{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "ad6b13cb01007316fa509551e4c8b998",
     "grade": false,
     "grade_id": "cell-98f724ece1aacb67",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "# CDS: Numerical Methods -- Final Assignment\n",
    "\n",
    "- See lecture notes and documentation on Brightspace for Python and Jupyter basics. If you are stuck, try to google or get in touch via Discord.\n",
    "\n",
    "- Solutions must be submitted <font color=red>**individually**</font> via the Jupyter Hub until <font color=red>**Monday, April 4th, 23:59**</font>.\n",
    "\n",
    "- Make sure you fill in any place that says `YOUR CODE HERE` or \"YOUR ANSWER HERE\".\n",
    "\n",
    "- Remember to document your source codes (docstrings, comments where necessary) and to write it as clear as possible.\n",
    "\n",
    "- Do not forget to fully annotate all of your plots.\n",
    "\n",
    "## Submission\n",
    "\n",
    "1. make sure everything runs as expected\n",
    "2. **restart the kernel** (in the menubar, select Kernel$\\rightarrow$Restart)\n",
    "3. **run all cells** (in the menubar, select Cell$\\rightarrow$Run All)\n",
    "4. Check all outputs (Out[\\*]) for errors and **resolve them if necessary**\n",
    "5. submit your solutions  **in time (before the deadline)**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "23a115c4a147aab2185c76637a509f7f",
     "grade": false,
     "grade_id": "cell-fd297f265de59887",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "## Tight-Binding Propagation Method Module\n",
    "\n",
    "### Tight-Binding Theory\n",
    "\n",
    "Solid state theory aims to describe crystalline structures defined by periodic arrangements of atomic positions $\\vec{R}_i$ with $i= 1 \\dots n$. To model the electronic properties of such a structure, we can use the so-called tight-binding method. Here one assumes that the problem for a single atom described by the Hamiltonian $H_{at}(\\vec{r})$ has already been solved, so that the atomic wave functions $\\phi_m(\\vec{r})$ are known. The Hamiltonian of the crystalline structure is then constructed from these atomic Hamiltonians as follows \n",
    "\n",
    "\\begin{align*}\n",
    "    H(\\vec{r}) = \\sum_{i} H_{at}(\\vec{r} - \\vec{R}_i) + \\Delta V(\\vec{r}),\n",
    "\\end{align*}\n",
    "\n",
    "where $\\Delta V(\\vec{r})$ describes the changes to the atomic potentials due to the periodic arrangement. Solutions to the time-dependent Schrödinger equation $\\psi_n(\\vec{r})$ can then be approximated by linear combinations of the atomic orbitals, i.e. \n",
    "\n",
    "\\begin{align*}\n",
    "    \\psi_m(\\vec{r}) = \\sum_{i} \\, c_{i,m} \\, \\phi_m(\\vec{r}-\\vec{R}_i). \n",
    "\\end{align*}\n",
    "\n",
    "Thus, our task is to find the coefficients $c_{i,m}$, which are the eigenfunctions of the tight-binding Hamiltonian $H_{tb}$. In the basis of the atomic orbitals $H_{tb}$ is an $n \\times n$ matrix which describes the \"hopping\" of an electron from one atomic position to the other. In this description the electrons are assumed to be tightly bound to the atomic positions, hence the name of the approach. In summary, we have reduced our original problem $H(\\vec{r})$, described in a continuous space $\\vec{r}$, to a strongly discretized problem $H_{tb}$ in the space of lattice coordinates $\\vec{R}_i$.\n",
    "\n",
    "### Propagation Method\n",
    "\t\n",
    "While this reduction already helps a lot, full diagonalizations of the tight-binding matrix is still not feasible if we need to describe realistic structures with thousands of atoms. For this case we like to have a method which allows us to study the electronic properties, without the need of fully diagonalizing the tight-binding matrix. The tight-biding propagation method allows for exactly this. By analyzing the propagation of an initial electronic state through the crystalline structure we also have access to the full eigenspectrum of $H_{tb}$, without explicit diagonalization.\n",
    "\t\n",
    "### Your Goal\n",
    "    \n",
    "In the following you will setup the tight-binding Hamiltonian for a one-dimensional chain of atoms and numerically study its properties using exact diagonalization. Then you will compare it to the results obtained using the tight-binding propagation method. You will need some of the algorithms which you have implemented in the weekly assignments before. Additionally, you will need to implement a few new algorithms, which we have discussed in the last lecture. In principle there will be no need to use Numpy or Scipy (except for Numpy's array handling and a few other exceptions). However, if you encounter any problems with your own implementations of specific functionalities, you can use the Numpy and Scipy alternatives. Therefore you should be able to perform all of the following tasks in any case.\n",
    "\n",
    "Let us start by importing the necessary packages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "5d73a1e28cac71eb63db02e72960f030",
     "grade": true,
     "grade_id": "cell-9a7b93b917f8bfed",
     "locked": false,
     "points": 0,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "46edf5bfda2392bd3743329097a4e7ae",
     "grade": false,
     "grade_id": "cell-0f4a00fe587d193a",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "## Step 1: Crystal Lattice\n",
    "\n",
    "### Task 1.1 [3 points]\n",
    "\n",
    "In the following exercises the atomic positions of the 1D crystal lattice will be fixed to $\\vec{R}_i = x_i = i a$, with $i = 0 \\dots n-1$ and $a$ being the lattice constant.\n",
    "\n",
    "Write a simple Python function that takes the chain length $n$ as an argument and returns the atomic positions $x_i$. Set $a = 1$ for all the following exercises."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "bad6e1d563be71de711926b41649c875",
     "grade": true,
     "grade_id": "cell-65a97e8f9f981da1",
     "locked": false,
     "points": 3,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "def atomic_positions(n, a=1):\n",
    "    \"\"\"\n",
    "    Creates an array of atomic position in a 1D crystal lattice\n",
    "    for lattice constant a having default value a = 1.\n",
    "    \n",
    "    Args:\n",
    "        n: number of atoms in the 1D lattice string\n",
    "        a: numerical value for the lattice constant\n",
    "\n",
    "    Returns:\n",
    "        A 1D array of atomic positions.\n",
    "    \"\"\"\n",
    "    \n",
    "    return np.arange(n)*a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "684ad7f7808a1d5b4360a0acb4e52921",
     "grade": false,
     "grade_id": "cell-a61043ba1148856d",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "## Step 2: Atomic Basis Functions\n",
    "\n",
    "Our atomic basis functions will be Gaussians of the form\n",
    "$$\n",
    "\\large\n",
    "\\phi(x, \\mu, \\sigma) = \\frac{1}{\\pi^{1/4} \\sigma^{1/2}} e^{-\\frac{1}{2} \\left(\\frac{x-\\mu}{\\sigma}\\right)^2},\n",
    "$$\n",
    "\twhere $\\mu$ is their localization position and $\\sigma$ their broadenings. We also choose to have just one orbital per atom so that we can drop the index $m$ from now on. \n",
    "\t\n",
    "### Task 2.1 [4 points]\n",
    "Implement a Python function which calculates $\\phi(x, \\mu, \\sigma)$ for a whole array of arbitrary $x$, centered at given $\\mu$ with a given broadening $\\sigma$.\n",
    "\n",
    "Plot all the atomic basis functions for a chain with $n = 10$ atoms, using $\\sigma = 0.25$. I.e. plot $\\phi(x, x_i, \\sigma)$ vs $x$, for all atomic positions $x_i$ in the chain."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "2ad9cc4c03612d5b9bba4824cff364cb",
     "grade": true,
     "grade_id": "cell-4689e172e70a4762",
     "locked": false,
     "points": 4,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def atomic_basis(x, mu, sigma, outer=False):\n",
    "    \"\"\"\n",
    "    Calculates the atomic basis functions for the 1D chain of atoms.\n",
    "    \n",
    "    Args:\n",
    "        x:     array of positions to calculate the wavefunction at\n",
    "        mu:    atomic position(s) to center Gaussian wavefunction at\n",
    "        sigma: broadening constant for Gaussian function(s)\n",
    "        outer: if mu is an array: whether to calculate the atomic basis\n",
    "               on a len(x) by len(mu) grid instead of the pairs x[i]\n",
    "               and mu[i]\n",
    "\n",
    "    Returns:\n",
    "        An array of values for the wavefunction over the positions\n",
    "        as given by x with shape len(x) by len(mu) if outer is False\n",
    "    \"\"\"\n",
    "    \n",
    "    if outer:\n",
    "        return np.pi**(-1/4)*sigma**(-1/2)*np.exp(-1/2*(np.subtract.outer(x, mu)/sigma)**2)\n",
    "    \n",
    "    return np.pi**(-1/4)*sigma**(-1/2)*np.exp(-1/2*((x - mu)/sigma)**2)\n",
    "\n",
    "n = 10\n",
    "sigma = .25\n",
    "x = np.linspace(-2, 12, 1000)\n",
    "\n",
    "plt.figure()\n",
    "plt.xlabel(\"$x$\")\n",
    "plt.ylabel(\"$\\phi$\")\n",
    "\n",
    "for mu in atomic_positions(n):\n",
    "    plt.plot(x, atomic_basis(x, mu, sigma), label=\"n = \" + str(mu))\n",
    "\n",
    "plt.legend()\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10000, 2)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.linspace(-1, 1, 10000)\n",
    "mu = np.array([1,2])\n",
    "atomic_basis(x, mu, .25, True).shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "e1c7774260f02916e34521c6236638f4",
     "grade": false,
     "grade_id": "cell-e5c9315357a401f9",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "### Task 2.2 [6 points]\n",
    "Implement a Python function to calculate numerical integrals (using for example the composite trapezoid or Simpson rule). This one should be general enough to calculate integrals $\\int_a^b f(x) dx$ for arbitrary functions $f(x)$, as you will need it for other tasks as well.\n",
    "\n",
    "Implement a simple unit test for your integration function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "aecc6d50a1ffd4e4bfbfe3573847edf8",
