Case Study: Finding the Maximum Iteratively

Given a vector, we have discussed the basic algorithm for fiding the maximum, by keep track of the maximum thus far while iterating through the vector.

Question: how many different elements qualify as being the maximum thus far during that process?

Goal: Develop a function peaks(v) that returns the number of elements that have value surpassing all previous elements in the vector. For example, peaks([5 1 8 3 8 11 10]) should return 3, as the first element, the third element and the sixth elements are new maximums (we do not count the fifth, because that value 8 did not surpass the previously visited maximum of 8).

Goal: Rewrite the function so that it can provide a second return value, which is a vector of indices achieving those peaks (akin to the second return value of the built-in max function). Thus peaks([5 1 8 3 8 11 10]) should return the pair [ 3 [1 3 6] ].

Files from Wednesday's class

• peaks.m
  The basic function for computing the number of peaks and their indices.


• harmonicTest.m
  A function that performed tests by generating random vectors and counting the number of peaks in those vectors.


• graphHarmonic.m
  A function that produces a plot of the theoretical predicted number of peaks for random data versus the observed data for random trials.