Difference between dtrtrs and dtrsm

Question

I am looking for some triangular solvers, and I have come across two solvers. One in BLAS: dtrsm and another in LAPACK: dtrtrs. From the looks of it both seem to have common functionality, with dtrsm having a little bit more functionality (scaling the right hand side before solving the system).

I would like to know
1) How else do these functions differ ?
2) When performing the same operation, which is faster ?
3) If the answer to (2) is not obvious, When is dtrsm suggested over dtrtrs and vice versa ?

Answer 1

1. Besides scaling, dtrsm can also solve systems in which the triangular matrix is right-multiplied into the unknown matrix (i.e., it can solve XA = B as well as AX = B). On the other hand, dtrsm can silently fail if A is singular, whereas dtrtrs checks for this condition and reports an error.

2. In a "typical" LAPACK distribution, dtrtrs is just a wrapper that checks for singularity and then calls dtrsm. dtrsm is therefore slightly faster, but that difference is insignificant for matrices of any reasonable size.