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% File src/library/stats/man/dist.Rd
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% File src/library/stats/man/dist.Rd
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% Part of the R package, https://www.R-project.org
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% Part of the R package, https://www.R-project.org
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% Copyright 1995-2014 R Core Team
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% Copyright 1995-2017 R Core Team
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% Distributed under GPL 2 or later
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% Distributed under GPL 2 or later
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\name{dist}
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\name{dist}
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\alias{dist}
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\alias{dist}
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\alias{print.dist}
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\alias{print.dist}
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\method{as.matrix}{dist}(x, \dots)
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\method{as.matrix}{dist}(x, \dots)
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}
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}
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\arguments{
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\arguments{
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  \item{x}{a numeric matrix, data frame or \code{"dist"} object.}
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  \item{x}{a numeric matrix, data frame or \code{"dist"} object.}
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  \item{method}{the distance measure to be used. This must be one of
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  \item{method}{the distance measure to be used.  This must be one of
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    \code{"euclidean"}, \code{"maximum"}, \code{"manhattan"},
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    \code{"euclidean"}, \code{"maximum"}, \code{"manhattan"},
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    \code{"canberra"}, \code{"binary"} or \code{"minkowski"}.
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    \code{"canberra"}, \code{"binary"} or \code{"minkowski"}.
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    Any unambiguous substring can be given.}
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    Any unambiguous substring can be given.}
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  \item{diag}{logical value indicating whether the diagonal of the
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  \item{diag}{logical value indicating whether the diagonal of the
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    distance matrix should be printed by \code{print.dist}.}
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    distance matrix should be printed by \code{print.dist}.}
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      and \eqn{y} (supremum norm)}
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      and \eqn{y} (supremum norm)}
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    \item{\code{manhattan}:}{Absolute distance between the two vectors (1 norm aka \eqn{L_1}).}
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    \item{\code{manhattan}:}{Absolute distance between the two vectors (1 norm aka \eqn{L_1}).}
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    \item{\code{canberra}:}{
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    \item{\code{canberra}:}{
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      %% till 2017-07-15: \eqn{\sum_i |x_i - y_i| / |x_i + y_i|}{sum(|x_i - y_i| / |x_i + y_i|)}.
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      \eqn{\sum_i |x_i - y_i| / |x_i + y_i|}{sum(|x_i - y_i| / |x_i + y_i|)}.
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      \eqn{\sum_i |x_i - y_i| / (|x_i| + |y_i|)}{sum(|x_i - y_i| / (|x_i| + |y_i|))}.
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      Terms with zero numerator and denominator are omitted from the sum
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      Terms with zero numerator and denominator are omitted from the sum
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      and treated as if the values were missing.
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      and treated as if the values were missing.
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      This is intended for non-negative values (e.g., counts): taking the
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      This is intended for non-negative values (e.g., counts), in which
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      absolute value of the denominator is a 1998 \R modification to
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      case the denominator can be written in various equivalent ways;
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      Originally, \R used \eqn{x_i + y_i}, then from 1998 to 2017,
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      avoid negative distances.
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      \eqn{|x_i + y_i|}, and then the correct \eqn{|x_i| + |y_i|}.
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    }
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    }
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    \item{\code{binary}:}{(aka \emph{asymmetric binary}): The vectors
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    \item{\code{binary}:}{(aka \emph{asymmetric binary}): The vectors
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      are regarded as binary bits, so non-zero elements are \sQuote{on}
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      are regarded as binary bits, so non-zero elements are \sQuote{on}
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      and zero elements are \sQuote{off}.  The distance is the
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      and zero elements are \sQuote{off}.  The distance is the