R: Inverse from Choleski or QR Decomposition - Matrix Methods

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 1.3-4 Index]