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#' Generalized Scales-Based Descriptors derived by Factor Analysis
#'
#' Generalized Scales-Based Descriptors derived by Factor Analysis
#'
#' This function calculates the generalized scales-based descriptors
#' derived by Factor Analysis (FA).
#' Users could provide customized amino acid property matrices.
#'
#' @param x A character vector, as the input protein sequence.
#' @param propmat A matrix containing the properties for the amino acids.
#' Each row represent one amino acid type, each column represents
#' one property.
#' Note that the one-letter row names must be provided for we need
#' them to seek the properties for each AA type.
#' @param factors Integer. The number of factors to be fitted.
#' Must be no greater than the number of AA properties provided.
#' @param scores Type of scores to produce. The default is \code{"regression"},
#' which gives Thompson's scores, \code{"Bartlett"} given
#' Bartlett's weighted least-squares scores.
#' @param lag The lag parameter. Must be less than the amino acids number
#' in the protein sequence.
#' @param scale Logical. Should we auto-scale the property matrix
#' (\code{propmat}) before doing Factor Analysis? Default is \code{TRUE}.
#' @param silent Logical. Whether we print the SS loadings,
#' proportion of variance and the cumulative proportion of
#' the selected factors or not.
#' Default is \code{TRUE}.
#'
#' @return A length \code{lag * p^2} named vector,
#' \code{p} is the number of scales (factors) selected.
#'
#' @keywords extract Factor Analysis extrPCMFAScales PCM
#'
#' @aliases extrPCMFAScales
#'
#' @author Min-feng Zhu <\email{wind2zhu@@163.com}>,
#' Nan Xiao <\url{http://r2s.name}>
#'
#' @export extrPCMFAScales
#'
#' @references
#' Atchley, W. R., Zhao, J., Fernandes, A. D., & Druke, T. (2005).
#' Solving the protein sequence metric problem.
#' Proceedings of the National Academy of Sciences of the
#' United States of America,
#' 102(18), 6395-6400.
#'
#' @examples
#' x = readFASTA(system.file('protseq/P00750.fasta', package = 'BioMedR'))[[1]]
#' data(AATopo)
#' tprops = AATopo[, c(37:41, 43:47)] # select a set of topological descriptors
#' fa = extrPCMFAScales(x, propmat = tprops, factors = 5, lag = 7, silent = FALSE)
#'
extrPCMFAScales = function (x, propmat, factors, scores = 'regression', lag,
scale = TRUE, silent = TRUE) {
if (checkProt(x) == FALSE) stop('x has unrecognized amino acid type')
factors = min(factors, ncol(propmat), nrow(propmat))
if (scale) propmat = scale(propmat)
prop.fa = factanal(propmat, factors = factors, scores = scores)
prop.scores = prop.fa$scores
accmat = matrix(0, factors, nchar(x))
x.split = strsplit(x, '')[[1]]
for (i in 1:nchar(x)) {
accmat[, i] = prop.scores[x.split[i], 1:factors]
}
result = acc(accmat, lag)
if (!silent) {
cat('Summary of the factor analysis result:\n')
print(prop.fa)
}
return(result)
}
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