

   PPrriinncciippaall CCoommppoonneennttss AAnnaallyyssiiss

        prcomp(x, retx = TRUE, center = TRUE, scale. = FALSE, tol = NULL)

   AArrgguummeennttss::

          x: a matrix (or data frame) which provides the data
             for the principal components analysis.

       retx: a logical value indicating whether the rotated
             variables should be returned.

     center: a logical value indicating whether the variables
             should be shifted to be zero centered. Alter-
             nately, a vector of length equal the number of
             columns of `x' can be supplied.  The value is
             passed to `scale'.

      scale: a logical value indicating whether the variables
             should be scaled to have unit variance before the
             analysis takes place. The default is `FALSE' for
             consistency with S, but in general scaling is
             advisable. Alternately, a vector of length equal
             the number of columns of `x' can be supplied.  The
             value is passed to `scale'.

        tol: a value indicating the magnitude below which com-
             ponents should be omitted. With the default null
             setting, no components are omitted.  Other set-
             tings for tol could be `tol = 0' or `tol =
             sqrt(.Machine$double.eps)'.

   DDeessccrriippttiioonn::

        Performs a principal components analysis on the given
        data matrix and returns the results as a `prcomp'
        object.

   DDeettaaiillss::

        The calculation is done with svd on the data matrix,
        not by using eigen on the covariance matrix.  This is
        generally the preferred method for numerical accuracy.
        The print method for the these objects prints the
        results in a nice format and the plot method produces a
        scree plot.

   VVaalluuee::

        `prcomp' returns an list with class `"prcomp"' contain-
        ing the following components:

       sdev: the standard deviation of the principal components
             (i.e., the eigenvalues of the cov matrix, though
             the calculation is actually done with the singular
             values of the data matrix).

   rotation: the matrix of variable loadings (i.e., a matrix
             whose olumns contain the eigenvectors).  The func-
             tion `princomp' returns this in the element `load-
             ings'.

          x: if `retx' is true the value of the rotated data
             (the data multiplied by the `rotation' matrix) is
             returned.

   RReeffeerreenncceess::

        Mardia, K. V., J. T. Kent, J and M. Bibby (1979), Mul-
        tivariate Analysis, London: Academic Press.

        Venables, W. N. and B. D. Ripley (1997), Modern Applied
        Statistics with S-Plus, Springer-Verlag.

   SSeeee AAllssoo::

        `princomp', `cor', `cov', `svd', `eigen'.

   EExxaammpplleess::

        ## the variances of the variables in the
        ## crimes data vary by orders of magnitude
        data(crimes)
        prcomp(crimes)
        prcomp(crimes, scale = TRUE)
        plot(prcomp(crimes))
        summary(prcomp(crimes))

