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<head><title>psb_spsm &#8212; Triangular System Solve</title>
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<h4 class="subsectionHead"><span class="titlemark">4.13 </span> <a
id="x31-680004.13"></a>psb_spsm &#8212; Triangular System Solve</h4>
<!--l. 1081--><p class="noindent" >This subroutine computes the Triangular System Solve:
<!--l. 1083--><p class="indent" > <div class="eqnarray">
<center class="math-display" >
<img
src="userhtml21x.png" alt="y &#x2190; &#x03B1;T- 1x + &#x03B2;y
-1
y &#x2190; &#x03B1;DT x +&#x03B2;y
y &#x2190; &#x03B1;T- 1Dx +&#x03B2;y
y &#x2190; &#x03B1;T- Tx+ &#x03B2;y
y &#x2190; &#x03B1;DT -Tx + &#x03B2;y
- T
y &#x2190; &#x03B1;T Dx + &#x03B2;y
y &#x2190; &#x03B1;T- Hx +&#x03B2;y
y &#x2190; &#x03B1;DT -Hx + &#x03B2;y
y &#x2190; &#x03B1;T- HDx + &#x03B2;y
" class="math-display" ></center>
</div>
<!--l. 1096--><p class="indent" > where:
<dl class="description"><dt class="description">
<span
class="cmmi-10">x</span> </dt><dd
class="description">is the global dense matrix <span
class="cmmi-10">x</span><sub><span
class="cmr-7">:</span><span
class="cmmi-7">,</span><span
class="cmr-7">:</span></sub>
</dd><dt class="description">
<span
class="cmmi-10">y</span> </dt><dd
class="description">is the global dense matrix <span
class="cmmi-10">y</span><sub><span
class="cmr-7">:</span><span
class="cmmi-7">,</span><span
class="cmr-7">:</span></sub>
</dd><dt class="description">
<span
class="cmmi-10">T</span> </dt><dd
class="description">is the global sparse block triangular submatrix <span
class="cmmi-10">T</span>
</dd><dt class="description">
<span
class="cmmi-10">D</span> </dt><dd
class="description">is the scaling diagonal matrix.</dd></dl>
<!--l. 1104--><p class="indent" > <span class="lstinline"></span><span
class="cmtt-10">call</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">psb_spsm</span><span
class="cmtt-10">(</span><span
class="cmtt-10">alpha</span><span
class="cmtt-10">,</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">t</span><span
class="cmtt-10">,</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">x</span><span
class="cmtt-10">,</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">beta</span><span
class="cmtt-10">,</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">y</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">)</span><br
class="newline" /><span class="lstinline"></span><span
class="cmtt-10">call</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">psb_spsm</span><span
class="cmtt-10">(</span><span
class="cmtt-10">alpha</span><span
class="cmtt-10">,</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">t</span><span
class="cmtt-10">,</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">x</span><span
class="cmtt-10">,</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">beta</span><span
class="cmtt-10">,</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">y</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">,</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">trans</span><span
class="cmtt-10">,</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">unit</span><span
class="cmtt-10">,</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">choice</span><span
class="cmtt-10">,</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">diag</span><span
class="cmtt-10">,</span><span
class="cmtt-10">&#x00A0;</span><span
class="cmtt-10">work</span><span
class="cmtt-10">)</span><br
class="newline" />
<div class="table">
<!--l. 1107--><p class="indent" > <a
id="x31-68002r13"></a><hr class="float"><div class="float"
>
<div class="center"
>
<!--l. 1108--><p class="noindent" >
<div class="tabular"> <table id="TBL-13" class="tabular"
cellspacing="0" cellpadding="0"
><colgroup id="TBL-13-1g"><col
id="TBL-13-1"><col
id="TBL-13-2"></colgroup><tr
class="hline"><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-13-1-"><td style="white-space:nowrap; text-align:left;" id="TBL-13-1-1"
