Given a QR factorization of a real or complex matrix A = Q*R, Q unitary and R upper trapezoidal, return the QR factorization of [A(:,1:j-1) A(:,j+1:n)], i.e. A with one column deleted (if orient is "col"), or the QR factorization of [A(1:j-1,:);A(:,j+1:n)], i.e. A with one row deleted (if orient is "row").
The default value of orient is "col".
If orient is "col", the matrix Q is not required to be square.
For Matlab compatibility, if Q is nonsquare on input, the updated factorization is always stripped to the economical form, i.e.
columns (Q) == rows (R) <= columns (R)
.To get the less intelligent but more natural behaviour when Q retains it shape and R loses one column, set orient to "col+" instead.
If orient is "row", Q must be square.