

_P_r_i_n_c_i_p_a_l _C_o_m_p_o_n_e_n_t_s _A_n_a_l_y_s_i_s

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

_A_r_g_u_m_e_n_t_s:

       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)'.

_D_e_s_c_r_i_p_t_i_o_n:

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

_D_e_t_a_i_l_s:

     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.

_V_a_l_u_e:

     `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.

_R_e_f_e_r_e_n_c_e_s:

     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.

_S_e_e _A_l_s_o:

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

_E_x_a_m_p_l_e_s:

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

