Shaped pulse xy.m

Shaped pulse function using Cartesian coordinates. Applies a user-specified pulse shape on user-specified operators while the rest of the drift Liouvillian continues to affect the spin system. The pulse is assumed to be piecewise-constant and should be supplied with sufficiently fine time discretization to properly reproduce the waveform.

Syntax

    [rho,traj,P]=shaped_pulse_xy(spin_system,drift,controls,...
                                     amplitudes,slice_durs,rho,method)

Parameters

      drift - the drift Liouvillian, the part of the Liouvillian that
              should continue running in the background. This should 
              include the transmitter offset term, if any. 

   controls - a cell array of control operators corresponding to each
              channel, this may include operators for spatial degrees
              of freedom, such as gradients and diffusion.

 amplitudes - a cell array of control amplitude vectors in rad/s, one
              vector per control channel; the elements of each vector
              correspond to different time points.

 slice_durs - a vector containing the duration of each pulse slice,
              seconds. For piecewise-constant methods, the number of
              durations should be equal to the nuber of amplitudes.
              For piecewise-linear methods, there should be one ele-
              ment more in the amplitude array.

        rho - initial state vector or a bookshelf matrix thereof

     method - propagation method and product quadrature: 

                Krylov algorithm (recommended):

                   'expv-pwc' - piecewise-constant
                   'expv-pwl' - 2nd order Lie quadrature

                Explicit matrix exponentiation:

                   'expm-pwc' - piecewise-constant
                   'expm-pwl' - 2nd order Lie quadrature

                Spinach evolution function call:

                   'evol-pwc' - piecewise-constant
                   'evol-pwl' - 2nd order Lie quadrature

Outputs

        rho - state vector for the final state, or a stack thereof

       traj - system trajectory as a [1 x (nsteps+1)] cell array, 
              the first point is the initial condition

          P - effective pulse propagator (expensive, best avoided)

Examples

An example of a Veshtort-Griffin shaped excitation pulse applied to a system with 31 J-coupled protons (examples/nmr_liquids/shaped_pulse_3.m):

Notes

1. Of the three propagation methods, 'expv' is recommended because it runs Krylov propagation that avoids explicit matrix exponentiation. The 'expm' option forces Matlab's very inefficient matrix exponentiation path and should only be used for debugging pourposes. In very anomalous cases (long pulses, large state vector stacks, very large state spaces), the 'evolution' option might become necessary.

See also

shaped_pulse_af.m, read_wave.m, vg_pulse.m, pulse_shape.m, chirp_pulse.m, bruker_write.m, cartesian2polar.m, grad_pulse.m, grad_sandw.m, pmlg5.m, polar2cartesian.m, restrans.m, rseq_compiler.m, rsequence.m, sawtooth.m, sech_pulse.m, spinal.m, triwave.m, wave_basis.m, Kernel_functions

Version 2.9, authors: Ilya Kuprov, Anupama Acharya