Linear
- Updated2023-02-17
- 7 minute(s) read
Linear
Finds the line that best represents an input signal or input data set using a specific fitting method.
Inputs/Outputs
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 y or signal.
Default value: False
signal
Input signal.
This input accepts a waveform or a 1D array of waveforms.
This input changes to y when the data type is a double-precision, floating-point number or a 1D array of double-precision, floating-point numbers.
y
Dependent values representing the y-values of the data set.
This input accepts a double-precision, floating-point number or a 1D array of double-precision, floating-point numbers.
This input changes to signal when the data type is a waveform or a 1D array of waveforms.
x
Independent values representing the x-values of the data set.
This input accepts a double-precision, floating-point number or a 1D array of double-precision, floating-point numbers.
This input is available only if you wire a double-precision, floating-point number or a 1D array of double-precision, floating-point numbers to y or signal.
weight
An array of weights for the data set.
This input is available only if you wire one of the following data types to signal or y:
- Waveform
- 1D array of waveforms
- 1D array of double-precision, floating-point numbers
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.
This input is available only if you wire one of the following data types to signal or y.
- Waveform
- 1D array of waveforms
- 1D array of double-precision, floating-point numbers
Default value: 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.
block size
Length of each set of data. The node performs computation for each set of data.
When you set block size to zero, the node calculates a cumulative solution for the input data from the time that you called or initialized the node. When block size is greater than zero, the node calculates the solution for only the newest set of input data.
This input is available only if you wire a double-precision, floating-point number to signal or y.
Default value: 100
error in
Error conditions that occur before this node runs.
The node responds to this input according to standard error behavior.
Default value: No error
parameter bounds
Upper and lower constraints for the slope and intercept of the calculated best linear fit.
This input is available only if you wire one of the following data types to signal or y:
- Waveform
- 1D array of waveforms
- 1D array of double-precision, floating-point numbers
slope min
Lower bound for the slope.
Default value: -Infinity
slope max
Upper bound for the slope.
Default value: Infinity
intercept min
Lower bound for the intercept.
Default value: -Infinity
intercept max
Upper bound for the intercept.
Default value: Infinity
method
Method of fitting data to a line.
This input is available only if you wire one of the following data types to signal or y:
- Waveform
- 1D array of waveforms
- 1D array of double-precision, floating-point numbers
| Least Square | 0 | Uses the least square method. |
| Least Absolute Residual | 1 | Uses the least absolute residual method. |
| Bisquare | 2 | Uses the bisquare method. |
Default value: Least Square
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:
where
- N is the length of y or the number of data values in a waveform
- w i is the ith element of weight
- f i is the ith element of best linear fit
- y i 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:
where
- N is the length of y or the number of data values in a waveform
- w i is the ith element of weight
- f i is the ith element of best linear fit
- y i 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:
where
- N is the length of y or the number of data values in a waveform
- w i is the ith element of weight
- f i is the ith element of best linear fit
- y i is the ith element of y or the ith data value in a waveform.
best linear fit
Linear curve that best fits the input signal.
This output can return the following data types:
- Waveform
- 1D array of waveforms
- 1D array of double-precision, floating-point numbers
slope
Slope of the calculated best linear fit.
This output can return a double-precision, floating-point number or a 1D array of double-precision, floating-point numbers.
intercept
Intercept of the calculated best linear fit.
This output can return a double-precision, floating-point number or a 1D array of double-precision, floating-point numbers.
error out
Error information.
The node produces this output according to standard error behavior.
residue
Weighted mean error of the fitted model.
This output can return a double-precision, floating-point number or a 1D array of double-precision, floating-point numbers.
Algorithm for Calculating residue When the Input Signal is a Double-Precision, Floating-Point Number
When the input signal is a double-precision, floating-point number, this node calculates residue according to the following equation:
where
- N is the number of elements in the data set
- f i is the ith element of best linear fit
- y i is the y component of the ith input data point
Examples
The following illustration shows a linear fit result using this node.
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:
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 a double-precision, floating-point number or 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: