Exponentials like exp(itA)

[Tyler Guglielmo]

To whom it may concern,

I am new to using expokit, and will be using it with large, real, symmetric matrices "A".  However, I would like to compute exp(i * t * A) where "i" is the imaginary number.  Should the standard symmetric/Hermitian expokit function work if I use a complex symmetric matrix "iA?" or should the code be modified somehow due to any kind of instability issues?

 Would really appreciate any help on this,  thanks in advance for your time!

Best,

Tyler

[Pranav Gupta]

I would use zgexpv in Fortran to do the calculations, but you might be able to use zhexpv by doing some clever transformations. You can't directly use zhexpv here. In am assuming you are using Fortran.

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[Tyler Guglielmo]

Thank you for the response Pranav, I am unfortunately having to translate all of this code into C -- so I am not too worried about the direct usage of the program.  I am mainly concerned about the algorithm and convergence issues with the Lanczos method.  Are you familiar with this?  Essentially I am trying to compute exp(itA) with A either symmetric or Hermitian so I would like to only use symmetric matrix multiplication.

Best,

Tyler

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Tyler Guglielmo

Ph.D. Candidate, Physics

University of Texas at Austin

[Tyler Guglielmo]

On a separate note, I have noticed some behavior that may be undefined in the "zhexpv.f" code.  Specifically, 

1    p2 = p1 - 1.0d0
     p3 = p2 + p2 + p2
     eps = ABS( p3-1.0d0 )
     if ( eps.eq.0.0d0 ) go to 1

It looks to me that this could be an infinite loop if eps == 0.0 b/b p1 has not changed.  However, it does not seem like it is ever possible to have eps = 0.0 with double precision arithmetic.  

Something else that looks confusing to me is the following call to compute the Pade approximation:

call ZGPADM( ideg, mx, sgn*t_step, wsp(ih),mh,
     .                wsp(ifree),lfree, iwsp, iexph, ns, iflag )
As far as I can tell, "iexph" has not been set at this point in the program.  Am I reading this correctly?  Thanks for your time again!
Best,
Tyler

[Tyler Guglielmo]

Ah I see what happens with iexph.  It simply just gets returned with new value iput.  So no worries, but I still think the goto 1 statement is potentially bad behavior.

Tyler