| chol {base} | R Documentation |
The Choleski Decomposition
Description
Compute the Choleski factorization of a symmetric (Hermitian), positive definite square matrix.
Usage
chol(x)
Arguments
x |
a symmetric, positive definite matrix. |
Details
Note that only the upper triangular part of x is
used such that the above only holds when x is symmetric.
If the matrix is not positive-definite an error is generated. A non-negative definite but not strictly positive-definite matrix may or may not give an error depending on the numerical errors.
Value
The upper triangular factor of the Choleski decomposition, i.e., the
matrix R such that R'R = x (see example).
References
Dongarra, J. J., Bunch, J. R., Moler, C. B. and Stewart, G. W. (1978) LINPACK Users Guide. Philadelphia: SIAM Publications.
See Also
chol2inv for its inverse,
backsolve for solving linear systems with upper
triangular left sides.
qr, svd for related matrix factorizations.
Examples
( 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