OPTIMIZE

The OPTIMIZE parameter defines the behaviour of full-dynamic optimization runs.

Syntax:

OPTIMIZE V0i = 0.5                                ! optimize the imaginary part of the inner potential, with an initial step of 0.5 eV.
OPTIMIZE V0i = step 0.5                           ! same as above
OPTIMIZE V0i = step -0.5                          ! same as above, but take the initial step towards smaller V0i rather than larger
OPTIMIZE theta = step 1, convergence 0.05         ! optimize beam incidence polar angle theta with initial step of 1 degree, define convergence at 0.05 degrees
OPTIMIZE phi = step 5, minpoints 5, maxpoints 8   ! optimize beam incidence azimuthal angle phi with intial step of 5 degrees, calculating at least 5 data points and at most 8 data points.
OPTIMIZE ab = 0.02                                ! optimize the unit cell dimensions ab (scaling together), with an initial step of 2% scaling

Acceptable values: see below for each flag.

The left-hand side defines which parameter to optimize. Allowed values (not case sensitive) are v0i for V0_IMAG, theta and phi for the BEAM_INCIDENCE angles, a, b and c for the unit cell vectors, as well as ab and abc for simultaneous, proportional scaling of multiple unit cell vectors.

Input on the right-hand side is expected in the form flag value, where the different flags and allowed values are described below. Values for the different flags can be set in one line with comma separation, as in the examples above. Alternatively, you can set different flags by having multiple lines OPTIMIZE x = flag value. If only one value is given, this is assigned as step.

The minimum form is to define only what parameter to optimize and the initial step width.

Values are always given relative to the input configuration, using

V0i: eV
theta, phi: degrees
unit cell: values are scaling factors. For example, a step of 0.02 corresponds to an initial data point scaling the unit vectors by a factor 1.02, i.e. +2%.

step

The initial step width, and direction of the first step.

Acceptable values: non-zero float

The first data point is always calculated at the input configuration. The second data point is defined entirely by the value of step, including the sign. For example, if the parameter under variation is V0i and the step is -0.5, then the second data point will be calculated at V0i_initial - 0.5 eV. After the initial step, the sign is not used any more; the third data point will be calculated at the same step width from either the first or second data point, going in the direction of the minimum. Afterwards, a parabola is fit; if the minimum is inside the range of known data point at that point, then step is not used further. If it is outside, step will still be used in the choice of further data points closer to the minimum.

convergence

Cutoff for stopping optimization.

Acceptable values: float

Default: 0.1 * step

During optimization, a new parabola is fit after every new data point. If the new minimum is close to a point that was already calculated, optimization will stop. The cutoff for this is given by the convergence value.

Note that convergence is given in units corresponding to the parameter, e.g., a convergence 0.1 for V0i means convergence is reached when the minimum is within 0.1 eV of a known point.

minpoints, maxpoints

The minimum and maximum number of data points to calculate.

Default: 4 and 10

Acceptable values: positive integer

minpoints defines a minimum number of data points. If less data points have been calculated, the convergence criterion is ignored. This can be used to ensure that the calculation does not stop with very few data points, which may make the parabola fit unreliable. However, if the new parabola minimum would fall within convergence of an already known data point, a new point other than the minimum is chosen; this is meant to ensure that new data points actually contribute new data to the parabola fit, rather than re-calculating known data.

maxpoints defines a maximum number of data points, after which optimization will stop regardless of convergence. This may happen if the \(R\) factor as a function of the parameter under variation is not parabolic, or if convergence is set too low. Can also be used to prevent excess computations.

maxstep

Defines a maximum step width.

Default: 3 * step

Acceptable values: positive float

If the initial three data points do not describe a convex parabola, further data points will be added outside the current scope with increasing step width. This is meant to ensure that a better parabola is found if the initial data points are noisy due to step having been chosen too small. maxstep defines the maximum step width to which the step will be extended.