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<head><title>Method apply</title>
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<!--l. 798--><div class="crosslinks"><p class="noindent"><span
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class="cmr-12">[</span><a
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href="userhtmlsu14.html" ><span
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class="cmr-12">next</span></a><span
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class="cmr-12">] [</span><a
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class="cmr-12">prev</span></a><span
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class="cmr-12">] [</span><a
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class="cmr-12">prev-tail</span></a><span
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class="cmr-12">] [</span><a
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class="cmr-12">tail</span></a><span
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class="cmr-12">] [</span><a
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class="cmr-12">up</span></a><span
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class="cmr-12">] </span></p></div>
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<h4 class="subsectionHead"><span class="titlemark"><span
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class="cmr-12">5.6 </span></span> <a
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id="x23-220005.6"></a><span
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class="cmr-12">Method apply</span></h4>
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<div class="center"
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>
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<!--l. 800--><p class="noindent" >
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<!--l. 801--><p class="noindent" ><span class="lstinline"></span><span
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class="cmtt-12">call</span><span
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class="cmtt-12"> </span><span
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class="cmtt-12">p</span><span
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class="cmtt-12">%</span><span
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class="cmtt-12">apply</span><span
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class="cmtt-12">(</span><span
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class="cmtt-12">x</span><span
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class="cmtt-12">,</span><span
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class="cmtt-12">y</span><span
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class="cmtt-12">,</span><span
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class="cmtt-12">desc_a</span><span
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class="cmtt-12">,</span><span
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class="cmtt-12">info</span><span
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class="cmtt-12"> </span><span
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class="cmtt-12">[,</span><span
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class="cmtt-12">trans</span><span
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class="cmtt-12">,</span><span
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class="cmtt-12">work</span><span
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class="cmtt-12">])</span><br />
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</div>
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<!--l. 804--><p class="noindent" ><span
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class="cmr-12">This method computes </span><span
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class="cmmi-12">y </span><span
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class="cmr-12">= </span><span
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class="cmmi-12">op</span><span
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class="cmr-12">(</span><span
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class="cmmi-12">B</span><sup><span
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class="cmsy-8">-</span><span
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class="cmr-8">1</span></sup><span
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class="cmr-12">) </span><span
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class="cmmi-12">x</span><span
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class="cmr-12">, where </span><span
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class="cmmi-12">B </span><span
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class="cmr-12">is a previously built preconditioner,</span>
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<span
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class="cmr-12">stored into </span><span class="lstinline"></span><span
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class="cmtt-12">p</span><span
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class="cmr-12">, and </span><span
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class="cmmi-12">op </span><span
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class="cmr-12">denotes the preconditioner itself or its transpose, according to the</span>
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<span
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class="cmr-12">value of </span><span class="lstinline"></span><span
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class="cmtt-12">trans</span><span
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class="cmr-12">. Note that, when AMG4PSBLAS is used with a Krylov solver from</span>
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<span
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class="cmr-12">PSBLAS, </span><span class="lstinline"></span><span
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class="cmtt-12">p</span><span
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class="cmtt-12">%</span><span
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class="cmtt-12">apply</span> <span
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class="cmr-12">is called within the PSBLAS method </span><span class="lstinline"></span><span
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class="cmtt-12">psb_krylov</span> <span
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class="cmr-12">and hence it is</span>
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<span
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class="cmr-12">completely transparent to the user.</span>
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<!--l. 813--><p class="noindent" ><span
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class="cmbx-12">Arguments</span>
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<div class="tabular"> <table id="TBL-14" class="tabular"
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cellspacing="0" cellpadding="0"
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><colgroup id="TBL-14-1g"><col
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id="TBL-14-1"><col
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id="TBL-14-2"></colgroup><tr
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style="vertical-align:baseline;" id="TBL-14-1-"><td style="white-space:normal; text-align:left;" id="TBL-14-1-1"
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class="td11"><!--l. 816--><p class="noindent" ><span class="lstinline"></span><span
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class="cmtt-12">x</span> </td><td style="white-space:normal; text-align:left;" id="TBL-14-1-2"
