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821 lines
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<!--l. 1--><div class="crosslinks"><p class="noindent">[<a
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href="userhtmlse10.html" >prev</a>] [<a
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href="userhtmlse10.html#tailuserhtmlse10.html" >prev-tail</a>] [<a
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href="userhtmlse8.html#tailuserhtmlse11.html">tail</a>] [<a
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href="userhtml.html# " >up</a>] </p></div>
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<h3 class="sectionHead"><span class="titlemark">11 </span> <a
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id="x17-14300011"></a>Iterative Methods</h3>
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<!--l. 4--><p class="noindent" >In this chapter we provide routines for preconditioners and iterative methods. The
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interfaces for iterative methods are available in the module <span class="obeylines-h"><span class="verb"><span
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class="cmtt-10">psb_linsolve_mod</span></span></span>.
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<h4 class="subsectionHead"><span class="titlemark">11.1 </span> <a
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id="x17-14400011.1"></a>psb_krylov — Krylov Methods Driver Routine</h4>
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<!--l. 17--><p class="noindent" >This subroutine is a driver that provides a general interface for all the Krylov-Subspace
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family methods implemented in PSBLAS version 2.
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<!--l. 20--><p class="indent" > The stopping criterion can take the following values:
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<dl class="description"><dt class="description">
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<!--l. 22--><p class="noindent" >
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<span
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class="pplb7t-">1</span> </dt><dd
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class="description">
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<!--l. 22--><p class="noindent" >normwise backward error in the infinity norm; the iteration is stopped
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when
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<div class="math-display" >
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<img
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src="userhtml30x.png" alt=" ------∥ri∥------
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err = (∥A ∥∥xi∥ + ∥b∥) < eps
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" class="math-display" ></div>
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<!--l. 24--><p class="nopar" >
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</dd><dt class="description">
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<!--l. 25--><p class="noindent" >
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<span
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class="pplb7t-">2</span> </dt><dd
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class="description">
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<!--l. 25--><p class="noindent" >Relative residual in the 2-norm; the iteration is stopped when
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<div class="math-display" >
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<img
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src="userhtml31x.png" alt=" ∥ri∥
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err = ∥b∥-2 < eps
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" class="math-display" ></div>
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<!--l. 27--><p class="nopar" >
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</dd><dt class="description">
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<!--l. 28--><p class="noindent" >
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<span
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class="pplb7t-">3</span> </dt><dd
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class="description">
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<!--l. 28--><p class="noindent" >Relative residual reduction in the 2-norm; the iteration is stopped when
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<div class="math-display" >
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<img
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src="userhtml32x.png" alt=" ∥ri∥
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err = ∥r0∥2 < eps
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" class="math-display" ></div>
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<!--l. 30--><p class="nopar" ></dd></dl>
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<!--l. 32--><p class="noindent" >The behaviour is controlled by the istop argument (see later). In the above formulae, <span
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class="zplmr7m-">x</span><sub><span
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class="zplmr7m-x-x-76">i</span></sub>
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is the tentative solution and <span
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class="zplmr7m-">r</span><sub><span
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class="zplmr7m-x-x-76">i</span></sub> <span
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class="zplmr7t-">= </span><span
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class="zplmr7m-">b</span><span
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class="zplmr7y-">-</span><span
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class="zplmr7m-">Ax</span><sub><span
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class="zplmr7m-x-x-76">i</span></sub> the corresponding residual at the <span
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class="zplmr7m-">i</span>-th
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iteration.
