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+   <div id="projectname">
+   <span id="projectnumber">1.11</span>
+   </div>
+   <div id="projectbrief">User Documentation for MADlib</div>
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+<div class="header">
+  <div class="summary">
+<a href="#func-members">Functions</a>  </div>
+  <div class="headertitle">
+<div class="title">dense_linear_systems.sql_in File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>SQL functions for linear systems.  
+<a href="#details">More...</a></p>
+<table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a 
name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:ad34728809ab3121705342cf91b34c6dd"><td class="memItemLeft" 
align="right" valign="top">bytea8&#160;</td><td class="memItemRight" 
valign="bottom"><a class="el" 
href="dense__linear__systems_8sql__in.html#ad34728809ab3121705342cf91b34c6dd">dense_residual_norm_transition</a>
 (bytea8 state, float8[] a, float8 b, float8[] x)</td></tr>
+<tr class="separator:ad34728809ab3121705342cf91b34c6dd"><td 
class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a73ebde08b8395fd7bddbe1dc37b9539f"><td class="memItemLeft" 
align="right" valign="top">bytea8&#160;</td><td class="memItemRight" 
valign="bottom"><a class="el" 
href="dense__linear__systems_8sql__in.html#a73ebde08b8395fd7bddbe1dc37b9539f">dense_residual_norm_merge_states</a>
 (bytea8 state1, bytea8 state2)</td></tr>
+<tr class="separator:a73ebde08b8395fd7bddbe1dc37b9539f"><td 
class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a01935dd8c4aef8c92e77b7f0f905fa4b"><td class="memItemLeft" 
align="right" valign="top">residual_norm_result&#160;</td><td 
class="memItemRight" valign="bottom"><a class="el" 
href="dense__linear__systems_8sql__in.html#a01935dd8c4aef8c92e77b7f0f905fa4b">dense_residual_norm_final</a>
 (bytea8 state)</td></tr>
+<tr class="separator:a01935dd8c4aef8c92e77b7f0f905fa4b"><td 
class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a52f2bcdd0d038f19e64a44d4bb07fefb"><td class="memItemLeft" 
align="right" valign="top">aggregate residual_norm_result&#160;</td><td 
class="memItemRight" valign="bottom"><a class="el" 
href="dense__linear__systems_8sql__in.html#a52f2bcdd0d038f19e64a44d4bb07fefb">dense_residual_norm</a>
 (float8[] left_hand_side, float8 right_hand_side, float8[] solution)</td></tr>
+<tr class="memdesc:a52f2bcdd0d038f19e64a44d4bb07fefb"><td 
class="mdescLeft">&#160;</td><td class="mdescRight">Compute the residual after 
solving the dense linear systems.  <a 
href="#a52f2bcdd0d038f19e64a44d4bb07fefb">More...</a><br /></td></tr>
+<tr class="separator:a52f2bcdd0d038f19e64a44d4bb07fefb"><td 
class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:acbfc47693d0b50ccfc6b7f7c38209b18"><td class="memItemLeft" 
align="right" valign="top">float8 []&#160;</td><td class="memItemRight" 
valign="bottom"><a class="el" 
href="dense__linear__systems_8sql__in.html#acbfc47693d0b50ccfc6b7f7c38209b18">dense_direct_linear_system_transition</a>
 (float8[] state, integer row_id, float8[] a, float8 b, integer num_rows, 
integer algorithm)</td></tr>
+<tr class="separator:acbfc47693d0b50ccfc6b7f7c38209b18"><td 
class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a607403f90e1921435183d031825e5e54"><td class="memItemLeft" 
align="right" valign="top">float8 []&#160;</td><td class="memItemRight" 
valign="bottom"><a class="el" 
href="dense__linear__systems_8sql__in.html#a607403f90e1921435183d031825e5e54">dense_direct_linear_system_merge_states</a>
 (float8[] state1, float8[] state2)</td></tr>
+<tr class="separator:a607403f90e1921435183d031825e5e54"><td 
class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a63a3ed2c811216d3d88c120005a13875"><td class="memItemLeft" 
align="right" valign="top">dense_linear_solver_result&#160;</td><td 
class="memItemRight" valign="bottom"><a class="el" 
href="dense__linear__systems_8sql__in.html#a63a3ed2c811216d3d88c120005a13875">dense_direct_linear_system_final</a>
 (float8[] state)</td></tr>
+<tr class="separator:a63a3ed2c811216d3d88c120005a13875"><td 
class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a379f260d8dfbf5c2be05c60776974188"><td class="memItemLeft" 
align="right" valign="top">aggregate dense_linear_solver_result&#160;</td><td 
class="memItemRight" valign="bottom"><a class="el" 
href="dense__linear__systems_8sql__in.html#a379f260d8dfbf5c2be05c60776974188">dense_direct_linear_system</a>
 (integer row_id, float8[] left_hand_side, float8 right_hand_side, integer 
numEquations, integer algorithm)</td></tr>
+<tr class="memdesc:a379f260d8dfbf5c2be05c60776974188"><td 
class="mdescLeft">&#160;</td><td class="mdescRight">Solve a system of linear 
equations using the direct method.  <a 
href="#a379f260d8dfbf5c2be05c60776974188">More...</a><br /></td></tr>
+<tr class="separator:a379f260d8dfbf5c2be05c60776974188"><td 
class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a885d6a36c07dc2c048948cb5287a3b92"><td class="memItemLeft" 
align="right" valign="top">varchar&#160;</td><td class="memItemRight" 
valign="bottom"><a class="el" 
href="dense__linear__systems_8sql__in.html#a885d6a36c07dc2c048948cb5287a3b92">linear_solver_dense</a>
 (varchar input_string)</td></tr>
+<tr class="memdesc:a885d6a36c07dc2c048948cb5287a3b92"><td 
class="mdescLeft">&#160;</td><td class="mdescRight">Help function, to print out 
the supported families.  <a 
href="#a885d6a36c07dc2c048948cb5287a3b92">More...</a><br /></td></tr>
+<tr class="separator:a885d6a36c07dc2c048948cb5287a3b92"><td 
class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a2272a21f30096a79cd543fe66a0aee19"><td class="memItemLeft" 
align="right" valign="top">varchar&#160;</td><td class="memItemRight" 
valign="bottom"><a class="el" 
href="dense__linear__systems_8sql__in.html#a2272a21f30096a79cd543fe66a0aee19">linear_solver_dense</a>
 ()</td></tr>
+<tr class="separator:a2272a21f30096a79cd543fe66a0aee19"><td 
class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ab7de234e67060a4fc48978e430642baa"><td class="memItemLeft" 
align="right" valign="top">void&#160;</td><td class="memItemRight" 
valign="bottom"><a class="el" 
href="dense__linear__systems_8sql__in.html#ab7de234e67060a4fc48978e430642baa">linear_solver_dense</a>
 (varchar source_table, varchar out_table, varchar row_id, varchar 
left_hand_side, varchar right_hand_side, varchar grouping_cols, varchar 
optimizer, varchar optimizer_options)</td></tr>
+<tr class="memdesc:ab7de234e67060a4fc48978e430642baa"><td 
class="mdescLeft">&#160;</td><td class="mdescRight">A wrapper function for the 
various marginal linear_systemsion analyzes.  <a 
href="#ab7de234e67060a4fc48978e430642baa">More...</a><br /></td></tr>
+<tr class="separator:ab7de234e67060a4fc48978e430642baa"><td 
class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a003b5a21cffde500fa808f1c6e9c14ae"><td class="memItemLeft" 
align="right" valign="top">void&#160;</td><td class="memItemRight" 
valign="bottom"><a class="el" 
href="dense__linear__systems_8sql__in.html#a003b5a21cffde500fa808f1c6e9c14ae">linear_solver_dense</a>
 (varchar source_table, varchar out_table, varchar row_id, varchar 
left_hand_side, varchar right_hand_side)</td></tr>
+<tr class="memdesc:a003b5a21cffde500fa808f1c6e9c14ae"><td 
class="mdescLeft">&#160;</td><td class="mdescRight">Marginal effects with 
default variables.  <a href="#a003b5a21cffde500fa808f1c6e9c14ae">More...</a><br 
/></td></tr>
+<tr class="separator:a003b5a21cffde500fa808f1c6e9c14ae"><td 
class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed 
Description</h2>
+<div class="textblock"><dl class="section date"><dt>Date</dt><dd>July 
2013</dd></dl>
+<dl class="section see"><dt>See also</dt><dd>Computes the solution of a 
consistent linear system, for more details see the module description at <a 
class="el" href="group__grp__dense__linear__solver.html">Dense Linear 
Systems</a> </dd></dl>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="a379f260d8dfbf5c2be05c60776974188"></a>
+<h2 class="memtitle"><span class="permalink"><a 
href="#a379f260d8dfbf5c2be05c60776974188">&#9670;&nbsp;</a></span>dense_direct_linear_system()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">aggregate dense_linear_solver_result 
dense_direct_linear_system </td>