     "grade": true,
     "grade_id": "cell-d851197b213e5d2d",
     "locked": false,
     "points": 3,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "def integrate(yk, x):\n",
    "    \"\"\"\n",
    "    Numerically integrates function yk over [x[0], x[-1]] using Simpson's 3/8\n",
    "    rule over the grid provided by x.\n",
    "    \n",
    "    Args:\n",
    "        yk: function of one numerical argument that returns a numeric\n",
    "            or an array of function values such that x[i] corresponds to yk[i]\n",
    "        x:  array of numerics as argument to yk\n",
    "\n",
    "    Returns:\n",
    "        A numeric value for the quadrature of yk over x with error\n",
    "        of order \n",
    "    \"\"\"\n",
    "    \n",
    "    # If yk is callable, we use it to determine the function values\n",
    "    # over array x.\n",
    "    if callable(yk):\n",
    "        yk = yk(x)\n",
    "    \n",
    "    # The distance h_i = x[i + 1] - x[i] is not necessarily constant. The choice of\n",
    "    # partitioning of the interval is subject to mathematical considerations I will\n",
    "    # not go into.\n",
    "    h = x[1:] - x[:-1]\n",
    "    \n",
    "    integral = 0\n",
    "    integral += 3/8*(x[1] - x[0])*yk[0]\n",
    "    integral += 9/8*h[1::3]@yk[1:-1:3]\n",
    "    integral += 9/8*h[2::3]@yk[2:-1:3]\n",
    "    integral += 6/8*h[ ::3]@yk[ :-1:3]\n",
    "    integral += 3/8*(x[-1] - x[-2])*yk[-1]\n",
    "    return integral"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "6ab06c87cf65c73463ed243e46d63b3d",
     "grade": true,
     "grade_id": "cell-59912b2862fbce5a",
     "locked": false,
     "points": 3,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "def test_integrate():\n",
    "    # Test integral 1 of f with F its primitive with integration constant 0\n",
    "    f = lambda x: x**2\n",
    "    F = lambda x: x**3/3\n",
    "    x = np.logspace(0, 3, 1000000)\n",
    "    assert np.isclose(integrate(f, x), F(x[-1]) - F(x[0]))\n",
    "    \n",
    "    # Test integral 2 of f with F its primitive with integration constant 0\n",
    "    f = lambda x: np.sin(2*x)/(2 + np.cos(2*x))\n",
    "    F = lambda x: -.5*np.log(np.cos(2*x) + 2)\n",
    "    x = np.linspace(0, 10, 1000)\n",
    "    assert np.isclose(integrate(f, x), F(x[-1]) - F(x[0]))\n",
    "    \n",
    "test_integrate()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "8c1413a8a11006398e962e8c803ae001",
     "grade": false,
     "grade_id": "cell-86005829da536b5b",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "### Task 2.3 [2 points]\n",
    "Use your Python integration function to check the orthogonality of the Gaussian basis functions by verifying the following condition $$\\delta_{ij} = \\int_{-\\infty}^{+\\infty} \\phi(x, x_i, \\sigma) \\, \\phi(x, x_j, \\sigma) \\, dx,$$ where $\\delta_{ii} \\approx 1$ and $\\delta_{ij} \\approx 0$ for $\\sigma = 0.25$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "4751becb5d3cb7663536a0624b3d9c54",
     "grade": true,
     "grade_id": "cell-8a6a8db84dcef484",
     "locked": false,
     "points": 2,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "delta_00 = 1.00000   (self)\n",
      "delta_01 = 0.01832   (nearest neighbours)\n",
      "delta_02 = 0.00000\n",
      "delta_03 = 0.00000\n",
      "delta_04 = 0.00000\n",
      "delta_05 = 0.00000\n",
      "delta_06 = 0.00000\n",
      "delta_07 = 0.00000\n",
      "delta_08 = 0.00000\n",
      "delta_09 = 0.00000\n",
      "delta_10 = 0.01832   (nearest neighbours)\n",
      "delta_11 = 1.00000   (self)\n",
      "delta_12 = 0.01832   (nearest neighbours)\n",
      "delta_13 = 0.00000\n",
      "delta_14 = 0.00000\n",
      "delta_15 = 0.00000\n",
      "delta_16 = 0.00000\n",
      "delta_17 = 0.00000\n",
      "delta_18 = 0.00000\n",
      "delta_19 = 0.00000\n",
      "delta_20 = 0.00000\n",
      "delta_21 = 0.01832   (nearest neighbours)\n",
      "delta_22 = 1.00000   (self)\n",
      "delta_23 = 0.01832   (nearest neighbours)\n",
      "delta_24 = 0.00000\n",
      "delta_25 = 0.00000\n",
      "delta_26 = 0.00000\n",
      "delta_27 = 0.00000\n",
      "delta_28 = 0.00000\n",
      "delta_29 = 0.00000\n",
      "delta_30 = 0.00000\n",
      "delta_31 = 0.00000\n",
      "delta_32 = 0.01832   (nearest neighbours)\n",
      "delta_33 = 1.00000   (self)\n",
      "delta_34 = 0.01832   (nearest neighbours)\n",
      "delta_35 = 0.00000\n",
      "delta_36 = 0.00000\n",
      "delta_37 = 0.00000\n",
      "delta_38 = 0.00000\n",
      "delta_39 = 0.00000\n",
      "delta_40 = 0.00000\n",
      "delta_41 = 0.00000\n",
      "delta_42 = 0.00000\n",
      "delta_43 = 0.01832   (nearest neighbours)\n",
      "delta_44 = 1.00000   (self)\n",
      "delta_45 = 0.01832   (nearest neighbours)\n",
      "delta_46 = 0.00000\n",
      "delta_47 = 0.00000\n",
      "delta_48 = 0.00000\n",
      "delta_49 = 0.00000\n",
      "delta_50 = 0.00000\n",
      "delta_51 = 0.00000\n",
      "delta_52 = 0.00000\n",
      "delta_53 = 0.00000\n",
      "delta_54 = 0.01832   (nearest neighbours)\n",
      "delta_55 = 1.00000   (self)\n",
      "delta_56 = 0.01832   (nearest neighbours)\n",
      "delta_57 = 0.00000\n",
      "delta_58 = 0.00000\n",
      "delta_59 = 0.00000\n",
      "delta_60 = 0.00000\n",
      "delta_61 = 0.00000\n",
      "delta_62 = 0.00000\n",
      "delta_63 = 0.00000\n",
      "delta_64 = 0.00000\n",
      "delta_65 = 0.01832   (nearest neighbours)\n",
      "delta_66 = 1.00000   (self)\n",
      "delta_67 = 0.01832   (nearest neighbours)\n",
      "delta_68 = 0.00000\n",
      "delta_69 = 0.00000\n",
      "delta_70 = 0.00000\n",
      "delta_71 = 0.00000\n",
      "delta_72 = 0.00000\n",
      "delta_73 = 0.00000\n",
      "delta_74 = 0.00000\n",
      "delta_75 = 0.00000\n",
      "delta_76 = 0.01832   (nearest neighbours)\n",
      "delta_77 = 1.00000   (self)\n",
      "delta_78 = 0.01832   (nearest neighbours)\n",
      "delta_79 = 0.00000\n",
      "delta_80 = 0.00000\n",
      "delta_81 = 0.00000\n",
      "delta_82 = 0.00000\n",
      "delta_83 = 0.00000\n",
      "delta_84 = 0.00000\n",
      "delta_85 = 0.00000\n",
      "delta_86 = 0.00000\n",
      "delta_87 = 0.01832   (nearest neighbours)\n",
      "delta_88 = 1.00000   (self)\n",
      "delta_89 = 0.01832   (nearest neighbours)\n",
      "delta_90 = 0.00000\n",
      "delta_91 = 0.00000\n",
      "delta_92 = 0.00000\n",
      "delta_93 = 0.00000\n",
      "delta_94 = 0.00000\n",
      "delta_95 = 0.00000\n",
      "delta_96 = 0.00000\n",
      "delta_97 = 0.00000\n",
      "delta_98 = 0.01832   (nearest neighbours)\n",
      "delta_99 = 1.00000   (self)\n"
     ]
    }
   ],
   "source": [
    "n = 10\n",
    "sigma = .25\n",
    "\n",
    "positions = atomic_positions(n)\n",
    "infty = 10000\n",
    "x = np.linspace(-infty, infty, 1000000)\n",
    "\n",
    "def ijlabel(i, j):\n",
    "    \"\"\"\n",
    "    Returns a string label describing the relation between two states in words,\n",
    "    if they are close enough.\n",
    "    \"\"\"\n",
    "    \n",
    "    if i == j:\n",
    "        return \"   (self)\"\n",
    "    if abs(i - j) == 1:\n",
    "        return \"   (nearest neighbours)\"\n",
    "    # Default:\n",
    "    return \"\"\n",
    "\n",
    "for i in range(n):\n",
    "    for j in range(n):\n",
    "        integrand = lambda x: atomic_basis(x, positions[i], sigma)*atomic_basis(x, positions[j], sigma)\n",
    "        print(\"delta_{}{} = {:.5f}{}\".format(i, j, integrate(integrand, x), ijlabel(i, j)))\n",
    "\n",
    "# Yann had output:\n",
    "#delta_00 = 1.00000\n",
    "#delta_01 = 0.01832\n",
    "#delta_02 = 0.00000\n",
    "#delta_34 = 0.01832\n",
    "# Explanation: next neighbours migth have some overlap. Further away, no overlap at all."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "e9ccbed5ba3e6b844bcc6e326053d8da",
     "grade": false,
     "grade_id": "cell-3cba7034f4eac62f",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "## Step 3: Tight-Binding Hamiltonian\n",
    "\n",
    "The tight-binding Hamiltonian for our 1D chain should describe the hopping of an electron from all atomic positions to their nearest left and right neighbours (i.e. no long-range hopping). The resulting matrix representation in the basis of the discrete $x_i$ positions is therefore given as a tri-diagonal $n \\times n$ matrix of the form\n",
    "\n",
    "\\begin{align}\n",
    "    \\mathbf{H}_{tb} =\n",
    "    \\left( \\begin{array}{cccc}\n",
    "    0 & t & & 0\\\\\n",
    "    t & \\ddots & \\ddots &  \\\\\n",
    "      & \\ddots & \\ddots &  t \\\\\n",
    "    0 &  & t & 0\n",
    "    \\end{array}  \\right),\n",
    "\\end{align}\n",
    "\n",
    "where $t = t_{i,i\\pm1}$ is the nearest-neighbour hopping matrix element. A hopping matrix element $t_{i,j}$ is a measure for the probability of an electron to hop from site $i$ to site $j$. They are defined as\n",
    "\n",
    "\\begin{align}\n",
    "    t_{i,j} = \\int_{-\\infty}^{+\\infty} \\phi(x, x_i, \\sigma) \\, \\Delta V(x) \\, \\phi(x, x_j, \\sigma) \\, dx,\n",
    "\\end{align}\n",
    "\n",
    "with the potential fixed to\n",
    "\n",
    "\\begin{align}\n",
    "    \\Delta V(x) = \\sum_i \\frac{-1}{|x - x_i| + 0.001}.\n",
    "\\end{align}\n",
    "\n",
    "### Task 3.1 [3 points]\n",
    "Write a Python function to calculate $t_{i,j}$, using $\\sigma = 0.25$. The function should have as input the indices $i$ and $j$, and the chain length $n$. Verify that the long-range hoppings $t_{i,i\\pm2}$ and $t_{i,i\\pm3}$ are negligible compared to $t_{i,i\\pm1}$.\n",
    "\n",
    "Hint: use your integration function from task 2.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "260ae3c806429aee5900599c01cb65c6",
     "grade": true,
     "grade_id": "cell-0abfcd1aa9fad2fa",
     "locked": false,
     "points": 3,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "def hopping(i, j, n, sigma=.25):\n",
    "    \"\"\"\n",
