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kudkudak/conditional_entropy.ipynb

Last active February 3, 2016 13:33
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Conditional entropy calculation in Python, Numba and Cython (ugly! sorry)
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conditional_entropy.ipynb
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"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
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"name": "stdout",
"output_type": "stream",
"text": [
"The cython extension is already loaded. To reload it, use:\n",
" %reload_ext cython\n"
]
}
],
"source": [
"import numpy as np\n",
"from numba import autojit\n",
"%load_ext cython"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Function code and checks"
]
},
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"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
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"source": [
"def conditional_entropy_python(X, Y):\n",
" \"\"\" \n",
" Calculate conditional entropy of all columns of X against Y (i.e. \\sum_i=1^{N} H(X_i | Y)).\n",
" \"\"\"\n",
" # Calculate distribution of y \n",
" Y_dist = np.zeros(shape=(int(Y.max()) + 1, ), dtype=np.float32)\n",
" for y in range(Y.max() + 1):\n",
" Y_dist[y] = (float(len(np.where(Y==y)[0]))/len(Y))\n",
" \n",
" Y_max = Y.max()\n",
" X_max = X.max()\n",
" \n",
" ce_sum = 0.\n",
" for i in range(X.shape[1]):\n",
" ce_sum_partial = 0.\n",
" \n",
" # Count \n",
" counts = np.zeros(shape=(X_max + 1, Y_max + 1), dtype=np.int32)\n",
" for row, x in enumerate(X[:, i]):\n",
" counts[x, Y[row]] += 1\n",
" \n",
" # For each value of y add conditional probability\n",
" for y in range(Y.max() + 1):\n",
" count_sum = float(counts[:, y].sum())\n",
" probs = counts[:, y] / count_sum\n",
" entropy = -probs * np.log2(probs)\n",
" ce_sum_partial += (entropy * Y_dist[y]).sum()\n",
"\n",
" ce_sum += ce_sum_partial\n",
" \n",
" return ce_sum"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Some data: two conditionally independent variables\n",
"X = np.random.randint(0, 2, size=(10000, 80))\n",
"Y = np.random.randint(0, 2, size=(10000))"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Check that function calculates correctly entropy\n",
"val = conditional_entropy_python(X, Y)\n",
"assert abs(val - X.shape[1]) < 0.1, \"X and Y are conditionally independent. 1 bit per column\""
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# nopython=True is very important, will fail for non-typed code\n",
"conditional_entropy_numba = autojit(nopython=True)(conditional_entropy_python)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
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"outputs": [
{
"data": {
"text/plain": [
"(79.989800335148786, 79.98980033514879)"
]
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"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
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],
"source": [
"# Always when optimizing check that we have same output\n",
"conditional_entropy_python(X, Y), conditional_entropy_numba(X, Y)"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"## Time measurement. Numba speeds up by 100x using just 1 line"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1 loops, best of 3: 1.69 s per loop\n",
"10 loops, best of 3: 17.5 ms per loop\n"
]
}
],
"source": [
"%timeit conditional_entropy_python(X, Y)\n",
"%timeit conditional_entropy_numba(X, Y)\n",
"\n",
"# 100 times faster!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Try cython"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Annotate will tell you if everything is truly Cython\n",
"\n",
"Code is very ugly, doesn't matter for now"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
