Determinant of a Matrix from QR Decomposition

DESCRIPTION:
Computes the modulus of the determinant (or its logarithm) of a square Matrix from its QR decomposition.

USAGE:
det.qr.Matrix(x, logarithm=T)

REQUIRED ARGUMENTS:
x:
an object of class "qr.Matrix" representing the QR decomposition of a square Matrix.

OPTIONAL ARGUMENTS:
logarithm:
a logical variable indicating whether or not the logarithm of the modulus of the determinant should be returned rather than the determinant itself. The default is to return the logarithm.

VALUE:
returns an object of class "det".

DETAILS:
The determinant is computed as the the determinant of the triangular factor in the QR factorization. The sign of the determinant is not given since it involves computing the determinant of the orthogonal or unitary factor, which may be less efficient than computing the determinant from x directly.

REFERENCES:
Golub, G., and Van Loan, C. F. (1989). Matrix Computations, 2nd edition, Johns Hopkins, Baltimore.

SEE ALSO:
det.object , det.Matrix .

EXAMPLES:
x <- Matrix( sample(-3:3, size = 9, replace = T), nrow = 3, ncol = 3)
det(qr(x))