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<head><title>psb_norm2 &#8212; 2-Norm of Vector</title>
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<h4 class="subsectionHead"><span class="titlemark">4.8 </span> <a
id="x26-630004.8"></a>psb_norm2 &#8212; 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=" &#x221A; -T--
nrm2 &#x2190; 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=" &#x221A;----
nrm2 &#x2190; 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&#x00A0;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,&#x00A0;desc_a,&#x00A0;info&#x00A0;[,global])
&#x00A0;<br />psb_norm2(x,&#x00A0;desc_a,&#x00A0;info&#x00A0;[,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>&#x00A0;containing numbers of type specified in Table&#x00A0;<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>&#x00A0;&#x00A0;&#x00A0;&#x00A0;vres(1)&#x00A0;=&#x00A0;psb_genrm2(x1,desc_a,info,global=.<span
class="cmbx-10">false</span>.)&#x00A0;<br /><span class="label"><a
id="x26-63005r2"></a></span>&#x00A0;&#x00A0;&#x00A0;&#x00A0;vres(2)&#x00A0;=&#x00A0;psb_genrm2(x2,desc_a,info,global=.<span
class="cmbx-10">false</span>.)&#x00A0;<br /><span class="label"><a
id="x26-63006r3"></a></span>&#x00A0;&#x00A0;&#x00A0;&#x00A0;vres(3)&#x00A0;=&#x00A0;psb_genrm2(x3,desc_a,info,global=.<span
class="cmbx-10">false</span>.)&#x00A0;<br /><span class="label"><a
id="x26-63007r4"></a></span>&#x00A0;&#x00A0;&#x00A0;&#x00A0;<span
class="cmbx-10">call</span>&#x00A0;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>
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