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@ -16,7 +16,7 @@ href="userhtmlse11.html#tailuserhtmlse11.html" >prev-tail</a>] [<a
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href="userhtmlse9.html#tailuserhtmlse12.html">tail</a>] [<a
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href="userhtmlse9.html#tailuserhtmlse12.html">tail</a>] [<a
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href="userhtml.html# " >up</a>] </p></div>
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href="userhtml.html# " >up</a>] </p></div>
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<h3 class="sectionHead"><span class="titlemark">12 </span> <a
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<h3 class="sectionHead"><span class="titlemark">12 </span> <a
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id="x19-14600012"></a>Extensions</h3>
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id="x19-14800012"></a>Extensions</h3>
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<!--l. 3--><p class="noindent" >The EXT, CUDA and RSB subdirectories contains a set of extensions to the base
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<!--l. 3--><p class="noindent" >The EXT, CUDA and RSB subdirectories contains a set of extensions to the base
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library. The extensions provide additional storage formats beyond the ones already
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library. The extensions provide additional storage formats beyond the ones already
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contained in the base library, as well as interfaces to:
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contained in the base library, as well as interfaces to:
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@ -49,7 +49,7 @@ in <span class="cite">[<a
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href="userhtmlli2.html#XOurTechRep">23</a>]</span>.
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href="userhtmlli2.html#XOurTechRep">23</a>]</span>.
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<!--l. 19--><p class="noindent" >
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<!--l. 19--><p class="noindent" >
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<h4 class="subsectionHead"><span class="titlemark">12.1 </span> <a
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<h4 class="subsectionHead"><span class="titlemark">12.1 </span> <a
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id="x19-14700012.1"></a>Using the extensions</h4>
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id="x19-14900012.1"></a>Using the extensions</h4>
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<!--l. 21--><p class="noindent" >A sample application using the PSBLAS extensions will contain the following
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<!--l. 21--><p class="noindent" >A sample application using the PSBLAS extensions will contain the following
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steps:
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steps:
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<ul class="itemize1">
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<ul class="itemize1">
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@ -82,7 +82,7 @@ matrices):
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<div class="minipage"><pre class="verbatim" id="verbatim-103">
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<div class="minipage"><pre class="verbatim" id="verbatim-105">
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program my_cuda_test
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program my_cuda_test
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  use psb_base_mod
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  use psb_base_mod
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  use psb_util_mod
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  use psb_util_mod
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@ -142,7 +142,7 @@ speed of the sparse matrix-vector product with the various data structures inclu
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in the library.
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in the library.
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<!--l. 146--><p class="noindent" >
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<!--l. 146--><p class="noindent" >
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<h4 class="subsectionHead"><span class="titlemark">12.2 </span> <a
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<h4 class="subsectionHead"><span class="titlemark">12.2 </span> <a
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id="x19-14800012.2"></a>Extensions’ Data Structures</h4>
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id="x19-15000012.2"></a>Extensions’ Data Structures</h4>
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<!--l. 150--><p class="noindent" >Access to the facilities provided by the EXT library is mainly achieved through
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<!--l. 150--><p class="noindent" >Access to the facilities provided by the EXT library is mainly achieved through
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the data types that are provided within. The data classes are derived from
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the data types that are provided within. The data classes are derived from
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the base classes in PSBLAS, through the Fortran 2003 mechanism of <span
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the base classes in PSBLAS, through the Fortran 2003 mechanism of <span
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@ -153,20 +153,20 @@ href="userhtmlli2.html#XMRC:11">18</a>]</span>.
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<!--l. 155--><p class="indent" > The data classes are divided between the general purpose CPU extensions, the
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<!--l. 155--><p class="indent" > The data classes are divided between the general purpose CPU extensions, the
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GPU interfaces and the RSB interfaces. In the description we will make use of the
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GPU interfaces and the RSB interfaces. In the description we will make use of the
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notation introduced in Table <a
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notation introduced in Table <a
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href="#x19-148001r22">22<!--tex4ht:ref: tab:notation --></a>.
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href="#x19-150001r22">22<!--tex4ht:ref: tab:notation --></a>.
