# Curve Fitting (Polynomial) (G Dataflow)

Version:
Last Modified: January 9, 2017

Finds the set of polynomial fit coefficients that best represents an input signal or input data set using a specific fitting method.

## coefficient constraint

Constraints on the polynomial coefficients of certain order.

Use this input if you know the exact values of certain polynomial coefficients.

### order

Constrained order.

Default: 0

### coefficient

Coefficient of the specific order.

Default: 0

## polynomial order

Order of the polynomial.

polynomial order must be greater than or equal to 0. If polynomial order is less than zero, this node sets polynomial coefficients to an empty array and returns an error. In real applications, polynomial order is less than 10. If polynomial order is greater than 25, the node sets polynomial coefficients to zero and returns a warning.

Default: 2

## signal

The input signal.

This input accepts the following data types:

• Waveform
• Array of waveforms

This input changes to y when the data type is an array of double-precision, floating-point numbers.

## y

An array of dependent values representing the y-values of the data set.

This input changes to signal when the data type is a waveform or an array of waveforms.

## x

An array of independent values representing the x-values of the data set.

This input is available only if you wire an array of double-precision floating-point numbers to y or signal.

## weight

An array of weights for the data set.

## tolerance

Value that determines when to stop the iterative adjustment of coefficients when you use the Least Absolute Residual or Bisquare methods.

If tolerance is less than or equal to 0, this node sets tolerance to 0.0001.

How tolerance Affects the Outputs with Different Fitting Methods

For the Least Absolute Residual method, if the relative difference of the weighted mean error of the polynomial fit in two successive iterations is less than tolerance, this node returns resulting polynomial coefficients. For the Bisquare method, if any relative difference between polynomial coefficients in two successive iterations is less than tolerance, this node returns the resulting polynomial coefficients.

Default: 0.0001

## error in

Error conditions that occur before this node runs. The node responds to this input according to standard error behavior.

Default: No error

## algorithm

Algorithm this node uses to compute the polynomial curve that best fits the input values.

Name Value Description
SVD 0 Uses the SVD algorithm.
Givens 1 Uses the Givens algorithm.
Givens2 2 Uses the Givens2 algorithm.
Householder 3 Uses the Householder algorithm.
LU Decomposition 4 Uses the LU Decomposition algorithm.
Cholesky 5 Uses the Cholesky algorithm.
SVD for Rank Deficient H 6 Uses the SVD for Rank Deficient H algorithm.

Default: SVD

## method

Method of fitting data to a polynomial curve.

Name Value Description
Least Square 0 Uses the least square method.
Least Absolute Residual 1 Uses the least absolute residual method.
Bisquare 2 Uses the bisquare method.

Algorithm for the Least Square Method

The least square method finds the polynomial coefficients of the polynomial model by minimizing the residue according to the following equation:

$\frac{1}{N}\underset{i=0}{\overset{N-1}{\sum }}{w}_{i}{\left({f}_{i}-{y}_{i}\right)}^{2}$

where

• N is the length of y or the number of data values in a waveform
• wi is the ith element of weight
• fi is the ith element of best polynomial fit
• yi is the ith element of y or the ith data value in a waveform

Algorithm for the Least Absolute Residual Method

The least absolute residual method finds the polynomial coefficients of the polynomial model by minimizing the residue according to the following equation:

$\frac{1}{N}\underset{i=0}{\overset{N-1}{\sum }}{w}_{i}|{f}_{i}-{y}_{i}|$

where

• N is the length of y or the number of data values in a waveform
• wi is the ith element of weight
• fi is the ith element of best polynomial fit
• yi is the ith element of y or the ith data value in a waveform

Algorithm for the Bisquare Method

The bisquare method finds the polynomial coefficients using an iterative process, as shown in the following illustration.

The node calculates residue according to the following equation:

$\frac{1}{N}\underset{i=0}{\overset{N-1}{\sum }}{w}_{i}{\left({f}_{i}-{y}_{i}\right)}^{2}$

where

• N is the length of y or the number of data values in a waveform
• wi is the ith element of weight
• fi is the ith element of best polynomial fit
• yi is the ith element of y or the ith data value in a waveform

Default: Least Square

## best polynomial fit

A waveform or array representing the polynomial curve that best fits the input signal.

## polynomial coefficients

Coefficients of the fitted model in ascending order of power. The total number of elements in polynomial coefficients is m + 1, where m is polynomial order.

## error out

Error information. The node produces this output according to standard error behavior.

## residue

Weighted mean error of the fitted model.

## Algorithm for Calculating best polynomial fit

This node fits data to a polynomial function of the general form described by the following equation:

${f}_{i}=\underset{j=0}{\overset{m}{\sum }}{a}_{j}{x}_{i}^{j}$

where

• f is the output sequence best polynomial fit
• x is the input sequence calculated from the dt component of the input signal
• a is polynomial coefficients
• m is polynomial order

This node finds the value of a that best fits the observations (X, Y). When the input signal is an array of double-precision, floating-point numbers, X is the x component of the input signal and Y is y component of the input signal. When the input signal is a waveform or an array of waveforms, X is the input sequence calculated from the start time of the waveform and Y is the data values in the waveform.

The following equation describes the polynomial curve resulting from the general polynomial fit algorithm:

$y\left[i\right]=\underset{j=0}{\overset{m}{\sum }}{a}_{j}{\left(x\left[i\right]\right)}^{j}$

The following illustration shows a general polynomial fit result using this node:

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported