# CubicInterp

## CubicInterp(xi, yi, x, i)

Given arrays of numerical coordinates «xi» and «yi», indexed by «i», it returns the y value corresponding to parameter «x», using cubic interpolation between the two values of «xi» nearest to «x». «xi», «yi», and «x» must be numbers. The numbers in «xi» must be in increasing order. If «xi» is itself a simple index, «yi» must be indexed by «xi», and parameter «i» may be omitted. Otherwise, «i» must be a common index of «xi» and «yi». «x» may be a scalar or have any dimensions. If «x» is less than the smallest (and first) value in «xi» (x < xi[@i = 1]), it returns that smallest value. Similarly, if «x» is larger than the largest (and last) value in «d» (x > xi[@i = Size(i)]), it returns that largest value.

Points having either «ci» or «yi» equal to Null are ignored. When «x» is Null, the result is Null.

A cubic interpolation can vary wildly from the actual values of the data points. In the above graph, all the «yi» values are positive, yet the interpolation is as small as -22.5 around x=33. Even if the «yi» values are monotonically increasing, this does not mean that the cubic interpolation will be monotonically increasing. The MonoCubicInterp function is a variation that provides a guarantee of monotonicity.

## Example

The following example can be found in the User Guide Examples.

`Cubicinterp(Index_b, Array_a, 1.5, Index_b) →`
a ▶
a b c
0.6875 -2.875 2.219

## Optional Parameters

### i

Specifies the common index of «xi» and «yi». You can omit this, if «xi» is itself an index of «yi».

### extrapolationMethod

Specifies the value to return if «x» is outside the values of «xi»:

• `1`: Use the «yi» for nearest «xi» (default method)
• `2`: Return Null
• `3`: Same as `1` (nearest point) for normal evaluation, but Null during optimization.

## History

• Analytica 4.1+
• Null values allowed in «xi» and «yi».