linked_cells-checkpoint.ipynb

{
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   "cell_type": "markdown",
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   "source": [
    "# Linked Cell Algorithm  <div style=\"text-align: right\">  </div>\n",
    "\n",
    "## Classical Linked-Cell Algorithm\n",
    "\n",
    "\n",
    "The naive direct particle to particle interaction has complexity $\\mathcal{O}(N^2)$. We will now have a look at methods that will reduce the complexity. <br/>\n",
    "In this assignment you will work with **Linked-Cell Algorithm**. There are many short range potentials like LJ potential (as shown in the figure below). For each molecule, an influence volume (closed sphere) with cut-off radius $r_c$ can be assumed. Every molecule outside this influence volume is neglected. \n",
    "<p align=\"center\">\n",
    "<img src=\"./figures/LJforce.png\"\n",
    "     alt=\"LJ force\"\n",
    "     width=\"356\" height=\"356\"/>\n",
    "</p>\n",
    "Therfore, during the calculation of force we need to calculate to consider the molecules within the sphere only. Since the total number of molecule within the sphere is small compared to the total number of molcules, the complexity of this algortihm is $\\mathcal{O}(N)$. <br/><br/>\n",
    "In the Linked-Cell Algorithm, you divide your domain into cells. The size of each cell is equal to the cut-off radius $r_c$. For every cell, there is a list of neighboring cells. The neighboring cells are those that are in direct contact with the current cell. In the figure below, the neighboring cells of the cell in red are shown in yellow and orange in color.\n",
    "<p align=\"center\">\n",
    "<img src=\"./figures/linked-cell1.png\"\n",
    "     alt=\"linked-cells\"\n",
    "     width=\"256\" height=\"256\"/>\n",
    "</p>\n",
    "Let us try to implement this algorithm first.\n",
    "\n",
    "## Variable Linked-Cell\n",
    "In linked-cell algorithm, we might interact with particles that are outside the cut-off radius. We can decrease these interactions using **Variable Linked-Cell Algorithm**. In variable linked-cell, the length of each cell is $\\frac{r_c}{a}$, where $a$ is generally an integer. We will call this as variable linked cell parameter. The neighboring cell of any cell will consist of those cells which might partially or completely fall within the cut-off sphere for any point inside the concerned cell. An example of variable linked-cell is shown below:\n",
    "<p align=\"center\">\n",
    "<img src=\"./figures/variable-linked-cells.png\"\n",
    "     alt=\"variable-linked-cells\"\n",
    "     width=\"1024\" height=\"1024\"/>\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import rcParams, patches\n",
    "import time\n",
    "from itertools import product\n",
    "import utils\n",
    "import particle as pr\n",
    "import cell_1\n",
    "import cell_2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We define the function **lj_potential** to calculate the Lennard Jones Potential. Then we calculate the potential between two particles separated at a distance of $0.1$, $0.2$, $0.3$ and $0.4$ respectively. Notice the rapid decay of potential. <br/>\n",
    "__NOTE__: The function **lj_potential** is implemented in file _utils.py_ which is inside the same directory as this iPython notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Potential when distance is 0.1:   -9.998999999999997\n",
      "Potential when distance is 0.2:   -0.15624975585937495\n",
      "Potential when distance is 0.3:   -0.013717419243152115\n",
      "Potential when distance is 0.4:   -0.0024414061903953546\n"
     ]
    }
   ],
   "source": [
    "print(\"Potential when distance is 0.1:  \", utils.lj_potential(0.1))\n",
    "print(\"Potential when distance is 0.2:  \", utils.lj_potential(0.2))\n",
    "print(\"Potential when distance is 0.3:  \", utils.lj_potential(0.3))\n",
    "print(\"Potential when distance is 0.4:  \", utils.lj_potential(0.4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Definition of class Particle\n",
    "\n",
    "Now we define the class **Point** and **Particle** to define the properties of a particular particle. \n",
    "<br/>\n",
    "Open file _particle.py_ and go through the implementation of both the classes and understand the implementation of both."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us create $N$ particles and plot their position."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
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     "output_type": "display_data"
    }
   ],
   "source": [
    "domain = 1.0\n",