+          <td>(</td>
+          <td class="paramtype">integer&#160;</td>
+          <td class="paramname"><em>row_id</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">float8 []&#160;</td>
+          <td class="paramname"><em>left_hand_side</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">float8&#160;</td>
+          <td class="paramname"><em>right_hand_side</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">integer&#160;</td>
+          <td class="paramname"><em>numEquations</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">integer&#160;</td>
+          <td class="paramname"><em>algorithm</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">row_id</td><td>Column containing the row_id 
</td></tr>
+    <tr><td class="paramname">left_hand_side</td><td>Column containing the 
left hand side of the system </td></tr>
+    <tr><td class="paramname">right_hand_side</td><td>Column containing the 
right hand side of the system </td></tr>
+    <tr><td class="paramname">numEquations</td><td>Number of equations 
</td></tr>
+    <tr><td class="paramname">algorithm</td><td>Algorithm used for the dense 
linear solver</td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>A composite value:<ul>
+<li><code>solution FLOAT8[] </code> - Array of marginal effects</li>
+<li><code>residual_norm FLOAT8</code> - Norm of the residual</li>
+<li><code>iters INTEGER</code> - Iterations taken</li>
+</ul>
+</dd></dl>
+<dl class="section user"><dt>Usage</dt><dd><ul>
+<li>Get all the diagnostic statistics:<br />
+ <pre> SELECT linear_system_dense(<em>row_id</em>,
+                                  <em>left_hand_side</em>,
+                                  <em> right_hand_side </em>,
+                                  <em> numEquations </em>)
+ FROM <em>dataTable</em>;
+</pre> </li>
+</ul>
+</dd></dl>
+
+</div>
+</div>
+<a id="a63a3ed2c811216d3d88c120005a13875"></a>
+<h2 class="memtitle"><span class="permalink"><a 
href="#a63a3ed2c811216d3d88c120005a13875">&#9670;&nbsp;</a></span>dense_direct_linear_system_final()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">dense_linear_solver_result 
dense_direct_linear_system_final </td>
+          <td>(</td>
+          <td class="paramtype">float8 []&#160;</td>
+          <td class="paramname"><em>state</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+
+</div>
+</div>
+<a id="a607403f90e1921435183d031825e5e54"></a>
+<h2 class="memtitle"><span class="permalink"><a 
href="#a607403f90e1921435183d031825e5e54">&#9670;&nbsp;</a></span>dense_direct_linear_system_merge_states()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">float8 [] 
dense_direct_linear_system_merge_states </td>
+          <td>(</td>
+          <td class="paramtype">float8 []&#160;</td>
+          <td class="paramname"><em>state1</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">float8 []&#160;</td>
+          <td class="paramname"><em>state2</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+
+</div>
+</div>
+<a id="acbfc47693d0b50ccfc6b7f7c38209b18"></a>
+<h2 class="memtitle"><span class="permalink"><a 
href="#acbfc47693d0b50ccfc6b7f7c38209b18">&#9670;&nbsp;</a></span>dense_direct_linear_system_transition()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">float8 [] dense_direct_linear_system_transition 
</td>
+          <td>(</td>
+          <td class="paramtype">float8 []&#160;</td>
+          <td class="paramname"><em>state</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">integer&#160;</td>
+          <td class="paramname"><em>row_id</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">float8 []&#160;</td>
+          <td class="paramname"><em>a</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">float8&#160;</td>
+          <td class="paramname"><em>b</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">integer&#160;</td>
+          <td class="paramname"><em>num_rows</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">integer&#160;</td>
+          <td class="paramname"><em>algorithm</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+
+</div>
+</div>
+<a id="a52f2bcdd0d038f19e64a44d4bb07fefb"></a>
