class=\"n\">fraction3</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_term1 = (2.0 * __pyx_v_fraction3);\n",
       "</pre><pre class=\"cython line score-5\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">035</span>:     <span class=\"n\">term2</span> <span class=\"o\">=</span> <span class=\"n\">fraction4</span><span class=\"o\">*</span><span class=\"n\">K</span><span class=\"o\">*</span><span class=\"n\">expo</span><span class=\"o\">/</span><span class=\"p\">(</span><span class=\"mf\">1</span> <span class=\"o\">+</span> <span class=\"n\">K</span><span class=\"o\">*</span><span class=\"n\">expo</span><span class=\"p\">)</span></pre>\n",
       "<pre class='cython code score-5 '>  __pyx_t_3 = __Pyx_c_prod_double(__pyx_t_double_complex_from_parts((__pyx_v_fraction4 * __pyx_v_54_cython_magic_29b43f5a1a5ff71efdfd0feb317c267eaae2123d_K), 0), __pyx_v_expo);\n",
       "  __pyx_t_4 = __Pyx_c_sum_double(__pyx_t_double_complex_from_parts(1, 0), __Pyx_c_prod_double(__pyx_t_double_complex_from_parts(__pyx_v_54_cython_magic_29b43f5a1a5ff71efdfd0feb317c267eaae2123d_K, 0), __pyx_v_expo));\n",
       "  if (unlikely(__Pyx_c_is_zero_double(__pyx_t_4))) {\n",
       "    <span class='py_c_api'>PyErr_SetString</span>(PyExc_ZeroDivisionError, \"float division\");\n",
       "    <span class='error_goto'>__PYX_ERR(0, 35, __pyx_L1_error)</span>\n",
       "  }\n",
       "  __pyx_v_term2 = __Pyx_c_quot_double(__pyx_t_3, __pyx_t_4);\n",
       "</pre><pre class=\"cython line score-7\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">036</span>:     <span class=\"k\">return</span> <span class=\"n\">term1</span> <span class=\"o\">+</span> <span class=\"n\">term2</span></pre>\n",
       "<pre class='cython code score-7 '>  __pyx_t_2 = <span class='pyx_c_api'>__Pyx_SoftComplexToDouble</span>(__Pyx_c_sum_double(__pyx_t_double_complex_from_parts(__pyx_v_term1, 0), __pyx_v_term2), 1); if (unlikely(__pyx_t_2 == ((double)-1) &amp;&amp; <span class='py_c_api'>PyErr_Occurred</span>())) <span class='error_goto'>__PYX_ERR(0, 36, __pyx_L1_error)</span>\n",
       "  __pyx_r = __pyx_t_2;\n",
       "  goto __pyx_L0;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">037</span>: </pre>\n",
       "<pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">038</span>: <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">end_cond</span><span class=\"p\">(</span><span class=\"n\">double</span> <span class=\"n\">phi</span><span class=\"p\">,</span> <span class=\"n\">double</span> <span class=\"n\">pi</span><span class=\"p\">,</span> <span class=\"n\">double</span> <span class=\"n\">N</span><span class=\"p\">,</span> <span class=\"n\">double</span> <span class=\"n\">phi_end</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-0 '>static int __pyx_f_54_cython_magic_29b43f5a1a5ff71efdfd0feb317c267eaae2123d_end_cond(double __pyx_v_phi, CYTHON_UNUSED double __pyx_v_pi, CYTHON_UNUSED double __pyx_v_N, double __pyx_v_phi_end) {\n",
       "  int __pyx_r;\n",
       "/* … */\n",
       "  /* function exit code */\n",
       "  __pyx_L0:;\n",
       "  return __pyx_r;\n",
       "}\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">039</span>:     <span class=\"k\">if</span> <span class=\"n\">phi</span><span class=\"o\">&lt;</span><span class=\"n\">phi_end</span><span class=\"p\">:</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_t_1 = (__pyx_v_phi &lt; __pyx_v_phi_end);\n",
       "  if (__pyx_t_1) {\n",
       "/* … */\n",
       "  }\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">040</span>:         <span class=\"k\">return</span> <span class=\"mf\">1</span></pre>\n",
       "<pre class='cython code score-0 '>    __pyx_r = 1;\n",
       "    goto __pyx_L0;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">041</span>:     <span class=\"k\">else</span><span class=\"p\">:</span></pre>\n",
       "<pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">042</span>:         <span class=\"k\">return</span> <span class=\"mf\">0</span></pre>\n",
       "<pre class='cython code score-0 '>  /*else*/ {\n",
       "    __pyx_r = 0;\n",
       "    goto __pyx_L0;\n",
       "  }\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">043</span>: </pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">044</span>: </pre>\n",
       "<pre class=\"cython line score-6\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">045</span>: <span class=\"k\">cdef</span> <span class=\"kt\">list</span> <span class=\"nf\">update</span><span class=\"p\">(</span><span class=\"n\">double</span> <span class=\"n\">phi</span><span class=\"p\">,</span> <span class=\"n\">double</span> <span class=\"n\">pi</span><span class=\"p\">,</span> <span class=\"n\">double</span> <span class=\"n\">A</span><span class=\"p\">,</span> <span class=\"n\">double</span> <span class=\"n\">N</span><span class=\"p\">,</span> <span class=\"n\">double</span> <span class=\"n\">dN</span><span class=\"p\">,</span> <span class=\"n\">double</span> <span class=\"p\">[:]</span> <span class=\"n\">dW</span><span class=\"p\">,</span> <span class=\"n\">double</span> <span class=\"p\">[:]</span> <span class=\"n\">noise</span><span class=\"p\">,</span></pre>\n",
       "<pre class='cython code score-6 '>static PyObject *__pyx_f_54_cython_magic_29b43f5a1a5ff71efdfd0feb317c267eaae2123d_update(double __pyx_v_phi, double __pyx_v_pi, double __pyx_v_A, CYTHON_UNUSED double __pyx_v_N, double __pyx_v_dN, __Pyx_memviewslice __pyx_v_dW, __Pyx_memviewslice __pyx_v_noise, double __pyx_v_bias_amp) {\n",
       "  double __pyx_v_phi_old;\n",
       "  PyObject *__pyx_r = NULL;\n",
       "/* … */\n",
       "  /* function exit code */\n",
       "  __pyx_L1_error:;\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_7);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_8);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_9);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_10);\n",
       "  <span class='pyx_c_api'>__Pyx_AddTraceback</span>(\"_cython_magic_29b43f5a1a5ff71efdfd0feb317c267eaae2123d.update\", __pyx_clineno, __pyx_lineno, __pyx_filename);\n",
       "  __pyx_r = 0;\n",
       "  __pyx_L0:;\n",
       "  <span class='refnanny'>__Pyx_XGIVEREF</span>(__pyx_r);\n",
       "  <span class='refnanny'>__Pyx_RefNannyFinishContext</span>();\n",
       "  return __pyx_r;\n",
       "}\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">046</span>:                  <span class=\"n\">double</span> <span class=\"n\">bias_amp</span><span class=\"p\">):</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">047</span>:     <span class=\"c\"># Store old phi value to be used in calculating velocity</span></pre>\n",
