Chapter 20, Problem 13ICA

Write a function named Prodstate that will accept a matrix Prodstate that has at least one row and at least two columns. The rows each represent a different machine in a factory and the columns represent successive days of production. The value in each element is the number of units produced by that machine on the given day.

Prodstate should return a new matrix Trend with the same dimensions as prodstate and a row vector Trendium with three elements.

Each element of Trend indicates whether that day’s production for that machine was less than, equal to or greater than the previous day’s production for that machine. Since the first day (first column) does not have previous data upon which to base the comparison, the first column of Trend will arbitrarily be set to all zeros. All other elements will be set to either -1 (lower production that previous day), 0 (equal production to previous day), or 1 (higher production than previous day).

The first element of Trendrum contains the total number of days that production decreased (In other words, the number of negative ones in Trend), the second element of Trendrum contains the number of days with no change in production (zero in Trend, not counting the zeros on the first day), and the thirds element contains the number of days with higher production (ones in Trend).

Example:

$\text{ProdData}=\left[\begin{array}{cccccc}1& 2& 4& 4& 5& 4\\ 7& 8& 9& 0& 1& 5\\ 9& 8& 5& 6& 7& 7\end{array}\right]$

$\text{Trend}=\left[\begin{array}{cccccc}0& 1& 1& 0& 1& -1\\ 0& 1& 1& -1& 1& 1\\ 0& -1& -1& 1& 1& 0\end{array}\right]\text{TrendNum}=\left[\begin{array}{ccc}4& 2& 9\end{array}\right]$