FLAPWxHZ

The Hari-Zimmermann complex generalized hyperbolic SVD and EVD.

A part of the supplementary material for the paper doi:10.1137/19M1277813 (arXiv:1907.08560 [math.NA]).

Building

Prerequisites

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

Have the Intel MKL (Math Kernel Library) installed.

Then, clone and build JACSD in a directory parallel to this one.

Make options

Run make 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 C/C++ and Fortran compilers (version 19.1+/2020+ recommended) to x64 (deprecated but recommended) or x64x for Xeons, or to x200 for Xeon Phi KNLs, respectively. If COMPILER is not set, GNU C/C++/Fortran compilers will be used instead. If x64x is used and some routines from the shared subdirectory fail to compile, their source file(s) should be replaced by the same-named one(s) from the x64x subdirectory.

GNU Fortran 9 and 10 are not supported! Please take a look here for the explanation regarding the MAX and MIN intrinsics. Currently, only GNU Fortran 8 is fully supported. On RHEL/CentOS it is provided by, e.g., devtoolset-8.

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.

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

Execution

Command line

In the examples below, TPC stands for threads-per-core. If the hyperthreading is not desired, it should be set to 1.

FN is the input and output file name prefix (without an extension).

Phase 0

/path/to/phase0.exe input.bin FN

Phase 0 is a data conversion phase from a custom data format to a set of plain binary files.

Phase 1

OMP_NUM_THREADS=T OMP_PLACES=CORES OMP_PROC_BIND=SPREAD,CLOSE /path/to/phase1.exe FN L a G TPC

L, a, and G are the problem-specific parameters.

Phase 2

OMP_NUM_THREADS=T OMP_PLACES=CORES OMP_PROC_BIND=SPREAD,CLOSE /path/to/phase2.exe FN M N TPC

Phase 3

OMP_NUM_THREADS=T OMP_PLACES=CORES OMP_PROC_BIND=SPREAD,CLOSE /path/to/phase3.exe FN M N TPC JSTRAT1 NSWP1 JSTRAT2 NSWP2

JSTRAT1 is the inner, and JSTRAT2 the outer Jacobi strategy.

JSTRAT1 can be 2 for cycwor or 4 for mmstep (recommended).

JSTRAT2 can be 3 for cycwor (recommended if a particular number of threads is supported) or 5 for mmstep.

NSWP1 (1 for block-oriented) and NSWP2 (30 should suffice in most cases) are the maximal numbers of the inner and of the outer sweeps allowed, respectively.

Phase 4

OMP_NUM_THREADS=T OMP_PLACES=CORES OMP_PROC_BIND=SPREAD,CLOSE /path/to/phase4.exe FN N TPC

Data format

All data is stored in the Fortran array order.

The testing dataset is available for download (please, conserve the bandwidth by downloading only what is of interest to you).

An example of data format of the test cases:

file name	data type	rows	columns
FN.X	COMPLEX(8)	2*L*a	G
FN.T	COMPLEX(8)	2*L	2*L
FN.U	REAL(8)	L*a	1
FN.YY	COMPLEX(8)	2*L*a	G
FN.WW	COMPLEX(8)	2*L*a	G
FN.JJ	INTEGER(8)	2*L*a	1
FN.Y	COMPLEX(8)	G	G
FN.W	COMPLEX(8)	G	G
FN.J	INTEGER(8)	G	1
FN.P	INTEGER(8)	G	1
FN.O	INTEGER(8)	G	1
FN.YU	COMPLEX(8)	G	G
FN.WV	COMPLEX(8)	G	G
FN.Z	COMPLEX(8)	G	G
FN.EY	REAL(8)	G	1
FN.EW	REAL(8)	G	1
FN.E	REAL(8)	G	1
FN.SY	REAL(8)	G	1
FN.SW	REAL(8)	G	1
FN.SS	REAL(8)	G	1
FN.ZZ	COMPLEX(8)	G	G

Phase 0

Outputs FN.X, FN.T, FN.U.

Phase 1

Input: FN.X, FN.T, FN.U.

Output: FN.YY, FN.WW, FN.JJ.

Phase 2

Input: FN.YY, FN.WW, FN.JJ.

Output: FN.Y, FN.W, FN.J, FN.P, FN.O.

Phase 3

Input: FN.Y, FN.W, FN.J.

Output: FN.YU, FN.WV, FN.Z; FN.EY, FN.EW, FN.E; FN.SY, FN.SW, FN.SS.

Phase 4

Input: FN.Z.

Output: FN.ZZ.

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