# step.m

From Spinach Documentation Wiki

Propagation step function optimised for one-off time evolution events, such as hard pulses or slices of shaped pulses. For large Liouvillians, this function computes the action by a matrix exponential on a vector without computing the matrix exponential.

## Contents

## Syntax

rho=step(spin_system,L,rho,time_step)

## Arguments

L - Liouvillian or Hamiltonian to be used for propagation rho - state vector or density matrix to be propagated time_step - length of the time step to take

## Outputs

rho - state vector or density matrix

## Examples

See the source code of shaped_pulse_xy.m and most NMR pulse sequences (cosy.m, hsqc.m, and others) for examples of this function being used.

## Notes

- The sequence is programmed with a rather peculiar order of algebraic operations. This was carefully optimised to ensure best possible performance under a variety of scenarios (parallelisation, GPUs, large sparse arrays) in Matlab.
- Long-term propagation under a static Liovillian should be handled with evolution.m or krylov.m functions instead.

## See also

evolution.m, krylov.m, shaped_pulse_xy.m, shaped_pulse_af.m

*Version 2.2, authors: Ilya Kuprov, Luke Edwards*