{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "92b5fa74",
   "metadata": {},
   "source": [
    "# Derivatives\n",
    "\n",
    " Börge Göbel, Jan 2022"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0711bcd",
   "metadata": {},
   "source": [
    "## 1. Mathematical definition of a derivative"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4875d43e",
   "metadata": {},
   "source": [
    "![Derivative](figure_04_derivatives.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ad10ced",
   "metadata": {},
   "source": [
    "\\\\( f'(x)=\\lim_{h\\rightarrow 0}\\frac{f(x+h)-f(x)}{h}\\\\)\n",
    "\n",
    "\\\\( f'(x)=\\lim_{h\\rightarrow 0}\\frac{f(x)-f(x-h)}{h}\\\\)\n",
    "\n",
    "\\\\( f'(x)=\\lim_{h\\rightarrow 0}\\frac{f(x+h)-f(x-h)}{2h}\\\\)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f91acf34",
   "metadata": {},
   "source": [
    "All three definitions are equivalent in case of a continuous function."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f64d0ed",
   "metadata": {},
   "source": [
    "## 2. Numerical implementation of first-order derivatives"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8d1a296b",
   "metadata": {},
   "source": [
    "Forward differences\n",
    "\\\\( f'(x_n)\\approx\\frac{f(x_{n+1})-f(x_n)}{x_{n+1}-x_n}\\\\)\n",
    "\n",
    "Backward differences\n",
    "\\\\( f'(x)\\approx\\frac{f(x_n)-f(x_{n-1})}{x_n-x_{n-1}}\\\\)\n",
    "\n",
    "Central differences\n",
    "\\\\( f'(x)\\approx\\frac{f(x_{n+1})-f(x_{n-1})}{x_{n+1}-x_{n-1}}\\\\)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f6c934ba",
   "metadata": {},
   "source": [
    "### Example function: \\\\( f(x)=\\sin(x)x-\\frac{1}{100}x^3 \\\\)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d336e105",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "db71be64",
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return np.sin(x)*x - 1/100*x**3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "902a8e36",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x124dbf3d340>]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "x_list = np.linspace(-10, 10, 201)\n",
    "y_list = f(x_list)\n",
    "\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "plt.plot(x_list, y_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c9a33631",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x124dc05f640>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "x_list = np.linspace(-10, 10, 201)\n",
    "analytical_d_list = np.cos(x_list)*x_list + np.sin(x_list) - 3/100*x_list**2\n",
    "\n",
    "h = 0.1\n",
    "forward_d_list = ( f(x_list+h) - f(x_list) ) / h\n",
    "backward_d_list = ( f(x_list) - f(x_list-h) ) / h\n",
    "central_d_list = ( f(x_list+h) - f(x_list-h) ) / (2*h)\n",
    "\n",
    "plt.xlabel('x')\n",
    "plt.ylabel(\"f'(x)\")\n",
    "plt.plot(x_list, analytical_d_list)\n",
    "plt.plot(x_list, forward_d_list)\n",
    "plt.plot(x_list, backward_d_list)\n",
    "plt.plot(x_list, central_d_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "fce303f1",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x124dc0d5fa0>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "plt.xlabel('x')\n",
    "plt.ylabel(\"Error of f'(x)\")\n",
    "\n",
    "plt.plot(x_list, analytical_d_list - forward_d_list, 'red')\n",
    "plt.plot(x_list, analytical_d_list - backward_d_list, 'blue')\n",
    "plt.plot(x_list, analytical_d_list - central_d_list, 'green')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51dcb403",
   "metadata": {},
   "source": [
    "### Why is central differences (typically) better than forward and backward differences?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "186b1b11",
