06-numpy-buffers-fused-types.ipynb

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   "source": [
    "# Cython and NumPy, buffers, fused types"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"https://imgs.xkcd.com/comics/password_strength.png\" width=600 height=600 />"
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   "source": [
    "%load_ext Cython\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pure Python implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# https://en.wiktionary.org/wiki/Shannon_entropy\n",
    "\n",
    "def shannon_entropy_py(p_x):\n",
    "    return - np.sum(p_x * np.log(p_x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cythonized version"
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  },
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    "%%cython -a\n",
    "\n",
    "import numpy as np\n",
    "cimport numpy as cnp\n",
    "\n",
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scipy.stats comparison"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy.stats import poisson\n",
    "poi = poisson(10.0)\n",
    "n = 100\n",
    "pmf = poi.pmf(np.arange(n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.5614099352749125\n",
      "2.56140993527\n",
      "2.56140993527\n"
     ]
    }
   ],
   "source": [
    "print(poi.entropy())\n",
    "print(shannon_entropy_py(pmf))\n",
    "print(shannon_entropy_cy(pmf))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "804 µs ± 12 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "poi.entropy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.2 µs ± 101 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "shannon_entropy_py(pmf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.12 µs ± 82.9 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "shannon_entropy_cy(pmf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Explicit `for` loop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
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   "source": [
    "%%cython -a\n",
    "\n",
    "from libc.math cimport log as clog\n",
    "\n",
    "def shannon_entropy_v1(p_x):\n",
    "    cdef double res = 0.0\n",
    "    cdef int n = p_x.shape[0]\n",
    "    cdef int i\n",
    "    for i in range(n):\n",
    "        res += p_x[i] * clog(p_x[i])\n",
    "    return -res"
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  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "21.4 µs ± 1.13 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "shannon_entropy_v1(pmf)"
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## NumPy buffer special declaration"
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   "source": [
    "%%cython -a\n",
    "\n",
    "cimport numpy as cnp\n",
    "from libc.math cimport log as clog\n",
    "\n",
    "def shannon_entropy_v2(cnp.ndarray[double] p_x):\n",
    "    cdef double res = 0.0\n",
    "    cdef int n = p_x.shape[0]\n",
    "    cdef int i\n",
    "    for i in range(n):\n",
    "        res += p_x[i] * clog(p_x[i])\n",
    "    return -res"
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  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.95 µs ± 110 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "shannon_entropy_v2(pmf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Turn off boundschecking and wraparound checking"
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       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">09</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">double</span> <span class=\"nf\">res</span> <span class=\"o\">=</span> <span class=\"mf\">0.0</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_res = 0.0;\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">10</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">n</span> <span class=\"o\">=</span> <span class=\"n\">p_x</span><span class=\"o\">.</span><span class=\"n\">shape</span><span class=\"p\">[</span><span class=\"mf\">0</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_n = (__pyx_v_p_x-&gt;dimensions[0]);\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">11</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">i</span></pre>\n",
       "<pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">12</span>:     <span class=\"k\">for</span> <span class=\"n\">i</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">n</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_t_1 = __pyx_v_n;\n",
       "  for (__pyx_t_2 = 0; __pyx_t_2 &lt; __pyx_t_1; __pyx_t_2+=1) {\n",
       "    __pyx_v_i = __pyx_t_2;\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">13</span>:         <span class=\"n\">res</span> <span class=\"o\">+=</span> <span class=\"n\">p_x</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">log</span><span class=\"p\">(</span><span class=\"n\">p_x</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"p\">])</span></pre>\n",
       "<pre class='cython code score-0 '>    __pyx_t_3 = __pyx_v_i;\n",
       "    __pyx_t_4 = __pyx_v_i;\n",
       "    __pyx_v_res = (__pyx_v_res + ((*__Pyx_BufPtrStrided1d(double *, __pyx_pybuffernd_p_x.rcbuffer-&gt;pybuffer.buf, __pyx_t_3, __pyx_pybuffernd_p_x.diminfo[0].strides)) * log((*__Pyx_BufPtrStrided1d(double *, __pyx_pybuffernd_p_x.rcbuffer-&gt;pybuffer.buf, __pyx_t_4, __pyx_pybuffernd_p_x.diminfo[0].strides)))));\n",