    "N = 50\n",
    "def get_list_particles(N):\n",
    "    list_particles = []\n",
    "    for i in range(N):\n",
    "        list_particles.append(pr.Particle(domain=domain))\n",
    "    return list_particles\n",
    "\n",
    "list_particles = get_list_particles(N)\n",
    "    \n",
    "# plotting\n",
    "ax = plt.gca()\n",
    "for particle in list_particles:\n",
    "    particle.plot(color='b', s=5)\n",
    "ax.tick_params(axis='both',labelsize=0, length = 0)\n",
    "plt.xlim(left=0, right=domain)\n",
    "plt.ylim(bottom=0, top=domain)\n",
    "ax.set_aspect('equal', adjustable='box')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will implement a class that defines **cell** in two different ways. We will call those two implementations as **Cell_1** and **Cell_2**. Both classes should be child classes of **Cell**. Let us discuss the first implementation(**Cell_1**).\n",
    "\n",
    "## Definition of class Cell_1\n",
    "\n",
    "There are five member variables of class **Cell_1**\n",
    "1. __cell_center__: Array of size two which contains the x and y coordinates of the center of the cell\n",
    "2. __side_length__: The side length of the cell\n",
    "3. __a__: Variable linked cell parameter\n",
    "4. __particle_index__: List that contains the indices of particles (inside the list __list_particles__) which fall inside the cell\n",
    "5. __neighbor_cell_index__: List that contain the indices of cells which are neighbors of current cell. These indices represents the location of cell in the list named **list_cells**. **list_cells** is list of all cells inside the domain. We will explain **list_cells** in detail later.\n",
    "6. __cell_index__: Index of current cell in __list_cells__.\n",
    "\n",
    "<p align=\"center\">\n",
    "<img src=\"./figures/cell_1_class.png\"\n",
    "     alt=\"cell_1_class\"\n",
    "     width=\"512\" height=\"512\"/>\n",
    "</p>\n",
    "\n",
    "For example: for the figure shown above, the cell has particle number 9 and 11. The neighboring cell indices are 3, 4, 7, 8, 9, 11, 12, 13.\n",
    "\n",
    "**Constructor of class**: In order to create an object of class __Cell_1__, one need to provide following parameters:\n",
    "1. lx : x-coordinate of bottom left corner of the cell\n",
    "2. ly : y-coordinate of bottom left corner of the cell\n",
    "3. r_c : Cut-off radius\n",
    "4. cell_index : Index of cell in list_cells\n",
    "5. neighbor_delta_coordinate : List of numpy array(of size 2). We will provide detailed explanation of this variable in the first task.\n",
    "6. a : Variable linked-cell parameter (default value 1)\n",
    "7. domain : Size of domain (default value 1.0)\n",
    "            \n",
    "\n",
    "Before we move further and describe the member functions of class **Cell_1**, we take a short detour and define **list_cells**. <br/>\n",
    "**list_cells**:  This is list of all the cells (object of type Cell_1) inside the domain. The cells are arranged in row major order. This means we store the cells in one row and then move to the next one. Let us take a simple example of domain which has 9 cells (index 0-8) with 3 rows and 3 columns. Then the arrangement is as shown below: \n",
    "<p align=\"center\">\n",
    "<img src=\"./figures/cell_arrangement.png\"\n",
    "     alt=\"cell_arrangement\"\n",
    "     width=\"512\" height=\"512\"/>\n",
    "</p>\n",
    "\n",
    "### Finding neighbors <div style=\"text-align: right\">  </div>\n",
    "Our first task is to find the neighbors of a cell. In order to efficiently calculate the neighbors, we will take advantage of the arrangement of cells. Let us take a simple example where $a=1$ as shown below:\n",
    "<p align=\"center\">\n",
    "<img src=\"./figures/delta_cells.png\"\n",
    "     alt=\"delta_cells\"\n",
    "     width=\"1024\" height=\"512\"/>\n",
    "</p>\n",
    "\n",
    "Let us consider x-axis as horizontal axis and y-axis as vertical axis. We want to know the neighbors of the cell marked in red. Since $a=1$, the colored cells are neighbor cells which interact with the red colored cell. The corresponding position of cell in __list_cells__ is also shown. If we consider the red cell as $[0,0]$, then the relative 2-d index of the neighboring interaction cell is also marked. The indices are symmetric about $[0,0]$. This property is independent of the position of the cell or the value of $a$. We will make use of this property to find the neighbors. <br/>\n",
