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<head><title>Method apply</title>
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<!--l. 714--><div class="crosslinks"><p class="noindent"><span
class="cmr-12">[</span><a
href="userhtmlsu13.html" ><span
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<h4 class="subsectionHead"><span class="titlemark"><span
class="cmr-12">5.6 </span></span> <a
id="x21-200005.6"></a><span
class="cmr-12">Method apply</span></h4>
<div class="center"
>
<!--l. 716--><p class="noindent" >
<!--l. 717--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-12">call</span><span
class="cmtt-12">&#x00A0;</span><span
class="cmtt-12">p</span><span
class="cmtt-12">%</span><span
class="cmtt-12">apply</span><span
class="cmtt-12">(</span><span
class="cmtt-12">x</span><span
class="cmtt-12">,</span><span
class="cmtt-12">y</span><span
class="cmtt-12">,</span><span
class="cmtt-12">desc_a</span><span
class="cmtt-12">,</span><span
class="cmtt-12">info</span><span
class="cmtt-12">&#x00A0;</span><span
class="cmtt-12">[,</span><span
class="cmtt-12">trans</span><span
class="cmtt-12">,</span><span
class="cmtt-12">work</span><span
class="cmtt-12">])</span><br />
</div>
<!--l. 720--><p class="noindent" ><span
class="cmr-12">This method computes </span><span
class="cmmi-12">y </span><span
class="cmr-12">= </span><span
class="cmmi-12">op</span><span
class="cmr-12">(</span><span
class="cmmi-12">B</span><sup><span
class="cmsy-8">-</span><span
class="cmr-8">1</span></sup><span
class="cmr-12">) </span><span
class="cmmi-12">x</span><span
class="cmr-12">, where </span><span
class="cmmi-12">B </span><span
class="cmr-12">is a previously built preconditioner,</span>
<span
class="cmr-12">stored into </span><span class="lstinline"></span><span
class="cmtt-12">p</span><span
class="cmr-12">, and </span><span
class="cmmi-12">op </span><span
class="cmr-12">denotes the preconditioner itself or its transpose, according to the</span>
<span
class="cmr-12">value of </span><span class="lstinline"></span><span
class="cmtt-12">trans</span><span
class="cmr-12">. Note that, when AMG4PSBLAS is used with a Krylov solver from</span>
<span
class="cmr-12">PSBLAS, </span><span class="lstinline"></span><span
class="cmtt-12">p</span><span
class="cmtt-12">%</span><span
class="cmtt-12">apply</span> <span
class="cmr-12">is called within the PSBLAS method </span><span class="lstinline"></span><span
class="cmtt-12">psb_krylov</span> <span
class="cmr-12">and hence it is</span>
<span
class="cmr-12">completely transparent to the user.</span>
<!--l. 729--><p class="noindent" ><span
class="cmbx-12">Arguments</span>
<div class="tabular"> <table id="TBL-13" class="tabular"
cellspacing="0" cellpadding="0"
><colgroup id="TBL-13-1g"><col
id="TBL-13-1"><col
id="TBL-13-2"></colgroup><tr
style="vertical-align:baseline;" id="TBL-13-1-"><td style="white-space:normal; text-align:left;" id="TBL-13-1-1"
class="td11"><!--l. 732--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-12">x</span> </td><td style="white-space:normal; text-align:left;" id="TBL-13-1-2"
class="td11"><!--l. 732--><p class="noindent" ><span
class="cmti-12">type</span><span class="lstinline"></span><span
class="cmtt-12">(</span><span
class="cmti-12">kind</span><span
class="cmti-12">_parameter</span><span class="lstinline"></span><span
class="cmtt-12">),</span><span
class="cmtt-12">&#x00A0;</span><span
class="cmtt-12">dimension</span><span
class="cmtt-12">(:),</span><span
class="cmtt-12">&#x00A0;</span><span
class="cmtt-12">intent</span><span
class="cmtt-12">(</span><span
class="cmtt-12">in</span><span
class="cmtt-12">)</span><span
class="cmr-12">.</span> </td>
</tr><tr
style="vertical-align:baseline;" id="TBL-13-2-"><td style="white-space:normal; text-align:left;" id="TBL-13-2-1"
