{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 1: Computing with Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Robert Johansson\n",
    "\n",
    "Source code listings for [Numerical Python - Scientific Computing and Data Science Applications with Numpy, SciPy and Matplotlib](https://link.springer.com/book/10.1007/979-8-8688-0413-7) (ISBN 979-8-8688-0412-0)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interpreter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting hello.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile hello.py\n",
    "print(\"Hello from Python!\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hello from Python!\n"
     ]
    }
   ],
   "source": [
    "!python hello.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Python 3.10.12\n"
     ]
    }
   ],
   "source": [
    "!python --version"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Input and output caching\n",
    "\n",
    "(restart the kernel for the same output and cell numbers)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "3 * 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'3 * 3'"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "In[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Out[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['', '3 * 3', 'In[1]', 'Out[1]', 'In']"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "In"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1: 9, 2: '3 * 3', 3: 9, 4: ['', '3 * 3', 'In[1]', 'Out[1]', 'In', 'Out']}"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1+2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "1+2;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "x = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = 2; x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Documentation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import os"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# try os.w<TAB>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[0;31mSignature:\u001b[0m \u001b[0mmath\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcos\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m/\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
       "\u001b[0;31mDocstring:\u001b[0m Return the cosine of x (measured in radians).\n",
       "\u001b[0;31mType:\u001b[0m      builtin_function_or_method"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "math.cos?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interaction with System Shell"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "!touch file1.py file2.py file3.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "file1.py file2.py file3.py\n"
     ]
    }
   ],
   "source": [
    "!ls file*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "files = !ls file*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(files)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['file1.py', 'file2.py', 'file3.py']"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "files"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "file = \"file1.py\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-rw-------@ 1 rob  staff  0 Nov  2 17:58 file1.py\n"
     ]
    }
   ],
   "source": [
    "!ls -l $file"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Running scripts from the IPython console"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting fib.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile fib.py\n",
    "\n",
    "def fib(N): \n",
    "    \"\"\" \n",
    "    Return a list of the first N Fibonacci numbers.\n",
    "    \"\"\" \n",
    "    f0, f1 = 0, 1\n",
    "    f = [1] * N\n",
    "    for n in range(1, N):\n",
    "        f[n] = f0 + f1\n",
    "        f0, f1 = f1, f[n]\n",
    "\n",
    "    return f\n",
    "\n",
    "print(fib(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 1, 2, 3, 5, 8, 13, 21, 34, 55]\n"
     ]
    }
   ],
   "source": [
    "!python fib.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 1, 2, 3, 5, 8, 13, 21, 34, 55]\n"
     ]
    }
   ],
   "source": [
    "%run fib.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 1, 2, 3, 5, 8]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fib(6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Debugger"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "can't multiply sequence by non-int of type 'float'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[25], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mfib\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m1.0\u001b[39;49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/OneDrive/Desktop/npbook-ed3/code/numerical-python-code-ed3-v2-github/fib.py:7\u001b[0m, in \u001b[0;36mfib\u001b[0;34m(N)\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;250m\u001b[39m\u001b[38;5;124;03m\"\"\" \u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;124;03mReturn a list of the first N Fibonacci numbers.\u001b[39;00m\n\u001b[1;32m      5\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m \n\u001b[1;32m      6\u001b[0m f0, f1 \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m0\u001b[39m, \u001b[38;5;241m1\u001b[39m\n\u001b[0;32m----> 7\u001b[0m f \u001b[38;5;241m=\u001b[39m \u001b[43m[\u001b[49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43m \u001b[49m\u001b[43mN\u001b[49m\n\u001b[1;32m      8\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m n \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(\u001b[38;5;241m1\u001b[39m, N):\n\u001b[1;32m      9\u001b[0m     f[n] \u001b[38;5;241m=\u001b[39m f0 \u001b[38;5;241m+\u001b[39m f1\n",
      "\u001b[0;31mTypeError\u001b[0m: can't multiply sequence by non-int of type 'float'"
     ]
    }
   ],
   "source": [
