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<head><title>psb_norm2 — 2-Norm of Vector</title>
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<h4 class="subsectionHead"><span class="titlemark">4.8 </span> <a
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id="x26-630004.8"></a>psb_norm2 — 2-Norm of Vector</h4>
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<!--l. 643--><p class="noindent" >This function computes the 2-norm of a vector <span
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class="cmmi-10">x</span>.<br
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class="newline" />If <span
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class="cmmi-10">x </span>is a real vector it computes 2-norm as:
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<center class="math-display" >
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<img
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src="userhtml13x.png" alt=" √ -T--
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nrm2 ← x x
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" class="math-display" ></center>
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<!--l. 646--><p class="nopar" > else if <span
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class="cmmi-10">x </span>is a complex vector then it computes 2-norm as:
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<center class="math-display" >
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<img
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src="userhtml14x.png" alt=" √----
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nrm2 ← xHx
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" class="math-display" ></center>
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<!--l. 648--><p class="nopar" >
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<div class="table">
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<!--l. 654--><p class="indent" > <a
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id="x26-63001r8"></a><hr class="float"><div class="float"
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>
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<div class="center"
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>
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<!--l. 655--><p class="noindent" >
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<div class="tabular"> <table id="TBL-8" class="tabular"
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cellspacing="0" cellpadding="0"
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><colgroup id="TBL-8-1g"><col
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id="TBL-8-1"><col
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id="TBL-8-2"><col
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id="TBL-8-3"></colgroup><tr
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class="hline"><td><hr></td><td><hr></td><td><hr></td></tr><tr
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style="vertical-align:baseline;" id="TBL-8-1-"><td style="white-space:nowrap; text-align:left;" id="TBL-8-1-1"
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class="td11"><span
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class="cmmi-10">nrm</span>2 </td><td style="white-space:nowrap; text-align:left;" id="TBL-8-1-2"
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class="td11"><span
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class="cmmi-10">x </span></td><td style="white-space:nowrap; text-align:left;" id="TBL-8-1-3"
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class="td11"><span
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class="cmbx-10">Function </span></td></tr><tr
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class="hline"><td><hr></td><td><hr></td><td><hr></td></tr><tr
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style="vertical-align:baseline;" id="TBL-8-2-"><td style="white-space:nowrap; text-align:left;" id="TBL-8-2-1"
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class="td11">Short Precision Real</td><td style="white-space:nowrap; text-align:left;" id="TBL-8-2-2"
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class="td11">Short Precision Real </td><td style="white-space:nowrap; text-align:left;" id="TBL-8-2-3"
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class="td11">psb_genrm2</td>
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</tr><tr
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style="vertical-align:baseline;" id="TBL-8-3-"><td style="white-space:nowrap; text-align:left;" id="TBL-8-3-1"
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class="td11">Long Precision Real </td><td style="white-space:nowrap; text-align:left;" id="TBL-8-3-2"
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class="td11">Long Precision Real </td><td style="white-space:nowrap; text-align:left;" id="TBL-8-3-3"
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class="td11">psb_genrm2</td>
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</tr><tr
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style="vertical-align:baseline;" id="TBL-8-4-"><td style="white-space:nowrap; text-align:left;" id="TBL-8-4-1"
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class="td11">Short Precision Real</td><td style="white-space:nowrap; text-align:left;" id="TBL-8-4-2"
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class="td11">Short Precision Complex</td><td style="white-space:nowrap; text-align:left;" id="TBL-8-4-3"
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class="td11">psb_genrm2</td>
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</tr><tr
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style="vertical-align:baseline;" id="TBL-8-5-"><td style="white-space:nowrap; text-align:left;" id="TBL-8-5-1"
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class="td11">Long Precision Real </td><td style="white-space:nowrap; text-align:left;" id="TBL-8-5-2"
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class="td11">Long Precision Complex </td><td style="white-space:nowrap; text-align:left;" id="TBL-8-5-3"
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class="td11">psb_genrm2</td>
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</tr><tr
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class="hline"><td><hr></td><td><hr></td><td><hr></td></tr><tr
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style="vertical-align:baseline;" id="TBL-8-6-"><td style="white-space:nowrap; text-align:left;" id="TBL-8-6-1"
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class="td11"> </td></tr></table></div></div>
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<br /> <div class="caption"
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><span class="id">Table 8: </span><span
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class="content">Data types</span></div><!--tex4ht:label?: x26-63001r8 -->
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</div><hr class="endfloat" />
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</div>
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<!--l. 670--><p class="indent" > <span class="lstinline"></span><span
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class="cmtt-10">psb_genrm2</span><span
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class="cmtt-10">(</span><span
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class="cmtt-10">x</span><span
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class="cmtt-10">,</span><span
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class="cmtt-10"> </span><span
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class="cmtt-10">desc_a</span><span
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class="cmtt-10">,</span><span
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class="cmtt-10"> </span><span
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class="cmtt-10">info</span><span
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class="cmtt-10"> </span><span
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class="cmtt-10">[,</span><span
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class="cmtt-10">global</span><span
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class="cmtt-10">])</span><br
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class="newline" /><span class="lstinline"></span><span
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class="cmtt-10">psb_norm2</span><span
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class="cmtt-10">(</span><span
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class="cmtt-10">x</span><span
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class="cmtt-10">,</span><span
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class="cmtt-10"> </span><span
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class="cmtt-10">desc_a</span><span
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class="cmtt-10">,</span><span
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class="cmtt-10"> </span><span
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class="cmtt-10">info</span><span
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class="cmtt-10"> </span><span
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class="cmtt-10">[,</span><span
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class="cmtt-10">global</span><span
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class="cmtt-10">])</span><br
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class="newline" />
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<dl class="description"><dt class="description">
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<span
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class="cmbx-10">Type:</span> </dt><dd
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class="description">Synchronous.
