FIZ371_LN80_EST_2DIsing.ipynb

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    "## 2D Ising Model\n",
    "**FIZ371 - Scientific & Technical Computations | 10/06/2020**\n",
    "\n",
    "**2D Ising Model**\n",
    "* Introduction\n",
    "    * Relevance of Ising models\n",
    "* Ferromagnetic Materials\n",
    "* Difficulties\n",
    "* Monte Carlo simulation\n",
    "    * Metropolis algorithm\n",
    "* Implementation\n",
    "* Homework\n",
    "* Appendix: Evolution of the configuration probabilities for a 2x2 Ising Grid\n",
    "* External link(s)\n",
    "  \n",
    "Dr. Emre S. Tasci <emre.tasci@hacettepe.edu.tr>"
   ]
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   "source": [
    "# Introduction\n",
    "\n",
    "The Ising model is the modelling of a network with nodes interacting with each other with respect to some order. Initially developed by Ernst Ising in 1925 to model the phase transition in 1D in order to observe critical variables in action, alas Ising didn't manage to encounter any phase transition and gave up the model, until much later. The model was analytically solved by Lars Onsager in 1944. The 3D version has not yet been solved although there are a couple of claims. "
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    "## Relevance of Ising models\n",
    "As for the relevance and importance of Ising models, I'm quoting directly from our textbook, [MacKay's \"Information Theory, Inference, and Learning Algorithms\"](http://www.inference.org.uk/mackay/itprnn/book.html):\n",
    "\n",
    "Ising models are relevant for three reasons.\n",
    "\n",
    "Ising models are important first as models of magnetic systems that have a phase transition. The theory of universality in statistical physics shows that all systems with the same dimension (here, two), and the same symmetries, have equivalent critical properties, i.e., the scaling laws shown by their phase transitions are identical. So by studying Ising models we can find out not only about magnetic phase transitions but also about phase transitions in many other systems.\n",
    "\n",
    "Second, if we generalize the energy function to\n",
    "\n",
    "$$E(\\vec{x};\\vec{J},\\vec{h}) =-\\left[\\frac{1}{2}\\sum_{m,n}{J_{mn}x_m x_n}+\\sum_n{h_n x_n}\\right]$$\n",
    "\n",
    "where the couplings $J_{mn}$ and applied fields $h_n$ are not constant, we obtain a family of models known as 'spin glasses' to physicists, and as 'Hopfield networks' or 'Boltzmann machines' to the neural network community. In some of these models, all spins are declared to be neighbours of each other, in which case physicists call the system an \"infinite-range\" spin glass, and networks call it a \"fully connected\" network.\n",
    "\n",
    "Third, the Ising model is also useful as a statistical model on its own right."
   ]
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ferromagnetic Materials\n",
    "A ferromagnetic material is a material whose atomic spins align with the applied external magnetic field and even at the lack of an external field, its atoms also tend to align their magnetic moments with that of their neighbours resulting in spin domains:\n",
    "\n",
    "![NdFeB-Domains.jpg](attachment:NdFeB-Domains.jpg)\n",
    "[Source: Wikipedia](https://en.wikipedia.org/wiki/Magnetic_domain)\n",
    "\n",
    "The magnetic contribution to the energy comes from the following interaction in the Hamiltonian:\n",
    "\n",
    "$$E(\\vec{x};J,H) =-\\left[\\frac{1}{2}\\sum_{m,n}{J_{mn}x_m x_n}+\\sum_n{Hx_n}\\right]$$\n",
    "\n",
    "Here, $\\vec{x}$ is the spin configuration of the sites; $x_i$ is the spin of the <i>i</i>th site (-1 for \"down\" and +1 for \"up\"); $J_{mn}$ is the coupling coefficient between the $m$ and $n$ sites and $H$ is the applied external field, if there is any.\n",
    "\n",
    "We can define the interaction depth of the spins via the coupling coefficient $J_{mn}$: for example, the coefficient can be 5 for the *nearest neighbours*, 3 for the *next nearest neighbours* and 0 for the rest of the atoms making them irrelevant to the site at hand. J's sign indicates the ferromagnetic/antiferromagnetic tendency, with $J>0$ the spins tend to align in the same direction whereas negative $J$ drives the antiferromagnetic behaviour.\n",
    "\n",
    "For simplicity, we will assume $J_{mn} = J$ if $m$ and $n$ are neighbours and $J_{mn} = 0$ otherwise, so the only manipulation to the spins will be due to the neighbours.\n",
    "\n",
    "As we have the energy equation, at equilibrium at temperature $T$, the probability that the state is $\\vec{x}$, will be given by:\n",
    "\n",
    "$$P(\\vec{x}|\\beta,J,H) = \\frac{1}{Z(\\beta,J,H)}\\exp\\left[-\\beta E(\\vec{x};J,H)\\right]$$\n",
    "\n",
    "here, $\\beta=1/k_B T$, $k_B$ is Boltzmann's contant and:\n",
    "\n",
    "$$Z(\\beta,J,H)\\equiv\\sum_{\\vec x}{\\exp\\left[-\\beta E(\\vec{x};J,H)\\right]}$$\n",
    "\n",
    "is the partition function. From statistics, we know that the entropy can be written as:\n",
    "\n",
    "$$S=-\\frac{\\partial F}{\\partial T}$$\n",
    "\n",
    "where $F$ is the free energy:\n",
    "\n",
    "$$F=-k_B T\\ln Z$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Difficulties\n",
    "So, from the previous section, as we have the probability equation, we can use the partition function $Z$ to first to calculate the free energy and then the entropy of our system. However, there is a very bit tiny problem with the calculation of the partition function. \n",
    "\n",
    "Even with a very small system of $10\\times10$ grid, where each site can have a sping value of $\\pm1$, we will have $2^{100}$ possible configurations ($\\{\\vec x\\}$), which will take more than the age of the universe to calculate on a supercomputer as we know it.\n",
    "\n",
    "In contrast to this, calculating the energy of any given configuration $\\vec{x}$ is pretty much straightforward and fast, so we need to be able to exploit this fact for _sampling_. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Monte Carlo simulation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Metropolis algorithm\n",
    "We will employ the Metropolis algorithm (which we have already considered as one of the stochastic activation functions of the artificial neural networks) and will randomly choose a site whose spin is in the state $x_n$. If the spin is flipped, the change in the energy will be equal to:\n",
    "\n",
    "$$\\Delta E=2x_n b_n$$\n",
    "\n",
    "where $b_n$ is the local field, that is:\n",
    "\n",
    "$$b_n = \\sum_{m:(m,n)\\in\\mathcal{N}}{Jx_m + H}$$\n",
    "\n",
    "As the Metropolis algorithm proposes, if the energy is decreased, we automatically accept this spin flip; else, we still accept it with a probability of $\\exp(-\\beta \\Delta E)$:\n",
    "\n",
    "$$P(\\text{accept};\\Delta E,\\beta)=\\begin{cases}1&&\\Delta E\\le0\\\\\\exp(-\\beta\\Delta E)&&\\Delta E\\gt0\\end{cases}$$\n",
    "\n",
    "After sufficient number of iterations, this method converges to the equilibrium distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Implementation\n",
    "The following code is more suitable for an environment other than Jupyter as it produces many output plots."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1  1 -1 -1 -1 -1  1 -1  1  1]\n",
      " [-1 -1 -1 -1  1  1  1 -1  1  1]\n",
      " [-1  1 -1  1 -1  1  1 -1  1 -1]\n",
      " [-1 -1 -1 -1 -1 -1 -1  1  1  1]\n",
      " [ 1  1 -1  1 -1  1 -1 -1  1 -1]\n",
      " [ 1 -1 -1  1 -1 -1 -1  1  1  1]\n",
      " [-1  1 -1  1 -1  1  1 -1 -1  1]\n",
      " [ 1 -1  1  1  1 -1  1 -1  1  1]\n",
      " [-1 -1  1 -1  1  1  1  1 -1 -1]\n",