    "fib(1.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "> \u001b[0;32m/Users/rob/OneDrive/Desktop/npbook-ed3/code/numerical-python-code-ed3-v2-github/fib.py\u001b[0m(7)\u001b[0;36mfib\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;32m      5 \u001b[0;31m    \"\"\" \n",
      "\u001b[0m\u001b[0;32m      6 \u001b[0;31m    \u001b[0mf0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\u001b[0;32m----> 7 \u001b[0;31m    \u001b[0mf\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mN\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\u001b[0;32m      8 \u001b[0;31m    \u001b[0;32mfor\u001b[0m \u001b[0mn\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mN\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\u001b[0;32m      9 \u001b[0;31m        \u001b[0mf\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mf0\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mf1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\n"
     ]
    },
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      "ipdb>  N\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n"
     ]
    },
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      "ipdb>  q\n"
     ]
    }
   ],
   "source": [
    "%debug"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Timing and profiling code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "11.6 µs ± 532 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit fib(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 21 µs, sys: 1 µs, total: 22 µs\n",
      "Wall time: 24.8 µs\n"
     ]
    }
   ],
   "source": [
    "result = %time fib(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "100"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "def random_walker_max_distance(M, N):\n",
    "    \"\"\"\n",
    "    Simulate N random walkers taking M steps, and return the largest distance\n",
    "    from the starting point achieved by any of the random walkers.\n",
    "    \"\"\"\n",
    "    trajectories = [np.random.randn(M).cumsum() for _ in range(N)]\n",
    "    return np.max(np.abs(trajectories))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " "
     ]
    },
    {
     "data": {
      "text/plain": [
       "         20013 function calls in 0.335 seconds\n",
       "\n",
       "   Ordered by: internal time\n",
       "\n",
       "   ncalls  tottime  percall  cumtime  percall filename:lineno(function)\n",
       "    10000    0.184    0.000    0.184    0.000 {method 'randn' of 'numpy.random.mtrand.RandomState' objects}\n",
       "    10000    0.071    0.000    0.071    0.000 {method 'cumsum' of 'numpy.ndarray' objects}\n",
       "        1    0.051    0.051    0.328    0.328 2615584822.py:3(random_walker_max_distance)\n",
       "        1    0.020    0.020    0.276    0.276 2615584822.py:8(<listcomp>)\n",
       "        1    0.007    0.007    0.335    0.335 <string>:1(<module>)\n",
       "        1    0.002    0.002    0.002    0.002 {method 'reduce' of 'numpy.ufunc' objects}\n",
       "        1    0.000    0.000    0.335    0.335 {built-in method builtins.exec}\n",
       "        1    0.000    0.000    0.002    0.002 fromnumeric.py:69(_wrapreduction)\n",
       "        1    0.000    0.000    0.002    0.002 <__array_function__ internals>:177(amax)\n",
       "        1    0.000    0.000    0.002    0.002 fromnumeric.py:2675(amax)\n",
       "        1    0.000    0.000    0.002    0.002 {built-in method numpy.core._multiarray_umath.implement_array_function}\n",
       "        1    0.000    0.000    0.000    0.000 fromnumeric.py:70(<dictcomp>)\n",
       "        1    0.000    0.000    0.000    0.000 fromnumeric.py:2670(_amax_dispatcher)\n",
       "        1    0.000    0.000    0.000    0.000 {method 'disable' of '_lsprof.Profiler' objects}\n",
       "        1    0.000    0.000    0.000    0.000 {method 'items' of 'dict' objects}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%prun random_walker_max_distance(400, 10000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Jupyter notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from IPython.display import display, Image, HTML, Math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"http://python.org/images/python-logo.gif\"/>"
      ],
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Image(url='http://python.org/images/python-logo.gif')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import scipy, numpy, matplotlib\n",
    "modules = [numpy, matplotlib, scipy]\n",
    "row = \"<tr> <td>%s</td> <td>%s</td> </tr>\"\n",
    "rows = \"\\n\".join([row % (module.__name__, module.__version__) for module in modules])\n",
    "s = \"<table> <tr><th>Library</th><th>Version</th> </tr> %s</table>\" % rows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'<table> <tr><th>Library</th><th>Version</th> </tr> <tr> <td>numpy</td> <td>1.22.3</td> </tr>\\n<tr> <td>matplotlib</td> <td>3.7.1</td> </tr>\\n<tr> <td>scipy</td> <td>1.7.3</td> </tr></table>'"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table> <tr><th>Library</th><th>Version</th> </tr> <tr> <td>numpy</td> <td>1.22.3</td> </tr>\n",
       "<tr> <td>matplotlib</td> <td>3.7.1</td> </tr>\n",
       "<tr> <td>scipy</td> <td>1.7.3</td> </tr></table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HTML(s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "class HTMLDisplayer(object):\n",
    "    def __init__(self, code):\n",
    "        self.code = code\n",
    "    \n",
    "    def _repr_html_(self):\n",
    "        return self.code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table> <tr><th>Library</th><th>Version</th> </tr> <tr> <td>numpy</td> <td>1.22.3</td> </tr>\n",
       "<tr> <td>matplotlib</td> <td>3.7.1</td> </tr>\n",
       "<tr> <td>scipy</td> <td>1.7.3</td> </tr></table>"
      ],
      "text/plain": [