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       "</pre><pre class=\"cython line score-6\" onclick='toggleDiv(this)'>+<span class=\"\">14</span>:     <span class=\"k\">return</span> <span class=\"o\">-</span><span class=\"n\">res</span></pre>\n",
       "<pre class='cython code score-6 '>  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_r);\n",
       "  __pyx_t_5 = <span class='py_c_api'>PyFloat_FromDouble</span>((-__pyx_v_res)); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 14, __pyx_L1_error)\n",
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   "source": [
    "%%cython -a\n",
    "\n",
    "cimport cython\n",
    "cimport numpy as cnp\n",
    "from libc.math cimport log\n",
    "\n",
    "@cython.boundscheck(False)\n",
    "@cython.wraparound(False)\n",
    "def shannon_entropy_v3(cnp.ndarray[double] p_x):\n",
    "    cdef double res = 0.0\n",
    "    cdef int n = p_x.shape[0]\n",
    "    cdef int i\n",
    "    for i in range(n):\n",
    "        res += p_x[i] * log(p_x[i])\n",
    "    return -res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.91 µs ± 141 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "shannon_entropy_v3(pmf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Typed memoryview syntax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
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       "<pre class='cython code score-0 '>  __pyx_t_1 = __pyx_v_n;\n",
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       "<pre class='cython code score-0 '>    __pyx_t_3 = __pyx_v_i;\n",
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       "</pre><pre class=\"cython line score-6\" onclick='toggleDiv(this)'>+<span class=\"\">13</span>:     <span class=\"k\">return</span> <span class=\"o\">-</span><span class=\"n\">res</span></pre>\n",
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    "%%cython -a\n",
    "\n",
    "cimport cython\n",
    "from libc.math cimport log\n",
    "\n",
    "@cython.boundscheck(False)\n",
    "@cython.wraparound(False)\n",
    "def shannon_entropy_mv(double[::1] p_x):\n",
    "    cdef double res = 0.0\n",
    "    cdef int n = p_x.shape[0]\n",
    "    cdef int i\n",
    "    for i in range(n):\n",
    "        res += p_x[i] * log(p_x[i])\n",
    "    return -res"
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  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.74 µs ± 95.2 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "shannon_entropy_mv(pmf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fused types example"
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  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
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       "<pre class=\"cython line score-473\" onclick='toggleDiv(this)'>+<span class=\"\">07</span>: <span class=\"k\">def</span> <span class=\"nf\">shannon_entropy_mv</span><span class=\"p\">(</span><span class=\"n\">cython</span><span class=\"o\">.</span><span class=\"n\">floating</span><span class=\"p\">[::</span><span class=\"mf\">1</span><span class=\"p\">]</span> <span class=\"n\">p_x</span><span class=\"p\">):</span></pre>\n",
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       "<pre class='cython code score-0 '>  __pyx_v_res = 0.0;\n",
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       "<pre class='cython code score-0 '>  __pyx_v_n = (__pyx_v_p_x.shape[0]);\n",
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       "<pre class='cython code score-0 '>      __pyx_t_5 = __pyx_v_i;\n",
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       "      __pyx_v_res = (__pyx_v_res + ((*((float *) ( /* dim=0 */ ((char *) (((float *) __pyx_v_p_x.data) + __pyx_t_5)) ))) * log((*((float *) ( /* dim=0 */ ((char *) (((float *) __pyx_v_p_x.data) + __pyx_t_6)) ))))));\n",
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       "</pre><pre class=\"cython line score-12\" onclick='toggleDiv(this)'>+<span class=\"\">14</span>:     <span class=\"k\">return</span> <span class=\"o\">-</span><span class=\"n\">res</span></pre>\n",
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     "metadata": {},
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   ],
   "source": [
    "%%cython -a\n",
    "\n",
    "cimport cython\n",
    "from libc.math cimport log\n",
    "\n",
    "@cython.boundscheck(False)\n",
    "@cython.wraparound(False)\n",
    "def shannon_entropy_mv(cython.floating[::1] p_x):\n",
    "    cdef double res = 0.0\n",
    "    cdef int n = p_x.shape[0]\n",
    "    cdef int i\n",
    "    for i in range(n):\n",
    "        if p_x[i] > 0.0: # Have to guard against underflow...\n",
    "            res += p_x[i] * log(p_x[i])\n",
    "    return -res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.5614099352749107\n",
      "2.5614099208867804\n"
     ]
    }
   ],
   "source": [
    "print(shannon_entropy_mv(pmf.astype('f8')))\n",
    "print(shannon_entropy_mv(pmf.astype('f4')))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
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