    "For any arbitrary integer value of $a$, we need to find the cells which partially or completely fall within the cut-off sphere for any point inside the concerned cell. The corner of cell is the outer most point of the cell which represent the maximum coverage of the cell. Imagine a circle of radius $r_c$ at all four corners of cell. We need to find all cells which partially or completely fall within any of the four circles. The naive way of doing that is to calculate the distance between the four corners of the current cell to all four corners of the other cell. This gives us 16 combinations. We take the minimum distance amongst those 16 distance. If that distance is less than the cut-off radius($r_c$) then the cell is the neighbor interaction cell. We can reduce this calculation by making use of the symmetry. <br/><br/>\n",
    "Finding the neighbor cells along the x and y axis is a trivial problem ($a$ cells along the x and y axis in both upward and downward directions) and does not require any calculations. Let us consider cells in first quadrant (upper right quadrant, see the figure above). The smallest distance between red cell and any cell in first quadrant is the distance between the top right corner of red cell and bottom left corner of the other cell. We can determine relative 2-d indices for the cells whose minimum distance is less that the cut-off radius in first quadrant. From this we can easily determine relative 2-d indices for other quadrants because of symmetry. So, we just store the relative 2-d indices for first quadrant. The list relative 2-d indices for first quadrant that falls inside the cut-off radius is the parameter __neighbor_delta_coordinate__ that we pass to the constructor of **Cell_1**. For $a=1$,  __neighbor_delta_coordinate = [np.array(1,1)]__.\n",
    "\n",
    "\n",
    "###  Creating list of cells <div style=\"text-align: right\">  </div>\n",
    "Complete the implementation of the function named __get_list_cell__ inside the file _cell_1.py_. It takes two parameter \n",
    "1. r_c: Cut-off radius\n",
    "2. neighbor_delta_coordinate\n",
    "2. domain: This is an optional parameter during function call. Default value is 1.\n",
    "3. a: Variable linked-cell parameter. Default value is 1\n",
    "This function creates and returns the list of cells in order as described before.\n",
    "\n",
    "###  Calculating Potential <div style=\"text-align: right\">  </div>\n",
    "\n",
    "\n",
    "First member function of class **Cell_1** that we need to implemet is __p2p_self__. This function calculates the potential on all particle inside a cell due to other particles inside the same cell. The potential calculated is added in the the variable **phi** of particle object. This function takes list of particles __list_particles__(list of particles that we created above) as parameter. <br/>\n",
    "Your task is to implement this function in file _cell_1.py_.\n",
    "\n",
    "\n",
    "The second function is __p2p_neigbor_cells__. This function calculates the potential on all particle inside a cell due to particles in the neighor cells (cells index fiven by the variable neighbor_cell_index). The potential calculated is added in the the variable **phi** of particle object. Arguments are:\n",
    "1. list_particles: List of all **Particle** objects\n",
    "2. list_cells: List of all **Cell_1** objects <br/>\n",
    "Your task is to implement this function in file _cell_1.py_.\n",
    "\n",
    "\n",
    "### Assigning particles to cells  <div style=\"text-align: right\">  </div>\n",
    "\n",
    "This function assigns a particle to the corresponding cell. The parameters are:\n",
    "1. list_particles: List of all **Particle** objects\n",
    "2. list_cells: List of all **Cell_1** objects \n",
    "3. r_c: Cut-off radius\n",
    "4. a: Variable linked-list parameter\n",
    "5. domain: size of domain\n",
    "<br/>\n",
    "To assign particle to a cell use the function __add_particle__."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "r_c, a = 0.2, 1\n",
    "delta_coordinate = utils.get_successor_neighbor_delta_coordinate(a=a)\n",
    "list_cells = cell_1.get_list_cell(r_c, delta_coordinate, domain=domain, a=a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "cell_1.assign_particle_to_cell(list_particles, list_cells, r_c, a=a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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": [
    "# This block can be used for debugging\n",
    "# In this block we plot all particles, choose a cell and plot it with different cell\n",
    "# Using this you can check if you are forming correct cells and assigning correct particles to correct cell or not\n",
