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<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
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"http://www.w3.org/TR/html4/loose.dtd">
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<html >
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<head><title>psb_norm1 — 1-Norm of Vector</title>
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<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
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<meta name="generator" content="TeX4ht (https://tug.org/tex4ht/)">
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<meta name="originator" content="TeX4ht (https://tug.org/tex4ht/)">
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<!-- html,3 -->
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<meta name="src" content="userhtml.tex">
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</head><body
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>
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<!--l. 476--><div class="crosslinks"><p class="noindent">[<a
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href="userhtmlsu19.html" >next</a>] [<a
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href="userhtmlsu14.html" >prev</a>] [<a
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href="userhtmlsu12.html#tailuserhtmlsu15.html">tail</a>] [<a
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href="userhtmlsu12.html#userhtmlsu18.html" >up</a>] </p></div>
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<h4 class="subsectionHead"><span class="titlemark">4.6 </span> <a
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id="x24-610004.6"></a>psb_norm1 — 1-Norm of Vector</h4>
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<!--l. 478--><p class="noindent" >This function computes the 1-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 1-norm as:
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<center class="math-display" >
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<img
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src="userhtml8x.png" alt="asum ← ∥xi∥
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" class="math-display" ></center>
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<!--l. 481--><p class="nopar" > else if <span
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class="cmmi-10">x </span>is a complex vector then it computes 1-norm as:
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<center class="math-display" >
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<img
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src="userhtml9x.png" alt="asum ← ∥re(x)∥ + ∥im (x)∥
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1 1
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" class="math-display" ></center>
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<!--l. 483--><p class="nopar" >
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<!--l. 486--><p class="indent" > <span class="lstinline"></span><span
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class="cmtt-10">psb_geasum</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> <span class="lstinline"></span><span
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class="cmtt-10">psb_norm1</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>
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<div class="table">
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<!--l. 489--><p class="indent" > <a
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id="x24-61001r6"></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. 490--><p class="noindent" >
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<div class="tabular"> <table id="TBL-6" class="tabular"
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cellspacing="0" cellpadding="0"
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><colgroup id="TBL-6-1g"><col
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id="TBL-6-1"><col
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id="TBL-6-2"><col
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id="TBL-6-3"></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-6-1-"><td style="white-space:nowrap; text-align:left;" id="TBL-6-1-1"
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class="td11"><span
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class="cmmi-10">asum </span></td><td style="white-space:nowrap; text-align:left;" id="TBL-6-1-2"
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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-6-1-3"
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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-6-2-"><td style="white-space:nowrap; text-align:left;" id="TBL-6-2-1"
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class="td11">Short Precision Real</td><td style="white-space:nowrap; text-align:left;" id="TBL-6-2-2"
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class="td11">Short Precision Real </td><td style="white-space:nowrap; text-align:left;" id="TBL-6-2-3"
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class="td11">psb_geasum</td>
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</tr><tr
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style="vertical-align:baseline;" id="TBL-6-3-"><td style="white-space:nowrap; text-align:left;" id="TBL-6-3-1"
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class="td11">Long Precision Real </td><td style="white-space:nowrap; text-align:left;" id="TBL-6-3-2"
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class="td11">Long Precision Real </td><td style="white-space:nowrap; text-align:left;" id="TBL-6-3-3"
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class="td11">psb_geasum</td>
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</tr><tr
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style="vertical-align:baseline;" id="TBL-6-4-"><td style="white-space:nowrap; text-align:left;" id="TBL-6-4-1"
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class="td11">Short Precision Real</td><td style="white-space:nowrap; text-align:left;" id="TBL-6-4-2"
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class="td11">Short Precision Complex</td><td style="white-space:nowrap; text-align:left;" id="TBL-6-4-3"
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class="td11">psb_geasum</td>
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</tr><tr
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style="vertical-align:baseline;" id="TBL-6-5-"><td style="white-space:nowrap; text-align:left;" id="TBL-6-5-1"
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class="td11">Long Precision Real </td><td style="white-space:nowrap; text-align:left;" id="TBL-6-5-2"
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class="td11">Long Precision Complex </td><td style="white-space:nowrap; text-align:left;" id="TBL-6-5-3"
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class="td11">psb_geasum</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-6-6-"><td style="white-space:nowrap; text-align:left;" id="TBL-6-6-1"
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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 6: </span><span
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class="content">Data types</span></div><!--tex4ht:label?: x24-61001r6 -->
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</div><hr class="endfloat" />
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</div>
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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="#x24-61001r6">6<!--tex4ht:ref: tab:f90asum --></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 1-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" />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. 543--><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="x24-61003x1">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. 558-->
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<div class="lstlisting" id="listing-3"><span class="label"><a
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id="x24-61004r1"></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"> </span><span
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class="cmtt-10">vres</span><span
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class="cmtt-10">(1)</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"> </span><span
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class="cmtt-10">psb_geasum</span><span
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class="cmtt-10">(</span><span
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class="cmtt-10">x1</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">info</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><span
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class="cmtt-10">false</span><span
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class="cmtt-10">.)</span><span
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class="cmtt-10"> </span><br /><span class="label"><a
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id="x24-61005r2"></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"> </span><span
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class="cmtt-10">vres</span><span
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class="cmtt-10">(2)</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"> </span><span
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class="cmtt-10">psb_geasum</span><span
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class="cmtt-10">(</span><span
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class="cmtt-10">x2</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">info</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><span
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class="cmtt-10">false</span><span
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class="cmtt-10">.)</span><span
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class="cmtt-10"> </span><br /><span class="label"><a
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id="x24-61006r3"></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"> </span><span
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class="cmtt-10">vres</span><span
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class="cmtt-10">(3)</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"> </span><span
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class="cmtt-10">psb_geasum</span><span
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class="cmtt-10">(</span><span
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class="cmtt-10">x3</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">info</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><span
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class="cmtt-10">false</span><span
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class="cmtt-10">.)</span><span
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class="cmtt-10"> </span><br /><span class="label"><a
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id="x24-61007r4"></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"> </span><span
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class="cmtt-10">call</span><span
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class="cmtt-10"> </span><span
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class="cmtt-10">psb_sum</span><span
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class="cmtt-10">(</span><span
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class="cmtt-10">ctxt</span><span
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class="cmtt-10">,</span><span
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class="cmtt-10">vres</span><span
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|
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class="cmtt-10">(1:3))</span>
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</div>
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<!--l. 565--><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. 570--><div class="crosslinks"><p class="noindent">[<a
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href="userhtmlsu19.html" >next</a>] [<a
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href="userhtmlsu14.html" >prev</a>] [<a
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href="userhtmlsu15.html" >front</a>] [<a
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