      " [ 1 -1 -1 -1  1 -1 -1  1 -1  1]]\n",
      "49 up | 51 down \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=============================================\n",
      "[[ 1  1  1  1 -1  1  1  1  1  1]\n",
      " [-1  1  1  1 -1 -1 -1  1 -1 -1]\n",
      " [ 1 -1 -1  1 -1  1  1  1 -1 -1]\n",
      " [-1 -1 -1  1 -1 -1  1  1 -1  1]\n",
      " [ 1  1  1 -1 -1 -1 -1  1  1  1]\n",
      " [ 1 -1  1 -1  1 -1 -1  1 -1 -1]\n",
      " [-1  1 -1 -1 -1 -1 -1 -1 -1 -1]\n",
      " [ 1 -1 -1 -1  1 -1  1  1 -1  1]\n",
      " [-1  1  1 -1 -1 -1 -1  1 -1  1]\n",
      " [ 1 -1  1  1  1 -1 -1 -1  1 -1]]\n",
      "T:10.0\t|47 up | 53 down\t|Mag: -0.06000 \n",
      "---------------------------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1 -1 -1 -1 -1 -1 -1  1  1  1]\n",
      " [ 1 -1 -1 -1 -1  1  1 -1 -1 -1]\n",
      " [-1 -1 -1 -1  1  1 -1 -1  1 -1]\n",
      " [ 1 -1  1 -1 -1  1  1  1  1  1]\n",
      " [ 1  1 -1  1 -1  1 -1  1  1  1]\n",
      " [-1 -1  1  1 -1  1 -1 -1 -1 -1]\n",
      " [ 1  1 -1  1  1 -1 -1 -1 -1  1]\n",
      " [ 1  1 -1 -1  1 -1  1  1  1 -1]\n",
      " [ 1 -1  1 -1 -1 -1  1 -1 -1 -1]\n",
      " [ 1 -1  1  1 -1 -1  1  1 -1 -1]]\n",
      "T:9.5\t|46 up | 54 down\t|Mag: -0.08000 \n",
      "---------------------------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPoAAAEhCAYAAABWYr1lAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8vihELAAAACXBIWXMAAAsTAAALEwEAmpwYAAASxklEQVR4nO3de7CcdX3H8feHBIQDQnQMQhLueMcLcrQgVSkwtip46VjFAjVUhzgWQUdlkOokdLS0DF7R2kSQ2oJaJ8aZotZiR1CgNu3hMnIJWgVMwkk0KuEWRi759o/fb3Fzci57cvY5u5vv5zWzk919fvvsdzf7Ob9nn31+v0cRgZnt3HbpdQFm1jwH3SwBB90sAQfdLAEH3SwBB90sAQfdLAEHfYYkPdR22Srpkbbbp/a6vh0h6R5JJ/bw+Z8i6VOSRiXdJ+kfJO06SfuQ9HDb+37pbNY7COb2uoBBFxF7ta5Lugd4V0T8Z+8qmpykuRHxeJ8/x3nAMHAEMAe4CvgIsHSSx7w4In42g+fcqblHb4ikXSSdJ+nnkn4j6euSnl6XHVx7oTMkrau91rslvUzSjyVtlvS5tnUtlnSDpEsk3S/pTkkntC3fR9JlkjZIulfSxyTNGfPYT0n6LbBM0mGSvl/r+rWkKyXNq+3/BTgQuKr2judKOk7S+jGv78leX9IySSslXSHpAWDxZDV14GTgsxHx24jYBHwW+Msd/K8wHPQmnQ28CXg1sAC4D/j8mDZ/ADwLeBvwaeCvgROBFwBvlfTqMW3vAp5B6dlWtf5wAF8GHgcOB44EXgO8a5zH7gt8HBBwYa3recABwDKAiDgdWAucHBF7RcRFHb7eNwIrgXnAlZPVJOnA+sfswAnWpXppv71I0j6TPP8PJW2UtErSwR3WnEdE+NKlC3APcGK9vgY4oW3Z/sBjlK9LBwMBLGxb/hvgbW23vwG8r15fDIwCalv+P8DpwDOB3wF7tC17O3BN22PXTlH3m4Cbx3sd9fZxwPpJXusy4IdtyyatqYP38WPADcB8YD9gdX2/9p+g/auA3Sh/ZD4H3AbM7fXnoZ8u/o7enIOAb0ra2nbfE5QQtPyy7foj49zeq+32vVE/1dUvKD3yQcCuwAbpyU5wF2BdW9v260jal7I5/ErgqbX9fR29qom1P0cnNU3m45TQ3kL5g/FFylbBr8ZrHBE/rFcflXQO8ABlS+XWjqvfyXnTvTnrgNdGxLy2y+4Rce8Orm+h2lJD+R49Wp/nd8Az2p5n74h4QVvbsUMUL6z3vSgi9gZOY9tN5bHtHwaGWjfqd+35Y9q0P6aTmiYUEY9ExFkRsTAiDqVs7dwYEU908vhai6ZslYiD3px/BD4u6SAASfMlvXEG69sXOFvSrpL+jNJjfSciNgBXA5+QtHfdCXjYmO/3Yz0VeAjYLGkh8KExy38JHNp2+6fA7pJeX3/m+gjwlIlWvoM1PUnSQkkLVBwNfJQJ9rhLeoGkl0iaI2kv4BPAvZSvTlY56M35DPBvwNWSHgT+m7JTbEetpuy4+zVl0/YtEfGbuuwvKN9R76Bsgq+k7BOYyAXAS4H7gW8Dq8YsvxD4SN1h9sGIuB94D3ApJUQPA+uZ3IQ11Z1xD02yM+4w4L/q83wZOC8irm4tlPTvks6vN58J/Ctlc/0uyv6PkyLisSnqS0Xbfu2zfiRpMeX3+T/sdS02mNyjmyXgoJsl4E13swTco5sl4KAnIsmbb0k56A2qA1cOH3PfMklXzHC9u9WBLdv9xCXpHEl312GbayQ9e4J1LJb0hH4/tPNuSZdP1H621AE0W7Xt8N93jNPu6ZI2Sbq+F3UOGgd9MH2IcQ4HlfQu4J3A6ymHz55E+d19Ij+KMsx2H8pgmkeAGyUd0fWKp2c0yoCa1uXL47T5e3xQTMcc9B5qDf+UdH4dLnqPppisQtIhlENWLxxz/y6Uo8feHxF3RPHziPjtVHVExBO17XuAH1BHstX1vkHS7fXgmWslPa/ef4akq9ra/UzS19tur5P0kno9VIbh/p/KkNzPjzmcd1okHUMZq375jq4jGwe99/ajDD1dCLwDWCHpOQCS/lzSj8e0vwQ4n9L7tltUL0fUkN0t6YL6B2A6VlEGu1A3478KvI9ybPt3KOPUd6P8QXhlPbx1f8oglmPr4w6lbFG0134S8DLgxcBbgT+ubccbsrqvpF/W1/ApSXu2FtTj7D8PnMX2x+TbBBz0/vDRiPhdRPyAckjqWwEi4isR8aJWI0lvpgy//OY461hU/30N8ELgjyhDQ985zVpGgdY497cB346I79VDSi8G9gBeERF3AQ8CL6GMuf8P4F5Jz623r4uI9pF7fxcRmyNiLXBNfRwRsbYOellb291Zl+0PHA8cBXyybT1nA6sj4sZpvq7UPEy1WU9Qerp2u1LGpbfcFxEPt91uDT/dRu3VLgJeN8FztXr4iyJiM2XAyvLa/ovTqHkh0NrcX1DrASAitkpaV9tA6dWPo0wu8QNgMyXkx9Tb7Ta2Xd/CtkNwnxQRG9va3i3pXMofvyWSFlCCftQ0Xo/hoDdtLWWQRftOo0Moo8FaniZpz7awH0iZOGGsZ9V1XVe/3u4G7CNpI3A08BPgUWa+Oftm4Lp6fZSydQBA/V59AGVgC5Qwn1xf099Sgn4qJehPToU1Q+1DTl9O6envqO/BHsAe9T1YOI1hrPn0euaLnflC2WF2A2WzehfKnu0HgSPq8uMo0y1dTAnuKykjtp47zrrmUr7Pty5/SgnifsCc2uafgW9RhqEuomwGv7NtHdF2fTFwfb0+hxLWSyjDV19Y739OrecEypbIBykjxHary59dX8/P6u29KVsDD7Rqaj0vcHjb7X8CPjbBe3Yc5Y9d64/KNcDlddlTxrwH51BG9e3X6//rfr/4O3qz/oYy3PJ6ylDNi4BTI6K9x95Yl41S5lp7d0TcCSDpVEm3A0TE4xGxsXWhBGprvd3qyc6iBHUU+BHwFeBLk9R3jKSHKMG8lhLUl0XErfU5f0LZw38J5We6kylzyT1al/+0Pt919XZrqOgN0WHvOs6Q1ZfW2h+u791tlM11ouzHaH8P7gceq9dtEj7WvYckHQdcERGLpmjareeLiPDMKwm5RzdLwEHP5YJeF2C94U13swTco5sl4KCbJdCzoEv6E0k/qYMhzutVHZ2SdICka+rQz9tVThTQ9+o0yDdL+lava+mEpHkq53G7s77Xx/S6pqlIen/9TNwm6auSdu91TWP1JOhtAxNeCzwfeLuk5/eilml4HPhARDyPciTaXw1AzVAOKhmk4ZyfAb4bEc+lDIDp69pV5sU/GxiOiNbZX0/pbVXb61WP/nLK0VR31YMvvkY5SV/fiogNEXFTvf4g5QO4cPJH9ZakRZSx6QNxvnBJe1POo3YZQEQ8GuW4/X43l3Io7lzKGW1Ge1zPdnoV9IVsex6u9fR5aNqpnK3zSMrhl/3s08C5wNYp2vWLQ4FNwOX168al7UNU+1GUU2xdTBnXsAG4P9pONtEvehX08Y7OGojf+VRO+9M60+kDva5nIpJOAn4VgzWccy7lENgvRMSRlMNg+3r/jaSnUbZGD6GM9ttT0mm9rWp7vQr6esqAhZZF9OHmzlgq5x37BnBlRIw9jVG/ORZ4g6R7KF+NjtcM56qbBespp2dubSmtpAS/n50I3B0Rm6KM2V8FvKLHNW2nV0H/X+BZkg6ps5WcQjlPWd+qQzQvA9ZExCenat9rEfHhiFgUEQdT3t/vR0Tf9TTt6uCUda0Zdiij5u7oYUmdWAscLWmofkZOoA93IPZkPHpEPC7pLMqsJHOAL0XE7b2oZRqOBU4HbpV0S73v/Ij4Tu9K2im9F7iydgB3AWf0uJ5JRcRqSSuBmyi/zNwMrOhtVdvzIbBmCfjIOLMEHHSzBBx0swQcdLMEHHSzBHoedEln9rqG6Ri0esE1z4Z+r7fnQQf6+g0ax6DVC655NvR1vf0QdDNrWCMHzAxpKOYxr6O2W9jCEEMdtV1w1IYZVNUdmzbB/Pm9rmJ6MtQ8euP+zRXTgel8jpu0mc1siS3bDRpr5BDYecxjCUu6vt6lI8u6vk7bOVyg7n/eBtFylo97vzfdzRJw0M0ScNDNEnDQzRJw0M0S6CjogzYHu5lta8qgD+gc7GbWppMefeDmYDezbXUS9IGeg93MOgt6R3OwSzpT0oikkS1smXllZtY1nQS9oznYI2JFRAxHxHA/HPNrZr/XSdAHbg52M9vWlINaBnQOdjNr09HotXqSAp+owGxA+cg4swQcdLMEHHSzBBx0swQcdLMEenLaZOtvF2hZr0uYtqWxrNcl9IWrhse/3z26WQIOulkCDrpZAg66WQIOulkCDrpZAg66WQIOulkCDrpZAg66WQIOulkCDrpZAg66WQIOulkCDrpZAg66WQIOulkCDrpZAg66WQIOulkCDrpZAg66WQKNTPe84KgNLB1Z1sSqrc2gTcs8iFMyN/kez+b74R7dLAEH3SwBB90sAQfdLAEH3SwBB90sAQfdLIEpgy7pAEnXSFoj6XZJ58xGYWbWPZ0cMPM48IGIuEnSU4EbJX0vIu5ouDYz65Ipe/SI2BARN9XrDwJrgIVNF2Zm3TOt7+iSDgaOBFY3Uo2ZNaLjoEvaC/gG8L6IeGCc5WdKGpE0smlTN0s0s5nqKOiSdqWE/MqIWDVem4hYERHDETE8f343SzSzmepkr7uAy4A1EfHJ5ksys27rpEc/FjgdOF7SLfXyuobrMrMumvLntYi4HtAs1GJmDfGRcWYJOOhmCTjoZgk46GYJOOhmCSgiur7SBVoQS1jS9fU2OWtmU7N9euZTm03LWc5ojG73K5l7dLMEHHSzBBx0swQcdLMEHHSzBBx0swQcdLMEHHSzBBx0swQcdLMEHHSzBBx0swQcdLMEHHSzBBx0swQcdLMEHHSzBBx0swQcdLMEHHSzBBx0swQcdLMEpjzJYj9pchripqZlHsSamzKI03XvLNyjmyXgoJsl4KCbJeCgmyXgoJsl4KCbJeCgmyXQcdAlzZF0s6RvNVmQmXXfdHr0c4A1TRViZs3pKOiSFgGvBy5tthwza0KnPfqngXOBrc2VYmZNmTLokk4CfhURN07R7kxJI5JGtrClawWa2cx10qMfC7xB0j3A14DjJV0xtlFErIiI4YgYHmKoy2Wa2UxMGfSI+HBELIqIg4FTgO9HxGmNV2ZmXePf0c0SmNZ49Ii4Fri2kUrMrDHu0c0ScNDNEnDQzRJw0M0ScNDNEmhkFtgFR21g6ciyJlbdGM8iOtgGbUbcplw1PP797tHNEnDQzRJw0M0ScNDNEnDQzRJw0M0ScNDNEnDQzRJw0M0ScNDNEnDQzRJw0M0ScNDNEnDQzRJw0M0ScNDNEnDQzRJw0M0ScNDNEnDQzRJw0M0SUER0faULtCCWsKTr621SU7OIDuLssp5RdXY08dlYznJGY1Rj73ePbpaAg26WgINuloCDbpaAg26WgINuloCDbpZAR0GXNE/SSkl3Sloj6ZimCzOz7un0tMmfAb4bEW+RtBsw1GBNZtZlUwZd0t7Aq4DFABHxKPBos2WZWTd1sul+KLAJuFzSzZIulbRnw3WZWRd1EvS5wEuBL0TEkcDDwHljG0k6U9KIpJEtbOlymWY2E50EfT2wPiJW19srKcHfRkSsiIjhiBge8ld4s74yZdAjYiOwTtJz6l0nAHc0WpWZdVWne93fC1xZ97jfBZzRXElm1m0dBT0ibgGGmy3FzJriI+PMEnDQzRJw0M0ScNDNEnDQzRJw0M0S6PR3dNtBTU6dPGhTSQ9avU1r4rNx1QQ/grtHN0vAQTdLwEE3S8BBN0vAQTdLwEE3S8BBN0vAQTdLwEE3S8BBN0vAQTdLwEE3S8BBN0vAQTdLwEE3S8BBN0vAQTdLwEE3S8BBN0vAQTdLwEE3S2CgZoEdxBlVm6y5yXUPGr8Xk3OPbpaAg26WgINuloCDbpaAg26WgINuloCDbpZAR0GX9H5Jt0u6TdJXJe3edGFm1j1TBl3SQuBsYDgijgDmAKc0XZiZdU+nm+5zgT0kzQWGgNHmSjKzbpsy6BFxL3AxsBbYANwfEVc3XZiZdU8nm+5PA94IHAIsAPaUdNo47c6UNCJpZAtbul+pme2wTjbdTwTujohNEfEYsAp4xdhGEbEiIoYjYniIoW7XaWYz0EnQ1wJHSxqSJOAEYE2zZZlZN3XyHX01sBK4Cbi1PmZFw3WZWRd1NB49IpYCSxuuxcwa4iPjzBJw0M0ScNDNEnDQzRJw0M0ScNDNEhio6Z4HUVPTSIOnOG43iNN1zyb36GYJOOhmCTjoZgk46GYJOOhmCTjoZgk46GYJOOhmCTjoZgk46GYJOOhmCTjoZgk46GYJOOhmCTjoZgk46GYJOOhmCTjoZgk46GYJOOhmCTjoZgkoIrq/UmkT8IsOmz8D+HXXi2jOoNULrnk29Eu9B0XE/LF3NhL06ZA0EhHDPS1iGgatXnDNs6Hf6/Wmu1kCDrpZAv0Q9BW9LmCaBq1ecM2zoa/r7fl3dDNrXj/06GbWMAfdLAEH3SwBB90sAQfdLIH/B01ZpTXXs0BJAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1 -1  1  1 -1  1  1  1  1 -1]\n",
