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<p>Matrix permutation operations.
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<div class="textblock"><code>#include "<a class="el" href="slu__ddefs_8h_source.html">slu_ddefs.h</a>"</code><br />
<code>#include "<a class="el" href="colamd_8h_source.html">colamd.h</a>"</code><br />
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Macros</h2></td></tr>
<tr class="memitem:a73502aac3d58c8346131a4c43ae1a2cd"><td class="memItemLeft" align="right" valign="top">#define </td><td class="memItemRight" valign="bottom"><a class="el" href="get__perm__c_8c.html#a73502aac3d58c8346131a4c43ae1a2cd">METISOPTIONS</a>   40</td></tr>
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Functions</h2></td></tr>
<tr class="memitem:af55322e1effcd284830c8cead2051be8"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="get__perm__c_8c.html#af55322e1effcd284830c8cead2051be8">genmmd_</a> (int *neqns, <a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> *xadj, <a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> *adjncy, int *invp, int *perm, <a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> *delta, <a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> *dhead, <a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> *qsize, <a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> *llist, <a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> *marker, <a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> *maxint, <a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> *nofsub)</td></tr>
<tr class="separator:af55322e1effcd284830c8cead2051be8"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a4d27a2c28e6a97a8480d587376f467de"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="get__perm__c_8c.html#a4d27a2c28e6a97a8480d587376f467de">get_colamd</a> (const int m, const int n, const <a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> nnz, <a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> *colptr, <a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> *rowind, int *perm_c)</td></tr>
<tr class="memdesc:a4d27a2c28e6a97a8480d587376f467de"><td class="mdescLeft"> </td><td class="mdescRight">Get COLAMD's permutation for matrix A. <a href="get__perm__c_8c.html#a4d27a2c28e6a97a8480d587376f467de">More...</a><br /></td></tr>
<tr class="separator:a4d27a2c28e6a97a8480d587376f467de"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a4366ba634b60299b1172c0313c5e8aea"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="get__perm__c_8c.html#a4366ba634b60299b1172c0313c5e8aea">get_metis</a> (int n, <a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> bnz, <a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> *b_colptr, <a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> *b_rowind, int *perm_c)</td></tr>
<tr class="memdesc:a4366ba634b60299b1172c0313c5e8aea"><td class="mdescLeft"> </td><td class="mdescRight">Get METIS' permutation for matrix B. <a href="get__perm__c_8c.html#a4366ba634b60299b1172c0313c5e8aea">More...</a><br /></td></tr>
<tr class="separator:a4366ba634b60299b1172c0313c5e8aea"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a357185b632937f39cc4a3b64db5903c9"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="get__perm__c_8c.html#a357185b632937f39cc4a3b64db5903c9">getata</a> (const int m, const int n, const <a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> nz, <a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> *colptr, <a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> *rowind, <a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> *atanz, <a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> **ata_colptr, <a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> **ata_rowind)</td></tr>
<tr class="memdesc:a357185b632937f39cc4a3b64db5903c9"><td class="mdescLeft"> </td><td class="mdescRight">Form the structure of A'*A. <a href="get__perm__c_8c.html#a357185b632937f39cc4a3b64db5903c9">More...</a><br /></td></tr>
<tr class="separator:a357185b632937f39cc4a3b64db5903c9"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a842fe36b4354a3434c1b340195c71e22"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="get__perm__c_8c.html#a842fe36b4354a3434c1b340195c71e22">at_plus_a</a> (const int n, const <a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> nz, <a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> *colptr, <a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> *rowind, <a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> *bnz, <a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> **b_colptr, <a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> **b_rowind)</td></tr>
<tr class="memdesc:a842fe36b4354a3434c1b340195c71e22"><td class="mdescLeft"> </td><td class="mdescRight">Form the structure of A'+A. <a href="get__perm__c_8c.html#a842fe36b4354a3434c1b340195c71e22">More...</a><br /></td></tr>
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<tr class="memitem:aaecb6e6e7a3e97356050bcfdf2573796"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="get__perm__c_8c.html#aaecb6e6e7a3e97356050bcfdf2573796">get_perm_c</a> (int ispec, <a class="el" href="structSuperMatrix.html">SuperMatrix</a> *<a class="el" href="zsymv_8c.html#af5d6242ff783dd9efca51eeec1c234f7">A</a>, int *perm_c)</td></tr>
<tr class="memdesc:aaecb6e6e7a3e97356050bcfdf2573796"><td class="mdescLeft"> </td><td class="mdescRight">Obtains a permutation matrix by applying the multiple minimum degree ordering code. <a href="get__perm__c_8c.html#aaecb6e6e7a3e97356050bcfdf2573796">More...</a><br /></td></tr>
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<h2 class="groupheader">Macro Definition Documentation</h2>
<a id="a73502aac3d58c8346131a4c43ae1a2cd" name="a73502aac3d58c8346131a4c43ae1a2cd"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a73502aac3d58c8346131a4c43ae1a2cd">◆ </a></span>METISOPTIONS</h2>