class="td11"><span
class="cmmi-10">T</span>, <span
class="cmmi-10">x</span>, <span
class="cmmi-10">y</span>, <span
class="cmmi-10">D</span>, <span
class="cmmi-10">&#x03B1;</span>, <span
class="cmmi-10">&#x03B2; </span></td><td style="white-space:nowrap; text-align:left;" id="TBL-13-1-2"
class="td11"><span
class="cmbx-10">Subroutine</span></td>
</tr><tr
class="hline"><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-13-2-"><td style="white-space:nowrap; text-align:left;" id="TBL-13-2-1"
class="td11">Short Precision Real </td><td style="white-space:nowrap; text-align:left;" id="TBL-13-2-2"
class="td11">psb_spsm </td>
</tr><tr
style="vertical-align:baseline;" id="TBL-13-3-"><td style="white-space:nowrap; text-align:left;" id="TBL-13-3-1"
class="td11">Long Precision Real </td><td style="white-space:nowrap; text-align:left;" id="TBL-13-3-2"
class="td11">psb_spsm </td>
</tr><tr
style="vertical-align:baseline;" id="TBL-13-4-"><td style="white-space:nowrap; text-align:left;" id="TBL-13-4-1"
class="td11">Short Precision Complex</td><td style="white-space:nowrap; text-align:left;" id="TBL-13-4-2"
class="td11">psb_spsm </td>
</tr><tr
style="vertical-align:baseline;" id="TBL-13-5-"><td style="white-space:nowrap; text-align:left;" id="TBL-13-5-1"
class="td11">Long Precision Complex </td><td style="white-space:nowrap; text-align:left;" id="TBL-13-5-2"
class="td11">psb_spsm </td>
</tr><tr
class="hline"><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-13-6-"><td style="white-space:nowrap; text-align:left;" id="TBL-13-6-1"
class="td11"> </td></tr></table></div></div>
<br /> <div class="caption"
><span class="id">Table&#x00A0;13: </span><span
class="content">Data types</span></div><!--tex4ht:label?: x31-68002r13 -->
</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">alpha</span> </dt><dd
class="description">the scalar <span
class="cmmi-10">&#x03B1;</span>.<br
class="newline" />Scope: <span
class="cmbx-10">global </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 number of the data type indicated in Table&#x00A0;<a
href="#x31-68002r13">13<!--tex4ht:ref: tab:f90spsm --></a>.
</dd><dt class="description">
<span
class="cmbx-10">t</span> </dt><dd
class="description">the global portion of the sparse matrix <span
class="cmmi-10">T</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: an object type specified in <span
class="cmsy-10"><3E></span>&#x00A0;<a
href="userhtmlse3.html#x12-90003">3<!--tex4ht:ref: sec:datastruct --></a>.
</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="#x31-68002r13">13<!--tex4ht:ref: tab:f90spsm --></a>. The
rank of <span
class="cmmi-10">x </span>must be the same of <span
class="cmmi-10">y</span>.
</dd><dt class="description">
<span
class="cmbx-10">beta</span> </dt><dd
class="description">the scalar <span
class="cmmi-10">&#x03B2;</span>.<br
class="newline" />Scope: <span
class="cmbx-10">global </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 number of the data type indicated in Table&#x00A0;<a
href="#x31-68002r13">13<!--tex4ht:ref: tab:f90spsm --></a>.
</dd><dt class="description">
<span
class="cmbx-10">y</span> </dt><dd
class="description">the local portion of global dense matrix <span
class="cmmi-10">y</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">inout</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="#x31-68002r13">13<!--tex4ht:ref: tab:f90spsm --></a>. The
rank of <span
class="cmmi-10">y </span>must be the same of <span
class="cmmi-10">x</span>.
</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">trans</span> </dt><dd
class="description">specify with <span
class="cmti-10">unitd </span>the operation to perform.
<dl class="description"><dt class="description">
<span
class="cmbx-10">trans = &#8217;N&#8217;</span> </dt><dd
class="description">the operation is with no transposed matrix
</dd><dt class="description">
<span
class="cmbx-10">trans = &#8217;T&#8217;</span> </dt><dd
class="description">the operation is with transposed matrix.
