<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> <html > <head><title>psb_norm2 — 2-Norm of Vector</title> <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> <meta name="generator" content="TeX4ht (http://www.tug.org/tex4ht/)"> <meta name="originator" content="TeX4ht (http://www.tug.org/tex4ht/)"> <!-- html,3 --> <meta name="src" content="userhtml.tex"> <link rel="stylesheet" type="text/css" href="userhtml.css"> </head><body > <!--l. 627--><div class="crosslinks"><p class="noindent">[<a href="userhtmlsu21.html" >next</a>] [<a href="userhtmlsu16.html" >prev</a>] [<a href="userhtmlsu16.html#tailuserhtmlsu16.html" >prev-tail</a>] [<a href="userhtmlsu14.html#tailuserhtmlsu17.html">tail</a>] [<a href="userhtmlsu12.html#userhtmlsu20.html" >up</a>] </p></div> <h4 class="subsectionHead"><span class="titlemark">4.8 </span> <a id="x26-630004.8"></a>psb_norm2 — 2-Norm of Vector</h4> <!--l. 629--><p class="noindent" >This function computes the 2-norm of a vector <span class="cmmi-10">x</span>.<br class="newline" />If <span class="cmmi-10">x </span>is a real vector it computes 2-norm as: <center class="math-display" > <img src="userhtml13x.png" alt=" √ -T-- nrm2 ← x x " class="math-display" ></center> <!--l. 632--><p class="nopar" > else if <span class="cmmi-10">x </span>is a complex vector then it computes 2-norm as: <center class="math-display" > <img src="userhtml14x.png" alt=" √---- nrm2 ← xHx " class="math-display" ></center> <!--l. 634--><p class="nopar" > <div class="table"> <!--l. 640--><p class="indent" > <a id="x26-630018"></a><hr class="float"><div class="float" > <div class="center" > <!--l. 641--><p class="noindent" > <div class="tabular"> <table id="TBL-8" class="tabular" cellspacing="0" cellpadding="0" ><colgroup id="TBL-8-1g"><col id="TBL-8-1"><col id="TBL-8-2"><col id="TBL-8-3"></colgroup><tr class="hline"><td><hr></td><td><hr></td><td><hr></td></tr><tr style="vertical-align:baseline;" id="TBL-8-1-"><td style="white-space:nowrap; text-align:left;" id="TBL-8-1-1" class="td11"><span class="cmmi-10">nrm</span>2 </td><td style="white-space:nowrap; text-align:left;" id="TBL-8-1-2" class="td11"><span class="cmmi-10">x </span></td><td style="white-space:nowrap; text-align:left;" id="TBL-8-1-3" class="td11"><span class="cmbx-10">Function </span></td></tr><tr class="hline"><td><hr></td><td><hr></td><td><hr></td></tr><tr style="vertical-align:baseline;" id="TBL-8-2-"><td style="white-space:nowrap; text-align:left;" id="TBL-8-2-1" class="td11">Short Precision Real</td><td style="white-space:nowrap; text-align:left;" id="TBL-8-2-2" class="td11">Short Precision Real </td><td style="white-space:nowrap; text-align:left;" id="TBL-8-2-3" class="td11">psb_genrm2</td> </tr><tr style="vertical-align:baseline;" id="TBL-8-3-"><td style="white-space:nowrap; text-align:left;" id="TBL-8-3-1" class="td11">Long Precision Real </td><td style="white-space:nowrap; text-align:left;" id="TBL-8-3-2" class="td11">Long Precision Real </td><td style="white-space:nowrap; text-align:left;" id="TBL-8-3-3" class="td11">psb_genrm2</td> </tr><tr style="vertical-align:baseline;" id="TBL-8-4-"><td style="white-space:nowrap; text-align:left;" id="TBL-8-4-1" class="td11">Short Precision Real</td><td style="white-space:nowrap; text-align:left;" id="TBL-8-4-2" class="td11">Short Precision Complex</td><td style="white-space:nowrap; text-align:left;" id="TBL-8-4-3" class="td11">psb_genrm2</td> </tr><tr style="vertical-align:baseline;" id="TBL-8-5-"><td style="white-space:nowrap; text-align:left;" id="TBL-8-5-1" class="td11">Long Precision Real </td><td style="white-space:nowrap; text-align:left;" id="TBL-8-5-2" class="td11">Long Precision Complex </td><td style="white-space:nowrap; text-align:left;" id="TBL-8-5-3" class="td11">psb_genrm2</td> </tr><tr class="hline"><td><hr></td><td><hr></td><td><hr></td></tr><tr style="vertical-align:baseline;" id="TBL-8-6-"><td style="white-space:nowrap; text-align:left;" id="TBL-8-6-1" class="td11"> </td></tr></table></div></div> <br /> <div class="caption" ><span class="id">Table 8: </span><span class="content">Data types</span></div><!