jupyter/HW1-VectorFieldsProblem.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Python numeric and plotting libraries\n",
    "\n",
    "The `numpy` library makes a number of useful functions available to you. Functions that can create a list of numbers, generate a matrix of numbers, and perform some more sophisticated calculations. Using the `matplotlib` library, we can start making plots of many styles. We will use both of these libraries a lot in this class. In this computational problem, you will use functions from these libraries to plot vector fields. As before, this notebook will go through a complete example, which you can use to solve your problems.\n",
    "\n",
    "### [Skip to problem to solve](./HW1-VectorFieldsProblem.ipynb#Problems-to-solve)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Getting started with `numpy` and `matplotlib`\n",
    "As we have done already, we will start by importing both libraries into the notebook. In this case, we use a different way of importing the libraries, which names the libraries with some shorthand (i.e., `np` and `plt`). Importing the libraries this way is helpful because sometimes the same function and/or method name appear in the base Python or other libraries you might using, which can cause a conflict as the function or method from the other library or the Python base might not do the exact same thing as the one you want. It is good practice to do this for `numpy` and `matplotlib`. \n",
    "\n",
    "Below, we import both libraries and tell `matplotlib` to use a plot style, which just makes the plots nicer looking (i.e., easier to read). We also make sure that matplotlib will produce the plots inline (i.e., in the notebook) rather than as a separate figure by calling `%matplotlib inline` ."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np                # imports the numerical library\n",
    "import matplotlib.pyplot as plt   # imports the plotting library\n",
    "plt.style.use('ggplot')  # sets up pretty plots\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Creating a vector field\n",
    "In this example, we intend to plot the vector field $\\vec{v}(x,y) = y\\hat{x}$, which should be a field where all the vector point along x-axis (or along the negative x-axis below y=0) and increase their magnitude as we move vertically away from the origin. *Do you see why?*\n",
    "\n",
    "### Creating a set of points for the x-y plane\n",
    "To do this, we must first construct set of points that describes the x-y plane, that is, we to make this plot, Python needs to know that we have a bunch of points across the x-y plane for which we intend to place vectors. The canonical way that this is done is using the `arange` and `meshgrid` methods of `numpy`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using `np.arange`\n",
    "\n",
    "For our purposes, the `arange` method will produce a list of numbers. It will start and end where we specify with whatever spacing we choose. As an example, we can produce a list from 1 through 10 by ones, from -1 to 1 in steps of 0.1, or anything else we choose. This method is really helpful for making a quick array of numbers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "One through Ten by Ones [ 1  2  3  4  5  6  7  8  9 10]\n",
      "Minus One to Plus One [-1.00000000e+00 -9.00000000e-01 -8.00000000e-01 -7.00000000e-01\n",
      " -6.00000000e-01 -5.00000000e-01 -4.00000000e-01 -3.00000000e-01\n",
      " -2.00000000e-01 -1.00000000e-01 -2.22044605e-16  1.00000000e-01\n",
      "  2.00000000e-01  3.00000000e-01  4.00000000e-01  5.00000000e-01\n",
      "  6.00000000e-01  7.00000000e-01  8.00000000e-01  9.00000000e-01\n",
      "  1.00000000e+00]\n"
     ]
    }
   ],
   "source": [
    "one_through_ten = np.arange(1,11,1)                        # Notice that 11 is the stop point\n",
    "print('One through Ten by Ones', one_through_ten)\n",
    "minus_one_to_plus_one = np.arange(-1,1.1,0.1)              # Notice that 1.1 is the stop point\n",
    "print('Minus One to Plus One', minus_one_to_plus_one)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using np.meshgrid\n",
    "\n",
    "As we will use it `meshgrid` creates a mesh - a set points on the x-y plane - where we can plot vectors. In a sense, it provides all the coorindates across the x-y plane that we want to specify. It does this by taking two linear arrays - lists of numbers - and producing two 2D arrays - think matrix - that contain repeated versions of each array.\n",