       "<__main__.HTMLDisplayer at 0x7fd091cbe680>"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HTMLDisplayer(s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\hat{H} = -\\frac{1}{2}\\epsilon \\hat{\\sigma}_z-\\frac{1}{2}\\delta \\hat{\\sigma}_x$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Math(r'\\hat{H} = -\\frac{1}{2}\\epsilon \\hat{\\sigma}_z-\\frac{1}{2}\\delta \\hat{\\sigma}_x')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "class QubitHamiltonian(object):\n",
    "    def __init__(self, epsilon, delta):\n",
    "        self.epsilon = epsilon\n",
    "        self.delta = delta\n",
    "\n",
    "    def _repr_latex_(self):\n",
    "        return \"$\\hat{H} = -%.2f\\hat{\\sigma}_z-%.2f\\hat{\\sigma}_x$\" % \\\n",
    "            (self.epsilon/2, self.delta/2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\hat{H} = -0.25\\hat{\\sigma}_z-0.12\\hat{\\sigma}_x$"
      ],
      "text/plain": [
       "<__main__.QubitHamiltonian at 0x7fd093a851e0>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "QubitHamiltonian(0.5, 0.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy import stats\n",
    "\n",
    "def f(mu):\n",
    "    X = stats.norm(loc=mu, scale=np.sqrt(mu))\n",
    "    N = stats.poisson(mu)\n",
    "    x = np.linspace(0, X.ppf(0.999))\n",
    "    n = np.arange(0, x[-1])\n",
    "\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.plot(x, X.pdf(x), color='black', lw=2, label=\"Normal($\\mu=%d, \\sigma^2=%d$)\" % (mu, mu))\n",
    "    ax.bar(n, N.pmf(n), align='edge', label=r\"Poisson($\\lambda=%d$)\" % mu)\n",
    "    ax.set_ylim(0, X.pdf(x).max() * 1.25)\n",
    "    ax.legend(loc=2, ncol=2)\n",
    "    plt.close(fig)\n",
    "    return fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from ipywidgets import interact\n",
    "import ipywidgets as widgets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "32de52fb68014fa792832416359e353e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=1.0, description='mu', max=20.0, min=1.0, step=1.0), Output()), _dom_c…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "interact(f, mu=widgets.FloatSlider(min=1.0, max=20.0, step=1.0));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Jupyter nbconvert"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[NbConvertApp] Converting notebook ch01-code-listing.ipynb to html\n",
      "[NbConvertApp] Writing 649717 bytes to ch01-code-listing.html\n"
     ]
    }
   ],
   "source": [
    "!jupyter nbconvert --to html ch01-code-listing.ipynb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[NbConvertApp] Converting notebook ch01-code-listing.ipynb to pdf\n",
      "[NbConvertApp] Writing 57494 bytes to notebook.tex\n",
      "[NbConvertApp] Building PDF\n",
      "[NbConvertApp] Running xelatex 3 times: ['xelatex', 'notebook.tex', '-quiet']\n",
      "[NbConvertApp] Running bibtex 1 time: ['bibtex', 'notebook']\n",
      "[NbConvertApp] WARNING | bibtex had problems, most likely because there were no citations\n",
      "[NbConvertApp] PDF successfully created\n",
      "[NbConvertApp] Writing 66341 bytes to ch01-code-listing.pdf\n"
     ]
    }
   ],
   "source": [
    "!jupyter nbconvert --to pdf ch01-code-listing.ipynb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting custom_template.tplx\n"
     ]
    }
   ],
   "source": [
    "%%writefile custom_template.tplx\n",
    "((*- extends 'article.tplx' -*))\n",
    "\n",
    "((* block title *)) \\title{Document title} ((* endblock title *))\n",
    "((* block author *)) \\author{Author's Name} ((* endblock author *))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "!jupyter nbconvert ch01-code-listing.ipynb --to pdf --template custom_template.tplx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[NbConvertApp] Converting notebook ch01-code-listing.ipynb to python\n",
      "[NbConvertApp] Writing 5152 bytes to ch01-code-listing.py\n"
     ]
    }
   ],
   "source": [
    "!jupyter nbconvert ch01-code-listing.ipynb --to python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Versions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "application/json": {
       "Software versions": [
        {
         "module": "Python",
         "version": "3.10.12 64bit [Clang 14.0.6 ]"
        },
        {
         "module": "IPython",
         "version": "8.12.0"
        },
        {
         "module": "OS",
         "version": "macOS 10.15.7 x86_64 i386 64bit"
        },
        {
         "module": "numpy",
         "version": "1.22.3"
        }
       ]
      },
      "text/html": [
       "<table><tr><th>Software</th><th>Version</th></tr><tr><td>Python</td><td>3.10.12 64bit [Clang 14.0.6 ]</td></tr><tr><td>IPython</td><td>8.12.0</td></tr><tr><td>OS</td><td>macOS 10.15.7 x86\\_64 i386 64bit</td></tr><tr><td>numpy</td><td>1.22.3</td></tr><tr><td colspan='2'>Sat Nov 02 17:59:59 2024 JST</td></tr></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{|l|l|}\\hline\n",
       "{\\bf Software} & {\\bf Version} \\\\ \\hline\\hline\n",
       "Python & 3.10.12 64bit [Clang 14.0.6 ] \\\\ \\hline\n",
       "IPython & 8.12.0 \\\\ \\hline\n",
       "OS & macOS 10.15.7 x86\\_64 i386 64bit \\\\ \\hline\n",
       "numpy & 1.22.3 \\\\ \\hline\n",
       "\\hline \\multicolumn{2}{|l|}{Sat Nov 02 17:59:59 2024 JST} \\\\ \\hline\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "Software versions\n",
       "Python 3.10.12 64bit [Clang 14.0.6 ]\n",
       "IPython 8.12.0\n",
       "OS macOS 10.15.7 x86_64 i386 64bit\n",
       "numpy 1.22.3\n",
       "Sat Nov 02 17:59:59 2024 JST"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%reload_ext version_information\n",
    "%version_information numpy"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.10.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}