      " [ 1  1 -1  1 -1 -1 -1  1  1 -1]\n",
      " [-1  1 -1  1 -1 -1  1 -1  1  1]\n",
      " [-1  1  1  1 -1  1  1 -1  1 -1]\n",
      " [-1 -1  1 -1  1  1 -1 -1  1  1]\n",
      " [ 1 -1 -1 -1  1  1  1  1 -1 -1]\n",
      " [ 1 -1 -1  1  1  1  1 -1  1  1]\n",
      " [-1 -1  1 -1  1 -1  1 -1 -1  1]\n",
      " [-1  1  1 -1 -1 -1 -1 -1  1  1]\n",
      " [-1 -1 -1 -1 -1 -1  1  1  1  1]]\n",
      "T:9.0\t|52 up | 48 down\t|Mag: 0.04000 \n",
      "---------------------------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-1  1 -1 -1  1 -1  1 -1 -1 -1]\n",
      " [-1  1 -1  1 -1  1 -1  1  1  1]\n",
      " [-1  1  1  1 -1 -1 -1  1  1  1]\n",
      " [-1 -1  1  1  1  1  1 -1 -1 -1]\n",
      " [ 1 -1 -1  1  1 -1  1 -1 -1 -1]\n",
      " [-1  1  1  1 -1 -1  1 -1 -1 -1]\n",
      " [-1 -1  1  1 -1 -1  1 -1 -1 -1]\n",
      " [-1  1  1 -1  1  1  1 -1  1  1]\n",
      " [ 1 -1  1  1 -1  1 -1 -1  1  1]\n",
      " [-1 -1 -1 -1  1 -1 -1 -1 -1  1]]\n",
      "T:8.5\t|46 up | 54 down\t|Mag: -0.08000 \n",
      "---------------------------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1 -1  1 -1 -1 -1 -1  1 -1  1]\n",
      " [-1 -1 -1 -1 -1  1  1  1  1  1]\n",
      " [ 1  1 -1  1 -1  1  1 -1 -1  1]\n",
      " [ 1  1  1  1  1  1  1 -1  1  1]\n",
      " [-1 -1 -1 -1  1 -1  1 -1 -1 -1]\n",
      " [-1 -1 -1  1  1 -1 -1  1 -1 -1]\n",
      " [ 1 -1  1 -1  1 -1 -1  1 -1 -1]\n",
      " [ 1 -1 -1 -1 -1  1 -1 -1  1 -1]\n",
      " [ 1  1 -1 -1  1 -1 -1  1  1 -1]\n",
      " [ 1  1 -1 -1 -1  1  1  1  1 -1]]\n",
      "T:8.0\t|47 up | 53 down\t|Mag: -0.06000 \n",
      "---------------------------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1 -1 -1 -1 -1  1 -1 -1  1  1]\n",
      " [ 1 -1 -1 -1 -1 -1 -1  1  1  1]\n",
      " [ 1 -1 -1 -1 -1  1  1  1  1  1]\n",
      " [-1  1  1  1  1 -1  1  1 -1  1]\n",
      " [-1 -1 -1  1  1 -1 -1  1  1  1]\n",
      " [ 1 -1 -1  1 -1 -1 -1 -1  1  1]\n",
      " [-1 -1 -1 -1  1  1  1  1  1  1]\n",
      " [-1  1  1  1  1 -1  1 -1  1  1]\n",
      " [ 1  1 -1 -1 -1  1  1  1  1  1]\n",
      " [ 1 -1 -1 -1 -1 -1  1  1 -1  1]]\n",
      "T:7.5\t|54 up | 46 down\t|Mag: 0.08000 \n",
      "---------------------------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1  1  1  1  1 -1  1  1  1  1]\n",
      " [ 1 -1  1 -1 -1 -1 -1 -1 -1  1]\n",
      " [ 1 -1  1 -1 -1  1 -1 -1  1  1]\n",
      " [ 1  1  1 -1 -1 -1  1  1  1 -1]\n",
      " [ 1 -1  1 -1 -1 -1 -1 -1  1 -1]\n",
      " [ 1  1  1 -1 -1 -1 -1 -1 -1 -1]\n",
      " [-1 -1  1 -1 -1 -1 -1 -1 -1 -1]\n",
      " [-1 -1  1  1  1 -1 -1  1  1 -1]\n",
      " [-1  1 -1 -1  1  1  1  1  1  1]\n",
      " [ 1  1  1 -1  1 -1  1  1 -1  1]]\n",
      "T:7.0\t|49 up | 51 down\t|Mag: -0.02000 \n",
      "---------------------------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-1 -1 -1 -1  1 -1  1 -1 -1 -1]\n",
      " [-1 -1 -1 -1  1 -1 -1  1  1 -1]\n",
      " [-1 -1 -1  1 -1 -1 -1  1  1 -1]\n",
      " [-1 -1 -1 -1  1  1  1  1  1  1]\n",
      " [ 1 -1 -1 -1  1  1  1  1 -1  1]\n",
      " [-1 -1  1 -1  1  1 -1  1  1  1]\n",
      " [ 1  1 -1 -1  1 -1 -1 -1  1  1]\n",
      " [ 1 -1  1 -1 -1 -1  1  1  1  1]\n",
      " [-1 -1 -1 -1 -1  1 -1  1  1 -1]\n",
      " [ 1 -1 -1 -1  1 -1 -1 -1 -1 -1]]\n",
      "T:6.5\t|42 up | 58 down\t|Mag: -0.16000 \n",
      "---------------------------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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LoOugS9pH0g2Svt5mQWbWe9MZ0c8FVrdViJm1p6ugS5oPnARc0m45ZtaGbkf0jwDvAh5qrxQza8uUQZd0MvCbiFg1xXqLJY1KGt3K1p4VaGa7r5sR/TjgFElrgM8BJ0q6rHOliFgeESMRMTKLWT0u08x2x5RBj4j3RMT8iFgAvA74TkSc1nplZtYz/h7dLIFp9aNHxNXA1a1UYmat8YhuloCDbpaAg26WgINuloCDbpZAK7PAzn3ORpaMLm1j061pa0ZOz1z7sGGcUXVPztTaJo/oZgk46GYJOOhmCTjoZgk46GYJOOhmCTjoZgk46GYJOOhmCTjoZgk46GYJOOhmCTjoZgk46GYJOOhmCTjoZgk46GYJOOhmCTjoZgk46GYJOOhmCbQyC+yGVXNYprPb2HRrPFvrw4bxb9FWzZ4F1syGhoNuloCDbpaAg26WgINuloCDbpaAg26WQFdBl3SIpBWSbpW0WtLz2y7MzHqn2xNmPgp8KyJeLWkmMKvFmsysx6YMuqSDgRcCZwBExDZgW7tlmVkvdbPrfjSwGfiUpBskXSLpgJbrMrMe6iboM4BnAx+PiGOBB4B3d64kabGkUUmjW9na4zLNbHd0E/T1wPqIuK7eX0EJ/k4iYnlEjETEyCwfwpsNlCmDHhGbgHWSnlwfWgjc0mpVZtZT3X7q/lbg8vqJ+23Ame2VZGa91lXQI+InwEi7pZhZW3xmnFkCDrpZAg66WQIOulkCDrpZAg66WQKtTPfcljanIW5rWt82ax62aZn3lqmTh5FHdLMEHHSzBBx0swQcdLMEHHSzBBx0swQcdLMEHHSzBBx0swQcdLMEHHSzBBx0swQcdLMEHHSzBBx0swQcdLMEHHSzBBx0swQcdLMEHHSzBBx0swQUET3f6MiIYnS055u1PWQYZ8Qdxhlm2/h7jIzA6Gio83GP6GYJOOhmCTjoZgk46GYJOOhmCTjoZgk46GYJdBV0SW+XdLOkmyR9VtJ+bRdmZr0zZdAlzQPOAUYi4hnAPsDr2i7MzHqn2133GcD+kmYAs4AN7ZVkZr02ZdAj4g7gAmAtsBG4JyKubLswM+udbnbdDwVOBY4C5gIHSDptnPUWSxqVNLp5c+8LNbNd182u+yLg9ojYHBG/B1YCL+hcKSKWR8RIRIzMnt3rMs1sd3QT9LXA8yTNkiRgIbC63bLMrJe6OUa/DlgBXA/cWJ+zvOW6zKyHZnSzUkQsAZa0XIuZtcRnxpkl4KCbJeCgmyXgoJsl4KCbJeCgmyXQynTPczU3zubsnm+3zemCh9EwTsts7fJ0z2aJOehmCTjoZgk46GYJOOhmCTjoZgk46GYJOOhmCTjoZgk46GYJOOhmCTjoZgk46GYJOOhmCTjoZgk46GYJOOhmCTjoZgk46GYJOOhmCTjoZgm0MguspM3Ar7pc/TBgS8+LaM+w1QuueU8YlHqPjIjZnQ+2EvTpkDQaESN9LWIahq1ecM17wqDX6113swQcdLMEBiHoy/tdwDQNW73gmveEga6378foZta+QRjRzaxlDrpZAg66WQIOulkCDrpZAv8PJImS+6Q+3aEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-1 -1 -1 -1  1  1 -1 -1  1 -1]\n",
      " [ 1  1 -1 -1  1 -1 -1  1  1 -1]\n",
      " [ 1  1  1  1  1 -1 -1 -1 -1  1]\n",
      " [-1  1  1  1  1 -1 -1 -1 -1  1]\n",
      " [ 1  1 -1 -1 -1 -1  1  1  1  1]\n",
      " [ 1  1  1 -1 -1 -1 -1  1  1  1]\n",
      " [-1 -1  1  1  1 -1 -1 -1  1  1]\n",
      " [-1  1  1  1  1 -1  1 -1  1  1]\n",
      " [-1  1  1 -1 -1 -1  1  1  1  1]\n",
      " [ 1 -1 -1 -1  1  1  1 -1 -1  1]]\n",
      "T:6.0\t|54 up | 46 down\t|Mag: 0.08000 \n",
      "---------------------------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1  1 -1 -1  1 -1 -1 -1  1  1]\n",
      " [ 1  1  1  1 -1 -1 -1 -1  1 -1]\n",
      " [ 1 -1 -1  1 -1  1 -1 -1  1  1]\n",
      " [-1 -1 -1 -1 -1 -1 -1 -1 -1  1]\n",
      " [-1  1  1  1 -1  1 -1 -1 -1 -1]\n",
      " [-1  1  1  1 -1 -1  1 -1 -1  1]\n",
      " [ 1  1  1  1 -1  1 -1 -1 -1 -1]\n",
      " [-1 -1 -1 -1 -1  1  1  1  1  1]\n",
      " [-1 -1 -1 -1 -1 -1 -1 -1  1 -1]\n",
      " [ 1  1  1 -1  1  1 -1 -1  1  1]]\n",
      "T:5.5\t|43 up | 57 down\t|Mag: -0.14000 \n",
      "---------------------------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1  1 -1 -1 -1  1 -1 -1  1 -1]\n",
      " [-1 -1 -1  1  1  1 -1  1 -1 -1]\n",
      " [ 1  1  1  1  1  1 -1 -1 -1  1]\n",
      " [ 1  1  1  1  1  1 -1  1  1  1]\n",
      " [ 1 -1 -1 -1 -1 -1 -1  1  1  1]\n",
      " [ 1 -1 -1  1 -1 -1  1  1 -1 -1]\n",
      " [ 1  1  1  1  1 -1 -1 -1 -1  1]\n",
      " [ 1  1 -1 -1  1  1 -1  1 -1 -1]\n",
      " [ 1  1 -1  1  1  1  1  1  1 -1]\n",
      " [ 1  1 -1  1 -1 -1 -1  1  1  1]]\n",
      "T:5.0\t|57 up | 43 down\t|Mag: 0.14000 \n",
      "---------------------------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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LcqdJGpM0tp3tPSvQzHZckz36EcBrJG0CvgQcI+nS7oUiYnVEjEbE6AgjPS7TzHbErEGPiPdFxPKIOBA4HrgqIk5svTIz6xn/O7pZAnPqjx4R64B1rVRiZq3xHt0sAQfdLAEH3SwBB90sAQfdLIGhGgV2GJ2rVa2te9hGxW1zW7Rl2LbxV0ennu49ulkCDrpZAg66WQIOulkCDrpZAg66WQIOulkCDrpZAg66WQIOulkCDrpZAg66WQIOulkCDrpZAg66WQIOulkCDrpZAg66WQIOulkCDrpZAg66WQKKiJ6vdKmWxumc3vP12sIYtpFPh1Ubo+JexEWMx7i6p3uPbpaAg26WgINuloCDbpaAg26WgINuloCDbpZAo6BLWiJpraRbJG2Q9JK2CzOz3ml62+RPAt+IiNdJ2hUYabEmM+uxWYMuaTHwcmAlQEQ8CDzYbllm1ktNDt0PBrYBn5N0vaSLJe3Rcl1m1kNNgr4IeD7wmYg4HLgfOKt7IUmnSRqTNLad7T0u08x2RJOgbwG2RMS19fVaSvAniYjVETEaEaMjPoU3GyizBj0ibgdulfTMOmkFcHOrVZlZTzW96v4OYE294r4ROLW9ksys1xoFPSJuAEbbLcXM2uKWcWYJOOhmCTjoZgk46GYJOOhmCTjoZgl4uOdqGIc4bmO44Da1uY3b2hbD9ncxOgpjY+Hhns0yctDNEnDQzRJw0M0ScNDNEnDQzRJw0M0ScNDNEnDQzRJw0M0ScNDNEnDQzRJw0M0ScNDNEnDQzRJw0M0ScNDNEnDQzRJw0M0ScNDNEnDQzRJoejdVm6dhG6m1TcO4LdqseSFHmPUe3SwBB90sAQfdLAEH3SwBB90sAQfdLAEH3SyBRkGX9C5JN0n6gaQvStqt7cLMrHdmDbqkZcAZwGhEHArsDBzfdmFm1jtND90XAbtLWgSMAOPtlWRmvTZr0CPiNuB8YDOwFbg7Iq5suzAz650mh+57AccBBwFLgT0knTjFcqdJGpM0tp3tva/UzOatyaH7scBPI2JbRDwEXA68tHuhiFgdEaMRMTrCSK/rNLMd0CTom4EXSxqRJGAFsKHdssysl5qco18LrAWuA75f37O65brMrIca9UePiHOAc1quxcxa4pZxZgk46GYJOOhmCTjoZgk46GYJOOhmCXi45yG2kMMFDzoPJV2Mc9GU071HN0vAQTdLwEE3S8BBN0vAQTdLwEE3S8BBN0vAQTdLwEE3S8BBN0vAQTdLwEE3S8BBN0vAQTdLwEE3S8BBN0vAQTdLwEE3S8BBN0vAQTdLwEE3S0AR0fuVStuAnzVc/MnAHT0voj3DVi+45oUwKPUeEBF7d09sJehzIWksIkb7WsQcDFu94JoXwqDX60N3swQcdLMEBiHoq/tdwBwNW73gmhfCQNfb93N0M2vfIOzRzaxlDrpZAg66WQIOulkCDrpZAv8Pq0upIetGI3AAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-1 -1 -1 -1  1  1  1  1  1  1]\n",
