root finding with scipy.ipynb

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   "source": [
    "# Root Finding using Scipy"
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    "# We're going to use ```scipy.optimize.root```\n",
    "\n",
    "- This is used to finds the roots of a function \n",
    "\n",
    "- It's is based on MINPACK which is a FORTRAN library for solving systems of nonlinear equations"
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    "# this cell is skipped.\n",
    "# it is to show the polynomial and do some basic plotting setup\n",
    "\n",
    "import numpy as np\n",
    "from scipy import optimize\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%config InlineBackend.figure_format = 'svg'\n",
    "plt.rcParams['figure.figsize'] = (14, 5.5)\n",
    "plt.rcParams.update({'font.size': 15})\n",
    "\n",
    "def fun(x, a=1, b=-7, c=5, d=13):\n",
    "    return a * x ** 3 + b * x ** 2 + c * x + d\n",
    "\n",
    "def make_plot():\n",
    "    x = np.linspace(-2, 7, 1000)\n",
    "    plt.plot(x, fun(x), label=r'$f(x)$', lw=3)\n",
    "    plt.axhline(0, color='gray', lw=0.5)\n",
    "    plt.yticks([-30, 0 , 30])\n",
    "    plt.legend()\n",
    "    plt.ylim(-30, 30)\n",
    "    plt.show()"
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   "source": [
    "Let's define a cubic  equation to find the roots of\n",
    "\n",
    "$$\n",
    "f(x) = x^3 - 7x^2 + 5x + 13 \n",
    "$$"
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   ],
   "source": [
    "import numpy as np\n",
    "from scipy import optimize\n",
    "\n",
    "def fun(x, a=1, b=-7, c=5, d=13):\n",
    "    return a * x ** 3 + b * x ** 2 + c * x + d\n",
    "\n",
    "x = np.linspace(-2, 7, 1000)\n",
    "sol = optimize.root(fun, [-2, 2, 6])\n",
    "\n",
    "plt.plot(x, fun(x), lw=3)\n",
    "plt.plot(sol.x, fun(sol.x), 'd', ms=10)\n",
    "plt.axhline(0, color='gray', lw=0.5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.        ,  5.73205081,  5.7320508 ])"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol = optimize.root(fun, [-2, 10, 6])\n",
    "sol.x"
   ]
  }
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