Section_1.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numba import jit\n",
    "import math"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### First steps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Here we will use the CPU compilation decorator:\n",
    "\n",
    "@jit\n",
    "def hypot(x, y):\n",
    "    # Implementation from https://en.wikipedia.org/wiki/Hypot\n",
    "    x = abs(x);\n",
    "    y = abs(y);\n",
    "    t = min(x, y);\n",
    "    x = max(x, y);\n",
    "    t = t / x;\n",
    "    return x * math.sqrt(1+t*t)"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "Or equivalent\n",
    "def hypot(x, y):\n",
    "    x = abs(x);\n",
    "    y = abs(y);\n",
    "    t = min(x, y);\n",
    "    x = max(x, y);\n",
    "    t = t / x;\n",
    "    return x * math.sqrt(1+t*t)\n",
    "\n",
    "hypot = jit(hypot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The first time we call hypot, the compiler\n",
    "# is triggered and compiles a machine code implementation for float inputs\n",
    "hypot(3.0, 4.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.0"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Numba also saves the original Python implementation\n",
    "# of the function in the .py_func attribute\n",
    "\n",
    "\n",
    "hypot.py_func(3.0, 4.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Benchmaring"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's first measure the speed of the original Python:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "970 ns ± 17.4 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit hypot.py_func(3.0, 4.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "198 ns ± 2.8 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit hypot(3.0, 4.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Python's built-in is even faster than Numba! \n",
    "\n",
    "Why not for this case?\n",
    "\n",
    "This is because Numba does introduce some overhead to each function call that is larger than the function call overhead of Python itself"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### How does Numba work?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "see pic"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see the result of type inference by using the .inspect_types() method, which prints an annotated version of the source code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "hypot (float64, float64)\n",
      "--------------------------------------------------------------------------------\n",
      "# File: <ipython-input-6-7b8e1dc134b8>\n",
      "# --- LINE 3 --- \n",
      "# label 0\n",
      "\n",
      "@jit\n",
      "\n",
      "# --- LINE 4 --- \n",
      "\n",
      "def hypot(x, y):\n",
      "\n",
      "    # --- LINE 5 --- \n",
      "\n",
      "    # Implementation from https://en.wikipedia.org/wiki/Hypot\n",
      "\n",
      "    # --- LINE 6 --- \n",
      "    #   x = arg(0, name=x)  :: float64\n",
      "    #   y = arg(1, name=y)  :: float64\n",
      "    #   $0.1 = global(abs: <built-in function abs>)  :: Function(<built-in function abs>)\n",
      "    #   $0.3 = call $0.1(x, kws=[], args=[Var(x, <ipython-input-6-7b8e1dc134b8> (6))], func=$0.1, vararg=None)  :: (float64,) -> float64\n",
      "    #   del x\n",
      "    #   del $0.1\n",
      "    #   x.1 = $0.3  :: float64\n",
      "    #   del $0.3\n",
      "\n",
      "    x = abs(x);\n",
      "\n",
      "    # --- LINE 7 --- \n",
      "    #   $0.4 = global(abs: <built-in function abs>)  :: Function(<built-in function abs>)\n",
      "    #   $0.6 = call $0.4(y, kws=[], args=[Var(y, <ipython-input-6-7b8e1dc134b8> (6))], func=$0.4, vararg=None)  :: (float64,) -> float64\n",
      "    #   del y\n",
      "    #   del $0.4\n",
      "    #   y.1 = $0.6  :: float64\n",
      "    #   del $0.6\n",
      "\n",
      "    y = abs(y);\n",
      "\n",
      "    # --- LINE 8 --- \n",
      "    #   $0.7 = global(min: <built-in function min>)  :: Function(<built-in function min>)\n",
      "    #   $0.10 = call $0.7(x.1, y.1, kws=[], args=[Var(x.1, <ipython-input-6-7b8e1dc134b8> (6)), Var(y.1, <ipython-input-6-7b8e1dc134b8> (7))], func=$0.7, vararg=None)  :: (float64, float64) -> float64\n",
      "    #   del $0.7\n",
      "    #   t = $0.10  :: float64\n",
      "    #   del $0.10\n",
      "\n",
      "    t = min(x, y);\n",
      "\n",
      "    # --- LINE 9 --- \n",
      "    #   $0.11 = global(max: <built-in function max>)  :: Function(<built-in function max>)\n",
