Harmonic Oscillator.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Quantum Harmonic Oscillator\n",
    "\n",
    "In this notebook we'll solve the quantum harmonic oscillator with machine learning techniques.\n",
    "\n",
    "The Hamiltonian of the oscillator is:\n",
    "\n",
    "$$ H = \\frac{1}{2m}p^2 + \\frac{m \\omega^2}{2}x^2 $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "According to the variational principle of quantum mechanics, for any wave function $|\\psi>$, \n",
    "\n",
    "$$ < \\psi | H | \\psi > ~ \\ge ~ E_0 $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When substitued into the variational principle, we have:\n",
    "\n",
    "$$ \\int_{-\\infty}^{\\infty} \\psi^*(x) H \\psi(x) dx $$\n",
    "$$ \\int_{-\\infty}^{\\infty} \\psi^*(x) [\\frac{1}{2m}p^2 + \\frac{m \\omega^2}{2}x^2 ] \\psi(x) dx$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Subsituting $p = -i \\hbar \\frac{\\partial}{\\partial x}$ :\n",
    "$$ \\int_{-\\infty}^{\\infty} \\psi^*(x) \\frac{1}{2m}[- \\hbar]^2 \\frac{\\partial^2}{\\partial x ^2}   \\psi dx + \\int_{-\\infty}^{\\infty} \\psi^* \\frac{m \\omega^2}{2}x^2  \\psi(x) dx$$\n",
    "\n",
    "$$ \\frac{-\\hbar^2}{2m} \\int_{-\\infty}^{\\infty} \\psi^*(x)  \\frac{\\partial^2}{\\partial x ^2}   \\psi dx + \\frac{m \\omega^2}{2} \\int_{-\\infty}^{\\infty} \\psi^* x^2  \\psi(x) dx $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To solve this numerically, let's integrate by parts to turn a second derivative into two first derivatives:\n",
    "$$ < \\psi | H | \\psi > = \\frac{m \\omega^2}{2} \\int_{-\\infty}^{\\infty} \\psi^* x^2  \\psi(x) dx - \\frac{\\hbar^2}{2m} \\left[\\psi^*(x)\\frac{\\partial \\psi (x)}{\\partial x}  \\Biggr|_{-\\infty}^{\\infty}  - \\int_{-\\infty}^{\\infty} \\frac{\\partial \\psi^*(x)}{\\partial x} \\frac{\\partial \\psi(x)}{\\partial x} dx \\right] $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The wavefunctions for the harmonic oscillator have to got to zero at $\\pm \\infty$, so the first term in the integration by parts can be dropped.  Then, the total integral to evaluate is:\n",
    "\n",
    "$$ < \\psi | H | \\psi > = \\frac{m \\omega^2}{2} \\int_{-\\infty}^{\\infty} \\psi^* x^2  \\psi(x) dx + \\frac{\\hbar^2}{2m}  \\int_{-\\infty}^{\\infty} \\frac{\\partial \\psi^*(x)}{\\partial x} \\frac{\\partial \\psi(x)}{\\partial x} dx $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have assumed above that the wave functions are normalized, but with our approximation scheme we won't have normalized wavefunctions.  In this case, let's add in the normalization ourselves:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ < \\psi | H | \\psi > = \\frac{1}{N} \\left[\\frac{m \\omega^2}{2} \\int_{-\\infty}^{\\infty} \\psi^* x^2  \\psi(x) dx + \\frac{\\hbar^2}{2m}  \\int_{-\\infty}^{\\infty} \\frac{\\partial \\psi^*(x)}{\\partial x} \\frac{\\partial \\psi(x)}{\\partial x} dx \\right]$$\n",
    "where \n",
    "$$ N = \\int_{-\\infty}^{\\infty} \\psi^*(x) \\psi(x) dx $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To solve this, and estimate the ground state energy of the system, we need to find a wave function and estimate these two integrals.\n",
    "\n",
    "We will use a tensorflow network to approximate our wavefunction, which we can then differentiate.  The requirements of this system are that:\n",
    "- the wavefunction must be normalizable\n",
    "- the wavefunction must go to zero at $\\pm \\infty$\n",
    "- the wavefunction must be twice differentiable (no ReLU!) since wavefunctions should have continuous derivatives."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## How to sample a wavefunction?\n",
    "\n",
    "In this simple notebook, we'll use basic grid sampling: compute the wave function at a fixed set of points.  In more advanced examples, we will use more complicated sampling schemes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy\n",
    "import time\n",
    "import tensorflow as tf\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These are physical constants in this problem, which we'll set to 1 for ease:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "omega = 1.0\n",
    "hbar  = 1.0\n",
    "M     = 1\n",
    "\n",
    "# This is a granularity parameter:\n",
    "delta = 0.0005"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are 3 available wavefunctions here:\n",
    "- A module based on Hermite Polynomials, up to degree 3, that is exact up to normalization.\n",
    "- A polynomial module that can be fit to any polynomial up to degree 3.\n",
    "- A neural network that has no polynomial terms.\n",
    "\n",
    "All components have the same submodule to handle the boundary conditions, which is an gaussian-like exponential that decays to zero at large $|x|$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "class ExponentialBoundaryCondition(tf.keras.layers.Layer):\n",
    "    \n",
    "    def __init__(self, exp=1.0, trainable=True):\n",
    "        tf.keras.layers.Layer.__init__(self)\n",
    "\n",
    "        # This is the parameter controlling the shape of the exponent:\n",
    "        self.exponent = tf.Variable(exp, trainable=trainable, dtype=tf.float32)\n",
    "\n",
    "\n",
    "    def call(self, inputs):\n",
    "\n",
    "        return tf.exp(- (self.exponent * inputs) **2 / 2.)\n",
    "        \n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "class CorrectWavefunction(tf.keras.layers.Layer):\n",
    "\n",
    "\n",
    "    def __init__(self, n):\n",
    "        tf.keras.layers.Layer.__init__(self)\n",
    "            \n",
    "        # N is the degree of the polynomial:\n",
    "        self.n = n\n",
    "    \n",
    "        self.alpha = M * omega / hbar\n",
    "        self.norm  = numpy.power(self.alpha / numpy.pi, 0.25)\n",
    "        \n",
    "        if self.n == 0:\n",
    "            pass\n",
    "        elif self.n == 1:\n",
    "            self.norm *= numpy.sqrt(2.)\n",
    "        elif self.n == 2:\n",
    "            self.norm *= numpy.sqrt(0.5)\n",
    "        else:\n",
    "            raise Exception(\"Unsupported degree of \", n)\n",
    "    \n",
    "        self.exp = ExponentialBoundaryCondition(exp=numpy.sqrt(self.alpha), trainable=False)\n",
    "    \n",
    "    def call(self, inputs):\n",
    "    \n",
    "        y = inputs\n",
    "        \n",
    "        boundary_condition = self.exp(y)\n",
    "        \n",
    "        if self.n == 0:\n",
    "            polynomial = 1\n",
    "        elif self.n == 1:\n",
    "            polynomial = y\n",
    "        elif self.n == 2:\n",
    "            polynomial = 2 * y**2 - 1\n",
    "            \n",
    "        return self.norm * boundary_condition * polynomial\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "class PolynomialWavefunction(tf.keras.layers.Layer):\n",
    "    \n",
    "    def __init__(self):\n",
    "        tf.keras.layers.Layer.__init__(self)\n",
    "        \n",
    "#         self.layer1 = torch.nn.Linear(1,64)\n",
    "#         self.layer2 = torch.nn.Linear(64, 1)\n",
    "    \n",
    "        self.const  = tf.Variable(0.3, trainable=True, dtype=tf.float32)\n",
    "        self.linear = tf.Variable(0.2, trainable=True, dtype=tf.float32)\n",
    "        self.quad   = tf.Variable(0.2, trainable=True, dtype=tf.float32)\n",
    "\n",
    "        self.norm   = 1.0\n",
    "    \n",
    "        self.exp = ExponentialBoundaryCondition()\n",
    "\n",
    "\n",
    "\n",
    "    def call(self, inputs):\n",
    "        x = inputs\n",
    "\n",
    "        boundary_condition = self.exp(x)\n",
    "\n",
    "\n",
    "        poly = self.const + self.linear * x + self.quad * x**2\n",
    "\n",
    "        # Multiply by a factor to enforce normalization and boundary conditions:\n",
    "        # Note the exponent is within the power of 2 to make it's sign irrelevant\n",
    "        x = self.norm *  poly * boundary_condition\n",
    "        return x\n",
    "    \n",
    "    def update_normalization(self, inputs):\n",
    "        # Inputs is expected to be a range of parameters along an x axis.\n",
    "        value = self.call(inputs)\n",
    "        N = value ** 2\n",
    "\n",
    "        delta = inputs[1]-inputs[0]\n",
    "\n",
    "        N = tf.reduce_sum(N) * delta\n",
    "        self.norm *= 1/tf.sqrt(N)\n",
    "\n",
    "        # The normalization condition is that the integral of the wavefunction squared\n",
    "        # should be equal to 1 (probability sums to 1.)\n",
    "\n",
    "        return\n",
    "    \n",
    "    def analytic_derivative(self, inputs):\n",
    "        \n",
    "        poly = self.const + self.linear * x + self.quad * x**2\n",
    "        poly_prime = self.linear + 2 * self.quad * inputs\n",
    "        exp = self.exp(x)\n",
    "        \n",
    "        res = exp * (-inputs) *poly + poly_prime * exp\n",
