va2577/maximum-drawdown.ipynb

## maximum-drawdown.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 最大ドローダウンの計算\n",
    "\n",
    "* [numpy - Start, End and Duration of Maximum Drawdown in Python - Stack Overflow](https://stackoverflow.com/questions/22607324/start-end-and-duration-of-maximum-drawdown-in-python)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f5e98d17710>]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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eiuySFQF/MBZOqeCceWOpPxi52tRKE5y3oCYVzRow+9hzc6cR8No8/h4rh0Z/qygvdNPpDfRaajnddHT7KS9w8aev1gLh2VpS5llkmxGfw0+GMSV5vLI+cmOVvS1GTZriHvbFTab/u6SW97cd7PvCfvIHg7xd10SXL9Bj5VCAv35tIePLjXUL1urlvS0eJg9wXGQ4+QJBDnb4InYxs6qTHuyUHr7ILtLDT0BxXg5dvkBEzvcb9y8HIrdDHCqnHFrNj86KX4Onv/7vktrQ7efX7eNL974H0OtA7Ikzq0LbMY4xA/6elt4riKaLz9+9jGfW7ImYbRQK+AkWvRNipJCAnwCr99sRp4RwooOl6eKUQ+NX61w0tSLu8WhjSo2cfryqm+nIqgNk37bSSunsPCh1/UV2kYCfACttY+2Fa5/D3VvVzUxyfB91eSxjzA3V+9ojIN0ssM1CsuoZ/ezpxKqcCjFSSMBPgDWg2W6uSL3pSaPg52mHVUfU7skUN583m1s+Oyd036rMmYii3ByKcnNCYxjpztpV7IdnHRI6Vmjr7WfS4LMQgyWDtgmwUjptHj/aVkrY5czAKmLAxcdOBoxZOut2t3DjufEXavVkVJGb/RmS/1bAt06YSm5OOMjbS05kyuCzEMkgPfwEFIV6+D46vPbNSDK7d3jlydO560tH9rjzV08qi3JjCrClo25/gG5/MGIjGMtVp84AMmcsQohkkICfACul0+bx02JbrNPbHrEjWWWhm4172yK+7aQja+/d6P2OAc6YbQxey9RMkU0k4CcgPGjrp8UWIBra0r+XOxRm15Syv8PL+j2xRcnSibU4Lt6iMquWTktXZqSmhEgGCfgJCOfwfTy6oj50fHx5QU+/MqItnGJM4WxO82BpDbLH6+GXm4Pt0sMX2UQGbROQ53KQ41ChzcKdDsWDX1/EYWNj69NnA6vH/N8vbaal08dZtnpCgaDmty9u5LCxJXx6XmrLToR7+LE5/HyXE5dThcpLCJENJOAnQClFUV5OKDg8ctnR1E5ObKHSSGRtuvL+tgO8v+1AxE5bf31nO79/dQsACyaUpfRbkFUNNF5KRylFYW4OXV7Z7lBkD0npJKjALCJ2+UnTsjrYQ2wA3d3cFff29x9ZhS+FJYh7S+mA8Z7aZ10JMdJJwE+Q16yHXzPAMssjSXSK5LIHloduW6tYAd7ffiBUqycVehu0BaMsRpcEfJFFJOAnyOqpVhQObsvEkcDpUGy/9RzGmh9+a3eFt0yMnqr5/rYDbNqXmtk8oR5+DwG/wJ0Ts8+BECOZBPwEWQG/vDDzSikMlT9ffBTWotUPth9g5Y6DtHcHcDsdVNs2Tll8xxspaV+rx4c7xxGxytYu3+0M7ecrRDaQgJ+g2TUlAFRKDz9kVk0JPz5nFmCUIT7/rnfo6PZTmOvEqVJfdqK1y09JD717MCpoZuviOZGdJOAn6N6Lj+LW8+cys7oo1U1JK9FlC4yAn8NxM0bFvb7+YCdbGtuHo2kc6OimorDnzcoLpIcvssygAr5S6vNKqXVKqaBSqjbq3HVKqTql1Eal1BmDa2bqlea7uHDhxIjCWyI8RdPS2N5NUW4OPzrrMP6jdkLouJXbP+5Xr3Lq7a8Pebu01jy/bl+vO3nlu3Jk0FZklcH28NcC5wMRSVql1CzgQmA2cCZwl1Iqs3YKEQkpzI18W9/c3ERhbg4VhW6+ecKU0PHo1EkgOLR1eKyNT1Z80vPWkEYPXwZtRfYYVMDXWq/XWm+Mc2oJ8HetdbfWehtQBywczHOJ9FTgjs2RW/Pea8ryQ8esGTOWgWyg0tLlC21CY9FaM/lHz/Cr5zZEHG82i9xddcr0Hh9PUjoi2wxVDn8csNN2v948JkaYgjhbPFoBv8CdExo07YzaHvJAe//r8My/+QWO/NmLEceu/NtKAP7w2paI482dxuN/5vCe/9nlu510+4MR3zb2tXp4Yd3efrdNiEzQZ8BXSr2klFob52dJMhqglLpMKbVcKbW8sbExGQ8phlG+KxzwrbL69jTPrz8/H4jt4e/vGFilUV9Ac8wvX+a+t7ehtebZNfGDs1UGw6qKGY/1YWVPNy36xctc9sCKmG8SQowEfQZ8rfVpWus5cX6e6OXXdgETbPfHm8fiPf49WutarXVtVVVi+6qK9GHfxN3q2RfaShlYx6zUiTXmPZiNR/a0eLj5qY9p9UR+iFgLvP723g7W7GpBqdhBZTsrHdVpfhg1tIXbtGN/54DbJ0S6GqqUzpPAhUqpXKXUFGAG8P4QPZdIIXtKxwr09to11vkOM6iOKjLWMbyyoaFfz+P1R9bkyc1xsL2pI+LY4jve4IZ/r+H6f6/hsZW7KMlz9bqbl/VNxPr20dAa/tax44AEfDHyDHZa5meVUvXAMcAzSqnnAbTW64B/AB8DzwFXaq1ldGwEysuxp3SM4Bqvh98RNRumqZ85/Pe3HYi47wsEeXbNHnIciv88I7xB+UPv7QjdLutjg3mrTMYX/vgu/kCQJtu2jfYicEKMFIOdpfNvrfV4rXWu1rpaa32G7dwtWutpWutDtNZLB99UkY4cDsXnjhjPn74aXoYR0cPPjRy0tXrqHd39mw65ckfk9Mqghtc3NXLImGKuOGkaJ86MTQf2lr8HqDK/bTS1d7N9fyf7bR9CP39mfcxzCpHpZKWtGLTbvzCf02dVh+4Xxenhf7Dd6KFbAT96ELcvW+Oszt2wt41DqotRSrGnJbZHXtZL/h6gqjhcJmPZ1v1c889VEeffqWvqVxuFSHcS8EXS2VM6pfkuZteUsGZXCwDeQM89fK11xMCp3Z4WD4eNLeH4GaP4weKZoeOHjDF2Hbv1c/Mozsvha58KL/aKLvsQzZ7y+fHja2POD/HaMCGGnQR8kTTW9MaKqIqitZPK2bC3jd++uCk05z26h+8LBLl16QYW3vIy+1o9bGvqCO1YdeMTa3lv2wEmVxbwwNcX8cVFk0K/N67cWNx1xMRy1vzkDG48d1ZoYLinOvgWl7P3f/7Wh5QQI4UEfJE0BzqMHPjEisKI49aK2ztf3gzAlFGF+AI6Iuh/64EV/PGNrYCxovbk37zGF//0HsGg5v5lnwDhGT7ltp55RZw8vXW+r4DfE3eO8b/F8u0H+rhSiMwiAV8kzeUnTQNgVFFkEB5rK7EAMGdcKQDbGsPTKu3TNHcdNPLxa3a10GRboGUFfKVUaH59eS/VMEt6KZzWm5euPpGpVYUc7PThT+EWjUIkmwR8kTQ/PPNQtt96TkxF0cKo8gsLJ5cD8NL6faFjLmf4dy79yweh23uawzl9+yDrERPLgPhTL7vNgeGe9rLty8TKAr51wlTj+VsGvkBMiHQjAV8MucMnloduz6wu4stHT+KkQ6p47MP60PEJFQVxf9c++8b+zeF3Fx3O3V8+krGl+TG/Y80ESiSl8+oPTuK+S47iV5+bC8B4c0xgQrnRnp2yAEuMIAPrAgnRDxWFbn501qHcunQDp8+qRinFIdXFvLt1f+ia4h5649c9tiZ0u7Io3MMvyXNx5pwxcX/Hbw4M91YL3zJlVCFTRhljDgXuHI6cZHw4WR9AOw9KwBcjhwR8MSy+tGgim/e1843jjFRJbo4Djy+I1hqlFJ3eALNrSli329gQvTTfRUuXj4NmEbS/fWNRKI3TFys91N9B23Pn14RuV5cYG7Tbyy0IkekkpSOGRXGei9u/MD80yJprVtm08u2d3gBjzCD77ROn8dGNp4d+9+y5Yzh2+qiEdxuzplsOdJYOGDN18lwO2vq5QEyIdCY9fJESeVbA9wXJcxk7T9WU5fPBDadRWeiOCO6Xn9jzJibxWD38vubZ96Ukz0Vrl5RJFiOH9PBFSuS5jH96Hr+xWKvDG6Ag10lVcS6OqAqXlUW918SJ9ovPzmXuuFIm9jAQnKiSfJfUxRcjivTwRUpYVTY9vgD+QBCvP0iBK/4/x4pe5trHs2hqJU/9v+MG3caSvBxapIcvRhDp4YuUsFI6Hl+QTrMkQ/SG6NHXDrfqkrzQIjAhRgIJ+CIlrJROtz9Al7kbVn6c/XFTaUZ1MTsOdOLxRW7l4AsECUplNZGBJOCLlLD38K3KmYXu9MowjivLI6iJ2BgFYMYNS5l6/bN0+2VPH5FZ0uv/MJE1cs0CZR5fgHe2GAuwonv4y647JVRdMxWsHbEOdHgZb668bbMN4r66obHHxV9CpCMJ+CIlrB7+k6t2s2lfG06HChVVs8QrmzCcrMFiqwrozgOdHH/bq6HzQS1pHZFZJKUjUsLK4T+6op797V6WLKhhXFlqA3y06ID/0c7miPOp/PYhxEBIwBcpkWvb/HxXcxcFaTZgC7EB3xG10tcabBYiU0jAFykRPdUy3QZswZiHn+NQoYDf4Y0ss9Dc5Y33a0KkLQn4IiWslI6lIA0DvlKK8kJ3KOBf++jqiPP7pLCayDAS8EVKpGoxVX9VFrrZ3xHZk1/xX6cxqsgdUatfiEyQft0qkRVyourlbG1qT1FLeldh6+GX5rtYsqCGyqJcZlYXs1d2wxIZRnr4IiWiSx1/+8RpKWpJ7yoK3Rzs8OIPBGnp8oUGckvzXbR6pHSyyCwS8EXKvHf9qYDR2z9sbEmKWxNfhZnSsYqolRcYAV9KJ4tMJAFfpIy1snbBhMR2skqFMrNEshXwrU1VSvJzaJMevsgwgwr4SqlfK6U2KKVWK6X+rZQqs527TilVp5TaqJQ6Y/BNFSNNSZ6L+y45insvrk11U3pUmJuD1tDUbuTxrX1yi/NcdPkC+ALBVDZPiH4ZbA//RWCO1noesAm4DkApNQu4EJgNnAncpZTKjGkZYlidfOhoygr6V+9+OBWYm6vvazUGaIvM+yVmT196+SKTDCrga61f0Fpb/+LfBcabt5cAf9dad2uttwF1wMLBPJcQqVBopp2sgB9O6Rg9fcnji0ySzBz+14Cl5u1xwE7buXrzmBAZxVoQFt3Dt1I7sgWiyCR9zsNXSr0ExKsBe4PW+gnzmhsAP/BQfxuglLoMuAxg4sSJ/f11IYaUFeD3mqtqi/IkpSMyV58BX2t9Wm/nlVKXAJ8GTtU6VC92FzDBdtl481i8x78HuAegtrZWyg+KtGIF+Lc2Nxr3o3v4ktIRGWSws3TOBK4FztNad9pOPQlcqJTKVUpNAWYA7w/muYRIhSmVhQAc7PThdjpCJSFGFRsDzfWy563IIIPN4f8vUAy8qJT6SCl1N4DWeh3wD+Bj4DngSq211JIVGae0wBW6bfX2AUYX5zF1VCHvbTuQimYJMSCDqqWjtZ7ey7lbgFsG8/hCpIOrTp3BnS9vjqnZP6GiIDSYK0QmkJW2QvShKNcI9G5n5P8u1SW5bG/qkKAvMoYEfCH6UGgO1E6oKIg4XlWcS1u3n0W/eDkVzRKi3yTgC9GH/WZZhRmjiyKOF+WG8/tf+OOyYW2TEAMhAV+IPtROKgdgyYLItYOFueGc/vsyeCsygGyAIkQfjp0+irpbziInKocfvQ+v1x/EnSN9KJG+5F+nEAmIDvYQu01jQ5sM3or0JgFfiAHq8kUuLZEtD0W6k4AvxABZ9XTGlOQBsEcCvkhzEvCFGKDTZ1Vzz1eO5JmrjgOgoa07xS0SoncyaCvEACmlWDx7DH5z16uObqmcKdKb9PCFGKQcp4M8l4OdBzr7vliIFJKAL0QSeHxB/rminn8s39n3xUKkiAR8IZLonje2proJA/J2XRP3vLGF8JYWYiSSHL4QSVTX0J7qJgzITU+uo66hnV0Hu7h5yZxUN0cMEenhC5EEP/70rNDt9gwcvD3QYdQL+uuyT2hq76auoY373t7G2l0tKW6ZSCbp4QuRBF8/bgqVhW6+98hH7Gv1UFRV1PcvpZHivJxQ0K8/2MVnfv926Nz2W89JVbNEkkkPX4gkGV2SC5CR9fELbHWB9jTLto0jlQR8IZKk2lxx29CaOQuwvP4g/kCQbl+AhVMqAGjq8DKtytjLtyQvMgmwp0U+DDKZBHwhksQK+OnUw+/2B/hg+wE8vtgtpbXWnH7H63z7wZV0eP2hEhE/fnwtWxo7AGj1+PH6jYVl6/e0cswvX+H+ZduHq/kiySTgC5EkRbk5FLid7E2jgL/wlpf5/N3LuP2FjTHfOQYlAAAdlUlEQVTn9nd4+WR/Jy+t38e+1m5GFeVGnHco478HO43c/iX3vQ/AjU+so8sb+wEi0p8EfCGSaHRxLk3mDlkA+9u7Qz3kVGjp8gGwK05ePjpoVxVHBvwpo4y0jrXj1z5bqmrljoNJbacYHhLwhUiiUUW5NJp18YNBzZE/f4nv/+OjlE3VtHLwM6uLY851+yMDfnVJZMA/emolAPs7jEBfXuAK7f71Vl0TVz38IfUHpZxEJpGAL0QSVRXnhgZtm83e9dOr9zDnpudp9fgirl26Zg+PfLBjSNvjCxgrZz2+2G8ZXd7IY9YYhOXkQ0YDsHz7QYJBTUuXj9k1JQD84bUtPLlqN8+t3TsUzRZDRAK+EEk0Y3QRW5s6mPeT5zn7d29GnFtTH17EpLXm8odW8sN/rRmytnR6/aFNWuIN2r5Z1xhxv7okl4e/eXTo/qKpFcyuKWHljoO0dfsJahhfXhCR+mlsz5wZSUICvhBJVTvZmNrY6vHHDN7usFXTbO6M7O0nWyCo+e0Lm0L3rfSNLxDk2kdXsb2pg9ueixzIrSrO45hplZQXuAAoznMxqbKA3c1dtJjtLStwcdz0UaHfyaQpqEJW2gqRVMdMq+zx3E1PrOOihROBoe8ZP7VqN/e+tS10f1tTB60eH3UN7fxjeX1EzZ/cHAfd/mAo3//MVcez2xzkrSnN55UNDaGZOuUFbgrc4b18ZQ+AzCI9fCGSyOV08NMls+Oe8waCoWqUjbbdsYaiQmV0CufdrQe48fG1OJUx13LTvnDA/8ulC3n9P09CmedqyvJD31RqyvLx+ILcunQDYPTw7QG/O4UzkET/DSrgK6V+ppRarZT6SCn1glKqxjyulFJ3KqXqzPNHJKe5QqS/0cV5PZ7bsLcNCM9tB+ODINn8wdgPkcc/2k2H1+iR22cNTasqZFJlYdzHGVeeD8CyrfsBI+Dnu+wBX+bjZ5LB9vB/rbWep7VeADwN3GgePwuYYf5cBvxhkM8jRMYoNlMjx00fxXvXnxpx7qzfvYnHFwjNjwfo7E5+0LQKodk5HYp2T2QK5qXvn8Dokp4/oGonlTN9dLgQXFmBm3xb3R3p4WeWQQV8rXWr7W4hYHUrlgD3a8O7QJlSauxgnkuITHHU5ArOP3wcNy+ZTXVJHo9cdjS/+tzc0PlN+9po7QoH3qGYo28va+x2Gv+bO5UK9fAtpfnuXh+nsiiXl75/Yuh+RYGbfFc4bHTHme4p0tegc/hKqVuUUjuBLxHu4Y8D7Hu91ZvH4v3+ZUqp5Uqp5Y2NjfEuESKjuHMc/PY/FjDNLJG8aGplxBz3/e3eiB7+lsbkb5qycV9b6PbDlxlTLf3BYGjVrKUot3/zNhwOFVFZU1I6maXPgK+UekkptTbOzxIArfUNWusJwEPAd/rbAK31PVrrWq11bVVVVf9fgRAZYGxpfuh2U3s3LV0+XE5jkPTp1XuS/nyNbd18+eiJrLpxMUdOKuf3XzyCoIaH3w8v9HI6FHmuxPp8R00uZ0KF8RpmmYuvQFI6mabPj3et9WkJPtZDwLPATcAuYILt3HjzmBBZaYYtD76v1UNrl48JFQVsbezg0RX13HTuLIrzXEl5rvZuP53eABPKCyg159QfNtYorWBVwQRQEJqZ05d/fvvY0O0540oZVeSmqd0rAT/DDHaWzgzb3SXABvP2k8BXzdk6RwMtWuvkd2OEyBAOh6LulrOYMbqI97YdoKXLR2l+OMDbUzyD9fpGIzVqn3kTbxaO05FYsI9n2XWncvExk1JaGE7032Bz+Lea6Z3VwGLgu+bxZ4GtQB3wJ+CKQT6PEBkvx+mgdnI5b25u4q26piEL+Nv3G734kw4Jp0jtwf3aMw8BYHIPUzET4XI6yHM7Q6UbRGYY1EpbrfXnejiugSsH89hCjESza0qx5jOU5rsYU5LH3lZPqHRBMrR6fLidDvJs8+XtPrNgHI8ur+dXF8wb1PMU5+bg9Qfx+oO4c2QNZyaQd0mIYXTegprQ7drJFfzfJUcBye3ht3v8obUAdkdPDa+efeUHJ7FgQtmgnscac2jzDG1dIJE8EvCFGEYlea7QzJijp1SEBlWTGfDbPH6K4gT8B76+iA0/OzNpz2N9qLR5MqeeTkuXj3k/eZ53tjSluikpIQFfiGFWZi52GluWT1n+UAR8X9wevquXNM9AWD38nzy1jhNuezUjCqnVNbTR6vHzq+dit3zMBhLwhRhmD35jETedOyu0B26OQyUt4De0eXh1YyN5OckL7D2xPlRe29jIjgOdPPLBzj5+I/XcTuPvcqAjO8s6S8AXYphNH13EpZ+aAhjz4EvzXaHdsQbrxsfXAbDattnKUBlXlh9x/6dPfzzkzzlY3oAxq2io9yNIVxLwhUix0nxX0nr4bd3G45TkD/