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<!--l. 37-->
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<pre class="lstlisting" id="listing-218"><span class="label"><a
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id="x17-144001r1"></a></span><span style="color:#000000"><span
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class="cmtt-10">call</span></span><span style="color:#000000"> </span><span style="color:#000000"><span
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class="cmtt-10">psb_krylov</span></span><span style="color:#000000"><span
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class="cmtt-10">(</span></span><span style="color:#000000"><span
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class="cmtt-10">method</span></span><span style="color:#000000"><span
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class="cmtt-10">,</span></span><span style="color:#000000"><span
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|
class="cmtt-10">a</span></span><span style="color:#000000"><span
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|
class="cmtt-10">,</span></span><span style="color:#000000"><span
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|
class="cmtt-10">prec</span></span><span style="color:#000000"><span
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|
class="cmtt-10">,</span></span><span style="color:#000000"><span
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|
class="cmtt-10">b</span></span><span style="color:#000000"><span
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|
class="cmtt-10">,</span></span><span style="color:#000000"><span
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|
class="cmtt-10">x</span></span><span style="color:#000000"><span
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class="cmtt-10">,</span></span><span style="color:#000000"><span
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|
class="cmtt-10">eps</span></span><span style="color:#000000"><span
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|
class="cmtt-10">,</span></span><span style="color:#000000"><span
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|
class="cmtt-10">desc_a</span></span><span style="color:#000000"><span
|
|
class="cmtt-10">,</span></span><span style="color:#000000"><span
|
|
class="cmtt-10">info</span></span><span style="color:#000000"><span
|
|
class="cmtt-10">,&</span></span>
|
|
<span class="label"><a
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|
id="x17-144002r2"></a></span><span
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class="cmtt-10"> </span><span
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class="cmtt-10"> </span><span
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class="cmtt-10"> </span><span
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class="cmtt-10"> </span><span style="color:#000000"><span
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class="cmtt-10">&</span></span><span style="color:#000000"> </span><span style="color:#000000"><span
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class="cmtt-10">itmax</span></span><span style="color:#000000"><span
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class="cmtt-10">,</span></span><span style="color:#000000"><span
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class="cmtt-10">iter</span></span><span style="color:#000000"><span
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class="cmtt-10">,</span></span><span style="color:#000000"><span
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class="cmtt-10">err</span></span><span style="color:#000000"><span
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class="cmtt-10">,</span></span><span style="color:#000000"><span
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class="cmtt-10">itrace</span></span><span style="color:#000000"><span
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class="cmtt-10">,</span></span><span style="color:#000000"><span
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class="cmtt-10">irst</span></span><span style="color:#000000"><span
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class="cmtt-10">,</span></span><span style="color:#000000"><span
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class="cmtt-10">istop</span></span><span style="color:#000000"><span
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class="cmtt-10">,</span></span><span style="color:#000000"><span
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class="cmtt-10">cond</span></span><span style="color:#000000"><span
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class="cmtt-10">)</span></span></pre>
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<!--l. 42--><p class="indent" >
|
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<dl class="description"><dt class="description">
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<!--l. 43--><p class="noindent" >
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<span
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class="pplb7t-">Type:</span> </dt><dd
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class="description">
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<!--l. 43--><p class="noindent" >Synchronous.
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</dd><dt class="description">
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<!--l. 44--><p class="noindent" >
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<span
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class="pplb7t-">On Entry</span> </dt><dd
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class="description">
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<!--l. 44--><p class="noindent" >
|
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</dd><dt class="description">
|
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<!--l. 45--><p class="noindent" >
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<span
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class="pplb7t-">method</span> </dt><dd
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class="description">
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|
<!--l. 45--><p class="noindent" >a string that defines the iterative method to be used. Supported values
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are:
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<dl class="description"><dt class="description">
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|
<!--l. 48--><p class="noindent" >
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<span
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class="pplb7t-">CG:</span> </dt><dd
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class="description">
|
|
<!--l. 48--><p class="noindent" >the Conjugate Gradient method;
|
|
</dd><dt class="description">
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<!--l. 49--><p class="noindent" >
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<span
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class="pplb7t-">CGS:</span> </dt><dd
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class="description">
|
|
<!--l. 49--><p class="noindent" >the Conjugate Gradient Stabilized method;
|
|
</dd><dt class="description">
|
|
<!--l. 51--><p class="noindent" >
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<span
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class="pplb7t-">GCR:</span> </dt><dd
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class="description">
|
|
<!--l. 51--><p class="noindent" >the Generalized Conjugate Residual method;
|
|
</dd><dt class="description">
|
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<!--l. 52--><p class="noindent" >
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<span
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class="pplb7t-">FCG:</span> </dt><dd
|
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class="description">
|
|
<!--l. 52--><p class="noindent" >the Flexible Conjugate Gradient method<span class="footnote-mark"><a
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href="userhtml18.html#fn5x0"><sup class="textsuperscript">5</sup></a></span><a
|
|
id="x17-144003f5"></a> ;
|
|
</dd><dt class="description">
|
|
<!--l. 55--><p class="noindent" >
|
|
<span
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|
class="pplb7t-">BICG:</span> </dt><dd
|
|
class="description">
|
|
<!--l. 55--><p class="noindent" >the Bi-Conjugate Gradient method;
|
|
</dd><dt class="description">
|
|
<!--l. 56--><p class="noindent" >
|
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<span
|
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class="pplb7t-">BICGSTAB:</span> </dt><dd
|
|
class="description">
|
|
<!--l. 56--><p class="noindent" >the Bi-Conjugate Gradient Stabilized method;
|
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|
|
|
|
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</dd><dt class="description">
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<!--l. 57--><p class="noindent" >
|
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<span
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class="pplb7t-">BICGSTABL:</span> </dt><dd
|
|
class="description">
|
|
<!--l. 57--><p class="noindent" >the Bi-Conjugate Gradient Stabilized method with restarting;
|
|
</dd><dt class="description">
|
|
<!--l. 58--><p class="noindent" >
|
|
<span
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class="pplb7t-">RGMRES:</span> </dt><dd
|
|
class="description">
|
|
<!--l. 58--><p class="noindent" >the Generalized Minimal Residual method with restarting.</dd></dl>
|
|
</dd><dt class="description">
|
|
<!--l. 60--><p class="noindent" >
|
|
<span
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|
class="pplb7t-">a</span> </dt><dd
|
|
class="description">
|
|
<!--l. 60--><p class="noindent" >the local portion of global sparse matrix <span
|
|
class="zplmr7m-">A</span>. <br
|
|
class="newline" />Scope: <span
|
|
class="pplb7t-">local </span><br
|
|
class="newline" />Type: <span
|
|
class="pplb7t-">required</span><br
|
|
class="newline" />Intent: <span
|
|
class="pplb7t-">in</span>.<br
|
|
class="newline" />Specified as: a structured data of type <a
|
|
href="userhtmlse3.html#spdata"><span
|
|
class="cmtt-10">psb</span><span
|
|
class="cmtt-10">_Tspmat</span><span
|
|
class="cmtt-10">_type</span></a>.
|
|
</dd><dt class="description">
|
|
<!--l. 66--><p class="noindent" >
|
|
<span
|
|
class="pplb7t-">prec</span> </dt><dd
|
|
class="description">
|
|
<!--l. 66--><p class="noindent" >The data structure containing the preconditioner.<br
|
|
class="newline" />Scope: <span
|
|
class="pplb7t-">local </span><br
|
|
class="newline" />Type: <span
|
|
class="pplb7t-">required</span><br
|
|
class="newline" />Intent: <span
|
|
class="pplb7t-">in</span>.<br
|
|
class="newline" />Specified as: a structured data of type <a
|
|
href="userhtmlse3.html#precdata"><span
|
|
class="cmtt-10">psb</span><span
|
|
class="cmtt-10">_Tprec</span><span
|
|
class="cmtt-10">_type</span></a>.
|
|
</dd><dt class="description">
|
|
<!--l. 71--><p class="noindent" >
|
|
<span
|
|
class="pplb7t-">b</span> </dt><dd
|
|
class="description">
|
|
<!--l. 71--><p class="noindent" >The RHS vector. <br
|
|
class="newline" />Scope: <span
|
|
class="pplb7t-">local </span><br
|
|
class="newline" />Type: <span
|
|
class="pplb7t-">required</span><br
|
|
class="newline" />Intent: <span
|
|
class="pplb7t-">in</span>.<br
|
|
class="newline" />Specified as: a rank one array or an object of type <a
|
|
href="userhtmlse3.html#vdata"><span
|
|
class="cmtt-10">psb</span><span
|
|
class="cmtt-10">_T</span><span
|
|
class="cmtt-10">_vect</span><span
|
|
class="cmtt-10">_type</span></a>.
|
|
</dd><dt class="description">
|
|
<!--l. 76--><p class="noindent" >
|
|
<span
|
|
class="pplb7t-">x</span> </dt><dd
|
|
class="description">
|
|
<!--l. 76--><p class="noindent" >The initial guess. <br
|
|
class="newline" />Scope: <span
|
|
class="pplb7t-">local </span><br
|
|
class="newline" />Type: <span
|
|
class="pplb7t-">required</span><br
|
|
class="newline" />Intent: <span
|
|
class="pplb7t-">inout</span>.<br
|
|
class="newline" />Specified as: a rank one array or an object of type <a
|
|
href="userhtmlse3.html#vdata"><span
|
|
class="cmtt-10">psb</span><span
|
|
class="cmtt-10">_T</span><span
|
|
class="cmtt-10">_vect</span><span
|
|
class="cmtt-10">_type</span></a>.
|
|
</dd><dt class="description">
|
|
<!--l. 81--><p class="noindent" >
|
|
<span
|
|
class="pplb7t-">eps</span> </dt><dd
|
|
class="description">
|
|
|
|
|
|
|
|
<!--l. 81--><p class="noindent" >The stopping tolerance. <br
|
|
class="newline" />Scope: <span
|
|
class="pplb7t-">global </span><br
|
|
class="newline" />Type: <span
|
|
class="pplb7t-">required</span><br
|
|
class="newline" />Intent: <span
|
|
class="pplb7t-">in</span>.<br
|
|
class="newline" />Specified as: a real number.
|
|
</dd><dt class="description">
|
|
<!--l. 86--><p class="noindent" >
|
|
<span
|
|
class="pplb7t-">desc</span><span
|
|
class="pplb7t-">_a</span> </dt><dd
|
|
class="description">
|
|
<!--l. 86--><p class="noindent" >contains data structures for communications.<br
|
|
class="newline" />Scope: <span
|
|
class="pplb7t-">local </span><br
|
|
class="newline" />Type: <span
|
|
class="pplb7t-">required</span><br
|
|
class="newline" />Intent: <span
|
|
class="pplb7t-">in</span>.<br
|
|
class="newline" />Specified as: a structured data of type <a
|
|
href="userhtmlse3.html#descdata"><span
|
|
class="cmtt-10">psb</span><span
|
|
class="cmtt-10">_desc</span><span
|
|
class="cmtt-10">_type</span></a>.
