Divendres, 17 de Maig del 1996.

    ftp://porthos.bio.ub.es~/pub/multicua/gifi


    This directory contains the octave programs (*.m files) for my
    course on nonlinear multivariate analysis, which follows closely
    the book by Albert Gifi.  The *.oct files are the data sets, also
    from the book.

    The postscript file contains the notes for the course (in
    Catalan).  [Currently under revision].

    For the moment both text and programs reach till chapter 3
    (HOMALS).

    The purpose of the programs is to understand the algorithms,
    rather than computational efficiency.


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    Description of the programs:
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    als1a.m
    als1b.m

    Columns of H are standardized.
    a  = Normalized scores algorithm.  (Gifi, p. 88)
    b  = Normalized weights algorithm. (Gifi, p. 92)

    These programs output the results of all the iterations, so they
    can be plotted together.

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    als2a.m
    als2b.m

    Columns of H have unequal variances.
    a  = Normalized scores algorithm.
    b  = Normalized weights algorithm. (Gifi, p. 95)

    These programs output the results of all the iterations, so they
    can be plotted together.

 ------------------------------------------------------------------

    als3a0.m
    als3a.m
    als3b.m

    Multiple solutions (Gifi, p. 98).
    Columns of H are standardized.
    a0 = Normalized scores algorithm. X is orthonormalized as
         X*(X'*X)^(-1/2). Apparently this algorithm does not
         converge [that is, it converges to different solutions
         depending on the initial value].

    a  = Normalized scores algorithm. X is orthonormalized either
         by Gram-Schmidt, or QR decomposition, or SVD decomposition.
    b  = Normalized weights algorithm. Gram-Schmidt.

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    svdcomp .m

    Multiple solutions.
    Columns of H are standardized.
    Singular value decomposition of H (to compare with ALS solutions).

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    als4a.m
    als4b.m

    Multiple solutions
    Columns of H have unequal variances.
    a  = Normalized scores algorithm.
    b  = Normalized weights algorithm.

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   homals1.m
   homals2.m
   homals3a.m

   1  = First solution. x standardized.
   2  = First solution. y standardized.
   3a = Multiple solutions. X standardized.

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   corresp.m

   Ordinary correspondence analysis of a two way contingency table


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   mca1.m


   One version of multiple correspondence analysis, to compare with
   Homals.

 ====================================================================

  Other auxiliary routines:

   burt.m

   * Compute the Burt matrix from a data matrix.

   eigsort.m

   * Sorted eigenvalue-eigenvector

   grschm.m

   * Gram-Schmidt orthonormalization (possibly with respect to
     a positive definite scalar product matrix).

   htoind.m

   * Computes the indicator matrix for a data matrix.

   optscal.m

   * Compute the optimally scaled data matrix, from the indicator
     matrix and the category quantifications computed by homals.

   percent.m

   * Compute percentages and cumulative percentages of a vector
     of nonnegative numbers.

   profile.m

   * Compute profiles of a two way contingency table

   ssq.m

   * Compute sum of squares of a matrix.

   tabtoind.m

   * Converts a two-way contingency table into an indicator matrix.


 ------------------------------------------------------------------
   Josep Fortiana
   josepf@porthos.bio.ub.es