# 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*