What to Hand In (see also: example project solution)

• a Program Organization Chart exhibiting the interactions between major program components. Attach a report to the chart providing a rationale for the program organization
• a listing of the Haskell script you write for your project, following the required standards
• a two transcripts of a session during which you entered the command main to demonstrate your program's behavior
  • data file for session 1: proj5.tst
  • data file for session 2: rainfall.dat
• a logical argument showing that the function average, defined in the NumericUtilities module, satisfies the following property:
  

  Property A

  If xs :: [Float], then average(xs) = sum(xs)/length(xs)

  Assume, in your proof, that arithmetic on type Float is exact. (It isn't, really, but assume it is, anyway.)

• Extra Credit: Assuming that the range of numbers a computer can perform arithmetic on is limited, give an example sequence xs where the formula defining average(xs) in the NumericUtilities module delivers a better approximation to the average of the numbers in xs than the formula sum(xs)/length(xs).

Write a program that reports, for each of the years after World War I in a file rainfall.dat on the Supplied Software page of the class web site, the three years from before and during World War I whose rainfall patterns most closely resemble the rainfall pattern of that post-war year. The program should also report the degree of resemblance between each of three most similar years and the post-war year in question. That is, for each post-war year y in the dataset, the program reports the three pre-armistice years whose rainfall patterns most closely match those of the post-war year y along with the degrees of resemblance between the three most similar pre-armistice years and the post-war year y.

The program may assume that:

Each year recorded in the data file will contain records for the same set of months.

The data file will contain records for some pre-armistice years and some post-armistice years.

The standard deviation of the rainfall figures for any given month in the pre-armistice years is not zero.

However, the program should not depend on the number of years of rainfall data recorded in the data file, nor should it depend on the number of months per year recorded in the file.

• Resemblance Between Rainfall Patterns
  A rainfall pattern is a sequence of numbers representing the rainfall amounts in the months of a given year in chronological order, January through December. The degree of resemblance between two rainfall patterns is the correlation between their normalized patterns -- the larger the correlation, the greater the resemblance.
• Normalized Rainfall Patterns
  A normalized rainfall pattern is sequence of numbers constructed by dividing the numbers in a rainfall pattern by the standard deviations of the numbers in the corresponding months of the pre-armistice years. For example, the January figure in a normalized pattern is the January figure from the original pattern divided by the standard deviation of the January figures for the pre-armistice years.
• Correlation Between Sequences
  Two sequences of numbers have a correlation if they contain the same number of elements. The correlation between two such sequences is the sum of the products of the corresponding elements of the two sequences divided by the product of the magnitudes of the two sequences. The magnitude of a sequence of numbers is the square root of the sum of the squares of its elements.

Ground Rules

• Depending on how you construct the program, it may consume a lot of space when it carries out the computation. Sometimes, when Hugs runs out of space, it collapses issuing a message indicating a floating point exception of some kind. If this occurs, try restarting Hugs with a command like this:

  hugs -h500000 yourProgramFilename.lhs

  The "-h500000" option makes five times more than the default amount of space available. The "h" stands for "heap."
• You may use any aspects of Haskell described in the Haskell textbook, any intrinsic operator or function you have learned from any source, and any software supplied for any project on the class web site.
  Note that
  • NumericUtilities exports functions for computing standard deviations
  • IOutilities exports functions for converting between numbers of various types and strings in various formats
  • SequenceUtilities exports the function transpose, which rearranges "matrices" as sequences of rows or columns, and the function quickSortWith, which rearranges a sequence to conform to a given ordering among its elements
  • Project3D exports a function to build table displays from columns of words
  • modules defined in the solution to Project 4 ( TableConversion, VarianceNormalization) export functions that you may find useful in this project
• The Project Style Guide describes additional report requirements.