examples/how-to-define-grids.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How to Define Grids\n",
    "\n",
    "Numerical grids are of utmost importance for many scientific and technical applications. Consider them as discrete versions of regular coordinate systems for some domain. Accordingly, a `Grid` in *numgrids* is basically a collection of coordinate axes. For each axis, you can specify how the coordinate axis shall be discretized. Depending which type of discretization you choose, you gain access to powerful spectral methods, which allow you to work with coarse grid and have extremely high accuracy, nonetheless. All this is greatly facilitated by *numgrids*.\n",
    "\n",
    "In this notebook, let's have a look how you can define grids. As mentioned, the basic entities are coordinate axes. Let's start with those before we continue and combine axes into grids."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "from numgrids import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Defining Coordinate Axes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "For each dimension in your grid, you define an axis. Let's start with the simplest (and least powerful) discretization type: the equidistant axis. To define it on the interval [0, 1] with 10 grid points, we say: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "axis = Axis(AxisType.EQUIDISTANT, 10, 0, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "If you are working in Jupyter, you can get a visualization of the axis by simply submitting the axis in a cell:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": []
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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CAAAAFEUIAwAAUBQhDAAAQFGEMAAAAEURwgAAABRFCAMAAFAUIQwAAEBR/g9Me3SBflB5tAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 1200x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "axis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Python in zero-based, so the first point in the axis is $x_0$ and the last of the ten points is $x_9$. You can get access to the coordinates of the points on the axis by the `coords` property:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.        , 0.11111111, 0.22222222, 0.33333333, 0.44444444,\n",
       "       0.55555556, 0.66666667, 0.77777778, 0.88888889, 1.        ])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "axis.coords"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "To get a single point on the axis, you can use the shortcut"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "axis[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Note that this includes both specified endpoints like the default behavior of *numpy*'s `linspace` function. In fact, `axis.coords` is just an ordinary *numpy* array, so you can work with that as you are used to."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The equidistant axis that we have defined above, is non-periodic by default. This is a severe limitation for many applications because this means that you cannot use any modern spectral methods for this type of axis. To get the power of spectral methods, you have two choice: \n",
    "\n",
    "1. if your use case is periodic, use a periodic equidistant grid, or \n",
    "2. if your use case is non-periodic, use a non-equidistant Chebyshev grid, instead.\n",
    "\n",
    "We will have a look at both types. Start with the periodic equidistant grid, let's say from 0 to 1 with 15 grid points:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": []
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "axis = Axis(AxisType.EQUIDISTANT_PERIODIC, 15, 0, 1)\n",
    "axis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, the identification of x=0 with x=1 has effectively turned this axis into a circle. Note that the endpoint is not included, because it is redundant:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.        , 0.06666667, 0.13333333, 0.2       , 0.26666667,\n",
       "       0.33333333, 0.4       , 0.46666667, 0.53333333, 0.6       ,\n",
       "       0.66666667, 0.73333333, 0.8       , 0.86666667, 0.93333333])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "axis.coords"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But we can still say:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "axis[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9333333333333333"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "axis[14]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "axis[15]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "as should be expected."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you have a non-periodic use case, use a Chebyshev axis, instead, to get access to spectral methods:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": []
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1200x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "axis = Axis(AxisType.CHEBYSHEV, 15, 0, 1)\n",
    "axis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, the grid points are more dense near the boundary and are almost equidistant in the center. This is the feature which opens the possibility to use spectral methods with amazing accuracy, even in the non-periodic case."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, for some applications, you may want to use an axis with a logarithmic spacing. You can do this by writing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": []
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1200x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "axis = Axis(AxisType.LOGARITHMIC, 30, 1.E-3, 100)\n",
    "axis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note, that like the equidistant non-periodic axis, the logarithmic axis is also not eligible for spectral methods, so that *numgrids* has to resort to more traditional methods to work with them."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Assembling a Grid from Axes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Having defined one or more axes, you can easily assemble them to a grid. For example, let's say we have defined a Chebyshev axis,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "axis = Axis(AxisType.CHEBYSHEV, 20, 0, 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A one-dimensional grid with this axis can be created by simply calling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "grid_1d = Grid(axis)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A multidimensional grid can be created by simply throwing in more axes. For instance, in 3D we could write"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "grid_2d = Grid(axis, axis, axis)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Of course, you can pass different axes for each dimension, like"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "grid_2d = Grid(\n",
    "    Axis(AxisType.CHEBYSHEV, 20, 0, 10),\n",
    "    Axis(AxisType.EQUIDISTANT, 20, 0, 5)\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can mix axes of any type or size, if you want."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Grids in *numgrids* are of type `Grid`, which has some useful properties. For example, we can get the coordinates along all axes by calling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "x, y = grid_2d.coords"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.        ,  0.06819348,  0.27091379,  0.60263124,  1.05429745,\n",
       "        1.61359214,  2.26525921,  2.99152288,  3.77257256,  4.58710327,\n",
       "        5.41289673,  6.22742744,  7.00847712,  7.73474079,  8.38640786,\n",
       "        8.94570255,  9.39736876,  9.72908621,  9.93180652, 10.        ])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.        , 0.26315789, 0.52631579, 0.78947368, 1.05263158,\n",
       "       1.31578947, 1.57894737, 1.84210526, 2.10526316, 2.36842105,\n",
       "       2.63157895, 2.89473684, 3.15789474, 3.42105263, 3.68421053,\n",
       "       3.94736842, 4.21052632, 4.47368421, 4.73684211, 5.        ])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that these are the one-dimensional coordinate arrays for each defined axis. For a multidimensional grid, `grid.coords` returns a tuple of arrays. For a one-dimensional grid, it just returns the one coordinate array.\n",
    "\n",
    "If you want to work on the grid, it is usually more comfortable to work with meshed coordinates:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, Y = grid_2d.meshed_coords"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(20, 20)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(20, 20)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This allows you to evaluate functions of the grid, like"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "f = np.sin(X) * np.cos(Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(20, 20)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also visualize the grid in Jupyter. Just submit the grid in a cell:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": []
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "grid_2d"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, we have Chebyshev spacing along the 0-axis and equidistant spacing along the 1-axis. Just as defined."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.6"
  },
  "varInspector": {
   "cols": {
    "lenName": 16,
    "lenType": 16,
    "lenVar": 40
   },
   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
    },
    "r": {
     "delete_cmd_postfix": ") ",
     "delete_cmd_prefix": "rm(",
     "library": "var_list.r",
     "varRefreshCmd": "cat(var_dic_list()) "
    }
   },
   "types_to_exclude": [
    "module",
    "function",
    "builtin_function_or_method",
    "instance",
    "_Feature"
   ],
   "window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}