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 <div class="header">
   <div class="headertitle">
 <div class="title">Linear Algebra Operations<div class="ingroups"><a class="el" href="group__grp__early__stage.html">Early Stage Development</a></div></div>  </div>
 </div><!--header-->
 <div class="contents">
 <div class="toc"><b>Contents</b> </p>
 <ul>
 <li>
 <a href="#functions">Linear Algebra Utility Functions</a> </li>
 <li>
 <a href="#related">Related Functions</a> </li>
 </ul>
 </div><dl class="section warning"><dt>Warning</dt><dd><em> This MADlib module is still in early stage development. There may be some issues that will be addressed in a future version. Interface and implementation is subject to change. </em></dd></dl>
 <p>The linalg module consists of useful utility functions for basic linear algebra operations. Several of these functions can be used while implementing new algorithms.</p>
 <p>Refer to the <a class="el" href="linalg_8sql__in.html" title="SQL functions for linear algebra. ">linalg.sql_in</a> file for documentation on each of the utility functions.</p>
 <p><a class="anchor" id="functions"></a></p>
 <dl class="section user"><dt>Linear Algebra Utility Functions </dt><dd><table  class="output">
 <tr>
 <th><a class="el" href="linalg_8sql__in.html#a300300fe4b8576ba0b97b95d8dea3057" title="1-norm of a vector ">norm1()</a> </th><td><p class="starttd">1-norm of a vector.</p>
 <p class="endtd"></p>
 </td></tr>
 <tr>
 <th><a class="el" href="linalg_8sql__in.html#a50fdfe30cc0edc6888a909dbb4b4c239" title="2-norm of a vector ">norm2()</a> </th><td><p class="starttd">2-norm of a vector. </p>
 <p class="endtd"></p>
 </td></tr>
 <tr>
 <th><a class="el" href="linalg_8sql__in.html#aad193850e79c4b9d811ca9bc53e13476" title="1-norm of the difference between two vectors ">dist_norm1()</a> </th><td><p class="starttd">1-norm of the difference between two vectors. </p>
 <p class="endtd"></p>
 </td></tr>
 <tr>
 <th><a class="el" href="linalg_8sql__in.html#aa58e51526edea6ea98db30b6f250adb4" title="2-norm of the difference between two vectors ">dist_norm2()</a> </th><td><p class="starttd">2-norm of the difference between two vectors. </p>
 <p class="endtd"></p>
 </td></tr>
 <tr>
 <th><a class="el" href="linalg_8sql__in.html#a00a08e69f27524f2096032214e15b668" title="Squared 2-norm of the difference between two vectors. ">squared_dist_norm2()</a> </th><td><p class="starttd">Squared 2-norm of the difference between two vectors. </p>
 <p class="endtd"></p>
 </td></tr>
 <tr>
 <th><a class="el" href="linalg_8sql__in.html#a8c7b9281a72ff22caf06161701b27e84" title="Angle between two vectors. ">dist_angle()</a> </th><td><p class="starttd">Angle between two vectors. </p>
 <p class="endtd"></p>
 </td></tr>
 <tr>
 <th><a class="el" href="linalg_8sql__in.html#afa13b4c6122b99422d666dedea136c18" title="Tanimoto distance between two vectors. ">dist_tanimoto()</a> </th><td><p class="starttd">Tanimoto distance between two vectors. </p>
 <p class="endtd"></p>
 </td></tr>
 <tr>
 <th><a class="el" href="linalg_8sql__in.html#aa2856d10fa6cb12a5b168bab217197ed" title="Given matrix  and vector  compute the column of  that is closest to . ">closest_column()</a> </th><td><p class="starttd">Given matrix \( M \) and vector \( \vec x \) compute the column of \( M \) that is closest to \( \vec x \).</p>
 <p class="endtd"></p>
 </td></tr>
 <tr>
 <th><a class="el" href="linalg_8sql__in.html#ad3e16fc5435474b96b182ba20905461e" title="Given matrix  and vector  compute the columns of  that are closest to . ">closest_columns()</a> </th><td><p class="starttd">Given matrix \( M \) and vector \( \vec x \) compute the columns of \( M \) that are closest to \( \vec x \). </p>
 <p class="endtd"></p>
 </td></tr>
 <tr>
 <th><a class="el" href="linalg_8sql__in.html#a1aa37f73fb1cd8d7d106aa518dd8c0b4" title="Compute the average of vectors. ">avg()</a> </th><td><p class="starttd">Compute the average of vectors. </p>
 <p class="endtd"></p>
 </td></tr>
 <tr>
 <th><a class="el" href="linalg_8sql__in.html#a0b04663ca206f03e66aed5ea2b4cc461" title="Compute the normalized average of vectors. ">normalized_avg()</a> </th><td>Compute the normalized average of vectors.   </td></tr>
 <tr>
 <th><a class="el" href="linalg_8sql__in.html#a9c439706f35d6cac89f151d553a5f111" title="Combine vectors to a matrix. ">matrix_agg()</a> </th><td><p class="starttd">Combine vectors to a matrix. </p>
 <p class="endtd"></p>
 </td></tr>
 <tr>
 <th><a class="el" href="linalg_8sql__in.html#a24a4f14f171a12ec31f609af2f07ac18" title="Return the column of a matrix. ">matrix_column()</a> </th><td><p class="starttd">Return the column of a matrix. </p>
 <p class="endtd"></p>
 </td></tr>
 </table>
 </dd></dl>
 <p><a class="anchor" id="related"></a></p>
 <dl class="section user"><dt>Related Topics</dt><dd>File <a class="el" href="linalg_8sql__in.html" title="SQL functions for linear algebra. ">linalg.sql_in</a> documenting the SQL functions. </dd></dl>