1WF9EBPxNYtX8CcaqJZgMJ+EKkWEm+i9YkBXxrD1tHgitoB8PhUMysDq8gnj++dMifc7A8Zu2f4BDsQZAJJOALkWJlBcnp4Wut6fYNb0C77uzDAHCozKirY/Xwg+nf1CEhAV+IFEtWSuf6f69llZm7P29+3OK0SXfSzCrev+FUPj2vJjMCvtlGbyDIV/78Hp3e9J9ZlEwS8IVIsdJ816AHEbXWoUqYc8aVcMM5hyWjaX1SSjG6OI88lyNmW8VU01rz2xc38erGhtAxexvf3NzEsi37U9G0lJFNzIVIsdJ8F60eH8GgxjHAgmb3vLE1dHvuuNJBFUYbiDyXM+0CfmuXnztf3gzA9lvPAWLTTi5ndvV5s+vVCpGGSvNdaA1tg1i49Py6vQBcftI0rll8SLKalrDcHEfapXT2tXlCt3ce6ARidxcbit3G0pkEfCFSzKqaOZiZOrk5To6YWMYPzzyUUUW5yWpawvJcTjq9gbSa7ri3JRzwj7/tVTy+QMyOX9F7/I50EvCFSDEr4C//5MCAH+NAh5eq4uEP9JYJ5QUAvLk5fbYpXbY1Mj//0Hs7aGrvZlJlAatuWgwM7ltVJpKAL0SKjTb3u/3N85sG/BhG/Zzk7Jg1EIvMSpwHOsI96LqGdhpaPT39ypDbdbAr4v7Pnv6YJ1ftZnRxbmgvX+nhCyGG1fzxpYwry2dXcxdrdw2sJEKrx09JCgN+vtuoUdPhNQZu6xraOe23r3PhPe8OyfP5A0H2t/deD6fLF4i7SfuJM6tCg9p3vLSJLm96DTYPJQn4QqSYUoozZo8B4NP/81a/fz8Q1LR3x6+BP1wK3MZzd3n9vLqhgd+Zs2O2NnUkdXMXy0+f/pgjf/5Sr/PoPb4A0217CVvGlEaWhHh0ZX3S25euZFqmEGnAvt1hf1lpiVQG/Hyz7PIvnt0Qc25rUzuHTyxP6vM9tWo3YMyycToULocjZkprlzdAgdvJ+p+eSYfXT+3PXwJi/06rdzbD0ZOS2r50JT18IdKALxCe0hjs50yXVo9VMC11KR2nQ/U497+xLfmliK2/UJvHz1E/f4kv//m9mGu6fAHyXU7y3U5GFeVy3PRRADF7AnxiTtnMBhLwhUgDPltxl6nXP8urGxp6uTpSKOCnsIcPsRUo544ziqk1mrn26dc/yy+Xrk/qc+5u7qLV4+edOCtmPb5ARHC36snpqDpDzZ2RUzVHMgn4QqSBK06azvjycG750r98kPDvtoVSOqnr4dudcuhoAM6dPxYwevif7O/AH9T88fWtvf1qwqyYvae551lAHl8wIuAbG8gTWqfw3/+xAIADHdlTG18CvhBpoDTfxfVnD6z+zY79RkoilTl8u2sWz+TuLx/BN46bSnFuDs2dPk789Wuh81c+tHJQj6+1DhWb293S1eM1bR4f+e5wiLtm8Uz++e1jmGN+8/jM4eO4/KRpNLV3s6WxfVBtyhQS8IVIE9bUxv669l+rgfTp4c8YXcyZc8bicChK8l385Z3tEeefWbNnUI9/1C0vh27vbg4HfL9tHGTd7lZaPX7mjy8LHXM5HRw1uSLiseaZwX/lJwcH1aZMkR5dAiEEhe7I/x0TKaZmn7dvTwmlwi2fncPSNXtx54T7kbua4/fAf/vCRr4/gJo/nV4/Tbb593tbw7fbu/089N4Otjd1sMIM4FZvvifHzTAGcu1lGEYy6eELkSbsgRKg3TbHvKHNw31vb4sZcLT3nlNd+fFLiybx4DcWJXTtna/U9Xs2EsDGvW0AfP/0mUDkDKDdzR5+/fxG/rminq1NHQDUlPb+IWgtzLr9xYGvcs4kEvCFSFNttmX/Vz60kpuf+piPdjZHXGN9ARhbmjecTUvY1afN7PGctd1goj7a2cxn73oHCL/eRltFzLPvfDPmd/ra21cNw1aQ6SQpAV8pdY1SSiulRpn3lVLqTqVUnVJqtVLqiGQ8jxAjmVX8bHKlUYjMXj1zc4MxqLh2d2vE71h72N7/tYXD0cR+++5pM3o819nPkgbrdofTV+PM9FVTe89TKv/nosMTCuhnzzVWOdvHAEaqQQd8pdQEYDGww3b4LGCG+XMZ8IfBPo8QI924snze+M+T+cl5s4FwD98fCIZ2xOqKKiXQ0e3n0DHFzKguHt7G9sNlJ0yNe7y/NWzs33jm9pGbh8RnLR0+wVgF3JVmG7gMhWT08O8AriW8+A1gCXC/NrwLlCmlxibhuYQY0SZWFlBW4AaMCpgAO21VH7u8kb3QDq+fwjgFwtLJ9WcfxrfiBP3+9vA3mfn7HyyeSXGeK5TO+tT0yrjXF7gT+7tYs6OyoYjaoAK+UmoJsEtrvSrq1Dhgp+1+vXlMCNEHq2dq9WitgUqIzXu3dwfSPuADXHzsZGbXlFBeEJ462p8NxO99cyuPfbiLUw4dzXdOMdJEVg9z4eRwwC+2/S0KEpzmal3X3w+gTNRnwFdKvaSUWhvnZwlwPXDjYBqglLpMKbVcKbW8sTF9Nk8QIlXCAd/o4a+qb8blVLhzHDG90M5uP4UDnL8/nGrK8nnmquND6SogNADbl93NXfz8GaMkw0mHVIWOWxOWRpfk8pNzZ3HnRYez5uYzQucTXddgFX4bypTOZ+96m7tf3zJkj5+oPrsGWuvT4h1XSs0FpgCrzIGR8cBKpdRCYBcwwXb5ePNYvMe/B7gHoLa2Nn32RxMiRay69q0eP+t2t/BOXRPjywvo9PpDG4Xf+MRaun1BOrrTP6Vjt2TBOI6eWsmiXxiLp/74+hbeqmvir5cujLvmYNO+Nhbf8Ubofrxyx2X5Ls5aODHmeKI9/Pwh7uF3dPv5cEczH+5o5tsnThuS50jUgFM6Wus1WuvRWuvJWuvJGGmbI7TWe4Enga+as3WOBlq01oNbXidElsjNcZDnctDU3s05d77FqvoWygtc5LucoV7o/cs+4ZHlO9nd4olIk2SC6pI8vrTICNC/XLqBNzc39bjV4C+fjSy2Vl0SO/20MmoPX6tWTr4r0ZSOVcs/+QF/T0sXVz38YcxxrTW/eHY9a+oHtuHNQA1V1+BZ4GygDugELh2i5xFixFFKMWtsCattwaCi0E2nN8CKTw7GrAqdVhXb60130YG7vdsfsydAS6cvouTymJK8iNdaXZLLvtZu5owrifi9f11+DM+s2ZPwHgPhHH7ytzv8+l+W8/EeYyrtqCJ36HinN8A9b2zlwXc/4WufmsJjK+t557pTk/780ZIW8M1evnVbA1cm67GFyDbHz6gK7RoFRg33MaV5vLaxkaN/+XLEtUdNqYj+9bQX3fvu6I6dbjr/py9EHPvG8VMi7j/5nePY0tAeMxtnUmUhV5w0PfG2uIcuh7+5ITzgbk+9WQPynd4A//tqXdKftyey0laINDR/QuQ882OnjeI/z4itPbPyx6dnZA+/O2q20U+f+jgipdIUZ7/a6B57dUkex5qbmgxGaNA2CSmdTq8/YktHa2EcEKrwCeEBebvov8lQkIAvRBoaXRxOebx73al8cdFEZteUstDWm59cWUBFoTver6c9e/ADeKuuiX+u2Nnj+XPn13DOvKFZypPMaZnf/ftHzP/pC6HBdbvWLl+oflCrJzZ91BbnWLJJwBciDVllFgDG2OrklNhKIEdv1ZdJJlYWAjChIlzcrKfecGm+i/+56PCEF1L1l5XSeXaQZZsBXvx4HwD1B2OrhAZ1uCBevB7+/l7KRCSLBHwh0lBV1MwTi30bwz9+5cjhak7SfWnhRP59xbG88L0TQ8cabIXQrIBfVuDizxfXDmlb3GaV0eVJrIkfHdBdTmPw2Ur3HOiIDe43/HtN0p6/J5kzgVeILOJwKJ76znFE1/6yFmUdOamcSWYvORM5HIrDJxo1bL64aCJ/e28HXd4AHl+AXz23IfQN57nvnhDxDWcoJKNi5v72bly28tZWeqbQ7WRqVRHfPGEqVz38IS1dPiYA1z1mBPePbjydTm+A3764iR8MYH+A/pKAL0Samjs+tkBYiTlwmeiiokzwi8/O5ZX1DXT7gixdu4f73t4eOpfo1MrBuvbMQ7jtuY10eQMD2nnsyJ+/FLHiub3bT7c/QIc3wMmHjqbCrI/U0e0nGNR0+42aSGUFbsoK4Defn5+cF9IHSekIkUGsHv5Iq+Oe63LQ7Q/g9UcWh8tzDU+IqjQHv/d3xM4OSlSHbdD3tY0NnG+Wjpg7rjT0Ojz+IE3mc5xsKxMxXCTgC5FBrEHb6J2vMl1ujoOnVu/hh/+KzGMP1wdbab4R8Fu7YtcD/OTJdTHrBPryj+X1rDP3LqidVB4aYPf4AuxrMQL+fxwVWw5iqEnAFyKDWOmGERbvyc1xEhjAlofJYn1zao8K7Pe9vY2/vLM9ZiP2/igrcIUC/qqdzXztrx8AqdmlTAK+EBnEqhPz6SGak54quTmxoeiihRPiXDk0rL1t27t9PLqinrW7WtBas8csY9HboqzoNFQ0pVQopXPXa1tC+/AO9WB0PDJoK0QGOXZaJS9fc2JGrq7tTW6cXP3XPjUlzpVDo8i2B8EP/mls7/Ff5xzGQ+8ZG/n5etn+0J7uyXM58Phir423ZmJUD1Nvh5L08IXIIEqpERfswUjpWC44cjybbzlrWLdttDZO+d9XwnVt6sx9hAG8vQV8W9G1j28+M+410QH/qlOmRxSGGy4S8IUQKWctfjp3fg23fW4eLufwhiarh7/ZFuTt48X2qaLRrCmWv7twAQ6HIl4cz4tKWV3ej+JuySQpHSFEyjnMeDhrbEncjVCGWr7LiUMZ5Q/AWNgWPWPnmdV7OGfeWLq8Ad6qa+L0WdVAOIdvjUMsu+5UlILXNjYyp8ZYS5Fj+wD7y6VHDWiufzJID18IkXLWDJ3qkuHPa4ORKrN/q+jo9rNmV+TmJFf+bSUAP316Hd+8fzkfm9Muu0MB3wji1SV5jC7O4wu1E5hVE67Vv/S7x3PRwgkcO23wFT4HSgK+ECLlrBS5PZc/3KzArRRs2NvGjgOdca/bYG4qX3/QOL/JvB9vppHdYWNL+OX583D3cd1QkoAvhEi5H511CAunVHD8zNT1fi1ftO2Pm+9y8qevRhZvs8Ybtu/vQGvNtf9abRxPYSBPVPq3UAgx4k0fXcw/vnVMRPnnVJldE65h9L9fPJzTZ1Vz7LTKUEE3a3bN1sYOHn4/XMM/ld9OEiWDtkIIAdz++fn4g0GmjDKmvToUnHqYMTA7taqQjWbqxtoo5e8f7IxI+2RCD18CvhBCAJ87cjwQrlVv300sL8cZ2sXKvtn5O1v2h273lcNPBxLwhRDCpqLQzbVnHsLJh4wOHct1OfCYg7o9bYWYioVU/SUBXwgholwRtTAqzyzu5g8E6fIGcDlVxJaMEL88RLpJ/xYKIUSKhcob+4N0egMRc+k/s6CGJ678VMTG8+lKAr4QQvShINcI+K1dPrp8AQ6fWMZ/nXMYYKzKnT+hLJXNS5ikdIQQog/WdNFdzV2h+5ccO5nx5fksnjUmlU3rFwn4QgjRmy1bOPJXP2fNvx6h6DYPa1x57NtyAY6xN3HmnGmpbl2/SEpHCCF6snQpzJvHmH8+RLG3C6U1xd4upj7+MMybZ5zPIIMK+EqpnyildimlPjJ/zradu04pVaeU2qiUOmPwTRVCiGG0ZQtccAF0duLw+yJOOfx+6Ow0zm/ZkqIG9l8yevh3aK0XmD/PAiilZgEXArOBM4G7lFLpv+5YCCEst98OPl/v1/h8cMcdw9OeJBiqlM4S4O9a626t9TagDlg4RM8lhBDJ9+CDiQX8Bx4YnvYkQTIC/neUUquVUv+nlCo3j40DdtquqTePCSFEZmhv7/ua/lyXBvoM+Eqpl5RSa+P8LAH+AEwDFgB7gNv72wCl1GVKqeVKqeWNjY39fgFCCDEkihLcOzjR69JAn9MytdanJfJASqk/AU+bd3cBE2ynx5vH4j3+PcA9ALW1tTreNUIIMey+/GW4997e0zouF3zlK8PXpkEa7Cydsba7nwXWmrefBC5USuUqpaYAM4D3B/NcQggxrK65xgjovXG54Oqrh6c9STDYhVe3KaUWABrYDnwLQGu9Tin1D+BjwA9cqbWOX2JOCCHS0bRp8OijxtRLny+yp+9yGT+PPmpclyGU1umTRamtrdXLly9PdTOEECJsyxZj6uUDDxgDtEVFRhrn6qvTJtgrpVZorWv7vE4CvhBCZLZEA76UVhBCiCwhAV8IIbKEBHwhhMgSaZXDV0o1Ap8M8NdHAU1JbE4mkNecHeQ1Z4fBvOZJWuuqvi5Kq4A/GEqp5YkMWowk8pqzg7zm7DAcr1lSOkIIkSUk4AshRJYYSQH/nlQ3IAXkNWcHec3ZYchf84jJ4QshhOjdSOrhCyGE6MWICPhKqTPNvXPrlFI/SnV7kkUpNUEp9apS6mOl1Dql1HfN4xVKqReVUpvN/5abx5VS6k7z77BaKXVEal/BwCilnEqpD5VST5v3pyil3jNf1yNKKbd5PNe8X2een5zKdg+GUqpMKfWoUmqDUmq9UuqYkfw+K6WuNv9Nr1VKPayUyhuJ77O5MVSDUmqt7Vi/31el1MXm9ZuVUhcPtD0ZH/DNvXJ/D5wFzAIuMvfUHQn8wDVa61nA0cCV5mv7EfCy1noG8LJ5H4y/wQzz5zKMDWoy0XeB9bb7v8LYO3k6cBD4unn868BB8/gd5nWZ6nfAc1rrQ4H5GK9/RL7PSqlxwFVArdZ6DuDE2AN7JL7Pf8HY19uuX++rUqoCuAlYhLFV7E223QX7R2ud0T/AMcDztvvXAdelul1D9FqfAE4HNgJjzWNjgY3m7T8CF9muD12XKT8Ym+W8DJyCsaGOwliMkhP9fgPPA8eYt3PM61SqX8MAXnMpsC267SP1fSa8BWqF+b49DZwxUt9nYDKwdqDvK3AR8Efb8Yjr+vOT8T18smT/XPNr7OHAe0C11nqPeWovUG3eHgl/i/8GrgWC5v1KoFlr7Tfv219T6PWa51vM6zPNFKARuM9MZd2rlCpkhL7PWutdwG+AHRhbo7YAKxj577Olv+9r0t7vkRDwRzylVBHwL+B7WutW+zltfOSPiKlWSqlPAw1a6xWpbsswywGOAP6gtT4c6CD8NR8Yce9zObAE44OuBigkNu2RFYb7fR0JAT/h/XMzkVLKhRHsH9JaP2Ye3mdtL2n+t8E8nul/i08B5ymltgN/x0jr/A4oU0pZu7PZX1Po9ZrnS4H9w9ngJKkH6rXW75n3H8X4ABip7/NpwDatdaPW2gc8hvHej/T32dLf9zVp7/dICPgfADPMEX43xuDPkyluU1IopRTwZ2C91vq3tlNPAtZI/cUYuX3r+FfN0f6jgRbbV8e0p7W+Tms9Xms9GeN9fEVr/SXgVeAC87Lo12v9HS4wr8+4XrDWei+wUyl1iHnoVIztQUfk+4yRyjlaKVVg/hu3Xu+Ifp9t+vu+Pg8sVkqVm9+OFpvH+i/VAxpJGhQ5G9gEbAFuSHV7kvi6jsP4urca+Mj8ORsjf/kysBl4Cagwr1cYM5a2AGswZkGk/HUM8LWfBDxt3p4KvA/UAf8Ecs3jeeb9OvP81FS3exCvdwGw3HyvHwfKR/L7DNwMbADWAg8AuSPxfQYexhin8GF8k/v6QN5X4Gvm668DLh1oe2SlrRBCZImRkNIRQgiRAAn4QgiRJSTgCyFElpCAL4QQWUICvhBCZAkJ+EIIkSUk4AshRJaQgC+EEFni/wN/gnFWNH3rQgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 1000\n",
    "xs = np.random.randn(n).cumsum()\n",
    "i = np.argmax(np.maximum.accumulate(xs) - xs) # end of the period\n",
    "j = np.argmax(xs[:i])\n",
    "plt.plot(xs)\n",
    "plt.plot([i, j], [xs[i], xs[j]], 'o', color='Red', markersize=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## randn\n",
    "\n",
    "* [numpy.random.randn](https://docs.scipy.org/doc/numpy/reference/generated/numpy.random.randn.html)\n",
    "* [numpy.random.standard_normal](https://docs.scipy.org/doc/numpy/reference/generated/numpy.random.standard_normal.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.19078308, -0.77451052,  1.08907138])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.randn(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.52867101,  1.40271136,  2.29026888],\n",
       "       [ 0.37268287, -0.44136897, -1.26289375]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.standard_normal((2, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## random\n",
    "\n",
    "* [numpy.random.random](https://docs.scipy.org/doc/numpy/reference/generated/numpy.random.random.html)\n",
