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  or, alternatively, \code{t(Q) \%*\% Q} equals \code{x[pivot,
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  or, alternatively, \code{t(Q) \%*\% Q} equals \code{x[pivot,
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    pivot]}.  See the examples.
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    pivot]}.  See the examples.
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  The value of \code{tol} is passed to LAPACK, with negative values
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  The value of \code{tol} is passed to LAPACK, with negative values
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  selecting the default tolerance of (usually) \code{nrow(x) *
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  selecting the default tolerance of (usually) \code{nrow(x) *
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  .Machine$double.neg.eps * max(diag(x)}.  The algorithm terminates once
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  .Machine$double.neg.eps * max(diag(x))}.  The algorithm terminates once
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  the pivot is less than \code{tol}.
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  the pivot is less than \code{tol}.
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  Unsuccessful results from the underlying LAPACK code will result in an
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  Unsuccessful results from the underlying LAPACK code will result in an
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  error giving a positive error code: these can only be interpreted by
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  error giving a positive error code: these can only be interpreted by
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  detailed study of the FORTRAN code.
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  detailed study of the FORTRAN code.