|
|
</dd><dt class="description">
|
|
<!--l. 91--><p class="noindent" >
|
|
<span
|
|
class="pplb7t-">itmax</span> </dt><dd
|
|
class="description">
|
|
<!--l. 91--><p class="noindent" >The maximum number of iterations to perform.<br
|
|
class="newline" />Scope: <span
|
|
class="pplb7t-">global </span><br
|
|
class="newline" />Type: <span
|
|
class="pplb7t-">optional</span><br
|
|
class="newline" />Intent: <span
|
|
class="pplb7t-">in</span>.<br
|
|
class="newline" />Default: <span
|
|
class="zplmr7m-">itmax </span><span
|
|
class="zplmr7t-">= </span>1000.<br
|
|
class="newline" />Specified as: an integer variable <span
|
|
class="zplmr7m-">itmax </span><span
|
|
class="zplmr7y-">≥ </span>1.
|
|
</dd><dt class="description">
|
|
<!--l. 97--><p class="noindent" >
|
|
<span
|
|
class="pplb7t-">itrace</span> </dt><dd
|
|
class="description">
|
|
<!--l. 97--><p class="noindent" >If <span
|
|
class="zplmr7m-">> </span>0 print out an informational message about convergence every <span
|
|
class="zplmr7m-">itrace</span>
|
|
iterations. If <span
|
|
class="zplmr7t-">= </span>0 print a message in case of convergence failure.<br
|
|
class="newline" />Scope: <span
|
|
class="pplb7t-">global </span><br
|
|
class="newline" />Type: <span
|
|
class="pplb7t-">optional</span><br
|
|
class="newline" />Intent: <span
|
|
class="pplb7t-">in</span>.<br
|
|
class="newline" />Default: <span
|
|
class="zplmr7m-">itrace </span><span
|
|
class="zplmr7t-">= </span><span
|
|
class="zplmr7y-">-</span>1.<br
|
|
class="newline" />
|
|
</dd><dt class="description">
|
|
<!--l. 104--><p class="noindent" >
|
|
<span
|
|
class="pplb7t-">irst</span> </dt><dd
|
|
class="description">
|
|
<!--l. 104--><p class="noindent" >An integer specifying the restart parameter.<br
|
|
class="newline" />Scope: <span
|
|
class="pplb7t-">global </span><br
|
|
class="newline" />Type: <span
|
|
class="pplb7t-">optional</span>.<br
|
|
class="newline" />Intent: <span
|
|
class="pplb7t-">in</span>.<br
|
|
class="newline" />Values: <span
|
|
class="zplmr7m-">irst > </span>0. This is employed for the BiCGSTABL or RGMRES methods,
|
|
otherwise it is ignored.
|
|
</dd><dt class="description">
|
|
<!--l. 111--><p class="noindent" >
|
|
<span
|
|
class="pplb7t-">istop</span> </dt><dd
|
|
class="description">
|
|
|
|
|
|
|
|
<!--l. 111--><p class="noindent" >An integer specifying the stopping criterion.<br
|
|
class="newline" />Scope: <span
|
|
class="pplb7t-">global </span><br
|
|
class="newline" />Type: <span
|
|
class="pplb7t-">optional</span>.<br
|
|
class="newline" />Intent: <span
|
|
class="pplb7t-">in</span>.<br
|
|
class="newline" />Values: 1: use the normwise backward error, 2: use the scaled 2-norm
|
|
of the residual, 3: use the residual reduction in the 2-norm. Default:
|
|
2.
|
|
</dd><dt class="description">
|
|
<!--l. 117--><p class="noindent" >
|
|
<span
|
|
class="pplb7t-">On Return</span> </dt><dd
|
|
class="description">
|
|
<!--l. 117--><p class="noindent" >
|
|
</dd><dt class="description">
|
|
<!--l. 118--><p class="noindent" >
|
|
<span
|
|
class="pplb7t-">x</span> </dt><dd
|
|
class="description">
|
|
<!--l. 118--><p class="noindent" >The computed solution. <br
|
|
class="newline" />Scope: <span
|
|
class="pplb7t-">local </span><br
|
|
class="newline" />Type: <span
|
|
class="pplb7t-">required</span><br
|
|
class="newline" />Intent: <span
|
|
class="pplb7t-">inout</span>.<br
|
|
class="newline" />Specified as: a rank one array or an object of type <a
|
|
href="userhtmlse3.html#vdata"><span
|
|
class="cmtt-10">psb</span><span
|
|
class="cmtt-10">_T</span><span
|
|
class="cmtt-10">_vect</span><span
|
|
class="cmtt-10">_type</span></a>.
|
|
</dd><dt class="description">
|
|
<!--l. 123--><p class="noindent" >
|
|
<span
|
|
class="pplb7t-">iter</span> </dt><dd
|
|
class="description">
|
|
<!--l. 123--><p class="noindent" >The number of iterations performed.<br
|
|
class="newline" />Scope: <span
|
|
class="pplb7t-">global </span><br
|
|
class="newline" />Type: <span
|
|
class="pplb7t-">optional</span><br
|
|
class="newline" />Intent: <span
|
|
class="pplb7t-">out</span>.<br
|
|
class="newline" />Returned as: an integer variable.
