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  % Name 'r' is not really making sense for upper.tri = FALSE
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  % Name 'r' is not really making sense for upper.tri = FALSE
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  % Name 'x' is also a  misnomer,  should rather be  'b'. -- is this S ??
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  % Name 'x' is also a  misnomer,  should rather be  'b'. -- is this S ??
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  \item{r,l}{an upper (or lower) triangular matrix giving the
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  \item{r,l}{an upper (or lower) triangular matrix giving the
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    coefficients for the system to be solved.  Values below (above)
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    coefficients for the system to be solved.  Values below (above)
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    the diagonal are ignored.}
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    the diagonal are ignored.}
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  \item{x}{a matrix whose columns give ``right-hand sides'' for
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  \item{x}{a matrix whose columns give \dQuote{right-hand sides} for
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    the equations.}
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    the equations.}
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  \item{k}{The number of columns of \code{r} and rows of \code{x} to use.}
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  \item{k}{The number of columns of \code{r} and rows of \code{x} to use.}
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  \item{upper.tri}{logical; if \code{TRUE} (default), the \emph{upper}
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  \item{upper.tri}{logical; if \code{TRUE} (default), the \emph{upper}
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    \emph{tri}angular part of \code{r} is used.  Otherwise, the lower one.}
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    \emph{tri}angular part of \code{r} is used.  Otherwise, the lower one.}
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  \item{transpose}{logical; if \code{TRUE}, solve \eqn{r' * y = x} for
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  \item{transpose}{logical; if \code{TRUE}, solve \eqn{r' * y = x} for
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  \code{\link{chol}},
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  \code{\link{chol}},
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  \code{\link{qr}},
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  \code{\link{qr}},
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  \code{\link{solve}}.
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  \code{\link{solve}}.
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}
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}
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\examples{
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\examples{
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## upper triangular matrix `r':
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## upper triangular matrix 'r':
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r <- rbind(c(1,2,3),
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r <- rbind(c(1,2,3),
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           c(0,1,1),
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           c(0,1,1),
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           c(0,0,2))
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           c(0,0,2))
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( y <- backsolve(r, x <- c(8,4,2)) ) # -1 3 1
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( y <- backsolve(r, x <- c(8,4,2)) ) # -1 3 1
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r \%*\% y # == x = (8,4,2)
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r \%*\% y # == x = (8,4,2)