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" __pyx_t_6 = 0;\n",
"</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">23</span>: </pre>\n",
"<pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">24</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=\"\">25</span>: <span class=\"k\">for</span> <span class=\"n\">j</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">M</span><span class=\"p\">):</span></pre>\n",
"<pre class='cython code score-0 '> __pyx_t_8 = __pyx_v_M;\n",
" for (__pyx_t_9 = 0; __pyx_t_9 &lt; __pyx_t_8; __pyx_t_9+=1) {\n",
" __pyx_v_j = __pyx_t_9;\n",
"</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">26</span>: <span class=\"n\">X_max</span> <span class=\"o\">=</span> <span class=\"nb\">max</span><span class=\"p\">(</span><span class=\"n\">X_max</span><span class=\"p\">,</span> <span class=\"n\">X</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"o\">*</span><span class=\"n\">M</span> <span class=\"o\">+</span> <span class=\"n\">j</span><span class=\"p\">])</span></pre>\n",
"<pre class='cython code score-0 '> __pyx_t_5 = (__pyx_v_X[((__pyx_v_i * __pyx_v_M) + __pyx_v_j)]);\n",
" __pyx_t_3 = __pyx_v_X_max;\n",
" if (((__pyx_t_5 &gt; __pyx_t_3) != 0)) {\n",
" __pyx_t_4 = __pyx_t_5;\n",
" } else {\n",
" __pyx_t_4 = __pyx_t_3;\n",
" }\n",
" __pyx_v_X_max = __pyx_t_4;\n",
" }\n",
" }\n",
"</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">27</span>: </pre>\n",
"<pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">28</span>: <span class=\"k\">for</span> <span class=\"n\">y</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">Y_max</span> <span class=\"o\">+</span> <span class=\"mf\">1</span><span class=\"p\">):</span></pre>\n",
"<pre class='cython code score-0 '> __pyx_t_4 = (__pyx_v_Y_max + 1);\n",
" for (__pyx_t_1 = 0; __pyx_t_1 &lt; __pyx_t_4; __pyx_t_1+=1) {\n",
" __pyx_v_y = __pyx_t_1;\n",
"</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">29</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_2 = __pyx_v_N;\n",
" for (__pyx_t_8 = 0; __pyx_t_8 &lt; __pyx_t_2; __pyx_t_8+=1) {\n",
" __pyx_v_i = __pyx_t_8;\n",
"</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">30</span>: <span class=\"k\">if</span> <span class=\"n\">Y</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"p\">]</span> <span class=\"o\">==</span> <span class=\"n\">y</span><span class=\"p\">:</span></pre>\n",
"<pre class='cython code score-0 '> __pyx_t_10 = (((__pyx_v_Y[__pyx_v_i]) == __pyx_v_y) != 0);\n",
" if (__pyx_t_10) {\n",
"/* … */\n",
" }\n",
" }\n",
"</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">31</span>: <span class=\"n\">Y_dist</span><span class=\"o\">.</span><span class=\"n\">data</span><span class=\"o\">.</span><span class=\"n\">as_floats</span><span class=\"p\">[</span><span class=\"n\">y</span><span class=\"p\">]</span> <span class=\"o\">+=</span> <span class=\"mf\">1</span></pre>\n",
"<pre class='cython code score-0 '> __pyx_t_9 = __pyx_v_y;\n",
" (__pyx_v_Y_dist-&gt;data.as_floats[__pyx_t_9]) = ((__pyx_v_Y_dist-&gt;data.as_floats[__pyx_t_9]) + 1.0);\n",
"</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">32</span>: <span class=\"n\">total</span> <span class=\"o\">+=</span> <span class=\"n\">Y_dist</span><span class=\"o\">.</span><span class=\"n\">data</span><span class=\"o\">.</span><span class=\"n\">as_floats</span><span class=\"p\">[</span><span class=\"n\">y</span><span class=\"p\">]</span></pre>\n",
"<pre class='cython code score-0 '> __pyx_v_total = (__pyx_v_total + (__pyx_v_Y_dist-&gt;data.as_floats[__pyx_v_y]));\n",
" }\n",
"</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">33</span>: </pre>\n",