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<td class="memname">#define METISOPTIONS   40</td>
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</table>
</div><div class="memdoc">
</div>
</div>
<h2 class="groupheader">Function Documentation</h2>
<a id="a842fe36b4354a3434c1b340195c71e22" name="a842fe36b4354a3434c1b340195c71e22"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a842fe36b4354a3434c1b340195c71e22">◆ </a></span>at_plus_a()</h2>
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<td class="memname">void at_plus_a </td>
<td>(</td>
<td class="paramtype">const int </td>
<td class="paramname"><em>n</em>, </td>
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<td class="paramname"><em>nz</em>, </td>
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<td class="paramtype"><a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> * </td>
<td class="paramname"><em>colptr</em>, </td>
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<td class="paramtype"><a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> * </td>
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<td class="paramtype"><a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> * </td>
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<td class="paramtype"><a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> ** </td>
<td class="paramname"><em>b_colptr</em>, </td>
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<td></td>
<td class="paramtype"><a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> ** </td>
<td class="paramname"><em>b_rowind</em> </td>
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<p >A is an n-by-n matrix in column oriented format represented by (colptr, rowind). The output A'+A is in column oriented format (symmetrically, also row oriented), represented by (b_colptr, b_rowind).</p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">n</td><td>number of columns in matrix A. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">nz</td><td>number of nonzeros in matrix A </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">colptr</td><td>column pointer of size n+1 for matrix A. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">rowind</td><td>row indices of size nz for matrix A. </td></tr>
<tr><td class="paramdir">[out]</td><td class="paramname">bnz</td><td>on exit, returns the actual number of nonzeros in matrix A'*A. </td></tr>
<tr><td class="paramdir">[out]</td><td class="paramname">b_colptr</td><td>column pointer of size n+1 for matrix A'+A. </td></tr>
<tr><td class="paramdir">[out]</td><td class="paramname">b_rowind</td><td>row indices of size bnz for matrix A'+A. </td></tr>
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</dd>
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<h2 class="memtitle"><span class="permalink"><a href="#af55322e1effcd284830c8cead2051be8">◆ </a></span>genmmd_()</h2>
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<td class="memname">int genmmd_ </td>
<td>(</td>
<td class="paramtype">int * </td>
<td class="paramname"><em>neqns</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> * </td>
<td class="paramname"><em>xadj</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> * </td>
<td class="paramname"><em>adjncy</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int * </td>
<td class="paramname"><em>invp</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int * </td>
<td class="paramname"><em>perm</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> * </td>
<td class="paramname"><em>delta</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> * </td>
<td class="paramname"><em>dhead</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> * </td>
<td class="paramname"><em>qsize</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> * </td>
<td class="paramname"><em>llist</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> * </td>
<td class="paramname"><em>marker</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> * </td>
<td class="paramname"><em>maxint</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> * </td>
<td class="paramname"><em>nofsub</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
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<h2 class="memtitle"><span class="permalink"><a href="#a4d27a2c28e6a97a8480d587376f467de">◆ </a></span>get_colamd()</h2>
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<td class="memname">void get_colamd </td>
<td>(</td>
<td class="paramtype">const int </td>
<td class="paramname"><em>m</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const int </td>
<td class="paramname"><em>n</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> </td>
<td class="paramname"><em>nnz</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> * </td>
<td class="paramname"><em>colptr</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> * </td>
<td class="paramname"><em>rowind</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int * </td>
<td class="paramname"><em>perm_c</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
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<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">m</td><td>Number of rows in matrix A. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">n</td><td>Number of columns in matrix A. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">nnz</td><td>Number of nonzeros in matrix A. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">colptr</td><td>Column pointer of size n+1 for matrix A. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">rowind</td><td>Row indices of size nnz for matrix A. </td></tr>
<tr><td class="paramdir">[out]</td><td class="paramname">perm_c</td><td>Column permutation vector. </td></tr>
</table>
</dd>
</dl>
