Curve Fitting (Linear) (G Dataflow)

Version:

Finds the line that best represents an input signal or input data set using a specific fitting method.

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 the slope and intercept 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 between residue in two successive iterations is less than tolerance, this node returns the resulting residue. For the Bisquare method, if any relative difference between slope and intercept in two successive iterations is less than tolerance, this node returns the resulting slope and intercept.

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

parameter bounds

Upper and lower constraints for the slope and intercept of the calculated best linear fit.

slope min

Lower bound for the slope.

Default: -Infinity

slope max

Upper bound for the slope.

Default: Infinity

intercept min

Lower bound for the intercept.

Default: -Infinity

intercept max

Upper bound for the intercept.

Default: Infinity

method

Method of fitting data to a line.

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 of fitting finds the slope and intercept of the linear model by minimizing 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 linear 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 slope and intercept of the linear model by minimizing 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 linear fit
• yi is the ith element of y or the ith data value in a waveform

Algorithm for the Bisquare Method

The bisquare method of fitting finds the slope and intercept 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 linear fit
• yi is the ith element of y or the ith data value in a waveform.

Default: Least Square

best linear fit

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

slope

Slope of the calculated best linear fit.

intercept

Intercept of the calculated best linear fit.

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 linear fit

This node uses the general least squares method to fit the data points in an input signal to a straight line of the general form described by the following equation:

$f=ax+b$

where x is an input sequence, a is the slope of best linear fit, and b is the intercept of best linear fit.

This node finds the values of a and b that best fit 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 linear curve resulting from the linear fit algorithm:

$y\left[i\right]=ax\left[i\right]+b$

The following illustration shows a linear fit result using this node.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported