ordering
Ordering of the points of this rank-1 lattice
Specification
Alias: None
Arguments: None
Default: Radical inverse ordering
Child Keywords:
Required/Optional |
Description of Group |
Dakota Keyword |
Dakota Keyword Description |
---|---|---|---|
Optional (Choose One) |
Ordering |
Natural ordering of the points of this rank-1 lattice |
|
Radical inverse ordering of the points of this rank-1 lattice |
Description
Specify the order in which the points of this rank-1 lattice should be returned.
Currently, Dakota supports natural
and radical_inverse
ordering.
The default behavior is to return points using radical inverse ordering, i.e.,
the points will be generated according to
where \(\phi_b(i)\) denotes the so-called radical inverse function in base \(b\) (usually, and also in Dakota, \(b = 2\)). This function transforms a number \(i = (\ldots i_2i_1)_b\) in its base-\(b\) representation to \(\phi_b(i) = (0.i_1i_2\ldots)_b\). Note that the radical inverse function agrees with the original formulation when \(N = b^m\) for any \(m \geq 0\). The advantage of the radical inverse ordering is that one can generate a good point set with an arbitrary number of points \(N\). Using the natural order, a good point set requires a number of points that is a power of 2. Semantically, the radical inverse ordering turns the lattice rule into a lattice sequence.
Usage Tips
When the natural
ordering of the points is used, it is implicitly assumed that the user will
only request a number of points that is a power of 2. Failing to do so will result in a set of points
for which one or more dimensions are not uniformly covered, resulting in bad low-discrepancy properties,
and ultimately bad performance of the method that uses these points. It is recommended to not use this option unless you know what you’re doing.
Examples
environment
tabular_data
tabular_data_file = 'samples.dat'
freeform
method
sampling
samples 8
sample_type
low_discrepancy
rank_1_lattice
generating_vector inline 1 5 # this is a Fibonacci lattice
m_max 3 # 8 points in total
no_random_shift
ordering natural
variables
uniform_uncertain = 2
lower_bounds 0.0 0.0
upper_bounds 1.0 1.0
interface
analysis_drivers = 'genz'
analysis_components = 'cp1'
direct
responses
response_functions = 1
no_gradients
no_hessians