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<head><title>Getting Started</title>
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<!--l. 1--><div class="crosslinks"><p class="noindent"><span
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class="cmr-12">[</span><a
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class="cmr-12">next</span></a><span
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class="cmr-12">prev</span></a><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">tail</span></a><span
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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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<h3 class="sectionHead"><span class="titlemark"><span
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class="cmr-12">4 </span></span> <a
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id="x13-120004"></a><span
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class="cmr-12">Getting Started</span></h3>
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<!--l. 5--><p class="noindent" ><span
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class="cmr-12">We describe the basics for building and applying AMG4PSBLAS one-level and</span>
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<span
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class="cmr-12">multilevel (i.e., AMG) preconditioners with the Krylov solvers included in PSBLAS</span>
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<span class="cite"><span
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class="cmr-12">[</span><a
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href="userhtmlli4.html#XPSBLASGUIDE"><span
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class="cmr-12">16</span></a><span
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class="cmr-12">]</span></span><span
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class="cmr-12">. The following steps are required:</span>
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<ol class="enumerate1" >
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<li
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class="enumerate" id="x13-12002x1"><span
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class="cmti-12">Declare the preconditioner data structure</span><span
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class="cmr-12">. It is a derived data type,</span>
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<span class="obeylines-h"><span class="verb"><span
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class="cmtt-12">amg_</span></span></span><span
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class="cmti-12">x</span><span class="obeylines-h"><span class="verb"><span
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class="cmtt-12">prec_</span></span></span> <span class="obeylines-h"><span class="verb"><span
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class="cmtt-12">type</span></span></span><span
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class="cmr-12">, where </span><span
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class="cmti-12">x </span><span
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class="cmr-12">may be </span><span class="obeylines-h"><span class="verb"><span
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class="cmtt-12">s</span></span></span><span
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class="cmr-12">, </span><span class="obeylines-h"><span class="verb"><span
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class="cmtt-12">d</span></span></span><span
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class="cmr-12">, </span><span class="obeylines-h"><span class="verb"><span
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class="cmtt-12">c</span></span></span> <span
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class="cmr-12">or </span><span class="obeylines-h"><span class="verb"><span
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class="cmtt-12">z</span></span></span><span
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class="cmr-12">, according to the basic data</span>
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<span
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class="cmr-12">type of the sparse matrix (</span><span class="obeylines-h"><span class="verb"><span
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class="cmtt-12">s</span></span></span> <span
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class="cmr-12">= real single precision; </span><span class="obeylines-h"><span class="verb"><span
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class="cmtt-12">d</span></span></span> <span
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class="cmr-12">= real double precision;</span>
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<span class="obeylines-h"><span class="verb"><span
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class="cmtt-12">c</span></span></span> <span
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class="cmr-12">= complex single precision; </span><span class="obeylines-h"><span class="verb"><span
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class="cmtt-12">z</span></span></span> <span
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class="cmr-12">= complex double precision). This data</span>
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<span
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class="cmr-12">structure is accessed by the user only through the AMG4PSBLAS routines,</span>
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<span
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class="cmr-12">following an object-oriented approach.</span>
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</li>
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<li
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class="enumerate" id="x13-12004x2"><span
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class="cmti-12">Allocate and initialize the preconditioner data structure, according to a</span>
