A Kogbetliantz-type SVD for general matrices.
(... work in progress ...)
This software is a supplementary material for:
- the preprint arXiv:2407.13116.
Several routines and executables require having quadruple precision (KIND=REAL128) fully supported by the compiler.
First, clone libpvn repository, with the same parent directory as this one has (e.g., venovako/libpvn and venovako/KogAcc).
Then, build the libpvn library, with the same family of compilers and (no-)debug mode as it is meant to be used here (e.g., with icx if ifx is desired).
Please set the make option SAFE=sv2 for libpvn.
For now, only little-endian platforms are supported, with the gfortran or ifx compilers.
Building the documentation requires a recent version of Doxygen and Graphviz. Many routines are documented only rudimentary for now.
The correctly-rounded cr_hypot and cr_hypotf functions are expected to be provided by the CORE-MATH project.
Please consult the description of libpvn for more information.
All testing has been performed with the correctly rounded functions.
Even though it is technically feasible not to use them, this should be attempted only if necessary.
Run make help (GNU make assumed) in the src subdirectory.
Setting NDEBUG to, e.g., 3 is recommened.
The available Jacobi strategies:
| J | description |
|---|---|
| 0 | row-cyclic (sequential) |
| 1 | column-cyclic (sequential) |
| 2 | generalized Mantharam-Eberlein |
| 3 | dynamic (max N/2 pairs) |
| 4 | modified modulus: quasi-cyclic |
| 5 | 2, but executed sequentially |
| 6 | 3, but executed sequentially |
| 7 | 4, but executed sequentially |
A block strategy pair is computed as:
J_inner + J_outer * 8where J_inner and J_outer are taken from the table above.
The GNU Fortran compiler is recommended for the J_outer = 3 case.
Please, set the block size B to at least 4, for now.
For both the blocked and the pointwise routines it is recommended that the matrix order be even.
The etc/env.sh script should be sourced, without arguments or with a single argument 2, as:
source etc/env.shbefore running any OpenMP-parallel executable.
The argument 2 enables the experimental, nested, two-level OpenMP parallelism for the block-method executables ?ksvd1.exe.
| routines | description |
|---|---|
xKSVD0 |
a pointwise method with a (quasi-)cyclic ordering |
xKSVDD |
a pointwise method with the dynamic ordering |
xKSVD1 |
a blocked method with any available ordering |
In general, the in-out INFO argument of the above routines should be preset in one of two ways:
INFO=M, for a faster but less accurate/reliable algorithm, orINFO=-M-1, for a slower but more accurate/reliable one, whereM≥0is the maximal number of (block-)steps, either parallel or sequential, to be performed.
The test executables always choose the latter option, and should be consulted for examples of properly allocating the various buffers and calling the routines.
Please note that the xKSVD2 routines are just wrappers around the 2×2 SVD routines from libpvn.
The complex routines have not been tested as thoroughly as the real ones. Use them with care.
More testing is generally needed.
If something seems wrong, recompiling without the NDEBUG option should turn on the error checking and might help with locating the issue.
This work has been supported in part by Croatian Science Foundation under the project IP-2014-09-3670 (MFBDA).