Difference between revisions of "Krylov.m"
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| − | Krylov propagation function. Avoids matrix exponentiation, but can be | + | {{DISPLAYTITLE:krylov.m}} |
| − | slow. Should be used when | + | Krylov propagation function. Avoids matrix exponentiation, but can be slow. Should be used when Liouvillian exponential does not fit into memory, but Liouvillian itself does. This function only supports Lioville space formalisms. |
| − | + | ||
| + | ==Syntax== | ||
answer=krylov(spin_system,L,coil,rho,time_step,nsteps,output) | answer=krylov(spin_system,L,coil,rho,time_step,nsteps,output) | ||
| − | Arguments | + | ==Arguments== |
L - the Liouvillian to be used during evolution | L - the Liouvillian to be used during evolution | ||
| − | + | ||
rho - the initial state vector or a horizontal stack thereof | 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 | 'final' - returns the final state vector or a horizontal | ||
stack thereof. | stack thereof. | ||
| − | + | ||
'trajectory' - returns the stack of state vectors giving | 'trajectory' - returns the stack of state vectors giving | ||
the trajectory of the system starting from | the trajectory of the system starting from | ||
rho with the user-specified number of steps | rho with the user-specified number of steps | ||
and step length. | and step length. | ||
| − | + | ||
'total' - returns the integral of the observable trace | 'total' - returns the integral of the observable trace | ||
from the simulation start to infinity. This | from the simulation start to infinity. This | ||
option requires the presence of relaxation. | option requires the presence of relaxation. | ||
| − | + | ||
'refocus' - evolves the first vector for zero steps, | 'refocus' - evolves the first vector for zero steps, | ||
second vector for one step, third vector for | second vector for one step, third vector for | ||
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stage of evolution in the indirect dimension | stage of evolution in the indirect dimension | ||
after a refocusing pulse. | after a refocusing pulse. | ||
| − | + | ||
'observable' - returns the time dynamics of an observable | 'observable' - returns the time dynamics of an observable | ||
as a vector (if starting from a single ini- | as a vector (if starting from a single ini- | ||
tial state) or a matrix (if starting from a | tial state) or a matrix (if starting from a | ||
stack of initial states). | stack of initial states). | ||
| − | + | ||
'multichannel' - returns the time dynamics of several | 'multichannel' - returns the time dynamics of several | ||
observables as rows of a matrix. Note | observables as rows of a matrix. Note | ||
| Line 41: | Line 42: | ||
less efficient when there are multiple | less efficient when there are multiple | ||
destinations to screen against. | destinations to screen against. | ||
| − | + | ||
coil - the detection state, used when 'observable' is specified as | coil - the detection state, used when 'observable' is specified as | ||
the output option. If 'multichannel' is selected, the coil | the output option. If 'multichannel' is selected, the coil | ||
| Line 47: | Line 48: | ||
observable vectors. | observable vectors. | ||
| − | + | ==Outputs== | |
| + | |||
| + | answer - a vector or a matrix, depending on the options set during | ||
| + | the call. | ||
| + | |||
| + | ==Notes== | ||
| + | GPUs are supported, add 'gpu' to sys.enable array during calculation setup. | ||
| + | |||
| + | ==See also== | ||
| + | [[evolution.m]], [[step.m]], [[propagator.m]] | ||
| + | |||
| + | |||
| + | ''Version 2.2, authors: [[Ilya Kuprov]]'' | ||
Revision as of 15:08, 27 August 2018
Krylov propagation function. Avoids matrix exponentiation, but can be slow. Should be used when Liouvillian exponential does not fit into memory, but Liouvillian itself does. This function only supports Lioville space formalisms.
Contents
Syntax
answer=krylov(spin_system,L,coil,rho,time_step,nsteps,output)
Arguments
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.
Outputs
answer - a vector or a matrix, depending on the options set during
the call.
Notes
GPUs are supported, add 'gpu' to sys.enable array during calculation setup.
See also
evolution.m, step.m, propagator.m
Version 2.2, authors: Ilya Kuprov
