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RELAPACK Configuration

ReLAPACK has two configuration files: make.inc, which is included by the Makefile, and config.h which is included in the source files.

Build and Testing Environment

The build environment (compiler and flags) and the test configuration (linker flags for BLAS and LAPACK) are specified in make.inc. The test matrix size and error bounds are defined in test/config.h.

The library librelapack.a is compiled by invoking make. The tests are performed by either make test or calling make in the test folder.

BLAS/LAPACK complex function interfaces

For BLAS and LAPACK functions that return a complex number, there exist two conflicting (FORTRAN compiler dependent) calling conventions: either the result is returned as a struct of two floating point numbers or an additional first argument with a pointer to such a struct is used. By default ReLAPACK uses the former (which is what gfortran uses), but it can switch to the latter by setting COMPLEX_FUNCTIONS_AS_ROUTINES (or explicitly the BLAS and LAPACK specific counterparts) to 1 in config.h.

For MKL, COMPLEX_FUNCTIONS_AS_ROUTINES must be set to 1.

(Using the wrong convention will break ctrsyl and ztrsyl and the test cases will segfault or return errors on the order of 1 or larger.)

BLAS extension xgemmt

The LDL decompositions require a general matrix-matrix product that updates only a triangular matrix called xgemmt. If the BLAS implementation linked against provides such a routine, set the flag HAVE_XGEMMT to 1 in config.h; otherwise, ReLAPACK uses its own recursive implementation of these kernels.

xgemmt is provided by MKL.

Routine Selection

ReLAPACK's routines are named RELAPACK_X (e.g., RELAPACK_dgetrf). If the corresponding INCLUDE_X flag in config.h (e.g., INCLUDE_DGETRF) is set to 1, ReLAPACK additionally provides a wrapper under the LAPACK name (e.g., dgetrf_). By default, wrappers for all routines are enabled.

Crossover Size

The crossover size determines below which matrix sizes ReLAPACK's recursive algorithms switch to LAPACK's unblocked routines to avoid tiny BLAS Level 3 routines. The crossover size is set in config.h and can be chosen either globally for the entire library, by operation, or individually by routine.

Allowing Temporary Buffers

Two of ReLAPACK's routines make use of temporary buffers, which are allocated and freed within ReLAPACK. Setting ALLOW_MALLOC (or one of the routine specific counterparts) to 0 in config.h will disable these buffers. The affected routines are:

  • xsytrf: The LDL decomposition requires a buffer of size n^2 / 2. As in LAPACK, this size can be queried by setting lWork = -1 and the passed buffer will be used if it is large enough; only if it is not, a local buffer will be allocated.

    The advantage of this mechanism is that ReLAPACK will seamlessly work even with codes that statically provide too little memory instead of breaking them.

  • xsygst: The reduction of a real symmetric-definite generalized eigenproblem to standard form can use an auxiliary buffer of size n^2 / 2 to avoid redundant computations. It thereby performs about 30% less FLOPs than LAPACK.

FORTRAN symbol names

ReLAPACK is commonly linked to BLAS and LAPACK with standard FORTRAN interfaces. Since these libraries usually have an underscore to their symbol names, ReLAPACK has configuration switches in config.h to adjust the corresponding routine names.