About the BENDING-Programs

BENDOPT and BENDPDF are two computer programs implementing different approaches of the so-called "BENDING" procedure (Hayes and Hill, 1981).

In BENDOPT, the appropriate bending factor is either chosen by an optimized procedure (Essl, 1991), which requires some prior knowledge, or may be preselected by the user in dependence of some sample properties. This approach was primarily intended to improve poorly estimated variance-covariance matrices for index selection purposes. However, this procedure can also be applied quite generally to any genetic variance-covariance matrix obtained from a small or poorly structured sample to get more reliable parameter-estimates (e.g. heritabilites and genetic correlations between traits).

In BENDPDF, a variance-covariance matrix (e.g. negative definite) is bent until its lowest eigenvalue exceeds a preset limit (e.g. zero to achieve non-negative-definiteness).

System requirements

Both programs are written in FORTRAN77 and have been tested under DOS.

How to get the program

The programs are available for DOS in a compressed self extracting file bending.rar. Just click on the filename to download it directly to your disk. The compressed files contain the source codes (BENDOPT.FOR and BENDPDF.FOR), exe-files(BENDOPT.EXE and BENDPDF.EXE), one example each for an input file (IN.OPT and IN.PDF) and output file (OUT.OPT and OUT.PDF) is provided. Documentation of the programs and further instructions may be found either in file MANUAL.ASC or in both source programs themselves.


Essl, A. (1991): Choice of an appropriate bending factor using prior knowledge of the parameters. J. Anim. Breed. Genet. 108, 89-101.

Hayes, J.F.; Hill, W.G. (1981): Modification of estimates of parameters in the construction of genetic selection indices ("Bending"). Biometrics 37, 483-493.