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class="td11"><!--l. 816--><p class="noindent" ><span
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class="cmti-12">type</span><span class="lstinline"></span><span
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class="cmtt-12">(</span><span
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class="cmtt-12">kind_parameter</span><span
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class="cmtt-12">)</span><span
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class="cmr-12">, dimension(:), intent(in)—.</span> </td>
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</tr><tr
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style="vertical-align:baseline;" id="TBL-14-2-"><td style="white-space:normal; text-align:left;" id="TBL-14-2-1"
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class="td11"><!--l. 817--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-14-2-2"
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class="td11"><!--l. 817--><p class="noindent" ><span
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class="cmr-12">The local part of the vector </span><span
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class="cmmi-12">x</span><span
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class="cmr-12">. Note that </span><span
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class="cmti-12">type </span><span
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class="cmr-12">and </span><span
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class="cmti-12">kind</span><span
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class="cmti-12">_parameter</span>
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<span
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class="cmr-12">must be chosen according to the </span><span class="lstinline"></span><span
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class="cmtt-12">real</span><span
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class="cmr-12">/</span><span class="lstinline"></span><span
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class="cmtt-12">complex</span><span
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class="cmr-12">, single/double</span>
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<span
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class="cmr-12">precision version of AMG4PSBLAS under use.</span> </td>
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</tr><tr
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style="vertical-align:baseline;" id="TBL-14-3-"><td style="white-space:normal; text-align:left;" id="TBL-14-3-1"
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class="td11"><!--l. 820--><p class="noindent" ><span class="lstinline"></span><span
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class="cmtt-12">y</span> </td><td style="white-space:normal; text-align:left;" id="TBL-14-3-2"
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class="td11"><!--l. 820--><p class="noindent" ><span
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class="cmti-12">type</span><span class="lstinline"></span><span
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class="cmtt-12">(</span><span
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class="cmtt-12">kind_parameter</span><span
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class="cmtt-12">)</span><span
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class="cmr-12">, dimension(:), intent(out)—.</span> </td>
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</tr><tr
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style="vertical-align:baseline;" id="TBL-14-4-"><td style="white-space:normal; text-align:left;" id="TBL-14-4-1"
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class="td11"><!--l. 821--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-14-4-2"
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class="td11"><!--l. 821--><p class="noindent" ><span
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class="cmr-12">The local part of the vector </span><span
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class="cmmi-12">y</span><span
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|
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class="cmr-12">. Note that </span><span
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class="cmti-12">type </span><span
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class="cmr-12">and </span><span
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class="cmti-12">kind</span><span
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class="cmti-12">_parameter</span>
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<span
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class="cmr-12">must be chosen according to the </span><span class="lstinline"></span><span
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class="cmtt-12">real</span><span
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class="cmr-12">/</span><span class="lstinline"></span><span
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|
class="cmtt-12">complex</span><span
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|
class="cmr-12">, single/double</span>
|
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<span
|
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|
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class="cmr-12">precision version of AMG4PSBLAS under use.</span> </td>
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</tr><tr
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style="vertical-align:baseline;" id="TBL-14-5-"><td style="white-space:normal; text-align:left;" id="TBL-14-5-1"
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class="td11"><!--l. 824--><p class="noindent" ><span class="lstinline"></span><span
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class="cmtt-12">desc_a</span></td><td style="white-space:normal; text-align:left;" id="TBL-14-5-2"
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class="td11"><!--l. 824--><p class="noindent" ><span class="lstinline"></span><span
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class="cmtt-12">type</span><span
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class="cmtt-12">(</span><span
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class="cmtt-12">psb_desc_type</span><span
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class="cmtt-12">),</span><span
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class="cmtt-12"> </span><span
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class="cmtt-12">intent</span><span
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class="cmtt-12">(</span><span
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class="cmtt-12">in</span><span
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class="cmtt-12">)</span><span
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class="cmr-12">.</span> </td>
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</tr><tr
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style="vertical-align:baseline;" id="TBL-14-6-"><td style="white-space:normal; text-align:left;" id="TBL-14-6-1"
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class="td11"><!--l. 825--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-14-6-2"
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class="td11"><!--l. 825--><p class="noindent" ><span
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class="cmr-12">The communication descriptor associated to the matrix to be</span>
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<span
