Dakota Reference Manual
Version 6.9
Explore and Predict with Confidence

Specifies the parameter set to be iterated by a particular method.
This keyword is related to the topics:
Alias: none
Argument(s): none
Child Keywords:
Required/Optional  Description of Group  Dakota Keyword  Dakota Keyword Description  

Optional  id_variables  Name the variables block; helpful when there are multiple  
Optional  active  Set the active variables view a method will see  
Optional (Choose One)  Variable Domain (Group 1)  mixed  Maintain continuous/discrete variable distinction  
relaxed  Allow treatment of discrete variables as continuous  
Optional  continuous_design  Design variable  continuous  
Optional  discrete_design_range  Design variable  discrete rangevalued  
Optional  discrete_design_set  Design variable  discrete setvalued  
Optional  normal_uncertain  Aleatory uncertain variable  normal (Gaussian)  
Optional  lognormal_uncertain  Aleatory uncertain variable  lognormal  
Optional  uniform_uncertain  Aleatory uncertain variable  uniform  
Optional  loguniform_uncertain  Aleatory uncertain variable  loguniform  
Optional  triangular_uncertain  Aleatory uncertain variable  triangular  
Optional  exponential_uncertain  Aleatory uncertain variable  exponential  
Optional  beta_uncertain  Aleatory uncertain variable  beta  
Optional  gamma_uncertain  Aleatory uncertain variable  gamma  
Optional  gumbel_uncertain  Aleatory uncertain variable  gumbel  
Optional  frechet_uncertain  Aleatory uncertain variable  Frechet  
Optional  weibull_uncertain  Aleatory uncertain variable  Weibull  
Optional  histogram_bin_uncertain  Aleatory uncertain variable  continuous histogram  
Optional  poisson_uncertain  Aleatory uncertain discrete variable  Poisson  
Optional  binomial_uncertain  Aleatory uncertain discrete variable  binomial  
Optional  negative_binomial_uncertain  Aleatory uncertain discrete variable  negative binomial  
Optional  geometric_uncertain  Aleatory uncertain discrete variable  geometric  
Optional  hypergeometric_uncertain  Aleatory uncertain discrete variable  hypergeometric  
Optional  histogram_point_uncertain  Aleatory uncertain variable  discrete histogram  
Optional  uncertain_correlation_matrix  Correlation among aleatory uncertain variables  
Optional  continuous_interval_uncertain  Epistemic uncertain variable  values from one or more continuous intervals  
Optional  discrete_interval_uncertain  Epistemic uncertain variable  values from one or more discrete intervals  
Optional  discrete_uncertain_set  Epistemic uncertain variable  discrete setvalued  
Optional  continuous_state  State variable  continuous  
Optional  discrete_state_range  State variables  discrete rangevalued  
Optional  discrete_state_set  State variable  discrete setvalued  
Optional  linear_inequality_constraint_matrix  Define coefficients of the linear inequality constraints  
Optional  linear_inequality_lower_bounds  Define lower bounds for the linear inequality constraint  
Optional  linear_inequality_upper_bounds  Define upper bounds for the linear inequality constraint  
Optional  linear_inequality_scale_types  Specify how each linear inequality constraint is scaled  
Optional  linear_inequality_scales  Define the characteristic values to scale linear inequalities  
Optional  linear_equality_constraint_matrix  Define coefficients of the linear equalities  
Optional  linear_equality_targets  Define target values for the linear equality constraints  
Optional  linear_equality_scale_types  Specify how each linear equality constraint is scaled  
Optional  linear_equality_scales  Define the characteristic values to scale linear equalities 
The variables
specification in a Dakota input file specifies the parameter set to be iterated by a particular method. In the case of
To accommodate these different studies, Dakota supports different:
Use the variables page to browse the available variables by type and domain.
Variable Types
initial_value
is used as the only value for the state variable for all other methods, unless active
state
is invoked.Variable Domains
Continuous variables are typically defined by bounds. Discrete variables can be defined in one of three ways, which are discussed on the page discrete_variables.
Ordering of Variables
The ordering of variables is important, and a consistent ordering is employed throughout the Dakota software. The ordering is shown in dakota.input.summary (and in the hierarchical order of this reference manual) and can be summarized as:
Ordering of variable types below this granularity (e.g., from normal to histogram bin within aleatory uncertain  continuous ) is defined somewhat arbitrarily, but is enforced consistently throughout the code.