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<div class="table">
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<div class="table">
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<!--l. 160--><p class="indent" > <a
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<!--l. 160--><p class="indent" > <a
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id="x19-148001r22"></a><hr class="float"><div class="float"
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id="x19-150001r22"></a><hr class="float"><div class="float"
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>
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>
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<div class="caption"
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<div class="caption"
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><span class="id">Table 22: </span><span
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><span class="id">Table 22: </span><span
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class="content">Notation for parameters describing a sparse matrix</span></div><!--tex4ht:label?: x19-148001r22 -->
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class="content">Notation for parameters describing a sparse matrix</span></div><!--tex4ht:label?: x19-150001r22 -->
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<div class="center"
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<div class="center"
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>
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>
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<!--l. 162--><p class="noindent" >
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<!--l. 162--><p class="noindent" >
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@ -276,7 +276,7 @@ class="td11"> </td></tr></table>
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<a
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<a
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id="x19-148002r5"></a>
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id="x19-150002r5"></a>
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@ -285,18 +285,18 @@ src="mat.png" alt="PIC"
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width="147" height="147" >
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width="147" height="147" >
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<br /> <div class="caption"
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<br /> <div class="caption"
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><span class="id">Figure 5: </span><span
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><span class="id">Figure 5: </span><span
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class="content">Example of sparse matrix</span></div><!--tex4ht:label?: x19-148002r5 -->
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class="content">Example of sparse matrix</span></div><!--tex4ht:label?: x19-150002r5 -->
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<!--l. 198--><p class="indent" > </div><hr class="endfigure">
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<!--l. 198--><p class="indent" > </div><hr class="endfigure">
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<h4 class="subsectionHead"><span class="titlemark">12.3 </span> <a
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<h4 class="subsectionHead"><span class="titlemark">12.3 </span> <a
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id="x19-14900012.3"></a>CPU-class extensions</h4>
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id="x19-15100012.3"></a>CPU-class extensions</h4>
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<!--l. 203--><p class="noindent" >
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<!--l. 203--><p class="noindent" >
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<h5 class="likesubsubsectionHead"><a
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<h5 class="likesubsubsectionHead"><a
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id="x19-150000"></a>ELLPACK</h5>
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id="x19-152000"></a>ELLPACK</h5>
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<!--l. 205--><p class="noindent" >The ELLPACK/ITPACK format (shown in Figure <a
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<!--l. 205--><p class="noindent" >The ELLPACK/ITPACK format (shown in Figure <a
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href="#x19-150001r6">6<!--tex4ht:ref: fig:ell --></a>) comprises two 2-dimensional
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href="#x19-152001r6">6<!--tex4ht:ref: fig:ell --></a>) comprises two 2-dimensional
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arrays <span class="obeylines-h"><span class="verb"><span
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arrays <span class="obeylines-h"><span class="verb"><span
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class="cmtt-10">AS</span></span></span> and <span class="obeylines-h"><span class="verb"><span
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class="cmtt-10">AS</span></span></span> and <span class="obeylines-h"><span class="verb"><span
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class="cmtt-10">JA</span></span></span> with <span class="obeylines-h"><span class="verb"><span
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class="cmtt-10">JA</span></span></span> with <span class="obeylines-h"><span class="verb"><span
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@ -317,7 +317,7 @@ row.