   "metadata": {},
   "source": [
    "Forward differences\n",
    "\\\\( f'(x)=\\frac{f(x+h)-f(x)}{h}+\\mathcal{O}(h)\\\\)\n",
    "\n",
    "Backward differences\n",
    "\\\\( f'(x)=\\frac{f(x)-f(x-h)}{h}+\\mathcal{O}(h)\\\\)\n",
    "\n",
    "Central differences\n",
    "\\\\( f'(x)=\\frac{f(x+h)-f(x-h)}{2h}+\\mathcal{O}(h^2)\\\\)\n",
    "\n",
    "- \\\\(\\mathcal{O}(h^n)\\\\) means that the error is proportional to h^n.\n",
    "- Since \\\\(h\\\\) is small, the central differences method is more accurate. Why?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f0b27259",
   "metadata": {},
   "source": [
    "Taylor expansion: \n",
    "\n",
    "\\\\(f(x+h)=f(x)+f'(x)h+\\frac{1}{2}f''(x)h^2+\\frac{1}{6}f'''(x)h^3+\\dots\\\\)\n",
    "\n",
    "\\\\(f(x-h)=f(x)-f'(x)h+\\frac{1}{2}f''(x)h^2-\\frac{1}{6}f'''(x)h^3\\pm\\dots\\\\)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e9eadb72",
   "metadata": {},
   "source": [
    "- From the first and second line we can imediately see the  \\\\(\\mathcal{O}(h)\\\\) dependence of the forward and backward differences methods"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f04d750",
   "metadata": {},
   "source": [
    "\\\\(f'(x)=\\frac{1}{h}\\left[f(x+h)-f(x)-\\frac{1}{2}f''(x)h^2-\\frac{1}{6}f'''(x)h^3+\\dots\\right]=\\frac{f(x+h)-f(x)}{h}-\\frac{1}{2}f''(x)h-\\frac{1}{6}f'''(x)h^2+\\dots\\\\)\n",
    "\n",
    "\\\\(f'(x)=\\frac{1}{h}\\left[f(x)-f(x-h)+\\frac{1}{2}f''(x)h^2-\\frac{1}{6}f'''(x)h^3\\pm\\dots\\right]=\\frac{f(x)-f(x-h)}{h}+\\frac{1}{2}f''(x)h-\\frac{1}{6}f'''(x)h^2\\pm\\dots\\\\)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d2cfa98f",
   "metadata": {},
   "source": [
    "- To find the \\\\(\\mathcal{O}(h^2)\\\\) dependence of the central differences method, we have to subtract the two terms"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "547ef3fd",
   "metadata": {},
   "source": [
    "\\\\(f(x+h)-f(x-h)=2f'(x)h+\\frac{1}{3}f'''(x)h^3+\\dots\\\\)\n",
    "\n",
    "\\\\(\\frac{1}{2h}\\left[f(x+h)-f(x-h)\\right]=f'(x)+\\frac{1}{6}f'''(x)h^2+\\dots\\\\)\n",
    "\n",
    "\\\\( f'(x)=\\frac{f(x+h)-f(x-h)}{2h}+\\mathcal{O}(h^2)\\\\)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2c7bd5d2",
   "metadata": {},
   "source": [
    "### Higher accuracy:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d8548fd7",
   "metadata": {},
   "source": [
    "Richardson: \\\\(f'(x)=\\frac{1}{12h}\\left[f(x-2h)-8f(x-h)+8f(x+h)-f(x+2h)\\right]+\\mathcal{O}(h^4)\\\\)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "a4c9a19b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def D1Richardson(f, x, h):\n",
    "    # f: Function\n",
    "    # x: Argument of f\n",
    "    # h: Stepsize\n",
    "    return 1/(12*h) * ( f(x-2*h) - 8*f(x-h) + 8*f(x+h) - f(x+2*h) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "04616d9b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x124dc149ac0>]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "plt.xlabel('x')\n",
    "plt.ylabel(\"Error of f'(x)\")\n",
    "\n",
    "richardson_d_list = D1Richardson(f, x_list, h)\n",
    "\n",
    "#plt.plot(x_list, analytical_d_list - forward_d_list, 'red')\n",
    "#plt.plot(x_list, analytical_d_list - backward_d_list, 'blue')\n",
    "plt.plot(x_list, analytical_d_list - central_d_list, 'green')\n",
    "plt.plot(x_list, analytical_d_list - richardson_d_list, 'black')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b57d06c",
   "metadata": {},
   "source": [
    "### Even higher accuracy"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01d07a1a",
   "metadata": {},
   "source": [
