The J-Kogbetliantz algorithm for the hyperbolic singular value decomposition (HSVD)

This software is a supplementary material for the paper doi:10.1007/s11075-021-01197-4 (arXiv:2003.06701 [math.NA]).

A recent 64-bit Linux (e.g., CentOS 7.9 with devtoolset-8), macOS (e.g., Big Sur), or Windows (e.g., 10) is needed.

On Linux or macOS, run make (GNU make assumed) or gmake as follows:

cd src
make [COMPILER=gnu|x64|x64x|x200|nvidia] [NDEBUG=0|1|2|3|4|5] [all|clean|help]

where COMPILER should be set for the Intel Fortran compiler to x64 or x64x for Xeons, or to x200 for Xeon Phi KNLs, respectively. Building with a recent Intel Fortran is possible on Windows as well:

cd src
nmake [FORT=ifort|ifx] [NDEBUG=d|1|2|3|4|5] [all|clean|help]

Here, NDEBUG should be set to the desired optimization level (3 is a sensible choice). If unset, the predefined debug-mode build options will be used.

If COMPILER is not set or is gnu, the GNU Fortran compiler will be used, but it is not recommended. Please see this explanation regarding the new MIN and MAX intrinsics. The major versions of gfortran above 8 thus require a fix from src/gnu.mk that can be turned off for the older compilers.

While the nvfortran compiler might work, the executables have not been tested. The support for Oracle and Absoft Fortran compilers has been removed.

For example, make COMPILER=x200 NDEBUG=3 clean all will trigger a full, release-mode rebuild for the KNLs.

In the examples below, FN is the input and output file name prefix (without an extension), N for the matrix order, and N_2 for the maximal number of transformations per step (up to N/2, with the fail-safe but the slowest option being 1).

Assuming the top directory of the cloned repository has been made current, execute either

src/D/djk.exe FN N N_2

for the real, or

src/Z/zjk.exe FN N N_2

for the complex variant. The standard OpenMP environment variables can be used to set the desired number and/or placement of threads.

FN.Y should be a binary (DOUBLE PRECISION or DOUBLE COMPLEX) file containing the input matrix in the Fortran (column-major) array order. FN.J should be a binary file containing a vector of N 8-byte INTEGERs (either 1 or -1), representing the diagonal of the sign matrix. The outputs will be stored in the binary files FN.SY (the hyperbolic singular values), FN.YU (for the left), and FN.ZZ (for the right hyperbolic singular vectors).

Makefiles for the old and unmaintained code are included for Windows and macOS; for Linux, please edit src/old/GNUmakefile.

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