<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> <html > <head><title>psb_norm1 — 1-Norm of Vector</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. 476--><div class="crosslinks"><p class="noindent">[<a href="userhtmlsu19.html" >next</a>] [<a href="userhtmlsu14.html" >prev</a>] [<a href="userhtmlsu14.html#tailuserhtmlsu14.html" >prev-tail</a>] [<a href="userhtmlsu12.html#tailuserhtmlsu15.html">tail</a>] [<a href="userhtmlsu12.html#userhtmlsu18.html" >up</a>] </p></div> <h4 class="subsectionHead"><span class="titlemark">4.6 </span> <a id="x24-610004.6"></a>psb_norm1 — 1-Norm of Vector</h4> <!--l. 478--><p class="noindent" >This function computes the 1-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 1-norm as: <center class="math-display" > <img src="userhtml8x.png" alt="asum ← ∥xi∥ " class="math-display" ></center> <!--l. 481--><p class="nopar" > else if <span class="cmmi-10">x </span>is a complex vector then it computes 1-norm as: <center class="math-display" > <img src="userhtml9x.png" alt="asum ← ∥re(x)∥ + ∥im (x)∥ 1 1 " class="math-display" ></center> <!--l. 483--><p class="nopar" > <!--l. 486--><p class="indent" > <span class="lstinline"></span><span class="cmtt-10">psb_geasum</span><span class="cmtt-10">(</span><span class="cmtt-10">x</span><span class="cmtt-10">,</span><span class="cmtt-10"> </span><span class="cmtt-10">desc_a</span><span class="cmtt-10">,</span><span class="cmtt-10"> </span><span class="cmtt-10">info</span><span class="cmtt-10"> </span><span class="cmtt-10">[,</span><span class="cmtt-10">global</span><span class="cmtt-10">])</span> <span class="lstinline"></span><span class="cmtt-10">psb_norm1</span><span class="cmtt-10">(</span><span class="cmtt-10">x</span><span class="cmtt-10">,</span><span class="cmtt-10"> </span><span class="cmtt-10">desc_a</span><span class="cmtt-10">,</span><span class="cmtt-10"> </span><span class="cmtt-10">info</span><span class="cmtt-10"> </span><span class="cmtt-10">[,</span><span class="cmtt-10">global</span><span class="cmtt-10">])</span> <div class="table"> <!--l. 489--><p class="indent" > <a id="x24-61001r6"></a><hr class="float"><div class="float" > <div class="center" > <!--l. 490--><p class="noindent" > <div class="tabular"> <table id="TBL-6" class="tabular" cellspacing="0" cellpadding="0" ><colgroup id="TBL-6-1g"><col id="TBL-6-1"><col id="TBL-6-2"><col id="TBL-6-3"></colgroup><tr class="hline"><td><hr></td><td><hr></td><td><hr></td></tr><tr style="vertical-align:baseline;" id="TBL-6-1-"><td style="white-space:nowrap; text-align:left;" id="TBL-6-1-1" class="td11"><span class="cmmi-10">asum </span></td><td style="white-space:nowrap; text-align:left;" id="TBL-6-1-2" class="td11"><span class="cmmi-10">x </span></td><td style="white-space:nowrap; text-align:left;" id="TBL-6-1-3" 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-6-2-"><td style="white-space:nowrap; text-align:left;" id="TBL-6-2-1" class="td11">Short Precision Real</td><td style="white-space:nowrap; text-align:left;" id="TBL-6-2-2" class="td11">Short Precision Real </td><td style="white-space:nowrap; text-align:left;" id="TBL-6-2-3" class="td11">psb_geasum</td> </tr><tr style="vertical-align:baseline;" id="TBL-6-3-"><td style="white-space:nowrap; text-align:left;" id="TBL-6-3-1" class="td11">Long Precision Real </td><td style="white-space:nowrap; text-align:left;" id="TBL-6-3-2" class="td11">Long Precision Real </td><td style="white-space:nowrap; text-align:left;" id="TBL-6-3-3" class="td11">psb_geasum</td> </tr><tr style="vertical-align:baseline;" id="TBL-6-4-"><td style="white-space:nowrap; text-align:left;" id="TBL-6-4-1" class="td11">Short Precision Real</td><td style="white-space:nowrap; text-align:left;" id="TBL-6-4-2" class="td11">Short Precision Complex</td><td style="white-space:nowrap; text-align:left;" id="TBL-6-4-3" class="td11">psb_geasum</td> </tr><tr style="vertical-align:baseline;" id="TBL-6-5-"><td style="white-space:nowrap; text-align:left;" id="TBL-6-5-1" class="td11">Long Precision Real </td><td style="white-space:nowrap; text-align:left;" id="TBL-6-5-2" class="td11">Long Precision Complex </td><td style="white-space:nowrap; text-align:left;" id="TBL-6-5-3" class="td11">psb_geasum</td> </tr><tr class="hline"><td><hr></td><td><hr></td><td><hr></td></tr><tr style="vertical-align:baseline;" id="TBL-6-6-"><td style="white-space:nowrap; text-align:left;" id="TBL-6-6-1" class="td11"> </td></tr></table></div></div> <br /> <div class="caption" ><span class="id">Table 6: </span><span class="content">Data types</span></div><!