    "Iteration formula:\n",
    "\n",
    "\\\\(D_{n+1}=\\frac{2^{2n}D_n(h)-D_n(2h)}{2^{2n}-1}\\\\)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "310265c4",
   "metadata": {},
   "outputs": [],
   "source": [
    "def D1nRichardson(nmax, f, x, h):\n",
    "    # nmax: Order of iteration for 1st derivative\n",
    "    # f: Function\n",
    "    # x: Argument of f\n",
    "    # h: Stepsize\n",
    "    #d0 = np.array([ D1Richardson(f, x, h*2**j) for j in range(0,n)])\n",
    "    d0 = np.array([ 1/(12*h*2**j) * ( f(x-2*h*2**j) - 8*f(x-h*2**j) + 8*f(x+h*2**j) - f(x+2*h*2**j) ) for j in range(0,nmax)])\n",
    "    for n in range(1,nmax):\n",
    "        print(d0)\n",
    "        d = np.array([(2**(2*n)*d0[j] - d0[j+1]) / (2**(2*n)-1) for j in range(0,len(d0)-1)])\n",
    "        d0 = d\n",
    "    return d"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "480468c9",
   "metadata": {},
   "source": [
    "Calculate f'(x) for \\\\( f(x)=\\sin(x)x-\\frac{1}{100}x^3 \\\\) at \\\\(x = 3\\\\)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "6d2c30e1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-3.09884994 -3.09873722 -3.09695717 -3.06993837 -2.72051967]\n",
      "[-3.09888752 -3.09933057 -3.10596344 -3.18641127]\n",
      "[-3.09885798 -3.09888837 -3.10060025]\n",
      "[-3.0988575 -3.0988612]\n"
     ]
    }
   ],
   "source": [
    "d1n = D1nRichardson(5, f, 3, h)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c21fa72e",
   "metadata": {},
   "source": [
    "Comparison to D1Richardson"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "17d25aef",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-3.0988499416783317\n",
      "-3.098737217338038\n",
      "-3.0969571739647574\n",
      "-3.0699383701235057\n",
      "-2.7205196742684765\n"
     ]
    }
   ],
   "source": [
    "print(D1Richardson(f, 3, h))\n",
    "print(D1Richardson(f, 3, 2*h))\n",
    "print(D1Richardson(f, 3, 4*h))\n",
    "print(D1Richardson(f, 3, 8*h))\n",
    "print(D1Richardson(f, 3, 16*h))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8eee3925",
   "metadata": {},
   "source": [
    "Analytical result: \\\\( f'(3)=3\\cos(3)+\\sin(3)-\\frac{3}{100}\\cdot 3^2 \\\\)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "469b513b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-3.098857481741469"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "3*np.cos(3) + np.sin(3) - 3/100*3**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "f1bfd614",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.18064047e-09])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "3*np.cos(3) + np.sin(3) - 3/100*3**2 - d1n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89a93179",
   "metadata": {},
   "source": [
    "## 3. Second derivatives"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eaa2c1de",
   "metadata": {},
   "source": [
    "We derive \\\\(f'(x)\\\\) another time"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "048cdc0b",
   "metadata": {},
   "source": [
    "\\\\( f''(x)=\\lim_{h\\rightarrow 0}\\frac{f'(x+h)-f'(x)}{h}\\\\)\n",
    "\n",
    "\\\\( f''(x)=\\lim_{h\\rightarrow 0}\\frac{f'(x)-f'(x-h)}{h}\\\\)\n",
    "\n",
    "\\\\( f''(x)=\\lim_{h\\rightarrow 0}\\frac{f'(x+h)-f'(x-h)}{2h}\\\\)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "818a0d68",
   "metadata": {},
   "source": [
    "This gives us many possibilities for the definition of \\\\(f''(x)\\\\) based on \\\\(f(x)\\\\), e. g."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30c84d6c",
   "metadata": {},
   "source": [
    "- Double forward & double backward\n",
    "\n",