      " [-1 -1 -1 -1  1  1 -1 -1 -1  1]\n",
      " [-1 -1  1 -1  1  1  1 -1 -1  1]\n",
      " [-1  1  1 -1  1  1  1  1 -1  1]\n",
      " [ 1 -1 -1 -1 -1  1  1  1 -1 -1]\n",
      " [ 1 -1 -1 -1 -1 -1  1 -1 -1  1]\n",
      " [ 1  1  1  1  1  1  1 -1 -1  1]\n",
      " [ 1  1  1  1  1 -1 -1 -1  1  1]\n",
      " [ 1 -1  1  1  1 -1 -1 -1 -1 -1]\n",
      " [-1  1 -1  1  1 -1  1  1  1 -1]]\n",
      "T:4.5\t|53 up | 47 down\t|Mag: 0.06000 \n",
      "---------------------------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1  1  1  1  1 -1  1  1 -1  1]\n",
      " [ 1  1  1  1  1 -1 -1  1 -1  1]\n",
      " [ 1  1  1  1  1  1  1  1  1  1]\n",
      " [-1 -1  1 -1  1  1 -1  1  1  1]\n",
      " [ 1  1  1 -1  1  1 -1  1  1  1]\n",
      " [-1 -1  1 -1 -1  1 -1 -1 -1 -1]\n",
      " [-1 -1 -1 -1 -1 -1  1 -1 -1 -1]\n",
      " [-1 -1 -1 -1  1  1  1 -1 -1  1]\n",
      " [-1 -1 -1 -1  1  1  1 -1 -1 -1]\n",
      " [-1  1 -1 -1 -1 -1  1  1 -1 -1]]\n",
      "T:4.0\t|52 up | 48 down\t|Mag: 0.04000 \n",
      "---------------------------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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1kr7WZkFm1n8zadHPBta0VYiZtadR0CUtAl4KXNhuOWbWhqYt+nnAu4FH2ivFzNoybdAlnQj8OiJWT7PdGZLGJI1tYUvfCjSzHdekRT8aeLmkW4HPA8dLurh3o4hYERGjETE6wkifyzSzHTFt0CPivRGxKCIOAU4GLo+IU1qvzMz6xn9HN0tgRuPRI+JK4MpWKjGz1rhFN0vAQTdLwEE3S8BBN0vAQTdLQBHR952OjirGxvq+21Yt17JW9rs02tlvm/xezF6jozA2Fupd7hbdLAEH3SwBB90sAQfdLAEH3SwBB90sAQfdLAEH3SwBB90sAQfdLAEH3SwBB90sAQfdLAEH3SwBB90sAQfdLAEH3SwBB90sAQfdLAEH3SwBB90sAc8CaztNW7PLgmeY7fAssGaJOehmCTjoZgk46GYJOOhmCTjoZgk46GYJNAq6pPmSVkm6WdIaSc9ruzAz65+5Dbf7OPCtiHilpN2AkRZrMrM+mzbokuYBLwROA4iIB4EH2y3LzPqpyaH7YmAT8GlJ10m6UNKeLddlZn3UJOhzgWcBn4qII4H7gff0biTpDEljksY2bepzlWa2Q5oEfT2wPiKuqY9XUYI/TkSsiIjRiBhdsKCfJZrZjpo26BFxO7BO0mF10RLgplarMrO+anrW/W3AynrG/Rbg9PZKMrN+axT0iLgeGG23FDNri3vGmSXgoJsl4KCbJeCgmyXgoJsl4KCbJdD07+g2hNqcPtna18b/3wYumHC5W3SzBBx0swQcdLMEHHSzBBx0swQcdLMEHHSzBBx0swQcdLMEHHSzBBx0swQcdLMEHHSzBBx0swQcdLMEHHSzBBx0swQcdLMEHHSzBBx0swQcdLMEPAus2YAsjWV93+elk1wK1S26WQIOulkCDrpZAg66WQIOulkCDrpZAg66WQKNgi7pHZJulPRjSZ+TtHvbhZlZ/0wbdEkLgbOA0Yg4HJgDnNx2YWbWP00P3ecCe0iaC4wAG9orycz6bdqgR8RtwLnAWmAjcHdEXNZ2YWbWP00O3fcFTgIOBQ4A9pR0ygTbnSFpTNLYpk39L9TMtl+TQ/cTgF9ExKaIeAi4BHh+70YRsSIiRiNidMGCfpdpZjuiSdDXAs+VNCJJwBJgTbtlmVk/NfmOfg2wCrgW+FF9zoqW6zKzPmo0Hj0ilgJLW67FzFrinnFmCTjoZgk46GYJOOhmCTjoZgk46GYJKCL6vtPRUcXYWN93y3It6/9Oqzam3rXx2vz/a8ts+70YHYWxsVDvcrfoZgk46GYJOOhmCTjoZgk46GYJOOhmCTjoZgk46GYJOOhmCTjoZgk46GYJOOhmCTjoZgk46GYJOOhmCTjoZgk46GYJOOhmCTjoZgk46GYJOOhmCbQyC6ykTcAvG27+OOCOvhfRntlWL7jmnWFY6j04Ihb0Lmwl6DMhaSwiRgdaxAzMtnrBNe8Mw16vD93NEnDQzRIYhqCvGHQBMzTb6gXXvDMMdb0D/45uZu0bhhbdzFrmoJsl4KCbJeCgmyXgoJsl8H/6V7lMs9BxBQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1 -1  1  1  1  1 -1  1 -1  1]\n",
      " [-1 -1  1  1 -1 -1 -1 -1 -1 -1]\n",
      " [ 1 -1 -1 -1  1  1  1 -1  1  1]\n",
      " [-1 -1  1  1  1  1  1  1  1 -1]\n",
      " [-1 -1 -1 -1  1 -1 -1 -1 -1 -1]\n",
      " [-1 -1 -1 -1  1 -1 -1 -1 -1 -1]\n",
      " [-1  1  1  1  1  1 -1 -1 -1 -1]\n",
      " [-1  1  1  1  1  1 -1 -1  1 -1]\n",
      " [ 1  1 -1  1  1 -1 -1  1  1  1]\n",
      " [ 1  1  1  1  1  1  1 -1 -1  1]]\n",
      "T:3.5\t|50 up | 50 down\t|Mag: 0.00000 \n",
      "---------------------------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1 -1 -1 -1 -1 -1 -1  1  1 -1]\n",
      " [ 1 -1 -1 -1 -1 -1 -1  1 -1  1]\n",
      " [-1 -1 -1 -1 -1 -1 -1  1  1 -1]\n",
      " [ 1 -1  1 -1 -1 -1  1  1  1  1]\n",
      " [ 1  1  1  1  1  1 -1  1  1 -1]\n",
      " [ 1  1  1  1  1  1  1  1  1  1]\n",
      " [ 1 -1  1  1  1  1  1  1  1  1]\n",
      " [-1 -1  1  1  1 -1  1  1  1  1]\n",
      " [-1 -1  1  1  1 -1 -1 -1 -1  1]\n",
      " [ 1 -1 -1 -1 -1 -1  1  1  1 -1]]\n",
      "T:3.0\t|56 up | 44 down\t|Mag: 0.12000 \n",
      "---------------------------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1  1  1 -1 -1 -1  1  1  1  1]\n",
      " [ 1  1  1  1 -1 -1 -1  1  1  1]\n",
      " [-1 -1 -1  1 -1 -1 -1  1  1  1]\n",
      " [ 1  1  1  1 -1  1  1  1  1  1]\n",
      " [ 1  1  1  1 -1  1  1 -1  1  1]\n",
      " [ 1  1 -1 -1 -1  1  1  1  1  1]\n",
      " [ 1 -1 -1 -1 -1  1 -1  1  1  1]\n",
      " [ 1  1  1 -1 -1 -1 -1  1  1  1]\n",
      " [ 1  1  1  1 -1 -1 -1  1  1  1]\n",
      " [ 1  1  1  1 -1 -1  1  1  1  1]]\n",
      "T:2.5\t|68 up | 32 down\t|Mag: 0.36000 \n",
      "---------------------------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1  1  1  1  1 -1  1  1  1  1]\n",
      " [ 1  1  1  1  1  1  1  1  1  1]\n",
      " [-1  1  1  1  1  1  1  1  1  1]\n",
      " [ 1  1  1  1  1  1  1  1  1  1]\n",
      " [ 1  1  1  1  1  1  1  1  1  1]\n",
      " [ 1  1  1  1  1  1  1  1  1  1]\n",
      " [ 1  1  1  1  1  1  1  1  1  1]\n",
      " [ 1  1  1  1  1  1  1  1  1  1]\n",
      " [ 1  1  1  1  1  1  1  1  1  1]\n",
      " [ 1  1  1  1  1  1  1  1  1  1]]\n",
      "T:2.0\t|98 up | 2 down\t|Mag: 0.96000 \n",
      "---------------------------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1  1  1  1  1  1  1  1  1  1]\n",
      " [ 1  1  1  1  1  1  1  1  1  1]\n",
      " [ 1 -1  1  1  1  1  1  1  1  1]\n",
      " [ 1  1  1  1  1  1  1  1  1  1]\n",
      " [ 1  1  1  1  1  1  1  1  1  1]\n",
      " [ 1  1  1  1  1  1  1  1  1  1]\n",
      " [ 1  1  1  1  1  1  1  1  1  1]\n",
      " [ 1  1 -1  1  1  1  1  1  1  1]\n",
      " [ 1  1  1  1  1  1  1  1  1  1]\n",
      " [ 1  1  1  1  1  1  1  1  1  1]]\n",
      "T:1.5\t|98 up | 2 down\t|Mag: 0.96000 \n",
      "---------------------------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1]]\n",
      "T:1.0\t|100 up | 0 down\t|Mag: 1.00000 \n",
      "---------------------------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1]]\n",
      "T:0.5\t|100 up | 0 down\t|Mag: 1.00000 \n",
      "---------------------------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[10.   -0.06]\n",
      " [ 9.5  -0.08]\n",
      " [ 9.    0.04]\n",
      " [ 8.5  -0.08]\n",
      " [ 8.   -0.06]\n",
      " [ 7.5   0.08]\n",
      " [ 7.   -0.02]\n",
      " [ 6.5  -0.16]\n",
      " [ 6.    0.08]\n",
      " [ 5.5  -0.14]\n",
      " [ 5.    0.14]\n",
      " [ 4.5   0.06]\n",
      " [ 4.    0.04]\n",
      " [ 3.5   0.  ]\n",
      " [ 3.    0.12]\n",
      " [ 2.5   0.36]\n",
      " [ 2.    0.96]\n",
      " [ 1.5   0.96]\n",
      " [ 1.    1.  ]\n",
      " [ 0.5   1.  ]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished.\n"
     ]
    }
   ],
   "source": [
    "#!/usr/bin/env python3\n",
    "# -*- coding: utf-8 -*-\n",
    "\"\"\"\n",
    "Implementation of the Metropolis algorithm \n",
    "for 2D Ising model evolution.\n",
    "\n",
    "Written for the FIZ371 Course, 10/06/2020\n",
    "Dr. Emre S. Tasci <emre.tasci@hacettepe.edu.tr>\n",
    "\"\"\"\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "# mpl.use('module://backend_interagg') # PyCharm doesn't always display the plots\n",