       "<pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">048</span>:     <span class=\"n\">phi_old</span> <span class=\"o\">=</span> <span class=\"n\">phi</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_phi_old = __pyx_v_phi;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">049</span>: </pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">050</span>:     <span class=\"c\"># Update field position</span></pre>\n",
       "<pre class=\"cython line score-6\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">051</span>:     <span class=\"n\">phi</span> <span class=\"o\">=</span> <span class=\"n\">phi</span> <span class=\"o\">+</span> <span class=\"p\">(</span><span class=\"n\">pi</span> <span class=\"o\">+</span> <span class=\"n\">bias_amp</span><span class=\"o\">*</span><span class=\"n\">noise</span><span class=\"p\">[</span><span class=\"mf\">0</span><span class=\"p\">])</span><span class=\"o\">*</span><span class=\"n\">dN</span> <span class=\"o\">+</span> <span class=\"n\">noise</span><span class=\"p\">[</span><span class=\"mf\">0</span><span class=\"p\">]</span><span class=\"o\">*</span><span class=\"n\">dW</span><span class=\"p\">[</span><span class=\"mf\">0</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-6 '>  __pyx_t_1 = 0;\n",
       "  __pyx_t_2 = -1;\n",
       "  if (__pyx_t_1 &lt; 0) {\n",
       "    __pyx_t_1 += __pyx_v_noise.shape[0];\n",
       "    if (unlikely(__pyx_t_1 &lt; 0)) __pyx_t_2 = 0;\n",
       "  } else if (unlikely(__pyx_t_1 &gt;= __pyx_v_noise.shape[0])) __pyx_t_2 = 0;\n",
       "  if (unlikely(__pyx_t_2 != -1)) {\n",
       "    <span class='pyx_c_api'>__Pyx_RaiseBufferIndexError</span>(__pyx_t_2);\n",
       "    <span class='error_goto'>__PYX_ERR(0, 51, __pyx_L1_error)</span>\n",
       "  }\n",
       "  __pyx_t_3 = 0;\n",
       "  __pyx_t_2 = -1;\n",
       "  if (__pyx_t_3 &lt; 0) {\n",
       "    __pyx_t_3 += __pyx_v_noise.shape[0];\n",
       "    if (unlikely(__pyx_t_3 &lt; 0)) __pyx_t_2 = 0;\n",
       "  } else if (unlikely(__pyx_t_3 &gt;= __pyx_v_noise.shape[0])) __pyx_t_2 = 0;\n",
       "  if (unlikely(__pyx_t_2 != -1)) {\n",
       "    <span class='pyx_c_api'>__Pyx_RaiseBufferIndexError</span>(__pyx_t_2);\n",
       "    <span class='error_goto'>__PYX_ERR(0, 51, __pyx_L1_error)</span>\n",
       "  }\n",
       "  __pyx_t_4 = 0;\n",
       "  __pyx_t_2 = -1;\n",
       "  if (__pyx_t_4 &lt; 0) {\n",
       "    __pyx_t_4 += __pyx_v_dW.shape[0];\n",
       "    if (unlikely(__pyx_t_4 &lt; 0)) __pyx_t_2 = 0;\n",
       "  } else if (unlikely(__pyx_t_4 &gt;= __pyx_v_dW.shape[0])) __pyx_t_2 = 0;\n",
       "  if (unlikely(__pyx_t_2 != -1)) {\n",
       "    <span class='pyx_c_api'>__Pyx_RaiseBufferIndexError</span>(__pyx_t_2);\n",
       "    <span class='error_goto'>__PYX_ERR(0, 51, __pyx_L1_error)</span>\n",
       "  }\n",
       "  __pyx_v_phi = ((__pyx_v_phi + ((__pyx_v_pi + (__pyx_v_bias_amp * (*((double *) ( /* dim=0 */ (__pyx_v_noise.data + __pyx_t_1 * __pyx_v_noise.strides[0]) ))))) * __pyx_v_dN)) + ((*((double *) ( /* dim=0 */ (__pyx_v_noise.data + __pyx_t_3 * __pyx_v_noise.strides[0]) ))) * (*((double *) ( /* dim=0 */ (__pyx_v_dW.data + __pyx_t_4 * __pyx_v_dW.strides[0]) )))));\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">052</span>: </pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">053</span>:     <span class=\"c\"># Update the velocity</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">054</span>:     <span class=\"n\">pi</span> <span class=\"o\">=</span>\\</pre>\n",
       "<pre class=\"cython line score-11\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">055</span>:         <span class=\"n\">pi</span> <span class=\"o\">-</span> <span class=\"p\">(</span><span class=\"mf\">3</span> <span class=\"o\">-</span> <span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"n\">pi</span><span class=\"o\">**</span><span class=\"mf\">2</span><span class=\"p\">)</span><span class=\"o\">*</span><span class=\"p\">(</span><span class=\"n\">pi</span> <span class=\"o\">+</span> <span class=\"n\">V_prime_by_V_cython</span><span class=\"p\">(</span><span class=\"n\">phi_old</span><span class=\"p\">))</span><span class=\"o\">*</span><span class=\"n\">dN</span> <span class=\"o\">+</span> <span class=\"n\">bias_amp</span><span class=\"o\">*</span><span class=\"n\">noise</span><span class=\"p\">[</span><span class=\"mf\">1</span><span class=\"p\">]</span><span class=\"o\">*</span><span class=\"n\">dN</span> <span class=\"o\">+</span> <span class=\"n\">noise</span><span class=\"p\">[</span><span class=\"mf\">1</span><span class=\"p\">]</span><span class=\"o\">*</span><span class=\"n\">dW</span><span class=\"p\">[</span><span class=\"mf\">0</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-11 '>  __pyx_t_5 = __pyx_f_54_cython_magic_29b43f5a1a5ff71efdfd0feb317c267eaae2123d_V_prime_by_V_cython(__pyx_v_phi_old); if (unlikely(__pyx_t_5 == ((double)-1) &amp;&amp; <span class='py_c_api'>PyErr_Occurred</span>())) <span class='error_goto'>__PYX_ERR(0, 55, __pyx_L1_error)</span>\n",
       "  __pyx_t_4 = 1;\n",
       "  __pyx_t_2 = -1;\n",
       "  if (__pyx_t_4 &lt; 0) {\n",
       "    __pyx_t_4 += __pyx_v_noise.shape[0];\n",
       "    if (unlikely(__pyx_t_4 &lt; 0)) __pyx_t_2 = 0;\n",
       "  } else if (unlikely(__pyx_t_4 &gt;= __pyx_v_noise.shape[0])) __pyx_t_2 = 0;\n",
       "  if (unlikely(__pyx_t_2 != -1)) {\n",
       "    <span class='pyx_c_api'>__Pyx_RaiseBufferIndexError</span>(__pyx_t_2);\n",
       "    <span class='error_goto'>__PYX_ERR(0, 55, __pyx_L1_error)</span>\n",
       "  }\n",
       "  __pyx_t_3 = 1;\n",
       "  __pyx_t_2 = -1;\n",
       "  if (__pyx_t_3 &lt; 0) {\n",
       "    __pyx_t_3 += __pyx_v_noise.shape[0];\n",
       "    if (unlikely(__pyx_t_3 &lt; 0)) __pyx_t_2 = 0;\n",
       "  } else if (unlikely(__pyx_t_3 &gt;= __pyx_v_noise.shape[0])) __pyx_t_2 = 0;\n",
       "  if (unlikely(__pyx_t_2 != -1)) {\n",
       "    <span class='pyx_c_api'>__Pyx_RaiseBufferIndexError</span>(__pyx_t_2);\n",
       "    <span class='error_goto'>__PYX_ERR(0, 55, __pyx_L1_error)</span>\n",
       "  }\n",
       "  __pyx_t_1 = 0;\n",
       "  __pyx_t_2 = -1;\n",
       "  if (__pyx_t_1 &lt; 0) {\n",
       "    __pyx_t_1 += __pyx_v_dW.shape[0];\n",
       "    if (unlikely(__pyx_t_1 &lt; 0)) __pyx_t_2 = 0;\n",
       "  } else if (unlikely(__pyx_t_1 &gt;= __pyx_v_dW.shape[0])) __pyx_t_2 = 0;\n",
       "  if (unlikely(__pyx_t_2 != -1)) {\n",