    "        \n",
    "        return self.norm * res\n",
    "    \n",
    "    def zero_grad(self):\n",
    "        \"\"\"Sets gradients of all model parameters to zero.\"\"\"\n",
    "        for p in self.parameters():\n",
    "            if p.grad is not None:\n",
    "                p.grad.data.zero_()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "class NeuralWavefunction(tf.keras.layers.Layer):\n",
    "    \n",
    "    def __init__(self):\n",
    "        tf.keras.layers.Layer.__init__(self)\n",
    "        \n",
    "        self.layer1 = tf.keras.layers.Dense(32)\n",
    "        self.layer2 = tf.keras.layers.Dense(32)\n",
    "        self.layer3 = tf.keras.layers.Dense(1)\n",
    "    \n",
    "        self.norm   = 1.0\n",
    "        \n",
    "        # This is an exponent for normalization:\n",
    "        self.exp = ExponentialBoundaryCondition()\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "    def call(self, inputs):\n",
    "        x = inputs\n",
    "        x = self.layer1(x)\n",
    "        x = tf.nn.tanh(x)\n",
    "        x = self.layer2(x)\n",
    "        x = tf.nn.tanh(x)\n",
    "        x = self.layer3(x)\n",
    "\n",
    "        boundary_condition = self.exp(inputs)\n",
    "\n",
    "        output = self.norm*x*boundary_condition\n",
    "        return output\n",
    "    \n",
    "    def update_normalization(self, inputs):\n",
    "        # Inputs is expected to be a range of parameters along an x axis.\n",
    "        value = self.call(inputs)\n",
    "        N = value ** 2\n",
    "\n",
    "        delta = inputs[1]-inputs[0]\n",
    "\n",
    "        N = tf.reduce_sum(N) * delta\n",
    "        self.norm *= 1/tf.sqrt(N)\n",
    "\n",
    "        # The normalization condition is that the integral of the wavefunction squared\n",
    "        # should be equal to 1 (probability sums to 1.)\n",
    "\n",
    "        return\n",
    "    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's test some basic properties of the wave functions.  The CorrectWavefuntion should be normalized off the bat.  If we integrate it, it ought to come out right."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# This is preparing input data that is differentiable:\n",
    "_x = numpy.arange(-10, 10, delta, dtype=numpy.float32)\n",
    "_x = _x.reshape((_x.shape[0], 1))\n",
    "\n",
    "x = tf.Variable(_x, trainable = True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, let's look at the correct wave functions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "w_0 = CorrectWavefunction(n=0)\n",
    "w_1 = CorrectWavefunction(n=1)\n",
    "w_2 = CorrectWavefunction(n=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_0 = w_0(x)\n",
    "y_1 = w_1(x)\n",
    "y_2 = w_2(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Are the wave functions normalized?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "N==0 integral:  tf.Tensor(1.0005497, shape=(), dtype=float32)\n",
      "N==1 integral:  tf.Tensor(1.0005496, shape=(), dtype=float32)\n",
      "N==2 integral:  tf.Tensor(1.0005497, shape=(), dtype=float32)\n"
     ]
    }
   ],
   "source": [
    "print(\"N==0 integral: \", tf.reduce_sum(y_0**2) * delta)\n",
    "print(\"N==1 integral: \", tf.reduce_sum(y_1**2) * delta)\n",
    "print(\"N==2 integral: \", tf.reduce_sum(y_2**2) * delta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Are the wave functions orthogonal?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "N_0 * N_1 integral:  tf.Tensor(-3.051758e-08, shape=(), dtype=float32)\n",
      "N_0 * N_2 integral:  tf.Tensor(-4.1246416e-08, shape=(), dtype=float32)\n",
      "N_1 * N_2 integral:  tf.Tensor(6.103516e-08, shape=(), dtype=float32)\n"
     ]
    }
   ],
   "source": [
    "print(\"N_0 * N_1 integral: \", tf.reduce_sum(y_0*y_1) * delta)\n",
    "print(\"N_0 * N_2 integral: \", tf.reduce_sum(y_0*y_2) * delta)\n",
    "print(\"N_1 * N_2 integral: \", tf.reduce_sum(y_1*y_2) * delta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Yes, to some approximation the wavefunctions are normalized and orthogonal."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Polynomial and NN wavefunctions are not normalized after initialization, but can be normalized:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "w_poly    = PolynomialWavefunction()\n",
    "w_nn      = NeuralWavefunction()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_poly    = w_poly(x)\n",
    "y_nn      = w_nn(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Poly function normalization:  tf.Tensor(0.3546857, shape=(), dtype=float32)\n",
      "Neural Network function normalization:  tf.Tensor(0.05031945, shape=(), dtype=float32)\n"
     ]
    }
   ],
   "source": [
    "print(\"Poly function normalization: \", tf.reduce_sum(y_poly**2)*delta)\n",
    "print(\"Neural Network function normalization: \", tf.reduce_sum(y_nn**2)*delta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Call the update_normalization function to fix this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "w_poly.update_normalization(x)\n",
    "w_nn.update_normalization(x)\n",
    "\n",
    "y_poly    = w_poly(x)\n",
    "y_nn      = w_nn(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Poly function normalization:  tf.Tensor(1.0005494, shape=(), dtype=float32)\n",
      "Neural Network function normalization:  tf.Tensor(1.0005497, shape=(), dtype=float32)\n"
     ]
    }
   ],
   "source": [
    "print(\"Poly function normalization: \", tf.reduce_sum(y_poly**2)*delta)\n",
    "print(\"Neural Network function normalization: \", tf.reduce_sum(y_nn**2)*delta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting Initial Wave functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see how the first few wavefunctions look as well as the polynomial and neural network versions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "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": [
    "\n",
    "plt.plot(x.numpy(), y_0.numpy(), label=\"N==0\")\n",
    "plt.plot(x.numpy(), y_1.numpy(), label=\"N==1\")\n",
    "plt.plot(x.numpy(), y_2.numpy(), label=\"N==2\")\n",
    "\n",
    "plt.xlim([-10,10])\n",
    "\n",
    "plt.legend()\n",
    "\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "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": [
    "plt.plot(x.numpy(), y_0.numpy(), label=\"N==0\")\n",
    "plt.plot(x.numpy(), y_poly.numpy(), label=\"Polynomial\")\n",
    "plt.plot(x.numpy(), y_nn.numpy(), label=\"N.N.\")\n",
    "''\n",
    "plt.xlim([-10,10])\n",
    "\n",
    "plt.legend()\n",
    "\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting Probability distributions\n",
    "\n",
    "We can also plot initial probability distributions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "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": [
    "plt.plot(x.numpy(), (y_0**2).numpy(), label=\"N==0\")\n",
    "plt.plot(x.numpy(), (y_1**2).numpy(), label=\"N==1\")\n",
    "plt.plot(x.numpy(), (y_2**2).numpy(), label=\"N==2\")\n",
    "\n",
    "plt.xlim([-10,10])\n",
    "\n",
    "plt.legend()\n",
    "\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "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": [
    "plt.plot(x.numpy(), (y_0**2).numpy(), label=\"N==0\")\n",
    "plt.plot(x.numpy(), (y_poly**2).numpy(), label=\"Polynomial\")\n",
    "plt.plot(x.numpy(), (y_nn**2).numpy(), label=\"N.N.\")\n",
    "\n",
    "plt.xlim([-10,10])\n",
    "\n",
    "plt.legend()\n",
    "\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computing the energy of a wave function\n",
    "\n",
    "To compute the energy, we need to know the derivative of the wave function with respect to x, the input.\n",
    "\n",
    "For the exact solutions, we can know we have things correct since the energy is known.\n",
    "\n",
    "For the polynomial wavefunction, we have an analytical derivative.  Let's check the analytical derivative first:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "tape = tf.GradientTape(persistent=True)\n",
    "\n",
    "with tape:\n",
    "    y_poly = w_poly(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tf.Tensor(\n",
      "[[ 5.805122e-20]\n",
      " [ 5.833296e-20]\n",
      " [ 5.861605e-20]\n",
      " ...\n",
      " [-8.000679e-20]\n",
      " [-7.961992e-20]\n",
      " [-7.923521e-20]], shape=(40000, 1), dtype=float32)\n"
     ]
    }
   ],
   "source": [
    "# We should be able to get d \\psi / dx with this:\n",
    "grad = tape.gradient(y_poly, x)\n",
    "print(grad)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We _know_ analytically what the derivative is for a polynomial wave function.  Let's compare the biggest offset between tensorflow's autograd computation and the analytic version:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tf.Tensor(1.7881393e-07, shape=(), dtype=float32)\n"
