{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Notes on Python"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "15bff986",
   "metadata": {},
   "source": [
    "## Data types"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51c125e8-1d3c-4583-b4fe-ea15b8ff5101",
   "metadata": {},
   "source": [
    "### tuple\n",
    "\n",
    "1. create\n",
    "    ```\n",
    "    a = tuple(range(10))\n",
    "    ```\n",
    "\n",
    "2. slice\n",
    "\n",
    "    `a[start:end:step]`\n",
    "\n",
    "\n",
    "### list\n",
    "\n",
    "1. create\n",
    "    ```\n",
    "    a = [i for i in range(10)]\n",
    "    b = list((1, 2, 3, 4))\n",
    "    ```\n",
    "\n",
    "2. slice\n",
    "\n",
    "    `a[start:end:step]`\n",
    "\n",
    "    ```\n",
    "    a[::2]\n",
    "    a[1:3]\n",
    "    a[:3]\n",
    "    a[-2:]\n",
    "    ```\n",
    "\n",
    "\n",
    "3. Inverse an array\n",
    "\n",
    "    ```\n",
    "    a = [1, 2, 3]\n",
    "    b = a[::-1]\n",
    "    print(a)\n",
    "    print(b)\n",
    "    ```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf78f0c9-002b-4bbe-8988-774569d9bc97",
   "metadata": {},
   "source": [
    "### dict\n",
    "\n",
    "1. create\n",
    "    ```\n",
    "    a = {'name': 'Yang Zongze', 'id': 1234, 'department': 'AMA'}\n",
    "    ```\n",
    "\n",
    "2. get item\n",
    "    ```\n",
    "    a['name']\n",
    "    a.get('age', 30)\n",
    "    ```\n",
    "\n",
    "    ```\n",
    "    for k, v in a.items():\n",
    "        print(k, v)\n",
    "    ```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a3e0550-0303-428c-a073-aa4ad2aac5ec",
   "metadata": {},
   "source": [
    "a = {'name': 'Yang Zongze', 'id': 1234, 'department': 'AMA'}\n",
    "for k, v in a.items():\n",
    "    print(k, v)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Builtin functions\n",
    "\n",
    "### `map`\n",
    "\n",
    "    ```\n",
    "    s = map(lambda x, y: x+y, [1, 2, 3], [4, 5, 6])\n",
    "    for i in s:\n",
    "        print(i)\n",
    "    ```\n",
    "\n",
    "### `reduce`\n",
    "\n",
    "    ```\n",
    "    from functools import reduce\n",
    "    from operator import add, mul\n",
    "    from math import sin\n",
    "\n",
    "    # reduce(lambda x, y: x+y, [1, 2, 3, 4, 5])\n",
    "\n",
    "    # sin(1)*sin(2)*sin(3)\n",
    "    reduce(mul, map(sin, [1, 2, 3]))\n",
    "    ```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e89ff0f5",
   "metadata": {},
   "source": [
    "## Packages"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "95dd0f3a-cdb9-4c54-a2e1-e12dee13730c",
   "metadata": {},
   "source": [
    "### os, sys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "a146bdab-19a7-4c14-8568-94d5747f5d8f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ". [] ['python_notes.ipynb', 'jupyter_book.md']\n"
     ]
    }
   ],
   "source": [
    "import os\n",
    "import sys\n",
    "\n",
    "# walk\n",
    "# path\n",
    "# join\n",
    "for pth, dirs, files in os.walk('.'):\n",
    "    print(pth, dirs, files)\n",
    "    break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "02ca4221",
   "metadata": {},
   "outputs": [],
   "source": [
    "## set environment\n",
    "os.environ['ABC'] = '3'"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cac5b22c-c563-41e4-ac13-e58be537af37",
   "metadata": {},
   "source": [
    "### signal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "38397675-f1e6-4073-b6cc-7d051aa5177a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Start ...\n",
      "Sig received with number 2\n",
      "End ...\n"
     ]
    }
   ],
   "source": [
    "import signal\n",
    "from time import sleep\n",
    "\n",
    "gframe = None\n",
    "def handler(sig_num, frame):\n",
    "    global gframe\n",
    "    print('Sig received with number %d'%sig_num)\n",
