QR decomposition for transposed matrices

Hi,

could you please help with a solution of the following issue.

There is a simple Z*beta=Y overdetermined linear system with respect to beta and I want to solve it with MKL/QR decomposition. I read manual and found two similar approaches to achieve the goal:

1. one 'sgels(...)' call or
2. sequence 'geqrf(...) + ormqr(...) + trsm(...)' of calls

The issue is, that matrices in my application are stored in transposed form, i.e. (X')*beta=Y system is under consideration. Is there any possibility to find QR decomposition for transposed?

Note. Solution with LQ factorization was tried, but it takes approximately 10 times longer than QR for transposed matrices.

Thank you in advance.