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| <div class="title">linalg.sql_in File Reference</div> </div> |
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| |
| <p>SQL functions for linear algebra. |
| <a href="#details">More...</a></p> |
| |
| <p><a href="linalg_8sql__in_source.html">Go to the source code of this file.</a></p> |
| <table class="memberdecls"> |
| <tr><td colspan="2"><h2><a name="func-members"></a> |
| Functions</h2></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="linalg_8sql__in.html#a300300fe4b8576ba0b97b95d8dea3057">norm1</a> (float8[] x)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">1-norm of a vector <a href="#a300300fe4b8576ba0b97b95d8dea3057"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="linalg_8sql__in.html#a50fdfe30cc0edc6888a909dbb4b4c239">norm2</a> (float8[] x)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">2-norm of a vector <a href="#a50fdfe30cc0edc6888a909dbb4b4c239"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="linalg_8sql__in.html#aad193850e79c4b9d811ca9bc53e13476">dist_norm1</a> (float8[] x, float8[] y)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">1-norm of the difference between two vectors <a href="#aad193850e79c4b9d811ca9bc53e13476"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="linalg_8sql__in.html#aa58e51526edea6ea98db30b6f250adb4">dist_norm2</a> (float8[] x, float8[] y)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">2-norm of the difference between two vectors <a href="#aa58e51526edea6ea98db30b6f250adb4"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="linalg_8sql__in.html#a00a08e69f27524f2096032214e15b668">squared_dist_norm2</a> (float8[] x, float8[] y)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Squared 2-norm of the difference between two vectors. <a href="#a00a08e69f27524f2096032214e15b668"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="linalg_8sql__in.html#a8c7b9281a72ff22caf06161701b27e84">dist_angle</a> (float8[] x, float8[] y)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Angle between two vectors. <a href="#a8c7b9281a72ff22caf06161701b27e84"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="linalg_8sql__in.html#afa13b4c6122b99422d666dedea136c18">dist_tanimoto</a> (float8[] x, float8[] y)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Tanimoto distance between two vectors. <a href="#afa13b4c6122b99422d666dedea136c18"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">closest_column_result </td><td class="memItemRight" valign="bottom"><a class="el" href="linalg_8sql__in.html#aa2856d10fa6cb12a5b168bab217197ed">closest_column</a> (float8[][] m, float8[] x, regproc dist="squared_dist_norm2")</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Given matrix \( M \) and vector \( \vec x \) compute the column of \( M \) that is closest to \( \vec x \). <a href="#aa2856d10fa6cb12a5b168bab217197ed"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">closest_columns_result </td><td class="memItemRight" valign="bottom"><a class="el" href="linalg_8sql__in.html#ad3e16fc5435474b96b182ba20905461e">closest_columns</a> (float8[][] m, float8[] x, integer num, regproc dist="squared_dist_norm2")</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Given matrix \( M \) and vector \( \vec x \) compute the columns of \( M \) that are closest to \( \vec x \). <a href="#ad3e16fc5435474b96b182ba20905461e"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">aggregate float8[] </td><td class="memItemRight" valign="bottom"><a class="el" href="linalg_8sql__in.html#a1aa37f73fb1cd8d7d106aa518dd8c0b4">avg</a> (float8[] x)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Compute the average of vectors. <a href="#a1aa37f73fb1cd8d7d106aa518dd8c0b4"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">aggregate float8[] </td><td class="memItemRight" valign="bottom"><a class="el" href="linalg_8sql__in.html#a0b04663ca206f03e66aed5ea2b4cc461">normalized_avg</a> (float8[] x)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Compute the normalized average of vectors. <a href="#a0b04663ca206f03e66aed5ea2b4cc461"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">aggregate float8[] </td><td class="memItemRight" valign="bottom"><a class="el" href="linalg_8sql__in.html#a9c439706f35d6cac89f151d553a5f111">matrix_agg</a> (float8[] x)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Combine vectors to a matrix. <a href="#a9c439706f35d6cac89f151d553a5f111"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8[] </td><td class="memItemRight" valign="bottom"><a class="el" href="linalg_8sql__in.html#a24a4f14f171a12ec31f609af2f07ac18">matrix_column</a> (float8[][] matrix, integer col)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Return the column of a matrix. <a href="#a24a4f14f171a12ec31f609af2f07ac18"></a><br/></td></tr> |