    "    gframe = frame\n",
    "\n",
    "signal.signal(signal.SIGINT, handler)\n",
    "\n",
    "print('Start ...')\n",
    "signal.raise_signal(2)\n",
    "print('End ...')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "c1eebc0a-03cc-42ae-92c5-ab862b7f844e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<frame at 0x110baf320, file '/var/folders/tf/v4zjvtw12yb3tszk813gmnvw0000gn/T/ipykernel_63421/3869011539.py', line 13, code <module>>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gframe"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "729a4d35-44ca-49fd-a344-20d470f31b9d",
   "metadata": {
    "tags": []
   },
   "source": [
    "### numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "bd93f173",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "0f167f3e-3d2b-4eec-abfb-6bccf2d57d06",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.True_"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.isinf(np.inf) or np.isnan"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38907668-299a-4b5b-b6ad-54d6c0c41d54",
   "metadata": {
    "tags": []
   },
   "source": [
    "### psutil"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "f70cd080-bb57-4b6a-bb33-f12279638ec6",
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import psutil\n",
    "pid = os.getpid()\n",
    "python_process = psutil.Process(pid)\n",
    "memoryUse = python_process.memory_info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "3aa418bc-263b-401e-adf7-a7a6dc9c0d51",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "pmem(rss=151994368, vms=446060953600, pfaults=17296, pageins=49)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "memoryUse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4848dac3-0142-4156-a9ec-affb2c7ed1d9",
   "metadata": {},
   "source": [
    "### Json\n",
    "\n",
    "```python\n",
    "import base64\n",
    "import json\n",
    "import numpy as np\n",
    "\n",
    "class MyEncoder(json.JSONEncoder):\n",
    "    def default(self, obj):\n",
    "        if isinstance(obj, complex):\n",
    "            return str(obj)\n",
    "        \n",
    "        return json.JSONEncoder(self, obj)\n",
    "\n",
    "json._default_encoder = MyEncoder()\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bcb14dcc",
   "metadata": {},
   "source": [
    "## Package not in standard path"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Load package\n",
    "Some times we would like to import files from other folds\n",
    "\n",
    "1. First add the path to system path by\n",
    "2. Import the package"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "c5d6b98c-b40e-4c14-91ed-228306245fe5",
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import sys \n",
    "mypath = '../firedrake/py'  # the path of your file\n",
    "sys.path.append(mypath) # ma\n",
    "\n",
    "from intro_utils import plot_mesh_with_label"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Reload package\n",
    "\n",
    "```\n",
    "import some_package\n",
    "import importlib\n",
    "\n",
    "some_package = importlib.reload(some_package)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## tqdm\n",
    "\n",
    "### How to use tqdm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8243f421-d78e-478d-9b8c-8492a6d933e5",
   "metadata": {},
   "outputs": [],
   "source": [
    "from tqdm import tqdm\n",
    "from time import sleep\n",
    "\n",
    "pbar = tqdm([\"a\", \"b\", \"c\", \"d\"])\n",
    "for char in pbar:\n",
    "    sleep(0.25)\n",
    "    pbar.set_description(\"Processing %s\" % char)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Progress bar in parallel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ecf54815-454b-42ba-abb0-86a87ea26c00",
   "metadata": {},
   "outputs": [],
   "source": [
    "import mpi4py\n",
    "from tqdm.auto import tqdm\n",
    "\n",
    "def isnotebook():\n",
    "    try:\n",
    "        shell = get_ipython().__class__.__name__\n",
    "        if shell == 'ZMQInteractiveShell':\n",
    "            return True   # Jupyter notebook or qtconsole\n",
    "        elif shell == 'TerminalInteractiveShell':\n",
    "            return False  # Terminal running IPython\n",
    "        else:\n",
    "            return False  # Other type (?)\n",
    "    except NameError:\n",
    "        return False      # Probably standard Python interpreter\n",
    "\n",
    "\n",
    "class ptqdm:\n",
    "    \n",
    "    __config__ = {'ncols': None if isnotebook() else 100, 'ascii': True}\n",
    "    \n",
    "    def __init__(self, *args, **kwargs):\n",
    "        \n",
    "        comm = kwargs['comm'] if 'comm' in kwargs.keys() else None\n",
    "        comm = comm or mpi4py.MPI.COMM_WORLD\n",
    "        self.rank = comm.Get_rank()  \n",
    "        \n",
    "        for key, val in ptqdm.__config__.items():\n",
    "            if key not in kwargs.keys():\n",
    "                kwargs[key] = val\n",
    "        \n",
    "        self.tqdm = tqdm(*args, **kwargs) if self.rank == 0 else None\n",
    "    \n",
    "    def update(self):\n",
    "        if self.tqdm is not None:\n",
    "            self.tqdm.update()\n",
    "            \n",
    "    def close(self):\n",
    "        if self.tqdm is not None:\n",
    "            self.tqdm.close()\n",
    "        \n",
    "    def __getattr__(self, attr):\n",
    "        return self.tqdm.__get_attr__(attr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Command Line options"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### How to use `getopt`\n",
    "\n",
    "```python\n",
    "import os\n",
    "import sys\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "import getopt\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    try:\n",
    "        opts, args = getopt.getopt(sys.argv[1:], '', [\"lcs=\",\"full-path=\"])\n",
    "    except getopt.GetoptError:\n",
    "        print('%s --lcs <[python list]> --full-path <full-path>' % sys.argv[0])\n",
    "        sys.exit(2)\n",
    "\n",
    "    for opt, arg in opts:\n",
    "        if opt == '--lcs':\n",
    "            print('lcs arg is %s' % arg)\n",
    "        elif opt == '--full-path':\n",
    "            print('path arg is %s' % arg)\n",
    "```\n",
    "\n",
    "### How to use `argparse`\n",
    "```python\n",
    "import os\n",
    "import sys\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "import argparse\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    parser = argparse.ArgumentParser(description='Learn Argparse')\n",
    "    parser.add_argument('--lcs', metavar='lcs', type=float, nargs='+', # default=None,\n",
    "                        help='A python list of mesh sizes.')\n",
    "    parser.add_argument('--fullpath', dest='full_path', action='store',\n",
    "                        default=None,\n",
    "                        help='The path where data stay.')\n",
    "\n",
    "    \n",
    "    args = parser.parse_args()\n",
    "    print(args)\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "11ed497f-5b34-460a-8fe9-80dae53aa4c0",
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import sys\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "import argparse\n",
    "\n",
    "\n",
    "parser = argparse.ArgumentParser(description='Learn Argparse')\n",
    "parser.add_argument('--lcs', metavar='lcs', type=float, nargs='+', # default=None,\n",
    "                    help='A python list of mesh sizes.')\n",
    "parser.add_argument('--fullpath', dest='full_path', action='store',\n",
    "                    default=None,\n",
    "                    help='The path where data stay.')\n",
    "\n",
    "\n",
    "# args = parser.parse_args()\n",
    "# print(args)\n",
    "    \n",
    "parser.parse_known_args('--lcs 1 -b'.split())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c95c64c6-48bd-4054-b8f5-579e53ae77e6",
   "metadata": {},
   "outputs": [],
   "source": [
    "arg, unknow = parser.parse_known_args(''.split())\n",
    "print((arg, unknow))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4518d6a3-3f54-4e88-a8db-db3a0080de78",
   "metadata": {},
   "outputs": [],
   "source": [
    "arg, unknow = parser.parse_known_intermixed_args(''.split())\n",
    "print((arg, unknow))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Matplotlib"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Basic usage"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "309cef00-1257-41f3-8b9a-3466be3c9b91",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.ticker as ticker\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "matplotlib.rcParams.update(\n",
    "    {'font.size': 16, \n",
    "     'savefig.bbox': 'tight',\n",
    "     \"figure.facecolor\":  (0.9, 0.9, 0.9, 0.3),  # red   with alpha = 30%\n",
    "     \"axes.facecolor\":    (0.8, 0.8, 0.8, 0.2),  # green with alpha = 50%\n",
    "     # \"savefig.facecolor\": (0.0, 0.0, 1.0, 0.2),  # blue  with alpha = 20%\n",
    "    }\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0f5c925c-b3eb-4448-8bd6-702bdb8d3ce9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x300 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1574.8x590.551 with 8 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# create fig with size 7X8 (in inches)   and 1inch = 2.54cm\n",
    "# figsize = [width, height]\n",
    "fig1 = plt.figure(figsize=[4, 3])\n",
    "\n",
    "# fig1.patch.set_facecolor('#E0E0E0')\n",
    "# fig1.patch.set_alpha(0.7)\n",
    "ax1 = fig1.add_subplot()   # default will same as add_subplot(1, 1, 1)\n",
    "ax1.plot(range(10))\n",
    "\n",
    "# or just change to cm by this way\n",
    "cm = 1/2.54 # inch\n",
    "fig2 = plt.figure(figsize=[40*cm, 15*cm])\n",
    "ax2 = fig2.subplots(2, 4)\n",
    "\n",
    "fig2.tight_layout()   # Otherwise the subplots will overlap"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a3e268d7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = [8*2**i for i in range(4)]\n",
    "y = [10*_**2 for _ in x]\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(5, 4))\n",
    "ax.semilogy(x, y, '-*')\n",
    "\n",
    "ax.xaxis.set_major_locator(ticker.MultipleLocator(base=16))\n",
    "ax.xaxis.set_minor_locator(ticker.MultipleLocator(base=8))\n",
    "\n",
    "ax.xaxis.set_major_formatter(ticker.FormatStrFormatter('%g'))\n",
    "ax.xaxis.set_minor_formatter(ticker.FormatStrFormatter('%g'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "18b558ce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = [8*2**i for i in range(4)]\n",
    "x_inv = [1/_ for _ in x]\n",
    "y = [10*_**2 for _ in x]\n",
    "\n",
    "fig = plt.figure(figsize=[5, 4])\n",
    "ax = fig.add_subplot()\n",
    "ax.loglog(x_inv, y, '-*')\n",
    "\n",
    "ax.xaxis.set_major_locator(ticker.LogLocator(base=2))\n",
    "ax.xaxis.set_minor_locator(ticker.LogLocator(base=2))\n",
    "\n",
    "if True:\n",
    "    def ticker_str(x, pos):\n",
    "        if x < 1:\n",
    "            n = int(np.round(1/x))\n",
    "            return \"1/%g\"%n\n",
    "        return  \"%g\"%x \n",
    "\n",
    "    ax.xaxis.set_major_formatter(ticker_str)\n",
    "    ax.xaxis.set_minor_formatter(ticker_str)\n",
    "else:\n",
    "    ax.xaxis.set_major_formatter(ticker.LogFormatterSciNotation(2))\n",
    "    ax.xaxis.set_minor_formatter(ticker.LogFormatterSciNotation(2))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0d0839ad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1400x500 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, [ax1, ax2] = plt.subplots(\n",
    "    nrows=1, ncols=2,\n",
