chol {base} | R Documentation |
Compute the Choleski factorization of a symmetric (Hermitian), positive definite square matrix.
chol(x)
x |
a symmetric, positive definite matrix. |
The upper triangular factor of the Choleski decomposition, i.e., the matrix R such that R'R = x (see example).
Note that effectively, only the upper triangular part of x
is
used such that the above only holds when x
is symmetric.
Dongarra, J. J., Bunch, J. R., Moler, C. B. and Stewart, G. W. (1978) LINPACK Users Guide. Philadelphia: SIAM Publications.
chol2inv
for its inverse,
backsolve
for solving linear systems with upper
triangular left sides.
qr
, svd
for related matrix factorizations.
( m <- matrix(c(5,1,1,3),2,2) ) ( cm <- chol(m) ) t(cm) %*% cm #-- = 'm' all(abs(m - t(cm) %*% cm) < 100* .Machine$double.eps) # TRUE