    "\n",
    "colors = ['yellow', 'purple', 'orange', 'blue', 'yellow', 'purple']\n",
    "bounds = [-1,1,2,3,4,5,6]\n",
    "# Up: Purple | Down: Yellow\n",
    "\n",
    "cmap = mpl.colors.ListedColormap(colors)\n",
    "norm = mpl.colors.BoundaryNorm(bounds, cmap.N)\n",
    "\n",
    "np.random.seed(371)\n",
    "\n",
    "N = 10\n",
    "num_iterations = 10000\n",
    "\n",
    "H = 0 # External field\n",
    "k_B = 1 # Boltzmann constant\n",
    "J = 1 # Coupling coefficient\n",
    "T0 = 10 # Temperature\n",
    "beta = 1/(k_B*T0)\n",
    "\n",
    "# Create our NxN grid, fill with random spin orientation\n",
    "mapN = np.random.randint(0,2,[N,N])\n",
    "#mapN = np.ones((N,N))\n",
    "mapN[mapN==0] = -1\n",
    "print(mapN)\n",
    "num_ups = np.sum(np.sum(mapN==1))\n",
    "num_downs = N**2 - num_ups\n",
    "print(\"{:} up | {:} down \".format(num_ups,num_downs))\n",
    "plt.matshow(mapN, interpolation=\"none\", cmap=cmap, norm=norm)\n",
    "#plt.savefig(\"/tmp/figs/\" + \"TS_%.3fs\" % (T0) + \".png\")\n",
    "plt.show()\n",
    "\n",
    "#input(\"devam?..\")\n",
    "magnetization_vs_T = np.empty([0,2])\n",
    "\n",
    "print(\"=\"*45)\n",
    "for T in np.arange(T0,0,-0.5):\n",
    "    if(T == 0):\n",
    "        continue\n",
    "    beta = 1/(k_B*T)\n",
    "    for step in range(num_iterations):\n",
    "        # Pick a random site and calculate its local field\n",
    "        i,j = np.random.randint(0,N,[1,2]).flatten()\n",
    "        x_n = mapN[i,j]\n",
    "        b_n = 0\n",
    "        ## print(i,j)\n",
    "        # Neighbours\n",
    "        ip1 = np.mod(i+1,N)\n",
    "        im1 = np.mod(i-1,N)\n",
    "        jp1 = np.mod(j+1,N)\n",
    "        jm1 = np.mod(j-1,N)\n",
    "        # Left, Right, Below, Above neighbours\n",
    "        neighbour_positions = np.array([[im1,j],[ip1,j],[i,jm1],[i,jp1]])\n",
    "        for n_i in range(4):\n",
    "            m_i,m_j = neighbour_positions[n_i,:].flatten()\n",
    "            b_n += J*mapN[m_i,m_j]\n",
    "        b_n += H\n",
    "        DeltaE=2*x_n*b_n\n",
    "        if(DeltaE<=0):\n",
    "            mapN[i,j] *= -1\n",
    "        elif(np.random.rand()<np.exp(-beta*DeltaE)):\n",
    "            mapN[i,j] *= -1\n",
    "        ##print(\"-\"*45)\n",
    "    print(mapN)\n",
    "    num_ups = np.sum(np.sum(mapN==1))\n",
    "    num_downs = N**2 - num_ups\n",
    "    magnetization = (num_ups-num_downs)/N**2\n",
    "    magnetization_vs_T = np.vstack((magnetization_vs_T,[T,magnetization]))\n",
    "    print(\"T:{:}\\t|{:} up | {:} down\\t|Mag: {:.5f} \".format(T,num_ups,num_downs,magnetization))\n",
    "    print(\"-\"*45)\n",
    "    plt.matshow(mapN, interpolation=\"none\", cmap=cmap, norm=norm,origin=\"upper\")\n",
    "    plt.title(\"Temperature: {:}\\nUp:{:d}|Down:{:d}\".format(T,num_ups,num_downs))\n",
    "    #plt.savefig(\"/tmp/figs/\" + \"T_%.3f\" % (T) + \".png\")\n",
    "    plt.show()\n",
    "print(magnetization_vs_T)\n",
    "plt.plot(magnetization_vs_T[:,0],magnetization_vs_T[:,1],\"*-\")\n",
    "plt.ylim(-1.1,1.1)\n",
    "plt.xlabel(\"T\")\n",
    "plt.ylabel(\"<M>\")\n",
    "#plt.savefig(\"/tmp/figs/\" + \"MeanMag\" + \".png\")\n",
    "plt.show()\n",
    "print(\"Finished.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Homework\n",
    "Show that a flip of the spin $x_n$ of site $n$ indeed changes the energy by:\n",
    "\n",
    "$$\\Delta E=2x_n b_n$$\n",
    "\n",
    "where $b_n$ is the local field defined as:\n",
    "\n",
    "$$b_n = \\sum_{m:(m,n)\\in\\mathcal{N}}{Jx_m + H}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Appendix : Evolution of the configuration probabilities for a 2x2 Ising Grid\n",
    "A 2x2 grid system can be in one of the $2^4=16$ configurations:\n",
    "\n",
    "| A |(x1)               |\\| | B |(x4)               |\\| | C |(x6)               |\\| | D |(x4)               |\\| | E |(x1)               |\n",
    "|:-------:|-------------| |:-------:|-------------||:-------:|-------------||:-------:|-------------||:-------:|-------------|\n",
    "| &uarr;      | &uarr;  |\\|  | &darr;      | &uarr;  |\\| | &uarr;      | &uarr;  |\\| | &uarr;      | &darr;  |\\| | &darr;      | &darr;  |\n",
    "| &uarr;       | &uarr; |\\|  | &uarr;       | &uarr; |\\| | &darr;       | &darr; |\\| | &darr;       | &darr; |\\| | &darr;       | &darr; |"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The calculated energies with respect to each spin's interaction with its neighbours yields (taking $J=1,\\,H=0$):\n",
    "\n",
    "$$E_A = -\\tfrac{1}{2}\\left[\\left(1.1+1.1+1.1\\right)+\\left(1.1+1.1+1.1\\right)+\n",
    "\\left(1.1+1.1+1.1\\right)+\\left(1.1+1.1+1.1\\right)\\right]=-6$$\n",
    "$$E_B = -\\tfrac{1}{2}\\left[\\left(-1.1+-1.1+-1.1\\right)+\\left(1.-1+1.1+1.1\\right)+\n",
    "\\left(1.-1+1.1+1.1\\right)+\\left(1.-1+1.1+1.1\\right)\\right]=0$$\n",
    "$$E_C = -\\tfrac{1}{2}\\left[\\left(1.1+1.-1+1.-1\\right)+\\left(1.1+1.-1+1.-1\\right)+\n",
    "\\left(-1.1+-1.1+-1.-1\\right)+\\left(-1.1+-1.1+-1.-1\\right)\\right]=2$$\n",
    "$$E_D = E_B = -\\tfrac{1}{2}\\left[\\left(1.-1+1.-1+1.-1\\right)+\\left(-1.1+-1.-1+-1.-1\\right)+\n",
    "\\left(-1.1+-1.-1+-1.-1\\right)+\\left(-1.1+-1.-1+-1.-1\\right)\\right]=0$$\n",
    "$$E_E = E_A = -\\tfrac{1}{2}\\left[\\left(-1.-1+-1.-1+-1.-1\\right)+\\left(-1.-1+-1.-1+-1.-1\\right)+\n",
    "\\left(-1.-1+-1.-1+-1.-1\\right)+\\left(-1.-1+-1.-1+-1.-1\\right)\\right]=-6$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's proceed by calculating the probabilites at a given temperature $T$ (with $k_B$ taken as $1$):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "300.0 [0.06376045 0.24999163 0.37249584 0.24999163 0.06376045]\n",
      "299.0 [0.0637647  0.24999157 0.37248745 0.24999157 0.0637647 ]\n",
      "298.0 [0.06376898 0.24999152 0.37247901 0.24999152 0.06376898]\n",
      "297.0 [0.06377329 0.24999146 0.37247051 0.24999146 0.06377329]\n",
      "296.0 [0.06377763 0.2499914  0.37246195 0.2499914  0.06377763]\n",
      "295.0 [0.06378199 0.24999134 0.37245333 0.24999134 0.06378199]\n",
      "294.0 [0.06378639 0.24999128 0.37244465 0.24999128 0.06378639]\n",
      "293.0 [0.06379082 0.24999122 0.37243592 0.24999122 0.06379082]\n",
      "292.0 [0.06379528 0.24999116 0.37242712 0.24999116 0.06379528]\n",
      "291.0 [0.06379977 0.2499911  0.37241826 0.2499911  0.06379977]\n",
      "290.0 [0.06380429 0.24999104 0.37240934 0.24999104 0.06380429]\n",
      "289.0 [0.06380884 0.24999098 0.37240037 0.24999098 0.06380884]\n",
      "288.0 [0.06381342 0.24999092 0.37239132 0.24999092 0.06381342]\n",
      "287.0 [0.06381804 0.24999085 0.37238222 0.24999085 0.06381804]\n",
      "286.0 [0.06382269 0.24999079 0.37237305 0.24999079 0.06382269]\n",
      "285.0 [0.06382737 0.24999072 0.37236382 0.24999072 0.06382737]\n",
      "284.0 [0.06383208 0.24999066 0.37235452 0.24999066 0.06383208]\n",
      "283.0 [0.06383683 0.24999059 0.37234515 0.24999059 0.06383683]\n",
      "282.0 [0.06384161 0.24999052 0.37233572 0.24999052 0.06384161]\n",
      "281.0 [0.06384643 0.24999046 0.37232622 0.24999046 0.06384643]\n",
      "280.0 [0.06385128 0.24999039 0.37231666 0.24999039 0.06385128]\n",
      "279.0 [0.06385617 0.24999032 0.37230702 0.24999032 0.06385617]\n",
      "278.0 [0.06386109 0.24999025 0.37229732 0.24999025 0.06386109]\n",
      "277.0 [0.06386605 0.24999018 0.37228754 0.24999018 0.06386605]\n",
      "276.0 [0.06387104 0.24999011 0.3722777  0.24999011 0.06387104]\n",
      "275.0 [0.06387607 0.24999003 0.37226778 0.24999003 0.06387607]\n",
      "274.0 [0.06388114 0.24998996 0.37225779 0.24998996 0.06388114]\n",
