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<p>Linear regression example using <a href="https://en.wikipedia.org/wiki/Ordinary_least_squares">Ordinary least squares</a>
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;iomanip&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
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Include dependency graph for ordinary_least_squares_regressor.cpp:</div>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Linear regression example using <a href="https://en.wikipedia.org/wiki/Ordinary_least_squares">Ordinary least squares</a> </p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala">Krishna Vedala</a> Program that gets the number of data samples and number of features per sample along with output per sample. It applies OLS regression to compute the regression output for additional test data samples. </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a38ff1d954e9b7de93eb20e2dd101a045"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a38ff1d954e9b7de93eb20e2dd101a045">&#9670;&nbsp;</a></span>fit_OLS_regressor()</h2>
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<div class="memproto">
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template&lt;typename T &gt; </div>
<table class="memname">
<tr>
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<td>(</td>
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<td class="paramname"><em>X</em>, </td>
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<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; const &amp;&#160;</td>
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</div><div class="memdoc">
<p>Perform Ordinary Least Squares curve fit. This operation is defined as </p><p class="formulaDsp">
\[\beta = \left(X^TXX^T\right)Y\]
</p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">X</td><td>feature matrix with rows representing sample vector of features </td></tr>
<tr><td class="paramname">Y</td><td>known regression value for each sample </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>fitted regression model polynomial coefficients </dd></dl>
<div class="fragment"><div class="line"><a name="l00310"></a><span class="lineno"> 310</span>&#160; {</div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span>&#160; <span class="comment">// NxF</span></div>
<div class="line"><a name="l00312"></a><span class="lineno"> 312</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;T&gt;</a>&gt; X2 = X;</div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; X2.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++)</div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>&#160; <span class="comment">// add Y-intercept -&gt; Nx(F+1)</span></div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>&#160; X2[i].push_back(1);</div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>&#160; <span class="comment">// (F+1)xN</span></div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;T&gt;</a>&gt; Xt = <a class="code" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a889f9de199fa793497c864d8e493af05">get_transpose</a>(X2);</div>
<div class="line"><a name="l00318"></a><span class="lineno"> 318</span>&#160; <span class="comment">// (F+1)x(F+1)</span></div>
<div class="line"><a name="l00319"></a><span class="lineno"> 319</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;T&gt;</a>&gt; tmp = <a class="code" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a98ab8f75d981088369b89b8be2182483">get_inverse</a>(Xt * X2);</div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span>&#160; <span class="comment">// (F+1)xN</span></div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;float&gt;</a>&gt; out = tmp * Xt;</div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>&#160; <span class="comment">// cout &lt;&lt; endl</span></div>
<div class="line"><a name="l00323"></a><span class="lineno"> 323</span>&#160; <span class="comment">// &lt;&lt; &quot;Projection matrix: &quot; &lt;&lt; X2 * out &lt;&lt; endl;</span></div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span>&#160; </div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>&#160; <span class="comment">// Fx1,1 -&gt; (F+1)^th element is the independent constant</span></div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>&#160; <span class="keywordflow">return</span> out * Y;</div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a98ab8f75d981088369b89b8be2182483">&#9670;&nbsp;</a></span>get_inverse()</h2>
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<div class="memproto">
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template&lt;typename T &gt; </div>
<table class="memname">
<tr>
<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;float&gt; &gt; get_inverse </td>
<td>(</td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt;&gt; const &amp;&#160;</td>
<td class="paramname"><em>A</em></td><td>)</td>
<td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Get matrix inverse using Row-trasnformations. Given matrix must be a square and non-singular. </p><dl class="section return"><dt>Returns</dt><dd>inverse matrix </dd></dl>