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class="cmr-12">preconditioned.</span> </td>
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</tr><tr
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style="vertical-align:baseline;" id="TBL-14-7-"><td style="white-space:normal; text-align:left;" id="TBL-14-7-1"
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class="td11"><!--l. 827--><p class="noindent" ><span class="lstinline"></span><span
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class="cmtt-12">info</span> </td><td style="white-space:normal; text-align:left;" id="TBL-14-7-2"
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class="td11"><!--l. 827--><p class="noindent" ><span class="lstinline"></span><span
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class="cmtt-12">integer</span><span
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class="cmtt-12">,</span><span
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class="cmtt-12"> </span><span
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class="cmtt-12">intent</span><span
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class="cmtt-12">(</span><span
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class="cmtt-12">out</span><span
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class="cmtt-12">)</span><span
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class="cmr-12">.</span> </td>
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</tr><tr
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style="vertical-align:baseline;" id="TBL-14-8-"><td style="white-space:normal; text-align:left;" id="TBL-14-8-1"
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class="td11"><!--l. 828--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-14-8-2"
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class="td11"><!--l. 828--><p class="noindent" ><span
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class="cmr-12">Error code. If no error, 0 is returned. See Section</span><span
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class="cmr-12"> </span><a
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href="userhtmlse7.html#x28-320007"><span
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class="cmr-12">7</span><!--tex4ht:ref: sec:errors --></a> <span
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class="cmr-12">for details.</span> </td>
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</tr><tr
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style="vertical-align:baseline;" id="TBL-14-9-"><td style="white-space:normal; text-align:left;" id="TBL-14-9-1"
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class="td11"><!--l. 829--><p class="noindent" ><span class="lstinline"></span><span
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class="cmtt-12">trans</span> </td><td style="white-space:normal; text-align:left;" id="TBL-14-9-2"
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class="td11"><!--l. 829--><p class="noindent" ><span class="lstinline"></span><span
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class="cmtt-12">character</span><span
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|
class="cmtt-12">(</span><span
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class="cmtt-12">len</span><span
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class="cmtt-12">=1),</span><span
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class="cmtt-12"> </span><span
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class="cmtt-12">optional</span><span
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class="cmtt-12">,</span><span
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class="cmtt-12"> </span><span
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class="cmtt-12">intent</span><span
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class="cmtt-12">(</span><span
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class="cmtt-12">in</span><span
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class="cmtt-12">).</span> </td>
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</tr><tr
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style="vertical-align:baseline;" id="TBL-14-10-"><td style="white-space:normal; text-align:left;" id="TBL-14-10-1"
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class="td11"><!--l. 830--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-14-10-2"
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class="td11"><!--l. 830--><p class="noindent" ><span
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class="cmr-12">If </span><span class="lstinline"></span><span
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class="cmtt-12">trans</span> <span
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class="cmr-12">= </span><span class="lstinline"></span><span
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class="cmtt-12">’</span><span
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class="cmtt-12">N</span><span
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class="cmtt-12">’</span><span
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class="cmtt-12">,</span><span
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class="cmtt-12">’</span><span
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class="cmtt-12">n</span><span
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class="cmtt-12">’</span> <span
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class="cmr-12">then </span><span
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class="cmmi-12">op</span><span
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class="cmr-12">(</span><span
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class="cmmi-12">B</span><sup><span
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class="cmsy-8">-</span><span
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class="cmr-8">1</span></sup><span
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class="cmr-12">) = </span><span
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class="cmmi-12">B</span><sup><span
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class="cmsy-8">-</span><span
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class="cmr-8">1</span></sup><span
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class="cmr-12">; if </span><span class="lstinline"></span><span
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class="cmtt-12">trans</span> <span
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class="cmr-12">= </span><span class="lstinline"></span><span
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class="cmtt-12">’</span><span
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class="cmtt-12">T</span><span
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class="cmtt-12">’</span><span
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class="cmtt-12">,</span><span
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class="cmtt-12">’</span><span
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class="cmtt-12">t</span><span
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class="cmtt-12">’</span>
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<span
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class="cmr-12">then </span><span
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class="cmmi-12">op</span><span
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class="cmr-12">(</span><span
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class="cmmi-12">B</span><sup><span
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class="cmsy-8">-</span><span
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class="cmr-8">1</span></sup><span