Active Variables
The reason variable types exist is that methods have the capability to treat variable types differently. All methods have default behavior that determines which variable types are "active" and will be assigned values by the method. For example, optimization methods will only vary the design variables  by default.
The default behavior should be described on each method page, or on topics pages that relate to classes of methods. In addition, the default behavior can be modified using the active keyword.
At least one type of variables that are active for the method in use must have nonzero size (at least 1 active variable) or an input error message will result.
Inferred Default Values and Bounds
The concept of active variables allows any Dakota variable type to be used in any method context. Some methods, e.g., boundconstrained optimization or multidimensional or centered parameter studies, require bounds and/or an initial point on the variables, however uncertain variables may not be naturally defined in terms of these characteristics.
Distribution lower and upper bounds are explicit portions of the normal, lognormal, uniform, loguniform, triangular, and beta specifications, whereas they are implicitly defined for others. For example, bounds are naturally defined for histogram bin, histogram point, and interval variables (from the extreme values within the bin/point/interval specifications) as well as for binomial (0 to num_trials
) and hypergeometric (0 to min(num_drawn
, num_selected
)) variables.
If not specified, distribution bounds are also inferred for normal and lognormal (if optional bounds are unspecified) as well as for exponential, gamma, gumbel, frechet, weibull, poisson, negative binomial, and geometric (which have no bounds specifications); these bounds are [0, ] for exponential, gamma, frechet, weibull, poisson, negative binomial, geometric, and unspecified lognormal, and [ , ] for gumbel and unspecified normal.
When an intial point is needed, uncertain variables are initialized to their means, where mean values for bounded normal and bounded lognormal may be further adjusted to satisfy any userspecified distribution bounds, mean values for discrete integer range distributions are rounded down to the nearest integer, and mean values for discrete set distributions are rounded to the nearest set value.
Several examples follow. In the first example, two continuous design variables are specified:
variables, continuous_design = 2 initial_point 0.9 1.1 upper_bounds 5.8 2.9 lower_bounds 0.5 2.9 descriptors 'radius' 'location'
In the next example, defaults are employed. In this case, initial_point
will default to a vector of 0
. values, upper_bounds
will default to vector values of DBL_MAX
(the maximum number representable in double precision for a particular platform), lower_bounds
will default to a vector of DBL_MAX
values, and descriptors
will default to a vector of 'cdv_i'
strings, where i
ranges from one to two:
variables, continuous_design = 2
In the following example, the syntax for a normallognormal distribution is shown. One normal and one lognormal uncertain variable are completely specified by their means and standard deviations. In addition, the dependence structure between the two variables is specified using the uncertain_correlation_matrix
.
variables, normal_uncertain = 1 means = 1.0 std_deviations = 1.0 descriptors = 'TF1n' lognormal_uncertain = 1 means = 2.0 std_deviations = 0.5 descriptors = 'TF2ln' uncertain_correlation_matrix = 1.0 0.2 0.2 1.0
An example of the syntax for a state variables specification follows:
variables, continuous_state = 1 initial_state 4.0 lower_bounds 0.0 upper_bounds 8.0 descriptors 'CS1' discrete_state_range = 1 initial_state 104 lower_bounds 100 upper_bounds 110 descriptors 'DS1'
And in a more advanced example, a variables specification containing a set identifier, continuous and discrete design variables, normal and uniform uncertain variables, and continuous and discrete state variables is shown:
variables, id_variables = 'V1' continuous_design = 2 initial_point 0.9 1.1 upper_bounds 5.8 2.9 lower_bounds 0.5 2.9 descriptors 'radius' 'location' discrete_design_range = 1 initial_point 2 upper_bounds 1 lower_bounds 3 descriptors 'material' normal_uncertain = 2 means = 248.89, 593.33 std_deviations = 12.4, 29.7 descriptors = 'TF1n' 'TF2n' uniform_uncertain = 2 lower_bounds = 199.3, 474.63 upper_bounds = 298.5, 712. descriptors = 'TF1u' 'TF2u' continuous_state = 2 initial_state = 1.e4 1.e6 descriptors = 'EPSIT1' 'EPSIT2' discrete_state_set integer = 1 initial_state = 100 set_values = 100 212 375 descriptors = 'load_case'