<div class="fragment"><div class="line"><a name="l00218"></a><span class="lineno"> 218</span>&#160; {</div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>&#160; <span class="comment">// Assuming A is square matrix</span></div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>&#160; <span class="keywordtype">size_t</span> N = A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>&#160; </div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;float&gt;</a>&gt; inverse(N);</div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; N; row++) {</div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>&#160; <span class="comment">// preallocatae a resultant identity matrix</span></div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>&#160; inverse[row] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a>(N);</div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col &lt; N; col++)</div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>&#160; inverse[row][col] = (row == col) ? 1.f : 0.f;</div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>&#160; }</div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>&#160; </div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>&#160; <span class="keywordflow">if</span> (!<a class="code" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a4921874435266592b222e3f2eda0e01f">is_square</a>(A)) {</div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;A must be a square matrix!&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>&#160; <span class="keywordflow">return</span> inverse;</div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>&#160; }</div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>&#160; </div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>&#160; <span class="comment">// preallocatae a temporary matrix identical to A</span></div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;float&gt;</a>&gt; temp(N);</div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; N; row++) {</div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> v(N);</div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col &lt; N; col++)</div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>&#160; v[col] = <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(A[row][col]);</div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>&#160; temp[row] = v;</div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>&#160; }</div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>&#160; </div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>&#160; <span class="comment">// start transformations</span></div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; N; row++) {</div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row2 = row; row2 &lt; N &amp;&amp; temp[row][row] == 0; row2++) {</div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span>&#160; <span class="comment">// this to ensure diagonal elements are not 0</span></div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>&#160; temp[row] = temp[row] + temp[row2];</div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>&#160; inverse[row] = inverse[row] + inverse[row2];</div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>&#160; }</div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>&#160; </div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col2 = row; col2 &lt; N &amp;&amp; temp[row][row] == 0; col2++) {</div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>&#160; <span class="comment">// this to further ensure diagonal elements are not 0</span></div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row2 = 0; row2 &lt; N; row2++) {</div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>&#160; temp[row2][row] = temp[row2][row] + temp[row2][col2];</div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>&#160; inverse[row2][row] = inverse[row2][row] + inverse[row2][col2];</div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>&#160; }</div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>&#160; }</div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>&#160; </div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>&#160; <span class="keywordflow">if</span> (temp[row][row] == 0) {</div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>&#160; <span class="comment">// Probably a low-rank matrix and hence singular</span></div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Low-rank matrix, no inverse!&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>&#160; <span class="keywordflow">return</span> inverse;</div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>&#160; }</div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>&#160; </div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>&#160; <span class="comment">// set diagonal to 1</span></div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>&#160; <span class="keywordtype">float</span> divisor = <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(temp[row][row]);</div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>&#160; temp[row] = temp[row] / divisor;</div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span>&#160; inverse[row] = inverse[row] / divisor;</div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>&#160; <span class="comment">// Row transformations</span></div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row2 = 0; row2 &lt; N; row2++) {</div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>&#160; <span class="keywordflow">if</span> (row2 == row)</div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>&#160; <span class="keywordflow">continue</span>;</div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>&#160; <span class="keywordtype">float</span> factor = temp[row2][row];</div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>&#160; temp[row2] = temp[row2] - factor * temp[row];</div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span>&#160; inverse[row2] = inverse[row2] - factor * inverse[row];</div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>&#160; }</div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>&#160; }</div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>&#160; </div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>&#160; <span class="keywordflow">return</span> inverse;</div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a889f9de199fa793497c864d8e493af05">&#9670;&nbsp;</a></span>get_transpose()</h2>
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<div class="memtemplate">
template&lt;typename T &gt; </div>
<table class="memname">
<tr>
<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;T&gt; &gt; get_transpose </td>
<td>(</td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt;&gt; const &amp;&#160;</td>
<td class="paramname"><em>A</em></td><td>)</td>
<td></td>
</tr>