      "    #   $0.14 = call $0.11(x.1, y.1, kws=[], args=[Var(x.1, <ipython-input-6-7b8e1dc134b8> (6)), Var(y.1, <ipython-input-6-7b8e1dc134b8> (7))], func=$0.11, vararg=None)  :: (float64, float64) -> float64\n",
      "    #   del y.1\n",
      "    #   del x.1\n",
      "    #   del $0.11\n",
      "    #   x.2 = $0.14  :: float64\n",
      "    #   del $0.14\n",
      "\n",
      "    x = max(x, y);\n",
      "\n",
      "    # --- LINE 10 --- \n",
      "    #   $0.17 = t / x.2  :: float64\n",
      "    #   del t\n",
      "    #   t.1 = $0.17  :: float64\n",
      "    #   del $0.17\n",
      "\n",
      "    t = t / x;\n",
      "\n",
      "    # --- LINE 11 --- \n",
      "    #   $0.19 = global(math: <module 'math' (built-in)>)  :: Module(<module 'math' (built-in)>)\n",
      "    #   $0.20 = getattr(attr=sqrt, value=$0.19)  :: Function(<built-in function sqrt>)\n",
      "    #   del $0.19\n",
      "    #   $const0.21 = const(int, 1)  :: int64\n",
      "    #   $0.24 = t.1 * t.1  :: float64\n",
      "    #   del t.1\n",
      "    #   $0.25 = $const0.21 + $0.24  :: float64\n",
      "    #   del $const0.21\n",
      "    #   del $0.24\n",
      "    #   $0.26 = call $0.20($0.25, kws=[], args=[Var($0.25, <ipython-input-6-7b8e1dc134b8> (11))], func=$0.20, vararg=None)  :: (float64,) -> float64\n",
      "    #   del $0.25\n",
      "    #   del $0.20\n",
      "    #   $0.27 = x.2 * $0.26  :: float64\n",
      "    #   del x.2\n",
      "    #   del $0.26\n",
      "    #   $0.28 = cast(value=$0.27)  :: float64\n",
      "    #   del $0.27\n",
      "    #   return $0.28\n",
      "\n",
      "    return x * math.sqrt(1+t*t)\n",
      "\n",
      "\n",
      "================================================================================\n"
     ]
    }
   ],
   "source": [
    "hypot.inspect_types()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that Numba's type names tend to mirror the NumPy type names, so a Python float is a float64 (also called \"double precision\" in other languages). Taking a look at the data types can sometimes be important in GPU code because the performance of float32 and float64 computations will be very different on CUDA devices. An accidental upcast can dramatically slow down a function."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### When Things Go Wrong"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Numba cannot compile all Python code. Some functions don't have a Numba-translation, and some kinds of Python types can't be efficiently compiled at all (yet). For example, Numba does not support dictionaries (as of this tutorial):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'value'"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@jit\n",
    "def cannot_compile(x):\n",
    "    return x['key']\n",
    "\n",
    "cannot_compile(dict(key='value'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wait, what happened?? By default, Numba will fall back to a mode, called \"object mode,\" which does not do type-specialization. Object mode exists to enable other Numba functionality, but in many cases, you want Numba to tell you if type inference fails. You can force \"nopython mode\" (the other compilation mode) by passing arguments to the decorator:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "ename": "TypingError",
     "evalue": "Failed at nopython (nopython frontend)\nInternal error at <numba.typeinfer.ArgConstraint object at 0x0000026579283D30>:\n--%<----------------------------------------------------------------------------\nTraceback (most recent call last):\n  File \"C:\\Users\\Nuclear\\Anaconda3\\lib\\site-packages\\numba\\errors.py\", line 577, in new_error_context\n    yield\n  File \"C:\\Users\\Nuclear\\Anaconda3\\lib\\site-packages\\numba\\typeinfer.py\", line 199, in __call__\n    assert ty.is_precise()\nAssertionError\n\nDuring handling of the above exception, another exception occurred:\n\nTraceback (most recent call last):\n  File \"C:\\Users\\Nuclear\\Anaconda3\\lib\\site-packages\\numba\\typeinfer.py\", line 142, in propagate\n    constraint(typeinfer)\n  File \"C:\\Users\\Nuclear\\Anaconda3\\lib\\site-packages\\numba\\typeinfer.py\", line 200, in __call__\n    typeinfer.add_type(self.dst, ty, loc=self.loc)\n  File \"C:\\Users\\Nuclear\\Anaconda3\\Lib\\contextlib.py\", line 77, in __exit__\n    self.gen.throw(type, value, traceback)\n  File \"C:\\Users\\Nuclear\\Anaconda3\\lib\\site-packages\\numba\\errors.py\", line 585, in new_error_context\n    six.reraise(type(newerr), newerr, tb)\n  File \"C:\\Users\\Nuclear\\Anaconda3\\lib\\site-packages\\numba\\six.py\", line 