# Spline Interpolation 1D (G Dataflow)

Version:

Performs one-dimensional interpolation using the spline interpolation method based on the lookup table defined by arrays of tabulated values of dependent and independent variables.

##### Programming Patterns

You can use the Evaluate Interpolating Polynomial node to find the interpolated values using the piecewise polynomial.

## y

Tabulated values of the dependent variable.

## x

Tabulated values of the independent variable. The length of x must equal the length of y.

## xi

Values of the independent variable at which this node computes the interpolated values of the dependent variables.

## 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

## initial boundary

Conditions at the initial boundary.

### boundary

Boundary condition type.

Name Value Description
natural spline 0 The second derivative at the initial boundary is 0 and this node ignores the derivative value input.
not-a-knot 1 The third derivative at the second data point x1 in X is continuous, which means this node fits one polynomial through the first three data points, and the polynomial between [x0, x1] is the same as the polynomial between [x1, x2]. This option is useful if you know nothing about the derivatives at the initial boundary. If you specify not-a-knot, this node ignores the derivative value input.
1st derivative 2 derivative value specifies the first derivative at the initial boundary.
2nd derivative 3 derivative value specifies the second derivative at the initial boundary.

Default: natural spline

### derivative value

Value of the first or second derivative at the initial boundary.

This node ignores derivative value when boundary is natural spline or not-a-knot.

## final boundary

Conditions at the final boundary.

### boundary

Sets the boundary condition type.

Name Value Description
natural spline 0 The second derivative at the final boundary is 0 and this node ignores the derivative value input.
not-a-knot 1 The third derivative at the second-to-last data point in X, xn - 2, is continuous, which means this node fits one polynomial through the last three data points, and the polynomial between [xn - 2, xn - 1] is the same as the polynomial between [xn - 3, xn - 2]. This option is useful if you know nothing about the derivatives at the final boundary. If you specify not-a-knot, this node ignores the derivative value input.
1st derivative 2 derivative value specifies the first derivative at the final boundary.
2nd derivative 3 derivative value specifies the second derivative at the final boundary.

Default: natural spline

### derivative value

Value of the first or second derivative at the final boundary.

This node ignores derivative value when boundary is natural spline or not-a-knot.

## yi

Interpolated values that correspond to the independent variable values.

## piecewise polynomial

A cluster that contains the x domain endpoint values and coefficients of the piecewise interpolating polynomial.

### x locations

The x domain endpoint values of the piecewise interpolating polynomial.

If x locations is of size N, the coefficients array should contain N - 1 rows of polynomial coefficients.

### coefficients

A 2D array of interpolating polynomial coefficients.

Row i of coefficients contains the coefficients for the interpolating polynomial between elements xi and xi + 1 of x locations.

## 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.

## Advantage of Using the Spline Interpolation Method

The spline interpolation method guarantees that the first and second derivative of the piecewise interpolating polynomial are continuous, even at the data points.

Where This Node Can Run:

Desktop OS: Windows

FPGA: This product does not support FPGA devices