# Basis Factorization Packages

Basis Factorization Package (shortened as BFP) is a unique lp_solve feature. Considerable effort has been put in this new feature and we have big expectations for this. BFP is a generic interface model and users can develop their own implementations based on the provided templates. We are very interested in providing as many different BFPs as possible to the community.

Until version 4, lp_solve always used the product form of the inverse (etaPFI) to perform its matrix pivot changes. However there are other methods like LU decomposition. Each method has its advantages and disadvantages. Some are faster/slower, other are numerical more/less stable. The speed and stability of a solver depends considerably on the BFP. One model will be solved better with one BFP and another with another BFP.
The following is a personal comment on the different BFPs by Kjell Eikland:
"Personally, I go for numerical robustness and size capability LUSOL is the one to beat. The LUSOL code has tremendous features for tackling even the toughest models, balancing accuracy and fill-in to a phenomenal extent. I have experimented with a maximum update limit before refactorization of 1500, and even at that level LUSOL was much more reliable than etaPFI! LUSOL does extremely well with some classes of very tough models, such as the PILOT models. For simple, not too large network-like models with little fill-in, etaPFI can be extremely fast and maintain accuracy if the numerics are not too bad. etaPFI v2 is typically both faster and numerically more robust and can handle much more challenging models than v1. The main reason is that v2 typically has quite a bit less fill-in and better pivot management, which automatically leads to better speed and accuracy. GLPK has an LU implementation model that is conceptually/numerically inferior to LUSOL, but updating and btran can be faster. For medium size models of a higher than average toughness, GLPK is definitely a good choice. However, in my experience GLPK is not robust from the perspective of memory management. With some unusually hard models prone to fill-in it simply bombs, which is not good in a production environment. Accuracy management is limited to refactorization (just like etaPFI)."

lp_solve version 5.5 has the LUSOL engine built in as default. In addition two other BFPs are included for both Windows and Linux: bfp_LUSOL.dll, bfp_etaPFI.dll for Windows and libbfp_LUSOL.so, libbfp_etaPFI.so for Linux. The standalone bfp_etaPFI is v2.0 and includes advanced column ordering using the COLAMD library, as well as better pivot management for stability. For complex models, however, the LU factorization approach is much better, and lp_solve now includes LUSOL as one of the most stable engines available anywhere. LUSOL was originally developed by Prof. Saunders at Stanford, and it has now been ported to C and enhanced by Kjell Eikland.

These BFPs are not statically linked, but are dynamically loaded when requested (except for the default LUSOL engine). It is even possible for people to write their own BFP. Under Windows, a BFP is provided as DLL (bfp_*.dll), under UNIX/LINUX as a dynamic linked library (libbfp_*.so).
To change the BFP with lp_solve, use the option -bfp <filename>. Via the API, use set_BFP. filename is the name of the dynamic linked library. It is possible to provide a path to this name to be sure that the BFP from the specified location is used. If no path is given, then it depends on the OS where it will be searched.

Under Windows, the following search order is used:

1. Current directory.
2. A semi-colon-separated (;) list of directories in the user's PATH environment variable.

Under Unix/Linux, following search order is used:

1. A colon-separated (:) list of directories in the user's LD_LIBRARY_PATH environment variable.
2. The list of libraries specified in /etc/ld.so.cache (which is generated from /etc/ld.so.conf).
3. /lib, followed by /usr/lib. Note the order here; this is the reverse of the order used by the old a.out loader. The old a.out loader, when loading a program, first searched /usr/lib, then /lib (see the man page ld.so(8)). This shouldn't normally matter, since a library should only be in one or the other directory (never both), and different libraries with the same name are a disaster waiting to happen.

Under Unix/Linux it is standard that a library has the lib prefix and a .so postfix. Under Windows there is no prefix and a .dll postfix.
To make the calling structure for BFPs uniform across different types of OS, lp_solve automatically adds the prefix and postfix if not provided. So the following commands are valid for both Windows and Unix/Linux:

lp_solve -bfp bfp_LUSOL input.lp
lp_solve -bfp ./bfp_LUSOL input.lp

The latter makes sure that the BFP is searched in the current directory, especially for Unix/Linux.

A third BFP based on GLPK may be included later, but license issues must first be resolved. In the interim, you may experiment with the working sample BFP interface files for GLPK.

If you compile BFPs yourself, make sure that under Windows, you use __stdcall convention and use 8 byte alignments. This is needed for the BFPs to work correctly with the general distribution of lp_solve and also to make sharing BFPs as uncomplicated as possible.