    "    Calculates hopping matrix elements t_ij for sigma = 0.25 in a 1D\n",
    "    chain of n atoms at distance a = 1 from eachother.\n",
    "    \n",
    "    Args:\n",
    "        i:     origin site index\n",
    "        j:     destination site index\n",
    "        n:     number of atoms in the chain\n",
    "        sigma: standard deviation to the Gaussian wave functions\n",
    "\n",
    "    Returns:\n",
    "        Hopping parameter t_ij.\n",
    "    \"\"\"\n",
    "    \n",
    "    positions = atomic_positions(n)\n",
    "    \n",
    "    # This 'infinity' is large enough, as the Gaussians decay quite quickly\n",
    "    # away from the atomic positions, which we already saw in the overlap\n",
    "    # above. In fact, 99.7% of all probability mass is under the integral\n",
    "    # for x radius of 3*sigma from the centers x_i.\n",
    "    h = 1e-5\n",
    "    x = np.arange(positions[0] - 10*sigma, positions[-1] - 10*sigma, h)\n",
    "    \n",
    "    def V(x):\n",
    "         ret = np.zeros(x.shape)\n",
    "         for x_i in positions:\n",
    "             ret += -1./(np.abs(x - x_i) + 0.001)\n",
    "         return ret\n",
    "    # Instead of using a loop, one could vectorize the problem further by calculating all sum\n",
    "    # terms as elements of a len(x) by len(positions) matrix and then summing along the rows.\n",
    "    # In testing I found that this was slower than using the loop, so I commented it out.\n",
    "    # This might be due to the large memory overhead O(len(x)*len(positions)), and the fact that\n",
    "    # the len(positions) iterations already do vectorized calculations on len(x) >> len(positions)\n",
    "    # numbers, making the theoretical speed gain only plausible at larger len(positions). \n",
    "    #V = lambda x: np.sum( -1/( np.abs(np.subtract.outer(x, positions)) + 0.001 ), axis=1 )\n",
    "    \n",
    "    integrand = lambda x: atomic_basis(x, positions[i], sigma)*V(x)*atomic_basis(x, positions[j], sigma)\n",
    "    return integrate(integrand, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "b1a56ecde33e723ff450defcf5dc2e74",
     "grade": true,
     "grade_id": "cell-ea36ee5a2b35154c",
     "locked": false,
     "points": 0,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For i = 0 ...\n",
      "\tt_{i,i+1} = -0.13849173441658025\n",
      "\tt_{i,i+2} = -3.088088057066831e-06\n",
      "\tt_{i,i+3} = -1.8833562200578063e-15\n",
      "\n",
      "For i = 1 ...\n",
      "\tt_{i,i-1} = -0.13849173441658025\n",
      "\tt_{i,i+1} = -0.14871538221422848\n",
      "\tt_{i,i+2} = -3.1306987950404085e-06\n",
      "\tt_{i,i+3} = -1.945630457066332e-15\n",
      "\n",
      "For i = 2 ...\n",
      "\tt_{i,i-1} = -0.14871538221422848\n",
      "\tt_{i,i+1} = -0.15363274031153992\n",
      "\tt_{i,i-2} = -3.088088057066831e-06\n",
      "\tt_{i,i+2} = -3.152251440766849e-06\n",
      "\tt_{i,i+3} = -1.9763481552880358e-15\n",
      "\n",
      "For i = 3 ...\n",
      "\tt_{i,i-1} = -0.15363274031153992\n",
      "\tt_{i,i+1} = -0.1560583006931239\n",
      "\tt_{i,i-2} = -3.1306987950404085e-06\n",
      "\tt_{i,i+2} = -3.1616643825949025e-06\n",
      "\tt_{i,i-3} = -1.8833562200578063e-15\n",
      "\tt_{i,i+3} = -1.9857521228152284e-15\n",
      "\n",
      "For i = 4 ...\n",
      "\tt_{i,i-1} = -0.1560583006931239\n",
      "\tt_{i,i+1} = -0.15680086580653224\n",
      "\tt_{i,i-2} = -3.1522514407668485e-06\n",
      "\tt_{i,i+2} = -3.1616580341274714e-06\n",
      "\tt_{i,i-3} = -1.945630457066332e-15\n",
      "\tt_{i,i+3} = -1.9763479030784917e-15\n",
      "\n",
      "For i = 5 ...\n",
      "\tt_{i,i-1} = -0.15680086580653224\n",
      "\tt_{i,i+1} = -0.1560582807779115\n",
      "\tt_{i,i-2} = -3.1616643825949025e-06\n",
      "\tt_{i,i+2} = -3.1503943708763577e-06\n",
      "\tt_{i,i-3} = -1.9763481552880358e-15\n",
      "\tt_{i,i+3} = -9.75855063584149e-16\n",
      "\n",
      "For i = 6 ...\n",
      "\tt_{i,i-1} = -0.15605828077791148\n",
      "\tt_{i,i+1} = -0.07705640452986241\n",
      "\tt_{i,i-2} = -3.1616580341274714e-06\n",
      "\tt_{i,i+2} = -1.8615080260773555e-09\n",
      "\tt_{i,i-3} = -1.985752122815229e-15\n",
      "\tt_{i,i+3} = -1.2516261372405081e-23\n",
      "\n",
      "For i = 7 ...\n",
      "\tt_{i,i-1} = -0.07705640452986241\n",
      "\tt_{i,i+1} = -9.883210483852472e-10\n",
      "\tt_{i,i-2} = -3.1503943708763577e-06\n",
      "\tt_{i,i+2} = -8.453472394803474e-24\n",
      "\tt_{i,i-3} = -1.9763479030784917e-15\n",
      "\n",
      "For i = 8 ...\n",
      "\tt_{i,i-1} = -9.88321048385247e-10\n",
      "\tt_{i,i+1} = -7.16787287550824e-31\n",
      "\tt_{i,i-2} = -1.8615080260773555e-09\n",
      "\tt_{i,i-3} = -9.75855063584149e-16\n",
      "\n",
      "For i = 9 ...\n",
      "\tt_{i,i-1} = -7.16787287550824e-31\n",
      "\tt_{i,i-2} = -8.453472394803472e-24\n",
      "\tt_{i,i-3} = -1.2516261372405081e-23\n",
      "\n"
     ]
    }
   ],
   "source": [
    "n = 10\n",
    "\n",
    "for i in range(n):\n",
    "    print(\"For i =\", i, \"...\")\n",
    "    for r in range(1, 4):\n",
    "        if i - r >= 0:\n",
    "            print(\"\\tt_{{i,i-{}}} = {}\".format(r, hopping(i, i - r, n)))\n",
    "        if i + r < n:\n",
    "            print(\"\\tt_{{i,i+{}}} = {}\".format(r, hopping(i, i + r, n)))\n",
    "    print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "7d2c8f74993fe38c2c979376961f869a",
     "grade": false,
     "grade_id": "cell-8a0f18c44306ae00",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "### Task 3.2 [3 points]\n",
    "Implement a diagonalization routine for tri-diagonal matrices which returns all eigenvalues, for example using the $QR$ decomposition (it is fine to use Numpy's $\\text{qr()}$). \n",
    "\n",
    "Hint: For tri-diagonal matrices with vanishing diagonal elements, the $QR$-decomposition-based diagonalization algorithm gets trapped. To get around this you could, for example, add a diagonal $1$ to your matrix, and later subtract $1$ from each eigenvalue."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "c20cbcce0a7df50b6ae7b90c7aa35721",
     "grade": true,
     "grade_id": "cell-9d4942b717eadeb2",
     "locked": false,
     "points": 3,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "def QREig(T, eps=1e-6, k_max=10000):\n",
    "    \"\"\"\n",
    "    Follows the method of the QR decomposition based diagonalization routine\n",
    "    for tridiagonal matrices. The matrix T is diagonalized, resulting in\n",
    "    all diagonal elements being an eigenvalue.\n",
    "    \n",
    "    Args:\n",
    "        T:     a tridiagonaliz matrix.\n",
    "        eps:   the desired accuracy.\n",
    "        k_max: maximum number of iterations after which to cut off\n",
    "    \n",
    "    Returns:\n",
    "        A one dimensional array with the eigenvalues of the matrix T.\n",
    "    \"\"\"\n",
    "    \n",
    "    e = eps + 1\n",
    "    k = 0\n",
    "    while e > eps and k < k_max:\n",
    "        k += 1\n",
    "        Q, R = np.linalg.qr(T)\n",
    "        T = np.matmul(R,Q)\n",
    "        e = np.sum(np.abs(np.diag(T, k=1)))\n",
    "    return np.diag(T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "19976946c5746804cb08c34f0bda50fc",
     "grade": false,
     "grade_id": "cell-2d8fb5c080951dd5",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "### Task 3.3 [3 points]\n",
    "Implement a unit test for your diagonalization routine."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "d95777361c07514a97ff1458f26f4f44",
     "grade": true,
     "grade_id": "cell-001cb3c043c4e371",
     "locked": false,
     "points": 3,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "def test_QREig():\n",
    "    # Test case one\n",
    "    T = np.array([\n",
    "        [1,4,0,0],\n",
    "        [3,4,1,0],\n",
    "        [0,2,3,4],\n",
    "        [0,0,1,3]\n",
    "    ])\n",
    "    # Eigenvalues are roots of λ^4 - 11*λ^3 + 25*λ^2 + 31*λ - 46.\n",
    "    eigenvalues_of_T = np.array([-1.45350244, 1., 4.65531023, 6.79819221])\n",
    "    assert np.allclose(np.sort(QREig(T)), eigenvalues_of_T)\n",
    "    \n",
    "    # Test case two\n",
    "    T = np.array([\n",
    "        [1,4,0,0],\n",
    "        [3,0,1,0],\n",
    "        [0,2,0,4],\n",
    "        [0,0,0,3]\n",
    "    ])\n",
    "    eigenvalues_of_T = np.sort(np.linalg.eig(T)[0])\n",
    "    assert np.allclose(np.sort(QREig(T)), eigenvalues_of_T)\n",
    "\n",
    "test_QREig()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "83df149b46d779a846f9de925342b681",
     "grade": false,
     "grade_id": "cell-85c89b0eb0930f2b",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "### Task 3.4 [4 points]\n",
    "First, write a function that generates your tight-binding Hamiltonian $\\mathbf{H}_{tb}$, for a given chain length $n$. Use $t = t_{i,i\\pm1}$, as calculated in task 3.1. You can choose any $i$ near the center of the chain for the calculation of $t$, as the chain is (approximately) periodic.\n",
    "\n",
    "Second, use your diagonalization routine to calculate all the eigenvalues $E_m$, for a variety of $n=10,20,40,80,100$. Sort the resulting $E_m$ and plot them vs. $m$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "a0779b496fd41a4664bb0cdd857c70fc",
     "grade": true,
     "grade_id": "cell-764cb41c37700042",
     "locked": false,
     "points": 3,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "def TBHamiltonian(n, sigma=.25):\n",
    "    \"\"\"\n",
    "    Generates the tight-binding hamiltonian H_tb for given chain length n,\n",
    "    using the approximation of constant hopping parameter in a periodic\n",
    "    chain of atoms.\n",
    "    \n",
    "    Args:\n",
    "        n:     number of atoms in the chain\n",
    "        sigma: standard deviation to the Gaussian wave functions\n",
    "\n",
    "    Returns:\n",
    "        Tight-binding hamiltonian H_tb.\n",
    "    \"\"\"\n",
    "    \n",
    "    # TODO: Comment on the weird 20% differences in hopping parameters.\n",
