Finds the set of polynomial fit coefficients that best represents an input signal or input data set using a specific fitting method.
Constraints on the polynomial coefficients of a certain order.
Use this input if you know the exact values of certain polynomial coefficients.
This input is available only if you wire one of the following data types to signal or y:
Constrained order.
Default: 0
Coefficient of the specific order.
Default: 0
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
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.
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.
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.
This input is available only if you wire one of the following data types to signal or y.
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
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: 100
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.
Default: No error
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 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:
where
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:
$\frac{1}{N}\sum _{i=0}^{N-1}{w}_{i}|{f}_{i}-{y}_{i}|$where
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:
where
Default: Least Square
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 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.
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
This node fits data to a polynomial function of the general form described by the following equation:
where
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:
Where This Node Can Run:
Desktop OS: Windows
FPGA: DAQExpress does not support FPGA devices
Web Server: Not supported in VIs that run in a web application