    "\\\\(f''(x)=\\lim_{h\\rightarrow 0}\\frac{\\left[f(x+2h)-f(x+h)\\right]-\\left[f(x+h)-f(x)\\right]}{h^2}=\\lim_{h\\rightarrow 0}\\frac{f(x+2h)-2f(x+h)+f(x)}{h^2}\\\\)\n",
    "\n",
    "\\\\(f''(x)=\\lim_{h\\rightarrow 0}\\frac{\\left[f(x)-f(x-h)\\right]-\\left[f(x-h)-f(x-2h)\\right]}{h^2}=\\lim_{h\\rightarrow 0}\\frac{f(x)-2f(x-h)+f(x-2h)}{h^2}\\\\)\n",
    "\n",
    "- Forward and backward\n",
    "\n",
    "\\\\(f''(x)=\\lim_{h\\rightarrow 0}\\frac{\\left[f(x+h)-f(x)\\right]-\\left[f(x)-f(x-h)\\right]}{h^2}=\\lim_{h\\rightarrow 0}\\frac{f(x+h)-2f(x)+f(x-h)}{h^2}\\\\)\n",
    "\n",
    "- Double central (same result as forward and backward for \\\\(2h=g\\\\))\n",
    "\n",
    "\\\\(f''(x)=\\lim_{h\\rightarrow 0}\\frac{\\left[f(x+2h)-f(x)\\right]-\\left[f(x)-f(x-2h)\\right]}{(2h)^2}=\\lim_{h\\rightarrow 0}\\frac{f(x+2h)-2f(x)+f(x-2h)}{4h^2}=\\lim_{g\\rightarrow 0}\\frac{f(x+g)-2f(x)+f(x-g)}{g^2}\\\\)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "2fe1145c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x124dc1d9a00>]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "x_list = np.linspace(-10, 10, 201)\n",
    "#analytical_d_list = np.cos(x_list)*x_list + np.sin(x_list) - 3/100*x_list**2\n",
    "analytical_d2_list = -np.sin(x_list)*x_list + 2*np.cos(x_list) - 6/100*x_list\n",
    "\n",
    "h = 0.1\n",
    "forward_d2_list = ( f(x_list+2*h) - 2*f(x_list+h) + f(x_list) ) / h**2\n",
    "backward_d2_list = ( f(x_list) - 2*f(x_list-h) + f(x_list-2*h) ) / h**2\n",
    "central_d2_list = ( f(x_list+h) - 2*f(x_list) + f(x_list-h) ) / h**2\n",
    "\n",
    "plt.xlabel('x')\n",
    "plt.ylabel(\"f''(x)\")\n",
    "plt.plot(x_list, analytical_d2_list)\n",
    "plt.plot(x_list, forward_d2_list)\n",
    "plt.plot(x_list, backward_d2_list)\n",
    "plt.plot(x_list, central_d2_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "5900ae0c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x124dc2551f0>]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "plt.xlabel('x')\n",
    "plt.ylabel(\"Error f''(x)\")\n",
    "\n",
    "plt.plot(x_list, analytical_d2_list - forward_d2_list, 'red')\n",
    "plt.plot(x_list, analytical_d2_list - backward_d2_list, 'blue')\n",
    "plt.plot(x_list, analytical_d2_list - central_d2_list, 'green')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "389a0ca6",
   "metadata": {},
   "source": [
    "### Higher accuracy:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7fc006fd",
   "metadata": {},
   "source": [
    "Richardson: \\\\(f''(x)=\\frac{1}{12h^2}\\left[-f(x-2h)+16f(x-h)-30f(x)+16f(x+h)-f(x+2h)\\right]+\\mathcal{O}(h^4)\\\\)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "00cb7a9a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def D2Richardson(f, x, h):\n",
    "    # f: Function\n",
    "    # x: Argument of f\n",
    "    # h: Stepsize\n",
    "    return 1/(12*h**2) * ( -f(x-2*h) + 16*f(x-h) - 30*f(x) + 16*f(x+h) - f(x+2*h) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "3d380fc2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x124dc2b9bb0>]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "plt.xlabel('x')\n",
    "plt.ylabel(\"Error of f''(x)\")\n",
    "\n",
    "richardson_d2_list = D2Richardson(f, x_list, h)\n",
    "\n",
    "#plt.plot(x_list, analytical_d2_list - forward_d2_list, 'red')\n",
    "#plt.plot(x_list, analytical_d2_list - backward_d2_list, 'blue')\n",
    "plt.plot(x_list, analytical_d2_list - central_d2_list, 'green')\n",
    "plt.plot(x_list, analytical_d2_list - richardson_d2_list, 'black')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "58915d60",
   "metadata": {},
   "source": [