"<pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">34</span>: <span class=\"k\">for</span> <span class=\"n\">y</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">Y_max</span> <span class=\"o\">+</span> <span class=\"mf\">1</span><span class=\"p\">):</span></pre>\n",
"<pre class='cython code score-0 '> __pyx_t_4 = (__pyx_v_Y_max + 1);\n",
" for (__pyx_t_1 = 0; __pyx_t_1 &lt; __pyx_t_4; __pyx_t_1+=1) {\n",
" __pyx_v_y = __pyx_t_1;\n",
"</pre><pre class=\"cython line score-5\" onclick='toggleDiv(this)'>+<span class=\"\">35</span>: <span class=\"n\">Y_dist</span><span class=\"o\">.</span><span class=\"n\">data</span><span class=\"o\">.</span><span class=\"n\">as_floats</span><span class=\"p\">[</span><span class=\"n\">y</span><span class=\"p\">]</span> <span class=\"o\">/=</span> <span class=\"n\">total</span></pre>\n",
"<pre class='cython code score-5 '> __pyx_t_2 = __pyx_v_y;\n",
" if (unlikely(__pyx_v_total == 0)) {\n",
" <span class='py_c_api'>PyErr_SetString</span>(PyExc_ZeroDivisionError, \"float division\");\n",
" <span class='error_goto'>{__pyx_filename = __pyx_f[0]; __pyx_lineno = 35; __pyx_clineno = __LINE__; goto __pyx_L1_error;}</span>\n",
" }\n",
" (__pyx_v_Y_dist-&gt;data.as_floats[__pyx_t_2]) = ((__pyx_v_Y_dist-&gt;data.as_floats[__pyx_t_2]) / __pyx_v_total);\n",
" }\n",
"</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">36</span>: </pre>\n",
"<pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">37</span>: <span class=\"n\">ce_sum</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span></pre>\n",
"<pre class='cython code score-0 '> __pyx_v_ce_sum = 0.;\n",
"</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">38</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\">M</span><span class=\"p\">):</span></pre>\n",
"<pre class='cython code score-0 '> __pyx_t_1 = __pyx_v_M;\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=\"\">39</span>: <span class=\"n\">ce_sum_partial</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span></pre>\n",
"<pre class='cython code score-0 '> __pyx_v_ce_sum_partial = 0.;\n",
"</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">40</span>: </pre>\n",
"<pre class=\"cython line score-0\">&#xA0;<span class=\"\">41</span>: <span class=\"c\"># Zero out count (could be done using memset)</span></pre>\n",
"<pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">42</span>: <span class=\"k\">for</span> <span class=\"n\">j</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">X_max</span> <span class=\"o\">+</span> <span class=\"mf\">1</span><span class=\"p\">):</span></pre>\n",
"<pre class='cython code score-0 '> __pyx_t_4 = (__pyx_v_X_max + 1);\n",
" for (__pyx_t_8 = 0; __pyx_t_8 &lt; __pyx_t_4; __pyx_t_8+=1) {\n",
" __pyx_v_j = __pyx_t_8;\n",
"</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">43</span>: <span class=\"k\">for</span> <span class=\"n\">k</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">Y_max</span> <span class=\"o\">+</span> <span class=\"mf\">1</span><span class=\"p\">):</span></pre>\n",
"<pre class='cython code score-0 '> __pyx_t_5 = (__pyx_v_Y_max + 1);\n",
" for (__pyx_t_9 = 0; __pyx_t_9 &lt; __pyx_t_5; __pyx_t_9+=1) {\n",
" __pyx_v_k = __pyx_t_9;\n",
"</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">44</span>: <span class=\"n\">counts</span><span class=\"o\">.</span><span class=\"n\">data</span><span class=\"o\">.</span><span class=\"n\">as_floats</span><span class=\"p\">[</span><span class=\"n\">j</span> <span class=\"o\">*</span> <span class=\"p\">(</span><span class=\"n\">Y_max</span> <span class=\"o\">+</span> <span class=\"mf\">1</span><span class=\"p\">)</span> <span class=\"o\">+</span> <span class=\"n\">k</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"mf\">0</span></pre>\n",
"<pre class='cython code score-0 '> (__pyx_v_counts-&gt;data.as_floats[((__pyx_v_j * (__pyx_v_Y_max + 1)) + __pyx_v_k)]) = 0.0;\n",