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</div><div class="memdoc">
<p>matrix transpose </p><dl class="section return"><dt>Returns</dt><dd>resultant matrix </dd></dl>
<div class="fragment"><div class="line"><a name="l00289"></a><span class="lineno"> 289</span>&#160; {</div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;T&gt;</a>&gt; result(A[0].size());</div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>&#160; </div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; A[0].<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); row++) {</div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> v(A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>());</div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col &lt; A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); col++) v[col] = A[col][row];</div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>&#160; </div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>&#160; result[row] = v;</div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>&#160; }</div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>&#160; <span class="keywordflow">return</span> result;</div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a4921874435266592b222e3f2eda0e01f">&#9670;&nbsp;</a></span>is_square()</h2>
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template&lt;typename T &gt; </div>
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<td class="memname">bool is_square </td>
<td>(</td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt;&gt; const &amp;&#160;</td>
<td class="paramname"><em>A</em></td><td>)</td>
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<span class="mlabels"><span class="mlabel">inline</span></span> </td>
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<p>function to check if given matrix is a square matrix </p><dl class="section return"><dt>Returns</dt><dd>1 if true, 0 if false </dd></dl>
<div class="fragment"><div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160; {</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160; <span class="comment">// Assuming A is square matrix</span></div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; <span class="keywordtype">size_t</span> N = A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; N; i++)</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; <span class="keywordflow">if</span> (A[i].size() != N)</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160; <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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<td class="memname">int main </td>
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<p>main function </p>
<div class="fragment"><div class="line"><a name="l00357"></a><span class="lineno"> 357</span>&#160; {</div>
<div class="line"><a name="l00358"></a><span class="lineno"> 358</span>&#160; <span class="keywordtype">size_t</span> N, F;</div>
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span>&#160; </div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter number of features: &quot;</span>;</div>
<div class="line"><a name="l00361"></a><span class="lineno"> 361</span>&#160; <span class="comment">// number of features = columns</span></div>
<div class="line"><a name="l00362"></a><span class="lineno"> 362</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; F;</div>
<div class="line"><a name="l00363"></a><span class="lineno"> 363</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter number of samples: &quot;</span>;</div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</span>&#160; <span class="comment">// number of samples = rows</span></div>
<div class="line"><a name="l00365"></a><span class="lineno"> 365</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; N;</div>
<div class="line"><a name="l00366"></a><span class="lineno"> 366</span>&#160; </div>
<div class="line"><a name="l00367"></a><span class="lineno"> 367</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;float&gt;</a>&gt; <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>(N);</div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> Y(N);</div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span>&#160; </div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div>
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span>&#160; &lt;&lt; <span class="stringliteral">&quot;Enter training data. Per sample, provide features ad one output.&quot;</span></div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span>&#160; &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span>&#160; </div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> rows = 0; rows &lt; N; rows++) {</div>
<div class="line"><a name="l00375"></a><span class="lineno"> 375</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> v(F);</div>
<div class="line"><a name="l00376"></a><span class="lineno"> 376</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Sample# &quot;</span> &lt;&lt; rows + 1 &lt;&lt; <span class="stringliteral">&quot;: &quot;</span>;</div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> cols = 0; cols &lt; F; cols++)</div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span>&#160; <span class="comment">// get the F features</span></div>
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; v[cols];</div>
<div class="line"><a name="l00380"></a><span class="lineno"> 380</span>&#160; <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[rows] = v;</div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span>&#160; <span class="comment">// get the corresponding output</span></div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; Y[rows];</div>
<div class="line"><a name="l00383"></a><span class="lineno"> 383</span>&#160; }</div>
<div class="line"><a name="l00384"></a><span class="lineno"> 384</span>&#160; </div>
<div class="line"><a name="l00385"></a><span class="lineno"> 385</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> beta = <a class="code" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a38ff1d954e9b7de93eb20e2dd101a045">fit_OLS_regressor</a>(<a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>, Y);</div>
