<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> <html > <head><title>psb_krylov — Krylov Methods Driver Routine</title> <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> <meta name="generator" content="TeX4ht (https://tug.org/tex4ht/)"> <meta name="originator" content="TeX4ht (https://tug.org/tex4ht/)"> <!-- html,3 --> <meta name="src" content="userhtml.tex"> <link rel="stylesheet" type="text/css" href="userhtml.css"> </head><body > <!--l. 15--><div class="crosslinks"><p class="noindent">[<a href="userhtmlsu87.html#tailuserhtmlsu90.html">tail</a>] [<a href="# " >up</a>] </p></div> <h4 class="subsectionHead"><span class="titlemark">11.1 </span> <a id="x107-14300011.1"></a>psb_krylov — 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 = -----∥ri∥------< eps (∥A ∥∥xi∥ + ∥b∥) " 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 = ∥ri∥-< eps ∥b∥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 = -∥ri∥-< eps ∥r0∥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"> </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">,&</span><span class="cmtt-10"> </span><br /><span class="label"><a id="x107-143002r2"></a></span><span class="cmtt-10"> </span><span class="cmtt-10"> </span><span class="cmtt-10"> </span><span class="cmtt-10"> </span><span class="cmtt-10">&</span><span class="cmtt-10"> </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">≥ </span>1. </dd><dt class="description"> <span class="cmbx-10">itrace</span> </dt><dd class="description">If <span class="cmmi-10">> </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 > </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> <!--l. 2--><div class="crosslinks"><p class="noindent">[<a href="userhtmlsu90.html" >front</a>] [<a href="# " >up</a>] </p></div> <!--l. 2--><p class="indent" > <a id="tailuserhtmlsu90.html"></a> </body></html>