| chol {base} | R Documentation |
The Choleski Decomposition
Usage
chol(x)
Arguments
x |
a symmetric positive-definite matrix. |
Value
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.
References
Dongarra, J. J., J. R. Bunch, C. B. Moler and G. W. Stewart (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