interactive_exponential.ipynb

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     "data": {
      "text/html": [
       "        <script type=\"text/javascript\">\n",
       "        window.PlotlyConfig = {MathJaxConfig: 'local'};\n",
       "        if (window.MathJax) {MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}\n",
       "        if (typeof require !== 'undefined') {\n",
       "        require.undef(\"plotly\");\n",
       "        requirejs.config({\n",
       "            paths: {\n",
       "                'plotly': ['https://cdn.plot.ly/plotly-2.3.1.min']\n",
       "            }\n",
       "        });\n",
       "        require(['plotly'], function(Plotly) {\n",
       "            window._Plotly = Plotly;\n",
       "        });\n",
       "        }\n",
       "        </script>\n",
       "        "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from ipywidgets import interactive, interact\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import ipywidgets as widgets\n",
    "import sympy as sym\n",
    "import seaborn as sns\n",
    "import plotly.graph_objects as go\n",
    "from plotly.offline import init_notebook_mode, iplot\n",
    "from numba import jit\n",
    "\n",
    "init_notebook_mode(connected=True)\n",
    "jit(nopython=True, parallel=True)\n",
    "sns.set()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "class plot():\n",
    "    \n",
    "    def __init__(self, preWidgetN):\n",
    "        \n",
    "        self.N = preWidgetN\n",
    "        \n",
    "        x,y,n ,k = sym.symbols('x, y,n,k', real=True)\n",
    "        X=np.linspace(0, 10, 100)\n",
    "        \n",
    "        #f = sym.Sum((-1)**k*(x**(2*k+1))/(sym.factorial(2*k+1)),(k,0, n))\n",
    "        #f = sym.Sum((-1)**k*(x**(2*k))/(sym.factorial(2*k)),(k,0, n))\n",
    "        f = sym.Sum((x**(k))/(sym.factorial(k)),(k,0, n))\n",
    "        #print(sym.latex(f))\n",
    "        f = f.subs(n, self.N.value)\n",
    "        f = sym.lambdify(x, f)\n",
    "        self.trace1 = go.Scatter(x=X, y=np.exp(X),\n",
    "                            mode='lines+markers',\n",
    "                            name='exp'\n",
    "                               )\n",
    "        self.trace2 = go.Scatter(x=X, y=f(X),\n",
    "                            mode='lines',\n",
    "                            name=r'$\\sum_{k=0}^{%s} \\frac{\\left(-1\\right)^{k} x^{k}}{\\left(k\\right)!}$' %(self.N.value)\n",
    "                               )\n",
    "        \n",
    "        layout = go.Layout(template='plotly_dark')\n",
    "\n",
    "        self.fig = go.FigureWidget(data=[self.trace1, self.trace2], \n",
    "                                   layout = layout,\n",
    "                                   layout_yaxis_range=[0 , 1000]\n",
    "                                  )\n",
    "\n",
    "\n",
    "    def sineSeries(self, change):\n",
    "\n",
    "        x,y,n ,k = sym.symbols('x, y,n,k', real=True)\n",
    "        X=np.linspace(0, 10, 100)\n",
    "        #f = sym.Sum((-1)**k*(x**(2*k+1))/(sym.factorial(2*k+1)),(k,0, n))\n",
    "        #f = sym.Sum((-1)**k*(x**(2*k))/(sym.factorial(2*k)),(k,0, n))\n",
    "        f = sym.Sum((x**(k))/(sym.factorial(k)),(k,0, n))\n",
    "        f = f.subs(n, self.N.value)\n",
    "        f = sym.lambdify(x, f)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "        with self.fig.batch_update():\n",
    "            self.fig.data[1].x = X\n",
    "            self.fig.data[1].y = f(X)\n",
    "            self.fig.data[1].mode = 'lines'\n",
    "            self.fig.data[1].name = r'$\\sum_{k=0}^{%s} \\frac{\\left(-1\\right)^{k} x^{2 k + 1}}{\\left(2 k + 1\\right)!}$' %(self.N.value)\n",
    "\n",
    "        return \n",
    "    \n",
    "    def show(self):\n",
    "        self.N.observe(self.sineSeries, names='value')\n",
    "        display(self.N, self.fig)\n",
    "        return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "model_id": "66ef2d739afc46e8ab7145b76836e2b1",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "IntSlider(value=0, description='partial sum order', max=20)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "57d5775318424c6aac59dd64941fef85",
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      "text/plain": [
       "FigureWidget({\n",
       "    'data': [{'mode': 'lines+markers',\n",
       "              'name': 'exp',\n",
       "              'type': 'scat…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = widgets.IntSlider(min=0, max=20, step=1, value=0, description='partial sum order')\n",
    "\n",
    "p = plot(N)\n",
    "\n",
    "p.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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