    "idx = np.random.randint(low=0, high=len(list_cells)-1, size=1)[0]\n",
    "a_cell = list_cells[idx]\n",
    "ax = plt.gca()\n",
    "for particle in list_particles:\n",
    "    particle.plot()\n",
    "utils.plot_all_cells(ax, list_cells, edgecolor='g', domain=domain)\n",
    "a_cell.plot_cell(ax, edgecolor='k')\n",
    "a_cell.plot_particles(list_particles, color='b')\n",
    "ax.tick_params(axis='both',labelsize=0, length = 0)\n",
    "plt.xlim(left=0, right=domain)\n",
    "plt.ylim(bottom=0, top=domain)\n",
    "ax.set_aspect('equal', adjustable='box')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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": [
    "# This block can be used for debugging\n",
    "# In this block we randomly choose a cell and plot its neighboring cells and particles in different colors\n",
    "# Using this you can check if you are assigning correct neighbors or not or not\n",
    "idx = np.random.randint(low=0, high=len(list_cells)-1, size=1)[0]\n",
    "a_cell = list_cells[idx]\n",
    "ax = plt.gca()\n",
    "utils.plot_all_cells(ax, list_cells, edgecolor='g', domain=domain)\n",
    "a_cell.plot_particles(list_particles, color='b')\n",
    "a_cell.plot_neighbor_cells(ax, list_cells, edgecolor='k')\n",
    "a_cell.plot_cell(ax, edgecolor='y')\n",
    "a_cell.plot_neighbor_cell_particles(list_cells, list_particles)\n",
    "ax.tick_params(axis='both',labelsize=0, length = 0)\n",
    "plt.xlim(left=0, right=domain)\n",
    "plt.ylim(bottom=0, top=domain)\n",
    "ax.set_aspect('equal', adjustable='box')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Check if correct potential is calculated or not\n",
    "N = 100\n",
    "list_particles = get_list_particles(N)\n",
    "cell_1.set_potential_zero(list_particles)\n",
    "delta_coordinate = utils.get_successor_neighbor_delta_coordinate(a=a)\n",
    "list_cells = cell_1.get_list_cell(r_c, delta_coordinate, domain=domain, a=a)\n",
    "cell_1.assign_particle_to_cell(list_particles, list_cells, r_c, a=a)\n",
    "cell_1.calculate_potential_linked_cell(list_cells, list_particles)\n",
    "direct_potential = cell_1.direct_potential_all_particles(list_particles)\n",
    "linked_cell_potential = cell_1.extract_linked_cell_potential(list_particles)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean relative error 0.0008075675529972737\n"
     ]
    }
   ],
   "source": [
    "print(\"Mean relative error\", utils.get_mean_relative_error(direct_potential, linked_cell_potential))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Time Scaling\n",
    "\n",
    "Scaling with respect to number of particles for fixed cut-off radius ($r_c = 0.2$) and variable linked cell term $a = 8$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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": [
    "num_particles = [np.int(100 * i) for i in range(1,11)]\n",
    "n_instances = len(num_particles)\n",
    "time_linked_cell = np.zeros(n_instances, dtype=np.float)\n",
    "time_direct = np.zeros(n_instances, dtype=np.float)\n",
    "r_c, a, domain = 0.2, 8, 1.0\n",
    "delta_coordinate = utils.get_successor_neighbor_delta_coordinate(a=a)\n",
    "for idx, N in enumerate(num_particles):\n",
    "    list_particles = get_list_particles(N)\n",
    "    cell_1.set_potential_zero(list_particles)\n",
    "    list_cells = cell_1.get_list_cell(r_c, delta_coordinate, domain=domain, a=a)\n",
    "    cell_1.assign_particle_to_cell(list_particles, list_cells, r_c, a=a)   \n",
    "    start_lc = time.time()\n",
    "    cell_1.calculate_potential_linked_cell(list_cells, list_particles)\n",
    "    end_lc = time.time()\n",
    "    linked_cell_potential = cell_1.extract_linked_cell_potential(list_particles)\n",
    "    time_linked_cell[idx] = end_lc - start_lc\n",
    "    start_direct = time.time()\n",
    "    direct_potential = cell_1.direct_potential_all_particles(list_particles)\n",
    "    end_direct = time.time()\n",
    "    time_direct[idx] = end_direct - start_direct\n",
    "plt.plot(num_particles, time_direct, label='Direct')\n",
    "plt.plot(num_particles, time_linked_cell, label='Linked Cell')\n",
    "plt.legend()\n",
    "plt.yscale('log')\n",
    "plt.xlabel('Number of particles')\n",
    "plt.ylabel('Evaluation time')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we find the ratio of approximate slope of the two curves (assuming it to be a straight line)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.1516567165753984\n"
     ]
    }
   ],
   "source": [
    "slope_direct = (np.log(time_direct[-1]) - np.log(time_direct[0])) / (num_particles[-1] - num_particles[0])\n",