659, in reraise\n    raise value\nnumba.errors.InternalError: \u001b[1m\u001b[1m\u001b[0m\n\u001b[0m\u001b[1m[1] During: typing of argument at <ipython-input-19-42c374763781> (3)\u001b[0m\n--%<----------------------------------------------------------------------------\n\n\u001b[1m\nFile \"<ipython-input-19-42c374763781>\", line 3:\u001b[0m\n\u001b[1mdef cannot_compile(x):\n\u001b[1m    return x['key']\n\u001b[0m    \u001b[1m^\u001b[0m\u001b[0m\n\nThis error may have been caused by the following argument(s):\n- argument 0: \u001b[1mcannot determine Numba type of <class 'dict'>\u001b[0m\n\nThis is not usually a problem with Numba itself but instead often caused by\nthe use of unsupported features or an issue in resolving types.\n\nTo see Python/NumPy features supported by the latest release of Numba visit:\nhttp://numba.pydata.org/numba-doc/dev/reference/pysupported.html\nand\nhttp://numba.pydata.org/numba-doc/dev/reference/numpysupported.html\n\nFor more information about typing errors and how to debug them visit:\nhttp://numba.pydata.org/numba-doc/latest/user/troubleshoot.html#my-code-doesn-t-compile\n\nIf you think your code should work with Numba, please report the error message\nand traceback, along with a minimal reproducer at:\nhttps://github.com/numba/numba/issues/new\n",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypingError\u001b[0m                               Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-19-42c374763781>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      3\u001b[0m     \u001b[1;32mreturn\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'key'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 5\u001b[1;33m \u001b[0mcannot_compile\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdict\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'value'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32m~\\Anaconda3\\lib\\site-packages\\numba\\dispatcher.py\u001b[0m in \u001b[0;36m_compile_for_args\u001b[1;34m(self, *args, **kws)\u001b[0m\n\u001b[0;32m    347\u001b[0m                 \u001b[0me\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpatch_message\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmsg\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    348\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 349\u001b[1;33m             \u001b[0merror_rewrite\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0me\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'typing'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    350\u001b[0m         \u001b[1;32mexcept\u001b[0m \u001b[0merrors\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mUnsupportedError\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0me\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    351\u001b[0m             \u001b[1;31m# Something unsupported is present in the user code, add help info\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Anaconda3\\lib\\site-packages\\numba\\dispatcher.py\u001b[0m in \u001b[0;36merror_rewrite\u001b[1;34m(e, issue_type)\u001b[0m\n\u001b[0;32m    314\u001b[0m                 \u001b[1;32mraise\u001b[0m \u001b[0me\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    315\u001b[0m             \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 316\u001b[1;33m                 \u001b[0mreraise\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtype\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0me\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0me\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    317\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    318\u001b[0m         \u001b[0margtypes\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Anaconda3\\lib\\site-packages\\numba\\six.py\u001b[0m in \u001b[0;36mreraise\u001b[1;34m(tp, value, tb)\u001b[0m\n\u001b[0;32m    656\u001b[0m             \u001b[0mvalue\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mtp\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    657\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mvalue\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__traceback__\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mtb\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 658\u001b[1;33m             \u001b[1;32mraise\u001b[0m \u001b[0mvalue\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mwith_traceback\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtb\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    659\u001b[0m         \u001b[1;32mraise\u001b[0m \u001b[0mvalue\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    