       "    <span class='pyx_c_api'>__Pyx_RaiseBufferIndexError</span>(__pyx_t_2);\n",
       "    <span class='error_goto'>__PYX_ERR(0, 55, __pyx_L1_error)</span>\n",
       "  }\n",
       "  __pyx_v_pi = (((__pyx_v_pi - (((3.0 - (0.5 * pow(__pyx_v_pi, 2.0))) * (__pyx_v_pi + __pyx_t_5)) * __pyx_v_dN)) + ((__pyx_v_bias_amp * (*((double *) ( /* dim=0 */ (__pyx_v_noise.data + __pyx_t_4 * __pyx_v_noise.strides[0]) )))) * __pyx_v_dN)) + ((*((double *) ( /* dim=0 */ (__pyx_v_noise.data + __pyx_t_3 * __pyx_v_noise.strides[0]) ))) * (*((double *) ( /* dim=0 */ (__pyx_v_dW.data + __pyx_t_1 * __pyx_v_dW.strides[0]) )))));\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">056</span>: </pre>\n",
       "<pre class=\"cython line score-2\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">057</span>:     <span class=\"k\">if</span> <span class=\"n\">noise</span><span class=\"p\">[</span><span class=\"mf\">0</span><span class=\"p\">]</span><span class=\"o\">&gt;</span><span class=\"mf\">0</span><span class=\"p\">:</span></pre>\n",
       "<pre class='cython code score-2 '>  __pyx_t_1 = 0;\n",
       "  __pyx_t_2 = -1;\n",
       "  if (__pyx_t_1 &lt; 0) {\n",
       "    __pyx_t_1 += __pyx_v_noise.shape[0];\n",
       "    if (unlikely(__pyx_t_1 &lt; 0)) __pyx_t_2 = 0;\n",
       "  } else if (unlikely(__pyx_t_1 &gt;= __pyx_v_noise.shape[0])) __pyx_t_2 = 0;\n",
       "  if (unlikely(__pyx_t_2 != -1)) {\n",
       "    <span class='pyx_c_api'>__Pyx_RaiseBufferIndexError</span>(__pyx_t_2);\n",
       "    <span class='error_goto'>__PYX_ERR(0, 57, __pyx_L1_error)</span>\n",
       "  }\n",
       "  __pyx_t_6 = ((*((double *) ( /* dim=0 */ (__pyx_v_noise.data + __pyx_t_1 * __pyx_v_noise.strides[0]) ))) &gt; 0.0);\n",
       "  if (__pyx_t_6) {\n",
       "/* … */\n",
       "  }\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">058</span>:         <span class=\"c\"># Calculate the weight. This is the same as the true 1d case with diffusion based bias</span></pre>\n",
       "<pre class=\"cython line score-2\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">059</span>:         <span class=\"n\">A</span> <span class=\"o\">+=</span> <span class=\"n\">bias_amp</span><span class=\"o\">*</span><span class=\"p\">(</span><span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"n\">bias_amp</span><span class=\"o\">*</span><span class=\"n\">dN</span> <span class=\"o\">+</span> <span class=\"n\">dW</span><span class=\"p\">[</span><span class=\"mf\">0</span><span class=\"p\">])</span></pre>\n",
       "<pre class='cython code score-2 '>    __pyx_t_1 = 0;\n",
       "    __pyx_t_2 = -1;\n",
       "    if (__pyx_t_1 &lt; 0) {\n",
       "      __pyx_t_1 += __pyx_v_dW.shape[0];\n",
       "      if (unlikely(__pyx_t_1 &lt; 0)) __pyx_t_2 = 0;\n",
       "    } else if (unlikely(__pyx_t_1 &gt;= __pyx_v_dW.shape[0])) __pyx_t_2 = 0;\n",
       "    if (unlikely(__pyx_t_2 != -1)) {\n",
       "      <span class='pyx_c_api'>__Pyx_RaiseBufferIndexError</span>(__pyx_t_2);\n",
       "      <span class='error_goto'>__PYX_ERR(0, 59, __pyx_L1_error)</span>\n",
       "    }\n",
       "    __pyx_v_A = (__pyx_v_A + (__pyx_v_bias_amp * (((0.5 * __pyx_v_bias_amp) * __pyx_v_dN) + (*((double *) ( /* dim=0 */ (__pyx_v_dW.data + __pyx_t_1 * __pyx_v_dW.strides[0]) ))))));\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">060</span>: </pre>\n",
       "<pre class=\"cython line score-27\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">061</span>:     <span class=\"k\">return</span> <span class=\"p\">[</span><span class=\"n\">phi</span><span class=\"p\">,</span> <span class=\"n\">pi</span><span class=\"p\">,</span> <span class=\"n\">A</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-27 '>  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_r);\n",
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       "  __pyx_r = ((PyObject*)__pyx_t_10);\n",
       "  __pyx_t_10 = 0;\n",
       "  goto __pyx_L0;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">062</span>: </pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">063</span>: </pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">064</span>: <span class=\"c\">#A let&#39;s us calculate the bias w=e^-A is the bias, which propagated along with </span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">065</span>: <span class=\"c\">#the importance sample path.</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">066</span>: <span class=\"c\">#See Eq. (33) of arXiv:nucl-th/9809075v1 for more info</span></pre>\n",
       "<pre class=\"cython line score-6\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">067</span>: <span class=\"k\">cdef</span> <span class=\"kt\">list</span> <span class=\"nf\">simulation_diff_general_end</span><span class=\"p\">(</span><span class=\"n\">double</span> <span class=\"n\">x_in</span><span class=\"p\">,</span> <span class=\"n\">double</span> <span class=\"n\">y_in</span><span class=\"p\">,</span> <span class=\"n\">double</span> <span class=\"n\">t_in</span><span class=\"p\">,</span> <span class=\"n\">double</span> <span class=\"n\">t_f</span><span class=\"p\">,</span> <span class=\"n\">double</span> <span class=\"n\">dt</span><span class=\"p\">,</span></pre>\n",
       "<pre class='cython code score-6 '>static PyObject *__pyx_f_54_cython_magic_29b43f5a1a5ff71efdfd0feb317c267eaae2123d_simulation_diff_general_end(double __pyx_v_x_in, double __pyx_v_y_in, double __pyx_v_t_in, double __pyx_v_t_f, double __pyx_v_dt, double __pyx_v_bias_amp, double __pyx_v_phi_end_in, PyObject *__pyx_v_noise_list, PyObject *__pyx_v_rng) {\n",
       "  double __pyx_v_t;\n",
       "  double __pyx_v_sqrt_dt;\n",
       "  double __pyx_v_x;\n",
       "  double __pyx_v_y;\n",
       "  double __pyx_v_A;\n",
       "  int __pyx_v_i;\n",
       "  int __pyx_v_end_cond_value;\n",
       "  int __pyx_v_len_rand_nums;\n",
       "  int __pyx_v_reduced_step;\n",
       "  int __pyx_v_num_steps;\n",
       "  __Pyx_memviewslice __pyx_v_rand_nums = { 0, 0, { 0 }, { 0 }, { 0 } };\n",
       "  __Pyx_memviewslice __pyx_v_dW = { 0, 0, { 0 }, { 0 }, { 0 } };\n",
       "  __Pyx_memviewslice __pyx_v_noise = { 0, 0, { 0 }, { 0 }, { 0 } };\n",
       "  PyObject *__pyx_r = NULL;\n",
       "/* … */\n",
       "  /* function exit code */\n",
       "  __pyx_L1_error:;\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_1);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_2);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_3);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_4);\n",
