aux_mat.m

Builds auxiliary matrices for the calculation of the directional derivatives of the trapezium product quadrature propagator:

        expm(-i*((HL+HR)/2+i*dt*(sqrt(3)/12)*[HL,HR])*dt)

with respect to control coefficients in the evolution generators HL and HR on the left and the right edge of the interval. The derivatives are calculated using Eq 16 of Goodwin and Kuprov (https://doi.org/10.1063/1.4928978).

Syntax

    [auxm_l,auxm_r]=aux_mat(drifts,controls,dt,cL,cR,k)

Arguments

    drifts - a cell array of two matrices containing drift 
             generators at the left (first element) and the
             right (second element) edge of the interval

  controls - a cell array of control generators
         
        dt - interval duration, seconds

        cL - control generator coefficients at the left 
             edge of the interval

        cR - control generator coefficients at the right
             edge of the interval

         k - the number of the generator inside controls 
             array that the differentiation refers to

Outputs

    auxm_l - auxilary matrix for the derivative of the
             interval propagator with respect to cL

    auxm_l - auxilary matrix for the derivative of the
             interval propagator with respect to cR

See also

Optimal control module, Numerical infrastructure

Version 2.7, authors: Uluk Rasulov, Ilya Kuprov