660\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mTypingError\u001b[0m: Failed at nopython (nopython frontend)\nInternal error at <numba.typeinfer.ArgConstraint object at 0x0000026579283D30>:\n--%<----------------------------------------------------------------------------\nTraceback (most recent call last):\n  File \"C:\\Users\\Nuclear\\Anaconda3\\lib\\site-packages\\numba\\errors.py\", line 577, in new_error_context\n    yield\n  File \"C:\\Users\\Nuclear\\Anaconda3\\lib\\site-packages\\numba\\typeinfer.py\", line 199, in __call__\n    assert ty.is_precise()\nAssertionError\n\nDuring handling of the above exception, another exception occurred:\n\nTraceback (most recent call last):\n  File \"C:\\Users\\Nuclear\\Anaconda3\\lib\\site-packages\\numba\\typeinfer.py\", line 142, in propagate\n    constraint(typeinfer)\n  File \"C:\\Users\\Nuclear\\Anaconda3\\lib\\site-packages\\numba\\typeinfer.py\", line 200, in __call__\n    typeinfer.add_type(self.dst, ty, loc=self.loc)\n  File \"C:\\Users\\Nuclear\\Anaconda3\\Lib\\contextlib.py\", line 77, in __exit__\n    self.gen.throw(type, value, traceback)\n  File \"C:\\Users\\Nuclear\\Anaconda3\\lib\\site-packages\\numba\\errors.py\", line 585, in new_error_context\n    six.reraise(type(newerr), newerr, tb)\n  File \"C:\\Users\\Nuclear\\Anaconda3\\lib\\site-packages\\numba\\six.py\", line 659, in reraise\n    raise value\nnumba.errors.InternalError: \u001b[1m\u001b[1m\u001b[0m\n\u001b[0m\u001b[1m[1] During: typing of argument at <ipython-input-19-42c374763781> (3)\u001b[0m\n--%<----------------------------------------------------------------------------\n\n\u001b[1m\nFile \"<ipython-input-19-42c374763781>\", line 3:\u001b[0m\n\u001b[1mdef cannot_compile(x):\n\u001b[1m    return x['key']\n\u001b[0m    \u001b[1m^\u001b[0m\u001b[0m\n\nThis error may have been caused by the following argument(s):\n- argument 0: \u001b[1mcannot determine Numba type of <class 'dict'>\u001b[0m\n\nThis is not usually a problem with Numba itself but instead often caused by\nthe use of unsupported features or an issue in resolving types.\n\nTo see Python/NumPy features supported by the latest release of Numba visit:\nhttp://numba.pydata.org/numba-doc/dev/reference/pysupported.html\nand\nhttp://numba.pydata.org/numba-doc/dev/reference/numpysupported.html\n\nFor more information about typing errors and how to debug them visit:\nhttp://numba.pydata.org/numba-doc/latest/user/troubleshoot.html#my-code-doesn-t-compile\n\nIf you think your code should work with Numba, please report the error message\nand traceback, along with a minimal reproducer at:\nhttps://github.com/numba/numba/issues/new\n"
     ]
    }
   ],
   "source": [
    "@jit(nopython=True)\n",
    "def cannot_compile(x):\n",
    "    return x['key']\n",
    "\n",
    "cannot_compile(dict(key='value'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we get an exception when Numba tries to compile the function, with an error that says:\n",
    "\n",
    "- argument 0: cannot determine Numba type of <class 'dict'>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Exercise "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below is a function that loops over two input NumPy arrays and puts their sum into the output array. Modify this function to call the hypot function we defined above. We will learn a more efficient way to write such functions in a future section.\n",
    "\n",
    "(Make sure to execute all the cells in this notebook so that hypot is defined.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jit(nopython=True)\n",
    "def ex1(x, y, out):\n",
    "    for i in range(x.shape[0]):\n",
    "        # out[i] = x[i] + y[i] # Wrong!\n",
    "        out[i] = np.sqrt(x[i]**2 + y[i]**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "in1: [0. 1. 2. 3. 4. 5. 6. 7. 8. 9.]\n",
      "in2: [ 1.  3.  5.  7.  9. 11. 13. 15. 17. 19.]\n",
      "out: [ 1.          3.16227766  5.38516481  7.61577311  9.8488578  12.08304597\n",
      " 14.31782106 16.55294536 18.78829423 21.02379604]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "in1 = np.arange(10, dtype=np.float64)\n",
    "in2 = 2 * in1 + 1\n",
    "out = np.empty_like(in1)\n",
    "\n",
    "print('in1:', in1)\n",
    "print('in2:', in2)\n",
    "\n",
    "ex1(in1, in2, out)\n",
    "\n",
    "print('out:', out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "# This test will fail until you fix the ex1 function\n",
    "np.testing.assert_almost_equal(out, np.hypot(in1, in2))"
   ]
  }
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