    "    figsize=(14, 5),\n",
    "    constrained_layout=True,\n",
    ")\n",
    "ax1.loglog(x_inv, y, '-*')\n",
    "ax1.set_xscale('log', base=2)\n",
    "\n",
    "ax2.loglog(x, y, '-*')\n",
    "ax2.set_xscale('log', base=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c77a6859",
   "metadata": {},
   "outputs": [],
   "source": [
    "def setup(ax):\n",
    "    ax.spines['right'].set_color('none')\n",
    "    ax.spines['left'].set_color('none')\n",
    "    ax.yaxis.set_major_locator(ticker.NullLocator())\n",
    "    ax.spines['top'].set_color('none')\n",
    "    ax.xaxis.set_ticks_position('bottom')\n",
    "    ax.tick_params(which='major', width=1.00, length=5)\n",
    "    ax.tick_params(which='minor', width=0.75, length=2.5, labelsize=10)\n",
    "    ax.set_xlim(0, 5)\n",
    "    ax.set_ylim(0, 1)\n",
    "    ax.patch.set_alpha(0.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "baae4964",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 500x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(5, 4))\n",
    "setup(ax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot errors with reference line"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "88d14ded-05ee-4fd4-864a-9dd4e8299677",
   "metadata": {},
   "outputs": [],
   "source": [
    "def minor_tick(x, pos):\n",
    "    if x < 0.1:\n",
    "        if (np.round(x*100) in [4, 6]):\n",
    "            return '%.2f' %x\n",
    "        else:\n",
    "            return ''\n",
    "            \n",
    "    return '%.1f' %x\n",
    "\n",
    "\n",
    "order = 1\n",
    "\n",
    "dim = 3\n",
    "lcs =  [0.125, 0.0625, 0.03125, 0.015625] # Gmsh lcs\n",
    "ndofs =  [628, 3603, 23472, 164356] # Number of dofs\n",
    "errors =  [0.04827200204462808, 0.013616633838663416, 0.0033094536713063377, 0.0008433901100836445] # Errors compared with Ref sol\n",
    "filename = None\n",
    "\n",
    "p = order + 1\n",
    "c01 = 2\n",
    "c02 = -1\n",
    "\n",
    "x1 = ndofs\n",
    "x2 = lcs\n",
    "y = errors\n",
    "\n",
    "        \n",
    "c1 = y[-1]/(x1[-1]**(-p/dim)) + c01\n",
    "c2 = y[-1]/(x2[-1]**p) + c02\n",
    "\n",
    "y1_ref = [c1*_**(-p/dim) for _ in x1]\n",
    "y2_ref = [c2*_**p for _ in x2]\n",
    "fig = plt.figure() # (figsize=[4,3])\n",
    "ax = fig.add_subplot()\n",
    "ax.loglog(x1, y, 'd-', x1, y1_ref, '--')\n",
    "ax.set_xlabel('Number of DOFs')\n",
    "ax.set_ylabel('$L^2$ errors')\n",
    "ax.text(x1[-2], y1_ref[-2], '$O(h^%d)$'%p, va='bottom', ha='left')\n",
    "\n",
    "filename and fig.savefig(filename + '-ndofs.eps', format='eps')\n",
    "\n",
    "fig = plt.figure() # (figsize=[4,3])\n",
    "ax = fig.add_subplot()\n",
    "ax.loglog(x2, y, 'd-', x2, y2_ref, '--')\n",
    "ax.set_xlabel('Mesh size')\n",
    "ax.set_ylabel('$L^2$ errors')\n",
    "ax.text(x2[2], y2_ref[2], '$O(h^%d)$'%p, va='top', ha='left')\n",
    "\n",
    "ax.xaxis.set_major_formatter(matplotlib.ticker.FormatStrFormatter('%.1f'))\n",
    "ax.xaxis.set_minor_formatter(minor_tick)\n",
    "\n",
    "filename and fig.savefig(filename + '-maxh.eps', format='eps')\n",
    "\n",
    "if filename:\n",
    "    print('filename1: ' + filename + '-ndofs.eps')\n",
    "    print('filename2: ' + filename + '-maxh.eps')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1870d58e-149c-42c7-9932-42febbbd63bf",
   "metadata": {},
   "outputs": [],
   "source": [
    "help(fig.autofmt_xdate)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac5ae25a",
   "metadata": {},
   "source": [
    "## Onedrive API"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "485af605",
   "metadata": {},
   "source": [
    "### Download from onedrive"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6eb3b98b",
   "metadata": {},
   "outputs": [],
   "source": [
    "share_url = 'https://1drv.ms/u/s!Au1wcoQGYu6djJofAu3qVd577D-xgg?e=wASCui'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9adee87b",
