OOF2: The Manual
Smooth (Smooth) — Move nodes to the average position of their neighbors and accept ones that meet the acceptance criterion.
- Which nodes to move. Type: An object of the
- Acceptance criterion Type: An object of the
- Failed moves will be accepted if T>0 and exp(-diffE/T) > r, where diffE is the energy gained and r is a random number between 0 and 1. Type: A real number.
- Iteration method. Type: An object of the
Typically, it takes about 3 iterations of
Smooth to get desirable result. The general
procedure for a single iteration is as follows:
Collect target nodes according to the given
targetsparameter. The collected
Nodesare re-ordered randomly to avoid any potential artifacts from the original ordering of
Nodes. This re-ordering is repeated at every iteration.
A node move is accepted only if the move satisfies the specified acceptance criterion. Moved nodes that fail to meet the criterion will spring back to their respective original positions, as shown in Figure 6.59(b).
If the move is unacceptable according to the acceptance
criterion, OOF2 may still accept the move if the smoothing is being done at a non-zero temperature. The parameter
Tsets the effective temperature of the annealing process. Unacceptable moves are accepted with a probability
where is the difference between the effective energies of the new and old
Skeleton usually requires a number of iterations. The
smoothing algorithm converges very quickly, so it's usually
sufficient to set the
iteration parameter to
to perform exactly three iterations. Nonetheless, it is possible
to use conditional
iteration, which can repeatedly smooth the
Skeleton until the
rate per iteration becomes too small.
Statistics for each step of the smoothing process are printed in the OOF2 Message window. For example,
Iteration 1: E = 1.0480e+02, deltaE=-2.6308e+00 ( 2.510%), Acceptance Rate = 55.3% Iteration 2: E = 9.0358e+01, deltaE=-9.1959e-01 ( 1.018%), Acceptance Rate = 47.9% Iteration 3: E = 8.5505e+01, deltaE=-2.0926e-01 ( 0.245%), Acceptance Rate = 40.1% Iteration 4: E = 8.4485e+01, deltaE=-3.1806e-02 ( 0.038%), Acceptance Rate = 37.2% Iteration 5: E = 8.4317e+01, deltaE=-3.5836e-03 ( 0.004%), Acceptance Rate = 35.6%
The listing shows the iteration number, the total energy
E) of the
Skeleton, the absolute
change in energy (
the iteration, the percentage change in energy, and the move acceptance rate.
If the change in energy or the acceptance rate gets too small, the
smoothing process is not being effective at improving the
Notice in the example that the energy change per step is
decreasing exponentially, indicating rapid convergence.