    "    \n",
    "    i = n//2\n",
    "    t = hopping(i, i + 1, n, sigma)\n",
    "    H_tb = (np.eye(n, n, -1) + np.eye(n, n, 1))*t\n",
    "    \n",
    "    return H_tb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "634e139137eead8808d1d8ccb793d5a5",
     "grade": true,
     "grade_id": "cell-39ada0528e69d2e5",
     "locked": false,
     "points": 1,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAY4AAAEYCAYAAABLOxEiAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAABXAElEQVR4nO3dd3hUxfrA8e+kN1JIgHQSSCihNxFFkKJiAxQLXiwoiGADO/fqz2sXroIFRKSIoFixgIogRURpSg8tpEB67z1b5vfHLhgxCdlkW5L5PA8P2d2zM+/ZPbvvnpk5M0JKiaIoiqI0loOtA1AURVFaFpU4FEVRFJOoxKEoiqKYRCUORVEUxSQqcSiKoigmUYlDURRFMYlKHIqiKIpJVOJQFEVRTKISRyshhDguhLjS1nHURwhxVggx1tZxnCOE6C6EOCyEKBVCPNpa6hVCfCSEeKXW7fPHxYV12+o1MIfmHE/N+azY6ji2t8+Pk60DsAUhxFmgE6CrdfdHUsqHbRNR80kpe9k6hhbmaeAXKWX/uh4UQvgBBUAXKeWZWve/C7hLKe+3RL3mdsFx8be6hRArrRnLhYyfw+lSyq3WrLclfFZs9do0Vls+47hRSulV659Zk4YQok0m5RakM3C8gcf7A2XA2Qvu7wMctmC9dTLT8XRh3U2KxYzxKC2VlLLN/cPwZTC2gceeBI4CxcAXgFutx4OBr4Fc4Azw6AXPfcb43GoMZ3QDgUNAKfCVsbxXjNs/BXx9Qf3vAu/UE9vF6h5r/LveOhtZTp37b9y3dRfE9A7wrvHvuUCisd4TwE31veaABKJq3f6o1utSb3y14kg31hMHjKnn9eoJ7ACKMHxBjjfevx3D2WYVhuTQrY7nPgbsq+P+HOCyJh53/6i3vhjrO57qKHMAcND4WnwBfH7Be30WGFtH3XW+Bo04Ni48vpt6LH0M6IFKY/1P17FvYcA3xrLzgcUmfE4bdSxerJyGvjuauu8X+4zW9do0orzGfiYeADYC7wF5QAZwlcnHclM+AC39HxdPHH8YD4r2wElgpvExB+AA8DzgAnQBkoBraj33sPGAdzdukwzMBpyBm4GaWgdIEFAO+BpvO2H4YhpUR1yNqXtsI+psTDn17X9noAJoZ7ztCGQClxpv32p8ngNwu3Hfgup6zakncTQivu5AKhBsvB0BdK3j9XIGEoD/GMsZjeFD1d34+A4MTQH1HSNrgJUX3HeuedOrGcfe+XobEeNZah1PdZR17r1+zFjWLYCGOhJHXftcx21Tj+8mH0uN+Bw6AkeAtwBPwA0Y3pjPqSnH4sXKqe+7ozn7zkU+o/V8Xhoqr1GfCeNjSzA0wV5j3If/AltNPY7bclPVd0KIolr/ardZvyulzJBSFgDfY2i2ABgCdJBSviSlrJFSJgHLgckXPDdVSlkJXIohGbwrpdRIKb/B8OYDIKXMBHZiOMgBxgF5UsoDdcTbmLq5WJ0m7MM/9l9KmYzh1+1Nxu1GAxVSyr3Gx78yPk8vpfwCiAcuqWNfGnKx+HSAKxAjhHCWUp6VUibWUc6lgBcwz1jOduAH4I5GxtEfuEMIkXfuH3AKSJBSlgEIIUYJIcKNf78hhDB1XxsTY+3jqa7nOwNvG9/rdcCfJsZQm6nHd5OPpUa4BMOX5FNSynIpZZWU8vcLtqm3bBOPxabE2Jx9v9hntD71ldfYzwRAXwzH22YppR7D2ZjJ2nI75URZf8dTVq2/KzAcwGD4xR0shCiq9bgj8Fut26m1/g4G0qUx1dfxOMBqYBaGg+5ODKepdWlM3Y2pszHl1Lf/AJ9i+GJbA/zLeBsAIcTdwOMYfvGA4UsxoJ79qU+D8UkpE4QQc4AXgF5CiM3A41LKjAvKCQZSjR+Oc5KBkIsFIIRwxdCEdBt//yJ+EOha6/Z9GM4WAHobYzJFY2K88Hi58PkXvtfJJsZQm6nHd3OPpYaEAclSSm0D29RbtonHYlNibM6+N+Z7odFxNvYzIYQQGProav9I7k0TkkdbThxNkQqckVJGN7BN7YMhEwgRQohaB0kYhrbXc74D3hdC9AZuwNCe2dS6G1NnY8upz1fAAiFEKIYzj2EAQojOGJLfGGCPlFInhDgMiHrKqQA8at0OBNIaE5+U8lPgUyGEN/ABMB+464LNMoAwIYRDrS/mcOB0I/axN4bT+C3nzi6M+xiNoXkCIcR4DO9XmHF0UjDwlhBiMLBCSrmkEfU0Jkb5z6edV9d7Hc7fjy9TmHp8N/dYamjfUoFwIYTTRZLHPzThWGyK5ux7Y74XGnpt/qGRn4kIDN/5cbXuG4DhO8gkbbmpqin+AEqFEM8IIdyFEI5CiN5CiCH1bL8Hw2nkw0IIJyHEBC44XZZSVgHrMPxy/0NKmdLMui9Wp6n78DdSylwMbeOrMHxwThof8sRwsOcCCCHuxfAFXJ/DwL+M9Y8DRjYmPuO1B6ONZwVVGDoQ9XWUvw9DcnpaCOFsHLd/I4bO44sZAJyonTSMhvDXiKofgANSyiuBnwA/DB2Ul/H3X3QNaU6MYHivtcCjxuffjOlNg7WZemw061gCsjH0DdRXdiYwTwjhKYRwE0Jc3shyTT0Wm6I5+37R7wUafm3+xoTPRF8g9oIz3AEY+pJM0pYTx/dCiLJa/7692BOklDoMvzL7YxhFkQesAHzq2b4GQ8fXNAyjZu7E8IVTfcGmqzGcQtbXTNXoui9Wp6n7UI9PMXQQnm+mklKeABZg+FBkG/dnVwNlzMbwJVkETMH4q6cR8bkC84z3ZwEdgX9fWLjxdbgRuNa47RLgbinlqUbsX38u6CsQQnTA0Dxx2HhXFIZ2czB8INdKKQuNPwQqGlFHc2Os/V5PxdDheTuGUUhN0oTju7nH0uvAc8Y+xifrKPtGDK9zCoaz0dsbuR+mHosma86+N/J7od7Xpg6N+kxgOE4Pn7shhAjAcKZ/7GIxX0j8vZlNsTQhxD5gqZRyVa37wjF0vAZKKUusUafSPEKIm4DOUsq3je3LAVLK54QQk4BoKeU820aotCQt7TOq+jgsTAgxEkObYh6GX9Z9gU21HnfA0In3ubmSxsXqVMwiDnhZCBEBtAMqhBBfYhh3P9OWgSn2r6V/RlXisLzuwJcY2l2TgFukYRguQghPDKfSyRiG4lq8TsU8jM0h5m43V9qOFv0ZVU1ViqIoiknacue4oiiK0gStvqkqICBARkRE2DoMRVGUFuXAgQN5UsoOdT3W6hNHREQE+/fvt3UYiqIoLYoQot5ZCFRTlaIoimISlTgURVEUk6jEoSiKophEJQ5FURTFJCpxKIqiKCZRiUNRFEUxiUociqIoikla/XUciqIorZVep6eipIbKUg1VZRoqy2uoqdShqdahrdHRIawdEX1NXYTz4lTiUBRFsWOaGh2FmeUUZpZTlFtJcU4lJXmVlBVUUVFSQ0PTDfYZGaISh6IoSmtWU6Ul52wJOcml5CSXkpdaSnFe5fmFZIWAdv5ueAe4E97LH08/V7x8XXFv54KblzNuns64ujvh7OqIk6sjDg7mXC33LypxKIrSakmdDl1JCfriYpzDwhCOjrYO6W+qyjSkxRWScbqQzKRi8tPKzp9BeAe40SGsHd0vDaR9kCftgz3xDnDH0cn2XdMqcSiK0mJJvR5NRiY1iQlUJyRSk5yMJjMTTWYG2pxc9CV/rY0Wvet3nPz9bRitoU8i60wJybH5pJzIJy+tDCQ4uToSGOnNoOsiCOriQ8fO3rh5Ods01oaoxKEoSouhKy2lYv9+Kg8dpupYLJWxx9CXlp5/3NHPD+fgYFwiIvC8ZCiOvr7Gfz44uLvbJGZNjY7U4wUkHs4hOTaf6gotwkEQ2MWbS26IJLRHezpGtMPR0fZnEo2lEoeiKHZL6vVUHT1K6Y4dlO/eQ9WxY6DXg5MTbt264X39dbjFxOAaFYVrly44+vraOmQAdBo9ycfzOf1HNsmxeWg1elw9nYjsG0DnPgGE9fTD1cN+zyguRiUORVHsitTpqNi3j5KffqJ0+y/o8vPB0RH3fv0ImPkAHpcMxb1/Pxzc3Gwd6t9IKclKKuHU7gwSDuZSU6nFvZ0zPYYF0WVgB0KifXFoQWcVDVGJQ1EUu1AVF0fRuq8p+ekndHl5OHh64jVyJF6jR+N1xXAcfXxsHWKdKktrOLk7k5O7MynKrsDJxYGuAzrS7ZJOhPbwazXJojaVOBRFsRl9ZSXF339P0VfrqIqNRTg74zVqFN7XX4/XyBF2d1ZxjpSSzMRijv2aTuKhHPRaSVCUDwOv6UHXgR1xcWvdX62te+8URbFLmowMCj/9lMKv1qEvLsY1OppO//kP3jfegJOfn63Dq5dOoyfhQDZHtqeRm1KKi7sTva8IodeIENoHedo6PKtRiUNRFKupTkwkf9lyin/4AaSk3VVX0f7uu3AfOBAhLHOxmjlUV2o5vjOdI9tSqSipwS/Qg5H/6k73oYE4u9rXtSHWoBKHoigWV3X6NHmL36N0yxaEmxt+U/6F/z334BwSYuvQGlRRUsPhrSkc25mOpkpHWEx7xowNI6xne7tOdJamEoeiKBZTk5xM7qLFlPz4Iw6envjPfID2d92FU/v2tg6tQeVF1Rz6OYXjv6Wj0+qJGtSRAVd3pkN4O1uHZhdU4lDanNyKXA7kHOBwzmGeHPwkTg7qY2Bu2sJC8hYtpvCLLxAuLvhPn47/tPvs5jqL+lSU1HBwczLHfk1Hr5d0H9qJQeMi8O3kYevQ7IpdfWKEEOOAdwBHYIWUcl49200C1gFDpJT7rRii0kJllGWw7vQ6fk7+meSSZADcndyZ3H0yET4Rtg2uFZE1NRR8/Al5S5eir6jA97Zb6fDggzh16GDr0BpUXanl0OZkjvyShq5GR/dLAxl8XSQ+HWxztbm9s5vEIYRwBN4DrgLSgD+FEBuklCcu2K4dMBvYZ/0olZZmf9Z+Vh5bya70XQghGBY0jFuib2Fw4GB6tO+hzjbMqHz3brJefoWaM2fwHDmCTk89hWtUlK3DapBOo+fYznT2bzxLVbmGqMEdueSGSPwC284Iqaawp0/NJUCClDIJQAjxOTABOHHBdi8D84GnrBue0pIklySzcP9CtqduJ8A9gBl9ZzApehJBXkG2Dq3V0WTnkP3665Ru2oRzeDhhyz7Aa8QIW4fVICkliQdz2fNtAiV5VYT19GPYTVGqD6OR7ClxhACptW6nAUNrbyCEGAiESSl/FELUmziEEDOAGQDh4eEWCFWxVxq9hvcPv8+qY6twdnTmkQGPcFfMXbg7qSYHc5N6PUVfrSPnjTeQGg0Bjz6C/7RpOLi62jq0BuUkl/D7V/FkJhTjH+LFjY/2IzzGtrPmtjT2lDgaJIRwABYCUy+2rZRyGbAMYPDgwQ2sj6W0JiklKTyz8xmO5R9jfNfxPDboMQLczb/6mWIYLZX53P9R8eefeAwdStBLL+LSubOtw2pQZWkNe75L5OTuTNy9nBl1Zw96XBZkscWOWjN7ShzpQFit26HG+85pB/QGdhjHTwcCG4QQ41UHubIxaSMv7nkRRwdHFoxcwNURV9s6pFZJ6vUUfvYZOW8uQDg5EfTKy/hMmmTX1zTo9ZLjO9PZtyEJTZWO/mPCGHJ9JC7u9vT117LY0yv3JxAthIjEkDAmA/8696CUshg4//NRCLEDeFIljbZNSsnSo0tZcngJAzsOZP6I+QR6Bto6rFZJk5lJ5rPPUr57D57DhxP06is4d+pk67AalJNcwo61ceSmlBLaw48rbu/WpqYGsRS7SRxSSq0Q4mFgM4bhuB9KKY8LIV4C9kspN9g2QsXeaHQaXtzzIusT1zO+63heGPYCzo4td40De1ayaTOZzz+P1GoJfOEFfG+/za7PMmoqtezdkMSxHWm4t3Ph6um9iBrU0a5jbknsJnEASCk3AhsvuO/5era90hoxKfapWlfN7F9msyt9Fw/2e5CZ/WaqLwUL0FdUkP366xR9tQ633r0JWfCm3fdlnD2ax6+fxVFWVE2fESEMndgVV9UsZVbq1VRanBpdDXN+mcOu9F28MOwFJnWbZOuQWqXqhATSZs+hJikJ//vvp8MjDyNcXGwdVr0qS2v47YvTxO/PoX2wJ5Nm9CYw0j7X8GjpVOJQ4ODH0L4LRFxu60guqkZXw2M7HuP39N9V0rCg4vXryXzhRRw8PAj/cCWew4bZOqQGJRzI4dfP4qip0nLJjZEMvKYzjk6tbwEle6ESR1um08Cmf8Ofy6H3LXafOHR6HU/9+hQ703byf5f+n0oaFqCvqSH75Vco+uorPIYMIXjBmzh37GjrsOpVWVrDr5/FkXgwl46d2zH6np74B3vZOqxWTyWOtqo8D768B5J/h2EPw9gXbR1Rg6SUzP9zPttTtzP3krnc1v02W4fU6miyskibPZuqI0cNTVOzH0U42e9XxJkjufzyySmqK7VcOrELA64Kb5XLtNoj+z0qFMupLIQVY6E0E25aBv1ut3VEF/XJyU/47NRn3B1zN1N6TrF1OK1Oxf79pM2eg6ysJGTRu3hfdZWtQ6pXTZWW37+M5+TuTPxDvZgwZwD+Ieosw5pU4mhrpITvHoTiNLjne+hs323XANtStvHGn28wNnwsTwx+wtbhtDqFX35J1ksv4xIWRuia1bh27WrrkOqVlVTMlg+PU5pfxcBxnbnkhkjVl2EDKnG0NXsWQ9xGGDevRSSN+MJ4/v3bv+kd0JvXrngNB6G+JMxFarVkz/8fhR9/jOcVVxCycAGO7exzkj+9Ts+BTcn8+eNZvPxcuemJgQRF+do6rDZLJY62JGUfbH0Bet4IQ2faOpqLKq0p5bEdj+Hp7Mk7o95RExWaka60lPQ5j1G+axftp06l41NPIhztc+3s0oIqtqw8TmZiMd2HBnLF5G7qugwbU69+W1FdBuvuA59QGL8Y7PxiOSkl/7fr/0grTWPlNSvp4GHfCwG1JJr0dFJnzqT6zFmCXnkZ31tusXVI9Uo6lMv2j0+i10uuui+Gbpeo6WTsgUocbcWexVCSBvdtBndfW0dzUauOr2JbyjaeGvwUgzoNsnU4rUZl7DFSH5yFrKomfPkyu70+Q6fRs+vrBGJ3pNEhvB1XT++Fb0e1fKu9UImjLSjNhl3vQs/xEH6praO5qCO5R3j34Ltc3flq7oq5y9bhtBqlO3aQ/tjjOLVvT9iqVXa7Ol9xbiWblx8jN6WUfqPDGHZzV9UBbmdU4mgLdrwGumoY+4KtI7mock05c3fOpZNHJ1647AU1/5SZFK1bR+Z/X8CtRw/CPliKU4B9rlOSdDiXbatPAnDtzD506a+aKO2RShytXc4pOLgGhtwP/vY7zPKc1/e9TkZ5BquuWUU7F/sc4dOSSCnJW7KEvEWL8Rw+nNB33sbB0/6mFdfr9Oz9LolDW1Lo2Lkd19zfG+8ANRjCXqnEYSdySqvwcHHCy9XMb8nW/4KLF4x8xrzlWsDms5tZn7ieGX1nMLDTQFuH0+JJvZ7sV1+jcO1afCZMIOiVlxHO9jftfHlxNT+vOE5GfBG9R4Qw/NZoHJ1V05Q9U4nDTiz8+TTbTuWwe+5onM01bUL6ATi9CcY8D572vaZybkUuL+15iT4BfZjZz/6HCts7qdGQMffflPz4I+3vvZeOTz9ll81+mYnFbFoWS02FlrFTe9L90iBbh6Q0gkocdqCkSsP6wxlM6B9svqQBsGcJuLQzNFPZMSklr+x9hWpdNa8OfxVnB/v7VdyS6KuqSJs9m/Jfd9Lh8cfxv3+63SUNKSXHf8vgty9O49XejRsf6U9AqJo2pKVQicMOfHconUqNjilDzbhATnE6nPgOLnkA3LzNV64FbE7ezPbU7Tw+6HEifSJtHU6LpisrJ23WLCr27yfwxRfxu93+JoPUafT8+nkcJ3dlEt7Ln6vui8HNU/1YaElU4rAxKSVr96bQN9SHPqFmXHTmj2Ug9TD0AfOVaQGFVYW8vu91evv3VkNvm0lXXEzKjBlUHTtO8Btv4HPD9bYO6R/Ki6v5aWks2WdKGHRtZy65sQsODvZ1NqRcnEocNnYguZC47FLmT+pjvkJryuHAR9DjBvCz72U+5/0xj5KaElZcvQInB3U4NpW2oICU+6ZRk5hI6Lvv0G7MGFuH9A/ZZ0r4aelRqiu1XHN/b6IG2e86H0rD1CfVxtbuS6GdqxM39gs2X6GHP4WqIhj2kPnKtIDf039n45mNPNjvQaL9om0dToulzcsj5d57qUlJJXTJEryuGG7rkP4hbl8Wv3x8Cg8fFyY9PVj1Z7RwKnHYUEF5DT/GZnLHkDA8XMz0Vuj1sPd9CBkEYUPNU6YFVGmreHXvq0R4RzCtzzRbh9NiaXJySJl6L5rMTMI++ADPS+3rPZd6yd4NSRzclExwtC/jHuiNu5f9rluuNI5KHDb09YE0arR6/mXOTvEzO6AgESattOuJDFceW0laWRorrl6Bi6P6ImkKTXY2KXffgzY3l/Dly/AYPNjWIf1NTZWWratOcOZIHjHDgxkxuZuaOqSVUInDhn6MzaRfmC/dA814hfThT8HN19C/YaeSS5JZGbuS6yKvY2iQff1Cbik02TmGpJGXR9iKFXgMHGDrkP6mrLCKH5ccJT+tjOG3RtN3dKjdDQlWmk4lDhspqdJwNK2Ih0eZcaK5yiI4+T0MuBOc3cxXrhlJKXl176u4Orry1JCnbB1Oi6TJySHlHsOZRtjKFXgMsK+kkZNcwsYlR6mp1nH9Q/3o3Nu+Lz5VTKcSh438eaYAvYRhXc042dzxb0FbBf3/Zb4yzWxrylb2ZO7h35f8mwB3+5xoz55pc3NJuWcq2pwcwlYst7ukkXQ4ly0fHsfdy4VJT/VXa4G3Uipx2MjuxHxcnRwYEO5rvkIPfwodekKwfc7zVK2rZsH+BUT7RXNbd/u7MM3eaQsKSL73XjTZ2YY+jYH29T4f2ZbK7+vi6djZm+sf7IuHt+q7aq1U4rCR3Yn5DI7ww83ZTMt15p6GtD/gqpfttlN8zfE1pJelq2s2mkBXVETKfdPQpKYRtmwZHoPsZ3ErvV7y+1fxxP6SRpcBHRh7bwzOLva5DK1iHmqIgw0UlNdwMrOEy8zZTHXkUxCO0Pd285VpRjkVOSyPXc7Y8LGqQ9xEutJSUqbfb7i477338Bx6ia1DOk9To+OnpbHE/pJG/7FhjLu/t0oabYD62WcDe5PyARjW1UydhnodHPkcoq+Cdp3MU6aZvXPwHbR6LY8PftzWobQo+ooKUh+YSdWpU4Quehev4ZfbOqTzKkpq+HHJUXKSS7ji9m70HRVq65AUK1GJwwZ2J+bh5epE3xAzzU115lcozYRx88xTnpkdyzvGhsQNTO8znbB2YbYOp8XQ19SQ9vAjVB4+TMjCBbQbNcrWIZ1XlF3B94sOU1Fcw7UPqJX62hqVOGxgd2I+l0S2x8lcU6gf/9awWFO3a8xTnhlJKXlz/5u0d2vP9D7TbR1OiyG1WtIff5zy3bsJeu01vMeNs3VI52WdKebH944CMOHxAQRGmnFyTqVFUH0cVpZVXEVSbjmXmauZSqeBkz9A92vB2f6W2vw17VcOZB/gof4P4elsf0uW2iOp15P57HOUbd1Gp2efxffmm2wd0nlnY/NY/9YhXNwcmfTUIJU02ii7ShxCiHFCiDghRIIQYm4djz8uhDghhDgqhNgmhLDvqV/rsCcpDzBj/8aZnVBZADETzVOeGWn1WhYeWEiEdwQ3RdvPl589k1KS/fo8itevp