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<p>Triangular system solving with Matrix routines.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include "<a class="el" href="misc_8h_source.html">misc.h</a>"</code><br/>
<code>#include "<a class="el" href="packedmatrix_8h_source.html">packedmatrix.h</a>"</code><br/>
</div>
<p><a href="trsm_8h_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">void </td><td class="memItemRight" valign="bottom"><a class="el" href="trsm_8h.html#a4b480a6ed0a1454871acac44078987b3">mzd_trsm_upper_right</a> (<a class="el" href="structmzd__t.html">mzd_t</a> *U, <a class="el" href="structmzd__t.html">mzd_t</a> *B, const int cutoff)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Solves X U = B with X and B matrices and U upper triangular. <a href="#a4b480a6ed0a1454871acac44078987b3"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="trsm_8h.html#afe43f6df7e257388031b503fab045f61">_mzd_trsm_upper_right</a> (<a class="el" href="structmzd__t.html">mzd_t</a> *U, <a class="el" href="structmzd__t.html">mzd_t</a> *B, const int cutoff)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Solves X U = B with X and B matrices and U upper triangular. <a href="#afe43f6df7e257388031b503fab045f61"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="trsm_8h.html#ae24359d2badde90268c5195b60ccd4d3">mzd_trsm_lower_right</a> (<a class="el" href="structmzd__t.html">mzd_t</a> *L, <a class="el" href="structmzd__t.html">mzd_t</a> *B, const int cutoff)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Solves X L = B with X and B matrices and L lower triangular. <a href="#ae24359d2badde90268c5195b60ccd4d3"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="trsm_8h.html#a1f9bc4c1f598bfa204be18780a76fa0f">_mzd_trsm_lower_right</a> (<a class="el" href="structmzd__t.html">mzd_t</a> *L, <a class="el" href="structmzd__t.html">mzd_t</a> *B, const int cutoff)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Solves X L = B with X and B with matrices and L lower triangular. <a href="#a1f9bc4c1f598bfa204be18780a76fa0f"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="trsm_8h.html#ab1a662a0af8c9c9e5317a3b52dc21317">mzd_trsm_lower_left</a> (<a class="el" href="structmzd__t.html">mzd_t</a> *L, <a class="el" href="structmzd__t.html">mzd_t</a> *B, const int cutoff)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Solves L X = B with X and B matrices and L lower triangular. <a href="#ab1a662a0af8c9c9e5317a3b52dc21317"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="trsm_8h.html#a41475e4084b0f38aafb85c99a8b59d08">_mzd_trsm_lower_left</a> (<a class="el" href="structmzd__t.html">mzd_t</a> *L, <a class="el" href="structmzd__t.html">mzd_t</a> *B, const int cutoff)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Solves L X = B with X and B matrices and L lower triangular. <a href="#a41475e4084b0f38aafb85c99a8b59d08"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="trsm_8h.html#a902aaad9b4ef1537de13b7650e28a308">mzd_trsm_upper_left</a> (<a class="el" href="structmzd__t.html">mzd_t</a> *U, <a class="el" href="structmzd__t.html">mzd_t</a> *B, const int cutoff)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Solves U X = B with X and B matrices and U upper triangular. <a href="#a902aaad9b4ef1537de13b7650e28a308"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="trsm_8h.html#afc954289367456878cc3645f120e1074">_mzd_trsm_upper_left</a> (<a class="el" href="structmzd__t.html">mzd_t</a> *U, <a class="el" href="structmzd__t.html">mzd_t</a> *B, const int cutoff)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Solves U X = B with X and B matrices and U upper triangular. <a href="#afc954289367456878cc3645f120e1074"></a><br/></td></tr>
</table>
<hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><p>Triangular system solving with Matrix routines. </p>
<dl class="author"><dt><b>Author:</b></dt><dd>Clement Pernet <<a href="mailto:clement.pernet@gmail.com">clement.pernet@gmail.com</a>> </dd></dl>
</div><hr/><h2>Function Documentation</h2>
<a class="anchor" id="a41475e4084b0f38aafb85c99a8b59d08"></a><!-- doxytag: member="trsm.h::_mzd_trsm_lower_left" ref="a41475e4084b0f38aafb85c99a8b59d08" args="(mzd_t *L, mzd_t *B, const int cutoff)" -->