    "slope_lc = (np.log(time_linked_cell[-1]) - np.log(time_linked_cell[0])) / (num_particles[-1] - num_particles[0])\n",
    "print(slope_direct / slope_lc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "With the increase in the number of particles, the runtime of both methods goes up. The linked cell algorithm clearly has a smaller runtime, because we are evaluating fewer inter-particle potentials. Moreover linked cell algorithm has O(N) complexity as opposed to O(N^2) of the direct method hence the ratio of the slopes should theoretically be close to 2. However we get a slope ratio closer to 1 this might be because we are using a small number of particles."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Evaluation time scaling\n",
    "\n",
    "Let us fix the number of particles $N = 1000$ and variable linked cell term $a = 8$. We analyse the error with respect cut-off radius and evaluation time with respect to the cut-off radius. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "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"
    },
    {
     "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 = 1000\n",
    "R = [0.1, 0.2, 0.4, 0.5]\n",
    "n_instances = len(R)\n",
    "time_linked_cell = np.zeros(n_instances, dtype=np.float)\n",
    "mean_relative_error = np.zeros(n_instances, dtype=np.float)\n",
    "a, domain = 8, 1.0\n",
    "list_particles = get_list_particles(N)\n",
    "direct_potential = cell_1.direct_potential_all_particles(list_particles)\n",
    "delta_coordinate = utils.get_successor_neighbor_delta_coordinate(a=a)\n",
    "for idx, r_c in enumerate(R):\n",
    "    cell_1.set_potential_zero(list_particles)\n",
    "    list_cells = cell_1.get_list_cell(r_c, delta_coordinate, domain=domain, a=a)\n",
    "    cell_1.assign_particle_to_cell(list_particles, list_cells, r_c, a=a)   \n",
    "    start_lc = time.time()\n",
    "    cell_1.calculate_potential_linked_cell(list_cells, list_particles)\n",
    "    end_lc = time.time()\n",
    "    linked_cell_potential = cell_1.extract_linked_cell_potential(list_particles)\n",
    "    time_linked_cell[idx] = end_lc - start_lc\n",
    "    mean_relative_error[idx] = utils.get_mean_relative_error(direct_potential, linked_cell_potential)\n",
    "plt.plot(R, time_linked_cell, label='Linked Cell')\n",
    "plt.legend()\n",
    "plt.yscale('log')\n",
    "plt.xlabel('Cut-off radius')\n",
    "plt.ylabel('Evaluation time')\n",
    "plt.show()\n",
    "plt.plot(R, mean_relative_error)\n",
    "plt.yscale('log')\n",
    "plt.xlabel('Cut-off radius')\n",
    "plt.ylabel('Mean_relative error')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "\n",
    "As the cut-off radius increases the side length of a single cell also increases. This reduces the number of cells in the domain and we end up having less cells. This means there are more particles inside the cells now. Because of that we are now using more particles while calculating potential due to particles in the same cell and due to partiles in the neighbor cells. This increases the evaluation time but since we are using more particles it also approximates the direct potential calculation better. Thus the relative error decreases. In fact if we keep increasing the cut-off radius, after some value we will end up having the same result as the direct potential calculation since we will be using all particles for calculating the potential.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us plot the Evaluation time with respect to cut-off radius (same as before),but with $N=500$ particles and $a=8$. Then we do the same with $N=100$ particles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "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 = 500\n",
    "R = [0.1, 0.2, 0.4, 0.5]\n",
    "n_instances = len(R)\n",
    "time_linked_cell = np.zeros(n_instances, dtype=np.float)\n",
    "a, domain = 8, 1.0\n",
    "list_particles = get_list_particles(N)\n",
    "direct_potential = cell_1.direct_potential_all_particles(list_particles)\n",
    "delta_coordinate = utils.get_successor_neighbor_delta_coordinate(a=a)\n",
    "for idx, r_c in enumerate(R):\n",
    "    cell_1.set_potential_zero(list_particles)\n",
    "    list_cells = cell_1.get_list_cell(r_c, delta_coordinate, domain=domain, a=a)\n",
    "    cell_1.assign_particle_to_cell(list_particles, list_cells, r_c, a=a)   \n",
    "    start_lc = time.time()\n",
    "    cell_1.calculate_potential_linked_cell(list_cells, list_particles)\n",
    "    end_lc = time.time()\n",
    "    linked_cell_potential = cell_1.extract_linked_cell_potential(list_particles)\n",