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<a
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<a
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id="x19-150001r6"></a>
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id="x19-152001r6"></a>
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@ -327,13 +327,13 @@ width="233" height="233" >
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<br /> <div class="caption"
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<br /> <div class="caption"
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><span class="id">Figure 6: </span><span
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><span class="id">Figure 6: </span><span
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class="content">ELLPACK compression of matrix in Figure <a
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class="content">ELLPACK compression of matrix in Figure <a
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href="#x19-148002r5">5<!--tex4ht:ref: fig:dense --></a></span></div><!--tex4ht:label?: x19-150001r6 -->
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href="#x19-150002r5">5<!--tex4ht:ref: fig:dense --></a></span></div><!--tex4ht:label?: x19-152001r6 -->
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<!--l. 225--><p class="indent" > </div><hr class="endfigure">
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<!--l. 225--><p class="indent" > </div><hr class="endfigure">
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<a
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<a
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id="x19-150002r1"></a>
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id="x19-152002r1"></a>
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@ -343,8 +343,8 @@ href="#x19-148002r5">5<!--tex4ht:ref: fig:dense --></a></span></div><!--tex4ht:l
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<!--l. 231-->
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<!--l. 231-->
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<pre class="lstlisting" id="listing-220"><span class="label"><a
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<pre class="lstlisting" id="listing-221"><span class="label"><a
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id="x19-150003r1"></a></span><span
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id="x19-152003r1"></a></span><span
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class="cmtt-9"> </span><span
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class="cmtt-9"> </span><span
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class="cmtt-9"> </span><span
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class="cmtt-9"> </span><span
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class="cmtt-9"> </span><span style="color:#000000"><span
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class="cmtt-9"> </span><span style="color:#000000"><span
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@ -353,7 +353,7 @@ class="cmtt-9">i</span></span><span style="color:#000000"><span
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class="cmtt-9">=1,</span></span><span style="color:#000000"><span
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class="cmtt-9">=1,</span></span><span style="color:#000000"><span
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class="cmtt-9">n</span></span>
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class="cmtt-9">n</span></span>
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<span class="label"><a
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<span class="label"><a
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id="x19-150004r2"></a></span><span
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id="x19-152004r2"></a></span><span
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class="cmtt-9"> </span><span
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class="cmtt-9"> </span><span
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class="cmtt-9"> </span><span
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class="cmtt-9"> </span><span
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class="cmtt-9"> </span><span
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class="cmtt-9"> </span><span
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@ -362,7 +362,7 @@ class="cmtt-9"> </span><span style="color:#000000"><span
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class="cmtt-9">t</span></span><span style="color:#000000"><span
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class="cmtt-9">t</span></span><span style="color:#000000"><span
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class="cmtt-9">=0</span></span>
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class="cmtt-9">=0</span></span>
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<span class="label"><a
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<span class="label"><a
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id="x19-150005r3"></a></span><span
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id="x19-152005r3"></a></span><span
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class="cmtt-9"> </span><span
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class="cmtt-9"> </span><span
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class="cmtt-9"> </span><span
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class="cmtt-9"> </span><span
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class="cmtt-9"> </span><span
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class="cmtt-9"> </span><span
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@ -373,7 +373,7 @@ class="cmtt-9">j</span></span><span style="color:#000000"><span
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class="cmtt-9">=1,</span></span><span style="color:#000000"><span
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class="cmtt-9">=1,</span></span><span style="color:#000000"><span
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class="cmtt-9">maxnzr</span></span>
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class="cmtt-9">maxnzr</span></span>
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<span class="label"><a
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<span class="label"><a
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id="x19-150006r4"></a></span><span
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id="x19-152006r4"></a></span><span
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class="cmtt-9"> </span><span
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class="cmtt-9"> </span><span
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class="cmtt-9"> </span><span
