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% File src/library/base/man/lower.tri.Rd
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% File src/library/base/man/lower.tri.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 1995-2017 R Core Team
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% Copyright 1995-2026 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{lower.tri}
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\name{lower.tri}
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\alias{lower.tri}
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\alias{lower.tri}
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\alias{upper.tri}
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\alias{upper.tri}
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  \item{x}{a matrix or other \R object with \code{length(dim(x)) == 2}.
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  \item{x}{a matrix or other \R object with \code{length(dim(x)) == 2}.
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    For back compatibility reasons, when the above is not fulfilled,
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    For back compatibility reasons, when the above is not fulfilled,
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    \code{\link{as.matrix}(x)} is called first.}
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    \code{\link{as.matrix}(x)} is called first.}
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  \item{diag}{logical.  Should the diagonal be included?}
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  \item{diag}{logical.  Should the diagonal be included?}
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}
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}
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\details{
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  Note that \code{!lower.tri(x)} gives the same as \code{upper.tri(x, diag=TRUE)}, and
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  analogously, \code{!upper.tri(x)} is equivalent to \code{lower.tri(x, diag=TRUE)},
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  and the \code{diag=TRUE} versions are very slightly more efficient.
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}
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\seealso{
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\seealso{
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  \code{\link{diag}}, \code{\link{matrix}}; further \code{\link{row}}
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  \code{\link{diag}}, \code{\link{matrix}}; further \code{\link{.row}}
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  and \code{\link{col}} on which \code{lower.tri()} and
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  and \code{\link{.col}} on which \code{lower.tri()} and
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  \code{upper.tri()} are built.
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  \code{upper.tri()} are built.
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}
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}
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\examples{
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\examples{
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(m2 <- matrix(1:20, 4, 5))
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(m2 <- matrix(1:20, 4, 5))
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lower.tri(m2)
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lower.tri(m2)
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m2[lower.tri(m2)] <- NA
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m2[lower.tri(m2)] <- NA
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m2
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m2
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## "prove" equivalence   lower.tri  <---> !upper.tri
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set.seed(12)
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for(i in 1:99) {
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    x <- matrix(as.integer(64*rnorm(6*4)), 6, 4)
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    stopifnot(identical( !lower.tri(x), upper.tri(x, diag=TRUE)),
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              identical( !upper.tri(x), lower.tri(x, diag=TRUE)))
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 }
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}
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}
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\keyword{array}
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\keyword{array}