R: The Choleski Decomposition

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

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