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<span
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class="cmti-12">preconditioner type chosen by the user</span><span
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class="cmr-12">. This is performed by the routine</span>
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<span class="lstinline"></span><span
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class="cmtt-12">init</span><span
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class="cmr-12">, which also sets defaults for each preconditioner type selected by</span>
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<span
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class="cmr-12">the user. The preconditioner types and the defaults associated with them</span>
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<span
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class="cmr-12">are given in Table</span><span
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class="cmr-12"> </span><a
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href="#x13-12015r1"><span
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class="cmr-12">1</span><!--tex4ht:ref: tab:precinit --></a><span
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class="cmr-12">, where the strings used by </span><span class="lstinline"></span><span
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class="cmtt-12">init</span> <span
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class="cmr-12">to identify the</span>
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<span
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class="cmr-12">preconditioner types are also given. Note that these strings are valid also if</span>
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<span
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class="cmr-12">uppercase letters are substituted by corresponding lowercase ones.</span>
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</li>
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<li
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class="enumerate" id="x13-12006x3"><span
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class="cmti-12">Modify the selected preconditioner type, by properly setting preconditioner</span>
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<span
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class="cmti-12">parameters. </span><span
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class="cmr-12">This is performed by the routine </span><span class="lstinline"></span><span
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class="cmtt-12">set</span><span
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class="cmr-12">. This routine must be</span>
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<span
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class="cmr-12">called only if the user wants to modify the default values of the parameters</span>
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<span
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class="cmr-12">associated with the selected preconditioner type, to obtain a variant of that</span>
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<span
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class="cmr-12">preconditioner. Examples of use of </span><span class="lstinline"></span><span
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class="cmtt-12">set</span> <span
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class="cmr-12">are given in Section</span><span
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class="cmr-12"> </span><a
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href="userhtmlsu6.html#x14-130004.1"><span
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class="cmr-12">4.1</span><!--tex4ht:ref: sec:examples --></a><span
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class="cmr-12">; a complete</span>
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<span
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class="cmr-12">list of all the preconditioner parameters and their allowed and default values</span>
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<span
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class="cmr-12">is provided in Section</span><span
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class="cmr-12"> </span><a
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href="userhtmlse5.html#x15-140005"><span
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class="cmr-12">5</span><!--tex4ht:ref: sec:userinterface --></a><span
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class="cmr-12">, Tables</span><span
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class="cmr-12"> </span><a
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href="userhtmlsu8.html#x17-16009r2"><span
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class="cmr-12">2</span><!--tex4ht:ref: tab:p_cycle --></a><span
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class="cmr-12">-</span><a
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href="userhtmlsu8.html#x17-16015r8"><span
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class="cmr-12">8</span><!--tex4ht:ref: tab:p_smoother_1 --></a><span
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class="cmr-12">.</span>
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</li>
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<li
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class="enumerate" id="x13-12008x4"><span
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class="cmti-12">Build the preconditioner for a given matrix</span><span
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class="cmr-12">. If the selected preconditioner is</span>
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<span
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class="cmr-12">multilevel, then two steps must be performed, as specified next.</span>
