ARPACK example driver gives different results from Matlab
 

Hi

Does anybody here know well ARPACK? I need your help.

I'm playing with ARPACK. I looked into the examples they provide, zndrv3.f, in the ARPACK/EXAMPLES/COMPLEX/ directory. I also came cross into NAG Fortran Library. In NAG, there are some linear-problem solvers F12***. The F12*** routines in NAG are equivalent to the znaupd in ARPACK. So I want to check if they will yield the same results.

I first looked into the example provided in the user guide of F12ARF at http://www.nag.co.uk/numeric/fl/nagd...F12/f12arf.pdf for example. In the end, it yields the results of

509.9390
380.9092
659.1558
271.9412

around the shift=500. I solved the same generalized eigenvalue problem in Matlab. Matlab gave the same results.

But when I used znaupd from ARPACK to solve the same problem, I obtained different answers. The 4 eigenvalues are now
rd1 = 501.65650188259684
rd2 = 480.15153312181440
rd3 = 526.52596256924164
rd4 = 461.99019999608828

The routines in NAG and ARPACK both use SHIFTED INVERSE mode and solve a generalized problem.
I'm not sure what was wrong. I attached my scripts for the ARPACK zndrv4.f (it's basically the same as the example file provided by ARPACK, I just need to change a little bit the matrices around line 174 to be the same as that in NAG.) and the Matlab file zndrv4.txt (you have to change the name to zndrv4.m).

Thanks a lot.

Update: The M matrix in F12ARF is normalized (entries divided by a six). I followed this and got the above wrong results in ARPACK. Now if I didn't divide the entries by six, the ARPACK script gives me the correct answer (the same as Matlab)........ So it's the problem of a 6? It seems ARPACK routine is not robust?