AccJac

Accurate complex Jacobi rotations

This software is a supplementary material for the paper doi:10.1016/j.cam.2024.116003, with the preprint doi:10.48550/arXiv.2308.14222, i.e., arXiv:2308.14222 [math.NA].

Prerequisites

A recent machine with Linux or macOS is needed. The Intel (icx) or GNU (gcc) C compiler, and the Intel (ifx) or GNU (gfortran 13+) Fortran compiler are required.

First, clone libpvn repository, with the same parent directory as this one has (e.g., venovako/libpvn and venovako/AccJac), and build it, with the COMPILER make option set to a C compiler from the same vendor and with the same (no-)debug mode as it is meant to be used here. Please, read the repository's notes carefully! The correctly-rounded cr_hypot[f] and cr_rsqrt[fl] functions are assumed to be provided by the CORE-MATH project.

Building

In the src subdirectory, run

make [COMPILER=gfortran|ifx] [COMPILER_PREFIX=...] [COMPILER_SUFFIX=...] [ABI=lp64|ilp64] [NDEBUG=optimization_level] [LAPACK=...] [MPFR=...] [GMP=...] [PROFILE=...] [all|help|clean]

The COMPILER and NDEBUG variables have to be compatible with those for building the libpvn repository; e.g., if COMPILER=gcc for libpvn, then COMPILER=gfortran here. It is recommended to set NDEBUG=3 for both repositories, unless debugging. Other variables should not be set unless their effects are fully understood.

Running

With N>0 being a desired number of random Hermitian/symmetric matrices of order two to be generated, run

./src/ttest.exe N

where t=c,d,s,z.

Here, c stands for COMPLEX(REAL32), d for REAL(REAL64), s for REAL(REAL32), and z for COMPLEX(REAL64). The executables with other values of t are of special purpose and have specific requirements to be built and run. Since there are no CORE-MATH cr_* functions for these other datatypes yet, the testing results are not quite relevant to the proposed algorithm. With GNU Fortran on Intel-compatible platforms, t=w stands for COMPLEX(10), and t=x for REAL(10) (the 80-bit extended floating-point datatype). With the MPFR and GMP libraries, and MPFR and GMP set to their respective installation prefixes, t=y stands for COMPLEX(REAL128) and t=q for REAL(REAL128).

Other

Additional material is available in the etc subdirectory.

TODO: direct lower-triangular, as well as real, variants of CJAEVD and ZJAEVD remain to be written.

This work has been supported in part by Croatian Science Foundation under the project IP-2014-09-3670 (MFBDA).