</dd><dt class="description">
<span
class="cmbx-10">trans = &#8217;C&#8217;</span> </dt><dd
class="description">the operation is with conjugate transposed matrix.</dd></dl>
<!--l. 1177--><p class="noindent" >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" />Default: <span
class="cmmi-10">trans </span>= <span
class="cmmi-10">N</span><br
class="newline" />Specified as: a character variable.
</dd><dt class="description">
<span
class="cmbx-10">unitd</span> </dt><dd
class="description">specify with <span
class="cmti-10">trans </span>the operation to perform.
<dl class="description"><dt class="description">
<span
class="cmbx-10">unitd = &#8217;U&#8217;</span> </dt><dd
class="description">the operation is with no scaling
</dd><dt class="description">
<span
class="cmbx-10">unitd = &#8217;L&#8217;</span> </dt><dd
class="description">the operation is with left scaling
</dd><dt class="description">
<span
class="cmbx-10">unitd = &#8217;R&#8217;</span> </dt><dd
class="description">the operation is with right scaling.</dd></dl>
<!--l. 1188--><p class="noindent" >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" />Default: <span
class="cmmi-10">unitd </span>= <span
class="cmmi-10">U</span><br
class="newline" />Specified as: a character variable.
</dd><dt class="description">
<span
class="cmbx-10">choice</span> </dt><dd
class="description">specifies the update of overlap elements to be performed on exit:
<dl class="description"><dt class="description">
</dt><dd
class="description"><span class="lstinline"></span><span
class="cmtt-10">psb_none_</span>
</dd><dt class="description">
</dt><dd
class="description"><span class="lstinline"></span><span
class="cmtt-10">psb_sum_</span>
</dd><dt class="description">
</dt><dd
class="description"><span class="lstinline"></span><span
class="cmtt-10">psb_avg_</span>
</dd><dt class="description">
</dt><dd
class="description"><span class="lstinline"></span><span
class="cmtt-10">psb_square_root_</span></dd></dl>
<!--l. 1201--><p class="noindent" >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" />Default: <span class="lstinline"></span><span
class="cmtt-10">psb_avg_</span><br
class="newline" />Specified as: an integer variable.
</dd><dt class="description">
<span
class="cmbx-10">diag</span> </dt><dd
class="description">the diagonal scaling matrix.<br
class="newline" />Scope: <span
class="cmbx-10">local </span><br
class="newline" />Type: <span
class="cmbx-10">optional</span><br
class="newline" />Intent: <span
class="cmbx-10">in</span>.<br
class="newline" />Default: <span
class="cmmi-10">diag</span>(1) = 1(<span
class="cmmi-10">noscaling</span>)<br
class="newline" />Specified as: a rank one array containing numbers of the type indicated in
Table&#x00A0;<a
href="#x31-68002r13">13<!--tex4ht:ref: tab:f90spsm --></a>.
</dd><dt class="description">
<span
class="cmbx-10">work</span> </dt><dd
class="description">a work array. <br
class="newline" />Scope: <span
class="cmbx-10">local </span><br
class="newline" />Type: <span
class="cmbx-10">optional</span><br
class="newline" />Intent: <span
class="cmbx-10">inout</span>.<br
class="newline" />Specified as: a rank one array of the same type of <span
class="cmmi-10">x </span>with the TARGET
attribute.
</dd><dt class="description">
<span
class="cmbx-10">On Return</span> </dt><dd
class="description">
</dd><dt class="description">
<span
class="cmbx-10">y</span> </dt><dd
class="description">the local portion of global dense matrix <span
class="cmmi-10">y</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">inout</span>.<br
class="newline" />Specified as: an array of rank one or two containing numbers of type specified
in Table&#x00A0;<a
href="#x31-68002r13">13<!--tex4ht:ref: tab:f90spsm --></a>.
</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>
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