--tex4ht:label?: x24-61001r6 --> </div><hr class="endfloat" /> </div> <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="#x24-61001r6">6<!--tex4ht:ref: tab:f90asum --></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="lstinline"></span><span class="cmtt-10">global</span><span class="cmtt-10">=.</span><span class="cmtt-10">true</span><span class="cmtt-10">.</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 1-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="lstinline"></span><span class="cmtt-10">global</span><span class="cmtt-10">=.</span><span class="cmtt-10">false</span><span class="cmtt-10">.</span> has been specified<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. 543--><p class="noindent" ><span class="cmbx-12">Notes</span> <ol class="enumerate1" > <li class="enumerate" id="x24-61003x1">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. 558--> <div class="lstlisting" id="listing-3"><span class="label"><a id="x24-61004r1"></a></span><span class="cmtt-10"> </span><span class="cmtt-10"> </span><span class="cmtt-10"> </span><span class="cmtt-10">vres</span><span class="cmtt-10">(1)</span><span class="cmtt-10"> </span><span class="cmtt-10">=</span><span class="cmtt-10"> </span><span class="cmtt-10">psb_geasum</span><span class="cmtt-10">(</span><span class="cmtt-10">x1</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">global</span><span class="cmtt-10">=.</span><span class="cmtt-10">false</span><span class="cmtt-10">.)</span><span class="cmtt-10"> </span><br /><span class="label"><a id="x24-61005r2"></a></span><span class="cmtt-10"> </span><span class="cmtt-10"> </span><span class="cmtt-10"> </span><span class="cmtt-10">vres</span><span class="cmtt-10">(2)</span><span class="cmtt-10"> </span><span class="cmtt-10">=</span><span class="cmtt-10"> </span><span class="cmtt-10">psb_geasum</span><span class="cmtt-10">(</span><span class="cmtt-10">x2</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">global</span><span class="cmtt-10">=.</span><span class="cmtt-10">false</span><span class="cmtt-10">.)</span><span class="cmtt-10"> </span><br /><span class="label"><a id="x24-61006r3"></a></span><span class="cmtt-10"> </span><span class="cmtt-10"> </span><span class="cmtt-10"> </span><span class="cmtt-10">vres</span><span class="cmtt-10">(3)</span><span class="cmtt-10"> </span><span class="cmtt-10">=</span><span class="cmtt-10"> </span><span class="cmtt-10">psb_geasum</span><span class="cmtt-10">(</span><span class="cmtt-10">x3</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">global</span><span class="cmtt-10">=.</span><span class="cmtt-10">false</span><span class="cmtt-10">.)</span><span class="cmtt-10"> </span><br /><span class="label"><a id="x24-61007r4"></a></span><span class="cmtt-10"> </span><span class="cmtt-10"> </span><span class="cmtt-10"> </span><span class="cmtt-10">call</span><span class="cmtt-10"> </span><span class="cmtt-10">psb_sum</span><span class="cmtt-10">(</span><span class="cmtt-10">ctxt</span><span class="cmtt-10">,</span><span class="cmtt-10">vres</span><span class="cmtt-10">(1:3))</span> </div> <!--l. 565--><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. 570--><div class="crosslinks"><p class="noindent">[<a href="userhtmlsu19.html" >next</a>] [<a href="userhtmlsu14.html" >prev</a>] [<a href="userhtmlsu14.html#tailuserhtmlsu14.html" >prev-tail</a>] [<a href="userhtmlsu15.html" >front</a>] [<a href="userhtmlsu12.html#userhtmlsu18.html" >up</a>] </p></div> <!--l. 570--><p class="indent" > <a id="tailuserhtmlsu15.html"></a> </body></html>