Description of the PCOP.zip file.

There are several files in PCOP.zip:

1. readme.html: This file.

 
2. PCOP.exe: This is the application executable file. It runs over Windows 98.

 
3. setup.dat: This file contains the commands required by PCOP.exe. The syntax of each line in the file is as follows:

                command_name+blank_space+command_value
There are six commands:
• datafile (character string) The name of the file with the original data.
• outfile (character string) The name of the output file.
• PROFREQ (integer) The required depth: the maximum order of the PCOP to be computed.

        Default value: 1
        Constraints: 0 < PROFREQ < p (p is the data dimension).
• NPARTS (integer) The search of optimum direction b*(c) is done by a grid search method. Parameter NPARTS  controls the search precision: is the number of points in each dimension of the b*(c) candidates grid.

        Default value: 4
        Constraints: 2 < NPARTS < 7
• C_H (float) The smoothing parameter h is C_H times the value given by the normal reference rule.

        Default value: 0.75
        Constraints: 0.5 <= C_H <=  1.5
• C_D (float) The distance between two consecutive principal oriented points in a PCOP is about C_D time the value of the smoothing parameter h.

        Default value: 0.3
        Constraints: 0.25 <= C_D <= .5
4. cp2pirpob.dat, cp4pirpob.dat: Two examples of data files. They contain the first 2 (resp. 4) principal component of the population pyramids data.

    The data file has n lines, each with p data separated by blank spaces, where n is the number of observed cases and p is the number of variables observed in each case.
 
5. cp2pirpob.alpha, cp4pirpob.alpha: They are the output files corresponding to cp2pirpob.dat and cp4pirpob.dat, respectively.

   The structure of output files is as follows. There is a line for each identified principal oriented point. Each line contains, separated by blank spaces,
• Order of the PCOP containing the principal oriented point, minus 1
• Value of the parameter t such the the principal oriented point is PCOP(t).
• Density estimation for the random variable induced over the PCOP at t.
• Span: proportion of original data involved in the determination of the principal oriented point.
• Variance over the hyperplane orthogonal to the PCOP at the principal oriented point.
• The p coordinates of the principal oriented point.
• The p coordinates of the principal direction for the principal oriented point.

 
6. graphPCrec.m: Matlab file for graphically post processing output files.
   
   
7. ej3Ddepth2.dat, ej3Ddepth2.alpha, setup3Ddepth2: Data file, output file and setup file for an example of 3-dimensional data where principal curves of first and second order are extracted. See Delicado, P.(2001) for a description of the data structure.