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class="cmr-12">) = </span><span
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class="cmmi-12">B</span><sup><span
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class="cmsy-8">-</span><span
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class="cmmi-8">T</span> </sup> <span
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class="cmr-12">(transpose of </span><span
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class="cmmi-12">B</span><sup><span
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class="cmsy-8">-</span><span
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class="cmr-8">1</span></sup><span
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class="cmr-12">); if </span><span class="lstinline"></span><span
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class="cmtt-12">trans</span> <span
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class="cmr-12">= </span><span class="lstinline"></span><span
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class="cmtt-12">’</span><span
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class="cmtt-12">C</span><span
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class="cmtt-12">’</span><span
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class="cmtt-12">,</span><span
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class="cmtt-12">’</span><span
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class="cmtt-12">c</span><span
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class="cmtt-12">’</span> <span
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class="cmr-12">then</span>
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<span
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class="cmmi-12">op</span><span
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class="cmr-12">(</span><span
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class="cmmi-12">B</span><sup><span
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class="cmsy-8">-</span><span
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class="cmr-8">1</span></sup><span
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class="cmr-12">) = </span><span
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class="cmmi-12">B</span><sup><span
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class="cmsy-8">-</span><span
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class="cmmi-8">C</span></sup> <span
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class="cmr-12">(conjugate transpose of </span><span
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class="cmmi-12">B</span><sup><span
|
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class="cmsy-8">-</span><span
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class="cmr-8">1</span></sup><span
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class="cmr-12">).</span> </td>
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</tr><tr
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style="vertical-align:baseline;" id="TBL-14-11-"><td style="white-space:normal; text-align:left;" id="TBL-14-11-1"
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class="td11"><!--l. 834--><p class="noindent" ><span class="lstinline"></span><span
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class="cmtt-12">work</span> </td><td style="white-space:normal; text-align:left;" id="TBL-14-11-2"
|
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class="td11"><!--l. 834--><p class="noindent" ><span
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class="cmti-12">type</span><span class="lstinline"></span><span
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class="cmtt-12">(</span><span
|
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|
class="cmtt-12">kind_parameter</span><span
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class="cmtt-12">)</span><span
|
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|
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class="cmr-12">, dimension(:), optional, target—.</span> </td>
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</tr><tr
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|
style="vertical-align:baseline;" id="TBL-14-12-"><td style="white-space:normal; text-align:left;" id="TBL-14-12-1"
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class="td11"><!--l. 835--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-14-12-2"
|
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class="td11"><!--l. 835--><p class="noindent" ><span
|
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class="cmr-12">Workspace. Its size should be at least </span><span class="lstinline"></span><span
|
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|
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class="cmtt-12">4</span><span
|
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class="cmtt-12"> </span><span
|
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class="cmtt-12">*</span><span
|
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class="cmtt-12"> </span><span
|
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|
class="cmtt-12">psb_cd_get_local_</span>
|
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|
|
<span class="lstinline"></span><span
|
|
|
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|
class="cmtt-12">cols</span><span
|
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|
class="cmtt-12">(</span><span
|
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class="cmtt-12">desc_a</span><span
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|
class="cmtt-12">)</span> <span
|
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|
|
|
class="cmr-12">(see the PSBLAS User’s Guide). Note that </span><span
|
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|
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|
class="cmti-12">type </span><span
|
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|
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class="cmr-12">and</span>
|
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|
<span
|
|
|
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|
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
|
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|
|
|
class="cmtt-12">real</span><span
|
|
|
|
|
class="cmr-12">/</span><span class="lstinline"></span><span
|
|
|
|
|
class="cmtt-12">complex</span><span
|
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|
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|
class="cmr-12">,</span>
|
|
|
|
|
<span
|
|
|
|
|
class="cmr-12">single/double precision version of AMG4PSBLAS under use.</span> </td>
|
|
|
|
|
</tr><tr
|
|
|
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|
style="vertical-align:baseline;" id="TBL-14-13-"><td style="white-space:normal; text-align:left;" id="TBL-14-13-1"
|
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class="td11"> </td> </tr></table></div>
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<!--l. 844--><div class="crosslinks"><p class="noindent"><span
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class="cmr-12">[</span><a
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href="userhtmlsu14.html" ><span
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class="cmr-12">prev-tail</span></a><span
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class="cmr-12">] [</span><a
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class="cmr-12">front</span></a><span
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class="cmr-12">] [</span><a
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