Tutorial: Linear Algebra

This tutorial will briefly cover the linear algebra in Owl. Specifically, I will introduce: 1) low-level interface to CBLAS and LAPACKE; 2) high-level wrapper functions in Linalg module; 3) some simple examples.

Low-level Interface to CBLAS & LAPACKE

Owl has implemented the full interface to CBLAS and LAPACKE. Comparing to Julia which chooses to interface to BLAS/LAPACK, you might notice the extra C in CBLAS and E in LAPACKE since they are the corresponding C-interface. It is often believed that C-interface can lead to degraded performance due to the extra overhead. However, it turns out you cannot really notice any difference at all in practice when dealing with medium or large problems.

Owl_cblas module provides the raw interface to CBLAS functions, from level-1 to level-3. The interfaced functions have the same names as those in CBLAS.

Owl_lapacke_generated module provides the raw interface to LAPACKE functions (over 1,000) which also have the same names defined in lapacke.h.

Owl_lapacke module is a very thin layer of interface between Owl_lapacke_generated module and Linalg module. The purpose is to provide a unified function to make generic functions over different number types.

high-level Wrappers in Linalg Module

The functions in Owl_cblas and Owl_lapacke_generated are very low-level, e.g., you need to deal with calculating parameters, allocating workspace, processing results, and many other details. You do not really want to use them directly unless you have enough background in numerical analysis and chase after the performance. In practice, you should use Linalg module which gives you a high-level wrapper for frequently used functions.

The Linalg has the following module structure.

• Owl.Linalg.Generic: generic functions over four number types S/D/C/Z.

• Owl.Linalg.S: only for float32 type.

• Owl.Linalg.D: only for float64 type.

• Owl.Linalg.C: only for complex32 type.

• Owl.Linalg.Z: only for complex64 type.