       "  __PYX_XCLEAR_MEMVIEW(&amp;__pyx_t_5, 1);\n",
       "  __PYX_XCLEAR_MEMVIEW(&amp;__pyx_t_6, 1);\n",
       "  <span class='pyx_c_api'>__Pyx_AddTraceback</span>(\"_cython_magic_29b43f5a1a5ff71efdfd0feb317c267eaae2123d.simulation_diff_general_end\", __pyx_clineno, __pyx_lineno, __pyx_filename);\n",
       "  __pyx_r = 0;\n",
       "  __pyx_L0:;\n",
       "  __PYX_XCLEAR_MEMVIEW(&amp;__pyx_v_rand_nums, 1);\n",
       "  __PYX_XCLEAR_MEMVIEW(&amp;__pyx_v_dW, 1);\n",
       "  __PYX_XCLEAR_MEMVIEW(&amp;__pyx_v_noise, 1);\n",
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       "  <span class='refnanny'>__Pyx_RefNannyFinishContext</span>();\n",
       "  return __pyx_r;\n",
       "}\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">068</span>:                                       <span class=\"n\">double</span> <span class=\"n\">bias_amp</span><span class=\"p\">,</span> <span class=\"n\">double</span> <span class=\"n\">phi_end_in</span><span class=\"p\">,</span> <span class=\"n\">noise_list</span><span class=\"p\">,</span> <span class=\"n\">rng</span><span class=\"p\">):</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">069</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">t</span><span class=\"p\">,</span> <span class=\"nf\">sqrt_dt</span><span class=\"p\">,</span> <span class=\"nf\">x</span><span class=\"p\">,</span> <span class=\"nf\">y</span><span class=\"p\">,</span> <span class=\"nf\">z</span><span class=\"p\">,</span> <span class=\"nf\">A</span></pre>\n",
       "<pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">070</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">i</span> <span class=\"o\">=</span> <span class=\"mf\">0</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_i = 0;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">071</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">end_cond_value</span></pre>\n",
       "<pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">072</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">len_rand_nums</span> <span class=\"o\">=</span> <span class=\"mf\">1000</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_len_rand_nums = 0x3E8;\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">073</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">reduced_step</span> <span class=\"o\">=</span> <span class=\"mf\">0</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_reduced_step = 0;\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">074</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">num_steps</span> <span class=\"o\">=</span> <span class=\"mf\">0</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_num_steps = 0;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">075</span>: </pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">076</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">double</span> [<span class=\"p\">:,</span> <span class=\"p\">:]</span> <span class=\"n\">rand_nums</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">077</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">double</span> [<span class=\"p\">:]</span> <span class=\"n\">dW</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">078</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">double</span> [<span class=\"p\">:]</span> <span class=\"n\">noise</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">079</span>: </pre>\n",
       "<pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">080</span>:     <span class=\"n\">t</span> <span class=\"o\">=</span> <span class=\"n\">t_in</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_t = __pyx_v_t_in;\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">081</span>:     <span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">x_in</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_x = __pyx_v_x_in;\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">082</span>:     <span class=\"n\">y</span> <span class=\"o\">=</span> <span class=\"n\">y_in</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_y = __pyx_v_y_in;\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">083</span>:     <span class=\"n\">sqrt_dt</span> <span class=\"o\">=</span> <span class=\"n\">dt</span><span class=\"o\">**</span><span class=\"mf\">0.5</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_sqrt_dt = pow(__pyx_v_dt, 0.5);\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">084</span>:     <span class=\"n\">A</span> <span class=\"o\">=</span> <span class=\"mf\">0.0</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_A = 0.0;\n",
       "</pre><pre class=\"cython line score-34\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">085</span>:     <span class=\"n\">rand_nums</span> <span class=\"o\">=</span> <span class=\"n\">rng</span><span class=\"o\">.</span><span class=\"n\">normal</span><span class=\"p\">(</span><span class=\"mf\">0</span><span class=\"p\">,</span> <span class=\"mf\">1</span><span class=\"p\">,</span> <span class=\"n\">size</span><span class=\"o\">=</span><span class=\"p\">(</span><span class=\"mf\">2</span><span class=\"p\">,</span> <span class=\"n\">len_rand_nums</span><span class=\"p\">))</span></pre>\n",
       "<pre class='cython code score-34 '>  __pyx_t_1 = <span class='pyx_c_api'>__Pyx_PyObject_GetAttrStr</span>(__pyx_v_rng, __pyx_n_s_normal);<span class='error_goto'> if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 85, __pyx_L1_error)</span>\n",
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       "  <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_2); __pyx_t_2 = 0;\n",
       "  __pyx_t_5 = <span class='pyx_c_api'>__Pyx_PyObject_to_MemoryviewSlice_dsds_double</span>(__pyx_t_4, PyBUF_WRITABLE);<span class='error_goto'> if (unlikely(!__pyx_t_5.memview)) __PYX_ERR(0, 85, __pyx_L1_error)</span>\n",
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       "  __pyx_t_5.memview = NULL;\n",
       "  __pyx_t_5.data = NULL;\n",
       "/* … */\n",
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       "</pre><pre class=\"cython line score-5\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">086</span>:     <span class=\"n\">dW</span> <span class=\"o\">=</span> <span class=\"n\">rand_nums</span><span class=\"p\">[:,</span> <span class=\"mf\">0</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-5 '>  __pyx_t_6.data = __pyx_v_rand_nums.data;\n",
       "  __pyx_t_6.memview = __pyx_v_rand_nums.memview;\n",
       "  __PYX_INC_MEMVIEW(&amp;__pyx_t_6, 1);\n",
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       "__pyx_t_6.strides[0] = __pyx_v_rand_nums.strides[0];\n",