      "273.0 [0.06388625 0.24998989 0.37224773 0.24998989 0.06388625]\n",
      "272.0 [0.06389139 0.24998981 0.37223759 0.24998981 0.06389139]\n",
      "271.0 [0.06389657 0.24998974 0.37222738 0.24998974 0.06389657]\n",
      "270.0 [0.06390179 0.24998966 0.37221709 0.24998966 0.06390179]\n",
      "269.0 [0.06390705 0.24998958 0.37220673 0.24998958 0.06390705]\n",
      "268.0 [0.06391235 0.24998951 0.37219628 0.24998951 0.06391235]\n",
      "267.0 [0.06391769 0.24998943 0.37218576 0.24998943 0.06391769]\n",
      "266.0 [0.06392307 0.24998935 0.37217516 0.24998935 0.06392307]\n",
      "265.0 [0.06392849 0.24998927 0.37216449 0.24998927 0.06392849]\n",
      "264.0 [0.06393395 0.24998918 0.37215372 0.24998918 0.06393395]\n",
      "263.0 [0.06393946 0.2499891  0.37214288 0.2499891  0.06393946]\n",
      "262.0 [0.063945   0.24998902 0.37213196 0.24998902 0.063945  ]\n",
      "261.0 [0.06395059 0.24998893 0.37212095 0.24998893 0.06395059]\n",
      "260.0 [0.06395623 0.24998885 0.37210985 0.24998885 0.06395623]\n",
      "259.0 [0.0639619  0.24998876 0.37209867 0.24998876 0.0639619 ]\n",
      "258.0 [0.06396762 0.24998867 0.3720874  0.24998867 0.06396762]\n",
      "257.0 [0.06397339 0.24998859 0.37207605 0.24998859 0.06397339]\n",
      "256.0 [0.0639792  0.2499885  0.37206461 0.2499885  0.0639792 ]\n",
      "255.0 [0.06398506 0.24998841 0.37205307 0.24998841 0.06398506]\n",
      "254.0 [0.06399096 0.24998831 0.37204145 0.24998831 0.06399096]\n",
      "253.0 [0.06399691 0.24998822 0.37202973 0.24998822 0.06399691]\n",
      "252.0 [0.06400291 0.24998813 0.37201792 0.24998813 0.06400291]\n",
      "251.0 [0.06400896 0.24998803 0.37200602 0.24998803 0.06400896]\n",
      "250.0 [0.06401506 0.24998794 0.37199402 0.24998794 0.06401506]\n",
      "249.0 [0.0640212  0.24998784 0.37198192 0.24998784 0.0640212 ]\n",
      "248.0 [0.0640274  0.24998774 0.37196973 0.24998774 0.0640274 ]\n",
      "247.0 [0.06403364 0.24998764 0.37195743 0.24998764 0.06403364]\n",
      "246.0 [0.06403994 0.24998754 0.37194504 0.24998754 0.06403994]\n",
      "245.0 [0.06404629 0.24998744 0.37193255 0.24998744 0.06404629]\n",
      "244.0 [0.06405269 0.24998733 0.37191995 0.24998733 0.06405269]\n",
      "243.0 [0.06405915 0.24998723 0.37190725 0.24998723 0.06405915]\n",
      "242.0 [0.06406566 0.24998712 0.37189444 0.24998712 0.06406566]\n",
      "241.0 [0.06407222 0.24998702 0.37188153 0.24998702 0.06407222]\n",
      "240.0 [0.06407884 0.24998691 0.37186851 0.24998691 0.06407884]\n",
      "239.0 [0.06408551 0.2499868  0.37185538 0.2499868  0.06408551]\n",
      "238.0 [0.06409225 0.24998669 0.37184214 0.24998669 0.06409225]\n",
      "237.0 [0.06409903 0.24998657 0.37182879 0.24998657 0.06409903]\n",
      "236.0 [0.06410588 0.24998646 0.37181532 0.24998646 0.06410588]\n",
      "235.0 [0.06411279 0.24998634 0.37180174 0.24998634 0.06411279]\n",
      "234.0 [0.06411975 0.24998622 0.37178804 0.24998622 0.06411975]\n",
      "233.0 [0.06412678 0.24998611 0.37177423 0.24998611 0.06412678]\n",
      "232.0 [0.06413387 0.24998599 0.37176029 0.24998599 0.06413387]\n",
      "231.0 [0.06414102 0.24998586 0.37174624 0.24998586 0.06414102]\n",
      "230.0 [0.06414823 0.24998574 0.37173206 0.24998574 0.06414823]\n",
      "229.0 [0.0641555  0.24998562 0.37171776 0.24998562 0.0641555 ]\n",
      "228.0 [0.06416284 0.24998549 0.37170333 0.24998549 0.06416284]\n",
      "227.0 [0.06417025 0.24998536 0.37168878 0.24998536 0.06417025]\n",
      "226.0 [0.06417772 0.24998523 0.3716741  0.24998523 0.06417772]\n",
      "225.0 [0.06418526 0.2499851  0.37165928 0.2499851  0.06418526]\n",
      "224.0 [0.06419287 0.24998496 0.37164433 0.24998496 0.06419287]\n",
      "223.0 [0.06420054 0.24998483 0.37162925 0.24998483 0.06420054]\n",
      "222.0 [0.06420829 0.24998469 0.37161404 0.24998469 0.06420829]\n",
      "221.0 [0.06421611 0.24998455 0.37159868 0.24998455 0.06421611]\n",
      "220.0 [0.064224   0.24998441 0.37158319 0.24998441 0.064224  ]\n",
      "219.0 [0.06423196 0.24998427 0.37156755 0.24998427 0.06423196]\n",
      "218.0 [0.06423999 0.24998412 0.37155177 0.24998412 0.06423999]\n",
      "217.0 [0.0642481  0.24998398 0.37153584 0.24998398 0.0642481 ]\n",
      "216.0 [0.06425629 0.24998383 0.37151977 0.24998383 0.06425629]\n",
      "215.0 [0.06426455 0.24998367 0.37150354 0.24998367 0.06426455]\n",
      "214.0 [0.0642729  0.24998352 0.37148716 0.24998352 0.0642729 ]\n",
      "213.0 [0.06428132 0.24998337 0.37147063 0.24998337 0.06428132]\n",
      "212.0 [0.06428982 0.24998321 0.37145395 0.24998321 0.06428982]\n",
      "211.0 [0.0642984  0.24998305 0.3714371  0.24998305 0.0642984 ]\n",
      "210.0 [0.06430707 0.24998289 0.3714201  0.24998289 0.06430707]\n",
      "209.0 [0.06431582 0.24998272 0.37140293 0.24998272 0.06431582]\n",
      "208.0 [0.06432465 0.24998255 0.37138559 0.24998255 0.06432465]\n",
      "207.0 [0.06433357 0.24998238 0.37136809 0.24998238 0.06433357]\n",
      "206.0 [0.06434258 0.24998221 0.37135042 0.24998221 0.06434258]\n",
      "205.0 [0.06435168 0.24998204 0.37133257 0.24998204 0.06435168]\n",
      "204.0 [0.06436086 0.24998186 0.37131455 0.24998186 0.06436086]\n",
      "203.0 [0.06437014 0.24998168 0.37129635 0.24998168 0.06437014]\n",
      "202.0 [0.06437952 0.2499815  0.37127797 0.2499815  0.06437952]\n",
      "201.0 [0.06438898 0.24998131 0.37125941 0.24998131 0.06438898]\n",
      "200.0 [0.06439855 0.24998113 0.37124066 0.24998113 0.06439855]\n",
      "199.0 [0.06440821 0.24998093 0.37122172 0.24998093 0.06440821]\n",
      "198.0 [0.06441796 0.24998074 0.37120259 0.24998074 0.06441796]\n",
      "197.0 [0.06442782 0.24998054 0.37118326 0.24998054 0.06442782]\n",
      "196.0 [0.06443778 0.24998034 0.37116374 0.24998034 0.06443778]\n",
      "195.0 [0.06444785 0.24998014 0.37114402 0.24998014 0.06444785]\n",
      "194.0 [0.06445802 0.24997994 0.37112409 0.24997994 0.06445802]\n",
      "193.0 [0.06446829 0.24997973 0.37110396 0.24997973 0.06446829]\n",
      "192.0 [0.06447868 0.24997951 0.37108361 0.24997951 0.06447868]\n",
      "191.0 [0.06448917 0.2499793  0.37106306 0.2499793  0.06448917]\n",
      "190.0 [0.06449978 0.24997908 0.37104228 0.24997908 0.06449978]\n",
      "189.0 [0.0645105  0.24997886 0.37102129 0.24997886 0.0645105 ]\n",
      "188.0 [0.06452134 0.24997863 0.37100007 0.24997863 0.06452134]\n",
      "187.0 [0.06453229 0.2499784  0.37097862 0.2499784  0.06453229]\n",
      "186.0 [0.06454336 0.24997817 0.37095694 0.24997817 0.06454336]\n",
      "185.0 [0.06455456 0.24997793 0.37093503 0.24997793 0.06455456]\n",
      "184.0 [0.06456587 0.24997769 0.37091288 0.24997769 0.06456587]\n",
      "183.0 [0.06457732 0.24997744 0.37089048 0.24997744 0.06457732]\n",
      "182.0 [0.06458889 0.24997719 0.37086784 0.24997719 0.06458889]\n",
      "181.0 [0.06460059 0.24997694 0.37084495 0.24997694 0.06460059]\n",
      "180.0 [0.06461242 0.24997668 0.3708218  0.24997668 0.06461242]\n",
      "179.0 [0.06462438 0.24997642 0.3707984  0.24997642 0.06462438]\n",
      "178.0 [0.06463648 0.24997615 0.37077473 0.24997615 0.06463648]\n",
      "177.0 [0.06464872 0.24997588 0.37075079 0.24997588 0.06464872]\n",
      "176.0 [0.06466111 0.2499756  0.37072658 0.2499756  0.06466111]\n",
      "175.0 [0.06467363 0.24997532 0.37070209 0.24997532 0.06467363]\n",
      "174.0 [0.0646863  0.24997504 0.37067732 0.24997504 0.0646863 ]\n",
      "173.0 [0.06469912 0.24997475 0.37065226 0.24997475 0.06469912]\n",
      "172.0 [0.06471209 0.24997445 0.37062691 0.24997445 0.06471209]\n",
      "171.0 [0.06472522 0.24997415 0.37060126 0.24997415 0.06472522]\n",
      "170.0 [0.0647385  0.24997385 0.37057531 0.24997385 0.0647385 ]\n",
      "169.0 [0.06475194 0.24997353 0.37054905 0.24997353 0.06475194]\n",
