integer_format

Specify format of integers in the generating matrices

Specification

• Alias: None

• Arguments: None

• Default: Most significant bit first

Child Keywords:

Required/Optional	Description of Group	Dakota Keyword	Dakota Keyword Description
Optional (Choose One)	Integer Format	most_significant_bit_first	Assume integers are stored with most significant bit first
		least_significant_bit_first	Assume integers are stored with least significant bit first

Description

Use this keyword to specify the format used to store the integers in the generating matrices. Generating matrices provided with the inline or file options are encoded as matrices of integers. Each line in the matrix (i.e., each generating matrix) is represented by m_max integers, which represent the bits of the columns in the generating matrix, with the least significant bit (LSB) of the integer representing the top row of the generating matrix. For example, the sequence 1 2 4 8 represents the 4 x 4 generating matrix

1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1

and the sequence 1 3 7 15 represents the 4 x 4 generating matrix

1 1 1 1
0 1 1 1
0 0 1 1
0 0 0 1

This representation has two advantages.

• The integers can be reused if the maximum number of bits in the representation t_max changes.

• It generally leads to smaller, human-readable numbers in the first few entries.

Obviously, generating matrices stored with least significant bit_first still need to be bit-reversed before they can be used, but this can easily be accomplished using some bit magic.

The integer_format allows the user to choose the representation of the integers in the generating matrices. As an example, the following two code snippets will generate identical points:

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
          integer_format least_significant_bit_first

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

environment
  tabular_data
    tabular_data_file = 'samples.dat'
    freeform

method
  sampling
    samples 32
    sample_type
      low_discrepancy
        digital_net
          generating_matrices inline
            16 8 4 2 1
            # 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
            16 24 20 30 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
          integer_format most_significant_bit_first

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