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<ol class="enumerate2" >
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<li
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class="enumerate" id="x13-12009x0"><span
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class="cmti-12">Build the AMG hierarchy for a given matrix. </span><span
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class="cmr-12">This is performed by the</span>
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<span
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class="cmr-12">routine </span><span class="lstinline"></span><span
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class="cmtt-12">hierarchy_build</span><span
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class="cmr-12">.</span>
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</li>
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<li
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class="enumerate" id="x13-12010x0"><span
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class="cmti-12">Build the preconditioner for a given matrix. </span><span
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class="cmr-12">This is performed by the</span>
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<span
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class="cmr-12">routine </span><span class="lstinline"></span><span
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class="cmtt-12">smoothers_build</span><span
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class="cmr-12">.</span></li></ol>
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<!--l. 41--><p class="noindent" ><span
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class="cmr-12">If the selected preconditioner is one-level, it is built in a single step, performed by</span>
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<span
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class="cmr-12">the routine </span><span class="lstinline"></span><span
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class="cmtt-12">bld</span><span
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class="cmr-12">.</span>
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</li>
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<li
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class="enumerate" id="x13-12012x5"><span
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class="cmti-12">Apply the preconditioner at each iteration of a Krylov solver. </span><span
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class="cmr-12">This is performed by</span>
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<span
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class="cmr-12">the method </span><span class="lstinline"></span><span
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class="cmtt-12">apply</span><span
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class="cmr-12">. When using the PSBLAS Krylov solvers, this step is</span>
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<span
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class="cmr-12">completely transparent to the user, since </span><span class="lstinline"></span><span
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class="cmtt-12">apply</span> <span
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class="cmr-12">is called by the PSBLAS routine</span>
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<span
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class="cmr-12">implementing the Krylov solver (</span><span class="lstinline"></span><span
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class="cmtt-12">psb_krylov</span><span
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class="cmr-12">).</span>
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</li>
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<li
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class="enumerate" id="x13-12014x6"><span
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class="cmti-12">Free the preconditioner data structure</span><span
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class="cmr-12">. This is performed by the routine </span><span class="lstinline"></span><span
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class="cmtt-12">free</span><span
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class="cmr-12">.</span>
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<span
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class="cmr-12">This step is complementary to step 1 and should be performed when the</span>
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<span
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class="cmr-12">preconditioner is no more used.</span></li></ol>
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<!--l. 52--><p class="indent" > <span
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class="cmr-12">All the previous routines are available as methods of the preconditioner object. A</span>
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<span
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class="cmr-12">detailed description of them is given in Section</span><span
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class="cmr-12"> </span><a
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href="userhtmlse5.html#x15-140005"><span
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class="cmr-12">5</span><!--tex4ht:ref: sec:userinterface --></a><span
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class="cmr-12">. Examples showing the basic use of</span>
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<span
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class="cmr-12">AMG4PSBLAS are reported in Section</span><span
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class="cmr-12"> </span><a
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href="userhtmlsu6.html#x14-130004.1"><span
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class="cmr-12">4.1</span><!--tex4ht:ref: sec:examples --></a><span