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class="cmtt-9"> </span><span
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class="cmtt-9"> </span><span
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class="cmtt-9"> </span><span
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@ -401,7 +401,7 @@ class="cmtt-9">,</span></span><span style="color:#000000"><span
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class="cmtt-9">j</span></span><span style="color:#000000"><span
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class="cmtt-9">j</span></span><span style="color:#000000"><span
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class="cmtt-9">))</span></span>
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class="cmtt-9">))</span></span>
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<span class="label"><a
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<span class="label"><a
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id="x19-150007r5"></a></span><span
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id="x19-152007r5"></a></span><span
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class="cmtt-9"> </span><span
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class="cmtt-9"> </span><span
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class="cmtt-9"> </span><span
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class="cmtt-9"> </span><span
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class="cmtt-9"> </span><span
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class="cmtt-9"> </span><span
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@ -410,7 +410,7 @@ class="cmtt-9"> </span><span style="color:#000000"><span
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class="cmtt-9">end</span></span><span style="color:#000000"> </span><span style="color:#000000"><span
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class="cmtt-9">end</span></span><span style="color:#000000"> </span><span style="color:#000000"><span
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class="cmtt-9">do</span></span>
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class="cmtt-9">do</span></span>
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<span class="label"><a
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<span class="label"><a
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id="x19-150008r6"></a></span><span
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id="x19-152008r6"></a></span><span
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class="cmtt-9"> </span><span
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class="cmtt-9"> </span><span
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class="cmtt-9"> </span><span
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class="cmtt-9"> </span><span
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class="cmtt-9"> </span><span
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class="cmtt-9"> </span><span
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@ -423,7 +423,7 @@ class="cmtt-9">)</span></span><span style="color:#000000"> </span><span style="c
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class="cmtt-9">=</span></span><span style="color:#000000"> </span><span style="color:#000000"><span
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class="cmtt-9">=</span></span><span style="color:#000000"> </span><span style="color:#000000"><span
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class="cmtt-9">t</span></span>
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class="cmtt-9">t</span></span>
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<span class="label"><a
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<span class="label"><a
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id="x19-150009r7"></a></span><span
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id="x19-152009r7"></a></span><span
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class="cmtt-9"> </span><span
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class="cmtt-9"> </span><span
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class="cmtt-9"> </span><span
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class="cmtt-9"> </span><span
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class="cmtt-9"> </span><span style="color:#000000"><span
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class="cmtt-9"> </span><span style="color:#000000"><span
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@ -431,9 +431,9 @@ class="cmtt-9">end</span></span><span style="color:#000000"> </span><span style=
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class="cmtt-9">do</span></span></pre>
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class="cmtt-9">do</span></span></pre>
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<a
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<a
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id="x19-150010r1"></a>
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id="x19-152010r1"></a>
|
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<a
|
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|
<a
|
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id="x19-150011"></a>
|
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id="x19-152011"></a>
|
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<span
|
|
|
|
<span
|
|
|
|
class="pplb7t-">Algorithm</span><span
|
|
|
|
class="pplb7t-">Algorithm</span><span
|
|
|
|
class="pplb7t-"> 1:</span>  Matrix-Vector product in ELL format
|
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|
class="pplb7t-"> 1:</span>  Matrix-Vector product in ELL format
|
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|
@ -446,7 +446,7 @@ class="zplmr7m-">y </span><span
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class="zplmr7t-">= </span><span
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class="zplmr7t-">= </span><span
|
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class="zplmr7m-">Ax </span>can be computed with the code shown in
|
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|
class="zplmr7m-">Ax </span>can be computed with the code shown in
|
|
|
|
Alg. <a
|
|
|
|
Alg. <a
|
|
|
|
href="#x19-150010r1">1<!--tex4ht:ref: alg:ell --></a>; it costs one memory write per outer iteration, plus three memory reads and
|
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href="#x19-152010r1">1<!--tex4ht:ref: alg:ell --></a>; it costs one memory write per outer iteration, plus three memory reads and
|
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|
two floating-point operations per inner iteration.
|
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two floating-point operations per inner iteration.