| </table> |
| <hr/><a name="details" id="details"></a><h2>Detailed Description</h2> |
| <div class="textblock"><dl class="see"><dt><b>See also:</b></dt><dd>For an overview of linear-algebra functions, see the module description <a class="el" href="group__grp__linalg.html">Linear-Algebra Operations</a>. </dd></dl> |
| |
| <p>Definition in file <a class="el" href="linalg_8sql__in_source.html">linalg.sql_in</a>.</p> |
| </div><hr/><h2>Function Documentation</h2> |
| <a class="anchor" id="a1aa37f73fb1cd8d7d106aa518dd8c0b4"></a><!-- doxytag: member="linalg.sql_in::avg" ref="a1aa37f73fb1cd8d7d106aa518dd8c0b4" args="(float8[] x)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">aggregate float8 [] avg </td> |
| <td>(</td> |
| <td class="paramtype">float8[] </td> |
| <td class="paramname"><em>x</em></td><td>)</td> |
| <td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <p>Given vectors \( x_1, \dots, x_n \), compute the average \( \frac 1n \sum_{i=1}^n x_i \).</p> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Point \( x_i \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>Average \( \frac 1n \sum_{i=1}^n x_i \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="linalg_8sql__in_source.html#l00291">291</a> of file <a class="el" href="linalg_8sql__in_source.html">linalg.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="aa2856d10fa6cb12a5b168bab217197ed"></a><!-- doxytag: member="linalg.sql_in::closest_column" ref="aa2856d10fa6cb12a5b168bab217197ed" args="(float8[][] m, float8[] x, regproc dist="squared_dist_norm2")" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">closest_column_result closest_column </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>m</em>[][], </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8[] </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">regproc </td> |
| <td class="paramname"><em>dist</em> = <code>"squared_dist_norm2"</code> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">M</td><td>Matrix \( M = (\vec{m_0} \dots \vec{m_{l-1}}) \in \mathbb{R}^{k \times l} \) </td></tr> |
| <tr><td class="paramname">x</td><td>Vector \( \vec x \in \mathbb R^k \) </td></tr> |
| <tr><td class="paramname">dist</td><td>The metric \( \operatorname{dist} \). This needs to be a function with signature <code>DOUBLE PRECISION[] x DOUBLE PRECISION[] -> DOUBLE PRECISION</code>.</td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>A composite value:<ul> |
| <li><code>columns_id INTEGER</code> - The 0-based index of the column of \( M \) that is closest to \( x \). In case of ties, the first such index is returned. That is, <code>columns_id</code> is the minimum element in the set \( \arg\min_{i=0,\dots,l-1} \operatorname{dist}(\vec{m_i}, \vec x) \).</li> |
| <li><code>distance DOUBLE PRECISION</code> - The minimum distance between any column of \( M \) and \( x \). That is, \( \min_{i=0,\dots,l-1} \operatorname{dist}(\vec{m_i}, \vec x) \). </li> |
| </ul> |
| </dd></dl> |
| |
| <p>Definition at line <a class="el" href="linalg_8sql__in_source.html#l00186">186</a> of file <a class="el" href="linalg_8sql__in_source.html">linalg.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="ad3e16fc5435474b96b182ba20905461e"></a><!-- doxytag: member="linalg.sql_in::closest_columns" ref="ad3e16fc5435474b96b182ba20905461e" args="(float8[][] m, float8[] x, integer num, regproc dist="squared_dist_norm2")" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">closest_columns_result closest_columns </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>m</em>[][], </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8[] </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">integer </td> |
| <td class="paramname"><em>num</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">regproc </td> |
| <td class="paramname"><em>dist</em> = <code>"squared_dist_norm2"</code> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <p>This function does essentially the same as <a class="el" href="linalg_8sql__in.html#aa2856d10fa6cb12a5b168bab217197ed">closest_column()</a>, except that it allows to specify the number of closest columns to return. The return value is a composite value:</p> |
| <ul> |
| <li><code>columns_ids INTEGER[]</code> - The 0-based indices of the <code>num</code> columns of \( M \) that are closest to \( x \). In case of ties, the first such indices are returned.</li> |