class="td11"><!--l. 733--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-13-2-2"
class="td11"><!--l. 733--><p class="noindent" ><span
class="cmr-12">The local part of the vector </span><span
class="cmmi-12">x</span><span
class="cmr-12">. Note that </span><span
class="cmti-12">type </span><span
class="cmr-12">and </span><span
class="cmti-12">kind</span><span
class="cmti-12">_parameter</span>
<span
class="cmr-12">must be chosen according to the </span><span class="lstinline"></span><span
class="cmtt-12">real</span><span
class="cmr-12">/</span><span class="lstinline"></span><span
class="cmtt-12">complex</span><span
class="cmr-12">, single/double</span>
<span
class="cmr-12">precision version of AMG4PSBLAS under use.</span> </td>
</tr><tr
style="vertical-align:baseline;" id="TBL-13-3-"><td style="white-space:normal; text-align:left;" id="TBL-13-3-1"
class="td11"><!--l. 736--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-12">y</span> </td><td style="white-space:normal; text-align:left;" id="TBL-13-3-2"
class="td11"><!--l. 736--><p class="noindent" ><span
class="cmti-12">type</span><span class="lstinline"></span><span
class="cmtt-12">(</span><span
class="cmti-12">kind</span><span
class="cmti-12">_parameter</span><span class="lstinline"></span><span
class="cmtt-12">),</span><span
class="cmtt-12">&#x00A0;</span><span
class="cmtt-12">dimension</span><span
class="cmtt-12">(:),</span><span
class="cmtt-12">&#x00A0;</span><span
class="cmtt-12">intent</span><span
class="cmtt-12">(</span><span
class="cmtt-12">out</span><span
class="cmtt-12">)</span><span
class="cmr-12">.</span> </td>
</tr><tr
style="vertical-align:baseline;" id="TBL-13-4-"><td style="white-space:normal; text-align:left;" id="TBL-13-4-1"
class="td11"><!--l. 737--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-13-4-2"
class="td11"><!--l. 737--><p class="noindent" ><span
class="cmr-12">The local part of the vector </span><span
class="cmmi-12">y</span><span
class="cmr-12">. Note that </span><span
class="cmti-12">type </span><span
class="cmr-12">and </span><span
class="cmti-12">kind</span><span
class="cmti-12">_parameter</span>
<span
class="cmr-12">must be chosen according to the </span><span class="lstinline"></span><span
class="cmtt-12">real</span><span
class="cmr-12">/</span><span class="lstinline"></span><span
class="cmtt-12">complex</span><span
class="cmr-12">, single/double</span>
<span
class="cmr-12">precision version of AMG4PSBLAS under use.</span> </td>
</tr><tr
style="vertical-align:baseline;" id="TBL-13-5-"><td style="white-space:normal; text-align:left;" id="TBL-13-5-1"
class="td11"><!--l. 740--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-12">desc_a</span></td><td style="white-space:normal; text-align:left;" id="TBL-13-5-2"
class="td11"><!--l. 740--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-12">type</span><span
class="cmtt-12">(</span><span
class="cmtt-12">psb_desc_type</span><span
class="cmtt-12">),</span><span
class="cmtt-12">&#x00A0;</span><span
class="cmtt-12">intent</span><span
class="cmtt-12">(</span><span
class="cmtt-12">in</span><span
class="cmtt-12">)</span><span
class="cmr-12">.</span> </td>
</tr><tr
style="vertical-align:baseline;" id="TBL-13-6-"><td style="white-space:normal; text-align:left;" id="TBL-13-6-1"
class="td11"><!--l. 741--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-13-6-2"
class="td11"><!--l. 741--><p class="noindent" ><span
class="cmr-12">The communication descriptor associated to the matrix to be</span>
<span
class="cmr-12">preconditioned.</span> </td>
</tr><tr
style="vertical-align:baseline;" id="TBL-13-7-"><td style="white-space:normal; text-align:left;" id="TBL-13-7-1"