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|
<!--l. 247--><p class="indent" > Unless all rows have exactly the same number of nonzeros, some of the
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<!--l. 247--><p class="indent" > Unless all rows have exactly the same number of nonzeros, some of the
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coefficients in the <span class="obeylines-h"><span class="verb"><span
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coefficients in the <span class="obeylines-h"><span class="verb"><span
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@ -455,12 +455,12 @@ overhead both in terms of memory space and redundant operations (multiplications
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by zero). The overhead can be acceptable if:
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by zero). The overhead can be acceptable if:
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<ol class="enumerate1" >
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<ol class="enumerate1" >
|
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<li
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<li
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class="enumerate" id="x19-150013x1">
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class="enumerate" id="x19-152013x1">
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<!--l. 253--><p class="noindent" >The maximum number of nonzeros per row is not much larger than the
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<!--l. 253--><p class="noindent" >The maximum number of nonzeros per row is not much larger than the
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average;
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average;
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</li>
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</li>
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<li
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|
<li
|
|
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|
class="enumerate" id="x19-150015x2">
|
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class="enumerate" id="x19-152015x2">
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<!--l. 255--><p class="noindent" >The regularity of the data structure allows for faster code, e.g. by allowing
|
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|
<!--l. 255--><p class="noindent" >The regularity of the data structure allows for faster code, e.g. by allowing
|
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|
|
vectorization, thereby offsetting the additional storage requirements.</li></ol>
|
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|
vectorization, thereby offsetting the additional storage requirements.</li></ol>
|
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<!--l. 259--><p class="noindent" >In the extreme case where the input matrix has one full row, the ELLPACK
|
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|
<!--l. 259--><p class="noindent" >In the extreme case where the input matrix has one full row, the ELLPACK
|
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@ -473,7 +473,7 @@ class="cmtt-10">psb_T_ell_sparse_mat</span></span></span>:
|
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|
<div class="center"
|
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|
<div class="center"
|
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>
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>
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<!--l. 281--><p class="noindent" >
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|
<!--l. 281--><p class="noindent" >
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|
<div class="minipage"><pre class="verbatim" id="verbatim-104">
|
|
|
|
<div class="minipage"><pre class="verbatim" id="verbatim-106">
|
|
|
|
  type, extends(psb_d_base_sparse_mat) :: psb_d_ell_sparse_mat
|
|
|
|
  type, extends(psb_d_base_sparse_mat) :: psb_d_ell_sparse_mat
|
|
|
|
    !
|
|
|
|
    !
|
|
|
|
    ! ITPACK/ELL format, extended.
|
|
|
|
    ! ITPACK/ELL format, extended.
|
|
|
|
@ -488,7 +488,7 @@ class="cmtt-10">psb_T_ell_sparse_mat</span></span></span>:
|
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|
</pre>
|
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|
|
</pre>
|
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|
<!--l. 295--><p class="nopar" > </div></div>
|
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|
<!--l. 295--><p class="nopar" > </div></div>
|
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|
|
<h5 class="likesubsubsectionHead"><a
|
|
|
|
<h5 class="likesubsubsectionHead"><a
|
|
|
|
id="x19-151000"></a>Hacked ELLPACK</h5>
|
|
|
|
id="x19-153000"></a>Hacked ELLPACK</h5>
|
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|
|
|
|
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@ -564,7 +564,7 @@ format.
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|
<a
|
|
|
|
<a
|
|
|
|
id="x19-151001r7"></a>
|
|
|
|
id="x19-153001r7"></a>
|
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@ -574,7 +574,7 @@ width="248" height="248" >
|
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|
<br /> <div class="caption"
|
|
|
|
<br /> <div class="caption"
|
|
|
|
><span class="id">Figure 7: </span><span
|
|
|
|
><span class="id">Figure 7: </span><span
|
|
|
|
class="content">Hacked ELLPACK compression of matrix in Figure <a
|
|
|
|
class="content">Hacked ELLPACK compression of matrix in Figure <a
|
|
|
|
href="#x19-148002r5">5<!--tex4ht:ref: fig:dense --></a></span></div><!--tex4ht:label?: x19-151001r7 -->
|
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|
|
href="#x19-150002r5">5<!--tex4ht:ref: fig:dense --></a></span></div><!--tex4ht:label?: x19-153001r7 -->
|
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@ -586,7 +586,7 @@ class="cmtt-10">psb_T_hll_sparse_mat</span></span></span>:
|
|
|
|
<div class="center"
|
|
|
|
<div class="center"
|
|
|
|
>
|
|
|
|
>
|
|
|
|
<!--l. 374--><p class="noindent" >
|
|
|
|
<!--l. 374--><p class="noindent" >
|
|
|
|
<div class="minipage"><pre class="verbatim" id="verbatim-105">
|
|
|
|
<div class="minipage"><pre class="verbatim" id="verbatim-107">
|
|
|
|
  type, extends(psb_d_base_sparse_mat) :: psb_d_hll_sparse_mat
|
|
|
|
  type, extends(psb_d_base_sparse_mat) :: psb_d_hll_sparse_mat
|
|
|
|
    !
|
|
|
|
    !