| <li><code>distances DOUBLE PRECISION[]</code> - The distances between the columns of \( M \) with indices in <code>columns_ids</code> and \( x \). That is, <code>distances[i]</code> contains \( \operatorname{dist}(\vec{m_j}, \vec x) \), where \( j = \) <code>columns_ids[i]</code>. </li> |
| </ul> |
| |
| <p>Definition at line <a class="el" href="linalg_8sql__in_source.html#l00232">232</a> of file <a class="el" href="linalg_8sql__in_source.html">linalg.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a8c7b9281a72ff22caf06161701b27e84"></a><!-- doxytag: member="linalg.sql_in::dist_angle" ref="a8c7b9281a72ff22caf06161701b27e84" args="(float8[] x, float8[] y)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 dist_angle </td> |
| <td>(</td> |
| <td class="paramtype">float8[] </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8[] </td> |
| <td class="paramname"><em>y</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Vector \( \vec x = (x_1, \dots, x_n) \) </td></tr> |
| <tr><td class="paramname">y</td><td>Vector \( \vec y = (y_1, \dots, y_n) \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( \arccos\left(\frac{\langle \vec x, \vec y \rangle} {\| \vec x \| \cdot \| \vec y \|}\right) \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="linalg_8sql__in_source.html#l00131">131</a> of file <a class="el" href="linalg_8sql__in_source.html">linalg.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="aad193850e79c4b9d811ca9bc53e13476"></a><!-- doxytag: member="linalg.sql_in::dist_norm1" ref="aad193850e79c4b9d811ca9bc53e13476" args="(float8[] x, float8[] y)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 dist_norm1 </td> |
| <td>(</td> |
| <td class="paramtype">float8[] </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8[] </td> |
| <td class="paramname"><em>y</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Vector \( \vec x = (x_1, \dots, x_n) \) </td></tr> |
| <tr><td class="paramname">y</td><td>Vector \( \vec y = (y_1, \dots, y_n) \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( \| x - y \|_1 = \sum_{i=1}^n |x_i - y_i| \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="linalg_8sql__in_source.html#l00082">82</a> of file <a class="el" href="linalg_8sql__in_source.html">linalg.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="aa58e51526edea6ea98db30b6f250adb4"></a><!-- doxytag: member="linalg.sql_in::dist_norm2" ref="aa58e51526edea6ea98db30b6f250adb4" args="(float8[] x, float8[] y)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 dist_norm2 </td> |
| <td>(</td> |
| <td class="paramtype">float8[] </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8[] </td> |
| <td class="paramname"><em>y</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Vector \( \vec x = (x_1, \dots, x_n) \) </td></tr> |
| <tr><td class="paramname">y</td><td>Vector \( \vec y = (y_1, \dots, y_n) \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( \| x - y \|_2 = \sqrt{\sum_{i=1}^n (x_i - y_i)^2} \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="linalg_8sql__in_source.html#l00098">98</a> of file <a class="el" href="linalg_8sql__in_source.html">linalg.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="afa13b4c6122b99422d666dedea136c18"></a><!-- doxytag: member="linalg.sql_in::dist_tanimoto" ref="afa13b4c6122b99422d666dedea136c18" args="(float8[] x, float8[] y)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 dist_tanimoto </td> |
| <td>(</td> |
| <td class="paramtype">float8[] </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8[] </td> |
| <td class="paramname"><em>y</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Vector \( \vec x = (x_1, \dots, x_n) \) </td></tr> |
| <tr><td class="paramname">y</td><td>Vector \( \vec y = (y_1, \dots, y_n) \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( 1 - \frac{\langle \vec x, \vec y \rangle} {\| \vec x \|^2 \cdot \| \vec y \|^2 - \langle \vec x, \vec y \rangle} \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="linalg_8sql__in_source.html#l00149">149</a> of file <a class="el" href="linalg_8sql__in_source.html">linalg.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a9c439706f35d6cac89f151d553a5f111"></a><!-- doxytag: member="linalg.sql_in::matrix_agg" ref="a9c439706f35d6cac89f151d553a5f111" args="(float8[] x)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">aggregate float8 [] matrix_agg </td> |
| <td>(</td> |
| <td class="paramtype">float8[] </td> |
| <td class="paramname"><em>x</em></td><td>)</td> |
