Figure 7
Global agreement statistics and individual structure-factor trajectories generated by the RRR algorithm (β = 0.80, test case 4bsj) following initiation of the algorithm with three different random phase sets (i), (ii) and (iii). For phase sets (i) and (ii) the algorithm converges to the global solution within 300 iterations, while for set (iii) it does not. (a) Evolution of the real-space map correlation coefficient, an overall agreement measure. (b) Trajectories for the Fourier coefficient with indices h = 12, k = 9, l = 8 for the three runs. The estimate for the Fourier coefficient at each iterate, obtained from equation (4b), is represented with a filled circle in the complex plane, and consecutive iterates are connected with thin lines. The progression of the trajectory over the 300 iterations allowed is indicated with a purple-to-red color gradient. The experimentally measured structure-factor amplitude at the model-derived phase angle is indicated by an open circle, connected to the origin by a thick black line. (c) Fit of the final 30 iterations in the algorithm trajectory to a bivariate probability density function, assuming independent von Mises distribution of the phases and Gaussian distribution of the amplitudes (equation 17). Points contributing to the fit of the PDF retain their color, while all remaining points in the trajectory are reverted to gray. The displayed isocontours of the fitted PDF pass through μG ± 2σ, μG ± 4σ and μG ± 6σ along the central symmetry axis of the distribution. |