|
|
|
|
    ! HLL format. (Hacked ELL)
|
|
|
|
    ! HLL format. (Hacked ELL)
|
|
|
|
@ -601,9 +601,9 @@ class="cmtt-10">psb_T_hll_sparse_mat</span></span></span>:
|
|
|
|
</pre>
|
|
|
|
</pre>
|
|
|
|
<!--l. 388--><p class="nopar" > </div></div>
|
|
|
|
<!--l. 388--><p class="nopar" > </div></div>
|
|
|
|
<h5 class="likesubsubsectionHead"><a
|
|
|
|
<h5 class="likesubsubsectionHead"><a
|
|
|
|
id="x19-152000"></a>Diagonal storage</h5>
|
|
|
|
id="x19-154000"></a>Diagonal storage</h5>
|
|
|
|
<!--l. 396--><p class="noindent" >The DIAgonal (DIA) format (shown in Figure <a
|
|
|
|
<!--l. 396--><p class="noindent" >The DIAgonal (DIA) format (shown in Figure <a
|
|
|
|
href="#x19-152001r8">8<!--tex4ht:ref: fig:dia --></a>) has a 2-dimensional array <span class="obeylines-h"><span class="verb"><span
|
|
|
|
href="#x19-154001r8">8<!--tex4ht:ref: fig:dia --></a>) has a 2-dimensional array <span class="obeylines-h"><span class="verb"><span
|
|
|
|
class="cmtt-10">AS</span></span></span>
|
|
|
|
class="cmtt-10">AS</span></span></span>
|
|
|
|
containing in each column the coefficients along a diagonal of the matrix, and an
|
|
|
|
containing in each column the coefficients along a diagonal of the matrix, and an
|
|
|
|
integer array <span class="obeylines-h"><span class="verb"><span
|
|
|
|
integer array <span class="obeylines-h"><span class="verb"><span
|
|
|
|
@ -614,7 +614,7 @@ are padded with zeros as necessary.
|
|
|
|
class="zplmr7m-">y </span><span
|
|
|
|
class="zplmr7m-">y </span><span
|
|
|
|
class="zplmr7t-">= </span><span
|
|
|
|
class="zplmr7t-">= </span><span
|
|
|
|
class="zplmr7m-">Ax </span>is shown in Alg. <a
|
|
|
|
class="zplmr7m-">Ax </span>is shown in Alg. <a
|
|
|
|
href="#x19-152003r2">2<!--tex4ht:ref: alg:dia --></a>; it
|
|
|
|
href="#x19-154003r2">2<!--tex4ht:ref: alg:dia --></a>; it
|
|
|
|
costs one memory read per outer iteration, plus three memory reads, one memory
|
|
|
|
costs one memory read per outer iteration, plus three memory reads, one memory
|
|
|
|
write and two floating-point operations per inner iteration. The accesses to
|
|
|
|
write and two floating-point operations per inner iteration. The accesses to
|
|
|
|
<span class="obeylines-h"><span class="verb"><span
|
|
|
|
<span class="obeylines-h"><span class="verb"><span
|
|
|
|
@ -627,7 +627,7 @@ required.