    "\n",
    "Consider the example below, where we use two arrays `a` and `b` that contain all the numbers from -2 to 2 by ones. `meshgrid` takes those two arrays as arguments and produces two 2D arrays `A` and `B`, which are repeated versions of `a` (`A` does this by row) and `b` (`B` does this by column) respectively.\n",
    "\n",
    "By combining `A` and `B`, we have a mesh that describes every *unit* point on the x-y plane in the box that is bounded by -2 and +2 in both x and y. \n",
    "\n",
    "*To see this, think about taking each cell in the matrix `A` and combining with its partner in `B` as an order pair.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A =  [[-2 -1  0  1  2]\n",
      " [-2 -1  0  1  2]\n",
      " [-2 -1  0  1  2]\n",
      " [-2 -1  0  1  2]\n",
      " [-2 -1  0  1  2]]\n",
      "B =  [[-2 -2 -2 -2 -2]\n",
      " [-1 -1 -1 -1 -1]\n",
      " [ 0  0  0  0  0]\n",
      " [ 1  1  1  1  1]\n",
      " [ 2  2  2  2  2]]\n"
     ]
    }
   ],
   "source": [
    "a = np.arange(-2,3,1)\n",
    "b = np.arange(-2,3,1)\n",
    "A, B = np.meshgrid(a,b)\n",
    "print('A = ', A)\n",
    "print('B = ', B)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Creating a vector function\n",
    "Now that we have a list of all the points in the x-y plane, we can construct a vector function. `meshgrid` produces the points for us, but those points need to be used to calclate the vector function of our choosing. In our case, we intend to use the vector function $\\vec{v}(x,y,z) = y\\hat{x}$ as our example function. \n",
    "\n",
    "We start by first preparing a mesh the describes all the points in the x-y plane from -5 to 5 in steps of 0.5. *This choice was arbitrary, but gives a decent visualization.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.arange(-5,6,0.5)\n",
    "y = np.arange(-5,6,0.5)\n",
    "X, Y = np.meshgrid(x,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To form the function that we want, we will describe it by its components ($v_x$ and $v_y$). From the above function we know that,\n",
    "\n",
    "$$v_x = y$$\n",
    "$$v_y = 0$$\n",
    "\n",
    "Because `X` and `Y` describe the points on the mesh, we will use them to perform our calculation of the vector field."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "vx = Y\n",
    "vy = 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting a vector function with `matplotlib`\n",
    "Until now, we have only used methods from the `numpy` library to perform the necessary mathematical calculations to construct the vector field. To visualize it, we will use the `quiver` method from the `matplotlib.pyplot` library.\n",
    "\n",
    "Quiver diagrams need 4 arguments:\n",
    "* The location of the points to plot the vectors (x-y plane points), which form 2 of the arguments, and\n",
    "* The size a direction of the vectors to plot at those points (the components of the vectors), which form the other two arguments\n",
    "\n",
    "We have all these arguments (`X` and `Y` are mesh points and `vx` and `vy` provide the components). We can now plot the field. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-5, 5)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,8))          # creates the figure object; used when you need a figure (8,8) is just a nice size\n",
    "plt.quiver(X,Y,vx,vy)              # The call to quiver actually generates the plot\n",
    "plt.xlim([-5, 5])                  # Sets the limits of the plot (not needed as Jupyter will autoscale)\n",
    "plt.ylim([-5, 5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problems to solve\n",
    "Now that you have seen an example of making a plot of a vector field using `quiver`, make similar plots for the following fields. Make sure you comment on possible physical situtations from which they might stem.\n",
    "\n",
    "1. \\\\(\\vec{v}(x,y)=r\\hat{r}\\\\) (where \\\\(\\vec{r}\\\\) refers to the usual \\\\(\\vec{r}\\\\)in spherical coordinates.)\n",
    "2. \\\\(\\vec{v}(x,y) = \\dfrac{x}{(\\sqrt{x^2+y^2})^3}\\hat{x}+\\dfrac{y}{(\\sqrt{x^2+y^2})^3}\\hat{y}\\\\)\n",
    "3. \\\\(\\vec{v}(x,y) = \\hat{\\phi}\\\\) (where \\\\(\\\\phi\\\\) is the usual plane-polar coordinate.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}