|
|
</dd><dt class="description">
|
|
<!--l. 128--><p class="noindent" >
|
|
<span
|
|
class="pplb7t-">err</span> </dt><dd
|
|
class="description">
|
|
<!--l. 128--><p class="noindent" >The convergence estimate on exit.<br
|
|
class="newline" />Scope: <span
|
|
class="pplb7t-">global </span><br
|
|
class="newline" />Type: <span
|
|
class="pplb7t-">optional</span><br
|
|
class="newline" />Intent: <span
|
|
class="pplb7t-">out</span>.<br
|
|
class="newline" />Returned as: a real number.
|
|
</dd><dt class="description">
|
|
<!--l. 133--><p class="noindent" >
|
|
<span
|
|
class="pplb7t-">cond</span> </dt><dd
|
|
class="description">
|
|
<!--l. 133--><p class="noindent" >An estimate of the condition number of matrix <span
|
|
class="zplmr7m-">A</span>; only available with the <span
|
|
class="zplmr7m-">CG</span>
|
|
method on real data.<br
|
|
class="newline" />Scope: <span
|
|
class="pplb7t-">global </span><br
|
|
class="newline" />Type: <span
|
|
class="pplb7t-">optional</span><br
|
|
class="newline" />Intent: <span
|
|
class="pplb7t-">out</span>.<br
|
|
class="newline" />Returned as: a real number. A correct result will be greater than or
|
|
equal to one; if specified for non-real data, or an error occurred, zero is
|
|
returned.
|
|
</dd><dt class="description">
|
|
<!--l. 141--><p class="noindent" >
|
|
<span
|
|
class="pplb7t-">info</span> </dt><dd
|
|
class="description">
|
|
<!--l. 141--><p class="noindent" >Error code.<br
|
|
class="newline" />Scope: <span
|
|
class="pplb7t-">local </span><br
|
|
class="newline" />Type: <span
|
|
class="pplb7t-">required </span><br
|
|
class="newline" />Intent: <span
|
|
class="pplb7t-">out</span>.<br
|
|
class="newline" />An integer value; 0 means no error has been detected.</dd></dl>
|
|
|
|
|
|
|
|
<h4 class="subsectionHead"><span class="titlemark">11.2 </span> <a
|
|
id="x17-14500011.2"></a>psb_richardson — Richardson Iteration Driver Routine</h4>
|
|
<!--l. 158--><p class="noindent" >This subroutine is a driver implementig a Richardson iteration
|
|
<div class="math-display" >
|
|
<img
|
|
src="userhtml33x.png" alt="x = M - 1(b - Ax )+ x ,
|
|
k+1 k k
|
|
" class="math-display" ></div>
|
|
<!--l. 159--><p class="nopar" > with the preconditioner operator <span
|
|
class="zplmr7m-">M </span>defined in the previous section.
|
|
<!--l. 162--><p class="indent" > The stopping criterion can take the following values:
|
|
<dl class="description"><dt class="description">
|
|
<!--l. 164--><p class="noindent" >
|
|
<span
|
|
class="pplb7t-">1</span> </dt><dd
|
|
class="description">
|
|
<!--l. 164--><p class="noindent" >normwise backward error in the infinity norm; the iteration is stopped
|
|
when
|
|
<div class="math-display" >
|
|
<img
|
|
src="userhtml34x.png" alt=" ------∥ri∥------
|
|
err = (∥A ∥∥xi∥ + ∥b∥) < eps
|
|
" class="math-display" ></div>
|
|
<!--l. 166--><p class="nopar" >
|
|
</dd><dt class="description">
|
|
<!--l. 167--><p class="noindent" >
|
|
<span
|
|
class="pplb7t-">2</span> </dt><dd
|
|
class="description">
|
|
<!--l. 167--><p class="noindent" >Relative residual in the 2-norm; the iteration is stopped when
|
|
<div class="math-display" >
|
|
<img
|
|
src="userhtml35x.png" alt=" ∥ri∥-
|
|
err = ∥b∥ 2 < eps
|
|
" class="math-display" ></div>
|
|
<!--l. 169--><p class="nopar" >
|
|
</dd><dt class="description">
|
|
<!--l. 170--><p class="noindent" >
|
|
<span
|
|
class="pplb7t-">3</span> </dt><dd
|
|
class="description">
|
|
<!--l. 170--><p class="noindent" >Relative residual reduction in the 2-norm; the iteration is stopped when
|
|
<div class="math-display" >
|
|
<img
|
|
src="userhtml36x.png" alt=" -∥ri∥-
|
|
err = ∥r0∥2 < eps
|
|
" class="math-display" ></div>
|
|
<!--l. 172--><p class="nopar" ></dd></dl>
|
|
|
|
|
|
|
|
<!--l. 174--><p class="noindent" >The behaviour is controlled by the istop argument (see later). In the above formulae, <span
|
|
class="zplmr7m-">x</span><sub><span
|
|
class="zplmr7m-x-x-76">i</span></sub>
|
|
is the tentative solution and <span
|
|
class="zplmr7m-">r</span><sub><span
|
|
class="zplmr7m-x-x-76">i</span></sub> <span
|
|
class="zplmr7t-">= </span><span
|
|
class="zplmr7m-">b</span><span
|
|
class="zplmr7y-">-</span><span
|
|
class="zplmr7m-">Ax</span><sub><span
|
|
class="zplmr7m-x-x-76">i</span></sub> the corresponding residual at the <span
|
|
class="zplmr7m-">i</span>-th
|
|
iteration.
