R/ginv.r

In ExpDes.pt: Pacote Experimental Designs (Portugues)

#' Generalized inverse
#'
#' \code{ginv} Inversa generalizada
#' @param X Matriz para a qual deseja-se a inversa de
#' Moore-Penrose.
#' @param tol Uma tolerancia relativa para detectar valores
#' singulares zero.
#' @return Uma inversa generalizada de Moore-Penrose para X.
#' @references Venables, W. N. and Ripley, B. D. (1999) Modern
#' Applied Statistics with S-PLUS. Third Edition. Springer.
#' p.100.
#' @seealso \code{\link{solve}}, \code{\link{svd}},
#' \code{\link{eigen}}
#' @export

ginv<-function(X, tol = sqrt(.Machine$double.eps))
{
    if (length(dim(X)) > 2L || !(is.numeric(X) || is.complex(X)))
        stop("'X' must be a numeric or complex matrix")
    if (!is.matrix(X))
        X <- as.matrix(X)
    Xsvd <- svd(X)
    if (is.complex(X))
        Xsvd$u <- Conj(Xsvd$u)
    Positive <- Xsvd$d > max(tol * Xsvd$d[1L], 0)
    if (all(Positive))
        Xsvd$v %*% (1/Xsvd$d * t(Xsvd$u))
    else if (!any(Positive))
        array(0, dim(X)[2L:1L])
    else Xsvd$v[, Positive, drop = FALSE] %*% ((1/Xsvd$d[Positive]) *
        t(Xsvd$u[, Positive, drop = FALSE]))
}