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<td class="memname">void _mzd_trsm_lower_left </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structmzd__t.html">mzd_t</a> * </td>
<td class="paramname"><em>L</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structmzd__t.html">mzd_t</a> * </td>
<td class="paramname"><em>B</em>, </td>
</tr>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">const int </td>
<td class="paramname"><em>cutoff</em> </td>
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<td></td>
<td>)</td>
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<p>Solves L X = B with X and B matrices and L lower triangular. </p>
<p>X is stored inplace on B.</p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">L</td><td>Input lower triangular matrix. </td></tr>
<tr><td class="paramname">B</td><td>Input matrix, being overwritten by the solution matrix X </td></tr>
<tr><td class="paramname">cutoff</td><td>Minimal dimension for Strassen recursion. </td></tr>
</table>
</dd>
</dl>
<p><div class="fragment"><pre class="fragment">
|\ ______
| \ | |
| \ | B0 |
|L00\ | |
|____\ |______|
| |\ | |
| | \ | |
| | \ | B1 |
|L10 |L11\ | |
|____|____\ |______|
</pre></div> <ul>
<li>L00 L10 B0 and B1 are possibly located at uneven locations. </li>
<li>Their column dimension is lower than 64. </li>
<li>The first column of L01, L11, B1 are aligned to words.</li>
</ul>
</p>
</div>
</div>
<a class="anchor" id="a1f9bc4c1f598bfa204be18780a76fa0f"></a><!-- doxytag: member="trsm.h::_mzd_trsm_lower_right" ref="a1f9bc4c1f598bfa204be18780a76fa0f" args="(mzd_t *L, mzd_t *B, const int cutoff)" -->
<div class="memitem">
<div class="memproto">
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<td class="memname">void _mzd_trsm_lower_right </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structmzd__t.html">mzd_t</a> * </td>
<td class="paramname"><em>L</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structmzd__t.html">mzd_t</a> * </td>
<td class="paramname"><em>B</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const int </td>
<td class="paramname"><em>cutoff</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
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<div class="memdoc">
<p>Solves X L = B with X and B with matrices and L lower triangular. </p>
<p>This version assumes that the matrices are at an even position on the RADIX grid and that their dimension is a multiple of RADIX. X is stored inplace on B.</p>
<dl class="attention"><dt><b>Attention:</b></dt><dd>Note, that the 'right' variants of TRSM are slower than the 'left' variants.</dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">L</td><td>Input lower triangular matrix. </td></tr>
<tr><td class="paramname">B</td><td>Input matrix, being overwritten by the solution matrix X </td></tr>
<tr><td class="paramname">cutoff</td><td>Minimal dimension for Strassen recursion. </td></tr>
</table>
</dd>
</dl>
<p><div class="fragment"><pre class="fragment">
|\
| \
| \
|L00\
|____\
| |\
| | \
| | \
|L10 |L11\
|____|____\
_________
|B0 |B1 |
|____|____|
</pre></div> <ul>
<li>L00 and B0 are possibly located at uneven locations. </li>
<li>Their column dimension is lower than 64. </li>
<li>The first column of L10, L11, B1 are aligned to words.</li>
</ul>
</p>
</div>
</div>
<a class="anchor" id="afc954289367456878cc3645f120e1074"></a><!-- doxytag: member="trsm.h::_mzd_trsm_upper_left" ref="afc954289367456878cc3645f120e1074" args="(mzd_t *U, mzd_t *B, const int cutoff)" -->
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<td class="memname">void _mzd_trsm_upper_left </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structmzd__t.html">mzd_t</a> * </td>
<td class="paramname"><em>U</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structmzd__t.html">mzd_t</a> * </td>
<td class="paramname"><em>B</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const int </td>
<td class="paramname"><em>cutoff</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>Solves U X = B with X and B matrices and U upper triangular. </p>
<p>X is stored inplace on B.</p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">U</td><td>Input upper triangular matrix. </td></tr>