       "    __pyx_t_6.suboffsets[0] = -1;\n",
       "\n",
       "{\n",
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       "\n",
       "__pyx_v_dW = __pyx_t_6;\n",
       "  __pyx_t_6.memview = NULL;\n",
       "  __pyx_t_6.data = NULL;\n",
       "</pre><pre class=\"cython line score-10\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">087</span>:     <span class=\"n\">noise</span> <span class=\"o\">=</span> <span class=\"n\">noise_list</span><span class=\"p\">[:,</span> <span class=\"mf\">0</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-10 '>  __pyx_t_4 = <span class='pyx_c_api'>__Pyx_PyObject_GetItem</span>(__pyx_v_noise_list, __pyx_tuple__10);<span class='error_goto'> if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 87, __pyx_L1_error)</span>\n",
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       "  __pyx_v_noise = __pyx_t_6;\n",
       "  __pyx_t_6.memview = NULL;\n",
       "  __pyx_t_6.data = NULL;\n",
       "/* … */\n",
       "  __pyx_tuple__10 = <span class='py_c_api'>PyTuple_Pack</span>(2, __pyx_slice__5, __pyx_int_0);<span class='error_goto'> if (unlikely(!__pyx_tuple__10)) __PYX_ERR(0, 87, __pyx_L1_error)</span>\n",
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       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">088</span>: </pre>\n",
       "<pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">089</span>:     <span class=\"k\">while</span> <span class=\"n\">t</span><span class=\"o\">&lt;</span><span class=\"n\">t_f</span><span class=\"p\">:</span></pre>\n",
       "<pre class='cython code score-0 '>  while (1) {\n",
       "    __pyx_t_7 = (__pyx_v_t &lt; __pyx_v_t_f);\n",
       "    if (!__pyx_t_7) break;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">090</span>:         <span class=\"c\"># Scale the step varaince to the dt used</span></pre>\n",
       "<pre class=\"cython line score-4\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">091</span>:         <span class=\"n\">dW</span><span class=\"p\">[</span><span class=\"mf\">0</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"n\">sqrt_dt</span><span class=\"o\">*</span><span class=\"n\">rand_nums</span><span class=\"p\">[</span><span class=\"mf\">0</span><span class=\"p\">,</span> <span class=\"n\">i</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-4 '>    __pyx_t_8 = 0;\n",
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       "</pre><pre class=\"cython line score-4\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">092</span>:         <span class=\"n\">dW</span><span class=\"p\">[</span><span class=\"mf\">1</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"n\">sqrt_dt</span><span class=\"o\">*</span><span class=\"n\">rand_nums</span><span class=\"p\">[</span><span class=\"mf\">1</span><span class=\"p\">,</span> <span class=\"n\">i</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-4 '>    __pyx_t_9 = 1;\n",
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       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">093</span>:         <span class=\"c\"># Find the noise from the list provided</span></pre>\n",
       "<pre class=\"cython line score-28\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">094</span>:         <span class=\"n\">noise</span><span class=\"p\">[</span><span class=\"mf\">0</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"n\">noise_list</span><span class=\"p\">[</span><span class=\"mf\">0</span><span class=\"p\">,</span> <span class=\"n\">num_steps</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-28 '>    __pyx_t_4 = <span class='pyx_c_api'>__Pyx_PyInt_From_int</span>(__pyx_v_num_steps);<span class='error_goto'> if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 94, __pyx_L1_error)</span>\n",
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       "</pre><pre class=\"cython line score-28\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">095</span>:         <span class=\"n\">noise</span><span class=\"p\">[</span><span class=\"mf\">1</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"n\">noise_list</span><span class=\"p\">[</span><span class=\"mf\">1</span><span class=\"p\">,</span> <span class=\"n\">num_steps</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-28 '>    __pyx_t_4 = <span class='pyx_c_api'>__Pyx_PyInt_From_int</span>(__pyx_v_num_steps);<span class='error_goto'> if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 95, __pyx_L1_error)</span>\n",
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       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">096</span>:         <span class=\"c\"># Define the Wiener step, using the pre-drawn random numbers.</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">097</span>:         <span class=\"c\"># Step in x and A simultanioues</span></pre>\n",
       "<pre class=\"cython line score-33\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">098</span>:         <span class=\"p\">[</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">y</span><span class=\"p\">,</span> <span class=\"n\">A</span><span class=\"p\">]</span> <span class=\"o\">=</span>\\</pre>\n",
       "<pre class='cython code score-33 '>    __pyx_t_12 = __pyx_<span class='py_c_api'>PyFloat_AsDouble</span>(__pyx_t_2); if (unlikely((__pyx_t_12 == (double)-1) &amp;&amp; <span class='py_c_api'>PyErr_Occurred</span>())) <span class='error_goto'>__PYX_ERR(0, 98, __pyx_L1_error)</span>\n",
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       "</pre><pre class=\"cython line score-18\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">099</span>:             <span class=\"n\">update</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">y</span><span class=\"p\">,</span> <span class=\"n\">A</span><span class=\"p\">,</span> <span class=\"n\">t</span><span class=\"p\">,</span> <span class=\"n\">dt</span><span class=\"p\">,</span> <span class=\"n\">dW</span><span class=\"p\">,</span> <span class=\"n\">noise</span><span class=\"p\">,</span> <span class=\"n\">bias_amp</span><span class=\"p\">)</span></pre>\n",
       "<pre class='cython code score-18 '>    __pyx_t_4 = __pyx_f_54_cython_magic_29b43f5a1a5ff71efdfd0feb317c267eaae2123d_update(__pyx_v_x, __pyx_v_y, __pyx_v_A, __pyx_v_t, __pyx_v_dt, __pyx_v_dW, __pyx_v_noise, __pyx_v_bias_amp);<span class='error_goto'> if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 99, __pyx_L1_error)</span>\n",
