When can we use parameter as both input and output? about blasfeo

[giaf]

In general the BLASFEO own API is closely related to the standard BLAS API, with the key difference that there is an additional argument for the result, such that the API is "non destructive".
The standard BLAS API is "destructive" and an explicit matrix copy has to be performed in the rather common case the input/output argument should be preserved.
So the BLASFEO API gives a bit more flexibility, and it is always possible to have the added output argument coincide with the argument acting as the input/output in the standard BLAS API.

E.g. if you take the dgemm in the standard BLAS API, it is something like
C = beta * C + alpha * A * B
then in BLASFEO there would be the additional argument D for the result
D = beta * C + alpha * A * B
that can possibly (but not necessarily) coincide with C.

Similarly, for dtrsm the standard BLAS API would be
B = alpha * inv(A) * B
and in the BLASFEO API again there is an additional argument D for the result
D = alpha * inv(A) * B
that can possibly (but not necessarily) coincide with B.

All other limitations about arguments overlapping are analogue to the standard BLAS API, where BTW are also not so clearly described but rather implicit in the understanding of the operation performed.
E.g. in case A and C coincide in dgemm in the BLAS API, clearly A would be overwritten with the result as soon as this is computed a bit at a time, so the result would be wrong in an unpredictable and implementation-dependent way.