| xTAx {statnet.common} | R Documentation |
Common quadratic forms
xTAx(x, A)
xAxT(x, A)
xTAx_solve(x, A, ...)
xTAx_qrsolve(x, A, tol = 1e-07, ...)
sandwich_solve(A, B, ...)
x |
a vector |
A |
a square matrix |
... |
additional arguments to subroutines |
tol |
tolerance argument passed to the relevant subroutine |
B |
a square matrix |
These are somewhat inspired by emulator::quad.form.inv() and others.
xTAx(): Evaluate x'Ax for vector x and square
matrix A.
xAxT(): Evaluate xAx' for vector x and square
matrix A.
xTAx_solve(): Evaluate x'A^{-1}x for vector x and
invertible matrix A using solve().
xTAx_qrsolve(): Evaluate x'A^{-1}x for vector x and
matrix A using QR decomposition and confirming that x
is in the span of A if A is singular; returns rank
and nullity as attributes just in case subsequent calculations
(e.g., hypothesis test degrees of freedom) are affected.
sandwich_solve(): Evaluate A^{-1}B(A')^{-1} for B a
square matrix and A invertible.