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       "<pre class='cython code score-0 '>    __pyx_v_t = (__pyx_v_t + __pyx_v_dt);\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">101</span>:         <span class=\"n\">i</span> <span class=\"o\">+=</span> <span class=\"mf\">1</span></pre>\n",
       "<pre class='cython code score-0 '>    __pyx_v_i = (__pyx_v_i + 1);\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">102</span>:         <span class=\"n\">num_steps</span> <span class=\"o\">+=</span> <span class=\"mf\">1</span></pre>\n",
       "<pre class='cython code score-0 '>    __pyx_v_num_steps = (__pyx_v_num_steps + 1);\n",
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       "<pre class=\"cython line score-5\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">104</span>:         <span class=\"n\">end_cond_value</span> <span class=\"o\">=</span> <span class=\"n\">end_cond</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">y</span><span class=\"p\">,</span> <span class=\"n\">t</span><span class=\"p\">,</span> <span class=\"n\">phi_end_in</span><span class=\"p\">)</span></pre>\n",
       "<pre class='cython code score-5 '>    __pyx_t_10 = __pyx_f_54_cython_magic_29b43f5a1a5ff71efdfd0feb317c267eaae2123d_end_cond(__pyx_v_x, __pyx_v_y, __pyx_v_t, __pyx_v_phi_end_in); if (unlikely(__pyx_t_10 == ((int)-1) &amp;&amp; <span class='py_c_api'>PyErr_Occurred</span>())) <span class='error_goto'>__PYX_ERR(0, 104, __pyx_L1_error)</span>\n",
       "    __pyx_v_end_cond_value = __pyx_t_10;\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">105</span>:         <span class=\"k\">if</span> <span class=\"n\">end_cond_value</span> <span class=\"o\">==</span> <span class=\"mf\">1</span><span class=\"p\">:</span></pre>\n",
       "<pre class='cython code score-0 '>    __pyx_t_7 = (__pyx_v_end_cond_value == 1);\n",
       "    if (__pyx_t_7) {\n",
       "/* … */\n",
       "    }\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">106</span>:             <span class=\"k\">break</span></pre>\n",
       "<pre class='cython code score-0 '>      goto __pyx_L4_break;\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">107</span>:         <span class=\"k\">elif</span> <span class=\"n\">end_cond_value</span> <span class=\"o\">==</span> <span class=\"o\">-</span><span class=\"mf\">1</span> <span class=\"ow\">and</span> <span class=\"n\">reduced_step</span> <span class=\"o\">==</span> <span class=\"mf\">0</span><span class=\"p\">:</span></pre>\n",
       "<pre class='cython code score-0 '>    __pyx_t_15 = (__pyx_v_end_cond_value == -1L);\n",
       "    if (__pyx_t_15) {\n",
       "    } else {\n",
       "      __pyx_t_7 = __pyx_t_15;\n",
       "      goto __pyx_L6_bool_binop_done;\n",
       "    }\n",
       "    __pyx_t_15 = (__pyx_v_reduced_step == 0);\n",
       "    __pyx_t_7 = __pyx_t_15;\n",
       "    __pyx_L6_bool_binop_done:;\n",
       "    if (__pyx_t_7) {\n",
       "/* … */\n",
       "      goto __pyx_L5;\n",
       "    }\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">108</span>:             <span class=\"n\">dt</span> <span class=\"o\">=</span> <span class=\"n\">dt</span><span class=\"o\">/</span><span class=\"mf\">100</span></pre>\n",
       "<pre class='cython code score-0 '>      __pyx_v_dt = (__pyx_v_dt / 100.0);\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">109</span>:             <span class=\"n\">sqrt_dt</span> <span class=\"o\">=</span> <span class=\"n\">dt</span><span class=\"o\">**</span><span class=\"mf\">0.5</span></pre>\n",
       "<pre class='cython code score-0 '>      __pyx_v_sqrt_dt = pow(__pyx_v_dt, 0.5);\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">110</span>:             <span class=\"n\">reduced_step</span> <span class=\"o\">=</span> <span class=\"mf\">1</span></pre>\n",
       "<pre class='cython code score-0 '>      __pyx_v_reduced_step = 1;\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">111</span>:         <span class=\"k\">elif</span> <span class=\"n\">end_cond_value</span> <span class=\"o\">==</span> <span class=\"mf\">0</span> <span class=\"ow\">and</span> <span class=\"n\">reduced_step</span> <span class=\"o\">==</span> <span class=\"mf\">1</span><span class=\"p\">:</span></pre>\n",
       "<pre class='cython code score-0 '>    __pyx_t_15 = (__pyx_v_end_cond_value == 0);\n",
       "    if (__pyx_t_15) {\n",
       "    } else {\n",
       "      __pyx_t_7 = __pyx_t_15;\n",
       "      goto __pyx_L8_bool_binop_done;\n",
       "    }\n",
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       "    __pyx_L8_bool_binop_done:;\n",
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       "    __pyx_L5:;\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">112</span>:             <span class=\"n\">dt</span> <span class=\"o\">=</span> <span class=\"mf\">100</span><span class=\"o\">*</span><span class=\"n\">dt</span></pre>\n",
       "<pre class='cython code score-0 '>      __pyx_v_dt = (100.0 * __pyx_v_dt);\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">113</span>:             <span class=\"n\">sqrt_dt</span> <span class=\"o\">=</span> <span class=\"n\">dt</span><span class=\"o\">**</span><span class=\"mf\">0.5</span></pre>\n",
       "<pre class='cython code score-0 '>      __pyx_v_sqrt_dt = pow(__pyx_v_dt, 0.5);\n",
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   "source": [
    "%%cython -a\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "cdef double V_0 = 7.903587107979402e-11\n",
    "cdef double e = 2.718281828459045\n",
    "cdef double pi_num = 3.141592653589793\n",
    "cdef double sigma_tilde = 1.59*(10**-2)\n",
    "cdef double phi_0 = 2.18812\n",
    "cdef double m_squared = 0.25\n",
    "cdef double K = 1.17*(10**-3)\n",
    "cdef double diff_const_squared = 6.351213422073874e-13\n",
    "cdef double phi_end\n",
    "cdef double expo\n",
    "cdef double fraction\n",
    "cdef double fraction3\n",
    "cdef double fraction4\n",
    "cdef double noise_value\n",
    "cdef double bias_value\n",
    "cdef double term1\n",
    "cdef double term2\n",
    "cdef double phi_old\n",
    "\n",
    "\n",
    "cdef double V(double phi):\n",
    "    expo = e**(-0.5*((phi-phi_0)/sigma_tilde)**2)\n",
    "    fraction = (phi**2)/(m_squared + phi**2)\n",
    "    return V_0*fraction*(1 + K*expo)\n",
    "\n",
    "cdef double V_prime_by_V_cython(double phi):\n",
    "    expo = e**(-0.5*((phi-phi_0)/sigma_tilde)**2)\n",
    "    fraction3 = 1/phi - (phi)/(m_squared + phi**2)\n",
    "    fraction4 = -(phi-phi_0)/(sigma_tilde**2)\n",
    "    \n",
    "    term1 = 2*fraction3\n",
    "    term2 = fraction4*K*expo/(1 + K*expo)\n",
    "    return term1 + term2\n",