   "metadata": {},
   "outputs": [],
   "source": [
    "import base64\n",
    "def create_onedrive_directdownload (onedrive_link):\n",
    "    data_bytes64 = base64.b64encode(bytes(onedrive_link, 'utf-8'))\n",
    "    data_bytes64_String = data_bytes64.decode('utf-8').replace('/','_').replace('+','-').rstrip(\"=\")\n",
    "    resultUrl = f\"https://api.onedrive.com/v1.0/shares/u!{data_bytes64_String}/root/content\"\n",
    "    return resultUrl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8e9a5442",
   "metadata": {},
   "outputs": [],
   "source": [
    "create_onedrive_directdownload(share_url)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b3b35dc",
   "metadata": {},
   "source": [
    "### Uploader"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d6b7f7c5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# file: uploader\n",
    "import os\n",
    "import requests\n",
    "import tqdm\n",
    "import click\n",
    "\n",
    "# Here, we get the token from https://developer.microsoft.com/en-us/graph/graph-explorer\n",
    "# and save it in file access_token\n",
    "# TODO: get the token automaticly.\n",
    "def load_access_token(path=None):\n",
    "    if path is None:\n",
    "        path = os.getcwd()\n",
    "    with open(os.path.join(path, \"access_token\"), \"r\") as f:\n",
    "        access_token = f.readline().strip('\\n')\n",
    "\n",
    "    return access_token\n",
    "\n",
    "\n",
    "def upload(file_to_upload, file_name, access_token, unit=1):\n",
    "    local_name = file_to_upload\n",
    "\n",
    "    if file_name is None:\n",
    "        file_name = os.path.basename(local_name)\n",
    "\n",
    "\n",
    "    request_body = {\n",
    "    }\n",
    "\n",
    "    base_url = \"https://graph.microsoft.com/v1.0\"\n",
    "    # folder_id = \"01VGN2QX6TWD75CHGPGRG2UCZAOOHFOKEM\"\n",
    "\n",
    "    url_put = base_url + f\"/me/drive/root:/{file_name}:/createUploadSession\"\n",
    "\n",
    "    headers = {\n",
    "        \"Authorization\": \"Bearer \" + access_token\n",
    "    }\n",
    "\n",
    "    response_upload_session = requests.post(\n",
    "        url_put, headers=headers, json=request_body\n",
    "    )\n",
    "\n",
    "    try:\n",
    "        upload_url = response_upload_session.json()['uploadUrl']\n",
    "    except Exception as e:\n",
    "        raise e\n",
    "\n",
    "    with open(local_name, \"rb\") as upload:\n",
    "        total_file_size = os.path.getsize(local_name)\n",
    "        chunk_size = 327680*unit\n",
    "        chunk_number = total_file_size // chunk_size\n",
    "        chunk_leftover = total_file_size - chunk_size * chunk_number\n",
    "        counter = 0\n",
    "        \n",
    "        bar = tqdm.tqdm(total=chunk_number + 1, \n",
    "                        desc=\"upload\")\n",
    "\n",
    "        while True:\n",
    "            chunk_data = upload.read(chunk_size)\n",
    "            start_index = counter * chunk_size\n",
    "            end_index = start_index + chunk_size\n",
    "\n",
    "            if not chunk_data:\n",
    "                break\n",
    "\n",
    "            if counter == chunk_number:\n",
    "                end_index = start_index + chunk_leftover\n",
    "\n",
    "            upload_headers = {\n",
    "                \"Content-Length\": f'{chunk_size}',\n",
    "                \"Content-Range\": f'bytes {start_index}-{end_index-1}/{total_file_size}'\n",
    "            }\n",
    "\n",
    "            chunk_data_upload_status = requests.put(\n",
    "                upload_url, \n",
    "                headers=upload_headers,\n",
    "                data=chunk_data)\n",
    "            # print('Upload Progress: {0}'.format(chunk_data_upload_status.json()['nextExpectedRanges']))\n",