<tr><td class="paramname">B</td><td>Input matrix, being overwritten by the solution matrix X </td></tr>
<tr><td class="paramname">cutoff</td><td>Minimal dimension for Strassen recursion. </td></tr>
</table>
</dd>
</dl>
<p><div class="fragment"><pre class="fragment">
__________ ______
\ U00| | | |
\ |U01 | | |
\ | | | B0 |
\ | | | |
\|____| |______|
\ | | |
\U11| | |
\ | | B1 |
\ | | |
\| |______|
</pre></div> <ul>
<li>U00, B0 and B1 are possibly located at uneven locations. </li>
<li>Their column dimension is greater than 64 </li>
<li>The first column of U01, U11, B0 and B1 are aligned to words.</li>
</ul>
</p>
</div>
</div>
<a class="anchor" id="afe43f6df7e257388031b503fab045f61"></a><!-- doxytag: member="trsm.h::_mzd_trsm_upper_right" ref="afe43f6df7e257388031b503fab045f61" args="(mzd_t *U, mzd_t *B, const int cutoff)" -->
<div class="memitem">
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<td class="memname">void _mzd_trsm_upper_right </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structmzd__t.html">mzd_t</a> * </td>
<td class="paramname"><em>U</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structmzd__t.html">mzd_t</a> * </td>
<td class="paramname"><em>B</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const int </td>
<td class="paramname"><em>cutoff</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>Solves X U = B with X and B matrices and U upper triangular. </p>
<p>X is stored inplace on B.</p>
<dl class="attention"><dt><b>Attention:</b></dt><dd>Note, that the 'right' variants of TRSM are slower than the 'left' variants.</dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">U</td><td>Input upper triangular matrix. </td></tr>
<tr><td class="paramname">B</td><td>Input matrix, being overwritten by the solution matrix X </td></tr>
<tr><td class="paramname">cutoff</td><td>Minimal dimension for Strassen recursion. </td></tr>
</table>
</dd>
</dl>
<p><div class="fragment"><pre class="fragment">
_________
\U00| |
\ |U01|
\ | |
\|___|
\U11|
\ |
\ |
\|
_______
|B0 |B1 |
|___|___|
</pre></div> <ul>
<li>U00 and B0 are possibly located at uneven locations. </li>
<li>Their column dimension is lower than 64. </li>
<li>The first column of U01, U11, B1 are aligned at words.</li>
</ul>
</p>
</div>
</div>
<a class="anchor" id="ab1a662a0af8c9c9e5317a3b52dc21317"></a><!-- doxytag: member="trsm.h::mzd_trsm_lower_left" ref="ab1a662a0af8c9c9e5317a3b52dc21317" args="(mzd_t *L, mzd_t *B, const int cutoff)" -->
<div class="memitem">
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<td class="memname">void mzd_trsm_lower_left </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structmzd__t.html">mzd_t</a> * </td>
<td class="paramname"><em>L</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structmzd__t.html">mzd_t</a> * </td>
<td class="paramname"><em>B</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const int </td>
<td class="paramname"><em>cutoff</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>Solves L X = B with X and B matrices and L lower triangular. </p>
<p>X is stored inplace on B.</p>
<p>This is the wrapper function including bounds checks. See <a class="el" href="trsm_8h.html#a41475e4084b0f38aafb85c99a8b59d08" title="Solves L X = B with X and B matrices and L lower triangular.">_mzd_trsm_lower_left()</a> for implementation details.</p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">L</td><td>Input lower triangular matrix. </td></tr>
<tr><td class="paramname">B</td><td>Input matrix, being overwritten by the solution matrix X </td></tr>
<tr><td class="paramname">cutoff</td><td>Minimal dimension for Strassen recursion. </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a class="anchor" id="ae24359d2badde90268c5195b60ccd4d3"></a><!-- doxytag: member="trsm.h::mzd_trsm_lower_right" ref="ae24359d2badde90268c5195b60ccd4d3" args="(mzd_t *L, mzd_t *B, const int cutoff)" -->
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<td class="memname">void mzd_trsm_lower_right </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structmzd__t.html">mzd_t</a> * </td>
<td class="paramname"><em>L</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structmzd__t.html">mzd_t</a> * </td>