    "    \n",
    "cdef int end_cond(double phi, double pi, double N, double phi_end):\n",
    "    if phi<phi_end:\n",
    "        return 1\n",
    "    else:\n",
    "        return 0\n",
    "\n",
    "\n",
    "cdef list update(double phi, double pi, double A, double N, double dN, double [:] dW, double [:] noise,\n",
    "                 double bias_amp):\n",
    "    # Store old phi value to be used in calculating velocity\n",
    "    phi_old = phi\n",
    "    \n",
    "    # Update field position\n",
    "    phi = phi + (pi + bias_amp*noise[0])*dN + noise[0]*dW[0]\n",
    "\n",
    "    # Update the velocity\n",
    "    pi =\\\n",
    "        pi - (3 - 0.5*pi**2)*(pi + V_prime_by_V_cython(phi_old))*dN + bias_amp*noise[1]*dN + noise[1]*dW[0]\n",
    "\n",
    "    if noise[0]>0:\n",
    "        # Calculate the weight. This is the same as the true 1d case with diffusion based bias\n",
    "        A += bias_amp*(0.5*bias_amp*dN + dW[0])\n",
    "\n",
    "    return [phi, pi, A]\n",
    "\n",
    "\n",
    "#A let's us calculate the bias w=e^-A is the bias, which propagated along with \n",
    "#the importance sample path.\n",
    "#See Eq. (33) of arXiv:nucl-th/9809075v1 for more info\n",
    "cdef list simulation_diff_general_end(double x_in, double y_in, double t_in, double t_f, double dt,\n",
    "                                      double bias_amp, double phi_end_in, noise_list, rng):\n",
    "    cdef double t, sqrt_dt, x, y, z, A\n",
    "    cdef int i = 0\n",
    "    cdef int end_cond_value\n",
    "    cdef int len_rand_nums = 1000\n",
    "    cdef int reduced_step = 0\n",
    "    cdef int num_steps = 0\n",
    "    \n",
    "    cdef double [:, :] rand_nums\n",
    "    cdef double [:] dW\n",
    "    cdef double [:] noise\n",
    "\n",
    "    t = t_in\n",
    "    x = x_in\n",
    "    y = y_in\n",
    "    sqrt_dt = dt**0.5\n",
    "    A = 0.0\n",
    "    rand_nums = rng.normal(0, 1, size=(2, len_rand_nums))\n",
    "    dW = rand_nums[:, 0]\n",
    "    noise = noise_list[:, 0]\n",
    "\n",
    "    while t<t_f:\n",
    "        # Scale the step varaince to the dt used\n",
    "        dW[0] = sqrt_dt*rand_nums[0, i]\n",
    "        dW[1] = sqrt_dt*rand_nums[1, i]\n",
    "        # Find the noise from the list provided\n",
    "        noise[0] = noise_list[0, num_steps]\n",
    "        noise[1] = noise_list[1, num_steps]\n",
    "        # Define the Wiener step, using the pre-drawn random numbers.\n",
    "        # Step in x and A simultanioues\n",
    "        [x, y, A] =\\\n",
    "            update(x, y, A, t, dt, dW, noise, bias_amp)\n",
    "        t += dt\n",
    "        i += 1\n",
    "        num_steps += 1\n",
    "        # Using 1/0 for True/False\n",
    "        end_cond_value = end_cond(x, y, t, phi_end_in)\n",
    "        if end_cond_value == 1:\n",
    "            break\n",
    "        elif end_cond_value == -1 and reduced_step == 0:\n",
    "            dt = dt/100\n",
    "            sqrt_dt = dt**0.5\n",
    "            reduced_step = 1\n",
    "        elif end_cond_value == 0 and reduced_step == 1:\n",
    "            dt = 100*dt\n",
    "            sqrt_dt = dt**0.5\n",
    "            reduced_step = 0\n",
    "        # If all of the random numbers have been used up, need to update them.\n",
    "        # This should still be more efficient than drawing a new random number\n",
    "        # each time.\n",
    "        if i == len_rand_nums:\n",
    "            rand_nums = rng.normal(0, 1, size=(2, len_rand_nums))\n",
    "            i = 0\n",
    "    return [t, e**(-A)]\n",
    "\n",
    "\n",
    "cpdef importance_sampling_simulations_2d_1d_noise(double x_in, double y_in, double t_in, double t_f,\n",
    "                                                double dt, int num_runs, double bias_amp, double phi_end_in,\n",
    "                                                noise_list):\n",
    "    # As this variable is global, I can just redfine it hear\n",
    "    rng = np.random.default_rng()\n",
    "    results =\\\n",
    "        [simulation_diff_general_end(x_in, y_in, t_in, t_f, dt, bias_amp, phi_end_in, noise_list, rng)\n",
    "         for i in range(num_runs)]\n",
    "\n",
    "    ts, ws = [[results[i][j] for i in range(num_runs)] for j in range(2)]\n",
    "    return ts, ws"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_func_full_1D(N_exit, N_start, bias_amp, num_runs, noise_matrix, sigma, phi_in_post,\n",
    "                                phi_deriv_in_post, phi_end, extra_label=None):\n",
    "\n",
    "    start = timer()\n",
    "    num_runs_per_core = int(num_runs/mp.cpu_count())\n",
    "\n",
    "    # Using multiprocessing\n",
    "    def multi_processing_func(x_in, y_in, t_i, t_f, dt, num_runs, bias_amp, phi_end, noise_matrix, queue_efolds,\n",
    "                              queue_ws):\n",
    "        results =\\\n",
    "            importance_sampling_simulations_2d_1d_noise(x_in, y_in, t_i, t_f, dt, num_runs, bias_amp, phi_end,\n",
    "                                                      noise_matrix)\n",
    "        fpt_values = np.array(results[0][:])\n",
    "        ws = np.array(results[1][:])\n",
    "        queue_efolds.put(fpt_values)\n",
    "        queue_ws.put(ws)\n",
    "    queue_efolds = Queue()\n",
    "    queue_ws = Queue()\n",
    "    cores = int(mp.cpu_count()/1)\n",
    "\n",
    "    print('Number of cores used: '+str(cores))\n",
    "    processes = [Process(target=multi_processing_func,\n",
    "                         args=(phi_in_post, phi_deriv_in_post, N_start, 80., dN, num_runs_per_core, bias_amp,\n",
    "                               phi_end, noise_matrix, queue_efolds, queue_ws))\n",
    "                 for k in range(cores)]\n",
    "\n",
    "    for p in processes:\n",
    "        p.start()\n",
    "\n",
    "    # More efficient to work with numpy arrays\n",
    "    fpt_array = np.array([queue_efolds.get() for p in processes])\n",
    "    ws_array = np.array([queue_ws.get() for p in processes])\n",
    "\n",
    "    end = timer()\n",
    "    print(f'The simulations took: {end - start} seconds')\n",
    "\n",
    "    # Combine into columns into 1\n",
    "    fpt_values = fpt_array.flatten()\n",
    "    w_values = ws_array.flatten()\n",
    "\n",
    "    # Sort in order of increasing Ns\n",
    "    sort_idx = np.argsort(fpt_values)\n",
    "    Ns = fpt_values[sort_idx]\n",
    "    ws = w_values[sort_idx]\n",
    "    if extra_label != None:\n",
