XYPairs Function

Returns the corresponding Y value for a given X value, based on the line shape defined by the specified XY matrix.

Overview

XYPairs is a fundamental function to define response curves by specifying a series of X and Y values. For a given input X, it returns a linearly interpolated value of Y based on the defined XY matrix. If outside the defined X range, it returns the first or last points of Y value at the boundary. This function is particularly useful for modeling relationships where empirical data is available, such as temperature responses or biomass partitioning in agricultural models.

Inputs

X: An array of X values defining the input domain.
Y: An array of Y values corresponding to each X value. Must be the same length as X.

Methodology

The XYPairs function performs linear interpolation between the user-defined X and Y value pairs. When the function is called with a given X value (\(dX\)), it locates the segment of the curve that contains the input and linearly interpolates to determine the corresponding Y value. If outside the defined X range, it returns the Y value at the nearest boundary point (either the first or last Y value).

The interpolation follows this equation between points \((x_i, y_i)\) and \((x_{i+1}, y_{i+1})\):

\[ Y = y_i + \frac{(dX - x_i)}{(x_{i+1} - x_i)} (y_{i+1} - y_i) \]

Events

Events Listened For

No events are listened by this function.

Events Raised to

No events are raised by this function.

Properties

Configurable and Reportable Properties

Property	Type	Description
`X`	double[]	The list of X values
`Y`	double[]	The list of Y values

Read-Only Reportable Properties

No read-only properties are available for this function.

User Interface

XYPairs can be added as a child of any functional models in the model tree. Right-click the parent node, select “Add Model…”, and search for XYPairs in the Filter Box.

Practical Example

Suppose you want to define a response curve for a process that increases linearly with thermal time up to a maximum, then decreases. Set:

X = [0, 26, 34]
Y = [0, 26, 0]

This means: - For thermal time (X) less than 0, the response (Y) is 0. - From 0 to 26, the response increases linearly from 0 to 26. - From 26 to 34, the response decreases linearly from 26 to 0. - For thermal time greater than 34, the response remains 0.