Could not solve a problem with phasepack

[MacroUniverse]

Hi,
I tried to solve a particular problem with phasepack, however, it seems most of the algorithms failed to give a reasonable solution (but my homemade algorithm does, except it takes too long), I used the parameters given in the example folder. A typical set of data can be downloaded from my dropbox as a .mat file. I really appreciate if you can tell me what the problem is. Thank you.

[rohanchandra30]

Hello, could you explain a bit more about what you are trying to do?

Thanks

[MacroUniverse]

I was trying to solve the Frog-Crab problem in ultra-fast laser physics (basically retrieving to wave forms from a 2D spectrum with no phase information). The problem is too complicated to fully explain here, see this paper for example. I'm assuming the infrared wave is known, Then the problem could be reduced to a generalized phase retrieval problem in the frequency domain.
Anyway, even without the background, can you tell why this matrix is so hard to solve by characterizing it (e.g. rank, norm, etc)? And what is the best way to solve it?