<div class="line"><a name="l00386"></a><span class="lineno"> 386</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <span class="stringliteral">&quot;beta:&quot;</span> &lt;&lt; beta &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00387"></a><span class="lineno"> 387</span>&#160; </div>
<div class="line"><a name="l00388"></a><span class="lineno"> 388</span>&#160; <span class="keywordtype">size_t</span> T;</div>
<div class="line"><a name="l00389"></a><span class="lineno"> 389</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter number of test samples: &quot;</span>;</div>
<div class="line"><a name="l00390"></a><span class="lineno"> 390</span>&#160; <span class="comment">// number of test sample inputs</span></div>
<div class="line"><a name="l00391"></a><span class="lineno"> 391</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; T;</div>
<div class="line"><a name="l00392"></a><span class="lineno"> 392</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;float&gt;</a>&gt; data2(T);</div>
<div class="line"><a name="l00393"></a><span class="lineno"> 393</span>&#160; <span class="comment">// vector&lt;float&gt; Y2(T);</span></div>
<div class="line"><a name="l00394"></a><span class="lineno"> 394</span>&#160; </div>
<div class="line"><a name="l00395"></a><span class="lineno"> 395</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> rows = 0; rows &lt; T; rows++) {</div>
<div class="line"><a name="l00396"></a><span class="lineno"> 396</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Sample# &quot;</span> &lt;&lt; rows + 1 &lt;&lt; <span class="stringliteral">&quot;: &quot;</span>;</div>
<div class="line"><a name="l00397"></a><span class="lineno"> 397</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> v(F);</div>
<div class="line"><a name="l00398"></a><span class="lineno"> 398</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> cols = 0; cols &lt; F; cols++) std::cin &gt;&gt; v[cols];</div>
<div class="line"><a name="l00399"></a><span class="lineno"> 399</span>&#160; data2[rows] = v;</div>
<div class="line"><a name="l00400"></a><span class="lineno"> 400</span>&#160; }</div>
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span>&#160; </div>
<div class="line"><a name="l00402"></a><span class="lineno"> 402</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> out = <a class="code" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a4bcaaf41c66da4d3a471dacef133def7">predict_OLS_regressor</a>(data2, beta);</div>
<div class="line"><a name="l00403"></a><span class="lineno"> 403</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> rows = 0; rows &lt; T; rows++) <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; out[rows] &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00404"></a><span class="lineno"> 404</span>&#160; </div>
<div class="line"><a name="l00405"></a><span class="lineno"> 405</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00406"></a><span class="lineno"> 406</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a9b2b5da35a6ba8ae203c33739ef0b91d">&#9670;&nbsp;</a></span>operator*() <span class="overload">[1/4]</span></h2>
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template&lt;typename T &gt; </div>
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<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;float&gt; operator* </td>
<td>(</td>
<td class="paramtype">float const&#160;</td>
<td class="paramname"><em>scalar</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; const &amp;&#160;</td>
<td class="paramname"><em>A</em>&#160;</td>
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<p>pre-multiplication of a vector by a scalar </p><dl class="section return"><dt>Returns</dt><dd>resultant vector </dd></dl>
<div class="fragment"><div class="line"><a name="l00130"></a><span class="lineno"> 130</span>&#160; {</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>&#160; <span class="comment">// Number of rows in A</span></div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>&#160; <span class="keywordtype">size_t</span> N_A = A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>&#160; </div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> result(N_A);</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>&#160; </div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; N_A; row++) {</div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>&#160; result[row] += A[row] * <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(scalar);</div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>&#160; }</div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>&#160; </div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>&#160; <span class="keywordflow">return</span> result;</div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>&#160;}</div>
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<td>(</td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt;&gt; const &amp;&#160;</td>
<td class="paramname"><em>A</em>, </td>
</tr>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt;&gt; const &amp;&#160;</td>
<td class="paramname"><em>B</em>&#160;</td>
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<p>Matrix multiplication such that if A is size (mxn) and B is of size (pxq) then the multiplication is defined only when n = p and the resultant matrix is of size (mxq)</p>
<dl class="section return"><dt>Returns</dt><dd>resultant matrix </dd></dl>
