gradient.ipynb

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    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt \n",
    "from mpl_toolkits.mplot3d import axes3d\n",
    "import matplotlib.cm as cm\n",
    "from IPython.display import display, Math, clear_output\n",
    "\n",
    "import sympy  #Sympy1.2 is from conda-forge: [sudo conda install -c conda-forge sympy]\n",
    "from sympy import *\n",
    "from sympy.physics.vector import ReferenceFrame, CoordinateSym\n",
    "from sympy.vector import CoordSys3D, divergence, curl\n",
    "\n",
    "import ipyvolume as ipv\n",
    "import time\n",
    "from ipywidgets import Output\n",
    "\n",
    "import helpers\n",
    "\n",
    "np.seterr(divide='ignore', invalid='ignore');"
   ]
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   "source": [
    "## Symbolic Calculation of the Gradient "
   ]
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     "text": [
      "Gradient of: x**2\n",
      "[2*x, 0, 0]\n",
      "(3,)\n",
      "(41, 41, 41), (41, 41, 41), (41, 41, 41)\n",
      "(41, 41, 41)\n",
      "[2, 0, 0]\n",
      "2\n"
     ]
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    "#define symbolic vars, function\n",
    "x,y,z =sympy.symbols('x y z')\n",
    "fun = x**2\n",
    "\n",
    "# evaluate the gradient symbolically\n",
    "gradfun = [sympy.diff(fun, var) for var in (x,y,z)]\n",
    "print('Gradient of: {}'.format(fun))\n",
    "print(gradfun)\n",
    "print(np.shape(gradfun))\n",
    "\n",
    "#turn into a bivariate lambda for numpy\n",
    "numgradfun = sympy.lambdify([x,y,z], gradfun)\n",
    "\n",
    "x = np.linspace(-10, 10, 41)\n",
    "y = np.linspace(-10, 10, 41)\n",
    "z = np.linspace(-10, 10, 41)\n",
    "X, Y, Z = np.meshgrid(x,y,z, indexing='ij')\n",
    "\n",
    "gradient_eval = sum(numgradfun(X, Y, Z))\n",
    "\n",
    "print('{}, {}, {}'.format(np.shape(X),np.shape(Y),np.shape(Z)))\n",
    "print(np.shape(gradient_eval))\n",
    "print(numgradfun(1,1,2))\n",
    "print(sum(numgradfun(1,1,2)))\n",
    "ipv.figure()\n",
    "ipv.volshow(gradient_eval.T, opacity=0.03, level_width=0.1, data_min=0, data_max=1)\n",
    "ipv.view(azimuth = 115, elevation = 90)\n",
    "ipv.show()"
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