      "168.0 [0.06476554 0.24997322 0.37052248 0.24997322 0.06476554]\n",
      "167.0 [0.06477931 0.24997289 0.37049559 0.24997289 0.06477931]\n",
      "166.0 [0.06479325 0.24997256 0.37046838 0.24997256 0.06479325]\n",
      "165.0 [0.06480736 0.24997223 0.37044083 0.24997223 0.06480736]\n",
      "164.0 [0.06482164 0.24997189 0.37041295 0.24997189 0.06482164]\n",
      "163.0 [0.0648361  0.24997154 0.37038472 0.24997154 0.0648361 ]\n",
      "162.0 [0.06485074 0.24997119 0.37035614 0.24997119 0.06485074]\n",
      "161.0 [0.06486557 0.24997083 0.37032721 0.24997083 0.06486557]\n",
      "160.0 [0.06488058 0.24997046 0.37029792 0.24997046 0.06488058]\n",
      "159.0 [0.06489579 0.24997009 0.37026825 0.24997009 0.06489579]\n",
      "158.0 [0.06491119 0.2499697  0.37023821 0.2499697  0.06491119]\n",
      "157.0 [0.06492679 0.24996932 0.37020778 0.24996932 0.06492679]\n",
      "156.0 [0.0649426  0.24996892 0.37017697 0.24996892 0.0649426 ]\n",
      "155.0 [0.06495861 0.24996851 0.37014575 0.24996851 0.06495861]\n",
      "154.0 [0.06497483 0.2499681  0.37011413 0.2499681  0.06497483]\n",
      "153.0 [0.06499127 0.24996768 0.37008209 0.24996768 0.06499127]\n",
      "152.0 [0.06500793 0.24996725 0.37004963 0.24996725 0.06500793]\n",
      "151.0 [0.06502481 0.24996682 0.37001674 0.24996682 0.06502481]\n",
      "150.0 [0.06504192 0.24996637 0.36998341 0.24996637 0.06504192]\n",
      "149.0 [0.06505927 0.24996592 0.36994963 0.24996592 0.06505927]\n",
      "148.0 [0.06507685 0.24996545 0.36991539 0.24996545 0.06507685]\n",
      "147.0 [0.06509468 0.24996498 0.36988069 0.24996498 0.06509468]\n",
      "146.0 [0.06511275 0.2499645  0.36984551 0.2499645  0.06511275]\n",
      "145.0 [0.06513108 0.249964   0.36980984 0.249964   0.06513108]\n",
      "144.0 [0.06514967 0.2499635  0.36977367 0.2499635  0.06514967]\n",
      "143.0 [0.06516852 0.24996298 0.369737   0.24996298 0.06516852]\n",
      "142.0 [0.06518764 0.24996246 0.3696998  0.24996246 0.06518764]\n",
      "141.0 [0.06520704 0.24996192 0.36966208 0.24996192 0.06520704]\n",
      "140.0 [0.06522672 0.24996137 0.36962382 0.24996137 0.06522672]\n",
      "139.0 [0.06524669 0.24996081 0.36958501 0.24996081 0.06524669]\n",
      "138.0 [0.06526695 0.24996024 0.36954563 0.24996024 0.06526695]\n",
      "137.0 [0.06528751 0.24995965 0.36950567 0.24995965 0.06528751]\n",
      "136.0 [0.06530838 0.24995905 0.36946512 0.24995905 0.06530838]\n",
      "135.0 [0.06532957 0.24995844 0.36942398 0.24995844 0.06532957]\n",
      "134.0 [0.06535108 0.24995782 0.36938221 0.24995782 0.06535108]\n",
      "133.0 [0.06537292 0.24995718 0.36933981 0.24995718 0.06537292]\n",
      "132.0 [0.06539509 0.24995652 0.36929677 0.24995652 0.06539509]\n",
      "131.0 [0.06541761 0.24995585 0.36925307 0.24995585 0.06541761]\n",
      "130.0 [0.06544048 0.24995517 0.3692087  0.24995517 0.06544048]\n",
      "129.0 [0.06546372 0.24995447 0.36916363 0.24995447 0.06546372]\n",
      "128.0 [0.06548732 0.24995375 0.36911786 0.24995375 0.06548732]\n",
      "127.0 [0.0655113  0.24995301 0.36907137 0.24995301 0.0655113 ]\n",
      "126.0 [0.06553567 0.24995226 0.36902413 0.24995226 0.06553567]\n",
      "125.0 [0.06556044 0.24995149 0.36897614 0.24995149 0.06556044]\n",
      "124.0 [0.06558562 0.2499507  0.36892736 0.2499507  0.06558562]\n",
      "123.0 [0.06561121 0.24994989 0.36887779 0.24994989 0.06561121]\n",
      "122.0 [0.06563723 0.24994906 0.36882741 0.24994906 0.06563723]\n",
      "121.0 [0.06566369 0.24994821 0.36877619 0.24994821 0.06566369]\n",
      "120.0 [0.0656906  0.24994734 0.36872411 0.24994734 0.0656906 ]\n",
      "119.0 [0.06571798 0.24994645 0.36867116 0.24994645 0.06571798]\n",
      "118.0 [0.06574582 0.24994553 0.3686173  0.24994553 0.06574582]\n",
      "117.0 [0.06577415 0.24994459 0.36856251 0.24994459 0.06577415]\n",
      "116.0 [0.06580298 0.24994363 0.36850678 0.24994363 0.06580298]\n",
      "115.0 [0.06583233 0.24994263 0.36845008 0.24994263 0.06583233]\n",
      "114.0 [0.06586219 0.24994162 0.36839238 0.24994162 0.06586219]\n",
      "113.0 [0.0658926  0.24994057 0.36833365 0.24994057 0.0658926 ]\n",
      "112.0 [0.06592356 0.2499395  0.36827387 0.2499395  0.06592356]\n",
      "111.0 [0.0659551 0.2499384 0.368213  0.2499384 0.0659551]\n",
      "110.0 [0.06598722 0.24993727 0.36815103 0.24993727 0.06598722]\n",
      "109.0 [0.06601994 0.24993611 0.36808791 0.24993611 0.06601994]\n",
      "108.0 [0.06605328 0.24993491 0.36802362 0.24993491 0.06605328]\n",
      "107.0 [0.06608726 0.24993368 0.36795812 0.24993368 0.06608726]\n",
      "106.0 [0.0661219  0.24993241 0.36789138 0.24993241 0.0661219 ]\n",
      "105.0 [0.06615721 0.24993111 0.36782336 0.24993111 0.06615721]\n",
      "104.0 [0.06619321 0.24992977 0.36775403 0.24992977 0.06619321]\n",
      "103.0 [0.06622993 0.24992839 0.36768334 0.24992839 0.06622993]\n",
      "102.0 [0.06626739 0.24992698 0.36761127 0.24992698 0.06626739]\n",
      "101.0 [0.06630561 0.24992551 0.36753776 0.24992551 0.06630561]\n",
      "100.0 [0.06634461 0.24992401 0.36746277 0.24992401 0.06634461]\n",
      "99.0 [0.06638442 0.24992245 0.36738626 0.24992245 0.06638442]\n",
      "98.0 [0.06642506 0.24992085 0.36730818 0.24992085 0.06642506]\n",
      "97.0 [0.06646656 0.2499192  0.36722848 0.2499192  0.06646656]\n",
      "96.0 [0.06650895 0.2499175  0.36714711 0.2499175  0.06650895]\n",
      "95.0 [0.06655225 0.24991574 0.36706403 0.24991574 0.06655225]\n",
      "94.0 [0.0665965  0.24991392 0.36697916 0.24991392 0.0665965 ]\n",
      "93.0 [0.06664172 0.24991205 0.36689246 0.24991205 0.06664172]\n",
      "92.0 [0.06668795 0.24991011 0.36680387 0.24991011 0.06668795]\n",
      "91.0 [0.06673523 0.24990811 0.36671332 0.24990811 0.06673523]\n",
      "90.0 [0.06678359 0.24990604 0.36662074 0.24990604 0.06678359]\n",
      "89.0 [0.06683306 0.24990391 0.36652607 0.24990391 0.06683306]\n",
      "88.0 [0.06688369 0.24990169 0.36642924 0.24990169 0.06688369]\n",
      "87.0 [0.06693551 0.2498994  0.36633018 0.2498994  0.06693551]\n",
      "86.0 [0.06698857 0.24989703 0.36622879 0.24989703 0.06698857]\n",
      "85.0 [0.06704292 0.24989458 0.36612501 0.24989458 0.06704292]\n",
      "84.0 [0.0670986  0.24989203 0.36601874 0.24989203 0.0670986 ]\n",
      "83.0 [0.06715566 0.24988939 0.3659099  0.24988939 0.06715566]\n",
      "82.0 [0.06721415 0.24988666 0.36579838 0.24988666 0.06721415]\n",
      "81.0 [0.06727413 0.24988382 0.3656841  0.24988382 0.06727413]\n",
      "80.0 [0.06733566 0.24988087 0.36556694 0.24988087 0.06733566]\n",
      "79.0 [0.06739879 0.24987781 0.3654468  0.24987781 0.06739879]\n",
      "78.0 [0.06746359 0.24987463 0.36532355 0.24987463 0.06746359]\n",
      "77.0 [0.06753013 0.24987133 0.36519709 0.24987133 0.06753013]\n",
      "76.0 [0.06759847 0.24986789 0.36506728 0.24986789 0.06759847]\n",
      "75.0 [0.06766869 0.24986431 0.36493398 0.24986431 0.06766869]\n",
      "74.0 [0.06774088 0.24986059 0.36479706 0.24986059 0.06774088]\n",
      "73.0 [0.06781511 0.24985671 0.36465636 0.24985671 0.06781511]\n",
      "72.0 [0.06789147 0.24985267 0.36451173 0.24985267 0.06789147]\n",
      "71.0 [0.06797005 0.24984845 0.364363   0.24984845 0.06797005]\n",
      "70.0 [0.06805096 0.24984405 0.36420999 0.24984405 0.06805096]\n",
      "69.0 [0.06813429 0.24983945 0.36405251 0.24983945 0.06813429]\n",
      "68.0 [0.06822017 0.24983465 0.36389037 0.24983465 0.06822017]\n",
      "67.0 [0.0683087  0.24982963 0.36372335 0.24982963 0.0683087 ]\n",
      "66.0 [0.06840001 0.24982437 0.36355124 0.24982437 0.06840001]\n",
      "65.0 [0.06849423 0.24981888 0.36337379 0.24981888 0.06849423]\n",
      "64.0 [0.06859151 0.24981311 0.36319076 0.24981311 0.06859151]\n",