8PsR2l/1522Dum8k7sz2Ph+LH6Bnkx6ejC+nTxsHZJiI3aTOIQQjsB7wLVADHCHECLmgs0OAYOllH2BdcD/rBtl8+1OyMfXw5megWZaXOnEd4Zmqij7m0b724RvOVN8hjmD5qhV/Ropb8kSCj/+mPb33IP/TPtYQldKyYFNZ9m+5hShPfyY+PgAdY1GG2c3iQO4BEiQUiZJKWuAz4EJtTeQUv4ipaww3twLtLhhHAeSCxkS0d48i9fYcTNVhaaC9w69x8COAxkdNtrW4bQIBWvXkrdoMT4TJ9LxmaftYm4nqZf8/mU8e79LInpIJ65/sC8ubqprtK2zp8QRAqTWup1mvK8+04Cf6npACDFDCLFfCLE/NzfXjCE2T2mVhqS8cjOOprLfZqo1J9aQX5XP44Mft4svQHtXsnEj2a+8itfo0QS98jLCwfYfTZ1Wz5ZVJzj6Sxr9Rodx1b0xanZbBWiho6qEEHcCg4GRdT0upVwGLAMYPHiwtGJoDTqeUQJAb3MtEXu+mWqsecozk6KqIlYfX83osNH069DP1uHYvbJdu0h/Zi7ugwYSsnABwsn2H0tNtY5Ny2JJOV7ApRO7MPCazuoHgHKe7Y/Qv6QDtQf5hxrv+xshxFjgWWCklLLaSrGZRWxaMQB9zHHG8bdmKvuaCXflsZWUa8p5ZMAjtg7F7lXGxpL2yKO4dulC2JIlOLjZ/r2sKtfw43tHyD5Twqg7exAz3IyrUyqtgj0ljj+BaCFEJIaEMRn42zSvQogBwAfAOClljvVDbJ7Y9GKCfdwI8HJtfmFnf7PLZqrs8mw+O/UZN3a9kSg/M04Z3wrVnD1L6owHcPLzI2z5Mhy9zTRgohnKi6rZ8O5hinIquGZGb7oOUOuCK/9kN4lDSqkVQjwMbAYcgQ+llMeFEC8B+6WUG4A3AC/gK+Npc4qUcrzNgjZRbHoxvc3Vv3FqIzh72N1oqg+OfoBO6pjVb5atQ7Fr2txcUqbfD0DYiuU4d7T9F3RxbiUb3jlEZamGGx7uR1iP9rYOSbFTdpM4AKSUG4GNF9z3fK2/7asx3wQlVRrO5JUzaWBD/f2NJCXE/QRdR9vVaKqUkhS+jf+WW7rdQmi7FjfgzWp0ZeWkPjATbX4+nT9ahWtkpK1DIj+9jA3vHkan1TNhzgA6Rdr+7EexX2qIhJUcTzd2jJvjjCPrKJSkGfo37Mj7R97HycGJB/o9YOtQ7JbUaEifPZuquDhC334L9362HzyQfaaEbxccRAA3PTFQJQ3louzqjKM1i00vAszUMR73EyAg2n7mpkoqSmLjmY3cE3OPWtmvHlJKMp//L+W7dhH06it4jaxzUKBVpccV8uOSo7i3c2bCnAF4B9jPGaxiv1TisJLY9BJCfN3xN0fHeNxGCBsKXvYzI+nSI0txdXRlau+ptg7FbuUtWkzxt98S8PDD+E6aZOtwOBubx6Zlx/AOcGfC7P54+prh2FTaBNVUZSWxaUX0DjFDE0BxGmQesatmqvjCeDad3cSUnlNo76Y6VOtStG4deUuW4DPpZgIeetDW4ZBwIIef3o/FP9iTm54YoJKGYhKVOKygpErD2fwKMzZTAd2va35ZZvL+kffxcPZgaq+ptg7FLpX99juZ/30Bz+HDCXrhBZtfSHdydyY/rzhGpy7eTJgzAHcvNe+UYhqVOKzgWLrxwr9Q3+YXFvcTtO8KAdHNL8sM4gri2JK8hbti7sLHVU2xfaGqkydJnz0b127dCHn7bYSzbSd7jN2RxvY1Jwnt4ceNj/THxV21ViumU4nDCsx2xXhViWF+qh7XgZ1M//D+kfdp59yOu2LusnUodkeTmUnqAzNx8PYmbOlSHL1sux7JwZ+T2fn5aSL7BXD9g/1wdlVrgytNo35uWEFsejEhvu6092xmk0DiNtBr7KaZKq4gjm0p25jVbxbeLmoIZ226sjJSH5iJvqKCzmvX4tzJdhf4SSn588ez/PnDGaIGd2TsvTE4mmv1SaVNUonDCo5nlJinYzx+C7j5QuglzS/LDD44+gFezl5M6TnF1qHYFanRkD7nMaqTkgj7YClu3bvZLhYp2ftdIgc3p9BjWCCj7uppnin9lTZN/eywsIoaLWfzy+nR3IWb9HpD4ogaA462z/fxhfFsSd7Cv3r+S/Vt1CKlJOuVVyn//XcC//s8XpdfbtNYfv8ynoObU+g1IoTRKmkoZmL7b6BWLj67DCmhR2C75hWUdQTKcyD6avME1kwfHP0ADycP7o6529ah2JWCDz+k6Isv8L//fvxuvdVmcUi95NfP4jj+Wwb9Rodx+a1RNh/NpbQe6ozDwuKySgHo3tzEEb8VENDV9pMaJhYl8vPZn9XZxgVKfv6ZnDfepN214+jw2BybxaHXS7Z/fJLjv2Uw8JrOKmkoZqfOOCzsVFYpbs4OdPZv5oia+J8hZKBdXC2+7Ogy3Jzc1NlGLZWxsWQ8/Qzu/foR/PrrNlvBT6/Ts/Wjk8T/mc2QGyIZcn2EShqK2akzDguLyy4humM7HJvTtlyeD2l/QtRV5gusiZJLktl0dhOTu0/Gz83P1uHYBU1GBqkPPoiTvz+hS96z2WJMOp2eLR+eIP7PbC6d2IVLbohUSUOxCJU4LCwuq7T5/RuJ2wFpF/0bK2NX4uzgzN291NkGGIfdzpyFrKwi7IOlOPn72yYOrZ6flx8n4UAOl02KYtC4CJvEobQNqqnKgvLKqskrqzFD/8bP4BEAwQPME1gTZZRl8H3i99zW/TY1Ay4gdTrSn3iC6sREwpZ9gGuUbVY81Gn0bFp+jLNH8xh+WzT9Rodd/EmK0gwqcVjQuY7xZg3F1esMF/5FXQU2ajc/Z9WxVSDg3t732jQOe5Hzv/9R/utOAl/4r82G3Wo1On5aeoyU4/mMvKMbvUeqBbQUy1OJw4JOmWNEVcYhqMiHaNv2b+RW5PJN/DdM6DqBQM9Am8ZiDwo//5yC1Wtof8/d+E2ebJMYtDU6Ni6NJfVEAVdO6U6vK8ywuqSiNIJKHBYUl1WCv6cLHdo1Y8rq+C0gHAzLxNrQ6uOr0Uot03pPs2kc9qB8926yXjYsxNTx6adtEoOmRsfGJUdJiytk1F09iLk82CZxKG2TShwWFJdV2vz+jYStEDIIPGy3zkVRVRFfnv6SayOvJcy7bbefVyclkTZ7Dq5duxK8YAHC0foTBWqqdfy45Ajpp4sYc09PelwaZPUYlLZNjaqyEL1ecjq7rHmJo6IAMg7a/KK/tafWUqmtZHrv6TaNw9a0hYWkzpyFcHEh7P0lNpnttqZKyw+Lj5BxuoixU2NU0lBsQp1xWEhKQQWVGl3zhuIm/QJSD1FjzReYico15aw9uZbRYaOJ8rPNqCF7IGtqSJ89B21mJuGrV+McYv3+hHNJIyuxmLH3xdBtiOprUmxDJQ4L+atjvBkjqhK2G2bDDRlonqCa4Mu4LymtKeX+vvfbLAZbk1KS+dJLVPzxB8H/m4/HQOsPiz6fNJJKuGpaL6IHd7J6DIpyjkocFhKXVYoQ0K2TV9MKkNIwDLfLleBgmwV3qnXVrD6+mmFBw+gd0NsmMdiDgtWrKV73Nf4zH8Bn/Hir119TpeWHRUfIOlPC1dN6ETXIdmt7KAqoxGExcdklhLf3wMOliS9xzgkozbRpM9V38d+RX5Xfps82yn79lZz/vUG7q66iw6OPWr3+mkot3y86QvZZlTQU+6ESh4XEZZXSvVMz+jcSthn+t9EwXI1ew6rjq+jXoR+DOw22SQy2Vh0fT/rjT+DaozvB8+dZfeJCQ9I4TM7ZUq6Z3ouuA1XSUOyDGlVlAdVaHWfzK5o3oiphK3SMAR/bXNS16cwm0svSmd5nepucKE9bWEjqrAcRHu6EvfceDh4eVq2/dtK4+n6VNBT7ohKHBSTllqPTS7o19YyjphxS9tjsbEMv9ayMXUmUbxQjQkfYJAZbkjU1pD/yKNqcHMIWL8Y5yLpDXqsrtWx4t1bSGKCShmJfVOKwgNPZhhFVTU4cZ38HXY1hmVgb2JG6g8TiRKb1mYaDaFuHyPkRVPv3E/Tqq7j362fV+qsrtXz/7mFyk0u55v7eKmkodqltfStYyensUpwcBJEBTbxALGEbOLlD+GXmDawRpJSsjF1JiFcI4yLGWb1+Wytcs8YwgmrWTHxuvMGqdV+YNLoMsP2iXYpSlyYlDiFEjBDiWiGEmoqzDqezy4gI8MTFqYl5OXE7RFwOztZfEOjPrD85mneUe3vdi5ND2xo7UbZzJ9nz/2cYQfXII1atWyUNpSVp6hnHi0A7YIYQYrUZ42kV4rNLm379RlEK5MfbbJqRFbEr8HfzZ2L0RJvUbyvViYmGEVTdrT+CSiUNpaVp6qdji5TySynl81LKe8wVjBBinBAiTgiRIISYW8fjrkKIL4yP7xNCRJirbnOp0uhILqhoev9G4nbD/zbo3zief5w9mXu4K+YuXB2bMaNvC3N+BJWbG2HvLbbqCCqVNJSWqKmJ4zIhxDdCiOVCiMfNEYgQwhF4D7gWiAHuEELEXLDZNKBQShkFvAXMN0fd5pSQU4aUzegYT9gG3iEQ0M28gTXCytiVtHNux+3db7d63bYiNRrS5zyGNjOT0EXv4hxsvenJVdJQWqqmJo5jUsqbgVnANjPFcgmQIKVMklLWAJ8DEy7YZgJwrmlsHTBG2NlFBn+NqGpCU5VOC0m/GobhWnm3zhSfYWvyVib3mIyXSxOb2VoYKSVZr75Kxb59BL3yMh4DrDcHlUoaSkvW1MRxgxBiOtBFSnnETLGEAKm1bqcZ76tzGymlFigG/C8sSAgxQwixXwixPzc310zhNc7p7DKcHQWd/ZswoirjIFQX2+T6jVXHVuHi6MKUnlOsXretFH76KUWff4H//dPxmXDhbxTLUUlDaekumjiEEL3quPt2DF/gNwkhlps9qmaSUi6TUg6WUg7u0MG6H8r47FK6BHjh7NiEnJywDRCGiQ2tKKs8i++TvuemqJvwd/9HHm6VynfvJvu11/EaNYoOjz1mtXpV0lBag8Z8u3187g/jWQZSymwp5WZgkZTSXDPgpQO1l5cLNd5X5zZCCCfAB8g3U/1mcTqnlG5NnWokcbthCnUrr/a35sQapJRM7T3VqvXaSvWZM6TNeQzXLl0IfuMNq42gUklDaS0a84mp3dj+4AWP/WbGWP4EooUQkUIIF2AysOGCbTYA50Zx3QJsl1JKM8bQLOXVWlILKunWsQl9BJWFkL7f6sNwi6qKWHd6HddFXkeIl23mxbImXXExabMeRDg6Evr++1ZbxU8lDaU1acwVXrW/mC/ssTXbTzUppVYI8TCwGXAEPpRSHhdCvATsl1JuAFYCHwshEoACDMnFbiTklAEQ3ZQRVWd2Glb7s3L/xqenPqVSW8l9ve+zar22ILVa0h97nJr0dDp/tAqXUOskSpU0lNamMYkjUAgxFTjCPxOHWX/tSyk3AhsvuO/5Wn9XAbeas05zataIqoRt4OoNodabwrxCU8Hak2sZFTaqTSwLmz1vPuW7dxP06it4DBpklTpV0lBao8YkjheAQcC9QKgQ4gRwEjgFBFgutJYnPqcMFycH00dUSWno34gcAY7OlgmuDl+d/oqSmhKm95lutTptpfDzzyn85BPaT52K76RJVqnzb0ljRm+69FdJQ2kdLpo4pJTLat82zk/VB+gL7LRQXC3S6exSojp44ehg4jUYeaehOBWuMMu1lI1So6thzfE1XBJ4CX079LVavbZQvncvWS+/gufIEXR86kmr1KmShtKamTyLnZQyDcM1Fj+ZP5yW7XRWKZdENmFE1PnV/qzXMb4hcQM5lTm8PPxlq9VpCzXJyaTNnoNLZAQhCxYgHC2/fnt1hYYN7x4hL1UlDaV1alvTn1pQSZWGjOKqpnWMJ24D/2jw62z+wOqg0+tYdWwVMf4xDAsaZpU6bUFXUkLqzFkIIQh7/30cvSx/RXx1hYYN7xwmL62McTN6E9lPJQ2l9VHrcZjJ6SxDx3gPU6/h0FQaFm6y4qSGW5K3kFKa0qqXhZVaLelzHqMmLY3QRe/iEhZ28Sc1U1V5raTxQB+VNJRWS51xmMkpY+IweZ3x5N2grbJaM5WUkuWxy4n0iWRMuG2mbreG7NfnGUZQvfIyHkOGWLy+c0kjP8OYNPqqcSNK66XOOMwkLquUdq5OhPi6m/bExO3g6GpYuMkKfkv/jdOFp5neZ3qrXRa28LPPKFy7lvb33ovvLbdYvL7aSeNalTSUNkCdcZhJXJZhqhGTm34StkLnYeBi+SuYpZQsO7qMYM9gro281uL12ULZrl1kvfIqXiNH0vHJJyxeX1WZhvXvHKIgs5xrH+hDRB+VNJTWr3X+5LQyKSWnskpMb6YqToPcU1ZrptqfvZ8juUe4t/e9ODtY73oRa6lOSiJ9zmO4du1KsBVGUFWW1fDd24cozKzgupl9VdJQ2gx1xmEGWSVVlFRpTe8YPzcMN2qs+YOqw/Kjyw3LwkZNtEp91qQtLDSMoHJxIez9JRafg6qytIb1bx+iKKeS62b1IbxX25hVWFFAnXGYxfmOcVOH4iZug3ZB0LGnBaL6u9jcWPZk7uHuXnfj5uRm8fqsSdbUkP7Io2izsghdvAjnEMvOQVVRUsN3bx2iOKeS6x/sq5KG0uaoMw4ziDs/FNe78U/SaSDxF4iZYJXV/pbFLsPbxbvVLQsrpSTzhRep2L+f4Df+Z/FV/MqLq1n/1iFKC6q4/qG+hPaw7hT4imIP1BmHGcRllRLo7YaPhwn9Bql/QHUJRF9tucCM4gri2JG6gztj7sTT2TrTiFtLwcqVFH/zDQEPPojPjTdatK7yomq+W3iI0sJqbni4n0oaSpulzjjM4FRWqekd4/E/g4OTVVb7Wx67HE9nT/7V418Wr8uaSrZsIWfBQryvu5aARx62aF1lhVV8t/AQFSU13PhIP4KjfC1an6LYM3XG0UwanZ7EnDLTO8bjt0D4MHAzoXmrCZKKk/j57M/c0eMOfFx9LFqXNVUeO07GU0/j1rcPQa+9ZtEr4EvyKvl2wUEqS2sYP7u/ShpKm6cSRzOdzSunRqc37YyjOA1yjlulmWpl7EpcHV25K+Yui9dlLZrMTNJmzcKpfXvC3nsPBzfLdfYX51by7cKDVFdoGT9nAIFdWk/yVZSmUk1VzdSkqUbitxj+j77KAhH9JbU0lR+TfuSOHnfQ3q11tMfryspJnTkLfWUlER+uxCnActdOFGVX8N1bh9BqdEyYM4AO4U1cS15RWhmVOJopLqsURwdBlCnrjCdsBZ8w6NDDcoFhuG7DUThyb+97LVqPtUitlvQnHqc6IYGwDz7ANTraYnUVZJSz/u1DSCmZ+NhAAkItP7OuorQUqqmqmU5llRIZ4ImrUyOvUtZWQ9IOw9mGBdvl00rT+D7xe27pdgsdPTparB5rkVKS/dprlP+6k8D/ew6v4Zab2ysvrZRvFx4EARMfV0lDUS6kEkczmTzVSMoeqCmzeP/GitgVCCG4r/d9Fq3HWgpWr6bw089of999+E2ebLF6cpJL+G7hIZycHbjp8YG0D2pdw5cVxRxUU1UzlFZpSCus5PbBJqz1EL8FHF0M64tbSEZZBusT1zMpehKdPDtZrB5rKd26lZz5/6Pd1VdbdOLCzIQiflh8BFdPZyY+NgDvABNnOlbshkajIS0tjaqqKluHYvfc3NwIDQ3F2bnx16GpxNEMxzNKAOgdYsJIm9ObIWK4RWfDXRm7EoDpfaZbrA5rqTx6lPQnn8Ktbx+C/zcf4WCZk+S0UwX8uOQoXn5uTJjTHy+/1jUtS1uTlpZGu3btiIiIaLWLlZmDlJL8/HzS0tKIjIxs9PNUU1UzHEsvBkxIHHnxkB8P3a+zWExZ5Vl8k/ANN0fdTKBnoMXqsYaatDRSZz2IU0AAYUuWWGzYbfKxfH547yjeAe7c9MRAlTRagaqqKvz9/VXSuAghBP7+/iafmakzjmaITS8m0NuNDu1cG/eEuI2G/7uNs1hMy48uB2Ban2kWq8MadEVFpN4/A7RawpYtw8nfMhMJJh7M4eeVx/EP8eLGR/vh7uVikXoU61NJo3Ga8jqpxNEMsWnF9Ak1oZkq7icI7AO+lln/Or0snW8SvmFS9CSCvYItUoc16KurSXv4ETRpaYSv+hDXLo0/hTbFqb2ZbF99kk6RPtzwSD9c3dXHQVEaQzVVNVFplYakvHL6NLaZqjwPUvdB9+stFtOyo8twwKFF921IvZ6MuXOp2L+foHmv4zF4sEXqOfZrGts+OklIdz/Gz+6vkobSItx333107NiR3r17/+3+goICrrrqKqKjo7nqqqsoLCy0aBwqcTTRuY7xRp9xnN4MUg/dLbNka2pJKusT1nNr91tbdN9GzhtvUvrTJjo+9RQ+11smyR7YdJZfPztNRN8Arn+oL86ull0pUFHMZerUqWzatOkf98+bN48xY8YQHx/PmDFjmDdvnkXjUD+zmuhcx3ijzzjiNoJ3CAT1s0g8S48uxcnBiWm9W27fRsGaNRSsWoXfnXfS/j7zX+0upWTvd0kc3JxM9JBOjJnaE0dH9duptXvx++OcMP7QM5eYYG/+e2Oveh8/e/Ys1157LcOHD2f37t2EhISwfv163N2bN8R7xIgRnD179h/3r1+/nh07dgBwzz33cOWVVzJ//vxm1dUQ9alpoqNpxQT5uBHg1YiOcU0lJG43nG1YoMPuTPEZfkj6gdu7304Hjw5mL98aSjZtIvv1eXiNHUOnf881e8em1Et2fn6ag5uT6XVFMGPvjVFJQ7Go+Ph4HnroIY4fP46vry9ff/31P7ZZu3Yt/fv3/8e/W265xaS6srOzCQoKAiAwMJDs7Gyz7EN91BlHEx1LL2782caZnaCpsFgz1XuH38PV0bXFXiVevu8PMp56Gvf+/Ql5802Eo3mbjnQ6Pds+Okn8n9kMuCqcYTd3VSNu2pCGzgwsKTIykv79+wMwaNCgOs8UpkyZwpQpU8xarxDC4se3ShxNcK5j/KYBjVzbOm4juLSDiCvMHsuJ/BNsPruZGX1n4O/e8ta+roo7TdrDD+McHk7Y++a/VkNTo2Pz8mMkx+Zz6cQuDBoXYdbyFaU+rq5/tUY4OjpSWVn5j23Wrl3LG2+88Y/7o6KiWLduXaPr6tSpE5mZmQQFBZGZmUnHjpadn04ljiY4lm5Cx7heB6c2QtQYcGrk9R4mePfQu3i7eDO111Szl21pmvR0Uu+/HwcPD8KXL8PR19es5VdXaPhxyVEyE4sZ+a/u9B7RyESvKFZirjOO8ePHs3r1aubOncvq1auZMGGCGaKrn1008goh2gshtggh4o3/+9WxTX8hxB4hxHEhxFEhxO22iBVM7BhP3g3lORBj/jdyf9Z+dqXvYlqfabRzaVlrRWgLCkiZNh19VRVhy5bhHGze607Ki6v5duEhss+UcPW0XippKK3CHXfcwbBhw4iLiyM0NJSVKw3TC82dO5ctW7YQHR3N1q1bmTt3rkXjsJczjrnANinlPCHEXOPtZy7YpgK4W0oZL4QIBg4IITZLKYusHCux6cUE+7jh35iO8RPfgZM7dLvGrDFIKXn30Lt0cO/AHT3uMGvZlqYvLyf1gZloMjMJ/3Albt27mbX84txKNrxziIpSDdc/1JfwmJbXhKe0bBERERw7duz87SeffNIs5X722Wd13u/v78+2bdvMUkdj2MUZBzABWG38ezUw8cINpJSnpZTxxr8zgBzAJkOIYtMbecW4XgcnNkC3q80+qeHOtJ0cyjnEzH4zcXdqObO4ypoa0h6dTdWJE4S89RYegwaZtfzc1FK+fuMA1ZVaJszpr5KGoliAvSSOTlLKTOPfWUCDc4ELIS4BXIDEeh6fIYTYL4TYn5uba9ZAS6o0nGnsFePnm6kmmjUGrV7LWwfeIrxdODdF32TWsi1J6nSkP/MM5bt2EfTSS7QbPcqs5afFFfLtgoM4OgpufnIQgZFqfXBFsQSrNVUJIbYCdV3S/GztG1JKKYSQDZQTBHwM3COl1Ne1jZRyGbAMYPDgwfWW1RQHzhou5R8Q/o9umH+yUDPV+oT1JBYnsvDKhTg7NH4OfVuSUpL14kuGq8KffhrfSTebtfzEgzn8/OFxfDp4MP7RfmqGW0WxIKslDinl2PoeE0JkCyGCpJSZxsSQU8923sCPwLNSyr0WCrVBuxPzcHFyYFDniyQOCzVTVWgqeO/we/Tr0I+x4fW+pHYnd+FbFH35Jf4PPIC/ma8KP/pLKr99GU9gpA/XP9QXN8+WkUwVpaWyl6aqDcA9xr/vAdZfuIEQwgX4FlgjpWz8AGcz252Yz6BwP9ycL3KRmoWaqdacWENuZS5PDn6yxVzElrd8OfnLl+M7+XY6zJlttnKllOz5NoHfvognsm8AE+b0V0lDUazAXhLHPOAqIUQ8MNZ4GyHEYCHECuM2twEjgKlCiMPGf/2tGWRheQ0nMksY1rURHa4WaKbKq8xj1bFVjA0fS/+O/c1WriUVrF1L7oKFeF9/PYH/939mS3Y6reFq8IObU+g1IoRxD/TByUVNVqgo1mAXiUNKmS+lHCOljJZSjpVSFhjv3y+lnG78+xMppbOUsn+tf4etGee+M/lICZddLHHoNHBiPURfZdZmqsWHFlOjq2H2QPP9arekom+/I/vlV/AaPZrgea+bbSqR6kotPyw+Qty+LIaOj2TkHd1wcGgZZ1+K0lSpqamMGjWKmJgYevXqxTvvvHP+MTWtuh3bnZiPh4sjfUN9G94wYRuU50K/yWar+1TBKb6J/4Y7et5BhE+E2cq1lJJNm8l89lk8hl1KyFsLEc7maUIqK6zi2zcPkHG6iDFTezL4usgW02SnKM3h5OTEggULOHHiBHv37uW9997jxIkTgJpW3a7tTsxnSER7XJwukm8PrwWPAIi+2iz1SimZ98c8fF19mdlvplnKtKTS7dtJf/JJ3Pv1I2zxYhxczTPVSm5qKT++d5SaKi03PNKPsJ7tzVKu0sr9NBeyYs1bZmAfuLb+L2dLTKseFBR0fgbcdu3a0bNnT9LT04mJiVHTqturnJIqEnLKLt5MVZ5vWCK27+3gaJ5f2T8n/8yB7AM8POBhvF28zVKmpZT99hvps+fg1rMnYcs+wMHTPE11Z2Pz+PbNgwgBNz85SCUNxe5Zclr1s2fPcujQIYYOHQqoadXt1p6kfAAu6xrQ8IbH1oFeA/3/ZZZ6q7RVLNy/kG5+3ZgUPcksZVpK+d69pD38CC5RUYSvWI5jO/PMn3VsZzo7P4vDP9SLGx7qh6ev+SeLVFqxBs4MLMlS06qXlZUxadIk3n77bby9//lDUk2rbkd2J+Tj7eZETPBFfvEfXguBfSGwd8PbNdKq46vIKM/gw+Ef4uhgv6OGyvfuI3XmLFzCwwn/cCWOPs2/aluvl+xel8CR7al07uPP1dN64eKmDlmlZbDEtOoajYZJkyYxZcoUbr75r4to1bTqdmp3Uh6XdvHHsaHRO1nHIPMIXPs/s9SZWpLKiqMruCbiGoYEDjFLmZZQvu8PUmfOxCUslPCPVuHk14ir6i+ipkrLlpXHORubT9/RoVx+S7QaOaW0OqaccUgpmTZtGj179uTxxx//22Ntclp1e5eSX0FqQeXF+zcOfwoOztDbtGUf6yKl5NU/XsXZ0Zmnhzzd7PIspeLPP0mdORPn0BDCP/oIJ//mTypYWlDFN28eJPl4ASMmd+OK29RwW0XZtWsXH3/8Mdu3bz/fF7Jx40ag7U6rbtfWHUxDCBjTs4G5F7XVcPQL6D4OPJv/5bk1ZSu70nfxzJBn6Ohh2dPOpirfs4fUWQ/iHBJCZzMljczEYn5aehSdRs8ND/UlvJea3VZpeSwxrfrw4cORsu6p96w9rbpKHBeh1en54s8URnbrQFh7j/o3PPY1VOTBoObPw1SuKWfeH/Po7tedyT3Mdy2IOZX99jtpDz+MS+fOhK/60CxJ49TeTH755BTt/Ny47vG+tA8y71T0iqKYh0ocF7HtVA7ZJdW8MrFz/RtJCXuWQIee0HV0s+tcfGgxORU5LBi5ACcH+3uLSnfsIP2RRw2jpz5c2ew+Db1Oz55vEzm8NZWQ7n6Mm9FbzTmlKHbM/r6V7MzafSkE+bgxqnsDa0ad/Q2yY2H8ImjmMLjDOYdZe3Itt3e/3S7noyrZtIn0J5/CrXt3wleuaPY64VXlGn5eeZzUEwX0uTKUy2+NwtFRdb0pij1TiaMBKfkV7Dydy2Nju+HU0JfZniWGK8X73Nas+qp11fx3938J9AzksUGPNassSyj69jsyn30W9/79CftgabOv08jPKOOn92MpLahi1J09iBlu3nXHFUWxDJU4GvDpHyk4OghuHxJW/0Z5CXD6Jxj5DDg3b/GgD458QFJxEkvHLsXT2b7a9wvWriX75VfwvGwYoYsX4+DRQH9PIyQcyGHbmpO4uDoy8fGBBHVVq/UpSkuhEkc9qrU6vtqfytieHQn0aSAh7HsfHF1gyPRm1Xcy/yQfHvuQCV0ncHnI5c0qy5yklOQtWULeosV4jR5NyFsLmzX3lF4v2bc+kYObUwjs4s24GX3UleCK0sKoxuR6bD2RQ355DVOGNtApXpZruHajz63g1fQhs9W6av7z+3/wc/PjqSFPNbkcc5N6PdmvvU7eosX4TJhA6LvvNCtpVJTUsOGdwxzcnELMFcFMfGygShqKYiKdTseAAQO44YYbzt935swZhg4dSlRUFLfffjs1NTUWjUEljnpc3asTK+8ZzPCoBuam+nWe4fqN4c3rj3j7wNskFCXw8uUv4+NqH002sqaGjGfmUvjxx7S/526CXn8N4dT0E9SspGK+fO1PspKKGX13D0ZN6YGjszr8FMVU77zzDj179vzbfc888wyPPfYYCQkJ+Pn5sXLlSovGoJqq6uHs6NDwBX958bB/FQy+FwKim1zPrvRdfHLyE6b0nMLwkOFNLsecdGVlpD/6KOW799Bhzhz8H5jR5EnTpJQc3Z7G7m8S8PJzZdLTg+gQZp7JDxWlMeb/MZ9TBafMWmaP9j145pJn6n3cEtOqA6SlpfHjjz/y7LPPsnDhQsDwGdu+fTuffvopYJhW/YUXXmDWrFnNqqsh6idfU235Lzh7wMimX9pfUFXAc7ueI8o3ym5GUWlzc0m+627K9/1B0GuvETDzgSYnjeoKDZs+OMbvX8UT3sufW/89RCUNpc2wxLTqc+bM4X//+x8ODn99defn5+Pr64uTsUUgNDSU9PR0y+yUkTrjaIrk3RD3I4x+DrwauL6jAXqp5/92/R/F1cUsHbsUV0fbt/VXJySQOuMBtEVFhC19H68rrmhyWTnJJWxefoyygmoumxRF/7FhaqU+xSYaOjOwJHNPq/7DDz/QsWNHBg0adH7RJltRicNUej38/By0C4ZLH2pyMcuPLmdn2k7+M/Q/dG/f3YwBNk357t2kzZ6DcHOl85o1uPfu1aRypF5yZHsqe75NxMPbhYlPqKG2Sttk7mnVd+3axYYNG9i4cSNVVVWUlJRw55138vHHH1NUVIRWq8XJyYm0tDRCQkLMv0O1qMRhqj2LIP0ATHwfXJp2LcPu9N28d/g9ru9yPZO7234uqqJ168h84UVcu3QhbOn7OAc37UK8ytIatq0+SfKxfCL7BTD67p5q6hBFaYApZxyvv/46r7/+OgA7duzgzTff5JNPPgFg1KhRrFu3jsmTJ1tlWnWVOEyRshe2vggxE6HfHU0qIqMsg2d+e4auvl15/tLnbdp8I3U6ct54k4KPPsLz8ssJeedtHL28mlRWyvF8tq4+SXWFhhGTu9F7ZIhqmlIUK5k/fz6TJ0/mueeeY8CAAUybNs2i9Yn6pultLQYPHiz379/f/ILK82DpFeDkCg/8Cm6mN79UaCqYumkqqaWpfH7D53T2buAaEQvTlZaS/vgTlP/2G3533UWnZ55u0nBbrUbH3m+TOLI9lfbBnlx1Xy8CQpuWfBTFXE6ePPmPIatK/ep6vYQQB6SUg+vaXp1xNIZeB98+ABX5MH1Lk5KGVq/lqZ1PEVcYx6LRi2yaNKqTkkh7+BFqUlIIfOlF/G5r2hxbeWmlbPnwBAUZ5fS5MpTLbu6Kk4v9Lm+rKIp5qMRxMZWF8PV0SNgK1y+EoH4mFyGlZN4f89iZtpNnhz7LiNARFgi0cUq3biXjmbkIV1c6r/oQjyGmL0mr10sO/ZzMH9+fwc3TmRse7kfn3mrBJUVpK1TiaEjOKfj8DihKhRvegsH3NamY1cdX80XcF0ztNdVmCzNJnY7cRYvIX/oBbn37EvruOzgHBppcTmFWOdvXnCQrqYSuAzty5b+64+alOsAVpS1RiaM+Z3bCZ3cYLvKb+gOEX9qkYj4/9TkLDizg6s5X2+wiP21uLulPPkXFvn343noLnZ57zuQ5p/R6yZFtqezbkISTswNj742h2yWdVAe4orRBKnHUxz8aIkfAdW+CT9PGRH91+ite3fcqV4Zdybwr5uEgrH+hfvm+P0h/8gn0pWUEvfYavjffZHIZ+Rll/PLxKbLPlBDRN4Arp3TH08f2FywqimIbKnHUxzsI7visyU//Jv4bXtrzEiNCR7Bg5AKcHa3bnCO1WsN06Es/MKwLvmIlbt27mVSGTqPnwKazHNiUjIubkzrLUBQFUInD7KSULDu6jMWHF3N5yOUsvHIhLo4uVo2hJi2NjCefovLwYXwmTqTTc8/h6GXawlAZ8YXsWBtHYVYF0UM6ccVt0bi3s+5+KIryd2+99RYrVqxACEGfPn1YtWoVbm5unDlzhsmTJ5Ofn8+gQYP4+OOPcXGx3OdVTXJoRhq9hud3P8/iw4sZ33U8i0YtsuocVFJKir75ljMTb6I6IYHgN98keN7rJiWNqjIN29ec5NsFh9DW6Ln+ob5cPa2XShqKYmPp6em8++677N+/n2PHjqHT6fj8888BNa16i5VXmcfcnXPZl7WPB/s9yMx+M63apKPNzSXzvy9Qtn077oMHETxvHi6hoY1+vl4vOfF7BnvXJ6Kp1DHwmnAGXx+Js7ouQ2nhsl57jeqT5p1W3bVnDwL/8596H7fUtOparZbKykqcnZ2pqKggODi47U6rLoRoL4TYIoSIN/7v18C23kKINCHEYmvG2JCdaTuZtGESh3MP8+rwV5nVf5bVkoaUkuLvfyDpxvGU//47Hec+Q+c1a0xKGllnilk3bz+/fhqHf7AXtz07hGE3RamkoSjNYO5p1UNCQnjyyScJDw8nKCgIHx8frr766jY9rfpcYJuUcp4QYq7xdn1zIb8M7LRaZA0oqSlh0cFFfB73Od38uvHhNR/S1ber1erXZGSQ+eKLlP+6E7d+fQl+7TVcuza+/tKCKvZ+l8jpP7Lx9HHh6mm9iBrcUXV+K61KQ2cGlmTuadULCwtZv349Z86cwdfXl1tvvZVPPvmEcePGmTHqxrGXxDEBuNL492pgB3UkDiHEIKATsAmocw4Va9Dqtaw7vY4lh5dQVF3EnT3vZM6gOVbrz5AaDQWfrCVv0SKklHT6z7/xmzIF4di4M4SaKi2HtqRw+OcUpIRB13Zm4DWdcXGzl8NBUVo+c0+rvnXrViIjI+nQwbAG0M0338zu3buZMmVKm51WvZOUMtP4dxaG5PA3QggHYAFwJzC2ocKEEDOAGQDh4eFmC7K0ppQfkn7g05OfcrbkLEMCh/Dk4CeJ8Y8xWx0XU/Hnn2S99DLV8fF4jhxB4P89j0to4w4SnU7Pyd8z+OOHM1SWaoga1JFhN3XFO6B57a6KojSNKWcc4eHh7N27l4qKCtzd3dm2bRuDBw9GCNF6p1UXQmwF6prj4tnaN6SUUghR15S9DwIbpZRpF2tKkVIuA5aBYXbcpkVskFeZx/7s/exK38Xms5up1FbSs31P3h31LleGXWm1Zp2atDRyFy6kZONPOAcHE/reYrxGj25U/VIvSTiQw77vkyjOqSQoyofrZkUR2EUtsKQoLcXQoUO55ZZbGDhwIE5OTgwYMIAZM2YAbXRadSFEHHCllDJTCBEE7JBSdr9gm7XAFYAe8AJcgCVSygYX/W7qtOp/Zv3JS3te4mzJWQA8nDwYFzmO27rdRq+Apq2O1xS6khLyly2jYPUacHTE/7778L9/Og6NGJ0hpeTMkTz++D6J/PRy2gd7cunErkT08Vf9GEqrpqZVN01LnVZ9A3APMM/4//oLN5BSnj+fE0JMBQZfLGk0h7+7PxHeEUyKnsSgToPo6d8TJwfrvVz6igoKPv6E/A8/RF9cjM/EiXSYM7tRExNKvSTpSC77N54lL7UMn47uXDUthuhBnRAOKmEoitI89pI45gFfCiGmAcnAbQBCiMHATCnldGsH1MWnC4vGLLJ2tejLyyn84kvyV65El5+P18iRdJj9KG4xF+9H0en0JOzP4eDmZAoyyvHp6M6Ye3rS7ZJOODjaxchrRVFaAbtIHFLKfGBMHffvB/6RNKSUHwEfWTwwK9IVFVGwdi2Faz5GV1yMx6WX0mHRIjwGDrjoc2uqtJzcncnhrSmUFVQbV+KLIWpwJxzUGYaiKGZmF4mjLatOSKBgzccUb9iArKrCa/RoAmbcj7tx/HdDSvIqObojjZO7Mqmp1BIU5cPIyd3p3NtfNUkpimIxKnHYgL66mtItWylat46KvXsRrq74jL8Rv7vuwq1bwzPY6vWSlOP5HP8tg+TYPIQQdB3Ygb6jw9QoKUVRrEIlDiuRej2Vhw5R8uOPFP+4EX1xMc6hoXSYMwff22/Dya/eWVYAw1Xep/ZkcnJ3JqX5Vbh7uzDwms70HhmCl5+blfZCURRFJQ6LkhoNFQcPUfbLL5Rs3ow2MxPh6kq7MWPwvfUWPIYORTjU32ldU6kl6UgucXuzSIsrBAkh3f0YdlNXuvTvgKOT6vBWlLbkvvvu44cffqBjx44cO3bs/P0FBQXcfvvtnD17loiICL788kv8/PyQUjJ79mw2btyIh4cHH330EQMHDmx2HCpxmJGUEk1yMuX7/qBi317Kft+FvqQE4eyM52WX4f34Y3iNGt3gNOc1VVpSjheQcCCbs7H56DR62vm7MeT6SHpcGqiu8laUNmzq1Kk8/PDD3H333X+7f968eYwZM4a5c+cyb9485s2bx/z58/npp5+Ij48nPj6effv2MWvWLPbt29fsOFTiaCIpJdqcHKoTEqg6dpzK2KNUHY1Fm5MDgFPHjrQbMwavUVfiednlDSaL8uJqko/lc+ZIHqknCtBp9bi3cybm8mC6XdKJTpHe6oI9RWmi3748TV5qmVnLDAjz4orb6u+PtNS06iNGjKhzssT169ezY8cOwDCt+pVXXsn8+fNZv349d999N0IILr30UoqKisjMzCQoKKhZcajEUQ9daSk1iYnoiosN/woL0WRlo8nMRJORQU1SEvqyvw5Gl4gIPIYOxWPQQDyGDsUlIqLeL3utRkdWYjFppwpJOVFAbkopAF5+rsRcEUzXAR0I6uqjrr1QlBYsPj6ezz77jOXLl3Pbbbfx9ddfc+edd/5tG1MmOWxIdnb2+WQQGBhIdnY2YFj8KSws7Px256ZcV4nDQioPHiT1gZl/u0+4uuIcFIRzcBA+48fjEtUV1y5dcevZA0ef+kc0VVdoyDpTQlZiMZmJRWQllaDT6BEOgsBIb4ZO6EJEH3/8Q7zUmYWimFlDZwaWZO5p1RtLCGHx7xGVOOrh1qcPYcs+wNHHBwdvbxx9fXH09W3wDZFSUlZYTX56GQUZ5eSmlpKbXEpxrmE6ZSEgIKwdva4IJqxHe4KjfXFxV2+BorRG5p5WvSGdOnU63wSVmZlJx44dAcPiT6mpqee3M9eU6+pbqx5O7dvjNWLE+dtSSjRVOirLNFSW1VBRVENZURVlBdWU5FVSlFtJSW4lmmrd+ed4tXelY7g3PS4LolOEN50ivdWaF4qinGeuM47x48ezevVq5s6d+7dp1cePH8/ixYuZPHky+/btw8fHp9nNVKASR70y4gvZsTYOTbXO8K9Kh17/z5mEHZwE3v7u+HR0JyTaF78gT9oHe9I+yBM3T2cbRK4oSmt1xx13sGPHDvLy8ggNDeXFF19k2rRpzJ07l9tuu42VK1fSuXNnvvzySwCuu+46Nm7cSFRUFB4eHqxatcoscdjFtOqW1NRp1fPSStm/MRlnN0ecXQ3/3Dydcfdyxs3TGU9fV7z8XHHzclb9EopiZ9S06qZpqdOq252A0HaMm9Hb1mEoiqLYHTXeU1EURTGJShyKorRKrb0Z3lya8jqpxKEoSqvj5uZGfn6+Sh4XIaUkPz8fNzfTJkpVfRyKorQ6oaGhpKWlkZuba+tQ7J6bmxuhoaEmPUclDkVRWh1nZ2ciIyNtHUarpZqqFEVRFJOoxKEoiqKYRCUORVEUxSSt/spxIUQukGzCUwKAPAuFY8/a4n63xX2GtrnfbXGfoXn73VlK2aGuB1p94jCVEGJ/fZfZt2Ztcb/b4j5D29zvtrjPYLn9Vk1ViqIoiklU4lAURVFMohLHPy2zdQA20hb3uy3uM7TN/W6L+wwW2m/Vx6EoiqKYRJ1xKIqiKCZRiUNRFEUxiUoctQghxgkh4oQQCUKIubaOxxKEEGFCiF+EECeEEMeFELON97cXQmwRQsQb//ezdayWIIRwFEIcEkL8YLwdKYTYZ3zPvxBCuNg6RnMSQvgKIdYJIU4JIU4KIYa1hfdaCPGY8fg+JoT4TAjh1hrfayHEh0KIHCHEsVr31fn+CoN3jft/VAgxsKn1qsRhJIRwBN4DrgVigDuEEDG2jcoitMATUsoY4FLgIeN+zgW2SSmjgW3G263RbOBkrdvzgbeklFFAITDNJlFZzjvAJillD6Afhn1v1e+1ECIEeBQYLKXsDTgCk2md7/VHwLgL7qvv/b0WiDb+mwG839RKVeL4yyVAgpQySUpZA3wOTLBxTGYnpcyUUh40/l2K4YskBMO+rjZuthqYaJMALUgIEQpcD6ww3hbAaGCdcZNWtd9CCB9gBLASQEpZI6Usog281xhm/nYXQjgBHkAmrfC9llLuBAouuLu+93cCsEYa7AV8hRBBTalXJY6/hACptW6nGe9rtYQQEcAAYB/QSUqZaXwoC+hkq7gs6G3gaUBvvO0PFEkptcbbre09jwRygVXG5rkVQghPWvl7LaVMB94EUjAkjGLgAK37va6tvvfXbN9xKnG0UUIIL+BrYI6UsqT2Y9IwRrtVjdMWQtwA5EgpD9g6FityAgYC70spBwDlXNAs1Urfaz8Mv64jgWDAk38257QJlnp/VeL4SzoQVut2qPG+VkcI4YwhaayVUn5jvDv73Gmr8f8cW8VnIZcD44UQZzE0Q47G0P7va2zOgNb3nqcBaVLKfcbb6zAkktb+Xo8Fzkgpc6WUGuAbDO9/a36va6vv/TXbd5xKHH/5E4g2jrxwwdCZtsHGMZmdsV1/JXBSSrmw1kMbgHuMf98DrLd2bJYkpfy3lDJUShmB4b3dLqWcAvwC3GLcrFXtt5QyC0gVQnQ33jUGOEErf68xNFFdKoTwMB7v5/a71b7XF6jv/d0A3G0cXXUpUFyrScsk6srxWoQQ12FoB3cEPpRSvmrbiMxPCDEc+A2I5a+2/v9g6Of4EgjHMA39bVLKCzvdWgUhxJXAk1LKG4QQXTCcgbQHDgF3SimrbRieWQkh+mMYDOACJAH3YvjB2KrfayHEi8DtGEYRHgKmY2jPb1XvtRDiM+BKDNOnZwP/Bb6jjvfXmEQXY2i2qwDulVLub1K9KnEoiqIoplBNVYqiKIpJVOJQFEVRTKISh6IoimISlTgURVEUk6jEoSiKophEJQ5FURTFJCpxKIqiKCZRiUNRrEgI8ZUQYrEQ4nchRLIQYrgQ4mMhxGkhxEpbx6cojeF08U0URTGjPsAeKeXDQoj/YJj+5UoMs9imCSFcW/rVzErrpxKHoliJEMIN8MUwrQ0YZi1deW6+ICGEDqixSXCKYgLVVKUo1tMLOCilPDdHWD8Mc4SdW2QqQ6o5gJQWQCUORbGePsCRWrf7AkeNf/er9bei2DWVOBTFevoAh+F8s5W7lLLQ+FjtJKIodk3NjqsoiqKYRJ1xKIqiKCZRiUNRFEUxiUociqIoiklU4lAURVFMohKHoiiKYhKVOBRFURSTqMShKIqimOT/AW8/ZgN8jAqBAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "\n",