class="td11"><!--l. 743--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-12">info</span> </td><td style="white-space:normal; text-align:left;" id="TBL-13-7-2"
class="td11"><!--l. 743--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-12">integer</span><span
class="cmtt-12">,</span><span
class="cmtt-12">&#x00A0;</span><span
class="cmtt-12">intent</span><span
class="cmtt-12">(</span><span
class="cmtt-12">out</span><span
class="cmtt-12">)</span><span
class="cmr-12">.</span> </td>
</tr><tr
style="vertical-align:baseline;" id="TBL-13-8-"><td style="white-space:normal; text-align:left;" id="TBL-13-8-1"
class="td11"><!--l. 744--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-13-8-2"
class="td11"><!--l. 744--><p class="noindent" ><span
class="cmr-12">Error code. If no error, 0 is returned. See Section</span><span
class="cmr-12">&#x00A0;</span><a
href="userhtmlse7.html#x26-300007"><span
class="cmr-12">7</span><!--tex4ht:ref: sec:errors --></a> <span
class="cmr-12">for details.</span> </td>
</tr><tr
style="vertical-align:baseline;" id="TBL-13-9-"><td style="white-space:normal; text-align:left;" id="TBL-13-9-1"
class="td11"><!--l. 745--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-12">trans</span> </td><td style="white-space:normal; text-align:left;" id="TBL-13-9-2"
class="td11"><!--l. 745--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-12">character</span><span
class="cmtt-12">(</span><span
class="cmtt-12">len</span><span
class="cmtt-12">=1),</span><span
class="cmtt-12">&#x00A0;</span><span
class="cmtt-12">optional</span><span
class="cmtt-12">,</span><span
class="cmtt-12">&#x00A0;</span><span
class="cmtt-12">intent</span><span
class="cmtt-12">(</span><span
class="cmtt-12">in</span><span
class="cmtt-12">).</span> </td>
</tr><tr
style="vertical-align:baseline;" id="TBL-13-10-"><td style="white-space:normal; text-align:left;" id="TBL-13-10-1"
class="td11"><!--l. 746--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-13-10-2"
class="td11"><!--l. 746--><p class="noindent" ><span
class="cmr-12">If </span><span class="lstinline"></span><span
class="cmtt-12">trans</span> <span
class="cmr-12">= </span><span class="lstinline"></span><span
class="cmtt-12">&#8217;</span><span
class="cmtt-12">N</span><span
class="cmtt-12">&#8217;</span><span
class="cmtt-12">,</span><span
class="cmtt-12">&#8217;</span><span
class="cmtt-12">n</span><span
class="cmtt-12">&#8217;</span> <span
class="cmr-12">then </span><span
class="cmmi-12">op</span><span
class="cmr-12">(</span><span
class="cmmi-12">B</span><sup><span
class="cmsy-8">-</span><span
class="cmr-8">1</span></sup><span
class="cmr-12">) = </span><span
class="cmmi-12">B</span><sup><span
class="cmsy-8">-</span><span
class="cmr-8">1</span></sup><span
class="cmr-12">; if </span><span class="lstinline"></span><span
class="cmtt-12">trans</span> <span
class="cmr-12">= </span><span class="lstinline"></span><span
class="cmtt-12">&#8217;</span><span
class="cmtt-12">T</span><span
class="cmtt-12">&#8217;</span><span
class="cmtt-12">,</span><span
class="cmtt-12">&#8217;</span><span
class="cmtt-12">t</span><span
class="cmtt-12">&#8217;</span>
<span
class="cmr-12">then </span><span
class="cmmi-12">op</span><span
class="cmr-12">(</span><span
class="cmmi-12">B</span><sup><span
class="cmsy-8">-</span><span
class="cmr-8">1</span></sup><span
class="cmr-12">) = </span><span
class="cmmi-12">B</span><sup><span
class="cmsy-8">-</span><span
class="cmmi-8">T</span> </sup> <span
class="cmr-12">(transpose of </span><span
class="cmmi-12">B</span><sup><span
class="cmsy-8">-</span><span
class="cmr-8">1</span></sup><span
class="cmr-12">); if </span><span class="lstinline"></span><span
class="cmtt-12">trans</span> <span
class="cmr-12">= </span><span class="lstinline"></span><span
class="cmtt-12">&#8217;</span><span
