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<head><title>psb_krylov &#8212; Krylov Methods Driver Routine</title>
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<h4 class="subsectionHead"><span class="titlemark">11.1 </span> <a
id="x107-14300011.1"></a>psb_krylov &#8212; Krylov Methods Driver Routine</h4>
<!--l. 17--><p class="noindent" >This subroutine is a driver that provides a general interface for all the Krylov-Subspace
family methods implemented in PSBLAS version 2.
<!--l. 20--><p class="indent" > The stopping criterion can take the following values:
<dl class="description"><dt class="description">
<span
class="cmbx-10">1</span> </dt><dd
class="description">normwise backward error in the infinity norm; the iteration is stopped when
<center class="math-display" >
<img
src="userhtml30x.png" alt="err = -----&#x2225;ri&#x2225;------&#x003C; eps
(&#x2225;A &#x2225;&#x2225;xi&#x2225; + &#x2225;b&#x2225;)
" class="math-display" ></center>
<!--l. 24--><p class="nopar" >
</dd><dt class="description">
<span
class="cmbx-10">2</span> </dt><dd
class="description">Relative residual in the 2-norm; the iteration is stopped when
<center class="math-display" >
<img
src="userhtml31x.png" alt="err = &#x2225;ri&#x2225;-&#x003C; eps
&#x2225;b&#x2225;2
" class="math-display" ></center>
<!--l. 27--><p class="nopar" >
</dd><dt class="description">
<span
class="cmbx-10">3</span> </dt><dd
class="description">Relative residual reduction in the 2-norm; the iteration is stopped when
<center class="math-display" >
<img
src="userhtml32x.png" alt="err = -&#x2225;ri&#x2225;-&#x003C; eps
&#x2225;r0&#x2225;2
" class="math-display" ></center>
<!--l. 30--><p class="nopar" ></dd></dl>
<!--l. 32--><p class="noindent" >The behaviour is controlled by the istop argument (see later). In the above formulae, <span
class="cmmi-10">x</span><sub><span
class="cmmi-7">i</span></sub>
is the tentative solution and <span
class="cmmi-10">r</span><sub><span
class="cmmi-7">i</span></sub> = <span
class="cmmi-10">b </span><span
class="cmsy-10">- </span><span
class="cmmi-10">Ax</span><sub><span
class="cmmi-7">i</span></sub> the corresponding residual at the <span
class="cmmi-10">i</span>-th
iteration.
<!--l. 37-->
<div class="lstlisting" id="listing-16"><span class="label"><a
id="x107-143001r1"></a></span><span
class="cmtt-10">call</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">psb_krylov</span><span
class="cmtt-10">(</span><span
class="cmtt-10">method</span><span
class="cmtt-10">,</span><span
class="cmtt-10">a</span><span
class="cmtt-10">,</span><span
class="cmtt-10">prec</span><span
class="cmtt-10">,</span><span
class="cmtt-10">b</span><span
class="cmtt-10">,</span><span
class="cmtt-10">x</span><span
class="cmtt-10">,</span><span
class="cmtt-10">eps</span><span
class="cmtt-10">,</span><span
class="cmtt-10">desc_a</span><span
class="cmtt-10">,</span><span
class="cmtt-10">info</span><span
class="cmtt-10">,&amp;</span><span
class="cmtt-10">&#x00A0;</span><br /><span class="label"><a
id="x107-143002r2"></a></span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">&amp;</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">itmax</span><span
class="cmtt-10">,</span><span
class="cmtt-10">iter</span><span
class="cmtt-10">,</span><span
class="cmtt-10">err</span><span
class="cmtt-10">,</span><span
class="cmtt-10">itrace</span><span
class="cmtt-10">,</span><span
class="cmtt-10">irst</span><span
class="cmtt-10">,</span><span
class="cmtt-10">istop</span><span
class="cmtt-10">,</span><span
class="cmtt-10">cond</span><span
class="cmtt-10">)</span>
</div>
<!--l. 42--><p class="indent" >
<dl class="description"><dt class="description">
<span
class="cmbx-10">Type:</span> </dt><dd
class="description">Synchronous.
