PairedData

PairedData is a class that is composed of multiple interfaces which define its behavior. The object consists of two primary members, x values and y values. This is the primary workhorse of the FDA compute. It facilitates one of the most central functionalities - the ability to compose two PairedData objects together - which allows for the computation of AEP and EAD. Additionally, for the special case of the Levee Fragility Curve, PairedData also supports the ability to multiply two curves together. Finally, for computing EAD, the PairedData object facilitates the integration of the relationship it represents.

A simple example of a PairedData instance is provided in the table below.

X Value	Y Value
1.0	1.0
2.0	4.0
3.0	9.0
4.0	16.0
5.0	25.0

Composition

Composing two functions is a way to combine two curves together. In composition, a function F is composed with a function G by relating the independent variable from G through the dependent variable of F to create a new curve "F of G" which has the independent variable of F and the resulting dependent variable of G.

Multiplication

This is a simple operation where the independent variable of two relationships is shared across some of the domain of the relationships, and their dependent variables are combined through multiplication. This is how levee fragility curves reduce damage across some portion of the frequency range.

Integration

The area under the damage frequency curve represents an estimate of EAD. Integrating the damage frequency curve is accomplished using trapezoidal Riemann sums. For more information on this method of integration, see: https://en.wikipedia.org/wiki/Trapezoidal_rule