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@@ -10,7 +10,7 @@
<link rel="stylesheet" type="text/css" href="userhtml.css">
</head><body
>
<!--l. 627--><div class="crosslinks"><p class="noindent">[<a
<!--l. 641--><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
@@ -18,7 +18,7 @@ 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 &#8212; 2-Norm of Vector</h4>
<!--l. 629--><p class="noindent" >This function computes the 2-norm of a vector <span
<!--l. 643--><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:
@@ -27,27 +27,27 @@ class="cmmi-10">x </span>is a real vector it computes 2-norm as:
src="userhtml13x.png" alt=" &#x221A; -T--
nrm2 &#x2190; x x
" class="math-display" ></center>
<!--l. 632--><p class="nopar" > else if <span
<!--l. 646--><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" >
<!--l. 648--><p class="nopar" >
<div class="table">
<!--l. 640--><p class="indent" > <a
id="x26-630018"></a><hr class="float"><div class="float"
<!--l. 654--><p class="indent" > <a
id="x26-63001r8"></a><hr class="float"><div class="float"
>
<div class="center"
>
<!--l. 641--><p class="noindent" >
<!--l. 655--><p class="noindent" >
<div class="tabular"> <table id="TBL-8" class="tabular"
cellspacing="0" cellpadding="0"
><colgroup id="TBL-8-1g"><col
@@ -88,20 +88,41 @@ class="hline"><td><hr></td><td><hr></td><td><hr></td></tr><tr
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 -->
class="content">Data types</span></div><!--tex4ht:label?: x26-63001r8 -->
</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" >
<!--l. 670--><p class="indent" > <span class="lstinline"></span><span
class="cmtt-10">psb_genrm2</span><span
class="cmtt-10">(</span><span
class="cmtt-10">x</span><span
class="cmtt-10">,</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">desc_a</span><span
class="cmtt-10">,</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">info</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">[,</span><span
class="cmtt-10">global</span><span
class="cmtt-10">])</span><br
class="newline" /><span class="lstinline"></span><span
class="cmtt-10">psb_norm2</span><span
class="cmtt-10">(</span><span
class="cmtt-10">x</span><span
class="cmtt-10">,</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">desc_a</span><span
class="cmtt-10">,</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">info</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">[,</span><span
class="cmtt-10">global</span><span
class="cmtt-10">])</span><br
class="newline" />
<dl class="description"><dt class="description">
<span
class="cmbx-10">Type:</span> </dt><dd
@@ -128,7 +149,7 @@ 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>.
href="#x26-63001r8">8<!--tex4ht:ref: tab:f90nrm2 --></a>.
</dd><dt class="description">
<span
class="cmbx-10">desc</span><span
@@ -156,8 +177,11 @@ 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" />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
@@ -169,8 +193,11 @@ 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
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" />Type: <span
class="cmbx-10">required </span><br
@@ -189,96 +216,26 @@ class="newline" />An integer value; 0 means no error has been detected.</dd></dl
<!--l. 706--><p class="noindent" ><span
<!--l. 718--><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-->
runtime efficiency by using the following scheme: <!--l. 725-->
<div class="lstlisting" id="listing-4"><span class="label"><a
id="x26-63004r1"></a></span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">vres</span><span
class="cmtt-10">(1)</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">=</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">psb_genrm2</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">&#x00A0;</span><br /><span class="label"><a
id="x26-63005r2"></a></span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">vres</span><span
class="cmtt-10">(2)</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">=</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">psb_genrm2</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">&#x00A0;</span><br /><span class="label"><a
id="x26-63006r3"></a></span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">vres</span><span
class="cmtt-10">(3)</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">=</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">psb_genrm2</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">&#x00A0;</span><br /><span class="label"><a
id="x26-63007r4"></a></span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">call</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">psb_nrm2</span><span
class="cmtt-10">(</span><span
class="cmtt-10">ictxt</span><span
class="cmtt-10">,</span><span
class="cmtt-10">vres</span><span
class="cmtt-10">(1:3))</span>
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(ctxt,vres(1:3))
</div>
<!--l. 719--><p class="noindent" >In this way the global communication, which for small sizes is a latency-bound
<!--l. 731--><p class="noindent" >In this way the global communication, which for small sizes is a latency-bound
operation, is invoked only once.</li></ol>
@@ -286,12 +243,12 @@ class="cmtt-10">(1:3))</span>
<!--l. 725--><div class="crosslinks"><p class="noindent">[<a
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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
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id="tailuserhtmlsu17.html"></a>
</body></html>