</dd><dt class="description">
<span
class="cmbx-10">On Entry</span> </dt><dd
class="description">
</dd><dt class="description">
<span
class="cmbx-10">method</span> </dt><dd
class="description">a string that defines the iterative method to be used. Supported values
are:
<dl class="description"><dt class="description">
<span
class="cmbx-10">CG:</span> </dt><dd
class="description">the Conjugate Gradient method;
</dd><dt class="description">
<span
class="cmbx-10">CGS:</span> </dt><dd
class="description">the Conjugate Gradient Stabilized method;
</dd><dt class="description">
<span
class="cmbx-10">GCR:</span> </dt><dd
class="description">the Generalized Conjugate Residual method;
</dd><dt class="description">
<span
class="cmbx-10">FCG:</span> </dt><dd
class="description">the Flexible Conjugate Gradient method<span class="footnote-mark"><a
href="userhtml108.html#fn5x0"><sup class="textsuperscript">5</sup></a></span><a
id="x107-143003f5"></a> ;
</dd><dt class="description">
<span
class="cmbx-10">BICG:</span> </dt><dd
class="description">the Bi-Conjugate Gradient method;
</dd><dt class="description">
<span
class="cmbx-10">BICGSTAB:</span> </dt><dd
class="description">the Bi-Conjugate Gradient Stabilized method;
</dd><dt class="description">
<span
class="cmbx-10">BICGSTABL:</span> </dt><dd
class="description">the Bi-Conjugate Gradient Stabilized method with
restarting;
</dd><dt class="description">
<span
class="cmbx-10">RGMRES:</span> </dt><dd
class="description">the Generalized Minimal Residual method with restarting.</dd></dl>
</dd><dt class="description">
<span
class="cmbx-10">a</span> </dt><dd
class="description">the local portion of global sparse matrix <span
class="cmmi-10">A</span>. <br
class="newline" />Scope: <span
class="cmbx-10">local </span><br
class="newline" />Type: <span
class="cmbx-10">required</span><br
class="newline" />Intent: <span
class="cmbx-10">in</span>.<br
class="newline" />Specified as: a structured data of type <a
href="userhtmlsu6.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">
<span
class="cmbx-10">prec</span> </dt><dd
class="description">The data structure containing the preconditioner.<br
class="newline" />Scope: <span
class="cmbx-10">local </span><br
class="newline" />Type: <span
class="cmbx-10">required</span><br
class="newline" />Intent: <span
class="cmbx-10">in</span>.<br
class="newline" />Specified as: a structured data of type <a
href="userhtmlsu8.html#precdata"><span
class="cmtt-10">psb</span><span
class="cmtt-10">_prec</span><span
class="cmtt-10">_type</span></a>.
</dd><dt class="description">
<span
class="cmbx-10">b</span> </dt><dd
class="description">The RHS vector. <br
class="newline" />Scope: <span
class="cmbx-10">local </span><br
class="newline" />Type: <span
class="cmbx-10">required</span><br
class="newline" />Intent: <span
class="cmbx-10">in</span>.<br
class="newline" />Specified as: a rank one array or an object of type <a
href="userhtmlsu7.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">
<span
class="cmbx-10">x</span> </dt><dd
class="description">The initial guess. <br
class="newline" />Scope: <span
class="cmbx-10">local </span><br
class="newline" />Type: <span
class="cmbx-10">required</span><br
class="newline" />Intent: <span
class="cmbx-10">inout</span>.<br
class="newline" />Specified as: a rank one array or an object of type <a
href="userhtmlsu7.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">
<span
class="cmbx-10">eps</span> </dt><dd
class="description">The stopping tolerance. <br
class="newline" />Scope: <span
class="cmbx-10">global </span><br
class="newline" />Type: <span
class="cmbx-10">required</span><br
class="newline" />Intent: <span
class="cmbx-10">in</span>.<br
class="newline" />Specified as: a real number.
