| chol2inv-methods {Matrix} | R Documentation |
Inverse from Cholesky Factor
Description
Given formally upper and lower triangular matrices
U and L, compute (U' U)^{-1}
and (L L')^{-1}, respectively.
This function can be seen as way to compute the inverse of a
symmetric positive definite matrix given its Cholesky factor.
Equivalently, it can be seen as a way to compute
(X' X)^{-1} given the R part of the
QR factorization of X, if R is constrained to have
positive diagonal entries.
Usage
chol2inv(x, ...)
## S4 method for signature 'dtrMatrix'
chol2inv(x, ...)
## S4 method for signature 'dtCMatrix'
chol2inv(x, ...)
## S4 method for signature 'generalMatrix'
chol2inv(x, uplo = "U", ...)
Arguments
x |
a square matrix or |
uplo |
a string, either |
... |
further arguments passed to or from methods. |
Value
A matrix, symmetricMatrix,
or diagonalMatrix representing
the inverse of the positive definite matrix whose
Cholesky factor is x.
The result is a traditional matrix if x is a
traditional matrix, dense if x is dense, and
sparse if x is sparse.
See Also
The default method from base, chol2inv,
called for traditional matrices x.
Generic function chol, for computing the upper
triangular Cholesky factor L' of a symmetric positive
semidefinite matrix.
Generic function solve, for solving linear systems
and (as a corollary) for computing inverses more generally.
Examples
(A <- Matrix(cbind(c(1, 1, 1), c(1, 2, 4), c(1, 4, 16))))
(R <- chol(A))
(L <- t(R))
(R2i <- chol2inv(R))
(L2i <- chol2inv(R))
stopifnot(exprs = {
all.equal(R2i, tcrossprod(solve(R)))
all.equal(L2i, crossprod(solve(L)))
all.equal(as(R2i %*% A, "matrix"), diag(3L)) # the identity
all.equal(as(L2i %*% A, "matrix"), diag(3L)) # ditto
})