--tex4ht:label?: x26-630018 --> </div><hr class="endfloat" /> </div> <div class="verbatim" id="verbatim-47"> psb_genrm2(x, desc_a, info [,global])  <br />psb_norm2(x, desc_a, info [,global]) </div> <!--l. 659--><p class="nopar" > <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">x</span> </dt><dd class="description">the local portion of global dense matrix <span class="cmmi-10">x</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 rank one or two 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> containing numbers of type specified in Table <a href="#x26-630018">8<!--tex4ht:ref: tab:f90nrm2 --></a>. </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: an object 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">global</span> </dt><dd class="description">Specifies whether the computation should include the global reduction across all processes.<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" />Specified as: a logical scalar. Default: <span class="obeylines-h"><span class="verb"><span class="cmtt-10">global=.true.</span></span></span><br class="newline" /> </dd><dt class="description"> <span class="cmbx-10">On Return</span> </dt><dd class="description"> </dd><dt class="description"> <span class="cmbx-10">Function Value</span> </dt><dd class="description">is the 2-norm of vector <span class="cmmi-10">x</span>.<br class="newline" />Scope: <span class="cmbx-10">global </span>unless the optional variable <span class="obeylines-h"><span class="verb"><span class="cmtt-10">global=.false.</span></span></span> has been specified<br class="newline" />Type: <span class="cmbx-10">required </span><br class="newline" />Specified as: a long precision real number. </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. 706--><p class="noindent" ><span class="cmbx-12">Notes</span> <ol class="enumerate1" > <li class="enumerate" id="x26-63003x1">The computation of a global result requires a global communication, which entails a significant overhead. It may be necessary and/or advisable to compute multiple norms at the same time; in this case, it is possible to improve the runtime efficiency by using the following scheme: <!--l. 713--> <div class="lstlisting" id="listing-4"><span class="label"><a id="x26-63004r1"></a></span>    vres(1) = psb_genrm2(x1,desc_a,info,global=.<span class="cmbx-10">false</span>.) <br /><span class="label"><a id="x26-63005r2"></a></span>    vres(2) = psb_genrm2(x2,desc_a,info,global=.<span class="cmbx-10">false</span>.) <br /><span class="label"><a id="x26-63006r3"></a></span>    vres(3) = psb_genrm2(x3,desc_a,info,global=.<span class="cmbx-10">false</span>.) <br /><span class="label"><a id="x26-63007r4"></a></span>    <span class="cmbx-10">call</span> psb_nrm2(ictxt,vres(1:3)) </div> <!--l. 719--><p class="noindent" >In this way the global communication, which for small sizes is a latency-bound operation, is invoked only once.</li></ol> <!--l. 725--><div class="crosslinks"><p class="noindent">[<a href="userhtmlsu21.html" >next</a>] [<a href="userhtmlsu16.html" >prev</a>] [<a href="userhtmlsu16.html#tailuserhtmlsu16.html" >prev-tail</a>] [<a href="userhtmlsu17.html" >front</a>] [<a href="userhtmlsu12.html#userhtmlsu20.html" >up</a>] </p></div> <!--l. 725--><p class="indent" > <a id="tailuserhtmlsu17.html"></a> </body></html>