|
|
<!--l. 179-->
|
|
<pre class="lstlisting" id="listing-219"><span class="label"><a
|
|
id="x17-145001r1"></a></span><span style="color:#000000"><span
|
|
class="cmtt-10">call</span></span><span style="color:#000000"> </span><span style="color:#000000"><span
|
|
class="cmtt-10">psb_richardson</span></span><span style="color:#000000"><span
|
|
class="cmtt-10">(</span></span><span style="color:#000000"><span
|
|
class="cmtt-10">a</span></span><span style="color:#000000"><span
|
|
class="cmtt-10">,</span></span><span style="color:#000000"><span
|
|
class="cmtt-10">prec</span></span><span style="color:#000000"><span
|
|
class="cmtt-10">,</span></span><span style="color:#000000"><span
|
|
class="cmtt-10">b</span></span><span style="color:#000000"><span
|
|
class="cmtt-10">,</span></span><span style="color:#000000"><span
|
|
class="cmtt-10">x</span></span><span style="color:#000000"><span
|
|
class="cmtt-10">,</span></span><span style="color:#000000"><span
|
|
class="cmtt-10">eps</span></span><span style="color:#000000"><span
|
|
class="cmtt-10">,</span></span><span style="color:#000000"><span
|
|
class="cmtt-10">desc_a</span></span><span style="color:#000000"><span
|
|
class="cmtt-10">,</span></span><span style="color:#000000"><span
|
|
class="cmtt-10">info</span></span><span style="color:#000000"><span
|
|
class="cmtt-10">,&</span></span>
|
|
<span class="label"><a
|
|
id="x17-145002r2"></a></span><span
|
|
class="cmtt-10"> </span><span
|
|
class="cmtt-10"> </span><span
|
|
class="cmtt-10"> </span><span
|
|
class="cmtt-10"> </span><span style="color:#000000"><span
|
|
class="cmtt-10">&</span></span><span style="color:#000000"> </span><span style="color:#000000"><span
|
|
class="cmtt-10">itmax</span></span><span style="color:#000000"><span
|
|
class="cmtt-10">,</span></span><span style="color:#000000"><span
|
|
class="cmtt-10">iter</span></span><span style="color:#000000"><span
|
|
class="cmtt-10">,</span></span><span style="color:#000000"><span
|
|
class="cmtt-10">err</span></span><span style="color:#000000"><span
|
|
class="cmtt-10">,</span></span><span style="color:#000000"><span
|
|
class="cmtt-10">itrace</span></span><span style="color:#000000"><span
|
|
class="cmtt-10">,</span></span><span style="color:#000000"><span
|
|
class="cmtt-10">istop</span></span><span style="color:#000000"><span
|
|
class="cmtt-10">)</span></span></pre>
|
|
|
|
<!--l. 184--><p class="indent" >
|
|
<dl class="description"><dt class="description">
|
|
<!--l. 185--><p class="noindent" >
|
|
<span
|
|
class="pplb7t-">Type:</span> </dt><dd
|
|
class="description">
|
|
<!--l. 185--><p class="noindent" >Synchronous.
|
|
</dd><dt class="description">
|
|
<!--l. 186--><p class="noindent" >
|
|
<span
|
|
class="pplb7t-">On Entry</span> </dt><dd
|
|
class="description">
|
|
<!--l. 186--><p class="noindent" >
|
|
</dd><dt class="description">
|
|
<!--l. 187--><p class="noindent" >
|
|
<span
|
|
class="pplb7t-">a</span> </dt><dd
|
|
class="description">
|
|
<!--l. 187--><p class="noindent" >the local portion of global sparse matrix <span
|
|
class="zplmr7m-">A</span>. <br
|
|
class="newline" />Scope: <span
|
|
class="pplb7t-">local </span><br
|
|
class="newline" />Type: <span
|
|
class="pplb7t-">required</span><br
|
|
class="newline" />Intent: <span
|
|
class="pplb7t-">in</span>.<br
|
|
class="newline" />Specified as: a structured data of type <a
|
|
href="userhtmlse3.html#spdata"><span
|
|
class="cmtt-10">psb</span><span
|
|
class="cmtt-10">_Tspmat</span><span
|
|
class="cmtt-10">_type</span></a>.