    "            bar.update()\n",
    "\n",
    "            counter += 1\n",
    "        bar.close()\n",
    "        \n",
    "    requests.delete(upload_url)\n",
    "\n",
    "\n",
    "@click.command()\n",
    "@click.option('--token_path', default=None, help='access_token path')\n",
    "@click.option('--unit', default=16, help='access_token path')\n",
    "@click.option('--name', default=None, help='remote file name')\n",
    "@click.argument('file_to_upload')\n",
    "def main(file_to_upload, name, token_path, unit):\n",
    "    token = load_access_token(token_path)\n",
    "    print(token)\n",
    "    upload(file_to_upload, name, token, unit)\n",
    "\n",
    "# if __name__ == '__main__':\n",
    "#     main()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f116fa47",
   "metadata": {},
   "source": [
    "## GC\n",
    "\n",
    "Ref:\n",
    "\n",
    "1. https://devguide.python.org/internals/garbage-collector/index.html\n",
    "1. https://jakevdp.github.io/blog/2014/05/09/why-python-is-slow/\n",
    "2. https://zhuanlan.zhihu.com/p/295062531"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b099a56d",
   "metadata": {},
   "source": [
    "### `id`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "67c1e924",
   "metadata": {},
   "outputs": [],
   "source": [
    "str1_addr = id('abc')\n",
    "str2_addr = id('abc')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4aeb3b2f",
   "metadata": {},
   "outputs": [],
   "source": [
    "print(f\"str1 addr: {str1_addr}, str2 addr: {str2_addr}\")\n",
    "str1_addr == str2_addr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7dc21c41",
   "metadata": {},
   "outputs": [],
   "source": [
    "# WARNNG: never do this!\n",
    "\n",
    "import ctypes\n",
    "\n",
    "class IntStruct(ctypes.Structure):\n",
    "    _fields_ = [(\"ob_refcnt\", ctypes.c_long),\n",
    "                (\"ob_type\", ctypes.c_void_p),\n",
    "                (\"ob_size\", ctypes.c_ulong),\n",
    "                (\"ob_digit\", ctypes.c_long)]\n",
    "    \n",
    "    def __repr__(self):\n",
    "        return (\"IntStruct(ob_digit={self.ob_digit}, \"\n",
    "                \"refcount={self.ob_refcnt})\").format(self=self)\n",
    "\n",
    "c113 = ctypes.c_long(113)\n",
    "iptr = IntStruct.from_address(id(113))\n",
    "print(f\"113 == 4 is {113 == 4}\")\n",
    "print(f\"id(4) = {id(4)}, id(113) = {id(113)}\")\n",
    "\n",
    "# be careful, remember restore the value, or restart the interpreter\n",
    "iptr.ob_digit = 4  # now Python's 113 contains a 4!\n",
    "print(f\"113 == 4 is {113 == 4}\")\n",
    "print(f\"id(4) = {id(4)}, id(113) = {id(113)}\")\n",
    "\n",
    "# restore the value\n",
    "iptr.ob_digit = c113\n",
    "print(f\"113 == 4 is {113 == 4}\")\n",
    "print(f\"id(4) = {id(4)}, id(113) = {id(113)}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0bcdfe0d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import ctypes\n",
    "import gc\n",
    "gc.disable()\n",
    "\n",
    "class Object(ctypes.Structure):\n",
    "    _fields_ = [(\"ob_refcnt\", ctypes.c_long)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "db6342b7",
   "metadata": {},
   "outputs": [],
   "source": [
    "l = []\n",
    "l.append(l)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fd167a73",
   "metadata": {},
   "outputs": [],
   "source": [
    "l_addr = id(l)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7828bb74",
   "metadata": {},
   "outputs": [],
   "source": [
    "l_addr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0aec29af",
   "metadata": {},
   "outputs": [],
   "source": [
    "del l"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ddf18020",
   "metadata": {},
   "outputs": [],
   "source": [
    "Object.from_address(l_addr).ob_refcnt"
   ]
  }
 ],
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