# Spline Interpolation (G Dataflow)

Returns a spline interpolated value at a single value given the tabulated values (x[i], y[i]) and the second derivatives of the cubic spline interpolating function that this node obtains from the Spline Interpolant node.

## reset

A Boolean that specifies whether to reset the internal state of the node.

 True Resets the internal state of the node. False Does not reset the internal state of the node.

This input is available only if you wire a double-precision, floating-point number to x or y.

Default: False

## y

Tabulated value of the dependent variable.

This input accepts a double-precision, floating-point number or a 1D array of double-precision, floating-point numbers.

## x

Tabulated value of the independent variable.

This input accepts a double-precision, floating-point number or a 1D array of double-precision, floating-point numbers.

## interpolant

Second derivative of the cubic spline interpolating function.

You can obtain interpolant from the Spline Interpolant node.

When x and y are 1D arrays of double-precision, floating-point numbers, the number of elements in x, y, and interpolant must be the same. Otherwise, this node sets yi to NaN and returns an error.

When x and y are double-precision, floating-point numbers, the number of elements in interpolant must equal sample length. Otherwise, this node sets yi to zero and returns an error.

## xi

A single value. xi must fall within the range [x0, xn - 1].

## error in

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.

error in does not contain an error error in contains an error
If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

Default: No error

## sample length

Length of each set of data. The node performs computation for each set of data.

sample length must be greater than zero.

This input is available only if you wire a double-precision, floating-point number to x or y.

Default: 100

## yi

Cubic spline interpolation of f at the single value.

## error out

Error information.

The node produces this output 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.

error in does not contain an error error in contains an error
If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

## Algorithm for Calculating the Interpolation Value

The points are formed by the input arrays x and y.

On the interval [xi, xi + 1], the following equation defines the interpolation value yi.

$\mathrm{yi}=A{y}_{i}+B{y}_{i+1}+C{y\prime \prime }_{i}+D{y\prime \prime }_{i+1}$

where

$A=\frac{{x}_{i+1}-x}{{x}_{i+1}-{x}_{i}}$
$B=1-A$
$C=\frac{1}{6}\left({A}^{3}-A\right){\left({x}_{i+1}-{x}_{i}\right)}^{2}$
$D=\frac{1}{6}\left({B}^{3}-B\right){\left({x}_{i+1}-{x}_{i}\right)}^{2}$

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported

Web Server: Not supported in VIs that run in a web application