Follow up on pr1146 (v2)

[langou]

Follow up on PR #1146. ( Thanks to @yizeyi18 for the PR.)

While reviewing, @angsch suggested

Shouldn't jobu = 'f' and jobu = 'r' be included here too?

I implemented the suggestion. This ended being easier for me to do a substantial rewrite.

I followed the explanation at

lapack/SRC/cgesvdq.f

Lines 159 to 198 in 034ada1

	*> \param[out] U
	*> \verbatim
	*> U is COMPLEX array, dimension
	*> LDU x M if JOBU = 'A'; see the description of LDU. In this case,
	*> on exit, U contains the M left singular vectors.
	*> LDU x N if JOBU = 'S', 'U', 'R' ; see the description of LDU. In this
	*> case, U contains the leading N or the leading NUMRANK left singular vectors.
	*> LDU x N if JOBU = 'F' ; see the description of LDU. In this case U
	*> contains N x N unitary matrix that can be used to form the left
	*> singular vectors.
	*> If JOBU = 'N', U is not referenced.
	*> \endverbatim
	*>
	*> \param[in] LDU
	*> \verbatim
	*> LDU is INTEGER.
	*> The leading dimension of the array U.
	*> If JOBU = 'A', 'S', 'U', 'R', LDU >= max(1,M).
	*> If JOBU = 'F', LDU >= max(1,N).
	*> Otherwise, LDU >= 1.
	*> \endverbatim
	*>
	*> \param[out] V
	*> \verbatim
	*> V is COMPLEX array, dimension
	*> LDV x N if JOBV = 'A', 'V', 'R' or if JOBA = 'E' .
	*> If JOBV = 'A', or 'V', V contains the N-by-N unitary matrix V**H;
	*> If JOBV = 'R', V contains the first NUMRANK rows of V**H (the right
	*> singular vectors, stored rowwise, of the NUMRANK largest singular values).
	*> If JOBV = 'N' and JOBA = 'E', V is used as a workspace.
	*> If JOBV = 'N', and JOBA.NE.'E', V is not referenced.
	*> \endverbatim
	*>
	*> \param[in] LDV
	*> \verbatim
	*> LDV is INTEGER
	*> The leading dimension of the array V.
	*> If JOBV = 'A', 'V', 'R', or JOBA = 'E', LDV >= max(1,N).
	*> Otherwise, LDV >= 1.
	*> \endverbatim

[mgates3]

Looks fine. Maybe a couple things could be improved later on.

[mgates3]

Ok, but since free( NULL ) does nothing, it would be simpler to have just one exit level and free all the pointers:

exit_level_0:
    LAPACKE_free( v_t );  v_t = NULL;
    LAPACKE_free( u_t );  u_t = NULL;
    LAPACKE_free( a_t );  a_t = NULL;

I tend to reset pointers to NULL after freeing them, to avoid any possible confusion.

If desired, perhaps that can be a future simplification of all of LAPACKE.

[langou]

I am slowing down on that, so, as you suggest: "could be improved later on." So, if we get there, for sure, let us do a separate pull request.

I do like the idea to reset pointers to NULL after freeing them, to avoid any possible confusion.

Here is why I am slowing down: While free(NULL) does nothing, is it true that LAPACKE_free( NULL ) does nothing? What do we ask LAPACKE_free() to do? This proposed change would implicitly state that we require LAPACKE_free( NULL ) to do nothing.

I like the logic "if you fail to allocate at level 2, then do not forget to free level 0 and level 1 that were previously allocated." I feel it could be useful in some context, but maybe not for a C wrapper.

So all in all, are there more opinions about what @mgates3 suggest? In favor? Against?