| <td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <p>Given vectors \( \vec x_1, \dots, \vec x_n \in \mathbb R^m \), return matrix \( ( \vec x_1 \dots \vec x_n ) \in \mathbb R^{m \times n}\).</p> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Vector \( x_i \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>Matrix with columns \( x_1, \dots, x_n \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="linalg_8sql__in_source.html#l00365">365</a> of file <a class="el" href="linalg_8sql__in_source.html">linalg.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a24a4f14f171a12ec31f609af2f07ac18"></a><!-- doxytag: member="linalg.sql_in::matrix_column" ref="a24a4f14f171a12ec31f609af2f07ac18" args="(float8[][] matrix, integer col)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 [] matrix_column </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>matrix</em>[][], </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">integer </td> |
| <td class="paramname"><em>col</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">matrix</td><td>Two-dimensional matrix </td></tr> |
| <tr><td class="paramname">col</td><td>Column of the matrix to return (0-based index) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| |
| <p>Definition at line <a class="el" href="linalg_8sql__in_source.html#l00382">382</a> of file <a class="el" href="linalg_8sql__in_source.html">linalg.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a300300fe4b8576ba0b97b95d8dea3057"></a><!-- doxytag: member="linalg.sql_in::norm1" ref="a300300fe4b8576ba0b97b95d8dea3057" args="(float8[] x)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 norm1 </td> |
| <td>(</td> |
| <td class="paramtype">float8[] </td> |
| <td class="paramname"><em>x</em></td><td>)</td> |
| <td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Vector \( \vec x = (x_1, \dots, x_n) \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( \| x \|_1 = \sum_{i=1}^n |x_i| \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="linalg_8sql__in_source.html#l00053">53</a> of file <a class="el" href="linalg_8sql__in_source.html">linalg.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a50fdfe30cc0edc6888a909dbb4b4c239"></a><!-- doxytag: member="linalg.sql_in::norm2" ref="a50fdfe30cc0edc6888a909dbb4b4c239" args="(float8[] x)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 norm2 </td> |
| <td>(</td> |
| <td class="paramtype">float8[] </td> |
| <td class="paramname"><em>x</em></td><td>)</td> |
| <td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Vector \( \vec x = (x_1, \dots, x_n) \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( \| x \|_2 = \sqrt{\sum_{i=1}^n x_i^2} \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="linalg_8sql__in_source.html#l00067">67</a> of file <a class="el" href="linalg_8sql__in_source.html">linalg.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a0b04663ca206f03e66aed5ea2b4cc461"></a><!-- doxytag: member="linalg.sql_in::normalized_avg" ref="a0b04663ca206f03e66aed5ea2b4cc461" args="(float8[] x)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">aggregate float8 [] normalized_avg </td> |
| <td>(</td> |
| <td class="paramtype">float8[] </td> |
| <td class="paramname"><em>x</em></td><td>)</td> |
| <td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <p>Given vectors \( x_1, \dots, x_n \), define \( \widetilde{x} := \frac 1n \sum_{i=1}^n \frac{x_i}{\| x_i \|} \), and compute the normalized average \( \frac{\widetilde{x}}{\| \widetilde{x} \|} \).</p> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Point \( x_i \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>Normalized average \( \frac{\widetilde{x}}{\| \widetilde{x} \|} \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="linalg_8sql__in_source.html#l00329">329</a> of file <a class="el" href="linalg_8sql__in_source.html">linalg.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a00a08e69f27524f2096032214e15b668"></a><!-- doxytag: member="linalg.sql_in::squared_dist_norm2" ref="a00a08e69f27524f2096032214e15b668" args="(float8[] x, float8[] y)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 squared_dist_norm2 </td> |
| <td>(</td> |
| <td class="paramtype">float8[] </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8[] </td> |
| <td class="paramname"><em>y</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Vector \( \vec x = (x_1, \dots, x_n) \) </td></tr> |
| <tr><td class="paramname">y</td><td>Vector \( \vec y = (y_1, \dots, y_n) \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( \| x - y \|_2^2 = \sum_{i=1}^n (x_i - y_i)^2 \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="linalg_8sql__in_source.html#l00114">114</a> of file <a class="el" href="linalg_8sql__in_source.html">linalg.sql_in</a>.</p> |
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