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class="cmr-12">.</span>
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<div class="table">
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<!--l. 56--><p class="indent" > <a
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id="x13-12015r1"></a><hr class="float"><div class="float"
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>
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<div class="center"
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>
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<!--l. 57--><p class="noindent" >
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<div class="tabular"> <table id="TBL-1" class="tabular"
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cellspacing="0" cellpadding="0"
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><colgroup id="TBL-1-1g"><col
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id="TBL-1-1"></colgroup><colgroup id="TBL-1-2g"><col
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id="TBL-1-2"></colgroup><colgroup id="TBL-1-3g"><col
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id="TBL-1-3"></colgroup><tr
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class="hline"><td><hr></td><td><hr></td><td><hr></td></tr><tr
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style="vertical-align:baseline;" id="TBL-1-1-"><td style="white-space:nowrap; text-align:left;" id="TBL-1-1-1"
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class="td11"><span
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class="cmcsc-10x-x-109"><span
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class="small-caps">t</span><span
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class="small-caps">y</span><span
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class="small-caps">p</span><span
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class="small-caps">e</span> </span></td><td style="white-space:wrap; text-align:left;" id="TBL-1-1-2"
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class="td11"><!--l. 61--><p class="noindent" ><span
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class="cmcsc-10x-x-109"><span
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class="small-caps">s</span><span
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class="small-caps">t</span><span
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class="small-caps">r</span><span
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class="small-caps">i</span><span
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class="small-caps">n</span><span
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class="small-caps">g</span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-1-1-3"
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class="td11"><!--l. 61--><p class="noindent" ><span
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class="cmcsc-10x-x-109"><span
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class="small-caps">d</span><span
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class="small-caps">e</span><span
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class="small-caps">f</span><span
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class="small-caps">a</span><span
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class="small-caps">u</span><span
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class="small-caps">l</span><span
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class="small-caps">t</span> <span
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class="small-caps">p</span><span
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class="small-caps">r</span><span
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class="small-caps">e</span><span
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class="small-caps">c</span><span
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class="small-caps">o</span><span
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class="small-caps">n</span><span
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class="small-caps">d</span><span
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class="small-caps">i</span><span
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class="small-caps">t</span><span
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class="small-caps">i</span><span
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class="small-caps">o</span><span
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class="small-caps">n</span><span
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class="small-caps">e</span><span
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class="small-caps">r</span></span> </td></tr><tr
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class="hline"><td><hr></td><td><hr></td><td><hr></td></tr><tr
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style="vertical-align:baseline;" id="TBL-1-2-"><td style="white-space:nowrap; text-align:left;" id="TBL-1-2-1"
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class="td11">No preconditioner </td><td style="white-space:wrap; text-align:left;" id="TBL-1-2-2"
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class="td11"><!--l. 62--><p class="noindent" ><span class="lstinline"></span><span
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class="cmtt-10x-x-109">’</span><span
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class="cmtt-10x-x-109">NONE</span><span
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class="cmtt-10x-x-109">’</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-1-2-3"
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class="td11"><!--l. 62--><p class="noindent" >Considered to use the PSBLAS Krylov
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solvers with no preconditioner. </td>
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</tr><tr
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class="hline"><td><hr></td><td><hr></td><td><hr></td></tr><tr
