Dakota Reference Manual: discrete_variables

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discrete_variables

## Description

This page discusses discrete design, uncertain, and state variables (which have `discrete` in their keyword name) as they have similar specifications. These include:

1. Integer ranges
2. Sets of integers
3. Sets of reals
4. Sets of strings and each is described below.

In addition, some aleatory uncertain variables, e.g., binomial_uncertain, are discrete integer-valued random variables specified using parameters. These are described on their individual keyword pages.

Sets

Sets of integers, reals, and strings have similar specifications, though different value types.

The variables are specified using three keywords:

- Variable declaration keyword - specifies the number of variables being defined
- `elements_per_variable` - a list of positive integers specifying how many set members each variable admits
  - Length = # of variables
- `elements` - a list of the permissible integer values in ALL sets, concatenated together.
  - Length = sum of `elements_per_variable`, or an integer multiple of number of variables
  - The order is very important here.
  - The list is partitioned according to the values of `elements_per_variable`, and each partition is assigned to a variable.
- The ordering of `elements_per_variable`, and the partitions of `elements` must match the strings from `descriptors`

For string variables, each string element value must be quoted and may contain alphanumeric, dash, underscore, and colon. White space, quote characters, and backslash/metacharacters are not permitted.

Examples are given on the pages:

- discrete design set integer
- discrete design set real
- discrete design set string
- discrete uncertain set integer
- discrete uncertain set real
- discrete uncertain set string

Range

For discrete variables defined by range(s), the `lower_bounds` and `upper_bounds` restrict the permisible values. For design variables, this constrains the feasible design space and is frequently used to prevent nonphysical designs. This is a discrete interval variable that may take any integer value within bounds (e.g., [1, 4], allowing values of 1, 2, 3, or 4). For some variable types, each variable is can be defined by multiple ranges.

Examples are given on the pages:

- discrete_interval_uncertain

## Related Topics

## Related Keywords

- binomial_uncertain : Aleatory uncertain discrete variable - binomial
- discrete_design_range : Design variable - discrete range-valued
- discrete_design_set : Design variable - discrete set-valued
- integer : Integer-valued discrete design variables
- real : Real-valued discrete design variables
- string : String-valued discrete design set variables
- discrete_interval_uncertain : Epistemic uncertain variable - values from one or more discrete intervals
- discrete_state_range : State variables - discrete range-valued
- discrete_state_set : State variable - discrete set-valued
- integer : Discrete state variables, each defined by a set of permissible integers
- real : Discrete state variables, each defined by a set of permissible real numbers
- string : String-valued discrete state set variables
- discrete_uncertain_set : Epistemic uncertain variable - discrete set-valued
- integer : Discrete, epistemic uncertain variable - integers within a set
- real : Discrete, epistemic uncertain variable - real numbers within a set
- string : Discrete, epistemic uncertain variable - strings within a set
- geometric_uncertain : Aleatory uncertain discrete variable - geometric
- histogram_point_uncertain : Aleatory uncertain variable - discrete histogram
- hypergeometric_uncertain : Aleatory uncertain discrete variable - hypergeometric
- negative_binomial_uncertain : Aleatory uncertain discrete variable - negative binomial
- poisson_uncertain : Aleatory uncertain discrete variable - Poisson