    "    time_linked_cell[idx] = end_lc - start_lc\n",
    "plt.plot(R, time_linked_cell, label='Linked Cell')\n",
    "plt.legend()\n",
    "plt.yscale('log')\n",
    "plt.xlabel('Cut-off radius')\n",
    "plt.ylabel('Evaluation time')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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 = 100\n",
    "R = [0.1, 0.2, 0.4, 0.5]\n",
    "n_instances = len(R)\n",
    "time_linked_cell = np.zeros(n_instances, dtype=np.float)\n",
    "a, domain = 8, 1.0\n",
    "list_particles = get_list_particles(N)\n",
    "direct_potential = cell_1.direct_potential_all_particles(list_particles)\n",
    "delta_coordinate = utils.get_successor_neighbor_delta_coordinate(a=a)\n",
    "for idx, r_c in enumerate(R):\n",
    "    cell_1.set_potential_zero(list_particles)\n",
    "    list_cells = cell_1.get_list_cell(r_c, delta_coordinate, domain=domain, a=a)\n",
    "    cell_1.assign_particle_to_cell(list_particles, list_cells, r_c, a=a)   \n",
    "    start_lc = time.time()\n",
    "    cell_1.calculate_potential_linked_cell(list_cells, list_particles)\n",
    "    end_lc = time.time()\n",
    "    linked_cell_potential = cell_1.extract_linked_cell_potential(list_particles)\n",
    "    time_linked_cell[idx] = end_lc - start_lc\n",
    "plt.plot(R, time_linked_cell, label='Linked Cell')\n",
    "plt.legend()\n",
    "plt.yscale('log')\n",
    "plt.xlabel('Cut-off radius')\n",
    "plt.ylabel('Evaluation time')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When the total number of particles is sufficiently large, potential calculations are the main \n",
    "contribution to the runtime. As the cutoff radius is increased more particles fall inside the cutoff radius hence more points are being evaluated for the potential. This increases the runtime.\n",
    "However, when the total number of particles is small, other things like cell traversal also become significant for the runtime. As we increase the cutoff radius side lengths of the cells get larger and we end up having less cells in the domain. This means there will be less time spent on traversing the cells and accessing its attributes. \n",
    "So, for a small number of particles time spent on cell traversal and time spent on potential calculation are both relevant and increasing r_c has opposite effects on these two. This is why we see a decrease in the runtime at the beginning and increase in runtime after some point. At the beginning time decrease in cell traversal is larger than time increase in potential calculation, but after some point time increase in potential calculation exceeds the other one."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us plot the Evaluation time and mean relative error with respect to variable linked list parameter $a$. We fix number of particles $N=2000$ paticles and cutoff radius $r_c=0.2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "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"
    },
    {
     "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 = 2000\n",
    "r_c = 0.2\n",
    "A = [1, 2, 4, 8]\n",
    "n_instances = len(A)\n",
    "time_linked_cell = np.zeros(n_instances, dtype=np.float)\n",
    "domain = 1.0\n",
    "list_particles = get_list_particles(N)\n",
    "direct_potential = cell_1.direct_potential_all_particles(list_particles)\n",
    "mean_relative_error = np.zeros(n_instances, dtype=np.float)\n",
    "for idx, a in enumerate(A):\n",
    "    cell_1.set_potential_zero(list_particles)\n",
    "    delta_coordinate = utils.get_successor_neighbor_delta_coordinate(a=a)\n",
    "    list_cells = cell_1.get_list_cell(r_c, delta_coordinate, domain=domain, a=a)\n",
    "    cell_1.assign_particle_to_cell(list_particles, list_cells, r_c, a=a)   \n",
    "    start_lc = time.time()\n",
    "    cell_1.calculate_potential_linked_cell(list_cells, list_particles)\n",
    "    end_lc = time.time()\n",
    "    linked_cell_potential = cell_1.extract_linked_cell_potential(list_particles)\n",
    "    time_linked_cell[idx] = end_lc - start_lc\n",
    "    mean_relative_error[idx] = utils.get_mean_relative_error(direct_potential, linked_cell_potential)\n",
    "plt.plot(A, time_linked_cell, label='Linked Cell')\n",
    "plt.legend()\n",
    "plt.yscale('log')\n",
    "plt.xlabel('Variable linked cell parameter(a)')\n",
    "plt.ylabel('Evaluation time')\n",
    "plt.show()\n",
    "plt.plot(A, mean_relative_error)\n",
    "plt.yscale('log')\n",
    "plt.xlabel('Variable linked cell parameter(a)')\n",