<div class="fragment"><div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160; {</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160; <span class="comment">// Number of rows in A</span></div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160; <span class="keywordtype">size_t</span> N_A = A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; <span class="comment">// Number of columns in B</span></div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; <span class="keywordtype">size_t</span> N_B = B[0].<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; </div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;T&gt;</a>&gt; result(N_A);</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160; </div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160; <span class="keywordflow">if</span> (A[0].size() != B.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()) {</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Number of columns in A != Number of rows in B (&quot;</span></div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160; &lt;&lt; A[0].<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() &lt;&lt; <span class="stringliteral">&quot;, &quot;</span> &lt;&lt; B.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() &lt;&lt; <span class="stringliteral">&quot;)&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160; <span class="keywordflow">return</span> result;</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160; }</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160; </div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; N_A; row++) {</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> v(N_B);</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col &lt; N_B; col++) {</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>&#160; v[col] = <span class="keyword">static_cast&lt;</span>T<span class="keyword">&gt;</span>(0);</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; j &lt; B.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); j++)</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160; v[col] += A[row][j] * B[j][col];</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160; }</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>&#160; result[row] = v;</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>&#160; }</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>&#160; </div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>&#160; <span class="keywordflow">return</span> result;</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160;}</div>
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<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;T&gt; operator* </td>
<td>(</td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt;&gt; const &amp;&#160;</td>
<td class="paramname"><em>A</em>, </td>
</tr>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; const &amp;&#160;</td>
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<p>multiplication of a matrix with a column vector </p><dl class="section return"><dt>Returns</dt><dd>resultant vector </dd></dl>
<div class="fragment"><div class="line"><a name="l00105"></a><span class="lineno"> 105</span>&#160; {</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>&#160; <span class="comment">// Number of rows in A</span></div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>&#160; <span class="keywordtype">size_t</span> N_A = A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>&#160; </div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> result(N_A);</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>&#160; </div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>&#160; <span class="keywordflow">if</span> (A[0].size() != B.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()) {</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Number of columns in A != Number of rows in B (&quot;</span></div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>&#160; &lt;&lt; A[0].<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() &lt;&lt; <span class="stringliteral">&quot;, &quot;</span> &lt;&lt; B.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() &lt;&lt; <span class="stringliteral">&quot;)&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>&#160; <span class="keywordflow">return</span> result;</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>&#160; }</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>&#160; </div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; N_A; row++) {</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>&#160; result[row] = <span class="keyword">static_cast&lt;</span>T<span class="keyword">&gt;</span>(0);</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; j &lt; B.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); j++) result[row] += A[row][j] * B[j];</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>&#160; }</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>&#160; </div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>&#160; <span class="keywordflow">return</span> result;</div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#aecef32c2a4f39a3f7398949256d180a6">&#9670;&nbsp;</a></span>operator*() <span class="overload">[4/4]</span></h2>
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<td class="paramname"><em>A</em>, </td>
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<td class="paramtype">float const&#160;</td>
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<p>post-multiplication of a vector by a scalar </p><dl class="section return"><dt>Returns</dt><dd>resultant vector </dd></dl>
<div class="fragment"><div class="line"><a name="l00148"></a><span class="lineno"> 148</span>&#160; {</div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>&#160; <span class="comment">// Number of rows in A</span></div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>&#160; <span class="keywordtype">size_t</span> N_A = A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>&#160; </div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> result(N_A);</div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>&#160; </div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; N_A; row++)</div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>&#160; result[row] = A[row] * <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(scalar);</div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>&#160; </div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>&#160; <span class="keywordflow">return</span> result;</div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a67249e31221231cf3aaf3cfd870372d0">&#9670;&nbsp;</a></span>operator+()</h2>