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	<div class="header">
	<div class="headertitle">
	<div class="title">Linear Algebra Operations<div class="ingroups"><a class="el" href="group__grp__early__stage.html">Early Stage Development</a></div></div> </div>
	</div><!--header-->
	<div class="contents">
	<div class="toc"><b>Contents</b> </p>
	<ul>
	<li>
	<a href="#functions">Linear Algebra Utility Functions</a> </li>
	<li>
	<a href="#related">Related Functions</a> </li>
	</ul>
	</div><dl class="section warning"><dt>Warning</dt><dd><em> This MADlib module is still in early stage development. There may be some issues that will be addressed in a future version. Interface and implementation is subject to change. </em></dd></dl>
	<p>The linalg module consists of useful utility functions for basic linear algebra operations. Several of these functions can be used while implementing new algorithms.</p>
	<p>Refer to the <a class="el" href="linalg_8sql__in.html" title="SQL functions for linear algebra. ">linalg.sql_in</a> file for documentation on each of the utility functions.</p>
	<p><a class="anchor" id="functions"></a></p>
	<dl class="section user"><dt>Linear Algebra Utility Functions </dt><dd><table class="output">
	<tr>
	<th><a class="el" href="linalg_8sql__in.html#a300300fe4b8576ba0b97b95d8dea3057" title="1-norm of a vector ">norm1()</a> </th><td><p class="starttd">1-norm of a vector.</p>
	<p class="endtd"></p>
	</td></tr>
	<tr>
	<th><a class="el" href="linalg_8sql__in.html#a50fdfe30cc0edc6888a909dbb4b4c239" title="2-norm of a vector ">norm2()</a> </th><td><p class="starttd">2-norm of a vector. </p>
	<p class="endtd"></p>
	</td></tr>
	<tr>
	<th><a class="el" href="linalg_8sql__in.html#aad193850e79c4b9d811ca9bc53e13476" title="1-norm of the difference between two vectors ">dist_norm1()</a> </th><td><p class="starttd">1-norm of the difference between two vectors. </p>
	<p class="endtd"></p>
	</td></tr>
	<tr>
	<th><a class="el" href="linalg_8sql__in.html#aa58e51526edea6ea98db30b6f250adb4" title="2-norm of the difference between two vectors ">dist_norm2()</a> </th><td><p class="starttd">2-norm of the difference between two vectors. </p>
	<p class="endtd"></p>
	</td></tr>
	<tr>
	<th><a class="el" href="linalg_8sql__in.html#a00a08e69f27524f2096032214e15b668" title="Squared 2-norm of the difference between two vectors. ">squared_dist_norm2()</a> </th><td><p class="starttd">Squared 2-norm of the difference between two vectors. </p>
	<p class="endtd"></p>
	</td></tr>
	<tr>
	<th><a class="el" href="linalg_8sql__in.html#a8c7b9281a72ff22caf06161701b27e84" title="Angle between two vectors. ">dist_angle()</a> </th><td><p class="starttd">Angle between two vectors. </p>
	<p class="endtd"></p>
	</td></tr>
	<tr>
	<th><a class="el" href="linalg_8sql__in.html#afa13b4c6122b99422d666dedea136c18" title="Tanimoto distance between two vectors. ">dist_tanimoto()</a> </th><td><p class="starttd">Tanimoto distance between two vectors. </p>
	<p class="endtd"></p>
	</td></tr>
	<tr>
	<th><a class="el" href="linalg_8sql__in.html#aa2856d10fa6cb12a5b168bab217197ed" title="Given matrix and vector compute the column of that is closest to . ">closest_column()</a> </th><td><p class="starttd">Given matrix \( M \) and vector \( \vec x \) compute the column of \( M \) that is closest to \( \vec x \).</p>
	<p class="endtd"></p>
	</td></tr>
	<tr>
	<th><a class="el" href="linalg_8sql__in.html#ad3e16fc5435474b96b182ba20905461e" title="Given matrix and vector compute the columns of that are closest to . ">closest_columns()</a> </th><td><p class="starttd">Given matrix \( M \) and vector \( \vec x \) compute the columns of \( M \) that are closest to \( \vec x \). </p>
	<p class="endtd"></p>
	</td></tr>
	<tr>
	<th><a class="el" href="linalg_8sql__in.html#a1aa37f73fb1cd8d7d106aa518dd8c0b4" title="Compute the average of vectors. ">avg()</a> </th><td><p class="starttd">Compute the average of vectors. </p>
	<p class="endtd"></p>
	</td></tr>
	<tr>
	<th><a class="el" href="linalg_8sql__in.html#a0b04663ca206f03e66aed5ea2b4cc461" title="Compute the normalized average of vectors. ">normalized_avg()</a> </th><td>Compute the normalized average of vectors. </td></tr>
	<tr>
	<th><a class="el" href="linalg_8sql__in.html#a9c439706f35d6cac89f151d553a5f111" title="Combine vectors to a matrix. ">matrix_agg()</a> </th><td><p class="starttd">Combine vectors to a matrix. </p>
	<p class="endtd"></p>
	</td></tr>
	<tr>
	<th><a class="el" href="linalg_8sql__in.html#a24a4f14f171a12ec31f609af2f07ac18" title="Return the column of a matrix. ">matrix_column()</a> </th><td><p class="starttd">Return the column of a matrix. </p>
	<p class="endtd"></p>
	</td></tr>
	</table>
	</dd></dl>
	<p><a class="anchor" id="related"></a></p>
	<dl class="section user"><dt>Related Topics</dt><dd>File <a class="el" href="linalg_8sql__in.html" title="SQL functions for linear algebra. ">linalg.sql_in</a> documenting the SQL functions. </dd></dl>
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