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,cc_comm_idx,cc_comm,dt,cL,cR,k,j)

Parameters

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 K control generators

cc_comm_idx - a KxK matrix of logicals indicating non-zero
             commutation of controls

   cc_comm - a KxK cell array control commutation relarions

        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 index of the generator inside controls
             array that the differentiation refers to

         j - (optional) the index of the 2nd generator
             inside controls array that the differentiation
             refers to. Required for 3x3 block auxiliary
             matrices

Outputs

auxm_l - auxilary matrix for the derivative of the

             interval propagator with respect to cL

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

See also

acomm.m, alpha_conds.m, arnoldi.m, atranspose.m, bfgs.m, binpack.m, cheap_norm.m, cheb_coeff.m, clean_up.m, cubic_interp.m, dirdiff.m, drifts.m, eigenfields.m, ensemble.m, expdrop.m, expmint.m, expmint2.m, fftdiff.m, fourdif.m, fourlap.m, frob_chop.m, gaussfun.m, hdot.m, herm_spline.m, hess_reorder.m, jacobianest.m, keep_rank.m, krondelta.m, kronm_new.m, logfactorial.m, lorentzcon.m, lorentzfun.m, md5_hash.m, mprealloc.m, objeval.m, optimcon.m, remncomm.m, remtrace.m, rspert.m, rspt_eig.m, snormpdf.m, svd_shrink.m, tikhoind.m, tikhonov.m, trapdiff.m, unit_oper.m, unit_state.m, vvpert.m, Optimal control module, Kernel_utilities

Version 2.7, authors: Uluk Rasulov, Ilya Kuprov