# Rational Interpolation (G Dataflow)

Version:

Interpolates or extrapolates a function f at a specific value using a rational function. The rational function passes through all the points formed by arrays of dependent and independent values.

## 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

Dependent value.

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

When x and y are 1D arrays of double-precision, floating-point numbers, if the number of elements in x is different from the number of elements in y, this node sets interpolation value and interpolation error to NaN and returns an error.

## x

Independent value.

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

When x and y are 1D arrays of double-precision, floating-point numbers, if the number of elements in x is different from the number of elements in y, this node sets interpolation value and interpolation error to NaN and returns an error.

## x value

Point at which the interpolation or extrapolation is performed.

If the value of x value is in the range of x, the node performs interpolation. Otherwise, the node performs extrapolation. If x value is too far from the range of x, the extrapolation error may be large. It is not a satisfactory extrapolation.

## 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: 10

## 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

## interpolation value

Interpolation of the function f at the point you specified.

## interpolation error

An estimate of the error in the interpolation.

## 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 rational function

$\frac{P\left({x}_{i}\right)}{Q\left({x}_{i}\right)}=\frac{{p}_{0}+{p}_{1}{x}_{i}+...{p}_{m}{x}_{i}^{m}}{{q}_{0}+{q}_{1}{x}_{i}+...{q}_{m}{x}_{i}^{m}}$

passes through all the points formed by y and x. P and Q are polynomials, and the rational function is unique, given a set of n points (xiyi), where f(xi) = yi, f is any function, and given a number x in the range of the xi values.

This node calculates interpolation value y using

$\frac{P\left(x\right)}{Q\left(x\right)}$

If the number of points is odd, the degrees of freedom of P and Q are using $\frac{n-1}{2}$. If the number of points is even, the degrees of freedom of P are $\frac{n}{2}-1$, and the degrees of freedom of Q are $\frac{n}{2}$, where n is the total number of points formed by y and x.

Where This Node Can Run:

Desktop OS: Windows

FPGA: This product does not support FPGA devices