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style="vertical-align:baseline;" id="TBL-1-3-"><td style="white-space:nowrap; text-align:left;" id="TBL-1-3-1"
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class="td11">Diagonal </td><td style="white-space:wrap; text-align:left;" id="TBL-1-3-2"
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class="td11"><!--l. 64--><p class="noindent" ><span class="lstinline"></span><span
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class="cmtt-10x-x-109">’</span><span
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class="cmtt-10x-x-109">DIAG</span><span
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class="cmtt-10x-x-109">’</span>,
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<span class="lstinline"></span><span
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class="cmtt-10x-x-109">’</span><span
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class="cmtt-10x-x-109">JACOBI</span><span
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class="cmtt-10x-x-109">’</span>,
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<span class="lstinline"></span><span
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class="cmtt-10x-x-109">’</span><span
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class="cmtt-10x-x-109">L1</span><span
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class="cmtt-10x-x-109">-</span><span
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class="cmtt-10x-x-109">JACOBI</span><span
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class="cmtt-10x-x-109">’</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-1-3-3"
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class="td11"><!--l. 64--><p class="noindent" >Diagonal preconditioner. For any zero
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|
|
diagonal entry of the matrix to be
|
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|
preconditioned, the corresponding entry
|
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|
of the preconditioner is set to 1. </td>
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</tr><tr
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class="hline"><td><hr></td><td><hr></td><td><hr></td></tr><tr
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style="vertical-align:baseline;" id="TBL-1-4-"><td style="white-space:nowrap; text-align:left;" id="TBL-1-4-1"
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class="td11">Gauss-Seidel </td><td style="white-space:wrap; text-align:left;" id="TBL-1-4-2"
|
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|
class="td11"><!--l. 67--><p class="noindent" ><span class="lstinline"></span><span
|
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|
class="cmtt-10x-x-109">’</span><span
|
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|
class="cmtt-10x-x-109">GS</span><span
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|
class="cmtt-10x-x-109">’</span>,
|
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|
<span class="lstinline"></span><span
|
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|
class="cmtt-10x-x-109">’</span><span
|
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|
|
|
class="cmtt-10x-x-109">L1</span><span
|
|
|
|
|
class="cmtt-10x-x-109">-</span><span
|
|
|
|
|
class="cmtt-10x-x-109">GS</span><span
|
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|
|
|
class="cmtt-10x-x-109">’</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-1-4-3"
|
|
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|
class="td11"><!--l. 67--><p class="noindent" >Hybrid Gauss-Seidel (forward), that is,
|
|
|
|
|
global block Jacobi with Gauss-Seidel as
|
|
|
|
|
local solver. </td>
|
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|
|
|
</tr><tr
|
|
|
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|
class="hline"><td><hr></td><td><hr></td><td><hr></td></tr><tr
|
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|
style="vertical-align:baseline;" id="TBL-1-5-"><td style="white-space:nowrap; text-align:left;" id="TBL-1-5-1"
|
|
|
|
|
class="td11">Symmetrized Gauss-Seidel</td><td style="white-space:wrap; text-align:left;" id="TBL-1-5-2"
|
|
|
|
|
class="td11"><!--l. 70--><p class="noindent" ><span class="lstinline"></span><span
|
|
|
|
|
class="cmtt-10x-x-109">’</span><span
|
|
|
|
|
class="cmtt-10x-x-109">FBGS</span><span
|
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|
|
class="cmtt-10x-x-109">’</span>,
|
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|
|
|
<span class="lstinline"></span><span
|
|
|
|
|
class="cmtt-10x-x-109">’</span><span
|
|
|
|
|
class="cmtt-10x-x-109">L1</span><span
|
|
|
|
|
class="cmtt-10x-x-109">-</span><span
|
|
|
|
|
class="cmtt-10x-x-109">FBGS</span><span
|
|
|
|
|
class="cmtt-10x-x-109">’</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-1-5-3"
|
|
|
|
|
class="td11"><!--l. 70--><p class="noindent" >Symmetrized hybrid Gauss-Seidel, that
|
|
|
|
|
is, forward Gauss-Seidel followed by
|
|
|
|
|
backward Gauss-Seidel. </td>
|
|
|
|
|
</tr><tr
|
|
|
|
|
class="hline"><td><hr></td><td><hr></td><td><hr></td></tr><tr
|
|
|
|
|
style="vertical-align:baseline;" id="TBL-1-6-"><td style="white-space:nowrap; text-align:left;" id="TBL-1-6-1"
|
|
|
|
|
class="td11">Block Jacobi </td><td style="white-space:wrap; text-align:left;" id="TBL-1-6-2"
|
|
|
|
|
class="td11"><!--l. 73--><p class="noindent" ><span class="lstinline"></span><span
|
|
|
|
|
class="cmtt-10x-x-109">’</span><span
|
|
|
|
|
class="cmtt-10x-x-109">BJAC</span><span
|
|
|
|
|
class="cmtt-10x-x-109">’</span>,
|
|
|
|
|
<span class="lstinline"></span><span
|
|
|
|
|
class="cmtt-10x-x-109">’</span><span
|
|
|
|
|
class="cmtt-10x-x-109">L1</span><span
|
|
|
|
|
class="cmtt-10x-x-109">-</span><span
|
|
|
|
|
class="cmtt-10x-x-109">BJAC</span><span
|
|
|
|
|
class="cmtt-10x-x-109">’</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-1-6-3"
|
|
|
|
|
class="td11"><!--l. 73--><p class="noindent" >Block-Jacobi with ILU(0) on the local
|
|
|
|
|
blocks. </td>
|
|
|
|
|
</tr><tr
|
|
|
|
|
class="hline"><td><hr></td><td><hr></td><td><hr></td></tr><tr
|
|
|
|
|
