LAEIN to return number of iterations

[Goddan-wq]

Sometimes it is useful to know the exact number of iterations performed in iterative algorithms. LAPACK provides several places where the iteration count is returned, such as in the work array. For example, the LASQ2 family of functions supports this feature.

Is it possible to add such functionality to the LAEIN function? The functions either include work or rwork in their interface, but the output of these arrays is not documented. This array is used internally only by the LATRS function and is supposed to contain the 1-norm of the columns of matrix B.

Since LATRS is always called with the parameter Uplo = UPPER, the first element of the array is always zero. Therefore, if the user for some reason uses the work/rwork array after the LAEIN function, it would be relatively simple to account for this in high-level code. Alternatively, you could increase the size of work by 1 and return the iteration count as the last element of the array.

If this feature does not contradict the documentation, the logic of the function, and your ideas, I could do a PR