title: Calculations between columns in data frame: week-on-week 'trending' sales detection
body: <p>I have a data.frame representing frequency book sales for a set of authors over 25 weeks:</p>
  
  <pre><code>author       week_1 week_2 week_3 week_4 ...
  author1      7      4      5          2
  author2      3      6      18         5
  author3      1      0      2          4
  author4      0      1      1          2
  author5      0      1      0          0
  </code></pre>
  
  <p>First, I want to use this data to build a new data frame, which shows the fraction of [currentWeek / previousWeek]. Something like this perhaps:</p>
  
  <pre><code>author       week_1 week_2  week_3 week_4 ...
  author1      NA      0.57   1.25   0.2
  author2      NA      2      3      0.28
  author3      NA      0      2      2
  author4      NA      1      1      2   
  author5      NA      1      0      0   
  </code></pre>
  
  <p>(I would like to substitute zeros with 1s to avoid dividing by zero.)</p>
  
  <p>Second, I want to run a quick iteration over all the rows, check for any triplets of adjacent weeks where sales for that authors have increased by 100% twice in two consecutive week-pairs, and report this in some kind of output table. Perhaps like this:</p>
  
  <pre><code>author  startTrendWeek endTrendWeek
  author2 1              3
  author3 2              4
  </code></pre>
  
  <p>Any ideas for how I could solve either of these in R? </p>