<td class="paramname"><em>B</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const int </td>
<td class="paramname"><em>cutoff</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>Solves X L = B with X and B matrices and L lower triangular. </p>
<p>X is stored inplace on B.</p>
<p>This is the wrapper function including bounds checks. See <a class="el" href="trsm_8h.html#afe43f6df7e257388031b503fab045f61" title="Solves X U = B with X and B matrices and U upper triangular.">_mzd_trsm_upper_right()</a> for implementation details.</p>
<dl class="attention"><dt><b>Attention:</b></dt><dd>Note, that the 'right' variants of TRSM are slower than the 'left' variants.</dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">L</td><td>Input upper triangular matrix. </td></tr>
<tr><td class="paramname">B</td><td>Input matrix, being overwritten by the solution matrix X </td></tr>
<tr><td class="paramname">cutoff</td><td>Minimal dimension for Strassen recursion. </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a class="anchor" id="a902aaad9b4ef1537de13b7650e28a308"></a><!-- doxytag: member="trsm.h::mzd_trsm_upper_left" ref="a902aaad9b4ef1537de13b7650e28a308" args="(mzd_t *U, mzd_t *B, const int cutoff)" -->
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<td class="memname">void mzd_trsm_upper_left </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structmzd__t.html">mzd_t</a> * </td>
<td class="paramname"><em>U</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structmzd__t.html">mzd_t</a> * </td>
<td class="paramname"><em>B</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const int </td>
<td class="paramname"><em>cutoff</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>Solves U X = B with X and B matrices and U upper triangular. </p>
<p>X is stored inplace on B.</p>
<p>This is the wrapper function including bounds checks. See <a class="el" href="trsm_8h.html#afc954289367456878cc3645f120e1074" title="Solves U X = B with X and B matrices and U upper triangular.">_mzd_trsm_upper_left()</a> for implementation details.</p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">U</td><td>Input upper triangular matrix. </td></tr>
<tr><td class="paramname">B</td><td>Input matrix, being overwritten by the solution matrix X </td></tr>
<tr><td class="paramname">cutoff</td><td>Minimal dimension for Strassen recursion. </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a class="anchor" id="a4b480a6ed0a1454871acac44078987b3"></a><!-- doxytag: member="trsm.h::mzd_trsm_upper_right" ref="a4b480a6ed0a1454871acac44078987b3" args="(mzd_t *U, mzd_t *B, const int cutoff)" -->
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<td class="memname">void mzd_trsm_upper_right </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structmzd__t.html">mzd_t</a> * </td>
<td class="paramname"><em>U</em>, </td>
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<td></td>
<td class="paramtype"><a class="el" href="structmzd__t.html">mzd_t</a> * </td>
<td class="paramname"><em>B</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">const int </td>
<td class="paramname"><em>cutoff</em> </td>
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<td>)</td>
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<p>Solves X U = B with X and B matrices and U upper triangular. </p>
<p>X is stored inplace on B.</p>
<dl class="attention"><dt><b>Attention:</b></dt><dd>Note, that the 'right' variants of TRSM are slower than the 'left' variants.</dd></dl>
<p>This is the wrapper function including bounds checks. See <a class="el" href="trsm_8h.html#afe43f6df7e257388031b503fab045f61" title="Solves X U = B with X and B matrices and U upper triangular.">_mzd_trsm_upper_right()</a> for implementation details.</p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">U</td><td>Input upper triangular matrix. </td></tr>
<tr><td class="paramname">B</td><td>Input matrix, being overwritten by the solution matrix X </td></tr>
<tr><td class="paramname">cutoff</td><td>Minimal dimension for Strassen recursion. </td></tr>
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</dd>
</dl>
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