scipy.linalg.solve_triangular uses *trtrs from LAPACK. I must take a great deal of the responsibility for this, since I might have suggested it... In retrospect I think this was a mistake. *trtrs can solve op(A) X = B where op(A) is A or A.T *trsm from BLAS is more general. It can solve op(A) X = alpha * B or X op(A) = alpha * B. The latter might e.g. be useful for constructing an efficient scipy.linalg.solve for C ordered arrays. *trtrs is just a shallow wrapper over *trsm. It optionally checks A for singularity and then calls *trsm. The optional singularity check just amounts to checking that none of the diagonal elements are zero. I think we should make scipy.linalg.blas expose *trsm and then use that method for solve_triangular. Later we can use *trsm to optimize scipy.linalg.solve for C ordered arrays (i.e. avoid generating transposed copies). Regards, Sturla