| % File src/library/base/man/chol2inv.Rd |
| % Part of the R package, https://www.R-project.org |
| % Copyright 1995-2020 R Core Team |
| % Distributed under GPL 2 or later |
| |
| \name{chol2inv} |
| \alias{chol2inv} |
| \title{Inverse from Cholesky (or QR) Decomposition} |
| \description{ |
| Invert a symmetric, positive definite square matrix from its Cholesky |
| decomposition. Equivalently, compute \eqn{(X'X)^{-1}}{(X'X)^(-1)} |
| from the (\eqn{R} part) of the QR decomposition of \eqn{X}. |
| } |
| \usage{ |
| chol2inv(x, size = NCOL(x), LINPACK = FALSE) |
| } |
| \arguments{ |
| \item{x}{a matrix. The first \code{size} columns of the upper triangle |
| contain the Cholesky decomposition of the matrix to be inverted.} |
| \item{size}{the number of columns of \code{x} containing the |
| Cholesky decomposition.} |
| \item{LINPACK}{logical. Defunct and gives an error.} |
| |
| } |
| \value{ |
| The inverse of the matrix whose Cholesky decomposition was given. |
| |
| Unsuccessful results from the underlying LAPACK code will result in an |
| error giving a positive error code: these can only be interpreted by |
| detailed study of the FORTRAN code. |
| } |
| \source{ |
| This is an interface to the LAPACK routine \code{DPOTRI}. |
| LAPACK is from \url{https://www.netlib.org/lapack/} and its guide is listed |
| in the references. |
| } |
| \references{ |
| Anderson. E. and ten others (1999) |
| \emph{LAPACK Users' Guide}. Third Edition. |
| SIAM. |
| Available on-line at |
| \url{https://www.netlib.org/lapack/lug/lapack_lug.html}. |
| |
| Dongarra, J. J., Bunch, J. R., Moler, C. B. and Stewart, G. W. (1978) |
| \emph{LINPACK Users Guide}. |
| Philadelphia: SIAM Publications. |
| } |
| \seealso{ |
| \code{\link{chol}}, \code{\link{solve}}. |
| } |
| \examples{ |
| cma <- chol(ma <- cbind(1, 1:3, c(1,3,7))) |
| ma \%*\% chol2inv(cma) |
| } |
| \keyword{algebra} |
| \keyword{array} |