" }\n",
" }\n",
"</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">45</span>: </pre>\n",
"<pre class=\"cython line score-0\">&#xA0;<span class=\"\">46</span>: <span class=\"c\"># Calculate count</span></pre>\n",
"<pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">47</span>: <span class=\"k\">for</span> <span class=\"n\">j</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_8 = __pyx_v_N;\n",
" for (__pyx_t_9 = 0; __pyx_t_9 &lt; __pyx_t_8; __pyx_t_9+=1) {\n",
" __pyx_v_j = __pyx_t_9;\n",
"</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">48</span>: <span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">X</span><span class=\"p\">[</span><span class=\"n\">j</span> <span class=\"o\">*</span> <span class=\"n\">M</span> <span class=\"o\">+</span> <span class=\"n\">i</span><span class=\"p\">]</span></pre>\n",
"<pre class='cython code score-0 '> __pyx_v_x = (__pyx_v_X[((__pyx_v_j * __pyx_v_M) + __pyx_v_i)]);\n",
"</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">49</span>: <span class=\"n\">counts</span><span class=\"o\">.</span><span class=\"n\">data</span><span class=\"o\">.</span><span class=\"n\">as_floats</span><span class=\"p\">[</span><span class=\"n\">x</span> <span class=\"o\">*</span> <span class=\"p\">(</span><span class=\"n\">Y_max</span> <span class=\"o\">+</span> <span class=\"mf\">1</span><span class=\"p\">)</span> <span class=\"o\">+</span> <span class=\"n\">Y</span><span class=\"p\">[</span><span class=\"n\">j</span><span class=\"p\">]]</span> <span class=\"o\">+=</span> <span class=\"mf\">1</span></pre>\n",
"<pre class='cython code score-0 '> __pyx_t_4 = ((__pyx_v_x * (__pyx_v_Y_max + 1)) + (__pyx_v_Y[__pyx_v_j]));\n",
" (__pyx_v_counts-&gt;data.as_floats[__pyx_t_4]) = ((__pyx_v_counts-&gt;data.as_floats[__pyx_t_4]) + 1.0);\n",
" }\n",
"</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">50</span>: </pre>\n",
"<pre class=\"cython line score-0\">&#xA0;<span class=\"\">51</span>: <span class=\"c\"># For each value of y add conditional probability</span></pre>\n",
"<pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">52</span>: <span class=\"k\">for</span> <span class=\"n\">y</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">Y_max</span> <span class=\"o\">+</span> <span class=\"mf\">1</span><span class=\"p\">):</span></pre>\n",
"<pre class='cython code score-0 '> __pyx_t_4 = (__pyx_v_Y_max + 1);\n",
" for (__pyx_t_8 = 0; __pyx_t_8 &lt; __pyx_t_4; __pyx_t_8+=1) {\n",
" __pyx_v_y = __pyx_t_8;\n",
"</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">53</span>: <span class=\"n\">count_sum</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span></pre>\n",
"<pre class='cython code score-0 '> __pyx_v_count_sum = 0.;\n",
"</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">54</span>: <span class=\"k\">for</span> <span class=\"n\">j</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_9 = __pyx_v_N;\n",
" for (__pyx_t_11 = 0; __pyx_t_11 &lt; __pyx_t_9; __pyx_t_11+=1) {\n",
" __pyx_v_j = __pyx_t_11;\n",
"</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">55</span>: <span class=\"n\">count_sum</span> <span class=\"o\">+=</span> <span class=\"n\">counts</span><span class=\"o\">.</span><span class=\"n\">data</span><span class=\"o\">.</span><span class=\"n\">as_floats</span><span class=\"p\">[</span><span class=\"n\">j</span> <span class=\"o\">*</span> <span class=\"p\">(</span><span class=\"n\">Y_max</span> <span class=\"o\">+</span> <span class=\"mf\">1</span><span class=\"p\">)</span> <span class=\"o\">+</span> <span class=\"n\">y</span><span class=\"p\">]</span></pre>\n",
"<pre class='cython code score-0 '> __pyx_v_count_sum = (__pyx_v_count_sum + (__pyx_v_counts-&gt;data.as_floats[((__pyx_v_j * (__pyx_v_Y_max + 1)) + __pyx_v_y)]));\n",