+<h2 class="memtitle"><span class="permalink"><a 
href="#a52f2bcdd0d038f19e64a44d4bb07fefb">&#9670;&nbsp;</a></span>dense_residual_norm()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">aggregate residual_norm_result 
dense_residual_norm </td>
+          <td>(</td>
+          <td class="paramtype">float8 []&#160;</td>
+          <td class="paramname"><em>left_hand_side</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">float8&#160;</td>
+          <td class="paramname"><em>right_hand_side</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">float8 []&#160;</td>
+          <td class="paramname"><em>solution</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">left_hand_side</td><td>Column containing the 
left hand side of the system </td></tr>
+    <tr><td class="paramname">right_hand_side</td><td>Column containing the 
right hand side of the system </td></tr>
+    <tr><td class="paramname">solution</td><td>Solution of the linear 
system</td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>residual_norm FLOAT8:</dd></dl>
+<dl class="section user"><dt>Usage</dt><dd><ul>
+<li>Get all the diagnostic statistics:<br />
+ <pre> SELECT dense_residual_norm(<em>row_id</em>,
+                                  <em>left_hand_side</em>,
+                                  <em> right_hand_side </em>,
+                                  <em> solution </em>)
+ FROM <em>dataTable</em>;
+</pre> </li>
+</ul>
+</dd></dl>
+
+</div>
+</div>
+<a id="a01935dd8c4aef8c92e77b7f0f905fa4b"></a>
+<h2 class="memtitle"><span class="permalink"><a 
href="#a01935dd8c4aef8c92e77b7f0f905fa4b">&#9670;&nbsp;</a></span>dense_residual_norm_final()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">residual_norm_result dense_residual_norm_final 
</td>
+          <td>(</td>
+          <td class="paramtype">bytea8&#160;</td>
+          <td class="paramname"><em>state</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+
+</div>
+</div>
+<a id="a73ebde08b8395fd7bddbe1dc37b9539f"></a>
+<h2 class="memtitle"><span class="permalink"><a 
href="#a73ebde08b8395fd7bddbe1dc37b9539f">&#9670;&nbsp;</a></span>dense_residual_norm_merge_states()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">bytea8 dense_residual_norm_merge_states </td>
+          <td>(</td>
+          <td class="paramtype">bytea8&#160;</td>
+          <td class="paramname"><em>state1</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">bytea8&#160;</td>
+          <td class="paramname"><em>state2</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+
+</div>
+</div>
+<a id="ad34728809ab3121705342cf91b34c6dd"></a>
+<h2 class="memtitle"><span class="permalink"><a 
href="#ad34728809ab3121705342cf91b34c6dd">&#9670;&nbsp;</a></span>dense_residual_norm_transition()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">bytea8 dense_residual_norm_transition </td>
+          <td>(</td>
+          <td class="paramtype">bytea8&#160;</td>
+          <td class="paramname"><em>state</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">float8 []&#160;</td>
+          <td class="paramname"><em>a</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">float8&#160;</td>
+          <td class="paramname"><em>b</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">float8 []&#160;</td>
+          <td class="paramname"><em>x</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+
+</div>
+</div>
+<a id="a885d6a36c07dc2c048948cb5287a3b92"></a>
+<h2 class="memtitle"><span class="permalink"><a 
href="#a885d6a36c07dc2c048948cb5287a3b92">&#9670;&nbsp;</a></span>linear_solver_dense()
 <span class="overload">[1/4]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">varchar linear_solver_dense </td>
+          <td>(</td>
+          <td class="paramtype">varchar&#160;</td>
+          <td class="paramname"><em>input_string</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+
+</div>
+</div>
+<a id="a2272a21f30096a79cd543fe66a0aee19"></a>
+<h2 class="memtitle"><span class="permalink"><a 
href="#a2272a21f30096a79cd543fe66a0aee19">&#9670;&nbsp;</a></span>linear_solver_dense()