style="vertical-align:baseline;" id="TBL-1-7-"><td style="white-space:nowrap; text-align:left;" id="TBL-1-7-1"
|
|
|
|
|
class="td11">Additive Schwarz </td><td style="white-space:wrap; text-align:left;" id="TBL-1-7-2"
|
|
|
|
|
class="td11"><!--l. 74--><p class="noindent" ><span class="lstinline"></span><span
|
|
|
|
|
class="cmtt-10x-x-109">’</span><span
|
|
|
|
|
class="cmtt-10x-x-109">AS</span><span
|
|
|
|
|
class="cmtt-10x-x-109">’</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-1-7-3"
|
|
|
|
|
class="td11"><!--l. 74--><p class="noindent" >Additive Schwarz (AS), with overlap 1
|
|
|
|
|
and ILU(0) on the local blocks. </td>
|
|
|
|
|
</tr><tr
|
|
|
|
|
class="hline"><td><hr></td><td><hr></td><td><hr></td></tr><tr
|
|
|
|
|
style="vertical-align:baseline;" id="TBL-1-8-"><td style="white-space:nowrap; text-align:left;" id="TBL-1-8-1"
|
|
|
|
|
class="td11">Multilevel </td><td style="white-space:wrap; text-align:left;" id="TBL-1-8-2"
|
|
|
|
|
class="td11"><!--l. 76--><p class="noindent" ><span class="lstinline"></span><span
|
|
|
|
|
class="cmtt-10x-x-109">’</span><span
|
|
|
|
|
class="cmtt-10x-x-109">ML</span><span
|
|
|
|
|
class="cmtt-10x-x-109">’</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-1-8-3"
|
|
|
|
|
class="td11"><!--l. 76--><p class="noindent" >V-cycle with one hybrid
|
|
|
|
|
forward Gauss-Seidel (GS) sweep as
|
|
|
|
|
pre-smoother and one hybrid backward
|
|
|
|
|
GS sweep as post-smoother, decoupled
|
|
|
|
|
smoothed aggregation as coarsening
|
|
|
|
|
algorithm, and LU (plus triangular solve)
|
|
|
|
|
as coarsest-level solver. See the default
|
|
|
|
|
values in Tables <a
|
|
|
|
|
href="userhtmlsu8.html#x17-16009r2">2<!--tex4ht:ref: tab:p_cycle --></a>-<a
|
|
|
|
|
href="userhtmlsu8.html#x17-16015r8">8<!--tex4ht:ref: tab:p_smoother_1 --></a> for further details of
|
|
|
|
|
the preconditioner. </td>
|
|
|
|
|
</tr><tr
|
|
|
|
|
class="hline"><td><hr></td><td><hr></td><td><hr></td></tr><tr
|
|
|
|
|
style="vertical-align:baseline;" id="TBL-1-9-"><td style="white-space:nowrap; text-align:left;" id="TBL-1-9-1"
|
|
|
|
|
class="td11"> </td></tr></table></div>
|
|
|
|
|
<br /> <div class="caption"
|
|
|
|
|
><span class="id">Table 1: </span><span
|
|
|
|
|
class="content">Preconditioner types, corresponding strings and default choices. </span></div><!--tex4ht:label?: x13-12015r1 -->
|
|
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
</div><hr class="endfloat" />
|
|
|
|
|
</div>
|
|
|
|
|
<!--l. 91--><p class="indent" > <span
|
|
|
|
|
class="cmr-12">Note that the module </span><span class="lstinline"></span><span
|
|
|
|
|
class="cmtt-12">amg_prec_mod</span><span
|
|
|
|
|
class="cmr-12">, containing the definition of the preconditioner</span>
|
|
|
|
|
<span
|
|
|
|
|
class="cmr-12">data type and the interfaces to the routines of AMG4PSBLAS, must be used</span>
|
|
|
|
|
<span
|
|
|
|
|
class="cmr-12">in any program calling such routines. The modules </span><span class="lstinline"></span><span
|
|
|
|
|
class="cmtt-12">psb_base_mod</span><span
|
|
|
|
|
class="cmr-12">, for the</span>
|
|
|
|
|
<span
|
|
|
|
|
class="cmr-12">sparse matrix and communication descriptor data types, and </span><span class="lstinline"></span><span
|
|
|
|
|
class="cmtt-12">psb_krylov_mod</span><span
|
|
|
|
|
class="cmr-12">,</span>
|
|
|
|
|
<span
|
|
|
|
|
class="cmr-12">for interfacing with the Krylov solvers, must be also used (see Section</span><span
|
|
|
|
|
class="cmr-12"> </span><a
|
|
|
|
|
href="userhtmlsu6.html#x14-130004.1"><span
|
|
|
|
|
class="cmr-12">4.1</span><!--tex4ht:ref: sec:examples --></a><span
|
|
|
|
|
class="cmr-12">).</span>
|
|
|
|
|
<br
|
|
|
|
|
class="newline" />
|
|
|
|
|
<!--l. 98--><p class="indent" > <span
|
|
|
|
|
class="cmbx-12">Remark 1. </span><span
|
|
|
|
|
class="cmr-12">Coarsest-level solvers based on the LU factorization, such as those</span>
|
|
|
|
|
<span
|
|
|
|
|
class="cmr-12">implemented in UMFPACK, MUMPS, SuperLU, and SuperLU</span><span
|
|
|
|
|
class="cmr-12">_Dist, usually lead to</span>
|
|
|
|
|
<span
|
|
|
|
|
class="cmr-12">smaller numbers of preconditioned Krylov iterations than inexact solvers, when the</span>
|
|
|
|
|
<span
|
|
|
|
|
class="cmr-12">linear system comes from a standard discretization of basic scalar elliptic PDE</span>
|
|
|
|
|
<span
|
|
|
|
|
class="cmr-12">problems. However, this does not necessarily correspond to the shortest execution time</span>
|
|
|
|
|
<span
|
|
|
|
|
class="cmr-12">on parallel computers.</span>
|
|
|
|
|
<div class="subsectionTOCS">
|
|
|
|
|
<span
|
|
|
|
|
class="cmr-12"> </span><span class="subsectionToc" ><span
|
|
|
|
|
class="cmr-12">4.1 </span><a
|
|
|
|
|
href="userhtmlsu6.html#x14-130004.1"><span
|
|
|
|
|
class="cmr-12">Examples</span></a></span>
|
|
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
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|
|
|
<!--l. 1--><div class="crosslinks"><p class="noindent"><span
|
|
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|
class="cmr-12">[</span><a
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|
|
href="userhtmlse5.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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href="userhtmlse3.html" ><span
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|
class="cmr-12">prev</span></a><span
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class="cmr-12">] [</span><a
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href="userhtmlse3.html#tailuserhtmlse3.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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href="userhtmlse4.html" ><span
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class="cmr-12">front</span></a><span
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class="cmr-12">] [</span><a
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href="userhtml.html#userhtmlse4.html" ><span
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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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id="tailuserhtmlse4.html"></a>
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