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<h2 class="memtitle"><span class="permalink"><a href="#a4366ba634b60299b1172c0313c5e8aea">◆ </a></span>get_metis()</h2>
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<td class="memname">void get_metis </td>
<td>(</td>
<td class="paramtype">int </td>
<td class="paramname"><em>n</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> </td>
<td class="paramname"><em>bnz</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> * </td>
<td class="paramname"><em>b_colptr</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> * </td>
<td class="paramname"><em>b_rowind</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int * </td>
<td class="paramname"><em>perm_c</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
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<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">n</td><td>Number of columns in matrix B. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">bnz</td><td>Number of nonzeros in matrix B. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">b_colptr</td><td>Column pointer of size n+1 for matrix B. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">b_rowind</td><td>Row indices of size bnz for matrix B. </td></tr>
<tr><td class="paramdir">[out]</td><td class="paramname">perm_c</td><td>Column permutation vector. </td></tr>
</table>
</dd>
</dl>
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<h2 class="memtitle"><span class="permalink"><a href="#aaecb6e6e7a3e97356050bcfdf2573796">◆ </a></span>get_perm_c()</h2>
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<td class="memname">void get_perm_c </td>
<td>(</td>
<td class="paramtype">int </td>
<td class="paramname"><em>ispec</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structSuperMatrix.html">SuperMatrix</a> * </td>
<td class="paramname"><em>A</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int * </td>
<td class="paramname"><em>perm_c</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
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<p >Obtains a permutation matrix Pc by applying the multiple minimum degree ordering code by Joseph Liu to matrix A'*A or A+A' or using approximate minimum degree column ordering by Davis et. al. The LU factorization of A*Pc tends to have less fill than the LU factorization of A.</p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">ispec</td><td>Specifies the type of column ordering to reduce fill:<br />
= 1: minimum degree on the structure of A^T * A<br />
= 2: minimum degree on the structure of A^T + A<br />
= 3: approximate minimum degree for unsymmetric matrices<br />
If ispec == 0, the natural ordering (i.e., Pc = I) is returned. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">A</td><td>Matrix A in A*X=B, of dimension (A->nrow, A->ncol). The number of the linear equations is A->nrow. Currently, the type of A can be: Stype = NC; Dtype = _D; Mtype = GE. In the future, more general A can be handled. </td></tr>
<tr><td class="paramdir">[out]</td><td class="paramname">perm_c</td><td>Column permutation vector of size A->ncol, which defines the permutation matrix Pc; perm_c[i] = j means column i of A is in position j in A*Pc. </td></tr>
</table>
</dd>
</dl>
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<h2 class="memtitle"><span class="permalink"><a href="#a357185b632937f39cc4a3b64db5903c9">◆ </a></span>getata()</h2>
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<td class="memname">void getata </td>
<td>(</td>
<td class="paramtype">const int </td>
<td class="paramname"><em>m</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const int </td>
<td class="paramname"><em>n</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> </td>
<td class="paramname"><em>nz</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> * </td>
<td class="paramname"><em>colptr</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> * </td>
<td class="paramname"><em>rowind</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> * </td>
<td class="paramname"><em>atanz</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> ** </td>
<td class="paramname"><em>ata_colptr</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> ** </td>
<td class="paramname"><em>ata_rowind</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
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</div><div class="memdoc">
<p >A is an m-by-n matrix in column oriented format represented by (colptr, rowind). The output A'*A is in column oriented format (symmetrically, also row oriented), represented by (ata_colptr, ata_rowind).</p>
<p >This routine is modified from GETATA routine by Tim Davis. The complexity of this algorithm is: SUM_{i=1,m} r(i)^2, i.e., the sum of the square of the row counts.</p>
<p >Questions<br />
</p><ul>
<li>
Do I need to withhold the <em>dense</em> rows? </li>
<li>
How do I know the number of nonzeros in A'*A? </li>
</ul>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">m</td><td>number of rows in matrix A. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">n</td><td>number of columns in matrix A. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">nz</td><td>number of nonzeros in matrix A </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">colptr</td><td>column pointer of size n+1 for matrix A. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">rowind</td><td>row indices of size nz for matrix A. </td></tr>
<tr><td class="paramdir">[out]</td><td class="paramname">atanz</td><td>on exit, returns the actual number of nonzeros in matrix A'*A. </td></tr>
<tr><td class="paramdir">[out]</td><td class="paramname">ata_colptr</td><td>column pointer of size n+1 for matrix A'*A. </td></tr>
<tr><td class="paramdir">[out]</td><td class="paramname">ata_rowind</td><td>row indices of size atanz for matrix A'*A. </td></tr>
</table>
</dd>
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