Finished Activity #1 of Matrix Multiplication

topic_rigid_programs/matrixmultiplication/2d_matrices.html

@@ -1,6 +1,6 @@
-<div class="ui container segment raised">In this activity we distributed the matrices across the MPI processes, which
-  entails dealing with local vs. global indexing. As opposed to what was seen in previous topics, we now use a 2-D data distribution,
-  which complicates indexing a bit.  We multiply square matrices: <i>A = B x C</i>.
+<div class="ui container segment raised">In this activity we distribute the matrices across the MPI processes, which
+  entails dealing with local vs. global indexing.  Recall that we consider 3 NxN matrices (A, B, and C). This
+  activity consists of a single step, as described below.
 </div>
 
 <div class="ui top attached tabular menu">

topic_rigid_programs/matrixmultiplication/cluster_crossbar_64.xml

@@ -0,0 +1,7 @@
+<?xml version='1.0'?>
+<!DOCTYPE platform SYSTEM "http://simgrid.gforge.inria.fr/simgrid.dtd">
+<platform version="3">
+<AS id="AS0" routing="Full">
+<cluster id="cluster" prefix="host-" suffix=".hawaii.edu" radical="0-63" power="1" bw="10Gbps" lat="20us"/>
+</AS>
+</platform>

topic_rigid_programs/matrixmultiplication/data_distribution.html

@@ -1,12 +1,96 @@
 <p class="ui">
-  Implement a program called <code>matmul_init</code> (<code>matmul_init.c</code>) that takes a
+  Implement an MPI program called <code>matmul_init</code> (<code>matmul_init.c</code>) that takes a
   single command-line argument, <i>N</i>, which is a strictly positive integer. <i>N</i> is the
-  dimension of the square matrices that we multiply.
+  dimension of the square matrices that we multiply. Your program should check that the number of processes
+  is a perfect square, and that its square root divides N (printing an error message and exiting if this is
+  not the case).
+</p>
+
+<p class="ui">
+  The objective of the program is for each process to allocate and initialize its block of each matrix.
+  We multiply particular matrices, defined by:
+  </p>
+<p class="ui">
+  <i>A<sub>i,j</sub> = i</i> &nbsp; and  &nbsp; <i>B<sub>i,j</sub> = i + j</i>.
+</p>
+
+
+
+<p class="ui">
+  <b>The above is with global indices, which go from 0 to N-1.</b>
+</p>
+
+
+<p class="ui">
+Given the above definitions of A and B, there is a simple analytical solution
+  for C. There is thus a closed-form expression for the sum of the
+  elements of C: <b><i>N<sup>3</sup> (N - 1)<sup>2</sup> / 2</i></b>.
+  You will use this formula to check the validity of your matrix
+  multiplication implementation in Activity #2.
+</p>
 
+<p class="ui">
+  Have each process allocate its blocks of A, B, and C, initialize its blocks
+  of A and B to the appropriate values, and then print out the content of
+  these blocks.  Each process should print its MPI rank (the "linear rank")
+  as well as its
+  2-D rank, which is easy to determine based on the linear rank. Note that MPI
+  provides a set of functions for handling Cartesian coordinates, which you
+  can also use (see the documentation for <code>MPI_Cart_rank</code> and
+  related functions).
+  </p>
 
+<p class="ui">
+  For instance, here is an excerpt from the output (that generated by the process of rank 2)
+  for p=4 and N=8, using
+  <a href="./cluster_crossbar_64.xml">cluster_crossbar_64.xml</a> as a platform file
+  and <a href="./hostfile_64.txt">hostfile_64.txt</a> as a hostfile (since this module is
+  about correctness, you can use pretty much any such valid files).
 </p>
 
+<div class="ui container raised segment">
+  {% highlight text %}
+% smpirun --cfg=smpi/running_power:1Gf -np 4 \
+          -platform cluster_crossbar_64.xml \
+          -hostfile hostfile_64.txt \
+          ./matmul_init 8
+[...]
+Process rank 2 (coordinates: 1,0), block of A:
+4.0 4.0 4.0 4.0
+5.0 5.0 5.0 5.0
+6.0 6.0 6.0 6.0
+7.0 7.0 7.0 7.0
+Process rank 2 (coordinates: 1,0), block of A:
+4.0 5.0 6.0 7.0
+5.0 6.0 7.0 8.0
+6.0 7.0 8.0 9.0
+7.0 8.0 9.0 10.0
+[...]
+{% endhighlight %}
+</div>
+
+
+
 <p class="ui">
-  YYY
+  Note that due to the convenience of simulation,
+  the output from one process will never be interleaved with the output of
+  another process. If you run this code "for real" with MPI instead of SMPI
+  output will be interleaved and additional synchronization will be needed
+  to make the output look nice.
+  The order in which the processes output their blocks is inconsequential.
+  You may want to use a barrier synchronization
+  to first see all blocks of A and then all blocks of B.
+
+  </p>
+
+<p class="ui">
+  Obviously, we won’t run this program for large N.
+  The goal is simply to make sure that matrix blocks are initialized
+  correctly on all processes. You can run this program on any XML
+  platform file.
+
 </p>
 