" }\n",
"</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">56</span>: </pre>\n",
"<pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">57</span>: <span class=\"k\">for</span> <span class=\"n\">j</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">X_max</span> <span class=\"o\">+</span> <span class=\"mf\">1</span><span class=\"p\">):</span></pre>\n",
"<pre class='cython code score-0 '> __pyx_t_5 = (__pyx_v_X_max + 1);\n",
" for (__pyx_t_9 = 0; __pyx_t_9 &lt; __pyx_t_5; __pyx_t_9+=1) {\n",
" __pyx_v_j = __pyx_t_9;\n",
"</pre><pre class=\"cython line score-5\" onclick='toggleDiv(this)'>+<span class=\"\">58</span>: <span class=\"n\">prob</span> <span class=\"o\">=</span> <span class=\"n\">counts</span><span class=\"o\">.</span><span class=\"n\">data</span><span class=\"o\">.</span><span class=\"n\">as_floats</span><span class=\"p\">[</span><span class=\"n\">j</span> <span class=\"o\">*</span> <span class=\"p\">(</span><span class=\"n\">Y_max</span> <span class=\"o\">+</span> <span class=\"mf\">1</span><span class=\"p\">)</span> <span class=\"o\">+</span> <span class=\"n\">y</span><span class=\"p\">]</span><span class=\"o\">/</span><span class=\"n\">count_sum</span></pre>\n",
"<pre class='cython code score-5 '> __pyx_t_12 = (__pyx_v_counts-&gt;data.as_floats[((__pyx_v_j * (__pyx_v_Y_max + 1)) + __pyx_v_y)]);\n",
" if (unlikely(__pyx_v_count_sum == 0)) {\n",
" <span class='py_c_api'>PyErr_SetString</span>(PyExc_ZeroDivisionError, \"float division\");\n",
" <span class='error_goto'>{__pyx_filename = __pyx_f[0]; __pyx_lineno = 58; __pyx_clineno = __LINE__; goto __pyx_L1_error;}</span>\n",
" }\n",
" __pyx_v_prob = (__pyx_t_12 / __pyx_v_count_sum);\n",
"</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">59</span>: <span class=\"k\">if</span> <span class=\"n\">prob</span> <span class=\"o\">&lt;</span> <span class=\"mf\">0.0001</span><span class=\"p\">:</span></pre>\n",
"<pre class='cython code score-0 '> __pyx_t_10 = ((__pyx_v_prob &lt; 0.0001) != 0);\n",
" if (__pyx_t_10) {\n",
"/* … */\n",
" }\n",
"</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">60</span>: <span class=\"n\">prob</span> <span class=\"o\">=</span> <span class=\"mf\">0.0001</span></pre>\n",
"<pre class='cython code score-0 '> __pyx_v_prob = 0.0001;\n",
"</pre><pre class=\"cython line score-5\" onclick='toggleDiv(this)'>+<span class=\"\">61</span>: <span class=\"n\">ce_sum_partial</span> <span class=\"o\">+=</span> <span class=\"o\">-</span><span class=\"n\">prob</span> <span class=\"o\">*</span> <span class=\"n\">log</span><span class=\"p\">(</span><span class=\"n\">prob</span><span class=\"p\">)</span><span class=\"o\">/</span><span class=\"n\">log</span><span class=\"p\">(</span><span class=\"mf\">2.</span><span class=\"p\">)</span><span class=\"o\">*</span> <span class=\"n\">Y_dist</span><span class=\"o\">.</span><span class=\"n\">data</span><span class=\"o\">.</span><span class=\"n\">as_floats</span><span class=\"p\">[</span><span class=\"n\">y</span><span class=\"p\">]</span></pre>\n",
"<pre class='cython code score-5 '> __pyx_t_13 = ((-__pyx_v_prob) * log(__pyx_v_prob));\n",
" __pyx_t_14 = log(2.);\n",
" if (unlikely(__pyx_t_14 == 0)) {\n",
" <span class='py_c_api'>PyErr_SetString</span>(PyExc_ZeroDivisionError, \"float division\");\n",
" <span class='error_goto'>{__pyx_filename = __pyx_f[0]; __pyx_lineno = 61; __pyx_clineno = __LINE__; goto __pyx_L1_error;}</span>\n",
" }\n",
" __pyx_v_ce_sum_partial = (__pyx_v_ce_sum_partial + ((__pyx_t_13 / __pyx_t_14) * (__pyx_v_Y_dist-&gt;data.as_floats[__pyx_v_y])));\n",
" }\n",
" }\n",
"</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">62</span>: </pre>\n",
"<pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">63</span>: <span class=\"n\">ce_sum</span> <span class=\"o\">+=</span> <span class=\"n\">ce_sum_partial</span></pre>\n",