    "plt.ylabel('Mean_relative error')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    " Increasing parameter a decreases the side length of cells hence resulting in more cells in the domain. Because of this, the cut-off radius is now approximated better and neighbor cells now span a smaller area. This means we are now using fewer particles while evaluating the potential of a particle due to particles in neighboring cells. Thus increasing 'a' decreases the potential evaluation time.\n",
    "\n",
    "As explained above increasing 'a' results in using fewer particles for evaluating the potential of a particle due to particles in the neighbor cells. Evaluating fewer particles for potential calculation increases the difference between linked cell algorithms and direct potential calculation. Thus the mean relative error increases."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us plot the Evaluation time with respect to $a$ (same as before), but with $N=500$ particles and $r_c=0.2$. Then we do the same with $N=25$ particles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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 = 500\n",
    "r_c = 0.2\n",
    "A = [1, 2, 4, 8]\n",
    "n_instances = len(A)\n",
    "time_linked_cell = np.zeros(n_instances, dtype=np.float)\n",
    "domain = 1.0\n",
    "list_particles = get_list_particles(N)\n",
    "direct_potential = cell_1.direct_potential_all_particles(list_particles)\n",
    "for idx, a in enumerate(A):\n",
    "    cell_1.set_potential_zero(list_particles)\n",
    "    delta_coordinate = utils.get_successor_neighbor_delta_coordinate(a=a)\n",
    "    list_cells = cell_1.get_list_cell(r_c, delta_coordinate, domain=domain, a=a)\n",
    "    cell_1.assign_particle_to_cell(list_particles, list_cells, r_c, a=a)   \n",
    "    start_lc = time.time()\n",
    "    cell_1.calculate_potential_linked_cell(list_cells, list_particles)\n",
    "    end_lc = time.time()\n",
    "    linked_cell_potential = cell_1.extract_linked_cell_potential(list_particles)\n",
    "    time_linked_cell[idx] = end_lc - start_lc\n",
    "plt.plot(A, time_linked_cell, label='Linked Cell')\n",
    "plt.legend()\n",
    "plt.yscale('log')\n",
    "plt.xlabel('Variable linked cell parameter(a)')\n",
    "plt.ylabel('Evaluation time')\n",
    "plt.show()"
   ]
  },
  {
   "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 = 25\n",
    "r_c = 0.2\n",
    "A = [1, 2, 4, 8]\n",
    "n_instances = len(A)\n",
    "time_linked_cell = np.zeros(n_instances, dtype=np.float)\n",
    "domain = 1.0\n",
    "list_particles = get_list_particles(N)\n",
    "direct_potential = cell_1.direct_potential_all_particles(list_particles)\n",
    "for idx, a in enumerate(A):\n",
    "    cell_1.set_potential_zero(list_particles)\n",
    "    delta_coordinate = utils.get_successor_neighbor_delta_coordinate(a=a)\n",
    "    list_cells = cell_1.get_list_cell(r_c, delta_coordinate, domain=domain, a=a)\n",
    "    cell_1.assign_particle_to_cell(list_particles, list_cells, r_c, a=a)   \n",
    "    start_lc = time.time()\n",
    "    cell_1.calculate_potential_linked_cell(list_cells, list_particles)\n",
    "    end_lc = time.time()\n",
    "    linked_cell_potential = cell_1.extract_linked_cell_potential(list_particles)\n",
    "    time_linked_cell[idx] = end_lc - start_lc\n",
    "plt.plot(A, time_linked_cell, label='Linked Cell')\n",
    "plt.legend()\n",
    "plt.yscale('log')\n",
    "plt.xlabel('Variable linked cell parameter(a)')\n",
    "plt.ylabel('Evaluation time')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When the total number of particles is sufficiently large, the main thing that contributes to the runtime is the potential calculation. As parameter 'a' is increased, the area of the neighboring cells decreases (we approximate the cutoff radius better with large a). This means there are now fewer particles to be evaluated for potential calculation thus total runtime decreases with the increase of a.\n",
    "When the total number of particles is low, time spent on cell traversal and accessing elements also becomes significant. With the increase of 'a' total number of the cells in the domain increases hence more time is being spent for cell traversal. However, as explained above increasing 'a' decreases the time spent on potential calculation. Thus there is a competition between the decrease of time spent on potential calculation and increase of time spent on cell traversal."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Memory Access\n",
    "\n",