    "* [numpy.random.random_sample](https://docs.scipy.org/doc/numpy/reference/generated/numpy.random.random_sample.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.14603611, 0.90276365, 0.64492619])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.random(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.25621421, 0.21111521, 0.47538457],\n",
       "       [0.20236014, 0.94825614, 0.01658783]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.random_sample((2, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## cumsum\n",
    "\n",
    "* [numpy.cumsum](https://docs.scipy.org/doc/numpy/reference/generated/numpy.cumsum.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  -20,  7655,  8620,  -170, -3633, 15082, 17608, 11909,  5525,\n",
       "       10390])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l = [-20, 7675, 965, -8790, -3463, 18715, 2526, -5699, -6384, 4865]\n",
    "ndarray1 = np.array(l).cumsum()\n",
    "ndarray1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f5e96a24cf8>]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ndarray1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## accumulate\n",
    "\n",
    "* [numpy.ufunc.accumulate](https://docs.scipy.org/doc/numpy/reference/generated/numpy.ufunc.accumulate.html)\n",
    "* [Universal Functions](https://docs.scipy.org/doc/numpy/user/quickstart.html#universal-functions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  -20,  7655,  8620,  8620,  8620, 15082, 17608, 17608, 17608,\n",
       "       17608])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ndarray2 = np.maximum.accumulate(ndarray1)\n",
    "ndarray2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ndarray1, label='numpy.cumsum')\n",
    "plt.plot(ndarray2, label='numpy.ufunc.accumulate')\n",
    "plt.legend(loc='best')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Basic Operations\n",
    "\n",
    "* [Basic Operations](https://docs.scipy.org/doc/numpy/user/quickstart.html#basic-operations)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([    0,     0,     0,  8790, 12253,     0,     0,  5699, 12083,\n",
       "        7218])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ndarray3 = ndarray2 - ndarray1\n",
    "ndarray3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## argmax\n",
    "\n",
    "* [numpy.argmax](https://docs.scipy.org/doc/numpy/reference/generated/numpy.argmax.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "index1 = np.argmax(ndarray3)\n",
    "index1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ndarray[n:n]\n",
    "\n",
    "* [Indexing, Slicing and Iterating](https://docs.scipy.org/doc/numpy/user/quickstart.html#indexing-slicing-and-iterating)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ -20, 7655, 8620, -170])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ndarray4 = ndarray1[:index1]\n",
    "ndarray4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "index2 = np.argmax(ndarray4)\n",
    "index2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f5e96a01d30>]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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pFsPjVwwnUFfeOz0g7f2LPyBxrZSapZRaq5RaW1paGohDCuEzNfWNFJZWyXiDH/x0bD8GpMbz2KI86hrDZ2qr2625552NHKyq59mfnkJCAKc/dzQc9nsvCeF9X+Ld7gD6ttivj3fbibb3Ocb2Y9Jav6S1HqO1HpOSktLB0oUwRl5xJW4td0b7Q4TVwgPTcth9sIbXvtttdDk+88/lhXy1tYQHpg0J+PdNR8PhA6B5xtENwPsttv/MO2tpPFDhvfz0KXCBUqqbdyD6AuBT7+dcSqnx3llKP2vxXEKElR+WzZDLSv5w5sAUzhqUwjNf7uBgVehPbV23u5y/fLqNi4b3ZOb49IAfvz1TWd8EVgCDlFJFSqmbgMeB85VSO4DzvB8DLAIKgXzgn8DtAFrrMuARYI337WHvNrz7zPE+pgBY7JsvTYjgkutwkRQXSc/EaKNLCVsPXDyEmoYmnvpiu9GldMqhGs84Q1rXaB6/ckTAxhlaimhrB6319ON86txj7KuB2cd5npeBl4+xfS0wrK06hAh1dmcFQ9MSDflBN4vs1ARmjk/ntRW7mDk+g0E9E4wu6aRprfnNOxspqazl3dtON2yZFblDWogAqGtsYvv+ShlvCIC7zh1AQrSNRz8OzVVb//XNTr7IK+F3U4cwok9Xw+qQcBAiAHbsr6KhScs01gDoFhfJXecOYPmOAyzZVtL2A4LIhj3lPL54Kxfk9ODGiRmG1iLhIEQAHBmMlmmsATFzQjqZKXE8+lEeDU1uo8tpl4qaBu6Yt4GeXaL5v6tGGn75UcLBrAoK4PbbITERLBbP+9tv92wXPmd3uEiIiqBfUqzRpZiCzWrhgYuHUHigmrkrgn9qq9aae+dvZL+rlr9PH02XWOOXc5dwMKPFi2HECJgzByorQWvP+zlzPNsXy4QxX7M7KxiSlojFIoPRgXL2oFTOGJDM01/uoLy63uhyTuiV73bx2Zb93Dd1MKP7dWv7AQEg4WA2BQVw1VVQUwMNDT/+XEODZ/tVV8kZhA81uTV5xdLDIdCUUjxwcQ6VtQ08/eUOo8s5ro17D/HHRXmcNySVmyb1N7qcIyQczOaJJ1qHwtEaGuCppwJTjwkUllZR2+CWm98MMKhnAj8d14+5K3eTX1JpdDmtVBxu4I4315OaEM1frzZ+nKElCQezef319oXD3LmBqccE7EfujJYzByPcfd5AYiOtPPpxntGl/IjWmvve3UTxoVqemT6arrGRRpf0IxIOJlBT38jX20p47OMtuCur2vegqnbuJ9pkd7iIirCQmRxndCmm1D0+ijvPGcDX20r5Ooimts5duZvF9n3ce+EgTk0PjnGGltq8Q1qEnsYmN5scFXy74wDf5B9g/Z5yGpo0kVYLd0fHEFtb0/aTxMf7v1CTyHVWMKRXIhFW+VvMKDecnsEbq3bz6Md5TMpONvz/wu6o4NGP8jh7UAo3n5FpaC3HI+EQBrTWFJRW822