|
|
</dd><dt class="description">
|
|
<!--l. 193--><p class="noindent" >
|
|
<span
|
|
class="pplb7t-">prec</span> </dt><dd
|
|
class="description">
|
|
<!--l. 193--><p class="noindent" >The data structure containing the preconditioner.<br
|
|
class="newline" />Scope: <span
|
|
class="pplb7t-">local </span><br
|
|
class="newline" />Type: <span
|
|
class="pplb7t-">required</span><br
|
|
class="newline" />Intent: <span
|
|
class="pplb7t-">in</span>.<br
|
|
class="newline" />Specified as: a structured data of type <a
|
|
href="userhtmlse3.html#precdata"><span
|
|
class="cmtt-10">psb</span><span
|
|
class="cmtt-10">_Tprec</span><span
|
|
class="cmtt-10">_type</span></a>.
|
|
</dd><dt class="description">
|
|
<!--l. 198--><p class="noindent" >
|
|
<span
|
|
class="pplb7t-">b</span> </dt><dd
|
|
class="description">
|
|
<!--l. 198--><p class="noindent" >The RHS vector. <br
|
|
class="newline" />Scope: <span
|
|
class="pplb7t-">local </span><br
|
|
class="newline" />Type: <span
|
|
class="pplb7t-">required</span><br
|
|
class="newline" />Intent: <span
|
|
class="pplb7t-">in</span>.<br
|
|
class="newline" />Specified as: a rank one array or an object of type <a
|
|
href="userhtmlse3.html#vdata"><span
|
|
class="cmtt-10">psb</span><span
|
|
class="cmtt-10">_T</span><span
|
|
class="cmtt-10">_vect</span><span
|
|
class="cmtt-10">_type</span></a>.
|
|
</dd><dt class="description">
|
|
<!--l. 203--><p class="noindent" >
|
|
<span
|
|
class="pplb7t-">x</span> </dt><dd
|
|
class="description">
|
|
|
|
|
|
|
|
<!--l. 203--><p class="noindent" >The initial guess. <br
|
|
class="newline" />Scope: <span
|
|
class="pplb7t-">local </span><br
|
|
class="newline" />Type: <span
|
|
class="pplb7t-">required</span><br
|
|
class="newline" />Intent: <span
|
|
class="pplb7t-">inout</span>.<br
|
|
class="newline" />Specified as: a rank one array or an object of type <a
|
|
href="userhtmlse3.html#vdata"><span
|
|
class="cmtt-10">psb</span><span
|
|
class="cmtt-10">_T</span><span
|
|
class="cmtt-10">_vect</span><span
|
|
class="cmtt-10">_type</span></a>.
|
|
</dd><dt class="description">
|
|
<!--l. 208--><p class="noindent" >
|
|
<span
|
|
class="pplb7t-">eps</span> </dt><dd
|
|
class="description">
|
|
<!--l. 208--><p class="noindent" >The stopping tolerance. <br
|
|
class="newline" />Scope: <span
|
|
class="pplb7t-">global </span><br
|
|
class="newline" />Type: <span
|
|
class="pplb7t-">required</span><br
|
|
class="newline" />Intent: <span
|
|
class="pplb7t-">in</span>.<br
|
|
class="newline" />Specified as: a real number.
|
|
</dd><dt class="description">
|
|
<!--l. 213--><p class="noindent" >
|
|
<span
|
|
class="pplb7t-">desc</span><span
|
|
class="pplb7t-">_a</span> </dt><dd
|
|
class="description">
|
|
<!--l. 213--><p class="noindent" >contains data structures for communications.<br
|
|
class="newline" />Scope: <span
|
|
class="pplb7t-">local </span><br
|
|
class="newline" />Type: <span
|
|
class="pplb7t-">required</span><br
|
|
class="newline" />Intent: <span
|
|
class="pplb7t-">in</span>.<br
|
|
class="newline" />Specified as: a structured data of type <a
|
|
href="userhtmlse3.html#descdata"><span
|
|
class="cmtt-10">psb</span><span
|
|
class="cmtt-10">_desc</span><span
|
|
class="cmtt-10">_type</span></a>.
|
|
</dd><dt class="description">
|
|
<!--l. 218--><p class="noindent" >
|
|
<span
|
|
class="pplb7t-">itmax</span> </dt><dd
|
|
class="description">
|
|
<!--l. 218--><p class="noindent" >The maximum number of iterations to perform.<br
|
|
class="newline" />Scope: <span
|
|
class="pplb7t-">global </span><br
|
|
class="newline" />Type: <span
|
|
class="pplb7t-">optional</span><br
|
|
class="newline" />Intent: <span
|
|
class="pplb7t-">in</span>.<br
|
|
class="newline" />Default: <span
|
|
class="zplmr7m-">itmax </span><span
|
|
class="zplmr7t-">= </span>1000.<br
|
|
class="newline" />Specified as: an integer variable <span
|
|
class="zplmr7m-">itmax </span><span
|
|
class="zplmr7y-">≥ </span>1.
