PCA

    Carry out a Principal Components Analysis (Karhunen-Loeve Transform)

    Results can be directed to the screen, a file, or output variables
    See notes below for comparison with the intrinsic IDL function PCOMP.

    PCA, data, eigenval, eigenvect, percentages, proj_obj, proj_atr,
             [MATRIX =, TEXTOUT = ,/COVARIANCE, /SSQ, /SILENT ]

     data -  2-d data matrix, data(i,j) contains the jth attribute value
               for the ith object in the sample.    If N_OBJ is the total
               number of objects (rows) in the sample, and N_ATTRIB is the
               total number of attributes (columns) then data should be
               dimensioned N_OBJ x N_ATTRIB.

     /COVARIANCE - if this keyword is set, then the PCA will be carried out
              on the covariance matrix (rare), the default is to use the
              correlation matrix
     /SILENT - If this keyword is set, then no output is printed
     /SSQ - if this keyword is set, then the PCA will be carried out on
               on the sums-of-squares & cross-products matrix (rare)
     TEXTOUT - Controls print output device, defaults to !TEXTOUT
              textout=1       TERMINAL using /more option
              textout=2       TERMINAL without /more option
              textout=3       .prt
              textout=4       laser.tmp
              textout=5      user must open file
              textout = filename (default extension of .prt)

     eigenval -  N_ATTRIB element vector containing the sorted eigenvalues
     eigenvect - N_ATRRIB x N_ATTRIB matrix containing the corresponding
               eigenvectors
     percentages - N_ATTRIB element containing the cumulative percentage
             variances associated with the principal components
     proj_obj - N_OBJ by N_ATTRIB matrix containing the projections of the
             objects on the principal components
     proj_atr - N_ATTRIB by N_ATTRIB matrix containing the projections of
               the attributes on the principal components

      MATRIX   = analysed matrix, either the covariance matrix if /COVARIANCE
              is set, the "sum of squares and cross-products" matrix if
              /SSQ is set, or the (by default) correlation matrix.    Matrix
              will have dimensions N_ATTRIB x N_ATTRIB

      This procedure performs Principal Components Analysis (Karhunen-Loeve
      Transform) according to the method described in "Multivariate Data
      Analysis" by Murtagh & Heck [Reidel : Dordrecht 1987], pp. 33-48.
      Keywords /COVARIANCE and /SSQ are mutually exclusive.
      The printout contains only (at most) the first seven principle
      eigenvectors.    However, the output variables EIGENVECT contain
      all the eigenvectors
      Different authors scale the covariance matrix in different ways.
      The eigenvalues output by PCA may have to be scaled by 1/N_OBJ or
      1/(N_OBJ-1) to agree with other calculations when /COVAR is set.
      PCA uses the non-standard system variables !TEXTOUT and !TEXTUNIT.
      These can be added to one's session using the procedure ASTROLIB.
      The intrinsic IDL function PCOMP (introduced in V5.0) duplicates most
      most of the functionality of PCA, but uses different conventions and
      normalizations.   Note the following:
   (1) PCOMP requires a N_ATTRIB x N_OBJ input array; this is the transpose
         of what PCA expects
   (2) PCA uses standardized variables; use /STANDARIZE keyword to PCOMP
         for a direct comparison.
   (3) PCA (unlike PCOMP) normalizes the eigenvectors by the square root
         of the eigenvalues.
   (4) PCA returns cumulative percentages; the VARIANCES keyword of PCOMP
         returns the variance in each variable

      Perform a PCA analysis on the covariance matrix of a data matrix, DATA,
      and write the results to a file
      IDL> PCA, data, /COVAR, t = 'pca.dat'
      Perform a PCA analysis on the correlation matrix.   Suppress all
      printing, and save the eigenvectors and eigenvalues in output variables
      IDL> PCA, data, eigenval, eigenvect, /SILENT

      TEXTOPEN, TEXTCLOSE

      Immanuel Freedman (after Murtagh F. and Heck A.).     December 1993
      Wayne Landsman, modified I/O              December 1993
      Converted to IDL V5.0   W. Landsman   September 1997
      Fix MATRIX output, remove GOTO statements   W. Landsman August 1998
      Changed some index variable to type LONG    W. Landsman March 2000

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