Test vector

Rationale

In computer science and engineering, a system acts as a computable function. An example of a specific function could be y = f ( x ) where y is the output of the system and x is the input; however, most systems' inputs are not one-dimensional. When the inputs are multi-dimensional, we could say that the system takes the form y = f ( x 1 , x 2 , . . . )  ; however, we can generalize this equation to a general form Y = C ( X ) where Y is the result of the system's execution, C belongs to the set of computable functions, and X is an input vector. While testing the system, various test vectors must be used to examine the system's behavior with differing inputs.

Example

For an example, consider a login page with two input fields: a username field and a password field. In that case, the login system can be described as:

y = L ( u , p )

with y ∈ { t r u e , f a l s e } and u , p ∈ { S t r i n g } , with t r u e designating login successful, and f a l s e designating login failure, respectively.

Making things more generic, we can suggest that the function L takes input as a 2-dimensional vector and outputs a one-dimensional vector (scalar). This can be written in the following way:-

Y = L ( X )

with X = [ x 1 , x 2 ] = [ u , p ] ; Y = [ y 1 ]

In this case, X is called the input vector, and Y is called the output vector.

In order to test the login page, it is necessary to pass some sample input vectors { X 1 , X 2 , X 3 , . . . } . In this context X i is called a test vector.