Table Of Contents

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.

    connector_pane_image
    datatype_icon

    coefficient constraint

    Constraints on the polynomial coefficients of certain order.

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

    datatype_icon

    order

    Constrained order.

    Default: 0

    datatype_icon

    coefficient

    Coefficient of the specific order.

    Default: 0

    datatype_icon

    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

    datatype_icon

    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.

    datatype_icon

    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.

    datatype_icon

    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.

    datatype_icon

    weight

    An array of weights for the data set.

    datatype_icon

    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

    datatype_icon

    error in

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

    Default: No error

    datatype_icon

    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

    datatype_icon

    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:

    1 N i = 0 N 1 w i ( f i y i ) 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:

    1 N i = 0 N 1 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:

    1 N i = 0 N 1 w i ( f i y i ) 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

    datatype_icon

    best polynomial fit

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

    datatype_icon

    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.

    datatype_icon

    error out

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

    datatype_icon

    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 = j = 0 m 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 [ i ] = j = 0 m a j ( x [ i ] ) j

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

    Where This Node Can Run:

    Desktop OS: Windows

    FPGA: Not supported


    Recently Viewed Topics