    "## 4. Gradient, Divergence & Curl"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4be6e5bd",
   "metadata": {},
   "source": [
    "Now we consider a multidimensional function which means, the function depends on multiple variables \n",
    "\n",
    "\\\\( f(x,y,z)\\\\)\n",
    "\n",
    "or it is a function that has multiple dimensions itself\n",
    "\n",
    "\\\\( \\vec{g}(x,y,z)=\\begin{pmatrix}g_x(x,y,z)\\\\g_y(x,y,z)\\\\g_z(x,y,z)\\end{pmatrix}\\\\)\n",
    "\n",
    "With the nabla operator \\\\( \\nabla = \\begin{pmatrix}\\frac{\\partial}{\\partial x}\\\\\\frac{\\partial}{\\partial y}\\\\\\frac{\\partial}{\\partial z}\\end{pmatrix}\\\\) we can calculate:\n",
    "\n",
    "- gradient \\\\( \\nabla f(x,y,z) = \\begin{pmatrix}\\frac{\\partial}{\\partial x}f(x,y,z)\\\\\\frac{\\partial}{\\partial y}f(x,y,z)\\\\\\frac{\\partial}{\\partial z}f(x,y,z)\\end{pmatrix}\\\\)\n",
    "\n",
    "- curl \\\\(\\nabla\\times \\vec{g}(x,y,z) = \\begin{pmatrix}\n",
    "\\frac{\\partial}{\\partial y}g_z(x,y,z) - \\frac{\\partial}{\\partial z}g_y(x,y,z)\\\\\n",
    "\\frac{\\partial}{\\partial z}g_x(x,y,z) - \\frac{\\partial}{\\partial x}g_z(x,y,z)\\\\\n",
    "\\frac{\\partial}{\\partial x}g_y(x,y,z) - \\frac{\\partial}{\\partial y}g_x(x,y,z)\\\\\n",
    "\\end{pmatrix}\\\\)\n",
    "\n",
    "- divergence \\\\(\\nabla\\cdot \\vec{g}(x,y,z) = \\frac{\\partial}{\\partial x}g_x(x,y,z)+\\frac{\\partial}{\\partial y}g_y(x,y,z)+\\frac{\\partial}{\\partial z}g_z(x,y,z)\\\\)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "05ce081d",
   "metadata": {},
   "source": [
    "### Example \n",
    "\n",
    "\\\\(\n",
    "f(\\vec{r})=f(x,y,z) = \\exp(-x^2-y^4)\n",
    "\\\\)\n",
    "\n",
    "\\\\(\n",
    "\\vec{g}(\\vec{r})=\\frac{\\vec{r}}{r}=\\begin{pmatrix}x/\\sqrt{x^2+y^2+z^2}\\\\y/\\sqrt{x^2+y^2+z^2}\\\\z/\\sqrt{x^2+y^2+z^2}\\end{pmatrix}\n",
    "\\\\)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "aa0547a7",
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(r):\n",
    "    return np.exp(-r[0]**2-r[1]**4)\n",
    "\n",
    "def g(r):\n",
    "    return r / np.linalg.norm(r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "b9ac0997",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.contour.QuadContourSet at 0x124dc17a5e0>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "x3, y3 = np.meshgrid(np.linspace(-2,2,201),np.linspace(-2,2,201))\n",
    "z3 = f( np.array([ x3, y3 ]) )\n",
    "\n",
    "plotproj = plt.axes(projection='3d')\n",
    "plotproj.contour3D(x3,y3,z3,100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "6a508d9f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Change standard size of all figures in this notebook\n",
    "plt.rcParams['figure.figsize'] = [15, 10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "37e7ac50",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<mpl_toolkits.mplot3d.art3d.Line3DCollection at 0x124dd9e0220>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x3, y3, z3 = np.meshgrid(np.linspace(-2,2,11),np.linspace(-2,2,11),np.linspace(-2,2,11))\n",
    "values = g( np.array([ x3, y3, z3 ]) )\n",
    "\n",
    "arrowplot = plt.axes(projection='3d')\n",
    "arrowplot.axis(False)\n",
    "\n",
    "scale=7\n",
    "arrowplot.quiver(\n",
    "    x3, y3, z3,\n",
    "    values[0]*scale,values[1]*scale,values[2]*scale\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a13581a0",
   "metadata": {},
   "source": [
    "### Gradient"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "7aff834f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient(f,r,h):\n",
    "    x,y,z = r\n",
    "    partialx = ( f(np.array([x+h,y,z])) - f(np.array([x-h,y,z]))) / (2*h)\n",
