chol {base} | R Documentation |
chol(x)
x |
a symmetric positive-definite matrix. |
This function computes the Choleski factorization
of the square matrix x
. It returns the upper triangular
factor of the 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., J. R. Bunch, C. B. Moler and G. W. Stewart (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