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<p>addition of two vectors of identical lengths </p><dl class="section return"><dt>Returns</dt><dd>resultant vector </dd></dl>
<div class="fragment"><div class="line"><a name="l00195"></a><span class="lineno"> 195</span>&#160; {</div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>&#160; <span class="comment">// Number of rows in A</span></div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>&#160; <span class="keywordtype">size_t</span> N = A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>&#160; </div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> result(N);</div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>&#160; </div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>&#160; <span class="keywordflow">if</span> (B.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() != N) {</div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Vector dimensions shouldbe identical!&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>&#160; <span class="keywordflow">return</span> A;</div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>&#160; }</div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>&#160; </div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; N; row++) result[row] = A[row] + B[row];</div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>&#160; </div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>&#160; <span class="keywordflow">return</span> result;</div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a31be3fe36e76b87d5616ff8e7918cd24">&#9670;&nbsp;</a></span>operator-()</h2>
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<p>subtraction of two vectors of identical lengths </p><dl class="section return"><dt>Returns</dt><dd>resultant vector </dd></dl>
<div class="fragment"><div class="line"><a name="l00174"></a><span class="lineno"> 174</span>&#160; {</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>&#160; <span class="comment">// Number of rows in A</span></div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>&#160; <span class="keywordtype">size_t</span> N = A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>&#160; </div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> result(N);</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>&#160; </div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>&#160; <span class="keywordflow">if</span> (B.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() != N) {</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Vector dimensions shouldbe identical!&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>&#160; <span class="keywordflow">return</span> A;</div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>&#160; }</div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>&#160; </div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; N; row++) result[row] = A[row] - B[row];</div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>&#160; </div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>&#160; <span class="keywordflow">return</span> result;</div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a30acf52af3184bc22274234ef5a73536">&#9670;&nbsp;</a></span>operator/()</h2>
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<td class="paramtype">float const&#160;</td>
<td class="paramname"><em>scalar</em>&#160;</td>
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<p>division of a vector by a scalar </p><dl class="section return"><dt>Returns</dt><dd>resultant vector </dd></dl>
<div class="fragment"><div class="line"><a name="l00165"></a><span class="lineno"> 165</span>&#160; {</div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>&#160; <span class="keywordflow">return</span> (1.<a class="code" href="../../d4/d32/fibonacci__fast_8cpp.html#a3ba232425d45f9e9c0b87a8cf7ab69d9">f</a> / scalar) * A;</div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a98eb5807f21b783c341cab402ced6732">&#9670;&nbsp;</a></span>operator&lt;&lt;() <span class="overload">[1/2]</span></h2>
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<td class="paramname"><em>out</em>, </td>
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<td></td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt;&gt; const &amp;&#160;</td>
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<p>operator to print a matrix </p>
<div class="fragment"><div class="line"><a name="l00020"></a><span class="lineno"> 20</span>&#160; {</div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> width = 10;</div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span>&#160; <span class="keyword">const</span> <span class="keywordtype">char</span> separator = <span class="charliteral">&#39; &#39;</span>;</div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span>&#160; </div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; v.size(); row++) {</div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col &lt; v[row].size(); col++)</div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>&#160; out &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">std::left</a> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setw.html">std::setw</a>(width) &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setfill.html">std::setfill</a>(separator)</div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>&#160; &lt;&lt; v[row][col];</div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>&#160; out &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>&#160; }</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>&#160; </div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>&#160; <span class="keywordflow">return</span> out;</div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>&#160;}</div>