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</dd><dt class="description">
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<span
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class="cmbx-10">On Entry</span> </dt><dd
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class="description">
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</dd><dt class="description">
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<span
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class="cmbx-10">x</span> </dt><dd
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class="description">the local portion of global dense matrix <span
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class="cmmi-10">x</span>.<br
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class="newline" />Scope: <span
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class="cmbx-10">local </span><br
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class="newline" />Type: <span
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class="cmbx-10">required </span><br
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class="newline" />Intent: <span
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class="cmbx-10">in</span>.<br
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class="newline" />Specified as: a rank one or two array or an object of type
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<a
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href="userhtmlsu7.html#vdata"><span
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class="cmtt-10">psb</span><span
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class="cmtt-10">_T</span><span
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class="cmtt-10">_vect</span><span
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class="cmtt-10">_type</span></a> containing numbers of type specified in Table <a
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href="#x26-63001r8">8<!--tex4ht:ref: tab:f90nrm2 --></a>.
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</dd><dt class="description">
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<span
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class="cmbx-10">desc</span><span
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class="cmbx-10">_a</span> </dt><dd
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class="description">contains data structures for communications.<br
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class="newline" />Scope: <span
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class="cmbx-10">local </span><br
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class="newline" />Type: <span
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class="cmbx-10">required</span><br
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class="newline" />Intent: <span
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class="cmbx-10">in</span>.<br
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class="newline" />Specified as: an object of type <a
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href="userhtmlsu5.html#descdata"><span
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class="cmtt-10">psb</span><span
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class="cmtt-10">_desc</span><span
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class="cmtt-10">_type</span></a>.
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</dd><dt class="description">
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<span
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class="cmbx-10">global</span> </dt><dd
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class="description">Specifies whether the computation should include the global reduction
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across all processes.<br
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class="newline" />Scope: <span
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class="cmbx-10">global </span><br
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class="newline" />Type: <span
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class="cmbx-10">optional</span>.<br
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class="newline" />Intent: <span
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class="cmbx-10">in</span>.<br
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class="newline" />Specified as: a logical scalar. Default: <span class="lstinline"></span><span
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class="cmtt-10">global</span><span
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class="cmtt-10">=.</span><span
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class="cmtt-10">true</span><span
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class="cmtt-10">.</span><br
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class="newline" />
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</dd><dt class="description">
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<span
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class="cmbx-10">On Return</span> </dt><dd
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class="description">
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</dd><dt class="description">
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<span
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class="cmbx-10">Function Value</span> </dt><dd
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class="description">is the 2-norm of vector <span
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class="cmmi-10">x</span>.<br
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class="newline" />Scope: <span
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class="cmbx-10">global </span>unless the optional variable <span class="lstinline"></span><span
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class="cmtt-10">global</span><span
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class="cmtt-10">=.</span><span
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class="cmtt-10">false</span><span
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class="cmtt-10">.</span> has been
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specified<br
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class="newline" />Type: <span
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class="cmbx-10">required </span><br
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class="newline" />Specified as: a long precision real number.
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</dd><dt class="description">
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<span
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class="cmbx-10">info</span> </dt><dd
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class="description">Error code.<br
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class="newline" />Scope: <span
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class="cmbx-10">local </span><br
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class="newline" />Type: <span
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class="cmbx-10">required </span><br
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class="newline" />Intent: <span
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class="cmbx-10">out</span>.<br
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class="newline" />An integer value; 0 means no error has been detected.</dd></dl>
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<!--l. 718--><p class="noindent" ><span
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class="cmbx-12">Notes</span>
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<ol class="enumerate1" >
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<li
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class="enumerate" id="x26-63003x1">The computation of a global result requires a global communication, which
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entails a significant overhead. It may be necessary and/or advisable to compute
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multiple norms at the same time; in this case, it is possible to improve the
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runtime efficiency by using the following scheme: <!--l. 725-->
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<div class="lstlisting" id="listing-4"><span class="label"><a
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id="x26-63004r1"></a></span>    vres(1) = psb_genrm2(x1,desc_a,info,global=.<span
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class="cmbx-10">false</span>.) <br /><span class="label"><a
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id="x26-63005r2"></a></span>    vres(2) = psb_genrm2(x2,desc_a,info,global=.<span
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class="cmbx-10">false</span>.) <br /><span class="label"><a
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id="x26-63006r3"></a></span>    vres(3) = psb_genrm2(x3,desc_a,info,global=.<span
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class="cmbx-10">false</span>.) <br /><span class="label"><a
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id="x26-63007r4"></a></span>    <span
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class="cmbx-10">call</span> psb_nrm2(ctxt,vres(1:3))
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</div>
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<!--l. 731--><p class="noindent" >In this way the global communication, which for small sizes is a latency-bound
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operation, is invoked only once.</li></ol>
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<!--l. 737--><div class="crosslinks"><p class="noindent">[<a
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href="userhtmlsu21.html" >next</a>] [<a
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href="userhtmlsu16.html" >prev</a>] [<a
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href="userhtmlsu16.html#tailuserhtmlsu16.html" >prev-tail</a>] [<a
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href="userhtmlsu17.html" >front</a>] [<a
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href="userhtmlsu12.html#userhtmlsu20.html" >up</a>] </p></div>
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<!--l. 737--><p class="indent" > <a
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id="tailuserhtmlsu17.html"></a>
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</body></html>
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