08_numpy.ipynb

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 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "# Install dependencies\n",
    "%pip install -Uqq numpy ds_tut\n",
    "\n",
    "import ds_tut\n",
    "ds_tut.setup()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Numpy Tutorial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Builtin Help\n",
    "\n",
    "It's very easy to get additional help just from within a notebook."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ? / help / ??\n",
    "\n",
    "- Just append a `?` to an item to see the docstring or call `help(item)`\n",
    "- Append `??` to view the source"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#np.array?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#help(np.array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#np.abs??"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## How to find Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#np.lookfor('diagonal')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Indices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.arange(9).reshape(3, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 1 2]\n",
      " [3 4 5]\n",
      " [6 7 8]]\n"
     ]
    }
   ],
   "source": [
    "print(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4, 5],\n",
       "       [7, 8]])"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[1:,1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[6, 7, 8],\n",
       "       [3, 4, 5],\n",
       "       [0, 1, 2]])"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[::-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 1 2]\n",
      " [3 4 5]\n",
      " [0 0 0]]\n"
     ]
    }
   ],
   "source": [
    "a[a > 5] = 0\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 1 1]\n",
      " [3 1 5]\n",
      " [1 0 1]]\n"
     ]
    }
   ],
   "source": [
    "a.ravel()[::2] = 1\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Broadcasting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.arange(9).reshape(3, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0 10 20]\n",
      " [30 40 50]\n",
      " [60 70 80]]\n"
     ]
    }
   ],
   "source": [
    "print(a * 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[10 10 10]\n"
     ]
    }
   ],
   "source": [
    "b = np.array((10, 10, 10))\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[10 11 12]\n",
      " [13 14 15]\n",
      " [16 17 18]]\n"
     ]
    }
   ],
   "source": [
    "print(a + b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0 10 20]\n",
      " [30 40 50]\n",
      " [60 70 80]]\n"
     ]
    }
   ],
   "source": [
    "print(a * b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Non Scalar Multiplication"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "17.320508075688775"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(b @ b) ** .5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 30, 120, 210]), array([ 30, 120, 210]))"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.dot(b), a @ b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 15,  18,  21],\n",
       "       [ 42,  54,  66],\n",
       "       [ 69,  90, 111]])"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a @ np.arange(9).reshape(3, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "c = np.arange(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "matmul: Input operand 1 has a mismatch in its core dimension 0, with gufunc signature (n?,k),(k,m?)->(n?,m?) (size 4 is different from 3)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[28], line 2\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;66;03m#| notest\u001b[39;00m\n\u001b[0;32m----> 2\u001b[0m \u001b[43ma\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m@\u001b[39;49m\u001b[43m \u001b[49m\u001b[43mc\u001b[49m\n",
      "\u001b[0;31mValueError\u001b[0m: matmul: Input operand 1 has a mismatch in its core dimension 0, with gufunc signature (n?,k),(k,m?)->(n?,m?) (size 4 is different from 3)"
     ]
    }
   ],
   "source": [
    "#| notest\n",
    "a @ c"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Elementwise Comparison"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.full((2, 3), fill_value=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "b = np.full((2, 3), fill_value=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a is b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ True,  True,  True],\n",
       "       [ True,  True,  True]])"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a == b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.all(a == b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "b[0, 0] = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.all(a == b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Performance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 1000000"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Arrays vs Lists"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "39.7 ms ± 668 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt\n",
    "long_list = list(range(n))\n",
    "%timeit [sqrt(_) for _ in long_list]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "879 µs ± 38.6 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n"
     ]
    }
   ],
   "source": [
    "long_array = np.arange(n)\n",
    "%timeit np.sqrt(long_array)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Loops are Bad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = 27"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "UsageError: Line magic function `%%timeit` not found.\n"
     ]
    }
   ],
   "source": [
    "#|notest\n",
    "%%timeit \n",
    "count = 0\n",
    "for i in range(1000000):\n",
    "    if i % x == 0:\n",
    "        count += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.arange(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#|notest\n",
    "%%timeit \n",
    "count = 0\n",
    "for i in a:\n",
    "    if i % x == 0:\n",
    "        count += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#|notest\n",
    "%timeit np.sum(np.mod(a, x) == 0)"
   ]
  }
 ],
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