# chol2inv

##### Inverse from Choleski (or QR) Decomposition

Invert a symmetric, positive definite square matrix from its Choleski decomposition. Equivalently, compute \((X'X)^{-1}\) from the (\(R\) part) of the QR decomposition of \(X\).

##### Usage

`chol2inv(x, size = NCOL(x), LINPACK = FALSE)`

##### Arguments

- x
a matrix. The first

`size`

columns of the upper triangle contain the Choleski decomposition of the matrix to be inverted.- size
the number of columns of

`x`

containing the Choleski decomposition.- LINPACK
logical. Defunct and ignored (with a warning for true value).

##### Value

The inverse of the matrix whose Choleski 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.

##### References

Anderson. E. and ten others (1999)
*LAPACK Users' Guide*. Third Edition.
SIAM.
Available on-line at
http://www.netlib.org/lapack/lug/lapack_lug.html.

Dongarra, J. J., Bunch, J. R., Moler, C. B. and Stewart, G. W. (1978)
*LINPACK Users Guide*.
Philadelphia: SIAM Publications.

##### See Also

##### Examples

`library(base)`

```
# NOT RUN {
cma <- chol(ma <- cbind(1, 1:3, c(1,3,7)))
ma %*% chol2inv(cma)
# }
```

*Documentation reproduced from package base, version 3.6.1, License: Part of R 3.6.1*