gray_code
Gray code ordering of the points of this digital net
Specification
Alias: None
Arguments: None
Description
Returns the points in Gray code order.
Usage tips
The advantage of the Gray code ordering is that one can generate a good point set with an arbitrary number of points \(N\).
Gray code ordering has an additional advantage in that there exists an iterative procedure by Antonov and Saleev [AS79] to generate the points of the sequence. Knowing the current point with index \(n\), the next point with index \(n + 1\) is obtained by XOR’ing the current point with the \(k\)th column of the \(j\)th generating matrix, i.e.,
where \(k\) is the rightmost zero-bit of \(n\) (the position of the bit that will change from \(n\) to \(n+1\) in Gray code).
Examples
environment
tabular_data
tabular_data_file = 'samples.dat'
freeform
method
sampling
samples 32
sample_type
low_discrepancy
digital_net
generating_matrices inline
1 2 4 8 16
# this encodes the generating matrix
# 1 0 0 0 0
# 0 1 0 0 0
# 0 0 1 0 0
# 0 0 0 1 0
# 0 0 0 0 1
1 3 5 15 17
# this encodes the generating matrix
# 1 1 1 1 1
# 0 1 0 1 0
# 0 0 1 1 0
# 0 0 0 1 0
# 0 0 0 0 1
m_max 5
t_max 5
no_scrambling
no_digital_shift
ordering gray_code
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