|
|
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|
|
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|
|
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|
|
|
|
|
|
|
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|
|
<a
|
|
|
|
<a
|
|
|
|
id="x19-152001r8"></a>
|
|
|
|
id="x19-154001r8"></a>
|
|
|
|
|
|
|
|
|
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|
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|
@ -637,13 +637,13 @@ width="248" height="248" >
|
|
|
|
<br /> <div class="caption"
|
|
|
|
<br /> <div class="caption"
|
|
|
|
><span class="id">Figure 8: </span><span
|
|
|
|
><span class="id">Figure 8: </span><span
|
|
|
|
class="content">DIA compression of matrix in Figure <a
|
|
|
|
class="content">DIA compression of matrix in Figure <a
|
|
|
|
href="#x19-148002r5">5<!--tex4ht:ref: fig:dense --></a></span></div><!--tex4ht:label?: x19-152001r8 -->
|
|
|
|
href="#x19-150002r5">5<!--tex4ht:ref: fig:dense --></a></span></div><!--tex4ht:label?: x19-154001r8 -->
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
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|
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|
|
<!--l. 419--><p class="indent" > </div><hr class="endfigure">
|
|
|
|
<!--l. 419--><p class="indent" > </div><hr class="endfigure">
|
|
|
|
<a
|
|
|
|
<a
|
|
|
|
id="x19-152002r2"></a>
|
|
|
|
id="x19-154002r2"></a>
|
|
|
|
|
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|
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|
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|
|
@ -655,7 +655,7 @@ href="#x19-148002r5">5<!--tex4ht:ref: fig:dense --></a></span></div><!--tex4ht:l
|
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|
|
<div class="center"
|
|
|
|
<div class="center"
|
|
|
|
>
|
|
|
|
>
|
|
|
|
<!--l. 437--><p class="noindent" >
|
|
|
|
<!--l. 437--><p class="noindent" >
|
|
|
|
<div class="minipage"><pre class="verbatim" id="verbatim-106">
|
|
|
|
<div class="minipage"><pre class="verbatim" id="verbatim-108">
|
|
|
|
    do j=1,ndiag
|
|
|
|
    do j=1,ndiag
|
|
|
|
      if (offset(j) > 0) then
|
|
|
|
      if (offset(j) > 0) then
|
|
|
|
        ir1 = 1; ir2 = m - offset(j);
|
|
|
|
        ir1 = 1; ir2 = m - offset(j);
|
|
|
|
@ -669,9 +669,9 @@ href="#x19-148002r5">5<!--tex4ht:ref: fig:dense --></a></span></div><!--tex4ht:l
|
|
|
|
</pre>
|
|
|
|
</pre>
|
|
|
|
<!--l. 450--><p class="nopar" > </div></div>
|
|
|
|
<!--l. 450--><p class="nopar" > </div></div>
|
|
|
|
<a
|
|
|
|
<a
|
|
|
|
id="x19-152003r2"></a>
|
|
|
|
id="x19-154003r2"></a>
|
|
|
|
<a
|
|
|
|
<a
|
|
|
|
id="x19-152004"></a>
|
|
|
|
id="x19-154004"></a>
|
|
|
|
<span
|
|
|
|
<span
|
|
|
|
class="pplb7t-">Algorithm</span><span
|
|
|
|
class="pplb7t-">Algorithm</span><span
|
|
|
|
class="pplb7t-"> 2:</span>  Matrix-Vector product in DIA format
|
|
|
|
class="pplb7t-"> 2:</span>  Matrix-Vector product in DIA format
|
|
|
|
@ -684,7 +684,7 @@ class="cmtt-10">psb_T_dia_sparse_mat</span></span></span>:
|
|
|
|
<div class="center"
|
|
|
|
<div class="center"
|
|
|
|
>
|
|
|
|
>
|
|
|
|
<!--l. 473--><p class="noindent" >
|
|
|
|
<!--l. 473--><p class="noindent" >
|
|
|
|
<div class="minipage"><pre class="verbatim" id="verbatim-107">
|
|
|
|
<div class="minipage"><pre class="verbatim" id="verbatim-109">
|
|
|
|
  type, extends(psb_d_base_sparse_mat) :: psb_d_dia_sparse_mat
|
|
|
|
  type, extends(psb_d_base_sparse_mat) :: psb_d_dia_sparse_mat
|
|
|
|
    !
|
|
|
|
    !
|
|
|
|
    ! DIA format, extended.
|
|
|
|
    ! DIA format, extended.
|
|
|
|
@ -698,7 +698,7 @@ class="cmtt-10">psb_T_dia_sparse_mat</span></span></span>:
|
|
|
|
</pre>
|
|
|
|
</pre>
|
|
|
|
<!--l. 486--><p class="nopar" > </div></div>
|
|
|
|
<!--l. 486--><p class="nopar" > </div></div>
|
|
|
|
<h5 class="likesubsubsectionHead"><a
|
|
|
|
<h5 class="likesubsubsectionHead"><a
|
|
|
|
id="x19-153000"></a>Hacked DIA</h5>
|
|
|
|
id="x19-155000"></a>Hacked DIA</h5>
|
|
|
|
<!--l. 495--><p class="noindent" >Storage by DIAgonals is an attractive option for matrices whose coefficients are
|
|
|
|
<!--l. 495--><p class="noindent" >Storage by DIAgonals is an attractive option for matrices whose coefficients are
|
|
|
|
located on a small set of diagonals, since they do away with storing explicitly the
|
|
|
|
located on a small set of diagonals, since they do away with storing explicitly the
|
|
|
|
indices and therefore reduce significantly memory traffic. However, having a few
|
|
|
|
indices and therefore reduce significantly memory traffic. However, having a few
|
|
|
|
@ -749,7 +749,7 @@ class="pplri7t-">hackOffsets[k]</span>.