    "    partialy = ( f(np.array([x,y+h,z])) - f(np.array([x,y-h,z]))) / (2*h)\n",
    "    partialz = ( f(np.array([x,y,z+h])) - f(np.array([x,y,z-h]))) / (2*h)\n",
    "    return np.array([ partialx, partialy, partialz ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "fb87e8d4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.09792044,  0.67682606,  0.        ])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r = np.array([0.5,-1.2,-8])\n",
    "h = 0.0001\n",
    "\n",
    "gradient(f,r,h)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "32664a8b",
   "metadata": {},
   "source": [
    "- analytical solution \n",
    "\n",
    "\\\\( \\nabla f(x,y,z) = \\begin{pmatrix}-2x\\exp(-x^2-y^4)\\\\-4y^3\\exp(-x^2-y^4)\\\\0\\end{pmatrix} \\\\)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "d7624dd3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.09792044,  0.67682606,  0.        ])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array([\n",
    "    -2*r[0] * np.exp( -r[0]**2 -r[1]**4 ),\n",
    "    -4*r[1]**3 * np.exp( -r[0]**2 -r[1]**4 ),\n",
    "    0\n",
    "])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ee77dda",
   "metadata": {},
   "source": [
    "### Divergence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "c7075978",
   "metadata": {},
   "outputs": [],
   "source": [
    "def divergence(g,r,h):\n",
    "    x,y,z = r\n",
    "    dgxdx = ( g(np.array([x+h,y,z]))[0] - g(np.array([x-h,y,z]))[0] ) / (2*h)\n",
    "    dgydy = ( g(np.array([x,y+h,z]))[1] - g(np.array([x,y-h,z]))[1] ) / (2*h)\n",
    "    dgzdz = ( g(np.array([x,y,z+h]))[2] - g(np.array([x,y,z-h]))[2] ) / (2*h)\n",
    "    return dgxdx + dgydy + dgzdz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "59cd9456",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.24676318364020428"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "divergence(g,r,h)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6cba35cf",
   "metadata": {},
   "source": [
    "- analytical solution \n",
    "\n",
    "\\\\( \\nabla \\cdot \\vec{g}(\\vec{r}) = \\frac{2}{r} \\\\)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "031d1eac",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.24676318365598574"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2 / np.linalg.norm(r)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44ad4c4d",
   "metadata": {},
   "source": [
    "### Curl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "41d1c7fa",
   "metadata": {},
   "outputs": [],
   "source": [
    "def curl(g,r,h):\n",
    "    x,y,z = r\n",
    "    dgxdy = ( g(np.array([x,y+h,z]))[0] - g(np.array([x,y-h,z]))[0] ) / (2*h)\n",
    "    dgxdz = ( g(np.array([x,y,z+h]))[0] - g(np.array([x,y,z-h]))[0] ) / (2*h)\n",
    "    dgydx = ( g(np.array([x+h,y,z]))[1] - g(np.array([x-h,y,z]))[1] ) / (2*h)\n",
    "    dgydz = ( g(np.array([x,y,z+h]))[1] - g(np.array([x,y,z-h]))[1] ) / (2*h)\n",
    "    dgzdx = ( g(np.array([x+h,y,z]))[2] - g(np.array([x-h,y,z]))[2] ) / (2*h)\n",
    "    dgzdy = ( g(np.array([x,y+h,z]))[2] - g(np.array([x,y-h,z]))[2] ) / (2*h)\n",
    "    return np.array([ dgzdy-dgydz, dgxdz-dgzdx, dgydx-dgxdy ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "6db92020",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 6.80011603e-12,  3.08780779e-12, -2.08166817e-13])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "curl(g,r,h)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "110e9bff",
   "metadata": {},
   "source": [
    "- analytical solution \n",
    "\n",
    "\\\\( \\nabla \\times \\vec{g}(\\vec{r}) = 0 \\\\)"
   ]
  }
 ],
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