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  Note that only the upper triangular part of \code{x} is used, so
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  Note that only the upper triangular part of \code{x} is used, so
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  that \eqn{R'R = x} when \code{x} is symmetric.
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  that \eqn{R'R = x} when \code{x} is symmetric.
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  If \code{pivot = FALSE} and \code{x} is not non-negative definite an
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  If \code{pivot = FALSE} and \code{x} is not non-negative definite an
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  error occurs.  If \code{x} is positive semi-definite (i.e. some zero
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  error occurs.  If \code{x} is positive semi-definite (i.e., some zero
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  eigenvalues) an error will also occur, as a numerical tolerance is used.
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  eigenvalues) an error will also occur, as a numerical tolerance is used.
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  If \code{pivot = TRUE}, then the Choleski decomposition of a positive
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  If \code{pivot = TRUE}, then the Choleski decomposition of a positive
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  semi-definite \code{x} can be computed.  The rank of \code{x} is
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  semi-definite \code{x} can be computed.  The rank of \code{x} is
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  returned as \code{attr(Q, "rank")}, subject to numerical errors.
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  returned as \code{attr(Q, "rank")}, subject to numerical errors.