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<p>operator to print a vector </p>
<div class="fragment"><div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160; {</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> width = 15;</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; <span class="keyword">const</span> <span class="keywordtype">char</span> separator = <span class="charliteral">&#39; &#39;</span>;</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; </div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; v.size(); row++)</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160; out &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">std::left</a> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setw.html">std::setw</a>(width) &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setfill.html">std::setfill</a>(separator)</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160; &lt;&lt; v[row];</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; </div>
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<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160;}</div>
</div><!-- fragment --><div class="dynheader">
Here is the call graph for this function:</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a4bcaaf41c66da4d3a471dacef133def7">&#9670;&nbsp;</a></span>predict_OLS_regressor()</h2>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;typename T &gt; </div>
<table class="memname">
<tr>
<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;float&gt; predict_OLS_regressor </td>
<td>(</td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt;&gt; const &amp;&#160;</td>
<td class="paramname"><em>X</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; float &gt; const &amp;&#160;</td>
<td class="paramname"><em>beta</em>&#160;</td>
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<tr>
<td></td>
<td>)</td>
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<p>Given data and OLS model coeffficients, predict regression estimates. This operation is defined as </p><p class="formulaDsp">
\[y_{\text{row}=i} = \sum_{j=\text{columns}}\beta_j\cdot X_{i,j}\]
</p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">X</td><td>feature matrix with rows representing sample vector of features </td></tr>
<tr><td class="paramname">beta</td><td>fitted regression model </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>vector with regression values for each sample </dd></dl>
<div class="fragment"><div class="line"><a name="l00341"></a><span class="lineno"> 341</span>&#160; {</div>
<div class="line"><a name="l00342"></a><span class="lineno"> 342</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> result(X.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>());</div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span>&#160; </div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> rows = 0; rows &lt; X.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); rows++) {</div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span>&#160; <span class="comment">// -&gt; start with constant term</span></div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span>&#160; result[rows] = beta[X[0].<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()];</div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> cols = 0; cols &lt; X[0].size(); cols++)</div>
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span>&#160; result[rows] += beta[cols] * X[rows][cols];</div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>&#160; }</div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span>&#160; <span class="comment">// Nx1</span></div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span>&#160; <span class="keywordflow">return</span> result;</div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span>&#160;}</div>
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<div class="ttc" id="afibonacci__fast_8cpp_html_a3ba232425d45f9e9c0b87a8cf7ab69d9"><div class="ttname"><a href="../../d4/d32/fibonacci__fast_8cpp.html#a3ba232425d45f9e9c0b87a8cf7ab69d9">f</a></div><div class="ttdeci">uint64_t f[MAX]</div><div class="ttdef"><b>Definition:</b> fibonacci_fast.cpp:27</div></div>
<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div><div class="ttdoc">STL class.</div></div>
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<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a></div></div>
<div class="ttc" id="aordinary__least__squares__regressor_8cpp_html_a4bcaaf41c66da4d3a471dacef133def7"><div class="ttname"><a href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a4bcaaf41c66da4d3a471dacef133def7">predict_OLS_regressor</a></div><div class="ttdeci">std::vector&lt; float &gt; predict_OLS_regressor(std::vector&lt; std::vector&lt; T &gt;&gt; const &amp;X, std::vector&lt; float &gt; const &amp;beta)</div><div class="ttdef"><b>Definition:</b> ordinary_least_squares_regressor.cpp:339</div></div>
<div class="ttc" id="ahash__search_8cpp_html_a6e1a77282bc65ad359d753d25df23243"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a></div><div class="ttdeci">int data[MAX]</div><div class="ttdoc">test data</div><div class="ttdef"><b>Definition:</b> hash_search.cpp:24</div></div>
<div class="ttc" id="aordinary__least__squares__regressor_8cpp_html_a38ff1d954e9b7de93eb20e2dd101a045"><div class="ttname"><a href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a38ff1d954e9b7de93eb20e2dd101a045">fit_OLS_regressor</a></div><div class="ttdeci">std::vector&lt; float &gt; fit_OLS_regressor(std::vector&lt; std::vector&lt; T &gt;&gt; const &amp;X, std::vector&lt; T &gt; const &amp;Y)</div><div class="ttdef"><b>Definition:</b> ordinary_least_squares_regressor.cpp:309</div></div>
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<div class="ttc" id="aleft_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/left.html">std::left</a></div><div class="ttdeci">T left(T... args)</div></div>
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