Hello,
using the intel MKL 11.1 for windows, i discovered what seems a bug in LAPACKE C interface to Lapack: calling LAPACKE_dpptrf (Cholesky decomposition) with a packed LT row major matrix does not produce the expected result. Results are correct only passing a column major matrix and thus the LAPACK dpptrf is right and i suspect the LAPACKE interface is not. Searching on the web i found the source file lapacke_dpptrf.c on the netlib site (with intel copyright) and the related lapacke_dpptrf_work.c which, i think, is the source of the bug. (see http://www.netlib.org/lapack/explore-html/de/ddd/lapacke_8h.html)
In the lapacke_dpptrf_work function a copy ap_t of the working matrix ap is transposed before and after the call of the factorization routine. The double transposition should not really necessary since a packed row major LT matrix has the same linear array representation of a packed column major UT matrix (and viceversa) and thus it would suffice to call LAPACK_dpptrf(&uplo,6n, &ap,&info) with uplo='U' if ap is a row major LT matrix and with uplo='L' if ap is a row major UT matrix.
The correct code is very simple and does not require temporaries (ap_t) nor transpositions:
char tmp_uplo=uplo;
if(matrix_order==RowMajor)
tmp_uplo=(uplo=='L')?'U':'L';
LAPACK_dpptrf( &tmp_uplo, &n, &ap_t, &info );
Note that after the factorization it isnt necessary to transpose the factor since it is already correct.
I tested the above code and the factor is the correct one.
Clearly also the companion solver routine LAPACKE_dpptrs_work should be affected by the same problem and there you make 3 transpositions! one for the working matrix and two for the rhs, while only a pre and a post rhs transposition would suffice (may be a better solution exists).
best regards