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<head><title>psb_norm1 &#8212; 1-Norm of Vector</title> 
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   <h4 class="subsectionHead"><span class="titlemark">4.6   </span> <a 
 id="x24-610004.6"></a>psb_norm1 &#8212; 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 &#x2190;  &#x2225;xi&#x2225;
" 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 &#x2190;  &#x2225;re(x)&#x2225; + &#x2225;im (x)&#x2225;
              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">&#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> <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">&#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>
   <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&#x00A0;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>&#x00A0;containing numbers of type specified in Table&#x00A0;<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">&#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_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">&#x00A0;</span><br /><span class="label"><a 
 id="x24-61005r2"></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_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">&#x00A0;</span><br /><span class="label"><a 
 id="x24-61006r3"></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_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">&#x00A0;</span><br /><span class="label"><a 
 id="x24-61007r4"></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_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>
                                                                  

                                                                  
                                                                  

                                                                  
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