     ]
    }
   ],
   "source": [
    "print(tf.reduce_max(grad- w_poly.analytic_derivative(x)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As desired, it matches well.  The largest difference is $10^{-7}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have the derivative, we can look at computing the energy.  We need three terms: kinetic energy, potential energy, and normalization."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can compute the other terms in the hamiltonian:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def potential_energy(wavefunction, inputs, delta):\n",
    "    temp = 0.5*(M * omega **2) * wavefunction(inputs)**2 * inputs**2\n",
    "    return tf.reduce_sum(temp) * delta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PE of w_0:  tf.Tensor(0.25013742, shape=(), dtype=float32)\n",
      "PE of w_1:  tf.Tensor(0.7504123, shape=(), dtype=float32)\n",
      "PE of w_2:  tf.Tensor(1.2506871, shape=(), dtype=float32)\n",
      "PE of w_poly:  tf.Tensor(0.6003297, shape=(), dtype=float32)\n",
      "PE of w_nn:  tf.Tensor(0.66206425, shape=(), dtype=float32)\n"
     ]
    }
   ],
   "source": [
    "print(\"PE of w_0: \", potential_energy(w_0, x, delta))\n",
    "print(\"PE of w_1: \", potential_energy(w_1, x, delta))\n",
    "print(\"PE of w_2: \", potential_energy(w_2, x, delta))\n",
    "print(\"PE of w_poly: \", potential_energy(w_poly, x, delta))\n",
    "print(\"PE of w_nn: \", potential_energy(w_nn, x, delta))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def kinetic_energy(wavefunction, inputs, delta):\n",
    "    tape = tf.GradientTape()\n",
    "    with tape:\n",
    "        y = wavefunction(inputs)\n",
    "    wavefunction_prime = tape.gradient(y, inputs)\n",
    "    return (hbar**2 / (2 *M)) * tf.reduce_sum(wavefunction_prime**2) * delta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "KE of w_0:  tf.Tensor(0.25013742, shape=(), dtype=float32)\n",
      "KE of w_1:  tf.Tensor(0.7504123, shape=(), dtype=float32)\n",
      "KE of w_2:  tf.Tensor(1.250687, shape=(), dtype=float32)\n",
      "KE of w_poly:  tf.Tensor(0.20010988, shape=(), dtype=float32)\n",
      "KE of w_nn:  tf.Tensor(0.8515113, shape=(), dtype=float32)\n"
     ]
    }
   ],
   "source": [
    "print(\"KE of w_0: \", kinetic_energy(w_0, x, delta))\n",
    "print(\"KE of w_1: \", kinetic_energy(w_1, x, delta))\n",
    "print(\"KE of w_2: \", kinetic_energy(w_2, x, delta))\n",
    "print(\"KE of w_poly: \", kinetic_energy(w_poly, x, delta))\n",
    "print(\"KE of w_nn: \", kinetic_energy(w_nn, x, delta))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "def normalization(wavefunction, inputs, delta):\n",
    "    psi = wavefunction(inputs)**2\n",
    "    return tf.reduce_sum(psi*delta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Therefore, the computed energy for this wavefunction is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "def energy_calculation(wavefunction, inputs, delta):\n",
    "    norm = normalization(wavefunction, inputs, delta)\n",
    "    pe = potential_energy(wavefunction, inputs, delta)\n",
    "    ke = kinetic_energy(wavefunction, inputs, delta)\n",
    "    energy = (1/norm) * ( pe +  ke)\n",
    "    return energy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Energy of w_0:  tf.Tensor(0.5, shape=(), dtype=float32)\n",
      "Energy of w_1:  tf.Tensor(1.5, shape=(), dtype=float32)\n",
      "Energy of w_2:  tf.Tensor(2.5000002, shape=(), dtype=float32)\n",
      "Energy of w_poly:  tf.Tensor(0.79999995, shape=(), dtype=float32)\n",
      "Energy of w_nn:  tf.Tensor(1.5127442, shape=(), dtype=float32)\n"
     ]
    }
   ],
   "source": [
    "print(\"Energy of w_0: \", energy_calculation(w_0, x, delta))\n",
    "print(\"Energy of w_1: \", energy_calculation(w_1, x, delta))\n",
    "print(\"Energy of w_2: \", energy_calculation(w_2, x, delta))\n",
    "print(\"Energy of w_poly: \", energy_calculation(w_poly, x, delta))\n",
    "print(\"Energy of w_nn: \", energy_calculation(w_nn, x, delta))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The harmonic oscillator has energy levels of:\n",
    "$$ E_n = \\hbar \\omega ( n + \\frac{1}{2} ) $$\n",
    "and so the ground state is $\\hbar \\omega / 2$. For this example, with $\\hbar = 1$ and $\\omega = 1$, we expect the estimate of the energy to be greater than or equal to 1/2.  The exact solutions are coming out exactly right.  Looks good above!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Optimizing the wave function to find the ground state"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the above, we used the autograd functionality to compute the expectation value of energy of a wavefunction for the harmonic oscillator.  But, now we will use autograd again to compute the derivative of the energy with respect to the wavefunction's parameters, and optimize the parameters to update the wave function.\n",
    "\n",
    "I re-wrote the energy computations to be more efficient.  I also introduced re-normalization of the wave function after every update."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "def energy_computation(wavefunction, inputs, delta):\n",
    "    \n",
    "    # This function takes the inputs (assumed to be a range of real value parameters)\n",
    "    # And computes the expectation value of the energy.\n",
    "    \n",
    "    # create a gradient tape:\n",
    "    tape = tf.GradientTape()\n",
    "    \n",
    "    # This is the value of the wave function:\n",
    "    with tape:\n",
    "        w_of_x = wavefunction(inputs)\n",
    "    \n",
    "    \n",
    "    # This is the first derivative of the wave function:\n",
    "    w_prime_dx = tape.gradient(w_of_x, inputs)\n",
    "    \n",
    "#     print(w_prime_dx)\n",
    "    \n",
    "    # Now we can compute integrals:\n",
    "    normalization = tf.reduce_sum(w_of_x**2) * delta\n",
    "    \n",
    "    pe = (0.5 * M * omega**2 ) * (w_of_x**2) * (inputs**2)\n",
    "    \n",
    "    ke = (hbar**2 / (2 *M)) * (w_prime_dx**2)\n",
    "    \n",
    "\n",
    "    ke = tf.reduce_sum(ke) * delta\n",
    "    pe = tf.reduce_sum(pe) * delta\n",
    "    \n",
    "#     print()\n",
    "#     print(\"pe: \", pe)\n",
    "#     print(\"ke: \", ke)\n",
    "#     print(\"norm: \", normalization)\n",
    "#     print()\n",
    "\n",
    "\n",
    "    energy = (pe + ke) / normalization\n",
    "    \n",
    "    return energy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_input(delta):\n",
    "    # Create fresh input data:\n",
    "    _x = numpy.arange(-10, 10, delta, dtype=numpy.float32)\n",
    "    _x = _x.reshape((_x.shape[0], 1))\n",
    "\n",
    "    x = tf.Variable(_x, trainable = True)\n",
    "\n",
    "    return x\n",
    "    \n",
    "def training_step(wavefunction, optimizer, delta):\n",
    "    # Clear all gradients from the optimizer:\n",
    "    exterior_tape = tf.GradientTape()\n",
    "    \n",
    "    x = generate_input(delta)\n",
    "\n",
    "    wavefunction.update_normalization(x)\n",
    "    \n",
    "    # Compute the energy:\n",
    "    with exterior_tape:\n",
    "        energy = energy_computation(wavefunction, x, delta)\n",
    "\n",
    "    # We back-prop'd through the wave function once already in the energy computation.  Clear the gradients:\n",
    "    \n",
    "    gradients = exterior_tape.gradient(energy, wavefunction.trainable_variables)\n",
    "\n",
    "    optimizer.apply_gradients(zip(gradients, wavefunction.trainable_variables))\n",
    "    \n",
    "    # Lastly, update the normaliztion \n",
    "    wavefunction.update_normalization(x)\n",
    "\n",
    "    return  energy\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's train the polynomial wave function for awhile and see if it converges:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Energy :0.8000000715255737, 0.06s per step\n",
      "Energy :0.5484876036643982, 0.022s per step\n",
      "Energy :0.5056378245353699, 0.02s per step\n",
      "Energy :0.5006784200668335, 0.021s per step\n",
      "Energy :0.5002404451370239, 0.021s per step\n"
     ]
    }
   ],
   "source": [
    "w_poly = PolynomialWavefunction()\n",
    "delta = 0.001\n",
    "\n",
    "optimizer = tf.keras.optimizers.Adam()\n",
    "\n",
    "energy_history = []\n",
    "step_history = []\n",
    "\n",
    "for i in range(500):\n",
    "    start = time.time()\n",
    "    energy = training_step(w_poly, optimizer, delta)\n",
    "    end = time.time()\n",
    "    if i % 100 == 0: print(f\"Energy :{energy.numpy()}, {end - start:.2}s per step\")\n",
    "    \n",
    "    energy_history.append(energy.numpy())\n",
    "    step_history.append(i)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hopefully, in your notebooks, this converged to about 0.5003 or less - pretty close!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,9))\n",
    "\n",