    "        extra_label = \"_Gaussian_bump_sigma_\"+str(sigma)+\"_scale_exited\"+str(round(N_exit, 5))\\\n",
    "            + \"_1D_noise_\" + extra_label\n",
    "    else:\n",
    "        extra_label = \"_Gaussian_bump_sigma_\"+str(sigma)+\"_scale_exited\"+str(round(N_exit, 5))\\\n",
    "        +\"_1D_noise\"\n",
    "\n",
    "    fpt.numerics.save_data_to_file(Ns, ws, round(phi_in_post, 5), num_runs, bias_amp,\n",
    "                      extra_label=extra_label)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we want to show the peak of the distribution is indepdent of the choice of $\\sigma$, we shall use a for loop to load in the required data and run many simulations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of cores used: 8\n",
      "The simulations took: 492.5769501320319 seconds\n",
      "Saved data to file IS_data_x_in_2.2_iterations_100000_bias_0.0_Gaussian_bump_sigma_1.0_scale_exited31.13832_1D_noise_bessel.csv\n",
      "Number of cores used: 8\n",
      "The simulations took: 481.7824220940238 seconds\n",
      "Saved data to file IS_data_x_in_2.2_iterations_100000_bias_0.0_Gaussian_bump_sigma_0.5_scale_exited31.13832_1D_noise_bessel.csv\n",
      "Number of cores used: 8\n",
      "The simulations took: 478.98700872890186 seconds\n",
      "Saved data to file IS_data_x_in_2.2_iterations_100000_bias_0.0_Gaussian_bump_sigma_0.1_scale_exited31.13832_1D_noise_bessel.csv\n",
      "Number of cores used: 8\n",
      "The simulations took: 479.3973133689724 seconds\n",
      "Saved data to file IS_data_x_in_2.2_iterations_100000_bias_0.0_Gaussian_bump_sigma_0.01_scale_exited31.13832_1D_noise_bessel.csv\n"
     ]
    }
   ],
   "source": [
    "sigma_values = np.array([1.0, 0.5, 0.1, 0.01])\n",
    "\n",
    "num_runs = 10**5\n",
    "\n",
    "bias_amp = 0.0\n",
    "\n",
    "for sigma_index in range(len(sigma_values)):\n",
    "    sigma = sigma_values[sigma_index]\n",
    "\n",
    "    noise_data = pd.read_csv(\"gaussian_bump_noise_curves_Bessel_matched_sigma_\"+str(sigma)+\"_1D.csv\",\n",
    "                                 index_col=0)\n",
    "\n",
    "    N_cg_values = np.array(noise_data[\"N\"])\n",
    "\n",
    "    noise_matrix_array = np.zeros((2, len(N_cg_values)))\n",
    "\n",
    "    noise_matrix_array[0, :] = np.array(noise_data[\"phi-phi noise\"])\n",
    "    noise_matrix_array[1, :] = np.array(noise_data[\"pi-pi noise\"])\n",
    "\n",
    "    # Need to add the zeros such there is enough noise to reach the end of the simulation\n",
    "    noise_matrix_array_with_zeros = np.zeros((2, len(noise_matrix_array[0,:])+int(4/dN)))\n",
    "\n",
    "    noise_matrix_array_with_zeros[:, :len(noise_matrix_array[0,:])] = noise_matrix_array\n",
    "    # Now need to find the correct start position and end value\n",
    "\n",
    "    aH_interpolation = CubicSpline(N_values, hubble_param_values*a_in*np.exp(N_values-N_sim_start))\n",
    "\n",
    "    N_start_sigma_exit = find_cg_time(aH_interpolation(N_sim_start), sigma, N_sim_start)\n",
    "    N_end_sigma_exit = find_cg_time(aH_interpolation(N_sim_end), sigma, N_sim_end)\n",
    "\n",
    "    # Scales at the start and end\n",
    "    k_in_scale = aH_interpolation(N_sim_start)\n",
    "    k_end_scale = aH_interpolation(N_sim_end)\n",
    "\n",
    "    # This returns an array, so need to convert to a float\n",
    "    phi_in = float(phi_with_scale_interpolation(k_in_scale/sigma))\n",
    "    phi_deriv_in = float(phi_diff_with_scale_interpolation(k_in_scale/sigma))\n",
    "\n",
    "    # end value\n",
    "    k_end_scale_later = aH_interpolation(N_sim_end_later)\n",
    "    N_sim_end_later_sigma_exit = find_cg_time(aH_interpolation(N_sim_end_later), sigma, N_sim_end_later)\n",
    "    phi_end = float(phi_with_scale_interpolation(k_end_scale_later/sigma))\n",
    "\n",
    "    run_func_full_1D(N_sim_start, N_start_sigma_exit, bias_amp, num_runs, noise_matrix_array_with_zeros, sigma,\n",
    "                                  phi_in, phi_deriv_in, phi_end, extra_label=\"bessel\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's process this data and compare it against the 2D case and the Gaussian prediction. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "sigma = 0.01\n",
    "\n",
    "raw_data = pd.read_csv(\"IS_data_x_in_2.2_iterations_100000_bias_0.0_Gaussian_bump_sigma_0.01_scale_exited\"+\n",
    "                       \"31.13832_2D_noise_bessel.csv\", index_col=0)\n",
    "\n",
    "# Easier to work with NumPy arrays\n",
    "Ns = np.array(raw_data['FPTs'])\n",
    "\n",
    "bin_centres_2D, heights_2D, errors_2D = fpt.numerics.re_processing(Ns, estimator=\"naive\", min_bin_size=100)\n",
    "# Apply the delta N formula\n",
    "bin_centres_2D = np.array(bin_centres_2D) - find_cg_time(k_end_scale_later, sigma, N_sim_end_later)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x520 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 800x520 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.errorbar(bin_centres_2D, heights_2D, yerr=errors_2D, fmt=\".\", ms=7, label=\"2D, $\\sigma=$\"+str(sigma),\n",
    "            color=color[0])\n",
    "plt.plot(bin_centres_2D, gaussian_pdf(bin_centres_2D), color=\"k\",\n",
    "         label=\"Gaussian\")\n",
    "\n",
    "# Now let's process and plot the 1D data\n",
    "for j in range(len(sigma_values)):\n",
    "    sigma = sigma_values[j]\n",
    "    raw_data = pd.read_csv(\"IS_data_x_in_2.2_iterations_100000_bias_0.0_Gaussian_bump_sigma_\"+str(sigma)+\n",
    "                           \"_scale_exited31.13832_1D_noise_bessel.csv\", index_col=0)\n",
    "\n",
    "    # Easier to work with NumPy arrays\n",
    "    Ns = np.array(raw_data['FPTs'])\n",
    "\n",
    "    bin_centres, heights, errors = fpt.numerics.re_processing(Ns, estimator=\"naive\", min_bin_size=100)\n",
    "    # Apply the delta N formula\n",
    "    bin_centres = np.array(bin_centres) - find_cg_time(k_end_scale_later, sigma, N_sim_end_later)\n",
    "\n",
    "    plt.errorbar(bin_centres, heights, yerr=errors, fmt=\".\", ms=7, label=\"1D, $\\sigma=$\"+str(sigma),\n",
    "                color=color[j+1])\n",
    "    \n",
    "plt.yscale('log')\n",
    "plt.legend(fontsize=18)\n",
    "plt.xlabel(r'$\\delta \\mathcal{N}$')\n",
    "plt.ylabel(r'$P(\\delta \\mathcal{N})$')\n",
    "plt.title(r\"Gaussian bump, $\\delta \\phi_{\\mathrm{h}}$\")\n",
    "plt.show()\n",
    "plt.clf()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Clearly all of the data sets are consistent!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}