# Krylov.m

Krylov propagation function. Avoids matrix exponentiation, but can be slow. Should be used when the Liouvillian exponential does not fit in- to the system memory, but the Liouvillian itself does. Syntax:

    answer=krylov(spin_system,L,coil,rho,time_step,nsteps,output)


Arguments for Liouville space calculations:

     L      - the Liouvillian to be used during evolution

     rho    - the initial state vector or a horizontal stack thereof

    output - a string giving the type of evolution that is required

               'final' - returns the final state vector or a horizontal
stack thereof.

               'trajectory' - returns the stack of state vectors giving
the trajectory of the system starting from
rho with the user-specified number of steps
and step length.

               'total'   - returns the integral of the observable trace
from the simulation start to infinity. This
option requires the presence of relaxation.

               'refocus' - evolves the first vector for zero steps,
second vector for one step, third vector for
two steps, etc., consistent with the second
stage of evolution in the indirect dimension
after a refocusing pulse.

               'observable' - returns the time dynamics of an observable
as a vector (if starting from a single ini-
tial state) or a matrix (if starting from a
stack of initial states).

               'multichannel' - returns the time dynamics of several
observables as rows of a matrix. Note
that destination state screening may be
less efficient when there are multiple
destinations to screen against.

     coil   - the detection state, used when 'observable' is specified as
the output option. If 'multichannel' is selected, the coil
should contain multiple columns corresponding to individual
observable vectors.


This function does not support Hilber space formalisms.