givens: Givens Rotation

Description

Givens Rotations and QR decomposition

Usage

givens(A)

Arguments

numeric square matrix.

Value

List with two matrices Q and R, Q orthonormal and R upper triangular, such that A=Q%*%R.

Details

givens(A) returns a QR decomposition (or factorization) of the square matrix A by applying unitary 2-by-2 matrices U such that U * [xk;xl] = [x,0] where x=sqrt(xk^2+xl^2)

References

Golub, G. H., and Ch. F. van Loan (1996). Matrix Computations. Third edition, John Hopkins University Press, Baltimore.

Examples

Run this code

##  QR decomposition
A <- matrix(c(0,-4,2, 6,-3,-2, 8,1,-1), 3, 3, byrow=TRUE)
gv <- givens(A)
(Q <- gv$Q); (R <- gv$R)
zapsmall(Q %*% R)

givens(magic(5))

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