|
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|
<a
|
|
|
|
<a
|
|
|
|
id="x19-153001r9"></a>
|
|
|
|
id="x19-155001r9"></a>
|
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|
@ -759,7 +759,7 @@ width="248" height="248" >
|
|
|
|
<br /> <div class="caption"
|
|
|
|
<br /> <div class="caption"
|
|
|
|
><span class="id">Figure 9: </span><span
|
|
|
|
><span class="id">Figure 9: </span><span
|
|
|
|
class="content">Hacked DIA compression of matrix in Figure <a
|
|
|
|
class="content">Hacked DIA compression of matrix in Figure <a
|
|
|
|
href="#x19-148002r5">5<!--tex4ht:ref: fig:dense --></a></span></div><!--tex4ht:label?: x19-153001r9 -->
|
|
|
|
href="#x19-150002r5">5<!--tex4ht:ref: fig:dense --></a></span></div><!--tex4ht:label?: x19-155001r9 -->
|
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@ -769,7 +769,7 @@ class="cmtt-10">psb_T_hdia_sparse_mat</span></span></span>:
|
|
|
|
<div class="center"
|
|
|
|
<div class="center"
|
|
|
|
>
|
|
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|
>
|
|
|
|
<!--l. 568--><p class="noindent" >
|
|
|
|
<!--l. 568--><p class="noindent" >
|
|
|
|
<div class="minipage"><pre class="verbatim" id="verbatim-108">
|
|
|
|
<div class="minipage"><pre class="verbatim" id="verbatim-110">
|
|
|
|
  type pm
|
|
|
|
  type pm
|
|
|
|
     real(psb_dpk_), allocatable  :: data(:,:)
|
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|
|
     real(psb_dpk_), allocatable  :: data(:,:)
|
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|
|
  end type pm
|
|
|
|
  end type pm
|
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|
|
@ -804,7 +804,7 @@ class="cmtt-10">psb_T_hdia_sparse_mat</span></span></span>:
|
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<h4 class="subsectionHead"><span class="titlemark">12.4 </span> <a
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<h4 class="subsectionHead"><span class="titlemark">12.4 </span> <a
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id="x19-15400012.4"></a>CUDA-class extensions</h4>
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id="x19-15600012.4"></a>CUDA-class extensions</h4>
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<!--l. 4--><p class="noindent" >For computing with CUDA we define a dual memorization strategy in which each
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<!--l. 4--><p class="noindent" >For computing with CUDA we define a dual memorization strategy in which each
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variable on the CPU (“host”) side has a GPU (“device”) side. When a GPU-type
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variable on the CPU (“host”) side has a GPU (“device”) side. When a GPU-type
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variable is initialized, the data contained is (usually) the same on both sides. Each
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variable is initialized, the data contained is (usually) the same on both sides. Each
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@ -846,7 +846,7 @@ a matrix-vector product
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<div class="center"
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<div class="center"
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>
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>
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<!--l. 39--><p class="noindent" >
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<!--l. 39--><p class="noindent" >
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<div class="minipage"><pre class="verbatim" id="verbatim-109">
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<div class="minipage"><pre class="verbatim" id="verbatim-111">
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    call psb_spmm(alpha,a,x,beta,y,desc_a,info)
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    call psb_spmm(alpha,a,x,beta,y,desc_a,info)
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</pre>
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</pre>
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<!--l. 43--><p class="nopar" > </div></div>
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<!--l. 43--><p class="nopar" > </div></div>
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sfilippone
1 week ago