"<pre class='cython code score-0 '> __pyx_v_ce_sum = (__pyx_v_ce_sum + __pyx_v_ce_sum_partial);\n",
" }\n",
"</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">64</span>: </pre>\n",
"<pre class=\"cython line score-6\" onclick='toggleDiv(this)'>+<span class=\"\">65</span>: <span class=\"k\">return</span> <span class=\"n\">ce_sum</span></pre>\n",
"<pre class='cython code score-6 '> <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_r);\n",
" __pyx_t_6 = <span class='py_c_api'>PyFloat_FromDouble</span>(__pyx_v_ce_sum);<span class='error_goto'> if (unlikely(!__pyx_t_6)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 65; __pyx_clineno = __LINE__; goto __pyx_L1_error;}</span>\n",
" <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_6);\n",
" __pyx_r = __pyx_t_6;\n",
" __pyx_t_6 = 0;\n",
" goto __pyx_L0;\n",
"</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">66</span>: </pre>\n",
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"%%cython --annotate\n",
"\n",
"cimport numpy as np\n",
"from cpython cimport array\n",
"import array\n",
"\n",
"cdef extern from \"math.h\":\n",
" double log(double x)\n",
"\n",
"\n",
"cdef _conditional_entropy_cython(long * X, long * Y, int N, int M):\n",
" cdef long Y_max=0, X_max=0\n",
" cdef int i=0, j=0, k=0\n",
" cdef float ce_sum=0, ce_sum_partial=0.\n",
" cdef int x=0, y=0\n",
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" cdef array.array Y_dist = array.array('f', [0 for _ in range(Y_max + 1)])\n",
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" \n",
" for i in range(N):\n",
" for j in range(M):\n",
" X_max = max(X_max, X[i*M + j]) \n",
"\n",
" for y in range(Y_max + 1):\n",
" for i in range(N):\n",
" if Y[i] == y:\n",
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" ce_sum_partial = 0.\n",
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" x = X[j * M + i]\n",
" counts.data.as_floats[x * (Y_max + 1) + Y[j]] += 1\n",
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" count_sum += counts.data.as_floats[j * (Y_max + 1) + y]\n",
" \n",
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" prob = counts.data.as_floats[j * (Y_max + 1) + y]/count_sum \n",
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" prob = 0.0001\n",
" ce_sum_partial += -prob * log(prob)/log(2.)* Y_dist.data.as_floats[y]\n",
"\n",
" ce_sum += ce_sum_partial\n",
" \n",
" return ce_sum\n",
"\n",
"def conditional_entropy_cython(np.ndarray[long, ndim=2, mode=\"c\"] X, np.ndarray[long, ndim=1, mode=\"c\"] Y):\n",
" \"\"\" \n",
" Calculate conditional entropy of all columns of X against Y (i.e. \\sum_i=1^{N} H(X_i | Y)).\n",
" \"\"\"\n",
" return _conditional_entropy_cython(&X[0,0], &Y[0], X.shape[0], X.shape[1])"
]
},
{
"cell_type": "markdown",
"metadata": {
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"source": [
"## Benchmark everything"
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},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1 loops, best of 3: 1.62 s per loop\n",
"100 loops, best of 3: 8.08 ms per loop\n",
"100 loops, best of 3: 7.3 ms per loop\n"
]
}
],
"source": [
"%timeit conditional_entropy_python(X, Y)\n",
"%timeit conditional_entropy_numba(X, Y)\n",
"%timeit conditional_entropy_cython(X, Y)"
]
},
{
"cell_type": "code",
"execution_count": 520,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"100 loops, best of 3: 9.29 ms per loop\n"
]
}
],
"source": [
"# Only 0.6ms faster, probably wasn't worth is.\n",
"# Warning: cython code has bug and returns different entropy, I didn't have patience to fix it"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.11"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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