    "plt.plot(step_history, energy_history)\n",
    "plt.grid(True)\n",
    "plt.yscale(\"log\")\n",
    "plt.ylabel(\"Energy\")\n",
    "plt.xlabel(\"Iteration\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's compare the fitted wave function with the REAL wavefunction for the ground state:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "# Create fresh input data:\n",
    "_x = numpy.arange(-10, 10, delta, dtype=numpy.float32)\n",
    "_x = _x.reshape((_x.shape[0], 1))\n",
    "\n",
    "x = tf.Variable(_x, trainable = True)\n",
    "\n",
    "y_exact = w_0(x)\n",
    "y_fit   = w_poly(x)\n",
    "\n",
    "x_numpy = x.numpy()\n",
    "\n",
    "energy_poly = energy_computation(w_poly, x, delta)\n",
    "\n",
    "fig = plt.figure(figsize=(16,9))\n",
    "\n",
    "plt.plot(x_numpy, y_exact.numpy(), label=\"Exact solution\")\n",
    "plt.plot(x_numpy, y_fit.numpy(), label=f\"Polynomial Fit, E={energy:.2}\")\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For completeness, we should also plot the probability distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "# Create fresh input data:\n",
    "_x = numpy.arange(-10, 10, delta, dtype=numpy.float32)\n",
    "_x = _x.reshape((_x.shape[0], 1))\n",
    "\n",
    "x = tf.Variable(_x, trainable = True)\n",
    "\n",
    "p_exact = w_0(x)**2\n",
    "p_fit   = w_poly(x)**2\n",
    "\n",
    "x_numpy = x.numpy()\n",
    "\n",
    "energy_poly = energy_computation(w_poly, x, delta)\n",
    "\n",
    "fig = plt.figure(figsize=(16,9))\n",
    "\n",
    "plt.plot(x_numpy, p_exact.numpy(), label=\"Exact solution\")\n",
    "plt.plot(x_numpy, p_fit.numpy(), label=f\"Polynomial Fit, E={energy:.2}\")\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are the parameters of the network:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "const term fit:  <tf.Variable 'Variable:0' shape=() dtype=float32, numpy=0.406595>\n",
      "linear term fit:  <tf.Variable 'Variable:0' shape=() dtype=float32, numpy=0.00059328927>\n",
      "quad term fit:  <tf.Variable 'Variable:0' shape=() dtype=float32, numpy=0.05739359>\n",
      "norm term fit:  tf.Tensor([1.8406935], shape=(1,), dtype=float32)\n"
     ]
    }
   ],
   "source": [
    "\n",
    "print(\"const term fit: \", w_poly.const)\n",
    "print(\"linear term fit: \", w_poly.linear)\n",
    "print(\"quad term fit: \", w_poly.quad)\n",
    "print(\"norm term fit: \", w_poly.norm)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In a perfect fit, we expect the linear and quadratic terms to go to 0.0 and the constant term to stay != 0.  The absolute normalization is not of much importance."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, we do the same process for the neural network wave function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "w_nn = NeuralWavefunction()\n",
    "delta = 0.0001\n",
    "\n",
    "x = generate_input(delta)\n",
    "y = w_nn(x)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Energy :1.5115118026733398, 0.46s per step\n",
      "Energy :1.205447793006897, 0.42s per step\n",
      "Energy :0.6232742667198181, 0.38s per step\n",
      "Energy :0.5135242938995361, 0.41s per step\n",
      "Energy :0.5091062188148499, 0.46s per step\n",
      "Energy :0.5070130825042725, 0.43s per step\n",
      "Energy :0.5033078193664551, 0.43s per step\n",
      "Energy :0.5032074451446533, 0.4s per step\n",
      "Energy :0.502446711063385, 0.45s per step\n",
      "Energy :0.5019896030426025, 0.42s per step\n",
      "Energy :0.5017051100730896, 0.45s per step\n",
      "Energy :0.5014486312866211, 0.46s per step\n",
      "Energy :0.5012436509132385, 0.44s per step\n",
      "Energy :0.5010810494422913, 0.47s per step\n",
      "Energy :0.5009473562240601, 0.45s per step\n",
      "Energy :0.5008354187011719, 0.42s per step\n",
      "Energy :0.5007409453392029, 0.46s per step\n",
      "Energy :0.5006600022315979, 0.49s per step\n",
      "Energy :0.5005897283554077, 0.48s per step\n",
      "Energy :0.5005282759666443, 0.52s per step\n",
      "Energy :0.5004743337631226, 0.4s per step\n",
      "Energy :0.5004266500473022, 0.45s per step\n",
      "Energy :0.500384509563446, 0.42s per step\n",
      "Energy :0.5003476142883301, 0.44s per step\n",
      "Energy :0.5003150701522827, 0.43s per step\n",
      "Energy :0.5002866983413696, 0.45s per step\n",
      "Energy :0.5002619624137878, 0.41s per step\n",
      "Energy :0.5002403259277344, 0.43s per step\n",
      "Energy :0.500221848487854, 0.4s per step\n",
      "Energy :0.5002058148384094, 0.49s per step\n",
      "Energy :0.5001920461654663, 0.42s per step\n",
      "Energy :0.5001803636550903, 0.42s per step\n",
      "Energy :0.5001704692840576, 0.55s per step\n",
      "Energy :0.5001620054244995, 0.47s per step\n",
      "Energy :0.5001548528671265, 0.45s per step\n",
      "Energy :0.5001490116119385, 0.5s per step\n",
      "Energy :0.5001439452171326, 0.38s per step\n",
      "Energy :0.5001397132873535, 0.45s per step\n",
      "Energy :0.5001363158226013, 0.39s per step\n",
      "Energy :0.5001333951950073, 0.44s per step\n",
      "Energy :0.5001307725906372, 0.46s per step\n",
      "Energy :0.5001286268234253, 0.49s per step\n",
      "Energy :0.500126838684082, 0.44s per step\n",
      "Energy :0.5001254081726074, 0.43s per step\n",
      "Energy :0.5001240372657776, 0.47s per step\n",
      "Energy :0.5001229047775269, 0.41s per step\n",
      "Energy :0.5001218914985657, 0.39s per step\n",
      "Energy :0.5001208782196045, 0.45s per step\n",
      "Energy :0.5001201033592224, 0.46s per step\n",
      "Energy :0.5001193284988403, 0.62s per step\n"
     ]
    }
   ],
   "source": [
    "optimizer = tf.keras.optimizers.Adam()\n",
    "\n",
    "energy_history = []\n",
    "step_history = []\n",
    "\n",
    "for i in range(500):\n",
    "    start = time.time()\n",
    "    energy = training_step(w_nn, optimizer, delta)\n",
    "    end = time.time()\n",
    "    if i % 10 == 0: print(f\"Energy :{energy.numpy()}, {end - start:.2}s per step\")\n",
    "    \n",
    "    \n",
    "    energy_history.append(energy.numpy())\n",
    "    step_history.append(i)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hopefully, in your notebook you saw the energy converge well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,9))\n",
    "\n",
    "plt.plot(step_history, energy_history)\n",
    "plt.grid(True)\n",
    "plt.ylabel(\"Energy\")\n",
    "plt.xlabel(\"Iteration\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As before, let's compare the exact and learned wavefunctions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/corey.adams/Library/Python/3.6/lib/python/site-packages/IPython/core/pylabtools.py:128: UserWarning: Creating legend with loc=\"best\" can be slow with large amounts of data.\n",
      "  fig.canvas.print_figure(bytes_io, **kw)\n"
     ]
    },
    {
     "data": {
      "image/png": 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d4rPtpXpy6XZ9c3yqrhqb6pd9/mzWcK3bV677F27SOYMSNLBXtF/2C6ALa8ORz470k5/8ROPGjdN3v/vdlvt8Pp+WL19+XHmVmpYLH/v+07q6upavo6P/8Xq3a9cuPfLII1q5cqXi4+N18803H7ftqUybNk333XefVqxY0XKftVa//e1vNXv27OO2zcvLO+72hAkTtGrVKg0aNEgzZ85UaWmpnnvuOY0fP75lPydzbH5JiouLU//+/fXpp5+etKh2tKqqqlMeUc3IyFB5ebk8Ho/cbrcKCwvVt2/fVrf/6v5BgwZp6tSpWrt2bbuLKu9RBQDAz2oaPLrnbxuUnhit/7zCf7+AuEKM/vfaMXK7jO752wb5fCf/pQgAAkFCQoKuvfba407CM2vWrOOO7n11VC8tLU1r1qyRJK1Zs0a7du1qdZ+VlZWKjo5WXFyciouLz+gESZL07//+7/rVr37Vcnv27Nl66qmn1NjYdMK6rVu3qrq6WrGxsccd6Q0LC1P//v31yiuv6Nxzz9XkyZP1yCOPtJS9KVOmaP78+fJ6vSopKdHHH3+siRMntpohLCxMb7zxhv785z+f9QmbTsz35JNPtnrU9FTPP/YESyeebMkYo9zc3JYjzX/60590xRVXfG0/R44cUX1905npS0tL9emnn7b5ZE2nQlEFAMDPHlu8VfvLa/XwNVl+v/5pn7hI3Xdppr7YdVh/WbHHr/sGgI7ws5/97Liz/z7xxBNatWqVsrKylJmZqaefflqSdM011+jw4cPKzs7WU089pWHDhrW6vzFjxmjs2LEaOXKkbrnlFk2aNOmM8lx88cXq3bt3y+1bb71VmZmZGjdunEaNGqXvf//78ng8ysrKktvt1pgxY1pOCjV58mQlJycrKipKkydPVmFhYUtRveqqq5SVlaUxY8Zo2rRp+tWvfqWUlJST5oiOjtbbb7+txx57TG+++eYZfQ+SdN111+nXv/61xo4dqx07dmjz5s3q1atXq9vOnz//uMvTfPbZZ20a4+GHH9ajjz6qIUOGqKysTN/73vckNV3e59Zbb5UkFRQUKCcnR2PGjFFubq7uvfdevxRVc6pD1E7LycmxrV0HKVA0XZx9qtMxcAzmJDAxL4GHOek4G/dX6Irffaprc/rrf64effonNDuTObHW6tt//ELr9pUr7/9NVa+Y8LNMi9Ph30rgYU5Or6CgQBkZGZ02XlVV1XEnJ4IzLr30Ui1YsKDlvbWBNi+t/b00xqy21ua0tj1HVAEA8BNrre5fuEnxUaG6d86IDhvHGKP7Lxup2gavHlm0pcPGAQAEj7fffvtrJ4AKZhRVAAD85P1NB7V6zxH908zhiosK7dCxhiTF6Obz0zRv5T59WVjRoWMBANDZKKoAAPhBo9enh/++RUOSYnRtjn/O8ns6P5oxVAlRYXr475s7ZTwAADoLRRUAAD94+Yu92lVarX+9aITcrs758dojIlQ/mDpYn2wv1fIdZZ0yJoDgEMjnoUH3czZ/HymqAAC0U12jV09+uF0T0xM0bURSp45947kDldwjXP+7aAu/mAKQJEVERKisrIzXBAQEa63KysoUERFxRs/z7znzAQDohl5dtU+Hqur1+NxsGWM6deyIUJfunjZU//HGRuVtLVHu8M4tygACT2pqqgoLC1VSUtIp49XV1Z1xCUHHC6R5iYiIUGrqmb0thqIKAEA7NHh8eipvh8YPjNd5g1u/fl1Huzanv57K26EnP9xOUQWg0NBQpaend9p4eXl5Gjt2bKeNh7YJ9nlh6S8AAO2wYE2hiirqdNe0IZ1+NPUrYe4Q3TY5Xav3HNHK3YcdyQAAgD9RVAEAOEten9Xv83YoKzVOU4f1djTL3AkDlBAdpqfzdjiaAwAAf6CoAgBwlhbnF2vv4RrdceFgx46mfiUyzKXvnJemDzYf0paDVY5mAQCgvSiqAACcpT9+ukv9ekZqVmay01EkSd8+b6AiQ1165mOOqgIAghtFFQCAs7Bxf4W+2HVYN5+f1mnXTT2d+OgwXZuTqrfXH1Dp0Xqn4wAAcNYC4ycrAABB5o+f7lJUmEvXTujvdJTj3HRemhq8Ps1fuc/pKAAAnDWKKgAAZ+hQVZ3eXn9A3xyfqrjIUKfjHGdIUowuGJKov67YI4/X53QcAADOCkUVAIAzNO+LfWrw+nTzpM67TuGZ+PZ5A3Wgok5LCg45HQUAgLNCUQUA4Ax4fVbzV+7T5KGJSk+MdjpOq6ZnJKtfz0j9eflup6MAAHBWKKoAAJyBZdtKtL+8VtdNGOB0lJNyhRh969wB+mxHmbYf4lI1AIDgQ1EFAOAMvPzFXvWKDtPMALkkzclcm9Nf7hDDSZUAAEGJogoAQBsdqqzTBwWH9I3xqQpzB/aP0MSYcM3ISNaCNfvV4OGkSgCA4BLYP2UBAAggr64ulMdnNTfALklzMtdOSFVZdYM+3MxJlQAAwYWiCgBAG/iaT6J07qAEDeod43ScNpkytLeSe4TrlVUs/wUABBeKKgAAbbBiV5n2Hq7R9RMD9yRKJ3K7QnTNuFTlbTmk4so6p+MAANBmFFUAANpgwZr9igl3a/bIFKejnJFrc/rLZ6W/rS50OgoAAG1GUQUA4DRqG7x678sDumhUiiJCXU7HOSNpidGamJ6gV1ftk7XW6TgAALQJRRUAgNNYlH9Q1Q1eXT0u1ekoZ+Ub41K1u6xG6/aVOx0FAIA2oagCAHAar6/dr349I3VOeoLTUc7KnNEpCnOH6M11RU5HAQCgTSiqAACcQklVvZZtK9UV2X0VEmKcjnNWekSEakZGkt5aX6RGL9dUBQAEPooqAACnsHB9kbw+q6vH9XM6Srtckd1PZdUN+mR7qdNRAAA4LYoqAACn8PraQo3uF6chSbFOR2mXqcN7q0eEW2+u3e90FAAATouiCgDASWwrrtLG/ZW6amxwH02VpHC3S5dk9dGi/GLVNHicjgMAwCn5pagaY+YYY7YYY7YbY+49yTZTjTHrjDGbjDEf+WNcAAA60lsbDijESJeN6et0FL+4Irufahq8Wpxf7HQUAABOqd1F1RjjkvQ7SRdJypR0vTEm84Rtekr6vaTLrbUjJX2zveMCANCRrLV6e0ORzh3US71jw52O4xcT0xLUNy5Cb7D8FwAQ4PxxRHWipO3W2p3W2gZJ8yRdccI2N0haYK3dK0nW2kN+GBcAgA6z+WCVdpZU65KsPk5H8ZuQEKPLsvvq422lOlLd4HQcAABOylhr27cDY74haY619tbm2zdJOsdae9cx2zwuKVTSSEmxkn5jrf3zSfZ3u6TbJSk5OXn8vHnz2pWvIx09elQxMTFOx8AxmJPAxLwEHubk9F7b2qB3djXq8dwo9Qjr+MvSdNac7K7w6hfL6/TdUWG6MDW0w8cLdvxbCTzMSeBhTgJTMMxLbm7uamttTmuPuf2w/9Z+ep/Yft2SxkuaLilS0nJjzApr7davPdHaZyU9K0k5OTl26tSpfojYMfLy8hTI+boj5iQwMS+Bhzk5NWutfrEyT5OGxOnyWed0ypidNSfWWv1hy1LtaIjR/VMndvh4wY5/K4GHOQk8zElgCvZ58cfS30JJ/Y+5nSqpqJVt/m6trbbWlkr6WNIYP4wNAIDfbSqq1O6yGl0yuuss+/2KMUYXj+6jz7aXqryG5b8AgMDkj6K6UtJQY0y6MSZM0nWSFp6wzZuSJhtj3MaYKEnnSCrww9gAAPjdO18ekDvEaPbIFKejdIhLRveRx2e1aBNn/wUABKZ2F1VrrUfSXZLeV1P5fMVau8kYc4cx5o7mbQok/V3SBklfSHreWruxvWMDAOBvX53td9KQRMVHhzkdp0OM7hen1PhIvfPlAaejAADQKn+8R1XW2nclvXvCfU+fcPvXkn7tj/EAAOgoX+6v0L7Dtbp72lCno3QYY4wuyeqjPyzbpfKaBvWM6pqFHAAQvPyx9BcAgC7jnQ0HFOoymp3ZNZf9fqVl+W8+y38BAIGHogoAQLOmZb8HdMGQRMVFde1Lt3y1/Pddlv8CAAIQRRUAgGabiiq1v7xWF3XBs/2eyBijS0b30afbS1VR0+h0HAAAjkNRBQCg2ZKCYhkjTR+R5HSUTnHx6D5q9Fotyj/odBQAAI5DUQUAoNni/GKNHxCvXjHhTkfpFFmpcerXM1Lvb6KoAgACC0UVAABJReW12lRUqZmZyU5H6TTGGM0amayPt5Wqut7jdBwAAFpQVAEAUNOyX0ma0Y2KqiTNykxRg8enj7eWOB0FAIAWFFUAANS07HdQ72gN7h3jdJRONSEtXvFRoVymBgAQUCiqAIBur7KuUSt2lmlmRvc6mipJbleIpmck64OCYjV6fU7HAQBAEkUVAAB9tKVEjV7brd6feqzZI1NUWefRip1lTkcBAEASRRUAAC0pKFav6DCNHRDvdBRHTB6aqMhQlxZtYvkvACAwUFQBAN1ao9enpZsPadqIJLlCjNNxHBER6tKFw3prUf5B+XzW6TgAAFBUAQDd28pdh1VZ5+m2y36/Mmtksoor67Vhf4XTUQAAoKgCALq3RfnFCneH6IKhiU5HcdT0EclyhRi9v+mg01EAAKCoAgC6L2utFucXa/LQREWFuZ2O46i4qFCdOyhBiyiqAIAAQFEFAHRbmw9WaX95rWZ0w8vStGb2yBTtKKnW9kNHnY4CAOjmKKoAgG5rcX6xjJGmU1QlqeV9uovyOaoKAHAWRRUA0G0tKShWdv+e6h0b7nSUgNAnLlJjUuP0PpepAQA4jKIKAOiWDlbUaUNhRbc/2++JZmQka/2+ch2qqnM6CgCgG6OoAgC6pSUFTUcNZ7Ls9zgzmov70s2HHE4CAOjOKKoAgG5pcX6x0npFaUhSjNNRAsqIlFj16xmpxfkUVQCAcyiqAIBu52i9R8t3lGlmZrKMMU7HCSjGGM3ISNIn20tU1+h1Og4AoJuiqAIAup2Pt5aowevjsjQnMT0jWXWNPn26vdTpKACAboqiCgDodhbnFys+KlTjB8Y7HSUgnTMoQTHh7pb38QIA0NkoqgCAbsXj9enDzYeUOyJJbhc/BlsT7nZpyrBEfVBwSD6fdToOAKAb4ic0AKBbWbn7iCpqGzWLy9Kc0oyMZB2qqteX+yucjgIA6IYoqgCAbmVJQbHC3CGaPLS301ECWu7wJIUY6QOW/wIAHEBRBQB0G9ZaLc4v1qTBvRQd7nY6TkCLjw5TzsAELS7gMjUAgM5HUQUAdBvbDh3V3sM1msGy3zaZkZmkggOVKjxS43QUAEA3Q1EFAHQbi/OblrFyWZq2md785/ThZo6qAgA6F0UVANBtLMov1pj+PZXcI8LpKEFhcO8YDUqMbin4AAB0FooqAKBbOFRZp/X7yjUzI8npKEFlekaSVuwsU1Vdo9NRAADdCEUVANAtLGk+KdDMzBSHkwSXGRnJavRaLdtW6nQUAEA3QlEFAHQLSwqK1T8hUsOSY5yOElTGD4xXXGSolnCZGgBAJ6KoAgC6vOp6jz7ZXqqZGSkyxjgdJ6i4XSGaNiJJSzcfksfrczoOAKCboKgCALq8ZdtK1eDxaUYm7089G9MzknSkplFr9pY7HQUA0E1QVAEAXd7i/GLFRYZqQlqC01GC0pRhvRXqMvqA5b8AgE5CUQUAdGker08fbi5W7vDeCnXxY+9s9IgI1bmDemkxRRUA0En4iQ0A6NLW7C3XkZpGzvbbTtNHJGlnSbV2lhx1OgoAoBugqAIAurTF+QcV5grRhcN7Ox0lqE3PSJYkfdB8mR8AADoSRRUA0GVZa7U4v1jnDu6lmHC303GCWv+EKI1IiWX5LwCgU1BUAQBd1o6So9pdVqOZmclOR+kSZmQka9XuwzpS3eB0FABAF0dRBQB0WYvzm5apzsjgsjT+MDMzWT4rLd3C8l8AQMeiqAIAuqzF+Qc1ul+c+sRFOh2lSxjdL05JseFanM/yXwBAx6KoAgC6pJKqeq3dV64ZGSz79ZeQEKPpGcn6aGuJ6hq9TscBAHRhFFUAQJf04eZiWSven+pnszKTVdPg1YqdZU5HAQB0YRRVAECXtDi/WP16RiqjT6zTUbqU8wb3UmSoi+W/AIAORVEFAHQ5tQ1eLdtWqpmZyTLGOB2nS4kIdWnKsF3e63sAACAASURBVEQtKSiWtdbpOACALoqiCgDocpZtK1G9x8ey3w4yMzNFxZX12ri/0ukoAIAuiqIKAOhylhQUKzbCrYnpCU5H6ZJyh/dWiGk6qzIAAB3BL0XVGDPHGLPFGLPdGHPvKbabYIzxGmO+4Y9xAQA4kddn9UHBIeUOT1Koi/+P7Qi9YsI1fmC8FhdwPVUAQMdo909wY4xL0u8kXSQpU9L1xpjMk2z3sKT32zsmAAAns3bvEZVVN2gGy3471MzMZBUcqFThkRqnowAAuiB//FfzREnbrbU7rbUNkuZJuqKV7e6W9Jok/vsVANBhFucXK9RlNHV4b6ejdGlfXZ92CWf/BQB0AH8U1X6S9h1zu7D5vhbGmH6SrpL0tB/GAwDgpBbnF+vcQb3UIyLU6Shd2qDeMRrUO1pLWP4LAOgApr2nljfGfFPSbGvtrc23b5I00Vp79zHbvCrpf621K4wxL0p621r7t5Ps73ZJt0tScnLy+Hnz5rUrX0c6evSoYmJinI6BYzAngYl5CTxddU6Kjvr0b5/U6qbMME0fEFxFNRjn5JUtDXp/d6N+Oy1KUaFd8zJAwTgvXR1zEniYk8AUDPOSm5u72lqb09pjbj/sv1BS/2Nup0oqOmGbHEnzmq9llyjpYmOMx1r7xok7s9Y+K+lZScrJybFTp071Q8SOkZeXp0DO1x0xJ4GJeQk8XXVOfp+3XdIW/fCKC9QnLtLpOGckGOckJu2w3n16uTxJwzV1TF+n43SIYJyXro45CTzMSWAK9nnxx9LflZKGGmPSjTFhkq6TtPDYDay16dbaNGttmqS/SfphayUVAID2WJxfrNH94oKupAarsQPi1Ss6jPepAgD8rt1F1VrrkXSXms7mWyDpFWvtJmPMHcaYO9q7fwAA2uJQZZ3W7SvXLM7222lcIUbTRiRp6ZZDavT6nI4DAOhC/LH0V9badyW9e8J9rZ44yVp7sz/GBADgWEsKDslaaeZIimpnmpGZrFdXF+qLXYc1aUii03EAAF0EV0IHAHQJi/MPakBClIYnxzodpVuZPDRR4e4QLWb5LwDAjyiqAICgd7Teo0+3l2lmZrKaT9yHThIV5tYFQxK1pKBY7b2SAAAAX6GoAgCC3sdbS9Tg9Wkm7091xIzMZBUeqdXmg1VORwEAdBEUVQBA0FucX6z4qFDlDIx3Okq3ND0jSZI4+y8AwG8oqgCAoNbo9emDgmJNG5Est4sfa05Iio1Qdv+eWlJAUQUA+Ac/0QEAQW3lrsOqrPOw7NdhMzOTtb6wQsWVdU5HAQB0ARRVAEBQW5RfrHB3iKYM49IoTvrqPwoWsfwXAOAHFFUAQNCy1mpxfrEmD01UVJhfLg2OszQ0KUbpidFatOmg01EAAF0ARRUAELTyD1Rqf3kty34DgDFGs0emaPmOMpXXNDgdBwAQ5CiqAICg9f6mYhkjTc+gqAaCi0alyOOzWlJwyOkoAIAgR1EFAAStv288oIlpCUqMCXc6CiRlpcapb1yE/r7xgNNRAABBjqIKAAhKO0qOamvxUV00KsXpKGhmjNHsUSn6eFupjtZ7nI4DAAhiFFUAQFD6+8amk/bMGdXH4SQ41kWj+qjB49PSzSz/BQCcPYoqACAovfvlAY0d0FMpcRFOR8Exxg+MV2JMmP7O2X8BAO1AUQUABJ29ZTXaVFTJst8A5AoxmjUyRUs3H1Jdo9fpOACAIEVRBQAEnb9vajpZz0Us+w1Ic0amqKbBq2XbSp2OAgAIUhRVAEDQeW/jQY3q10P9E6KcjoJWnDe4l3pEuFveRwwAwJmiqAIAgsqBilqt3VvO0dQAFuoK0YzMZC0pKFaj1+d0HABAEKKoAgCCyj/O9sv7UwPZRaP6qKK2USt2ljkdBQAQhCiqAICg8t7GgxqeHKvBvWOcjoJTmDw0UVFhLr3H8l8AwFmgqAIAgkZJVb1W7j7M0dQgEBHqUu6IJC3adFBen3U6DgAgyFBUAQBBY1H+QVkrXTSaohoMLhndR6VHG/Q5y38BAGeIogoACBrvbDigQYnRGp4c63QUtEHu8CRFh7n01oYip6MAAIIMRRUAEBQOVdZp+c4yXTqmr4wxTsdBG0SGuTQjM1nvbTzI2X8BAGeEogoACArvfnlA1kqXZXFZmmByWVZfldc06pPtpU5HAQAEEYoqACAovLXhgEakxGooy36DyuRhiYqNcOvt9QecjgIACCIUVQBAwCs8UqPVe47osjF9nY6CMxTudmnOyBQt2nRQdY1ep+MAAIIERRUAEPDe3tB0NO6yLIpqMLpsTF9V1Xv00dYSp6MAAIIERRUAEPDeWl+k7P49NaBXlNNRcBbOH9xLCdFhLf/hAADA6VBUAQABbUfJUW0qqmTZbxBzu0J00agULckvVk2Dx+k4AIAgQFEFAAS0t9cfkDHSJaM5228wuzSrr2obvfpw8yGnowAAggBFFQAQsKy1Wrh+vyamJSglLsLpOGiHiekJSooN18J1RU5HAQAEAYoqACBgFRyo0o6Sapb9dgGuEKNLsvoob0uJKmoanY4DAAhwFFUAQMB6Y91+uUOMLmbZb5dw9dhUNXh9eudLTqoEADg1iioAICB5vD69vna/ckckKSE6zOk48INR/XpoaFKMFqwpdDoKACDAUVQBAAHp0x1lKqmq1zXj+jkdBX5ijNFV4/pp1Z4j2lNW7XQcAEAAo6gCAALSgjWFiosMVe6IJKejwI+uzO4nY6TX1+53OgoAIIBRVAEAAedovUfvbzqoS7P6KNztcjoO/Khvz0idN6iXXl+7X9Zap+MAAAIURRUAEHDe+/KA6hp9unpcqtNR0AGuGttPe8pqtGbvEaejAAACFEUVABBwFqzZr7ReURo3oKfTUdABLhrdRxGhIVqwhuW/AIDWUVQBAAGl8EiNlu8s09XjUmWMcToOOkBMuFuzR6bo7Q0HVO/xOh0HABCAKKoAgIDy5roiSU3LQ9F1XT0uVRW1jfqw4JDTUQAAAYiiCgAIGNZavbpqnyamJ6h/QpTTcdCBJg3upZQeEZq/ap/TUQAAAYiiCgAIGCt2HtbushpdN6G/01HQwdyuEH0zJ1UfbS1RUXmt03EAAAGGogoACBjzVu5VbIRbF4/u43QUdIJrc5r+Q+IVjqoCAE5AUQUABITymga9t/GgrhrbTxGhXDu1O+ifEKULhiTq1VWF8vq4pioA4B8oqgCAgPD62v1q8Ph03YQBTkdBJ7puwgDtL6/Vsm0lTkcBAAQQiioAwHHWWs37Yp+yUuOU2beH03HQiWZkJikhOkzzV7L8FwDwDxRVAIDj1u0r15biKo6mdkPhbpeuGddPi/OLVVJV73QcAECAoKgCABw374t9igx16bIxnESpO5o7ob88PqvX1hQ6HQUAECD8UlSNMXOMMVuMMduNMfe28vi3jDEbmj8+M8aM8ce4AIDgV1HbqLc2FOmyMX0UGxHqdBw4YEhSrCakxevlL/bKx0mVAADyQ1E1xrgk/U7SRZIyJV1vjMk8YbNdki601mZJ+i9Jz7Z3XABA1/C31YWqafDq2+elOR0FDrrpvDTtKavRR1s5qRIAwD9HVCdK2m6t3WmtbZA0T9IVx25grf3MWnuk+eYKSal+GBcAEOR8Pqu/LN+tcQN6alS/OKfjwEFzRqaod2y4/rR8t9NRAAABwB9FtZ+kY0/VV9h838l8T9J7fhgXABDkPt5Wot1lNfrO+WlOR4HDwtwh+tY5A5S3pUS7SqudjgMAcJixtn3vBTHGfFPSbGvtrc23b5I00Vp7dyvb5kr6vaQLrLVlJ9nf7ZJul6Tk5OTx8+bNa1e+jnT06FHFxMQ4HQPHYE4CE/MSeAJlTh5dXafdFT49OjVS7hDjdBxHBcqcOKm8zqeffVSr6QPcuiEj3Ok4kpiXQMScBB7mJDAFw7zk5uauttbmtPaY2w/7L5TU/5jbqZKKTtzIGJMl6XlJF52spEqStfZZNb+HNScnx06dOtUPETtGXl6eAjlfd8ScBCbmJfAEwpzsLq3Wl+/n6e5pQzVj2jBHswSCQJiTQPDhkbVauvmQHrvlAkWH++PXlPZhXgIPcxJ4mJPAFOzz4o+lvyslDTXGpBtjwiRdJ2nhsRsYYwZIWiDpJmvtVj+MCQAIcn9dsUcuY/Stc7h2Kv7hO+cPVFW9R6+v3e90FACAg9pdVK21Hkl3SXpfUoGkV6y1m4wxdxhj7mje7OeSekn6vTFmnTFmVXvHBQAEr6P1Hs1ftU+zR6UouUeE03EQQMYNiNeofj304me7uVQNAHRjfllTY619V9K7J9z39DFf3yrpVn+MBQAIfvO+2KuqOo9uvSDd6SgIMMYY3TIpXf/0ynrlbT2kaSOSnY4EAHCAP5b+AgDQZo1en/74yS5NTE/Q2AHxTsdBALpsTF/1jYvQMx/tdDoKAMAhFFUAQKd6e0ORiirq9P0pg5yOggAV6grRLRek6/Ndh7VuX7nTcQAADqCoAgA6jbVWz3y0U0OTYpQ7PMnpOAhg100coNgIt579eIfTUQAADqCoAgA6zbJtpdp8sEq3TRmkkG5+3VScWky4WzedO1DvbTyo3aXVTscBAHQyiioAoNM88/EOJcWG64rsvk5HQRC4eVKaQkNC9Nwy3qsKAN0NRRUA0ClW7zmsT7eX6dbJ6Qp3u5yOgyCQFBuha8b306urC1VcWed0HABAJ6KoAgA6xeNLtqlXdJhuPHeg01EQRH5w4RD5fFZP5fFeVQDoTiiqAIAOt3rPES3bVqrbpwxSVJhfLuGNbmJAryhdMy5VL32xVwcrOKoKAN0FRRUA0OF+88E2JUSH6abzOJqKM3fXtKajqk9/xFFVAOguKKoAgA61du8Rfby1RLdN5mgqzk7/hCh9YzxHVQGgO6GoAgA61KOLtyo+KlTf5mgq2uHO3K/eq7rd6SgAgE5AUQUAdJhPt5dq2bZS/XDqEEWHczQVZ69/QpS+mdN0VHXf4Rqn4wAAOhhFFQDQIXw+q/95r0D9ekby3lT4xY+nD5MrxOhX729xOgoAoINRVAEAHeKtDUXauL9SP5s1TBGhXDcV7ZcSF6HbJg/SW+uLtH5fudNxAAAdiKIKAPC7eo9Xjyzaoow+PXRldj+n46ALuX3KIPWKDtN/v1sga63TcQAAHYSiCgDwu78s36N9h2t170UjFBJinI6DLiQ2IlQ/mTFUn+86rA83H3I6DgCgg1BUAQB+daiqTr9Zsk1ThvXWlKGJTsdBF3TdxAEalBitB98pUL3H63QcAEAHoKgCAPzq4fe2qM7j1S8uy5QxHE2F/4W6QvTzyzK1s7Razy/b5XQcAEAHoKgCAPxm9Z7Dem1NoW6dPEiDesc4HQdd2NThSZozMkW//XCbCo9wuRoA6GooqgAAv/D6rH7+5ib1iYvQ3dOGOB0H3cB9l2VKkv7r7XyHkwAA/I2iCgDwixc+3aVNRZX690syFBXmdjoOuoF+PSN197Shen9TsZZyYiUA6FIoqgCAdttdWq1HFm3RjIwkXTK6j9Nx0I3cNnmQhiTF6N9e/1KVdY1OxwEA+AlFFQDQLj6f1b0LNig0JEQPXDmaEyihU4W5Q/Srb2SpuLJO//1OgdNxAAB+QlEFALTLyyv3asXOw/qPSzOUEhfhdBx0Q+MGxOu2yYM0b+U+fby1xOk4AAA/oKgCAM7a7tJq/fc7BbpgSKKuzenvdBx0Yz+dOUyDe0fr3tc2sAQYALoAiioA4Kw0eHz60by1cruall6y5BdOigh16dffHKPiqnr924IvZa11OhIAoB0oqgCAs/K/i7doQ2GFHr4mS317RjodB9C4AfH6p5nD9PaGA5q/cp/TcQAA7UBRBQCcsWXbSvTMRzt1wzkDNGdUitNxgBY/uHCwLhiSqF+8tUlbi6ucjgMAOEsUVQDAGdl3uEZ3v7xWw5JjdN8lmU7HAY4TEmL06Nwxigl364f/t0ZH6z1ORwIAnAWKKgCgzWobvLr9L6vl9Vk9c1OOIsNcTkcCviYpNkJPXDdWu0qr9ZN56+Tz8X5VAAg2FFUAQJtYa/Uvr23Q5oOVeuL6sUpPjHY6EnBS5w9J1H2XZGhJQbEeXbzV6TgAgDPkdjoAACA4PLZ4qxauL9I9s4crd3iS03GA0/rO+WnafLBKTy7drqHJMboiu5/TkQAAbURRBQCc1v99vkdPfLhdc3P664dTBzsdB2gTY4x+ecUo7Syt1v97db3io8I0ZVhvp2MBANqApb8AgFNatOmg7ntjo3KH99aDV43ieqkIKmHuED337RwNSYrVHX9drXX7yp2OBABoA4oqAOCkPtxcrLteWqvRqT31u2+Nk9vFjw0En7jIUP3plglKjAnXd1/4QpsPVjodCQBwGvzGAQBo1Yebi3XHX9ZoWEqM/vzdiYoK490iCF5JsRH6y/cmKtzt0nXPrtDG/RVORwIAnAJFFQDwNe9vOthSUv/ve+cqLirU6UhAuw3sFa353z9X0WFu3fDcCq3de8TpSACAk6CoAgCO85flu/WDv65WRt8elFR0OV+V1Z5RYfrW85/rw83FTkcCALSCogoAkCT5fFYP/32z7ntzk6aNSNK82yip6JpS46P06h3nKT0xWrf+aZX+vHy305EAACegqAIAVFHTqO/9aaWeytuhG84ZoKdvHK/IMJfTsYAOk9wjQq98/zxNG5Gkn7+5Sfe9sVH1Hq/TsQAAzSiqANDNbdxfoUufXKZPtpfqv64cpQevHMXZfdEtRIe79cxNObp9yiD9ZcUeffPp5dpbVuN0LACAKKoA0G15vD79bul2XfX7T9XosZr//fN007kDuU4quhVXiNG/XZyhZ24ar12l1brkt8v0xtr9stY6HQ0AujWuNQAA3VDRUZ+++cxyrd1brotHp+iBK0crITrM6ViAY2aPTFFmnx760by1+sn8dXp7Q5EeuHK007EAoNuiqAJAN1JV16jffrhdf/i0VjERHv3mumxdPqYvR1EBSf0TovS3O87XC5/u0iOLtmjmYx/p0rQQne/xKczNIjQA6EwUVQDoBho8Pr22plCPLt6qkqp6Te7n1qM3X6jeseFORwMCiivE6NbJgzQjI1k/X7hJL28u0fLHPtK9F43Q7JEp/KcOAHQSiioAdGENHp8WrCnUk0u3q/BIrcYO6Knnvp2j8h3rKKnAKaQlRuvPt0zUE68u0Vv7QnTHX9cos08P3Zk7RHNGpcgVQmEFgI5EUQWALuhQVZ1e+nyvXvp8rw5V1WtMapz+68pRmjqst4wxytvhdEIgOGT1duuHV0/WgrX79VTeDt350hoN6h2t75yXpivH9lNcJNcaBoCOQFEFgC6i3uNV3pYSLVxXpEX5B9XotZo6vLd+dX6aLmwuqADOnNsVomtz+uuacal698sDevbjnbp/4Sb9z3sFuiyrr64el6qJ6QkcZQUAP6KoAkAQq6xr1Gfby/RBQbH+vumgquo86hUdppvOTdNN5w1UemK00xGBLsMVYnTZmL66bExffVlYoZe+2KM31xXp1dWFSowJ15xRyZozso9y0uIVEepyOi4ABDWKKgAEkaP1Hq3fV67Ve47ok+2lWrPniDw+q9hwt2aOTNYV2f00aXAvuV2coRToSKNT4/Q/qVm679JMfbj5kN798oD+trpQf12xVxGhIZqQlqALhiRqYnqCMvr0oLgCwBnyS1E1xsyR9BtJLknPW2sfOuFx0/z4xZJqJN1srV3jj7EBoCuy1upQVb22FR/V1uIqbS2u0rp95dpaXCWfbdoms08P3T5lkC4c1lvjBsYrlHIKdLqoMLcuzeqrS7P6qqbBo+U7yvTJ9lJ9sq1U//PeZklSqMsoo08PjUntqYw+PTQkKUaDe0erVwwnNAOAk2l3UTXGuCT9TtJMSYWSVhpjFlpr84/Z7CJJQ5s/zpH0VPNnAOh2rLWqbvDqSHWDDlc36EBFnYrKa7W/vLbl856yGlXUNrY8Jz4qVKP6xWn2yBSNGxiv7NSeioviJC5AIIkKc2t6RrKmZyRLkoor67R27xGt21eh9fvKtWBNoaobvC3bx0eFalDvGPXrGak+PSOaPsdFqk9chHrFhCk+KowjsQC6LX8cUZ0oabu1dqckGWPmSbpC0rFF9QpJf7bWWkkrjDE9jTF9rLUH/DB+wGr6dk+3zWke99c4bdpPG7Zpw57asp+OylLvsapp8JzhftqSp5P+jDtxDjrz+66otyqpqj/FPvwT2J9/zz1eq0avTx5f82evlcfnU6O3+TFf831enxp9VvWNXtU2elVd71Vtg0fVDV7VNHhU09B0X3W9R0dqGpo+qhvV4PV9bdyI0BD16xmpfvFRGt0vTsOSYzU0OUZDk2KVGBPGyZCAIJPcI0JzRvXRnFF9JEk+n9X+8lptLzmqHYeOakfJUe0sqda6feV6b2OtGr1ff4GKDHUpPipU8dFNxTU63KXoMLciw1yKDncrKszV/OFWZKhLoe4QhYYYhbpCmr52GYW5QuR2Hf91iJFCjJFp/vzV18feDjGSkZEJUcvtlu108tejU71UnepV7GSvcSfe67NWvualJacci9dMIKj5o6j2k7TvmNuF+vrR0ta26ScpaIvq57/9tqaWvSnlnXwba0//Ann63nLqfZz+8dM73T5O/WPFP2P46/uYJMm3rOPGaO+fxen/rNufszPGON2fw4ljnCfJfnZmY3TG9+G1LjXKJa9c8sglj0Lkkbvps23+LNc/7pNLjXKrzoapVuGqUbhqm7+uVbhqbLjqFKZaRajeHav60Dg1hveULzRW0RGhSo2PUlZqnOKjw9Sr+ZfO+KgwpcRFqG/PSMVHhfKLFdCFhYQY9U+IUv+EKOUOTzruMZ/PqrS6XgfK63Sgok5HappWXBypblB5db3qjx6Wr7pIIUeq5G08qlpPtRo9R1XjrVWMalVv6lSneoXJozA1Ksw0fQ6XR41qVJg88ppGeeWRSz6FyNf82Sqk+bNLPoWYf3xtmrdxySefrCQrnyRzzKvrsa9YX91/ssfVzsdDTNP90yTpozb8gaPTTJVO+TsxnDFV0orN39K5d/ze6ShnxR9FtbXfqk78/bAt2zRtaMztkm6XpOTkZOXl5bUrXEepiMrQO7UhcrlOtiTnqxfb0zv5Nqf+Nduc9vG2jN3xY5zs+zBtfvz0AUzzYTKv19vKnJjTfh/+qGbt/bNs2zin+3vln4p56uef+RgnzsvZzseZ/Xs6/fcRYr1Nv6BZj0LkU7j1KNJ6FSKvXNarphpbK5f1NdVU61WI9SrU1svta/oI0dePjLbwSqqRrELUWBMrT2WMGkNj1RAWr/rwRNVFJKo+vJfqwxO1Jbzpa5nOeZ/p0aNHA/b1tbtiTgJTR89LiLdeEXWHFFFXovD6Q+pZd0gpdSUKayhXaGOFQhsrFdZQIdPaa01I84eaXmc8IWHyhoTKZ0LlNaHyGrc8xi2vCZVHofKYCHlMqLxyycrIa0LkkZG3pa42V1MTIivTXGe/+hzSXFVN08oU0/qr7T/+A/Fkr8bmhO3O/Plf/UzxwwIu+Enrv3/BaV6vV57w9KD92eKPolooqf8xt1MlFZ3FNpIka+2zkp6VpJycHDt16lQ/ROwAU6cqLy9PAZuvm8rLy9MU5iTgdNl/K9ZK3gapoVpqrJUaa5o+Gqqlugqp5rBUe0Sm9rDCao8orOawVFMmHS2WDm2QGquP3587Uuo1WOo1REocKiUOl/pmSwmDpRD/FtguOydBjDkJTH6bF59XKtksHdgglRRIhzY3fS7fe/x2IW6pRz8pNkWK6i9F95Kie0tRiVJ0ohTeQwqPkcJipPDYpo+wGJnQSIUao+7wznX+rQQe5iQwBfu8+KOorpQ01BiTLmm/pOsk3XDCNgsl3dX8/tVzJFV09fenAugGjJHc4U0fZ8paqb5SqiySKvdL5fuksu1S6Tbp4AapYKFkm4+ghMU2Fda+Y6UB50oDJ0mRPf37vQDwr8Zaac+n0p7PpMKV0v41UsPRpsdcYVKvoVLqBCn7RikhXeo5QIrr31RQQzgyBQDtLqrWWo8x5i5J76vp8jR/tNZuMsbc0fz405LeVdOlabar6fI0323vuAAQ1IyRIuKaPpIyvv64p76ptB5YJxWtbfr4/Gnpsyealgf3yZYGXSgNnS31n8gvtkAgOLxL2vyOtOODpoLqqWs6Qpo8ShpzfVMx7TtWShgkubiUPQCcil9eJa2176qpjB5739PHfG0l3emPsQCgW3CHSymjmj7G3th0n6deKlwl7fpI2vmR9NlvpU8ek6KTpBGXSJlXSOlTKK1AZ6rYL21aIG1cIBU1XyK+9wgp53vSkGnSgPOlsChnMwJAEOK/8wAgWLjDpbRJTR+5/ybVVUrbF0v5C6UNr0irX5B6pDYV27HfalpKCMD/fD5p54fSyj9KW99rWqbfJ/v/t3fn8VWVB/7HPw/7vrkAKoJICAjihkurVaigAq61tVprHW1r7XS6zEw70/n1N7922mnHdjozbaeL49iFrti6VFrA1g2XCi7gAgIREWQRWWSRVZY8vz9ObBETEnJz85x77+f9evFKbu5Jzpc8OUm+Oc95Doz/Mhx3KfQemDqhJJU8i6oklapOPWDk5dm/3TvghXtg7s/goa9n/6onwJmfzq5rlVS4PbvguSnw6LdgwxLocgi881Nw8oeyhdAkSS3GoipJ5aB9ZxhxWfZv0/KssD55K9RMhwGnw7s+C1Xj33JLCUlNtHc3zJ2cFdTNK7Kzp++5FY67uHmLqUmSGmVRlaRy0+toePcX4KzPwNM/h8e+C798X7Za8Pgvw1GjUyeUSkOMHLL+Sfj+Z+G1xdkffS78Fgw51z/6SFKRWVQlqVx16AqnfwxGXw9zfpJNB771XBjxHjr0uCh1OinfNiyFaX/H8UseyO5tfNVtMPR8C6oktRKLqiSVu7bt4bSPwglX1q0U/C1O4x7oswFOuR7atEmdbc57xQAAIABJREFUUMqP2r3wxC1w/5chtGXxkI9QddVN2XEkSWo1/nYiSZWiY/dsteC/nsWW7kNg2t/DjyfAxpdTJ5PyYfMqmHwR3PN5GHQWfGI2q466yJIqSQlYVCWp0hxyLM+e8GW49Aew5nm4+V0w/47UqaS0Ft8LN58FrzwDl3wfPvBr6HlU6lSSVLEsqpJUiUKAEz8ANz4Ch1bB7dfD1E/BnjdSJ5NaV4zw4NfgF++F7v3hYw9l9yH2WlRJSsqiKkmVrM8xcP09cNbfZrffmHwxbF2XOpXUOnbvhDs+nC00duLV8NH7sz/cSJKSs6hKUqVr2x7GfQne+yNY/SzcMgZenZ84lFRk217Lrkedf0f29X/J97L7EUuScsGiKknKjLw8O7saa+HHE2H57NSJpOLYsgZ+MglefQ6u+Gk2o8CpvpKUKxZVSdJfHHEifPiP0O0w+Oml8MIfUyeSWtbmldlq15uWw9W/geMuSZ1IklQPi6ok6a16DYDr/wCHDYUpV8GiaakTSS1j86qspG5bB9fcBcecnTqRJKkBFlVJ0tt1PRSu/T0ccRL85q9g8X2pE0mF2fYa/Owy2L4RPnQ3HH166kSSpAOwqEqS6tepB1x9Oxw2DG67Gl56KHUiqXne2JLdfmbTy/CBKXDkyakTSZIaYVGVJDWscy+45rfQZzBM+QC8Oi91Iung7N0Nt12TrWj9vp/AoLNSJ5IkNYFFVZJ0YF0PgQ/eCZ16wi+uyK7zk0rFPf8ELz0IF38HqiekTiNJaiKLqiSpcT36wwd+nU2h/OX7s5dS3j35Q3jyf+Gdn4STPpg6jSTpIFhUJUlN028kXPETWLsA7rwBamtTJ5IatuxRmPEPUHUejPuX1GkkSQfJoipJaroh4+D8r0HNdPjTf6VOI9Vv61q4/XrofQxc/kNo0zZ1IknSQbKoSpIOzukfg5HvhQf+FV6amTqN9Fa1tdkZ/52b4YrJ2erVkqSSY1GVJB2cEOCib8OhQ7OzVi6upDx59D+zxZMmfB36jkidRpLUTBZVSdLB69gN3v9z2L0Tfnuj16sqH1Y8AQ9+NTvjf/K1qdNIkgpgUZUkNc+hVTDhJlj6MMz+fuo0qnS7tsNdN0KPo+DC/8rO/EuSSpZFVZLUfCddA8MuhPv/BV6dnzqNKtkD/woblsAl3/W6VEkqAxZVSVLzhQAXfQc694Y7Pwp73kidSJXo5ceys/qnfhQGn5M6jSSpBVhUJUmF6XoIXPzd7P6qj/xn6jSqNLu2w2//GnoPhHFfSp1GktRCLKqSpMINPQ+Ofx888h+wdlHqNKokj/wHbFya/bGkY7fUaSRJLcSiKklqGef/W1YUfvcpVwFW61i/GP70bRh1JRzzrtRpJEktyKIqSWoZ3Q6D878GKx6Hp36YOo3KXYww7e+hQxc47yup00iSWphFVZLUck64Co45B+7/CmxbnzqNytn8O2DpQ3Du/4Nuh6dOI0lqYRZVSVLLCQEm/jvs3gb3fzl1GpWrXdvgj/8X+p8Ip1yXOo0kqQgsqpKklnVYNZx2A8z9Kax+NnUalaNZ34Mtq2HC16FN29RpJElFYFGVJLW8c/4RuhwCM/4xu5ZQailbXoVHvwXDL4ajz0idRpJUJBZVSVLL69wLzv1nWD4ru5ZQaikPfg32vuE9UyWpzFlUJUnFcdI10Pd4eOArsGdX6jQqB2sWwNM/g1M/CoccmzqNJKmILKqSpOJo0xbGfRE2LoO5k1OnUTm470vQsTuc8w+pk0iSisyiKkkqniHjYOCZ8NA34I2tqdOolK14Ehb/Ad75KejSJ3UaSVKRWVQlScUTQnYt4ba18PgPUqdRKZv5tWyBrtM/ljqJJKkVWFQlScU14DSongR/+g5s35A6jUrRy7NgyQNw5qezqb+SpLJnUZUkFd+5/wxvbIHH/jt1EpWimV+DrodniyhJkiqCRVWSVHyHD4cRl8IT/+tZVR2cpY/A0ofhrL+FDl1Sp5EktRKLqiSpdZz9Odi1BR6/OXUSlZKHvwHd+sLo61InkSS1IouqJKl19B0Bwy6E2TfDzs2p06gUrJqbnU19xyegfefUaSRJrciiKklqPWd/Dt7YDE/ckjqJSsGfvgUde8Ipnk2VpEpjUZUktZ4jToSq82HW97LFlaSGrH8RFkyFUz8MnXqkTiNJamUWVUlS6zr7c7BjIzz989RJlGePfQfadoAzPp46iSQpAYuqJKl1DTgVBpwBs78Pe/ekTqM82vIqPPsrOOlq6HZ46jSSpAQsqpKk1vfOT8Km5bBwauokyqPZP4DaPdnXiSSpIhVUVEMIfUII94YQFte97F3PNgNCCA+GEBaGEJ4PIXy6kH1KkspA9QTocyw89t8QY+o0ypNd22DOj2H4xdBncOo0kqRECj2j+nng/hhjFXB/3eP97QH+PsY4HDgD+EQI4bgC9ytJKmVt2ma3HHllLiyflTqN8uS527LbF3ltqiRVtEKL6iXA5LrXJwOX7r9BjHF1jHFu3etbgIXAkQXuV5JU6k64Cjr3yc6qSpCdXX/8f6D/CTDg9NRpJEkJFVpU+8YYV0NWSIEDrngQQhgEnAQ8XuB+JUmlrkMXOO2jUDMdXluSOo3yYOlDsG4RnH4jhJA6jSQpoRAbuTYohHAf0K+ep74ATI4x9tpn240xxrddp1r3XDfgIeCrMcY7D7C/G4AbAPr27XvKlClTGv1PpLJ161a6deuWOob24Zjkk+OSP3kZkw5vbOCM2R9h1ZGTWDLkw6njJJWXMUlp5Lyv0uP1GmafcSu1bTukjgM4LnnkmOSPY5JPpTAuY8eOnRNjHF3fc40W1QMJIdQAY2KMq0MI/YGZMcbqerZrD/we+EOM8T+b+vFHjx4dn3rqqWbnK7aZM2cyZsyY1DG0D8cknxyX/MnVmPzmOlhyP/zdQujQNXWaZHI1JilsWArfOQnO/iy8+/+mTvNnFT8uOeSY5I9jkk+lMC4hhAaLaqFTf6cC19a9fi1wdz07D8APgYUHU1IlSRXitI9mi+fM+03qJErpyVuzRbZGX586iSQpBwotqjcB40MIi4HxdY8JIRwRQphet82ZwDXAu0MIz9T9m1jgfiVJ5eLod0DfkfDErd6qplLt3gFP/xyGXwQ9jkidRpKUA+0KeecY42vAufW8/RVgYt3rjwKuiCBJql8IcOpH4PefgRWPw9FnpE6k1rZgKuzc5NlUSdKfFXpGVZKkwo26Ajr2hCduSZ1EKcz5CfQZDIPelTqJJCknLKqSpPQ6dIWTroYFd8OWNanTqDWtq4Hlj8Epf+UtaSRJf2ZRlSTlwynXQe0eePZXqZOoNc2ZDG3awwkfSJ1EkpQjFlVJUj4cNjRbWOnpn7moUqXYvROe/SUMvxC6HZY6jSQpRyyqkqT8OOkaeO1FWD4rdRK1hoW/gx0bs2m/kiTtw6IqScqPEZdCh+4w92epk6g1zPkJ9D4GBp2dOokkKWcsqpKk/OjQFY6/HJ6/C3ZuTp1GxfTaEnj5UTj5Q9DGX0ckSW/lTwZJUr6c9CHYswPm35E6iYrpmV9CaAMnuoiSJOntLKqSpHw58mQ4fATM/WnqJCqW2lp47jY49t3QvV/qNJKkHLKoSpLyJQQ4+Rp45Wl4dV7qNCqGZY/A5hVwwlWpk0iScsqiKknKn1Hvh7YdsumhKj/PToGOPWDYpNRJJEk5ZVGVJOVPlz5QdR7Mux327kmdRi3pja2w4O5shef2nVOnkSTllEVVkpRPJ1wJ29bCSw+mTqKWtPB3sHsbnOAiSpKkhllUJUn5VHUedOqVTRNV+Xj2l9m9U48+I3USSVKOWVQlSfnUriOMfA8smgZvbEmdRi1h0wpY+ki2iFIIqdNIknLMoipJyq9RV2b3VF0wNXUStYTnbgMinPD+1EkkSTlnUZUk5deA06D3oLqCo5I373Y4+h3ZmEqSdAAWVUlSfoWQ3apm6cOweVXqNCrEmudh3UIYeXnqJJKkEmBRlSTl26j3AxHm/SZ1EhVi3u0Q2sKIy1InkSSVAIuqJCnfDjkWjjrV6b+lLEaYfwcMHgNdD02dRpJUAiyqkqT8O/4KWLsA1ixInUTNsWoObHrZab+SpCazqEqS8u+4SyC0gefvTJ1EzTHvdmjbEYZfmDqJJKlEWFQlSfnXvS8MOgvm35lNI1XpqN2b/YGhajx06pk6jSSpRFhUJUmlYeTlsGEJvPpc6iQ6GMseha1r4Pj3pk4iSSohFlVJUmkYfjG0aZedVVXpmH87dOgGQy9InUSSVEIsqpKk0tClT7Zq7PNO/y0Ze3bBgqkwbBK075w6jSSphFhUJUmlY+TlsGl5toqs8m/JA7Bzk6v9SpIOmkVVklQ6hk2Cth2c/lsqFtydLaA0eGzqJJKkEmNRlSSVjk49Ych4eP4uqK1NnUYHsmcX1EyD6knQrkPqNJKkEmNRlSSVlpHvgS2vwIrZqZPoQJY+DDs3Z/fAlSTpIFlUJUmlZegF0K5TdlZV+bXwbujQHY512q8k6eBZVCVJpaVjNxgyDhb+3um/ebV3TzY+1RdAu46p00iSSpBFVZJUeoZfnE3/dfXffHr5UdixwWm/kqRms6hKkkrP0POhTXtYODV1EtVnwVRo3wWOPTd1EklSibKoSpJKT+deMPicrKjGmDqN9lW7Fxb+DqrOgw5dUqeRJJUoi6okqTQNvxg2LoNX56VOon0tnw3b1jrtV5JUEIuqJKk0DZsEoU129k75sXBqtipz1Xmpk0iSSphFVZJUmroeCgPP9DrVPKmtza5PHTIuW51ZkqRmsqhKkkrX8Itg3SJY90LqJAJY9VS2GrPTfiVJBbKoSpJK1/CLspeeVc2HBXdnqzEPPT91EklSibOoSpJKV48j4KhTLap5ECMsmgaDx0CnnqnTSJJKnEVVklTahl8Eq5+FjS+nTlLZ1tXAxqUwbGLqJJKkMmBRlSSVtj9P/3X136Rqpmcvh16QNockqSxYVCVJpa3PYOh7vEU1tZrpcMRJ2XRsSZIKZFGVJJW+YZNgxeOwdV3qJJVpyxpY+RRUO+1XktQyLKqSpNI3bCIQ4YV7UiepTIv/AESLqiSpxVhUJUmlr98o6DngL9dJqnXVzICeR0PfEamTSJLKhEVVklT6QoDqCbDkQdi1PXWayrJre/Z5r56QjYMkSS3AoipJKg/VE2HPDnhpZuokleWlmdnnvXpC6iSSpDJiUZUklYeBZ0LHHlAzLXWSylIzPfu8DzwzdRJJUhmxqEqSykO7DlA1Hmrugdq9qdNUhtrabAGrqvHZ51+SpBZSUFENIfQJIdwbQlhc97L3AbZtG0J4OoTw+0L2KUlSg6onwvb1sPLJ1Ekqw6o5sG2dq/1KklpcoWdUPw/cH2OsAu6ve9yQTwMLC9yfJEkNqxoPbdrDIqf/toqa6dCmHQw5N3USSVKZKbSoXgJMrnt9MnBpfRuFEI4CJgG3Frg/SZIa1qknDDrL29S0lprpMPCd0LnBCVWSJDVLiDE2/51D2BRj7LXP440xxrf9tAoh3A78G9Ad+GyM8cIDfMwbgBsA+vbte8qUKVOana/Ytm7dSrdu3VLH0D4ck3xyXPKnnMfkiFXTGLr4Fp449Xts73pU6jhNVmpj0nn7ak5/4kYWD/kIq466KHWcoim1cakEjkn+OCb5VArjMnbs2DkxxtH1PdeusXcOIdwH9KvnqS80ZechhAuBtTHGOSGEMY1tH2O8BbgFYPTo0XHMmEbfJZmZM2eS53yVyDHJJ8clf8p6TDYdC9+6hdN6roezPpg6TZOV3JjM+h4AVZM+SVXvQWmzFFHJjUsFcEzyxzHJp1Ifl0aLaoxxXEPPhRDWhBD6xxhXhxD6A2vr2exM4OIQwkSgE9AjhPDzGGPp/PYgSSodvQZAv1HZtNSzPpM6TfmqmQGHj4AyLqmSpHQKvUZ1KnBt3evXAnfvv0GM8Z9ijEfFGAcBVwIPWFIlSUU1bBKseAK21vf3UxVs+wZ4+TGonpA6iSSpTBVaVG8CxocQFgPj6x4TQjgihOBKFpKkNKonAjG7x6da3uJ7Ie71tjSSpKJpdOrvgcQYXwPetiZ9jPEV4G0/vWKMM4GZhexTkqRG9Tseeg6ARdPh5A+lTlN+aqZDt75wxEmpk0iSylShZ1QlScqfELJpqS89CLu2p05TXva8AS/eD0MvgDb+GiFJKg5/wkiSylP1RNizE16amTpJeVn2KOzakl0HLElSkVhUJUnlaeCZ0LFHNk1VLadmBrTvAsecnTqJJKmMWVQlSeWpXQcYMi5bUKm2NnWa8hBjVlSPfTe075w6jSSpjFlUJUnlq3oibFsHq+akTlIeXn0OXl/pbWkkSUVnUZUkla+qcRDaQs201EnKQ80MIEDV+amTSJLKnEVVklS+OveGQWfWFSwVrGY6DDgduh2WOokkqcxZVCVJ5a16IqxbBK8tSZ2ktG1eBaufddqvJKlVWFQlSeVt6AXZyxfuSZuj1L25enL1xLQ5JEkVwaIqSSpvfY6Bw49z+m+hamZAn2Ph0KrUSSRJFcCiKkkqf9UT4OXHYPuG1ElK087XYenD2ecxhNRpJEkVwKIqSSp/1RMh7oUX70udpDQteQBqd8OwSamTSJIqhEVVklT+jjgZuvX9y3WWOjg1M6BzHzjqtNRJJEkVwqIqSSp/bdpkiyotvg/2vJE6TWnZuwcW/wGGng9t26VOI0mqEBZVSVJlqJ4Iu7bAskdTJyktK2bDjo3elkaS1KosqpKkyjD4HGjX2dV/D1bNDGjbAY59d+okkqQKYlGVJFWG9p2zslUzA2JMnaY0xAiLpsExZ0PH7qnTSJIqiEVVklQ5qifA6yvh1Xmpk5SG9S/AxqXZtGlJklqRRVWSVDmGng8Ep/821aJp2cuhF6TNIUmqOBZVSVLl6HY4DDjN29Q0Vc0M6H8i9DwydRJJUoWxqEqSKkv1BFj9DGxelTpJvm1dCyufdNqvJCkJi6okqbK8WbxecPrvAb3wByB6WxpJUhIWVUlSZTl0KPQZ7HWqjamZAT0HQL/jUyeRJFUgi6okqbKEkJ1VXfowvLEldZp82rUdljyQLaIUQuo0kqQKZFGVJFWe6gmwd1dWxvR2L82EPTtgmNenSpLSsKhKkirPgDOgc2+n/zakZhp07AEDz0qdRJJUoSyqkqTK07YdVJ2fLRi0d0/qNPlSuxdq7oGq8dCuQ+o0kqQKZVGVJFWm6gmwYwOsfCJ1knxZ+RRsX+9taSRJSVlUJUmVaci50LYD1ExPnSRfaqZBm/bZGVVJkhKxqEqSKlPH7jDoXbBoOsSYOk1+LJoOg86CTj1TJ5EkVTCLqiSpclVPgA1LYP3i1EnyYf1ieG2x034lSclZVCVJlat6QvbS6b+ZRdOyl29+XiRJSsSiKkmqXD2Pgv4neJuaN9VMh36joNeA1EkkSRXOoipJqmzVE2HF47BtfeokaW1dCyuegGGTUieRJMmiKkmqcNUTgJjdU7WSvXAPEL0+VZKUCxZVSVJl6zcKehzpdao1M6Dn0dDv+NRJJEmyqEqSKlwI2VnVJQ/A7p2p06SxazsseTD7PISQOo0kSRZVSZKongC7t8PSh1InSeOlB2HPDhjmtF9JUj5YVCVJGvQu6NC9cqf/LpoOnXrCwDNTJ5EkCbCoSpIE7TrCkHOh5h6orU2dpnXV7s0WUqo6D9q2T51GkiTAoipJUqZ6Imx9FVY/nTpJ61o+C7av97Y0kqRcsahKkgRQNR5C22z120qyYCq06wRDxqdOIknSn1lUJUkC6NIHjn5HZRXV2lpY+DsYMg46dkudRpKkP7OoSpL0puoJsGY+bHw5dZLWsWoObHkFhl+cOokkSW9hUZUk6U1v3p7lhXvS5mgtC++GNu1h6Pmpk0iS9BYWVUmS3tRnMBw2DBZNS52k+GLMpv0OPgc690qdRpKkt7CoSpK0r+oJ8PKfYMfG1EmK69V5sHGZ034lSblkUZUkaV/DL4baPbBoeuokxbVwKoQ23pZGkpRLFlVJkvZ1xEnQ62h4/q7USYprwVQYeCZ0PTR1EkmS3saiKknSvkKAEZfBSw+W7/TfdTWwvgaOuyR1EkmS6lVQUQ0h9Akh3BtCWFz3sncD2/UKIdweQlgUQlgYQnhHIfuVJKmojru0bvpvmS6qtGBq9nLYhWlzSJLUgELPqH4euD/GWAXcX/e4Pt8G7okxDgNOABYWuF9Jkornz9N/f5s6SXEsvBuOOg169E+dRJKkehVaVC8BJte9Phm4dP8NQgg9gLOBHwLEGHfFGDcVuF9Jkopn3+m/2zekTtOy1i/OVvwd8bYf2ZIk5UaIMTb/nUPYFGPstc/jjTHG3vttcyJwC7CA7GzqHODTMcZtDXzMG4AbAPr27XvKlClTmp2v2LZu3Uq3bt1Sx9A+HJN8clzyxzFpXPfXF3PK3M+yqPqTvNp/XNH311pjMnDZFAYtm8Ksd/yQXR0PKfr+Sp3HSv44JvnjmORTKYzL2LFj58QYR9f3XKNFNYRwH9Cvnqe+AExuQlEdDcwGzowxPh5C+DbweozxnxsLPnr06PjUU081tlkyM2fOZMyYMaljaB+OST45LvnjmDRBjPDtE+DQKvjgHUXfXauMSYzwvdOgW1/4q98Xd19lwmMlfxyT/HFM8qkUxiWE0GBRbdfYO8cYG/wzcghhTQihf4xxdQihP7C2ns1WAitjjI/XPb6dhq9llSQpH0LIpsfO+l42/bdLn9SJCrdmPqx/Ac74eOokkiQdUKHXqE4Frq17/Vrg7v03iDG+CqwIIVTXvelcsmnAkiTl24jLymv133m3Q5t2MNzb0kiS8q3QonoTMD6EsBgYX/eYEMIRIYTp+2z3SeAXIYTngBOBrxW4X0mSiq//idBrIDx/V+okhYsR5t8Jg8dCV69NlSTlW6NTfw8kxvga2RnS/d/+CjBxn8fPAPXOPZYkKbdCgJHvgT99B7auhW6Hp07UfCufhM3LYez/SZ1EkqRGFXpGVZKk8jbq/RD3ZmcjS9n8O6BtRxg2KXUSSZIaZVGVJOlADh8O/UbBc/m9XVqjavdm05eHngedeqROI0lSoyyqkiQ1ZtT74ZWnYd0LqZM0z0sPwtY1MPK9qZNIktQkFlVJkhpz/HshtIF5v06dpHme+RV06gXVE1InkSSpSSyqkiQ1pns/GDwGnrsNamtTpzk4OzfDot/DyMuhXcfUaSRJahKLqiRJTTHqSti0HFY8njrJwXn+t7BnJ5z4gdRJJElqMouqJElNMWwStO9SeosqPfsrOKQKjjwldRJJkprMoipJUlN07AbDL8pWz929M3WaptnwEiyfBSdeld0TVpKkEmFRlSSpqU64Krvmc+HvUidpmmenACGbtixJUgmxqEqS1FTHnAO9BsLcyamTNK52b7ba7+Ax0PPI1GkkSTooFlVJkpqqTRs45VpY9gisfzF1mgNb8gBsXp7llSSpxFhUJUk6GCdeDaFt/s+qPvUj6Ho4VE9KnUSSpINmUZUk6WB07wfVE+CZX8KeXanT1G/zSnjhHjjpg9CuQ+o0kiQdNIuqJEkH65S/gu3roWZa6iT1m/sziNFpv5KkkmVRlSTpYB37bug5AOb8JHWSt9u7J5uWPGQc9B6UOo0kSc1iUZUk6WC1aZudrXxpJqxdmDrNW70wA7ashtHXp04iSVKzWVQlSWqOU66Ddp3g8ZtTJ3mrWd+HXkdD1Xmpk0iS1GwWVUmSmqProTDqCnh2CmzfkDpNZtUcWP4YnP5xaNsudRpJkprNoipJUnOd/nHYsxPm/Dh1ksys70PHHtlqv5IklTCLqiRJzdX3OBg8Fp74X9i7O22WzSvh+bvg5A9Bpx5ps0iSVCCLqiRJhTjjr7PFi+bdnjbH7B8AEU7/WNockiS1AIuqJEmFqBoPfY+HR74JtXvTZNi2Hp76EYy8PFtISZKkEmdRlSSpECHAOZ+D117Mpt6mMOu7sHsHnP25NPuXJKmFWVQlSSrUsIvgsOHw8L9DbW3r7nv7huwa2RGXwWHVrbtvSZKKxKIqSVKh2rSBsz8L6xbBwrtbd9+zvgu7tsE5/9C6+5UkqYgsqpIktYQRl8Fhw+D+L8OeXa2zz9dfyW5JM+IyOHx46+xTkqRWYFGVJKkltGkL478MG15qvfuqPvhViHth3BdbZ3+SJLUSi6okSS2l6jw45hyYeRPs2FTcfb06H57+BZx2A/QeVNx9SZLUyiyqkiS1lBDgvH+FHRvhoa8Xbz+1tTDjH6Bzr+zaWEmSyoxFVZKkltR/FIy+Dh6/GVbNKc4+nv4ZvPynbKpx597F2YckSQlZVCVJamnjvgTd+sLUT8He3S37sbesgXv/GQaeBSdd07IfW5KknLCoSpLU0jr1hInfhDXz4eFvttzHra2Fuz8Bu3fCRd/KphpLklSGLKqSJBXD8AvhhKuya1WXPtwyH3P29+HFe+H8r8KhVS3zMSVJyiGLqiRJxTLxm1mhvOMjsHlVYR9r2aNw35dg2IVw6kdaJJ4kSXllUZUkqVg6doP3TYZd2+EX723+LWvWL4YpV0OfwXDJd53yK0kqexZVSZKKqe9xcOXPs7L5yysOvqyuewEmXwxt28PVv3aVX0lSRbCoSpJUbIPHwOW3wqq58OOJsPHlpr3fskfhxxOgdjd86G7oPaiIISVJyg+LqiRJrWHEpXD1b2DzCrj5LJj7U9i7p/5t39gK9/1Ldia1cy+47h7oO6J180qSlFC71AEkSaoYx46FGx+Fu26EqZ+ER/8LRr0fjhxNj81LYOHW7Czqc7fBjg1wwgdg4jegY/fUySVJalUWVUmSWlPvgXDddFg0DWZ9D2beBEROBngaaNMehk2Cd/wNDDg1bVZJkhKxqEqS1NpCyO6zOvxC2PYarK/huaceY9TpY7Ipvu07p04oSVJSFlVJklLqegh0fScblu6Co0anTiNJUi64mJIkSZKNRrrsAAAIiklEQVQkKVcsqpIkSZKkXLGoSpIkSZJyxaIqSZIkScoVi6okSZIkKVcsqpIkSZKkXLGoSpIkSZJyxaIqSZIkScqVgopqCKFPCOHeEMLiupe9G9jub0MIz4cQ5ocQfhVC6FTIfiVJkiRJ5avQM6qfB+6PMVYB99c9fosQwpHAp4DRMcaRQFvgygL3K0mSJEkqU4UW1UuAyXWvTwYubWC7dkDnEEI7oAvwSoH7lSRJkiSVqRBjbP47h7Apxthrn8cbY4xvm/4bQvg08FVgB/DHGOPVB/iYNwA3APTt2/eUKVOmNDtfsW3dupVu3bqljqF9OCb55Ljkj2OSP45JPjku+eOY5I9jkk+lMC5jx46dE2McXd9z7Rp75xDCfUC/ep76QlN2Xnfd6iXAMcAm4DchhA/GGH9e3/YxxluAWwBGjx4dx4wZ05TdJDFz5kzynK8SOSb55Ljkj2OSP45JPjku+eOY5I9jkk+lPi6NFtUY47iGngshrAkh9I8xrg4h9AfW1rPZOGBpjHFd3fvcCbwTqLeoSpIkSZIqW6HXqE4Frq17/Vrg7nq2WQ6cEULoEkIIwLnAwgL3K0mSJEkqU4UW1ZuA8SGExcD4useEEI4IIUwHiDE+DtwOzAXm1e3zlgL3K0mSJEkqU41O/T2QGONrZGdI93/7K8DEfR5/EfhiIfuSJEmSJFWGQs+oSpIkSZLUoiyqkiRJkqRcsahKkiRJknIlxBhTZ2hQCGEd8HLqHAdwKLA+dQi9hWOST45L/jgm+eOY5JPjkj+OSf44JvlUCuMyMMZ4WH1P5Lqo5l0I4akY4+jUOfQXjkk+OS7545jkj2OST45L/jgm+eOY5FOpj4tTfyVJkiRJuWJRlSRJkiTlikW1MLekDqC3cUzyyXHJH8ckfxyTfHJc8scxyR/HJJ9Kely8RlWSJEmSlCueUZUkSZIk5YpFtREhhPeFEJ4PIdSGEEbv99w/hRBeDCHUhBDOb+D9+4QQ7g0hLK572bt1kleGEMJtIYRn6v4tCyE808B2y0II8+q2e6q1c1aaEMKXQgir9hmbiQ1sd0Hd8fNiCOHzrZ2zkoQQ/j2EsCiE8FwI4a4QQq8GtvNYKbLGvu5D5jt1zz8XQjg5Rc5KEUIYEEJ4MISwsO7n/afr2WZMCGHzPt/T/l+KrJWmse9HHiutK4RQvc8x8EwI4fUQwmf228ZjpRWEEH4UQlgbQpi/z9ua1DlK6Xcvp/42IoQwHKgF/gf4bIzxqbq3Hwf8CjgNOAK4DxgaY9y73/t/A9gQY7yp7ouhd4zxH1vz/1ApQgj/AWyOMX65nueWAaNjjHm/l1RZCCF8CdgaY/zmAbZpC7wAjAdWAk8CV8UYF7RKyAoTQjgPeCDGuCeE8HWA+r4XeawUV1O+7uv+sPNJYCJwOvDtGOPpCeJWhBBCf6B/jHFuCKE7MAe4dL8xGUP2O8CFiWJWpMa+H3mspFP3vWwVcHqM8eV93j4Gj5WiCyGcDWwFfhpjHFn3tkY7R6n97uUZ1UbEGBfGGGvqeeoSYEqM8Y0Y41LgRbLSWt92k+tenwxcWpyklS2EEIAryP54oNJwGvBijPGlGOMuYArZ8aIiiDH+Mca4p+7hbOColHkqWFO+7i8h++UjxhhnA73qypSKIMa4OsY4t+71LcBC4Mi0qdREHivpnAss2bekqvXEGB8GNuz35qZ0jpL63cui2nxHAiv2ebyS+n+w9Y0xrobshyFweCtkq0TvAtbEGBc38HwE/hhCmBNCuKEVc1Wyv6mbivWjBqafNPUYUsu7HpjRwHMeK8XVlK97j41EQgiDgJOAx+t5+h0hhGdDCDNCCCNaNVjlauz7kcdKOlfS8MkBj5U0mtI5SuqYaZc6QB6EEO4D+tXz1BdijHc39G71vM151EXQxPG5igOfTT0zxvhKCOFw4N4QwqK6v0apmQ40LsAPgK+QHRNfAf6DrBy95UPU874eQwVoyrESQvgCsAf4RQMfxmOluJryde+xkUAIoRtwB/CZGOPr+z09FxgYY9xaN930t0BVa2esQI19P/JYSSCE0AG4GPinep72WMm3kjpmLKpAjHFcM95tJTBgn8dHAa/Us92aEEL/GOPquukoa5uTsZI1Nj4hhHbAe4BTDvAxXql7uTaEcBfZ1Ad/+S5AU4+bEML/Ar+v56mmHkNqoiYcK9cCFwLnxgYWKPBYKbqmfN17bLSyEEJ7spL6ixjjnfs/v29xjTFODyF8P4RwqNdyF1cTvh95rKQxAZgbY1yz/xMeK0k1pXOU1DHj1N/mmwpcGULoGEI4huyvRU80sN21da9fCzR0hlbNNw5YFGNcWd+TIYSudQtkEELoCpwHzK9vW7WM/a4Ruoz6P99PAlUhhGPq/jp7JdnxoiIIIVwA/CNwcYxxewPbeKwUX1O+7qcCH6pb0fQMskXiVrd20EpRt8bBD4GFMcb/bGCbfnXbEUI4jez3p9daL2XlaeL3I4+VNBqcxeaxklRTOkdJ/e7lGdVGhBAuA/4bOAyYFkJ4JsZ4fozx+RDCr4EFZNPoPvHmir8hhFuBm+tWCL4J+HUI4cPAcuB9Sf4j5e1t10mEEI4Abo0xTgT6AnfVfd9sB/wyxnhPq6esLN8IIZxINp1kGfAxeOu41K0++zfAH4C2wI9ijM+nClwBvgt0JJs+BzA7xnijx0rraujrPoRwY93zNwPTyVYxfRHYDlyXKm+FOBO4BpgX/nKLs/8DHA1/HpP3Ah8PIewBdgBXNjQrQS2m3u9HHitphRC6kK0Y+7F93rbvmHistIIQwq+AMcChIYSVwBdpoHOU8u9e3p5GkiRJkpQrTv2VJEmSJOWKRVWSJEmSlCsWVUmSJElSrlhUJUmSJEm5YlGVJEmSJOWKRVWSJEmSlCsWVUmSJElSrlhUJUmSJEm58v8B5F13EINDp7QAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1152x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "# Create fresh input data:\n",
    "_x = numpy.arange(-10, 10, delta, dtype=numpy.float32)\n",
    "_x = _x.reshape((_x.shape[0], 1))\n",
    "\n",
    "x = tf.Variable(_x)\n",
    "\n",
    "y_exact = w_0(x)\n",
    "y_fit   = w_nn(x)\n",
    "\n",
    "x_numpy = x.numpy()\n",
    "\n",
    "fig = plt.figure(figsize=(16,9))\n",
    "\n",
    "plt.plot(x_numpy, y_exact.numpy(), label=\"Exact solution\")\n",
    "plt.plot(x_numpy, y_fit.numpy(), label=f\"Neural Network Fit, E={energy:.2}\")\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And the probability:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "# Create fresh input data:\n",
    "_x = numpy.arange(-10, 10, delta, dtype=numpy.float32)\n",
    "_x = _x.reshape((_x.shape[0], 1))\n",
    "\n",
    "x = tf.Variable(_x, trainable = True)\n",
    "\n",
    "p_exact = w_0(x)**2\n",
    "p_fit   = w_nn(x)**2\n",
    "\n",
    "x_numpy = x.numpy()\n",
    "\n",
    "fig = plt.figure(figsize=(16,9))\n",
    "\n",
    "plt.plot(x_numpy, p_exact.numpy(), label=\"Exact solution\")\n",
    "plt.plot(x_numpy, p_fit.numpy(), label=f\"Neural Network Fit, E={energy:.2}\")\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Higher level states\n",
    "\n",
    "Can we use ML techniques to learn higher level states?  The next wave function needs to be orthogonal to the ground state, so if our approximation is good, we should be able to minimize the energy and the orthogonal-ness of the first excited state at the same time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "def training_step_excited_state(wavefunction, known_wavefunction, optimizer, delta, alpha=50):\n",
    "    \n",
    "    x = generate_input(delta)\n",
    "\n",
    "    # Compute the energy:\n",
    "    tape = tf.GradientTape()\n",
    "    \n",
    "    with tape:\n",
    "        energy = energy_computation(wavefunction, x, delta)\n",
    "\n",
    "    # Now, we have the energy.  We should make sure it is orthogonal to the known wavefunction:\n",
    "    y0 = known_wavefunction(x)\n",
    "    with tape:\n",
    "        y1 = wavefunction(x)\n",
    "        ortho = (tf.reduce_sum(y0 * y1) * delta)**2\n",
    "    \n",
    "        # We scale here the orthogonality condition.  Note that it's a really high scaling compared to the energy.\n",
    "        # We need the orthogonality to be very good to have any hope of converging!\n",
    "        \n",
    "        # At home: Try with a lower constraint.  Does it still work?\n",
    "        energy += alpha*ortho\n",
    "    \n",
    "    \n",
    "    gradients = tape.gradient(energy, wavefunction.trainable_variables)\n",
    "\n",
    "    optimizer.apply_gradients(zip(gradients, wavefunction.trainable_variables))\n",
    "    \n",
    "\n",
    "    return  energy - alpha*ortho, ortho\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Step 0, E ==1.5037400722503662, Orthogonality=1.7396829532501101e-09\n",
      "Step 10, E ==1.4996711015701294, Orthogonality=9.57599186222069e-05\n",
      "Step 20, E ==1.5003547668457031, Orthogonality=2.888108197041106e-09\n",
      "Step 30, E ==1.4998559951782227, Orthogonality=1.0786769962578546e-05\n",
      "Step 40, E ==1.5000048875808716, Orthogonality=1.393030686358543e-07\n",
      "Step 50, E ==1.4999762773513794, Orthogonality=1.4634913441113895e-06\n",
      "Step 60, E ==1.500008463859558, Orthogonality=4.129794106688678e-08\n",
      "Step 70, E ==1.5000042915344238, Orthogonality=9.051220928313342e-08\n",
      "Step 80, E ==1.5000030994415283, Orthogonality=6.94517297006314e-08\n",
      "Step 90, E ==1.5000028610229492, Orthogonality=1.5164493660790868e-08\n"
     ]
    }
   ],
   "source": [
    "w_nn_excited = NeuralWavefunction()\n",
    "delta = 0.0001\n",
    "\n",
    "optimizer = tf.keras.optimizers.Adam()\n",
    "\n",
    "energy_history = []\n",
    "ortho_history = []\n",
    "step_history = []\n",
    "\n",
    "for i in range(100):\n",
    "    energy, ortho = training_step_excited_state(w_nn_excited, w_nn, optimizer, delta, alpha=500)\n",
    "    if i % 10 == 0:\n",
    "        print(f\"Step {i}, E =={energy}, Orthogonality={ortho}\")\n",
    "    \n",
    "    energy_history.append(energy.numpy())\n",
    "    ortho_history.append(ortho.numpy())\n",
    "    step_history.append(i)\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This technique is not as stable as searching for the ground state.  If you run this and the orthogonality constraint is 0.001 or larger, likely the energy has fallen into the ground state instead of the first excited state.  Try again, increase the alpha parameter maybe, and see if it works."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In principle, this *ought* to come out somewhere near the first excited state.  Let's take a look at the wavefunctions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "# Create fresh input data:\n",
    "_x = numpy.arange(-10, 10, delta, dtype=numpy.float32)\n",
    "_x = _x.reshape((_x.shape[0], 1))\n",
    "\n",
    "x = tf.Variable(_x, trainable = True)\n",
    "\n",
    "# Make sure the normalization is updated:\n",
    "w_nn_excited.update_normalization(x)\n",
    "\n",
    "y_exact = w_1(x)\n",
    "y_fit   = w_nn_excited(x)\n",
    "\n",
    "x_numpy = x.numpy()\n",
    "\n",
    "fig = plt.figure(figsize=(16,9))\n",
    "\n",
    "plt.plot(x_numpy, y_exact.numpy(), label=\"Exact solution\")\n",
    "plt.plot(x_numpy, y_fit.numpy(), label=f\"Neural Network Fit, E={energy:.2}\")\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This looks pretty great!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "# Create fresh input data:\n",
    "_x = numpy.arange(-10, 10, delta, dtype=numpy.float32)\n",
    "_x = _x.reshape((_x.shape[0], 1))\n",
    "\n",
    "x = tf.Variable(_x, trainable = True)\n",
    "\n",
    "p_exact = w_1(x)**2\n",
    "p_fit   = w_nn_excited(x)**2\n",
    "\n",
    "x_numpy = x.numpy()\n",
    "\n",
    "fig = plt.figure(figsize=(16,9))\n",
    "\n",
    "plt.plot(x_numpy, p_exact.numpy(), label=\"Exact solution\")\n",
    "plt.plot(x_numpy, p_fit.numpy(), label=f\"Neural Network Fit, E={energy:.2}\")\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All in all, this is not a terrible solution to the second excited state.  Likely more sophisticate optimization tricks can make this better.  Extending to multiple particles and multiple dimensions is more complicated - we'll work towards that next."
   ]
  }
 ],
 "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": "3.6.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}