chol2inv-methods {Matrix} | R Documentation |

## Inverse from Choleski or QR Decomposition – Matrix Methods

### Description

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`

.

Even more generally, given an upper triangular matrix `R`

,
compute `(R'R)^{-1}`

.

### Methods

- x = "ANY"
the default method from base, see
`chol2inv`

, for traditional matrices.

- x = "dtrMatrix"
method for the numeric triangular matrices,
built on the same LAPACK `DPOTRI`

function as the base
method.

- x = "denseMatrix"
if `x`

is coercable to a
`triangularMatrix`

, call the `"dtrMatrix"`

method above.

- x = "sparseMatrix"
if `x`

is coercable to a
`triangularMatrix`

, use `solve()`

currently.

### See Also

`chol`

(for `Matrix`

objects);
further, `chol2inv`

(from the base package),
`solve`

.

### Examples

```
(M <- Matrix(cbind(1, 1:3, c(1,3,7))))
(cM <- chol(M)) # a "Cholesky" object, inheriting from "dtrMatrix"
chol2inv(cM) %*% M # the identity
stopifnot(all(chol2inv(cM) %*% M - Diagonal(nrow(M))) < 1e-10)
```

[Package

*Matrix* version 1.5-1

Index]