Conformal Mapping Demo

conformal_maps.ipynb

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  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
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   "source": [
    "import numpy as np\n",
    "from numpy import sin, cos, tan, arcsin, arccos, arctan\n",
    "from numpy import sinh, cosh, tanh, arcsinh, arccosh, arctanh\n",
    "from numpy import log\n",
    "from bqplot import Figure, Scale, Scatter, Axis, LinearScale, Lines\n",
    "import ipywidgets as widgets\n",
    "from sympy import latex, sympify"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.arange(-5, 5, 0.2)\n",
    "y = np.arange(-5, 5, 0.2)\n",
    "xx, yy = np.meshgrid(x, y)\n",
    "\n",
    "Min_Input = 0\n",
    "Max_Input = 5\n",
    "Num_Segments = 200\n",
    "Num_Gridlines = 10\n",
    "sc_x = LinearScale(min=-5, max=5)\n",
    "sc_y = LinearScale(min=-5, max=5)\n",
    "LineBasis = np.linspace(Min_Input, Max_Input, num=Num_Segments+1) + 0.00001\n",
    "GridBasis = np.linspace(Min_Input, Max_Input, num=Num_Gridlines) + 0.00001\n",
    "HLineX, HLineY = np.meshgrid(LineBasis, GridBasis)\n",
    "GridLineX = np.vstack([HLineX, HLineY])\n",
    "GridLineY = np.vstack([HLineY, HLineX])\n",
    "GridLineX = np.vstack([HLineX, HLineX, -HLineX, -HLineX, HLineY, -HLineY, HLineY, -HLineY])\n",
    "GridLineY = np.vstack([HLineY, -HLineY, HLineY, -HLineY, HLineX, HLineX, -HLineX, -HLineX])\n",
    "GridLines = Lines(x=GridLineX, y=GridLineY, colors = ['black'], scales={'x': sc_x, 'y': sc_y})\n",
    "ZGrid = GridLineX + 1j*GridLineY\n",
    "Z = ZGrid\n",
    "ZLines = Lines(x=Z.real, y=Z.imag, colors = ['blue'], scales={'x': sc_x, 'y': sc_y})\n",
    "Fig = Figure(marks=[GridLines, ZLines])\n",
    "Fig.layout.width='800px'\n",
    "Fig.layout.height='800px'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "Controller = widgets.FloatSlider(value=1, min=0, max=4, step=0.01)\n",
    "FuncBox = widgets.Text()\n",
    "FuncRepBox = widgets.Label()\n",
    "\n",
    "def UpdateFunc(change):\n",
    "    FuncBox.Func = eval('lambda Z, a: {}'.format(change['new']))\n",
    "    ZTrans=FuncBox.Func(ZGrid, Controller.value)\n",
    "    ZLines.x = ZTrans.real\n",
    "    ZLines.y = ZTrans.imag\n",
    "    FuncRepBox.value = '${}$'.format(latex(sympify(change['new'])))\n",
    "\n",
    "    \n",
    "def UpdateParam(change):\n",
    "    ZTrans=FuncBox.Func(ZGrid, change['new'])\n",
    "    ZLines.x = ZTrans.real\n",
    "    ZLines.y = ZTrans.imag\n",
    "    \n",
    "    \n",
    "Controller.observe(UpdateParam, names='value')\n",
    "FuncBox.observe(UpdateFunc, names='value')\n",
    "FuncBox.value='1/(1+Z**a)**(1/a)'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "VBox(children=(Text(value='1/(1+Z**a)**(1/a)'), Label(value='$\\\\left(Z^{a} + 1\\\\right)^{- \\\\frac{1}{a}}$'), Fl…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "widgets.VBox([FuncBox,FuncRepBox,Controller, Fig])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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