History

LAPACK is a library of functions for dealing with dense and banded matrices. It includes functions for solving systems of equations, linear least-squares, eigenvalue problems, singular value problems, and matrix factorizations such as QR, LU, Cholesky, SVD, and Schur forms. Functions in LAPACK are designed to call optimized BLAS functions whenever possible for maximum performance.

The full LAPACK library includes over 1700 functions and remains under active development. For compatibility purposes QML contains implementations of all public LAPACK functions with limitations and caveats discussed below. A subset of higher-level functions is documented in the API Reference. Documentation for other functions can be found on Netlib.

Conventions

Most functions in LAPACK are named following a similar convention to BLAS. The first letter indicates the numerical precision of the computation and is one of SDCZ. The next two letters indicate the storage format of the main matrices involved in the routine. Choices include all the formats supported by BLAS along with many more specialized formats. The final three letters indicate the operation to be performed. For example, DGEQRF means a double precision computation (D) on a general dense matrix (GE) performing a QR factorization (QRF).

Interface

The LAPACK interface follows the same conventions as the BLAS interface. As in the BLAS interface, the interface to LAPACK library functions follows Fortran conventions. All arguments to functions are passed by reference. In the C function prototypes this means every argument is a pointer, even simple scalar values. Functions that return complex values use a void return type and instead put their output into a result pointer.

As in the BLAS interface, matrices are stored in column-major order and indexing is 1-based. No aliasing of pointers is allowed in the LAPACK interface.

Function Pointers

Some LAPACK functions accept functions as arguments. A typical example is DGEES which accepts an argument SELECT that decides which eigenvalues should be sorted in the output. QML does not currently support function pointers. When interfacing to these functions using C, the type used is void *. Any values passed as function pointers are ignored and never called.

Booleans

Many functions accept or return Boolean values or arrays. In the C interface to these functions the type used is qml_int. This type is 4 bytes on 32-bit platforms and 8 bytes on 64-bit platforms. This type usually corresponds to the type LOGICAL and INTEGER in Fortran compilers.

Performance Considerations

Not all LAPACK functions provided by QML are highly optimized. For best performance limit calls to the functions documented in this guide. Many of the problems solved by LAPACK have significant sequential sections that cannot be easily parallelized so performance will necessarily be limited for these problems.

References

The official homepage of LAPACK is on Netlib. The most convenient way to browse function documentation is through the online explorer.