Grape xy.m

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Cost function for optimal control using the GRAPE algorithm.

Syntax

    [fidelity,gradient,hessian]=grape_xy(waveform,spin_system)

Description

Returns fidelity, gradient and hessian for a given waveform, specified in Cartesian coordinates (x and y channels).

Arguments

  waveform      - normalised set of control amplitudes.

Returns

  fidelity      - figure of merit for the overlap of the current state
                  of the system and the desired state(s). When penalty
                  methods are specified, fidelity is returned as an ar-
                  ray separating the penalties from the simulation
                  fidelity.

  gradient      - gradient of the fidelity with respect to the control 
                  sequence. When penalty methods are specified, gradi-
                  ent is returned as an array separating penalty gra-
                  dients from the fidelity gradient.

  hessian       - Hessian of the fidelity with respect to the control 
                  sequence. When penalty methods are specified, gradi-
                  ent is returned as an array separating penalty Hes-
                  sians from the fidelity Hessian.

Examples

A typical call would be from an optimisation function (see examples/optimal_control):

    % Optimisation parameters
    optim.method='lbfgs';                   % Optimisation method
    optim.extremum='maximum';               % Extremum type

    % Run the optimization
    fminnewton(@grape_xy,guess,optim,spin_system);

Notes

The fidelity, the gradient and the Hessian may be supplied to any optimisation routine, including those in the Optimisation Toolbox of Matlab.

See also

grape.m, grape_phase.m, ensemble.m, optimcon.m


Version 2.0, authors: Ilya Kuprov, David Goodwin