+JwxWFhyksq4RpTwdx34xqT+TspMZk55ETPkNnllJJ7q0ZLPBzJmB+wLCmNutyXW4uGx0mtGlmFpkhIX7LxrCrLnrmLd6Dz+bkGFYLZW1Dcyet56kuEieuGZU0M5gk3AIUSWuWr4tOMA3Ow7ybf4B9rlqAeiXFMu0kWlMyk5mQlZ3kuKOuo55zz3w6qtth8Pdd/uxevPYW15DZV2j9HAIAufn9GBCZnee+nw7l43sbci9BFpr7luwmaLyw7w1a3zrn88gIuEQIqrqGllVeJBv8g/wbf4Btu/3jAl0i7VxenYyk7KTmZiVTL/ubdxklZUF8+d7pqs2NPwoJNwREVgiIz2fz8ry55djGrlOFyB3RgcDpRQPTsvh4r8v55mvdvDgtJyA1/DGqj18vKmY/54yiNMykgJ+/JMh4RCk6hvdfL/3EN/kH+C7/ANs2HuIJrcm2mbhtIwkrjylDxOzk8np1YEbq6ZOhU2bPNNV585FV1VRbYtmzaSLOPvFxyUYfMjuqCDCohjYU8ZwgkFOWiLXndaXV7/bxfXj+pGZErj/l1xnBQ9/tIUzB6Zw6+Tg/xmTcAgSWmu27a/kmx2eM4NVO8uoqW/ComB4n67cemYmE7OTOaVfN6Jt1s4fMCsL/vEP+Mc/UMBzn2zlhaUFfNM9Dbk67jt2p4uBPRKIivDB/5nwiV+fP4gPNxbzx0VbmXPDmIAcs6qukTvmbaBbrI0nrxkZtOMMLUk4GMh56PCRy0Tf5h/kgLd7VWZKHFed2ofTs5KZkNk9INdGp4/tx/NLC3hz9R7uuWCQ349nBlprch0VnDM41ehSRAspCVHMPjubP3+ylW92HGDSgGS/Hk9rzf0LNrP7YDVv3jye7vFRfj2er0g4GKCusYkZc1axZlc5AMnxUUzK7s7E7GQmZieT1jUm4DX1TYrlnEGpvLVmL786ZwCRETLtsrP2u+o4WF0vN78FoRsnZjBv9W4e+WgLH985ya9TW99as5cPNjr5zQUDGZfZ3W/H8TUJBwMsWO9gza5y7jx3ABcP78XAHvFBcdv8jAnp3PjvNXy2ZR/TRsjFpc6yO6RndLCKtlm5f+oQbntjPf9Zu5frx/mnR3NesYv//SCXMwYkc/tZ2X45hr/In4cB1tjk5oWlBYzo04W7zxvAoJ4JQREMAGcOSKFvUkxILHEcCuzOCpSCwT0lHILRlGE9Gds/iSc/246rto0lZTqguq6R2fPWkxhj48kgvp/heCQcAmyRfR+7D9Zw+1lZQRMKzSwWxYxx6azaWcb2/cG3SFmoyXW6yEyOIy5KTtCDkVKKBy/Ooaymnme/yvfpc2uteWChnV0Hqnn6ulGkJITGOENLEg4BpLXm+a8LyEqJ44KcnkaXc0xXj+lLZISF11fK2UNn5ToqZLwhyA3v04WrTunDy9/uZPfBap897ztri3hvg4M7zx3A6Vn+HfD2FwmHAPp6Wyl5xS5uPTMraE8xk+IimTa8FwvWO6iuazS6nJB1sKoOZ0Wt3PwWAu69cBA2q4U/Ldrqk+fbtq+S//nAzulZ3fnVOQN88pxGkHAIoGeX5NO7awyXj+5tdCknNGNCOlV1jSz83mF0KSGr+c7ooWky3hDsUhOjuf2sLD7J3ceKgoOdeq6aes84Q3yUjb9dNwprkP4R2B4SDgGyemcZa3eXc/MZ/bEF+eqco/t2ZWhaInNX7EZrbXQ5IemHcJAzh1DwyzMy6d01hkc+2kKTu+Pf8w8uzKWgtIqnrxtFakK0DysMvOD+LRVGnvs6n+5xkVx7Wj+jS2mTUoqZ49PZuq+SdbvLjS4nJNmdFfRNigmKRvGibdE2K/dNHcyWYhfz1+3t0HPMX1fEu+uL+NXZ2UzMDs1xhpYkHAIg11nB19tKuXFiBjGRobGMwqWj0kiIjmCuDEx3SK6jgqG95KwhlEwb0YtT07vxf59up+okx9t27K/kwYV2xvVP4q7zBvqpwsCScAiA578uID4qgpkGriF/smIjI7jq1D4s2lx8ZFkP0T6VtQ3sOlgjN7+FmOZVWw9U1fHckvZPbT1c38TseeuJjbTyzPTRIT3O0JKEg5/tPFDNos3FzBifTpeY0LrEcP24dBqaNP9Z07HTbLPa0jzeINNYQ86ovl25YnRv5nyzk71l7eiYCDz0gZ0dJVU8de0oeiSG9jhDSxIOfvbi0gIirBZ+MSnD6FJOWnZqPKdndWfeqj2dGqQzG7v0cAhp904ZhFUpHv+k7amt720o4u21Rdx+VhaTB6YEoLrAkXDwo30Vtby7vohrxvQJ2ZkLM8en4zh0OKgaswe7XGcFqQlRIXlXrIBeXWK45cxMPt5UzJpdZcfdL7+kit+/Z2dsRhJ3h8k4Q0sSDn40Z3khbg23hEBjj+M5L6cHPRKjZGD6JOQ6XHJndIi7ZXIWvbpE8/CHW3Af46y5tqGJO+atJyrCwtPTR/l1VVejhN9XFCTKq+uZt3oPl45Mo29SG607g5jNamH62H4s3V7q0+UFwtXh+iZ2lFQyTG5+C2kxkVZ+O2Uwmx0VvLeh9c2gf/gwl637Knny2lH06hL4JfYDQcLBT175bhc19U3cdlbonjU0mz62HxalmLdqj9GlBL2t+1y4NeTIeEPIu3RkGqP6duUvn2790VIy73/v4M3Ve7n1zCzOHhS+jZwkHPyguq6RV77bxXlDejCwR4LR5XRaj8RoLsjpwdtr91Lb0GR0OUGt+c5omcYa+iwWz9TW/a46XlxaAEBhaRX3L9jMqenduOeC8BtnaEnCwQ/eXL2HisMN3H526J81NJs5Pp3ymgYWbS42upSgluusoGusjd4GdPMTvndqejcuHZnGi8sKKSytYva8DdgiLPx9+uigXwans8L7qzNAXWMT/1xeyITM7pzSr5vR5fjMhKzuZKbEycB0G+wOF0PTEoOuV4fouN9OHQzA5c9+S16xiyeuHmlIK99Ak3DwsQXrHex31YXVWQP8sN7Shj2HjrS/FD/W0ORm275Kub8hzPTuGsOsyZm4ahuZNTmTc4f0MLqkgJBw8KEmt+bFpQUM792FSWGw8NbRrjilDzE2qzQCOo4d+6uob3LLndFh6I5zsvnnz8Zw74WDjC4lYDoVDkqpXUqpzUqp75VSa73bkpRSnyuldnjfd/NuV0qpZ5RS+UqpTUqpU1o8zw3e/XcopW7o3JdknEWbi9kVpC1AfaFLjI3LR6ex8HsHFYd933M31NmdnjMqmcYafqIirJyf0yPsxxla8sVXerbWepTWeoz34/uAL7XWA4AvvR8DTAUGeN9mAc+DJ0yAh4BxwFjgoeZACSVaa577uoDMlDguHBqcLUB94fpx6dQ2uHl3XZHRpQSdXEcFcZFWMrrHGV2KEJ3mjxi8DHjV++9XgctbbH9Ne6wEuiqlegEXAp9rrcu01uXA58AUP9TlV19v97QAvS2IW4D6wrDeXRjdryuvr5JGQEfLdbrISUsM6/9/YR6dDQcNfKaUWqeUmuXd1kNr3TzfcR/QPHrTG2i5vGeRd9vxtoeU55bkk9YlmstGhVzpJ23m+HQKS6s73VIxnDS5NVuKXdL5TYSNzobDJK31KXguGc1WSk1u+Unt+dPSZ39eKqVmKaXWKqXWlpaW+uppO23NrjLW7Crn5smZREaE/zXJi4b3olusTaa1trDzQDU19U3SM1qEjU79JtNaO7zvS4D38IwZ7PdeLsL7vnk5TwfQt8XD+3i3HW/7sY73ktZ6jNZ6TEpK8CyP+9ySfJLiIrkuBFqA+kK0zco1p/Xlsy372VdRa3Q5QSG3eTBaZiqJMNHhcFBKxSmlEpr/DVwA2IEPgOYZRzcA73v//QHwM++spfFAhffy06fABUqpbt6B6Au820JCrrOCJdtKufH00GkB6gvXj03HrTVvrpb1lsAz3hAZYSE7Nd7oUoTwiYhOPLYH8J53ymYEME9r/YlSag3wtlLqJmA3cI13/0XARUA+UAPcCKC1LlNKPQKs8e73sNb6+IuoB5nmFqA/C6EWoL7Qr3ssZw5M4c3Ve7jjnGxTTfE7FrujgiE9E0z/Oojw0eFw0FoXAiOPsf0gcO4xtmtg9nGe62Xg5Y7WYpRd3hagN0/OpEtsaLUA9YWZ49O56dW1fL5lPxcN72V0OYbRWmN3VHDxiDSjSxHCZ+TPnE54cZmnBehNk/obXYohzhqUSu+uMaa/Y7qo/DCu2kZZiVWEFQmHDtrvquXddQ6uPjV0W4B2ltWiuH58P74rOEh+SaXR5RjmyGC0TGMVYUTCoYPmLC+kSeuQbgHqC9eM6Uuk1cLrK807MG13uLBaFIN6hn7vDiGaSTh0QHl1PW+s2sMlI3rRr3votgD1heT4KC4a3pN31xVRU9/Y9gPCUK6zggGp8UTbzDNbTYQ/CYcOeHVFcwvQbKNLCQozxqdTWdfI+987jS7FEHan3Bktwo+Ew0n6oQVoqlxG8Do1vRuDeyYwd4X51lsqcdVSWlkng9Ei7Eg4nKQ3V+/hUE2DnDW0oJRi5oR0thS72LD3kNHlBFTzMt1y5iDCjYTDSahrbGLO8p2Mz0zi1PSQW1Xcry4f1Zv4qAheX2Guaa25DhcAObKmkggzEg4n4b31Dva5arldzhpaiYuK4MpTevPRpmLKquuNLidg7M4KMpNMwfMGAAAOXUlEQVTjiI/qzGIDQgQfCYd2anJrXlxWyLDeiZwxIPxagPrCjPHp1De5eXvt3rZ3DhN2h0vOGkRYknBop8X2YnYeqOb2s7LDsgWoLwzokcC4/km8sWo3Te7wH5g+VFOP49BhWYlVhCUJh3bQWvPckvBvAeoLMyeks7fsMMu2B0+/DX/JdXrGG+TOaBGOJBza4evtpWwpdnHrmVlYpQXkCV2Q05OUhChTrLdkdzTPVJLLSiL8SDi0w/NLCujVJZrLTdACtLMiIyxMP60vX20rYW9ZjdHl+JXd6aJ31xi6xUUaXYoQPifh0Ia1u8pYvauMm88wRwtQX5g+rh8WpZgX5o2Acp0VctYgwpb8tmvDc18X0C3WxnVj+7a9swCgV5cYzhuSyn/W7KWuscnocvyiqq6RnQeqZTBahC0JhxPY4nTx1dYSfjGxP7GRMo/9ZMwYn05ZdT2LN+8zuhS/yCt2obWMN4jwJeFwAs8vLSAu0mq6FqC+MDErmf7JccwN04HpXO9gtJw5iHAl4XAcuw5U8/EmJzPGp5uyBWhnWSyK68f1Y93ucrZ4p3yGE7vTRXJ8FKkJUUaXIoRfSDgcx4vLCk3dAtQXrj61L9E2C6+vCr+zB7ujgmG9E+WGSBG2JByOwdMCtIirTu1DaqI5W4D6QpdYG5eOTGPhBgeu2gajy/GZ2oYm8kuqZLxBhDUJh2OYs7yQRrebW03eAtQXZo7PoKa+iffWO4wuxWe276+k0a3lzmgR1iQcjnKoxtsCdGSa6VuA+sLwPl0Y2acLc1eGTyMgu3eZbhmMFuFMwuEor36329sCVM4afGXG+HTyS6pYWVhmdCk+YXdWkBgdQZ9uMUaXIoTfSDi0UFPfyCvf7eTcwakM7inXk33lkpFpdImxhc16S7nentEyGC3CmYRDC2+u3kt5TQO3ny3NfHwp2mblmjF9+DR3HyWuWqPL6ZSGJjd5xS7pGS3CnoSDV11jE/9cVsi4/tIC1B+uH5dOo1vz1prQbgRUUFpFfaNbekaLsCfh4LVwg7cFqJw1+EVGchyTB6Ywb9UeGpvcRpfTYblHBqPlzEGENwkHPC1AX1hayNC0RCZLC1C/mTGuH/tctXyRV2J0KR1md1YQY7PSPzne6FKE8CsJB+AT+z5pARoA5wxOJa1LdEgPTOd6e0ZL0ycR7kwfDlprnl2ST2ZyHFOGSQtQf4qwWvjpuH58k3+AwtIqo8s5aW63lh4OwjRMHw5LpQVoQF1zWl9sVsUbq0KvEdDushqq65vkzmhhCqYPh+e+9rYAHS0tQAMhNSGaKcN68c7avRyuD61GQEd6RstgtDABU4fDut1lrN5Zxi+lBWhAzRjXD1dtIx9udBpdykmxOyuwWRUDUhOMLkUIvzP1b8TnlnhagE6XFqABNbZ/EgN7xPPayl0htd7SFqeLQT0T5A8JYQqm/S7PK3bx5dYSbpQWoAGnlGLm+HTsDhcbiyqMLqddtNaeHg4y3iBMwrTh8PzXnhagN0gLUENcPro3cZFW5q4IjWmtzopaymsaGCorsQqTCJpwUEpNUUptU0rlK6Xu8+exdh+s5qNNTq6XFqCGSYi28ZNTevPRJifl1fVGl9OmI4PRMo1VmERQhINSygo8C0wFcoDpSqkcfx3vxWWFRFikBajRZoxPp67Rzfx1RUaX0qZcpwuLgiGyWq8wiaAIB2AskK+1LtRa1wNvAZf540Alrlrmry3iqjF96CEtQA01uGcip2V04/VVu3G7g3tgOtdRQXZqPDGRVqNLESIggiUcegMtl+ss8m7zuTnf7KTR7eaWyZn+eHpxkmaMT2f3wRqW5x8wupQTsjsrZCVWYSrBEg7topSapZRaq5RaW1paetKPb3Jrvtiyn2kj0kjvHueHCsXJmjKsJ8nxkUE9MF1aWcd+V52MNwhTCZZwcAAtbzbo4932I1rrl7TWY7TWY1JSUk76IFaLYtFdZ/DQJX4bzhAnKSrCyrWn9eWrrfv5Mm+/0eUcU67TMxgtPaOFmQRLOKwBBiil+iulIoHrgA/8caBom5Xu8VH+eGrRQbMmZzGsdxdumbuOjzYF313TuU5PD4ccOXMQJhIU4aC1bgTuAD4F8oC3tda5xlYlAqVLjI03fjmO0f26cuebG3hnbXB1i7M7KkjvHktitEx7FuYRFOEAoLVepLUeqLXO0lo/ZnQ9IrASom28+ouxTMxO5t75m3htxS6jSzoi1+mSO6OF6QRNOAgRGxnBP382hvOG9OB/3s/lhaUFRpdERU0De8pqZCVWYToSDiKoRNusPD/jFC4dmcbji7fy5GfbDF2cL7e4+c5oOXMQ5iIrzomgY7NaeOraUcTYrDzzVT7V9U08cPEQQ1q4bvEORss0VmE2Eg4iKFktij9dMZyYSCv/+mYnNfWNPHr58IB367M7KujVJZpkmeEmTEbCQQQti0Xx0CU5xEVZeXZJAYfrm/jr1SOJsAbuaqjd6ZJLSsKUJBxEUFNKce+Fg4mNjOD/Pt3G4YYmnpk+mqgI/69xVFPfSEFpFRcP7+X3YwkRbGRAWoSE2Wdn87+X5PBp7n5ufm1dQPpP5xVXorXcGS3MScJBhIyfT+zPX64cwfIdpdzw79VU1jb49Xg/LJshg9HCfCQcREi55rS+PH3daNbvLmfGv1ZzqMZ/jYLsjgqS4iLpKUu7CxOScBAh59KRaTw/41TynC6ue2klpZV1fjlOrtPF0LREQ6bQCmE0CQcRks7P6cG/fj6G3QdruPalFRRXHPbp89c1NrF9f6WMNwjTknAQIeuMASm8dtNYSl11XP3CCvYcrPHZc+/YX0VDk5Y1lYRpSTiIkHZaRhJv3DyOqrpGrn7xO/JLKn3yvM2D0XJntDArCQcR8kb06cp/Zk2gyQ3XvrjyyC/2zrA7XCRERdAvKdYHFQoReiQcRFgY1DOBd26dQFSEhekvrWT9nvJOPZ/dWUFOWiKWAC/XIUSwkHAQYaN/chxv3zqBbnGRzJyzihUFBzv0PE1uTV6xLJshzE3CQYSVPt1ieeeWCaR1jeHn/17Nkm0lJ/0chaVV1Da45eY3YWoSDiLspCZG859bJpCdGs+s19ayeHPxST3efuTOaDlzEOYl4SDCUlJcJPNuHs+IPl2ZPW89C9YXtfuxdoeLqAgLmclxfqxQiOAm4SDCVpcYG6/9YizjM7tzzzsbeWPV7nY9LtdZwZBeiQFdGlyIYCPf/SKsxUVF8PLPT+PsQan8/j07c5YXnnB/t1uT63DJeIMwPQkHEfaibVZemHEqFw/vxaMf5/H0FzuO25d6b3kNlXWNcme0MD1p9iNMITLCwjPTRxMTaeWpL7ZTXd/I76YObrWont3R3DNawkGYm4SDMA2rRfGXK0cQG2nlpWWF1NQ38vClw350o1uus4IIi2Jgz3gDKxXCeBIOwlQsFsUfLh1KTKSVF5cWUlPfxF9GxRHxt6fg9de5t7KK2VExRB26Ae65B7KyjC5ZCEPImIMwHaUU900ZzD3nD6TsnfdpGj4CPWcOVFai0MTV1cCcOTBiBCxebHS5QhhCzhyEKSml+FWGhYaP/oytvrb1Dg0NnrerroJNm+QMQpiOnDkI83riCWxNjSfep6EBnnoqMPUIEUQkHIR5vf6655f/iTQ0wNy5galHiCAi4SDMq6rKt/sJEUYkHIR5xbdzump79xMijEg4CPOaMQNsthPvY7PBzJmBqUeIICLhIMzrnnvaFw533x2YeoQIIhIOwryysmD+fIiNbR0SNptn+/z5Mo1VmJKEgzC3qVM99zHMmgWJiWCxeN7PmuXZPnWq0RUKYQh1vNUpg92YMWP02rVrjS5DCCFCilJqndZ6TFv7yZmDEEKIViQchBBCtCLhIIQQopWQHXNQSpUC7WsK3FoycMCH5YQ6eT1+IK/Fj8nr8YNweS3StdYpbe0UsuHQGUqpte0ZkDELeT1+IK/Fj8nr8QOzvRZyWUkIIUQrEg5CCCFaMWs4vGR0AUFGXo8fyGvxY/J6/MBUr4UpxxyEEEKcmFnPHIQQQpyAqcJBKTVFKbVNKZWvlLrP6HqMpJTqq5RaopTaopTKVUrdZXRNwUApZVVKbVBKfWR0LUZSSnVVSs1XSm1VSuUppSYYXZORlFJ3e39O7EqpN5VS0UbX5G+mCQellBV4FpgK5ADTlVI5xlZlqEbgHq11DjAemG3y16PZXUCe0UUEgaeBT7TWg4GRmPg1UUr1Bu4ExmithwFW4Dpjq/I/04QDMBbI11oXaq3rgbeAywyuyTBa62Kt9Xrvvyvx/PD3NrYqYyml+gAXA3OMrsVISqkuwGTgXwBa63qt9SFjqzJcBBCjlIoAYgGnwfX4nZnCoTewt8XHRZj8l2EzpVQGMBpYZWwlhvsb8N+A2+hCDNYfKAX+7b3ENkcpFWd0UUbRWjuAvwJ7gGKgQmv9mbFV+Z+ZwkEcg1IqHngX+C+ttcvoeoyilJoGlGit1xldSxCIAE4BntdajwaqAdOO0SmluuG5ytAfSAPilFIzjK3K/8wUDg6gb4uP+3i3mZZSyoYnGN7QWi8wuh6DTQQuVUrtwnPJ8Ryl1OvGlmSYIqBIa918JjkfT1iY1XnATq11qda6AVgAnG5wTX5npnBYAwxQSvVXSkXiGVD6wOCaDKOUUniuKedprZ80uh6jaa1/p7Xuo7XOwPO98ZXWOuz/OjwWrfU+YK9SapB307nAFgNLMtoeYLxSKtb7c3MuJhigjzC6gEDRWjcqpe4APsUz2+BlrXWuwWUZaSIwE9islPreu+1+rfUiA2sSweNXwBveP6QKgRsNrscwWutVSqn5wHo8s/w2YIK7peUOaSGEEK2Y6bKSEEKIdpJwEEII0YqEgxBCiFYkHIQQQrQi4SCEEKIVCQchhBCtSDgIIYRoRcJBCCFEK/8PwcM9A46twr8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ndarray1)\n",
