Update QR when matrix left-multipied with diagonal matrix Suppose I have a matrix $A$ and its $QR$-factorization, $A = QR$.
Now I need to find the $QR$-factorization of $DA$, where 


*

*$D$ is a diagonal matrix.

*$D$ is a diagonal matrix where just one
element differs from the rest.


Is there a way to reuse the previously computed $QR$ of $A$?
 A: Probably not.
The reason for this opinion is a kind of inductive reasoning.
It is a known fact that (see http://home.utah.edu/~nahaj/math/luul2qr.html), QR factorization of $A$ is linked to Cholesky factorization of $A^TA$, as displayed by this Matlab program:
A=rand(4)
[Q,R]=qr(A)
S=A'*A;
r=chol(S)
q=m*inv(r)

that will show you that (q,r) is identical to (Q,R), up to sign changes. In this way, there is a sort of equivalence between:
Finding an "easy" way to take advantage of the QR factorization of $A$ to find a QR factorization of $DA$
and
Finding an "easy" way from Cholesky factorization of $A^TA$ to Cholesky factorization of: $(DA)^T(DA)=A^T(D^TD)A$.
But I dont see how it is possible, because the insertion of a diagonal matrix $D^TD$ deeply modifies the structure of  $A^TA$.
Another remark: Left-multiplying by the diagonal matrix $D=diag(a_1,a_2,\cdots a_n)$ amounts to multiply the $k$-th row of $A $ by $a_k(k=1 \cdots n)$, whereas right multiplication yields, column -multiplication of $A$'s columns by the $a_k$s, and this is very easy to tackle.
A: Regarding your point 1, I agree with Jean Marie.
Your point 2 should be doable:


*

*Delete from the $QR$ factorisation the row of $A$ corresponding to the element of $D$ which is different from the rest (see, e.g. qr_delete);

*Multiply the resulting $R$ by the scalar which is the common element of $D$;

*Re-insert the deleted row multiplied by the correct coefficient (see, e.g. qr_insert).