class="cmtt-12">C</span><span
class="cmtt-12">&#8217;</span><span
class="cmtt-12">,</span><span
class="cmtt-12">&#8217;</span><span
class="cmtt-12">c</span><span
class="cmtt-12">&#8217;</span> <span
class="cmr-12">then</span>
<span
class="cmmi-12">op</span><span
class="cmr-12">(</span><span
class="cmmi-12">B</span><sup><span
class="cmsy-8">-</span><span
class="cmr-8">1</span></sup><span
class="cmr-12">) = </span><span
class="cmmi-12">B</span><sup><span
class="cmsy-8">-</span><span
class="cmmi-8">C</span></sup> <span
class="cmr-12">(conjugate transpose of </span><span
class="cmmi-12">B</span><sup><span
class="cmsy-8">-</span><span
class="cmr-8">1</span></sup><span
class="cmr-12">).</span> </td>
</tr><tr
style="vertical-align:baseline;" id="TBL-13-11-"><td style="white-space:normal; text-align:left;" id="TBL-13-11-1"
class="td11"><!--l. 750--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-12">work</span> </td><td style="white-space:normal; text-align:left;" id="TBL-13-11-2"
class="td11"><!--l. 750--><p class="noindent" ><span
class="cmti-12">type</span><span class="lstinline"></span><span
class="cmtt-12">(</span><span
class="cmti-12">kind</span><span
class="cmti-12">_parameter</span><span class="lstinline"></span><span
class="cmtt-12">),</span><span
class="cmtt-12">&#x00A0;</span><span
class="cmtt-12">dimension</span><span
class="cmtt-12">(:),</span><span
class="cmtt-12">&#x00A0;</span><span
class="cmtt-12">optional</span><span
class="cmtt-12">,</span><span
class="cmtt-12">&#x00A0;</span><span
class="cmtt-12">target</span><span
class="cmr-12">.</span> </td>
</tr><tr
style="vertical-align:baseline;" id="TBL-13-12-"><td style="white-space:normal; text-align:left;" id="TBL-13-12-1"
class="td11"><!--l. 751--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-13-12-2"
class="td11"><!--l. 751--><p class="noindent" ><span
class="cmr-12">Workspace. Its size should be at least </span><span class="lstinline"></span><span
class="cmtt-12">4</span><span
class="cmtt-12">&#x00A0;</span><span
class="cmtt-12">*</span><span
class="cmtt-12">&#x00A0;</span><span
class="cmtt-12">psb_cd_get_local_</span>
<span class="lstinline"></span><span
class="cmtt-12">cols</span><span
class="cmtt-12">(</span><span
class="cmtt-12">desc_a</span><span
class="cmtt-12">)</span> <span
class="cmr-12">(see the PSBLAS User&#8217;s Guide). Note that </span><span
class="cmti-12">type </span><span
class="cmr-12">and</span>
<span
class="cmti-12">kind</span><span
class="cmti-12">_parameter </span><span
class="cmr-12">must be chosen according to the </span><span class="lstinline"></span><span
class="cmtt-12">real</span><span
class="cmr-12">/</span><span class="lstinline"></span><span
class="cmtt-12">complex</span><span
class="cmr-12">,</span>
<span
class="cmr-12">single/double precision version of AMG4PSBLAS under use.</span> </td>
</tr><tr
style="vertical-align:baseline;" id="TBL-13-13-"><td style="white-space:normal; text-align:left;" id="TBL-13-13-1"
class="td11"> </td> </tr></table></div>
<!--l. 760--><div class="crosslinks"><p class="noindent"><span
class="cmr-12">[</span><a
href="userhtmlsu13.html" ><span
class="cmr-12">next</span></a><span
class="cmr-12">] [</span><a
href="userhtmlsu11.html" ><span
class="cmr-12">prev</span></a><span
class="cmr-12">] [</span><a
href="userhtmlsu11.html#tailuserhtmlsu11.html" ><span
class="cmr-12">prev-tail</span></a><span
class="cmr-12">] [</span><a
href="userhtmlsu12.html" ><span
class="cmr-12">front</span></a><span
class="cmr-12">] [</span><a
href="userhtmlse5.html#userhtmlsu12.html" ><span
class="cmr-12">up</span></a><span
class="cmr-12">] </span></p></div>
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id="tailuserhtmlsu12.html"></a>
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