    "In the implementation of class __Cell_1__, we stored the indices of the particles that are inside the cell. In the computer memory those particles may not be close to each other. While calculating the potential, we access particles inside a cell one at a time. With our current implementation, our access to memory is not continuous. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Less cache misses. We load only the particles we want for a particular cell, as opposed to loading only that many particles from list_particles that fit into the cache and if we need to access some out of that range we need to reload it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One of the solutions of this is to directly store the list of particles inside the object cell instead of storing particle indices inside the cell. So, we do not need a separate variable __list_particles__. Firstly, we will create __list_cells__ in the same way as before, then create particles and directly add them to the required cell. The function that does that is already implemented inside file _cell_1.py_. Read and understand the function **create_assign_particle_to_cell**\n",
    "\n",
    "\n",
    "Open the file _cell_2.py_ and implement the functions to calculate the potential as described below:\n",
    "\n",
    "First member function of class **Cell_2** that we need to implement is __p2p_self__. This function calculates the potential on all particle inside a cell due to other particles inside the same cell. \n",
    "\n",
    "The second function is __p2p_neigbor_cells__. This function calculates the potential on all particle inside a cell due to particles in the neighor cells (cells index given by the variable neighbor_cell_index). The potential calculated is added in the variable **phi** of particle object. This function takes __list_cells__ as argument.\n",
    "\n",
    "Implement the function __calculate_potential__. This function calls the functions implemented in **5.1** and **5.2** and calculates the total potential of particles inside the cell. Parameters are same as __p2p_neigbor_cells__.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "N, r_c, a = 100, 0.2, 5\n",
    "delta_coordinate = utils.get_successor_neighbor_delta_coordinate(a=a)\n",
    "list_cells2 = cell_2.get_list_cell(r_c, delta_coordinate, domain=domain, a=a)\n",
    "cell_2.create_assign_particle_to_cell(N, list_cells2, r_c, domain=1, a=a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "direct_potential = cell_2.direct_interaction_v2(N, list_cells2)\n",
    "cell_2.calculate_linked_cell_potential(list_cells2)\n",
    "linked_cell_potential = cell_2.extract_linked_cell_potential(N, list_cells2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Evaluation time scaling\n",
    "\n",
    "Let us fix the number of particles $N = 1000$ and variable linked cell term $a = 8$. We analyse the error with respect cut-off radius and evaluation time with respect to the cut-off radius. "
   ]
  },
  {
   "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": [
    "num_particles = [np.int(100 * i) for i in range(1,11)]\n",
    "n_instances = len(num_particles)\n",
    "time_linked_cell = np.zeros(n_instances, dtype=np.float)\n",
    "time_direct = np.zeros(n_instances, dtype=np.float)\n",
    "r_c, a, domain = 0.2, 8, 1.0\n",
    "for idx, N in enumerate(num_particles):\n",
    "    delta_coordinate = utils.get_successor_neighbor_delta_coordinate(a=a)\n",
    "    list_cells2 = cell_2.get_list_cell(r_c, delta_coordinate, domain=domain, a=a)\n",
    "    cell_2.create_assign_particle_to_cell(N, list_cells2, r_c, domain=1, a=a)\n",
    "    start_lc = time.time()\n",
    "    cell_2.calculate_linked_cell_potential(list_cells2)\n",
    "    end_lc = time.time()\n",
    "    linked_cell_potential = cell_2.extract_linked_cell_potential(N, list_cells2)\n",
    "    time_linked_cell[idx] = end_lc - start_lc\n",
    "    start_direct = time.time()\n",
    "    direct_potential = cell_2.direct_interaction_v2(N, list_cells2)\n",
    "    end_direct = time.time()\n",
    "    time_direct[idx] = end_direct - start_direct\n",
    "plt.plot(num_particles, time_direct, label='Direct')\n",
    "plt.plot(num_particles, time_linked_cell, label='Linked Cell')\n",
    "plt.legend()\n",
    "plt.yscale('log')\n",
    "plt.xlabel('Number of particles')\n",
    "plt.ylabel('Evaluation time')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If particles move between cells, we have to move them from Cell A to Cell B. This requires moving the objects which is a costly operation to perform often. With the Cell_1 implementation, this could have been performed by simply changing the index in a list."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}