    "plt.plot([index1, index2], [ndarray1[index1], ndarray1[index2]], 'o', color='Red', markersize=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## max\n",
    "\n",
    "* [numpy.amax](https://docs.scipy.org/doc/numpy/reference/generated/numpy.amax.html)\n",
    "* [numpy.ndarray.max](https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.max.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12253\n",
      "12253\n"
     ]
    }
   ],
   "source": [
    "print(np.amax(ndarray3))\n",
    "print(ndarray3.max())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### NumPy ndarray 最大ドローダウン"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12253"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def mdd(a):\n",
    "    a1 = a.cumsum()\n",
    "    a2 = np.maximum.accumulate(a1)\n",
    "    a3 = a2 - a1\n",
    "    return a3.max()\n",
    "\n",
    "mdd(np.array(l))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## pandas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0      -20\n",
       "1     7675\n",
       "2      965\n",
       "3    -8790\n",
       "4    -3463\n",
       "5    18715\n",
       "6     2526\n",
       "7    -5699\n",
       "8    -6384\n",
       "9     4865\n",
       "dtype: int64"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = pd.Series(l)\n",
    "s"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### cumsum\n",
    "\n",
    "* [pandas.DataFrame.cumsum](https://pandas.pydata.org/pandas-docs/stable/generated/pandas.DataFrame.cumsum.html)\n",
    "* [pandas.Series.cumsum](https://pandas.pydata.org/pandas-docs/stable/generated/pandas.Series.cumsum.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0      -20\n",
       "1     7655\n",
       "2     8620\n",
       "3     -170\n",
       "4    -3633\n",
       "5    15082\n",
       "6    17608\n",
       "7    11909\n",
       "8     5525\n",
       "9    10390\n",
       "dtype: int64"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s2 = s.cumsum()\n",
    "s2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### cummax\n",
    "\n",
    "* [pandas.DataFrame.cummax](https://pandas.pydata.org/pandas-docs/stable/generated/pandas.DataFrame.cummax.html)\n",
    "* [pandas.Series.cummax](https://pandas.pydata.org/pandas-docs/stable/generated/pandas.Series.cummax.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0      -20\n",
       "1     7655\n",
       "2     8620\n",
       "3     8620\n",
       "4     8620\n",
       "5    15082\n",
       "6    17608\n",
       "7    17608\n",
       "8    17608\n",
       "9    17608\n",
       "dtype: int64"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s3 = s2.cummax()\n",
    "s3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0        0\n",
       "1        0\n",
       "2        0\n",
       "3     8790\n",
       "4    12253\n",
       "5        0\n",
       "6        0\n",
       "7     5699\n",
       "8    12083\n",
       "9     7218\n",
       "dtype: int64"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s4 = s3 - s2\n",
    "s4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### max\n",
    "\n",
    "* [pandas.DataFrame.max](https://pandas.pydata.org/pandas-docs/stable/generated/pandas.DataFrame.max.html)\n",
    "* [pandas.Series.max](https://pandas.pydata.org/pandas-docs/stable/generated/pandas.Series.max.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12253"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s4.max()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### pandas Series 最大ドローダウン"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12253"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def mdd(s):\n",
    "    s1 = s.cumsum()\n",
    "    s2 = s1.cummax()\n",
    "    s3 = s2 - s1\n",
    "    return s3.max()\n",
    "\n",
    "mdd(pd.Series(l))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}