</dd><dt class="description">
<span
class="cmbx-10">desc</span><span
class="cmbx-10">_a</span> </dt><dd
class="description">contains data structures for communications.<br
class="newline" />Scope: <span
class="cmbx-10">local </span><br
class="newline" />Type: <span
class="cmbx-10">required</span><br
class="newline" />Intent: <span
class="cmbx-10">in</span>.<br
class="newline" />Specified as: a structured data of type <a
href="userhtmlsu5.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">
<span
class="cmbx-10">itmax</span> </dt><dd
class="description">The maximum number of iterations to perform.<br
class="newline" />Scope: <span
class="cmbx-10">global </span><br
class="newline" />Type: <span
class="cmbx-10">optional</span><br
class="newline" />Intent: <span
class="cmbx-10">in</span>.<br
class="newline" />Default: <span
class="cmmi-10">itmax </span>= 1000.<br
class="newline" />Specified as: an integer variable <span
class="cmmi-10">itmax </span><span
class="cmsy-10">&#x2265; </span>1.
</dd><dt class="description">
<span
class="cmbx-10">itrace</span> </dt><dd
class="description">If <span
class="cmmi-10">&#x003E; </span>0 print out an informational message about convergence every <span
class="cmmi-10">itrace</span>
iterations. If = 0 print a message in case of convergence failure.<br
class="newline" />Scope: <span
class="cmbx-10">global </span><br
class="newline" />Type: <span
class="cmbx-10">optional</span><br
class="newline" />Intent: <span
class="cmbx-10">in</span>.<br
class="newline" />Default: <span
class="cmmi-10">itrace </span>= <span
class="cmsy-10">-</span>1.<br
class="newline" />
</dd><dt class="description">
<span
class="cmbx-10">irst</span> </dt><dd
class="description">An integer specifying the restart parameter.<br
class="newline" />Scope: <span
class="cmbx-10">global </span><br
class="newline" />Type: <span
class="cmbx-10">optional</span>.<br
class="newline" />Intent: <span
class="cmbx-10">in</span>.<br
class="newline" />Values: <span
class="cmmi-10">irst &#x003E; </span>0. This is employed for the BiCGSTABL or RGMRES methods,
otherwise it is ignored.
</dd><dt class="description">
<span
class="cmbx-10">istop</span> </dt><dd
class="description">An integer specifying the stopping criterion.<br
class="newline" />Scope: <span
class="cmbx-10">global </span><br
class="newline" />Type: <span
class="cmbx-10">optional</span>.<br
class="newline" />Intent: <span
class="cmbx-10">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">
<span
class="cmbx-10">On Return</span> </dt><dd
class="description">
</dd><dt class="description">
<span
class="cmbx-10">x</span> </dt><dd
class="description">The computed solution. <br
class="newline" />Scope: <span
class="cmbx-10">local </span><br
class="newline" />Type: <span
class="cmbx-10">required</span><br
class="newline" />Intent: <span
class="cmbx-10">inout</span>.<br
class="newline" />Specified as: a rank one array or an object of type <a
href="userhtmlsu7.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">
<span
class="cmbx-10">iter</span> </dt><dd
class="description">The number of iterations performed.<br
class="newline" />Scope: <span
class="cmbx-10">global </span><br
class="newline" />Type: <span
class="cmbx-10">optional</span><br
class="newline" />Intent: <span
class="cmbx-10">out</span>.<br
class="newline" />Returned as: an integer variable.
</dd><dt class="description">
<span
class="cmbx-10">err</span> </dt><dd
class="description">The convergence estimate on exit.<br
class="newline" />Scope: <span
class="cmbx-10">global </span><br
class="newline" />Type: <span
class="cmbx-10">optional</span><br
class="newline" />Intent: <span
class="cmbx-10">out</span>.<br
class="newline" />Returned as: a real number.
</dd><dt class="description">
<span
class="cmbx-10">cond</span> </dt><dd
class="description">An estimate of the condition number of matrix <span
class="cmmi-10">A</span>; only available with the <span
class="cmmi-10">CG</span>
method on real data.<br
class="newline" />Scope: <span
class="cmbx-10">global </span><br
class="newline" />Type: <span
class="cmbx-10">optional</span><br
class="newline" />Intent: <span
class="cmbx-10">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">
<span
class="cmbx-10">info</span> </dt><dd
class="description">Error code.<br
class="newline" />Scope: <span
class="cmbx-10">local </span><br
class="newline" />Type: <span
class="cmbx-10">required </span><br
class="newline" />Intent: <span
class="cmbx-10">out</span>.<br
class="newline" />An integer value; 0 means no error has been detected.</dd></dl>
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