    "for n in [10, 20, 40, 80, 100]:\n",
    "    H_tb = TBHamiltonian(n)\n",
    "    # TODO: Decide whether to implement this + 1 - 1 trick here or in QREig above.\n",
    "    E_m  = QREig(H_tb + np.eye(n)) - 1\n",
    "    plt.plot(np.arange(len(E_m)) + 1, np.sort(E_m), label=\"n = {}\".format(n))\n",
    "\n",
    "plt.legend()\n",
    "plt.title(\"Energy eigenvalues of $H_{{tb}}$ for different chain lengths $n$\")\n",
    "plt.xlabel(\"$m$\")\n",
    "plt.ylabel(\"$E_m$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "c2b46d2fef4b0c243103a5a6f1111e2d",
     "grade": false,
     "grade_id": "cell-b7c84b8c4ed4c1be",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "### Task 3.5 [3 points]\n",
    "Implement a function to calculate the so-called density-of-states \n",
    "\n",
    "\\begin{align*}\n",
    "    \\rho(\\omega) = \\frac{1}{N} \\sum_i \\delta(\\omega - E_i),\n",
    "\\end{align*}\n",
    "\n",
    "for a variable energy grid $\\omega$. Do this by approximating the $\\delta$-distribution with a Gaussian. In detail, you can use your atomic orbital function $\\delta(\\omega - E_i) \\approx \\phi(\\omega, E_i, \\sigma_\\rho)$. Calculate the normalization factor $N$ such that $\\int \\rho(\\omega) dw = 1$ is fulfilled.\n",
    "\n",
    "Your function should take as input the energy grid $\\omega$, the eigenenergies $E_i$ and the broadening $\\sigma_\\rho$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "ca46cf0b09305fafb522fc0395d1e495",
     "grade": true,
     "grade_id": "cell-d7c225b7687b5a9c",
     "locked": false,
     "points": 3,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "def getDOS_ED(w, Ei, sigma):\n",
    "    \"\"\"\n",
    "    Calculates the density-of-states (DOS) for energy grid w by\n",
    "    counting the occupation using a Gaussian approximation to the\n",
    "    delta function.\n",
    "    \n",
    "    Args:\n",
    "        w:     grid of energies to calculate the DOS over\n",
    "        Ei:    array of n eigenenergies for the system\n",
    "        sigma: standard deviation to the Gaussian\n",
    "\n",
    "    Returns:\n",
    "        Tight-binding hamiltonian H_tb.\n",
    "    \"\"\"\n",
    "    \n",
    "    # TODO: Kijk nog eens kritisch naar de omschrijving hierboven van de functie.\n",
    "    \n",
    "    # Luckily, the function is built in such a way it can also\n",
    "    # handle an array input as its first argument.\n",
    "    delta = atomic_basis(w, Ei, sigma, True)\n",
    "    \n",
    "    rho = np.sum(delta, axis=1)\n",
    "    \n",
    "    # Now normalize rho.\n",
    "    N = integrate(rho, w)\n",
    "    rho /= N\n",
    "    \n",
    "    return rho"
   ]
  },
  {
   "attachments": {
    "dosN010.png": {
     "image/png": "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"
    },
    "dosN100.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "b2049bb4d5fb56c59e7d0e742a91d3c8",
     "grade": false,
     "grade_id": "cell-7560c4658b1da5d3",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "### Task 3.6 [3 points]\n",
    "Use your density-of-states routine to calculate $\\rho(\\omega)$ for $n=10,20,40,80,100$ for $\\sigma_\\rho \\approx 0.005$. See below for two examples with $t \\approx -0.195$ and $n=10$ and $n=100$.\n",
    "\n",
    "Hint: if your plots look like they are smoothed out, try decreasing $\\sigma_\\rho$. If they look like there is a lot of noise, try increasing $\\sigma_\\rho$.\n",
    "\n",
    "$n = 10$ | $n = 100$\n",
    ":-: | :-:\n",
    "![dosN010.png](attachment:dosN010.png) | ![dosN100.png](attachment:dosN100.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "10cb847540f9e1998c9c1b40c5e43a7b",
     "grade": true,
     "grade_id": "cell-c3083a03553a2aa9",
     "locked": false,
     "points": 3,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sigma = .005\n",
    "w = np.linspace(-.5, .5, 1000)\n",
    "\n",
    "plt.figure(figsize=(10, 6))\n",
    "\n",
    "for n in [10, 20, 40, 80, 100]:\n",
    "    H_tb = TBHamiltonian(n)\n",
    "    # TODO: Decide whether to implement this + 1 - 1 trick here or in QREig above.\n",
    "    E_m  = QREig(H_tb + np.eye(n)) - 1\n",
    "    DOS = getDOS_ED(w, E_m, sigma)\n",
    "    plt.plot(w, DOS, label=\"n = {}\".format(n))\n",
    "\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.title(\"Density of states $\\\\rho(\\\\omega)$ for different chain lengths $n$\")\n",
    "plt.xlabel(\"$m$\")\n",
    "plt.ylabel(\"$E_m$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "69c457b9ef8fbd13ad935fe12c37c81c",
     "grade": false,
     "grade_id": "cell-362439917c95705f",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "## Step 4: Tight-Binding Propagation Method\n",
    "\n",
    "Now we turn to the time-dependent Schrödinger equation\n",
    "\n",
    "\\begin{align}\n",
    "    i\\hbar\\frac{\\partial}{\\partial t} \\psi(x,t) = H \\psi(x,t),\n",
    "\\end{align}\n",
    "\n",
    "which has the formal solution\n",
    "\n",
    "\\begin{align}\n",
    "    \\psi(x,t) = U(t) \\psi(x,t=0),\n",
    "\\end{align}\n",
    "\n",
    "with \n",
    "\n",
    "\\begin{align}\n",
    "    U(t) = e^{-i \\hbar H t}\n",
    "\\end{align}\n",
    "\n",
    "being the time-propagation operator. Within the propagation method we can calculate the so-called local density-of-states\n",
    "\n",
    "\\begin{align}\n",
    "    \\rho_{loc}(\\omega) = \\frac{1}{2\\pi} \\int_{-\\infty}^{+\\infty} \\, e^{i\\omega t} \\, f(t) \\ dt,\n",
    "\\end{align}\n",
    "\n",
    "with respect to an (arbitrary) initial state $\\psi(x,t=0)$, where\n",
    "\n",
    "\\begin{align}\n",
    "    f(t) &= \\int_{-\\infty}^{+\\infty} \\, \\psi^*(x,t) \\, \\psi(x,t=0) \\, dx \\\\\n",
    "         &\\approx \\int_{-\\infty}^{+\\infty} \\sum_i c_i^*(t) \\phi(x,x_i,\\sigma) \\, \\sum_j c_j(0) \\phi(x,x_j,\\sigma) \\, dx \\notag \\\\\n",
    "         &\\approx \\sum_i c_i^*(t) c_i(0). \\notag\n",
    "\\end{align}\n",
    "\n",
    "Thus, the time propagation of an initial state towards positive *and* negative times followed by a Fourier transform of $f(t)$ yields the local density-of-states. To obtain the full density-of-states we need to average $\\rho_{loc}(\\omega)$ as follows\n",
    "\n",
    "\\begin{align}\n",
    "    \\rho(\\omega) = \\lim_{S \\to \\infty} \\frac{1}{S} \\sum_p^S \\rho^{(p)}_{loc}(\\omega)\n",
    "\\end{align}\n",
    "\n",
    "over a variety of *random* initial states $p$.\n",
    "\n",
    "### Task 4.1 [3 points]\n",
    "Implement a function which calculates the exact time-propagation matrix $U(\\tau)$ for a small time-step $\\tau$ given the Hamiltonian $H$. For simplicity, set $\\hbar = 1$ in the following. \n",
    "\n",
    "Hint: Use Scipy's $\\text{expm()}$ function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "6cb01e4b3c6c192a0df3c4111b91c8fa",
     "grade": true,
     "grade_id": "cell-42a7aac3f0fa4d1b",
     "locked": false,
     "points": 3,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "def getU_exact(tau, H):\n",
    "    # YOUR CODE HERE\n",
    "    raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "79f8101b73fbb28ff9138437e9767178",
     "grade": false,
     "grade_id": "cell-9b02ad5515424242",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "### Task 4.2 [3 points]\n",
    "Implement a function which performs the step-by-step time propagation given an initial state $\\vec{c}(0)$, the matrix $U(\\tau)$ and the discretized time grid $t_j$. In other words, your function should calculate \n",
    "\n",
    "$$\\vec{c}(j+1) = U(\\tau) \\cdot \\vec{c}(j)$$ \n",
    "\n",
    "for all $j$ of a given discretized time grid $t_j = j \\tau$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "dc040cc32e832b097bfb8c367f4203a1",
     "grade": true,
     "grade_id": "cell-4e444f44bf3bc9c1",
     "locked": false,
     "points": 3,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "def timePropagate(U, c0, t):\n",
    "    # YOUR CODE HERE\n",
    "    raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "61362905e7a2d19219ae21f10a417823",
     "grade": false,
     "grade_id": "cell-62bfe608c358ff6d",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "### Task 4.3 [4 points]\n",
    "Use both of the above functions to calculate and animate the time propagation of an initial state\n",
    "\n",
    "$$\\psi(x,t=0) = \\phi(x, x_{i=n/2}, \\sigma) \\leftrightarrow \\vec{c}(0) = [c_{i=n/2}(0) = 1, c_{i\\neq n/2}(0) = 0]$$\n",
    "\n",
    "for a $n=100$ chain. Discretize your time grid as $t_j=j\\tau$ with $j=0 \\dots 200$, and $\\tau=1.5$. Use again $a = 1$ and $\\sigma=0.25$. \n",
    "\n",
    "To plot / animate the time propagation you should plot the real-space wave function $\\psi(x,t) \\approx \\sum_i c_i(t) \\phi(x, x_i, \\sigma)$.\n",
    "\n",
    "Hint: use your function from task 3.4 to get the Hamiltonian $H$.\n",
    "\n",
    "For the animation you can use the following draft:\n",
    "```python\n",
    "# use matplotlib's animation package\n",
    "import matplotlib.pylab as plt\n",
    "import matplotlib\n",
    "import matplotlib.animation as animation\n",
    "# set the animation style to \"jshtml\" (for the use in Jupyter)\n",
    "matplotlib.rcParams['animation.html'] = 'jshtml'\n",
    "\n",
    "# create a figure for the animation\n",
    "fig = plt.figure()\n",
    "plt.grid(True)\n",
    "plt.xlim( ... )     # fix x limits\n",
    "plt.ylim( ... )     # fix y limits\n",
    "\n",
    "# Create an empty plot object and prevent its showing (we will fill it each frame)\n",
    "myPlot, = plt.plot([0], [0])\n",
    "plt.close()\n",
    "\n",
    "# This function is called each frame to generate the animation (f is the frame number)\n",
    "def animate(f):                   \n",
    "    myPlot.set_data( ... )  # update plot\n",
    "\n",
    "# Show the animation\n",
    "frames = np.arange(1, np.size(t))  # t is the time grid here\n",
    "myAnimation = animation.FuncAnimation(fig, animate, frames, interval = 20)\n",