      "63.0 [0.06869199 0.24980707 0.36300187 0.24980707 0.06869199]\n",
      "62.0 [0.06879585 0.24980073 0.36280684 0.24980073 0.06879585]\n",
      "61.0 [0.06890324 0.24979408 0.36260537 0.24979408 0.06890324]\n",
      "60.0 [0.06901435 0.24978708 0.36239713 0.24978708 0.06901435]\n",
      "59.0 [0.06912939 0.24977972 0.36218177 0.24977972 0.06912939]\n",
      "58.0 [0.06924856 0.24977198 0.36195893 0.24977198 0.06924856]\n",
      "57.0 [0.06937208 0.24976381 0.36172821 0.24976381 0.06937208]\n",
      "56.0 [0.06950021 0.24975521 0.36148917 0.24975521 0.06950021]\n",
      "55.0 [0.0696332  0.24974612 0.36124137 0.24974612 0.0696332 ]\n",
      "54.0 [0.06977133 0.24973652 0.36098431 0.24973652 0.06977133]\n",
      "53.0 [0.06991491 0.24972636 0.36071747 0.24972636 0.06991491]\n",
      "52.0 [0.07006427 0.2497156  0.36044026 0.2497156  0.07006427]\n",
      "51.0 [0.07021976 0.2497042  0.36015209 0.2497042  0.07021976]\n",
      "50.0 [0.07038176 0.24969209 0.35985229 0.24969209 0.07038176]\n",
      "49.0 [0.0705507  0.24967923 0.35954013 0.24967923 0.0705507 ]\n",
      "48.0 [0.07072703 0.24966555 0.35921484 0.24966555 0.07072703]\n",
      "47.0 [0.07091125 0.24965097 0.35887557 0.24965097 0.07091125]\n",
      "46.0 [0.07110388 0.24963542 0.3585214  0.24963542 0.07110388]\n",
      "45.0 [0.07130553 0.2496188  0.35815133 0.2496188  0.07130553]\n",
      "44.0 [0.07151684 0.24960102 0.35776427 0.24960102 0.07151684]\n",
      "43.0 [0.07173853 0.24958197 0.357359   0.24958197 0.07173853]\n",
      "42.0 [0.07197136 0.24956152 0.35693423 0.24956152 0.07197136]\n",
      "41.0 [0.07221621 0.24953954 0.35648851 0.24953954 0.07221621]\n",
      "40.0 [0.07247402 0.24951586 0.35602024 0.24951586 0.07247402]\n",
      "39.0 [0.07274585 0.24949031 0.35552769 0.24949031 0.07274585]\n",
      "38.0 [0.07303288 0.24946268 0.35500889 0.24946268 0.07303288]\n",
      "37.0 [0.0733364  0.24943274 0.35446172 0.24943274 0.0733364 ]\n",
      "36.0 [0.07365789 0.24940023 0.35388376 0.24940023 0.07365789]\n",
      "35.0 [0.07399898 0.24936484 0.35327236 0.24936484 0.07399898]\n",
      "34.0 [0.07436151 0.24932623 0.35262452 0.24932623 0.07436151]\n",
      "33.0 [0.07474756 0.249284   0.35193688 0.249284   0.07474756]\n",
      "32.0 [0.0751595  0.24923766 0.35120567 0.24923766 0.0751595 ]\n",
      "31.0 [0.07560001 0.24918668 0.35042662 0.24918668 0.07560001]\n",
      "30.0 [0.07607215 0.24913042 0.34959487 0.24913042 0.07607215]\n",
      "29.0 [0.07657944 0.24906811 0.3487049  0.24906811 0.07657944]\n",
      "28.0 [0.07712594 0.24899887 0.34775037 0.24899887 0.07712594]\n",
      "27.0 [0.07771637 0.24892162 0.34672401 0.24892162 0.07771637]\n",
      "26.0 [0.07835621 0.24883509 0.34561741 0.24883509 0.07835621]\n",
      "25.0 [0.0790519  0.24873771 0.34442077 0.24873771 0.0790519 ]\n",
      "24.0 [0.07981104 0.24862762 0.34312268 0.24862762 0.07981104]\n",
      "23.0 [0.08064268 0.24850249 0.34170966 0.24850249 0.08064268]\n",
      "22.0 [0.08155764 0.24835946 0.3401658  0.24835946 0.08155764]\n",
      "21.0 [0.08256901 0.24819495 0.33847206 0.24819495 0.08256901]\n",
      "20.0 [0.08369275 0.24800446 0.33660557 0.24800446 0.08369275]\n",
      "19.0 [0.08494851 0.24778221 0.33453856 0.24778221 0.08494851]\n",
      "18.0 [0.08636076 0.24752076 0.33223696 0.24752076 0.08636076]\n",
      "17.0 [0.08796037 0.24721033 0.3296586  0.24721033 0.08796037]\n",
      "16.0 [0.08978677 0.24683794 0.32675058 0.24683794 0.08978677]\n",
      "15.0 [0.09189118 0.24638599 0.32344567 0.24638599 0.09189118]\n",
      "14.0 [0.09434121 0.24583021 0.31965716 0.24583021 0.09434121]\n",
      "13.0 [0.097228   0.24513635 0.3152713  0.24513635 0.097228  ]\n",
      "12.0 [0.10067707 0.24425493 0.310136   0.24425493 0.10067707]\n",
      "11.0 [0.10486603 0.24311229 0.30404337 0.24311229 0.10486603]\n",
      "10.0 [0.11005378 0.24159517 0.2967021  0.24159517 0.11005378]\n",
      "9.5 [0.11313717 0.24064346 0.29243874 0.24064346 0.11313717]\n",
      "9.0 [0.11663153 0.2395225  0.28769194 0.2395225  0.11663153]\n",
      "8.5 [0.12062154 0.23819028 0.28237637 0.23819028 0.12062154]\n",
      "8.0 [0.12521586 0.23659113 0.27638603 0.23659113 0.12521586]\n",
      "7.5 [0.1305559  0.23465018 0.26958784 0.23465018 0.1305559 ]\n",
      "7.0 [0.13682844 0.2322651  0.26181292 0.2322651  0.13682844]\n",
      "6.5 [0.14428422 0.22929344 0.25284468 0.22929344 0.14428422]\n",
      "6.0 [0.15326567 0.22553316 0.24240235 0.22553316 0.15326567]\n",
      "5.5 [0.16424874 0.22069182 0.23011887 0.22069182 0.16424874]\n",
      "5.0 [0.17790641 0.21433753 0.21551211 0.21433753 0.17790641]\n",
      "4.5 [0.19520357 0.20582041 0.19795202 0.20582041 0.19520357]\n",
      "4.0 [0.21753067 0.19415061 0.17663745 0.19415061 0.21753067]\n",
      "3.5 [0.24685587 0.17782738 0.15063351 0.17782738 0.24685587]\n",
      "3.0 [0.28574833 0.15468733 0.11912868 0.15468733 0.28574833]\n",
      "2.5 [0.33666442 0.12216603 0.0823391  0.12216603 0.33666442]\n",
      "2.0 [0.39869382 0.07939919 0.04381399 0.07939919 0.39869382]\n",
      "1.5 [0.45966596 0.0336763  0.01331547 0.0336763  0.45966596]\n",
      "1.0 [0.4945983  0.00490395 0.00099552 0.00490395 0.4945983 ]\n",
      "0.5 [4.99987543e-01 1.22881186e-05 3.37597113e-07 1.22881186e-05\n",
      " 4.99987543e-01]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "k_B = 1\n",
    "\n",
    "E = np.array([-6,0,2,0,-6])\n",
    "multiplicity = np.array([1,4,6,4,1])\n",
    "\n",
    "results = []\n",
    "for T in np.concatenate((np.arange(300,10,-1),np.arange(10,0,-0.5))):\n",
    "    Probabilities = multiplicity*np.exp(-E/(k_B*T))\n",
    "    Z = Probabilities.sum()\n",
    "    Probabilities /= Z\n",
    "    print(T,Probabilities)\n",
    "    results.append([T,*Probabilities])\n",
    "results = np.array(results)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1200x800 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "fig=plt.figure(figsize=(12,8), dpi= 100, facecolor='w', edgecolor='k')\n",
    "\n",
    "plt.subplot(2,3,1)\n",
    "plt.plot(results[:,0],results[:,1],\".b\")\n",
    "plt.legend([\"$P_A$\"],loc=\"right\")\n",
    "plt.xlabel(\"T\")\n",
    "\n",
    "plt.subplot(2,3,2)\n",
    "plt.plot(results[:,0],results[:,2],\".g\")\n",
    "plt.legend([\"$P_B$\"],loc=\"right\")\n",
    "plt.xlabel(\"T\")\n",
    "\n",
    "plt.subplot(2,3,3)\n",
    "plt.plot(results[:,0],results[:,3],\".r\")\n",
    "plt.legend([\"$P_C$\"],loc=\"right\")\n",
    "plt.xlabel(\"T\")\n",
    "\n",
    "plt.subplot(2,3,5)\n",
    "plt.plot(results[:,0],results[:,4],\".g\")\n",
    "plt.legend([\"$P_D$\"],loc=\"right\")\n",
    "plt.xlabel(\"T\")\n",
    "\n",
    "plt.subplot(2,3,4)\n",
    "plt.plot(results[:,0],results[:,5],\".b\")\n",
    "plt.legend([\"$P_E$\"],loc=\"right\")\n",
    "plt.xlabel(\"T\")\n",
    "\n",
    "plt.subplot(2,3,6)\n",
    "plt.plot(results[-20:,0],results[-20:,1],\".-b\")\n",
    "plt.plot(results[-20:,0],results[-20:,2],\".-g\")\n",
    "plt.plot(results[-20:,0],results[-20:,3],\".-r\")\n",
    "plt.legend([\"$P_A$\",\"$P_B$\",\"$P_C$\"])\n",
    "plt.xlabel(\"T\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# External link(s)\n",
    "* Dr. David Boyce - Magnetic ordering https://twitter.com/DrDavidBoyce/status/1176921195507310593\n",
    "* Marco Koschny - Magnetic Domain Movement and Wall Motion ([1](https://www.youtube.com/watch?v=HzxTqQ40wSU), [2](https://www.youtube.com/watch?v=LFC6tbbMUaA))\n",
    "* Andrea Benassi - [Labyrinthine magnetic domains (small stray field)](https://www.youtube.com/watch?v=A5NmVqNSIqw)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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