A simple Jupyter notebook for visualizing scalar-valued functions of two variables.

Plotting multivariate functions.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plotting multivariate functions $\\rightarrow f(x,y) = z$\n",
    "\n",
    "### Step 1: Import libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib notebook\n",
    "import numpy as np\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from matplotlib import cm, colors\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 2: Define functions\n",
    "\n",
    "Both $f: \\mathbb{R}^2 \\rightarrow \\mathbb{R}$\n",
    "\n",
    "$f_1(x,y) = x^2 - y^2$\n",
    "\n",
    "$f_2(x,y) = 1 - (x^2 + y^2)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "f_1 = lambda x,y: x ** 2 - y ** 2\n",
    "f_2 = lambda x,y: 1 - (x ** 2 + y ** 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 3: Create sample inputs and get outputs\n",
    "\n",
    "$x,y \\in [-1, 1]$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.arange(-1, 1, 0.025)\n",
    "y = np.arange(-1, 1, 0.025)\n",
    "X, Y = np.meshgrid(x, y)\n",
    "\n",
    "Z = f_1(X, Y)\n",
    "W = f_2(X, Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 4: Plot the surfaces"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "# Create colors from normalized output range\n",
    "norm = colors.Normalize(Z.min(), Z.max())\n",
    "z_color = cm.jet(norm(Z))\n",
    "norm_2 = colors.Normalize(W.min(), W.max())\n",
    "w_color = cm.jet(norm_2(W))\n",
    "\n",
    "# Create a figure with enough space for 2 rows\n",
    "fig = plt.figure(figsize=(8, 12))\n",
    "\n",
    "# plot f_1 on first row\n",
    "ax = fig.add_subplot(2,1,1,projection='3d')\n",
    "ax.plot_surface(X, Y, Z,\n",
    "                    rstride=1, cstride=1, alpha=1, facecolors=z_color)\n",
    "\n",
    "# plot f_2 on second row\n",
    "ax_imag = fig.add_subplot(2,1,2,projection='3d')\n",
    "ax_imag.plot_surface(X, Y, W,\n",
    "                    rstride=1, cstride=1, alpha=0.5, facecolors=w_color)\n",
    "\n",
    "plt.savefig('sample.png', transparent=True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exporting & Importing Figures using pickle "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Save object as pickle\n",
    "import pickle\n",
    "pickle.dump(fig, open('FigureObject.fig.pickle', 'wb')) # This is for Python 3 - py2 may need `file` instead of `open`\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Read figure from pickle\n",
    "\n",
    "import pickle\n",
    "figx = pickle.load(open('FigureObject.fig.pickle', 'rb'))\n",
    "\n",
    "figx.show()\n",
    "\n",
    "# Can also view data\n",
    "data = figx.axes[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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Sample figure of two plots created with this notebook: