Version:

Last Modified: March 15, 2017

Uses cubic spline fitting to smooth an input data set.

Dependent values. **y** must contain at least two points.

Independent values. **x** must be the same size as **y**. The elements of **x** must be in ascending order.

Weights for the observations.

**weight** must be the same size as **y**. **weight** also must contain non-zero elements. If an element in **weight** is less than 0, this node uses the absolute value of the element. If you do not wire an input to **weight**, this node sets all elements of **weight** to 1.

Smoothness for each interval between two contiguous data points.

The larger the **smoothness**, the smoother the curve. The number of elements in **smoothness** *n* - 1, where *n* is the length of **y**. If **smoothness** is unwired, this node sets all elements of **smoothness** to 1.

Error conditions that occur before this node runs.

The node responds to this input according to standard error behavior.

Standard Error Behavior

Many nodes provide an **error in** input and an **error out** output so that the node can respond to and communicate errors that occur while code is running. The value of **error in** specifies whether an error occurred before the node runs. Most nodes respond to values of **error in** in a standard, predictable way.

**Default: **No error

Balance between the smoothness of the cubic spline fit and the accuracy with which it fits the observations.

**balance parameter** must fall within the range [0, 1]. If **balance parameter** is 0, the cubic spline fit is equivalent to a linear fit. If **balance parameter** is 1, the cubic spline fit interpolates between the data points. If **balance parameter** is out of the range [0, 1], this node calculates an appropriate value for **balance parameter** automatically according to the values of **x**.

Y-values of the fitted model.

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

**error in** input and an **error out** output so that the node can respond to and communicate errors that occur while code is running. The value of **error in** specifies whether an error occurred before the node runs. Most nodes respond to values of **error in** in a standard, predictable way.

This node fits the observations (**x**, **y**) by minimizing the following function:

$p\underset{i=1}{\overset{n-1}{\sum}}{w}_{i}{({y}_{i}-f\left({x}_{i}\right))}^{2}+(1-p){\int}_{{x}_{0}}^{{x}_{n-1}}\lambda \left(x\right){(f"\left(x\right))}^{2}dx$

where

*p*is**balance parameter***w*_{i}is the*i*^{th}element of**weight***y*_{i}is the*i*^{th}element of**y***x*_{i}is the*i*^{th}element of**x**- f''(
*x*) is the second-order derivative of the cubic spline function,*f*(*x*) -
$\lambda \left(x\right)$ is the piecewise constant function
$\lambda \left(x\right)={\lambda}_{i},{x}_{i}\le x<{x}_{i+1}$, for
*i*= 0, 1, ...,*n*- 2 -
${\lambda}_{i}$ is the
*i*^{th}element of**smoothness**

**Where This Node Can Run: **

Desktop OS: Windows

FPGA: This product does not support FPGA devices