|
|
</dd><dt class="description">
|
|
<!--l. 224--><p class="noindent" >
|
|
<span
|
|
class="pplb7t-">itrace</span> </dt><dd
|
|
class="description">
|
|
<!--l. 224--><p class="noindent" >If <span
|
|
class="zplmr7m-">> </span>0 print out an informational message about convergence every <span
|
|
class="zplmr7m-">itrace</span>
|
|
iterations. If <span
|
|
class="zplmr7t-">= </span>0 print a message in case of convergence failure.<br
|
|
class="newline" />Scope: <span
|
|
class="pplb7t-">global </span><br
|
|
class="newline" />Type: <span
|
|
class="pplb7t-">optional</span><br
|
|
class="newline" />Intent: <span
|
|
class="pplb7t-">in</span>.<br
|
|
class="newline" />Default: <span
|
|
class="zplmr7m-">itrace </span><span
|
|
class="zplmr7t-">= </span><span
|
|
class="zplmr7y-">-</span>1.<br
|
|
class="newline" />
|
|
</dd><dt class="description">
|
|
<!--l. 232--><p class="noindent" >
|
|
<span
|
|
class="pplb7t-">istop</span> </dt><dd
|
|
class="description">
|
|
|
|
|
|
|
|
<!--l. 232--><p class="noindent" >An integer specifying the stopping criterion.<br
|
|
class="newline" />Scope: <span
|
|
class="pplb7t-">global </span><br
|
|
class="newline" />Type: <span
|
|
class="pplb7t-">optional</span>.<br
|
|
class="newline" />Intent: <span
|
|
class="pplb7t-">in</span>.<br
|
|
class="newline" />Values: 1: use the normwise backward error, 2: use the scaled 2-norm of
|
|
the residual, 3: use the residual reduction in the 2-norm. Default: 2.
|
|
</dd><dt class="description">
|
|
<!--l. 238--><p class="noindent" >
|
|
<span
|
|
class="pplb7t-">On Return</span> </dt><dd
|
|
class="description">
|
|
<!--l. 238--><p class="noindent" >
|
|
</dd><dt class="description">
|
|
<!--l. 239--><p class="noindent" >
|
|
<span
|
|
class="pplb7t-">x</span> </dt><dd
|
|
class="description">
|
|
<!--l. 239--><p class="noindent" >The computed solution. <br
|
|
class="newline" />Scope: <span
|
|
class="pplb7t-">local </span><br
|
|
class="newline" />Type: <span
|
|
class="pplb7t-">required</span><br
|
|
class="newline" />Intent: <span
|
|
class="pplb7t-">inout</span>.<br
|
|
class="newline" />Specified as: a rank one array or an object of type <a
|
|
href="userhtmlse3.html#vdata"><span
|
|
class="cmtt-10">psb</span><span
|
|
class="cmtt-10">_T</span><span
|
|
class="cmtt-10">_vect</span><span
|
|
class="cmtt-10">_type</span></a>.
|
|
</dd><dt class="description">
|
|
<!--l. 244--><p class="noindent" >
|
|
<span
|
|
class="pplb7t-">iter</span> </dt><dd
|
|
class="description">
|
|
<!--l. 244--><p class="noindent" >The number of iterations performed.<br
|
|
class="newline" />Scope: <span
|
|
class="pplb7t-">global </span><br
|
|
class="newline" />Type: <span
|
|
class="pplb7t-">optional</span><br
|
|
class="newline" />Intent: <span
|
|
class="pplb7t-">out</span>.<br
|
|
class="newline" />Returned as: an integer variable.
|
|
</dd><dt class="description">
|
|
<!--l. 249--><p class="noindent" >
|
|
<span
|
|
class="pplb7t-">err</span> </dt><dd
|
|
class="description">
|
|
<!--l. 249--><p class="noindent" >The convergence estimate on exit.<br
|
|
class="newline" />Scope: <span
|
|
class="pplb7t-">global </span><br
|
|
class="newline" />Type: <span
|
|
class="pplb7t-">optional</span><br
|
|
class="newline" />Intent: <span
|
|
class="pplb7t-">out</span>.<br
|
|
class="newline" />Returned as: a real number.
|
|
</dd><dt class="description">
|
|
<!--l. 254--><p class="noindent" >
|
|
<span
|
|
class="pplb7t-">info</span> </dt><dd
|
|
class="description">
|
|
<!--l. 254--><p class="noindent" >Error code.<br
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class="newline" />Scope: <span
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class="pplb7t-">local </span><br
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class="newline" />Type: <span
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class="pplb7t-">required </span><br
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class="newline" />Intent: <span
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class="pplb7t-">out</span>.<br
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class="newline" />An integer value; 0 means no error has been detected.</dd></dl>
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