The R Project SVN R

Rev

Rev 61622 | Rev 68407 | Go to most recent revision | Show entire file | Ignore whitespace | Details | Blame | Last modification | View Log | RSS feed

Rev 61622 Rev 62149
Line 19... Line 19...
19 
\arguments{
 19 
\arguments{
20 
  \item{x}{an object for which a method exists.  The default method
 20 
  \item{x}{an object for which a method exists.  The default method
21 
    applies to numeric (or logical) symmetric, positive-definite matrices.}
 21 
    applies to numeric (or logical) symmetric, positive-definite matrices.}
22 
  \item{\dots}{arguments to be based to or from methods.}
 22 
  \item{\dots}{arguments to be based to or from methods.}
23 
  \item{pivot}{Should pivoting be used?}
 23 
  \item{pivot}{Should pivoting be used?}
24 
  \item{LINPACK}{logical.  Should LINPACK be used (which is deprecated)?}
 24 
  \item{LINPACK}{logical.  Should LINPACK be used (now ignored)?}
25 
  \item{tol}{A numeric tolerance for use with \code{pivot = TRUE,
 25 
  \item{tol}{A numeric tolerance for use with \code{pivot = TRUE}.}
26 
      LINPACK = FALSE)}.}
 - 
 
27 
}
 26 
}
28 
\value{
 27 
\value{
29 
  The upper triangular factor of the Choleski decomposition, i.e., the
 28 
  The upper triangular factor of the Choleski decomposition, i.e., the
30 
  matrix \eqn{R} such that \eqn{R'R = x} (see example).
 29 
  matrix \eqn{R} such that \eqn{R'R = x} (see example).
31 
 
 30 
 
Line 51... Line 50...
51 
  \code{pivot <- attr(Q, "pivot")} and \code{oo <- order(pivot)}, it
 50 
  \code{pivot <- attr(Q, "pivot")} and \code{oo <- order(pivot)}, it
52 
  is true that \code{t(Q[, oo]) \%*\% Q[, oo]} equals \code{x},
 51 
  is true that \code{t(Q[, oo]) \%*\% Q[, oo]} equals \code{x},
53 
  or, alternatively, \code{t(Q) \%*\% Q} equals \code{x[pivot,
 52 
  or, alternatively, \code{t(Q) \%*\% Q} equals \code{x[pivot,
54 
    pivot]}.  See the examples.
 53 
    pivot]}.  See the examples.
55
54
56 
  Use of \code{chol(pivot = FALSE, LINPACK = TRUE)} was deprecated in \R
 - 
 
57 
  1.7.0.   Pivoting with LAPACK requires LAPACK >= 3.2 and was added in \R
 55 
  Pivoting with LAPACK requires LAPACK >= 3.2 and was added in \R 2.15.2
58 
  2.15.2.  The value of \code{tol} is passed to LAPACK, with negative
 56 
  (it was previously available using LINPACK).  The value of \code{tol}
59 
  values selecting the default tolerance of (usually) \code{nrow(x) *
 57 
  is passed to LAPACK, with negative values selecting the default
60 
  .Machine$double.neg.eps * max(diag(x)}.  The algorithm terminates once
 58 
  tolerance of (usually) \code{nrow(x) * .Machine$double.neg.eps *
61 
  the pivot is less than \code{tol}.
 - 
 
62 
 
 - 
 
63 
  The LINPACK interface is restricted to matrices \code{x} with less
 59 
  max(diag(x)}.  The algorithm terminates once the pivot is less than
64 
  than \eqn{2^{31}}{2^31} elements.
 60 
  \code{tol}.
65 
}
 61 
}
66 
 
 62 
 
67 
\section{Warning}{
 63 
\section{Warning}{
68 
  The code does not check for symmetry.
 64 
  The code does not check for symmetry.
69 
 
 65 
 
Line 73... Line 69...
73 
  by construction.
 69 
  by construction.
74 
}
 70 
}
75 
 
 71 
 
76 
\source{
 72 
\source{
77 
  This is an interface to the LAPACK routines \code{DPOTRF} and
 73 
  This is an interface to the LAPACK routines \code{DPOTRF} and
78 
  \code{DPSTRF} and the LINPACK routines \code{DPOFA} and \code{DCHDC}.
 74 
  \code{DPSTRF},
79 
 
 75 
 
80 
  LAPACK and LINPACK are from \url{http://www.netlib.org/lapack} and
 - 
 
81 
  \url{http://www.netlib.org/linpack} and their guides are listed
 76 
  LAPACK is from \url{http://www.netlib.org/lapack} and its guide is listed
82 
  in the references.
 77 
  in the references.
83 
}
 78 
}
84 
\references{
 79 
\references{
85 
  Anderson. E. and ten others (1999)
 80 
  Anderson. E. and ten others (1999)
86 
  \emph{LAPACK Users' Guide}. Third Edition. SIAM.\cr
 81 
  \emph{LAPACK Users' Guide}. Third Edition. SIAM.\cr
Line 88... Line 83...
88 
  \url{http://www.netlib.org/lapack/lug/lapack_lug.html}.
 83 
  \url{http://www.netlib.org/lapack/lug/lapack_lug.html}.
89 
 
 84 
 
90 
  Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988)
 85 
  Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988)
91 
  \emph{The New S Language}.
 86 
  \emph{The New S Language}.
92 
  Wadsworth & Brooks/Cole.
 87 
  Wadsworth & Brooks/Cole.
93 
 
 - 
 
94 
  Dongarra, J. J., Bunch, J. R., Moler, C. B. and Stewart, G. W. (1978)
 - 
 
95 
  \emph{LINPACK Users Guide.}  Philadelphia: SIAM Publications.
 - 
 
96 
}
 88 
}
97 
 
 89 
 
98 
\note{
 - 
 
99 
  \code{LINPACK = TRUE, pivot = FALSE} (for compatibility with \R <
 - 
 
100 
  1.7.0) was formally deprecated in \R 2.15.2.
 - 
 
101 
}
 - 
 
102 
 
 - 
 
103 
 
 - 
 
104 
\seealso{
 90 
\seealso{
105 
  \code{\link{chol2inv}} for its \emph{inverse} (without pivoting),
 91 
  \code{\link{chol2inv}} for its \emph{inverse} (without pivoting),
106 
  \code{\link{backsolve}} for solving linear systems with upper
 92 
  \code{\link{backsolve}} for solving linear systems with upper
107 
  triangular left sides.
 93 
  triangular left sides.
108 
 
 94