+
+
+

topic_rigid_programs/matrixmultiplication/hostfile_64.txt

@@ -0,0 +1,64 @@
+host-0.hawaii.edu
+host-1.hawaii.edu
+host-2.hawaii.edu
+host-3.hawaii.edu
+host-4.hawaii.edu
+host-5.hawaii.edu
+host-6.hawaii.edu
+host-7.hawaii.edu
+host-8.hawaii.edu
+host-9.hawaii.edu
+host-10.hawaii.edu
+host-11.hawaii.edu
+host-12.hawaii.edu
+host-13.hawaii.edu
+host-14.hawaii.edu
+host-15.hawaii.edu
+host-16.hawaii.edu
+host-17.hawaii.edu
+host-18.hawaii.edu
+host-19.hawaii.edu
+host-20.hawaii.edu
+host-21.hawaii.edu
+host-22.hawaii.edu
+host-23.hawaii.edu
+host-24.hawaii.edu
+host-25.hawaii.edu
+host-26.hawaii.edu
+host-27.hawaii.edu
+host-28.hawaii.edu
+host-29.hawaii.edu
+host-30.hawaii.edu
+host-31.hawaii.edu
+host-32.hawaii.edu
+host-33.hawaii.edu
+host-34.hawaii.edu
+host-35.hawaii.edu
+host-36.hawaii.edu
+host-37.hawaii.edu
+host-38.hawaii.edu
+host-39.hawaii.edu
+host-40.hawaii.edu
+host-41.hawaii.edu
+host-42.hawaii.edu
+host-43.hawaii.edu
+host-44.hawaii.edu
+host-45.hawaii.edu
+host-46.hawaii.edu
+host-47.hawaii.edu
+host-48.hawaii.edu
+host-49.hawaii.edu
+host-50.hawaii.edu
+host-51.hawaii.edu
+host-52.hawaii.edu
+host-53.hawaii.edu
+host-54.hawaii.edu
+host-55.hawaii.edu
+host-56.hawaii.edu
+host-57.hawaii.edu
+host-58.hawaii.edu
+host-59.hawaii.edu
+host-60.hawaii.edu
+host-61.hawaii.edu
+host-62.hawaii.edu
+host-63.hawaii.edu

topic_rigid_programs/matrixmultiplication/introduction.html

@@ -15,15 +15,16 @@ <h3 class="ui header">Overview</h3>
   <h3 class="ui header">2-D Data Distribution</h3>
 
   <p class="ui">
-    We consider the standard outer-product parallel matrix multiplication, as described throughout this module,
-    for a <i>2-D block data distribution</i>. More precisely, we consider the C = A×B multiplication
-    where all three matrices are square of dimensions N×N, and contain double precision floating point numbers.
+    As opposed to what was seen in previous topics, we now use a <i>2-D block data distribution</i>,
+    which complicates indexing a bit.
+    More precisely, we consider the C = A×B multiplication
+    where all three matrices are square of dimensions N×N.
     The execution takes place on p processors, <b>where p is a perfect square and √p
     divides N</b>. Each processor thus holds a
     N/√p × N/√p square block of each matrix. </p>
 
   <p class="ui">
-    For instance, with N=6, consider example matrix A as shown below:
+    For instance, with N=6, consider the example matrix A as shown below:
   </p>
 
   <p style="text-align:center;" class="ui">
@@ -83,7 +84,7 @@ <h3 class="ui header">2-D Data Distribution</h3>
     </pre>
   </p>
 
-  <p>At process #2, element with value 54 has local indices (1,1), but its global indices are (5,5), assuming that
+  <p>At process #2, element with value 54 has local indices (1,1), but its global indices are (4,4), assuming that
       indices start at 0.
   </p>