 <span class="overload">[2/4]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">varchar linear_solver_dense </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+
+</div>
+</div>
+<a id="ab7de234e67060a4fc48978e430642baa"></a>
+<h2 class="memtitle"><span class="permalink"><a 
href="#ab7de234e67060a4fc48978e430642baa">&#9670;&nbsp;</a></span>linear_solver_dense()
 <span class="overload">[3/4]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void linear_solver_dense </td>
+          <td>(</td>
+          <td class="paramtype">varchar&#160;</td>
+          <td class="paramname"><em>source_table</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">varchar&#160;</td>
+          <td class="paramname"><em>out_table</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">varchar&#160;</td>
+          <td class="paramname"><em>row_id</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">varchar&#160;</td>
+          <td class="paramname"><em>left_hand_side</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">varchar&#160;</td>
+          <td class="paramname"><em>right_hand_side</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">varchar&#160;</td>
+          <td class="paramname"><em>grouping_cols</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">varchar&#160;</td>
+          <td class="paramname"><em>optimizer</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">varchar&#160;</td>
+          <td class="paramname"><em>optimizer_options</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">source_table</td><td>String identifying the 
input table </td></tr>
+    <tr><td class="paramname">out_table</td><td>String identifying the output 
table to be created </td></tr>
+    <tr><td class="paramname">row_id</td><td>Column containing the row_id 
</td></tr>
+    <tr><td class="paramname">left_hand_side</td><td>Column containing the 
left hand side of the system </td></tr>
+    <tr><td class="paramname">right_hand_side</td><td>Column containing the 
right hand side of the system </td></tr>
+    <tr><td class="paramname">grouping_cols</td><td>Columns to group by 
</td></tr>
+    <tr><td class="paramname">optimizer</td><td>Optimizer to be used </td></tr>
+    <tr><td class="paramname">optimizer_options</td><td>Optimal parameters for 
the algorithms</td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>void</dd></dl>
+<dl class="section user"><dt>Usage</dt><dd>For function summary information. 
Run sql&gt; select linear_solver_dense('help'); OR sql&gt; select <a class="el" 
href="dense__linear__systems_8sql__in.html#a885d6a36c07dc2c048948cb5287a3b92" 
title="Help function, to print out the supported families. 
">linear_solver_dense()</a>; OR sql&gt; select linear_solver_dense('?'); For 
function usage information. Run sql&gt; select linear_solver_dense('usage'); 
</dd></dl>
+
+</div>
+</div>
+<a id="a003b5a21cffde500fa808f1c6e9c14ae"></a>
+<h2 class="memtitle"><span class="permalink"><a 
href="#a003b5a21cffde500fa808f1c6e9c14ae">&#9670;&nbsp;</a></span>linear_solver_dense()
 <span class="overload">[4/4]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void linear_solver_dense </td>
+          <td>(</td>
+          <td class="paramtype">varchar&#160;</td>
+          <td class="paramname"><em>source_table</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">varchar&#160;</td>
+          <td class="paramname"><em>out_table</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">varchar&#160;</td>
+          <td class="paramname"><em>row_id</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">varchar&#160;</td>
+          <td class="paramname"><em>left_hand_side</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">varchar&#160;</td>
+          <td class="paramname"><em>right_hand_side</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+
+</div>
+</div>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
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+    <li class="navelem"><a class="el" 
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+    <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.13 </li>
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