    "myAnimation\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "dac0e917be4cfe57c7d30715f3f61912",
     "grade": true,
     "grade_id": "cell-dd676b90f6a61df6",
     "locked": false,
     "points": 4,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "# YOUR CODE HERE\n",
    "raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "6786036a70e4fffbda4c92e340ff90de",
     "grade": true,
     "grade_id": "cell-70e223783d806888",
     "locked": false,
     "points": 0,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "# Animate here ...\n",
    "\n",
    "# YOUR CODE HERE\n",
    "raise NotImplementedError()\n",
    "\n",
    "# Yann has an animation about an atomic orbital that starts\n",
    "# moving to left and right and then bounce back."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "74ab18f8b5e98bc5456ef221449f9299",
     "grade": false,
     "grade_id": "cell-0395602360fd9e4c",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "### Task 4.4 [3 points]\n",
    "Implement a function which calculates the Crank-Nicolson time-propagation matrix \n",
    "\n",
    "\\begin{align*}\n",
    "    U_{CN}(\\tau) = (I - i \\tau H / 2)\\cdot(I + i \\tau H / 2)^{-1}.\n",
    "\\end{align*}\n",
    "\n",
    "Here, $I$ is the diagonal identity matrix. Use Numpy's $\\text{inv()}$ function to invert the needed expression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "1b2677753953d9a528f0dbb71d4077bb",
     "grade": true,
     "grade_id": "cell-d74914e5d0a13365",
     "locked": false,
     "points": 3,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "def getU_CN(tau, H):\n",
    "    # YOUR CODE HERE\n",
    "    raise NotImplementedError()\n",
    "\n",
    "# Yann notes that the definition of $U_{CN}(\\tau)$ here is a little\n",
    "# different from what Malte used on the slides. He recommends using\n",
    "# what is stated here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "3746f3298575d0e0c37d35c01039e60e",
     "grade": false,
     "grade_id": "cell-1daec83575502040",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "### Task 4.5 [5 points]\n",
    "Implement a function which calculates the time-propagation matrix using the Trotter-Suzuki decomposition \n",
    "\n",
    "\\begin{align*}\n",
    "    U_{TZ}(\\tau) = e^{-i\\tau H_1} \\cdot e^{-i \\tau H_2}.\n",
    "\\end{align*}\n",
    "\n",
    "In this approach you choose a decomposition of the tight-binding Hamiltonian $H = H_1 + H_2$, which allows you to analytically diagonalize $H_1$ and $H_2$ (see last lecture). From this analytic diagonalization you will be able to calculate the matrix exponentials $e^{-i\\tau H_1}$ and $e^{-i \\tau H_2}$.\n",
    "\n",
    "Write your definition of the 2x2 blocks in $e^{-i\\tau H_1}$ and $e^{-i \\tau H_2}$ in the Markdown cell below. (Double click on \"YOUR ANSWER HERE\" to open the cell, and ctrl+enter to compile.) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "566fe9a7f8031baea9812438b155671c",
     "grade": true,
     "grade_id": "cell-bef909a443eb2a68",
     "locked": false,
     "points": 2,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "source": [
    "YOUR ANSWER HERE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "f9f25759b1a81bbac8c1834c2f4565b8",
     "grade": true,
     "grade_id": "cell-1425de6027596dea",
     "locked": false,
     "points": 3,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "def getU_TZ(tau, H):\n",
    "    # YOUR CODE HERE\n",
    "    raise NotImplementedError()\n",
    "\n",
    "# Yann mentions again that this is slightly different wrong what\n",
    "# is in the slides/lecture."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "1747285f36e24921cb5c2811632f33c3",
     "grade": false,
     "grade_id": "cell-f53dc443bd1858b1",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "### Task 4.6 [3 points]\n",
    "In your implementation of $U_{TZ}(\\tau)$ you analytically evaluate the matrix exponentials $e^{-i\\tau H_1}$ and $e^{-i \\tau H_2}$. Test your implementation by comparing your results for these matrix exponentials to those obtained using Scipy's $\\text{expm()}$ function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "684e4173792cb10809386ef097c561e4",
     "grade": true,
     "grade_id": "cell-5aa3ffce9359fa7e",
     "locked": false,
     "points": 3,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "# YOUR CODE HERE\n",
    "raise NotImplementedError()\n",
    "\n",
    "# Yann printed\n",
    "#Biggest differences of U1 with Scipy:\n",
    "#Real: 1e-16 \n",
    "#Imag: 2.77e-17\n",
    "#    \n",
    "# and difference with U_exact in the order of 1e-1 or 1e-2."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "94ca5bdd479043f3c73214a3c4916923",
     "grade": false,
     "grade_id": "cell-c255a2bf5eac4e2b",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "### Task 4.7 [6 points]\n",
    "In the next task you will need a Fourier transform to calculate the local density-of-states. Therefore you will need to implement a function that returns the Fourier transform $f(\\omega)$ of a given function $f(t)$ defined on a time grid $t$, for a given energy grid $\\omega$. I.e. it should calculate:\n",
    "\n",
    "\\begin{align}\n",
    "    f(\\omega) = \\frac{1}{2\\pi} \\int_{-\\infty}^{+\\infty} \\, e^{i\\omega t} \\, f(t) \\ dt.\n",
    "\\end{align}\n",
    "\n",
    "Hint: use your integration function from task 2.2.\n",
    "\n",
    "Then implement a unit test for your function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "37055009cb70e69bc9b1dbc761859c51",
     "grade": true,
     "grade_id": "cell-87ece8e50b1f8de5",
     "locked": false,
     "points": 3,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "# YOUR CODE HERE\n",
    "raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "49aa23055a91a51494bcb9d64924cc75",
     "grade": true,
     "grade_id": "cell-46e1530333341bc6",
     "locked": false,
     "points": 3,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "# Implement your unit test here ...\n",
    "\n",
    "# YOUR CODE HERE\n",
    "raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "028bf13b6bf982c70fd1057c9d6f23f6",
     "grade": false,
     "grade_id": "cell-dc5656a6bdea875a",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "### Task 4.8 [3 points]\n",
    "Calculate the local density-of-states $\\rho_{loc}(\\omega)$ from the Fourier transform of $f(t)$ using all three time propagation methods: $U(\\tau)$, $U_{CN}(\\tau)$ and $U_{TZ}(\\tau)$.\n",
    "\n",
    "Start from $\\psi(x,t=0) = \\phi(x, x_{i=0}, \\sigma)$ and $\\psi(x,t=0) = \\phi(x, x_{i=n/2}, \\sigma)$, using a $n=100$ chain. Discretize your integration time grid as $t_j=j\\tau$, with $j=-150 \\dots 150$ and $\\tau=1.5$. Use again $a = 1$ and $\\sigma=0.25$.\n",
    "\n",
    "Be careful: for the Fourier transform you will need positive *and* negative time steps! Thus you will need to do two time propagations: one using $U(\\tau)$ towards positive times and one using $U(-\\tau)$ towards negative times, both starting from $\\psi(x,t=0)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "29ff620823bca3839839fbc35ba9b236",
     "grade": true,
     "grade_id": "cell-316f9c26031f89df",
     "locked": false,
     "points": 3,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "# YOUR CODE HERE\n",
    "raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "1c27de03eb5f84673d52e1e621c316ee",
     "grade": true,
     "grade_id": "cell-d7a678fdeef64ea2",
     "locked": false,
     "points": 0,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "# Do your own testing here ...\n",
    "\n",
    "# YOUR CODE HERE\n",
    "raise NotImplementedError()\n",
    "\n",
    "# Yann had a plot for Tau = 1.5\n",
    "# DOS: looking like a hill (\"like a dome with a peak around zero energy 0\")\n",
    "# for CN, TS and the exact one\n",
    "# a plot of f(t)\n",
    "# a plot of local DOS\n",
    "# in the title he mentiones the inital values."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "c3e0ecb1b67f93590abf1a796bd507b8",
     "grade": false,
     "grade_id": "cell-ffbf1e8460ac69d8",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "### Task 4.9 [6 points]\n",
    "Use the Trotter-Suzuki decomposition to calculate the full density-of-states by averaging over about $100$ local density-of-states you obtained from the time propagation of $100$ random initial states $\\vec{c}(0)$. To this end, you will need to make sure that each $\\vec{c}(0)$ is (a) normalized and (b) can have positive *and* negative elements. \n",
    "\n",
    "Compare this approximation to the total density-of-states to the exact one from task 3.6, which you obtained directly from the eigenvalues.\n",
    "\n",
    "Hint: don't expect the results to be the exact same. Check for the location of the peaks, and whether they have a similar order of magnitude.\n",
    "\n",
    "Hint: if you did not get the Trotter-Suzuki decomposition to work, you can instead use the exact or the Crank-Nicolson time-propagation matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "81edbb8d07068d29021696fd87a961ba",
     "grade": true,
     "grade_id": "cell-2493a46a63277eda",
     "locked": false,
     "points": 3,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "# YOUR CODE HERE\n",
    "raise NotImplementedError()\n",
    "\n",
    "# Yann says the initial states do need to be negative, too."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "5438067dfec55e69ee224e67178d9e36",
     "grade": true,
     "grade_id": "cell-a40dfcd993da467c",
     "locked": false,
     "points": 3,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "# Do your plotting here ...\n",
    "\n",
    "# YOUR CODE HERE\n",
    "raise NotImplementedError()\n",
    "\n",
    "# Yann plotted the exact diagonalisation and the TS propagation results\n",
    "# he had two plots, one peaky, one with peaks on the edges (looking a little\n",
    "# like my 1f/2f results in my bachelor internship hmmpfff)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}