title: Reporting/visualizing scalability results from MPI code... which would be the best way?
body: <p>As part of my research, I have computed the parallel solution to different banded systems using <code>ScaLAPACK</code>. I am interested in reporting the achieved speedup as a function of both the rank for the matrix, <em>r</em>, and its bandwidth, <em>b</em>.  </p>
  
  <p>How would this be better achieved?  </p>
  
  <p>Here's my selected universes for both values:</p>
  
  <p><em>r</em> in <code>{10,000 25,000 50,000 75,000 100,000 500,000 1,000,000 5,000,000 10,000,000}</code>  </p>
  
  <p><em>b</em> in <code>{2 4 8 16 32 64 128 256 512 1024}</code>  </p>
  
  <p>The cluster I am using has 64 cores total, so <em>p</em> is in <code>{1, ..., 64}</code>.</p>
  
  <p>I have computed both the speedup  and the efficiency, <em>s</em> and <em>e</em>, as a function of <em>p</em>, <em>r</em> and <em>b</em>.</p>
  
  <p>My goal is to somehow show how the speedup is performing based on <em>r</em> and <em>b</em>. I was thinking of creating some kind of surface projection of the (r,b)-space. But how can I resume the behavior of the speedup in one value?</p>
  
  <p>A suggestion I had was to compute the Pearson correlation coefficient using both the attained and ideal (linear) speedup, however, this does NOT seem to work, since it does not take into account the existence of "speedup sweet-spots" that arise for smaller values of <em>r</em>.  </p>
  
  <p>Any hint?  </p>
  
  <p>Thanks in advance!  </p>