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Curve Fitting (Gaussian Peak) (G Dataflow)

Version:
    Last Modified: March 30, 2017

    Returns the Gaussian fit of a data set using a specific fitting method.

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    initial guess

    Initial guesses of the amplitude, center, standard deviation, and offset for use in the iterative algorithm.

    If initial amplitude, initial center, initial standard deviation, or offset is NaN, this node calculates the initial guess automatically.

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    initial amplitude

    Initial guess of the amplitude.

    Default: NaN

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    initial center

    Initial guess of the center.

    Default: NaN

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    initial standard deviation

    Initial guess of the standard deviation.

    Default: NaN

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    offset

    Initial guess of the offset.

    Default: NaN

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    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.

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    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.

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    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.

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    weight

    An array of weights for the data set.

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    tolerance

    Value that determines when to stop the iterative adjustment of the amplitude, center, standard deviation, and offset.

    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 Square and Least Absolute Residual methods, 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 amplitude, center, standard deviation, and offset in two successive iterations is less than tolerance, this node returns the resulting amplitude, center, standard deviation, and offset.

    Default: 0.0001

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    error in

    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.

    error in does not contain an error error in contains an error
    If no error occurred before the node runs, the node begins execution normally.

    If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

    If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

    Default: No error

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    parameter bounds

    Upper and lower constraints for the amplitude, center, standard deviation, and offset.

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    amplitude min

    Lower bound for the amplitude.

    Default: -Infinity, which means no lower bound is imposed on the amplitude.

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    amplitude max

    Upper bound for the amplitude.

    Default: Infinity, which means no upper bound is imposed on the amplitude.

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    center min

    Lower bound for the center.

    Default: -Infinity, which means no lower bound is imposed on the center.

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    center max

    Upper bound for the center.

    Default: Infinity, which means no upper bound is imposed on the center.

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    deviation min

    Lower bound for the standard deviation.

    Default: -Infinity, which means no lower bound is imposed on the standard deviation.

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    deviation max

    Upper bound for the standard deviation.

    Default: Infinity, which means no upper bound is imposed on the standard deviation.

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    offset min

    Lower bound for the offset.

    Default: 0

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    offset max

    Upper bound for the offset.

    Default: 0

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    method

    The fitting method.

    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 amplitude, center, standard deviation, and offset of the Gaussian 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 Gaussian 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 amplitude, center, standard deviation, and offset of the Gaussian 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 Gaussian 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 amplitude, center, standard deviation, and offset 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 Gaussian fit
    • yi is the ith element of y or the ith data value in a waveform.

    Default: Least Square

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    offset

    Offset of the fitted model.

    This output can return a double-precision, floating-point number or a 1D array of double-precision, floating-point numbers.

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    best Gaussian fit

    Y-values of the fitted model.

    This output can return the following data types:

    • Waveform
    • 1D array of waveforms
    • 1D array of double-precision, floating-point numbers.
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    amplitude

    Amplitude of the fitted model.

    This output can return a double-precision, floating-point number or a 1D array of double-precision, floating-point numbers.

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    center

    Center of the fitted model.

    This output can return a double-precision, floating-point number or a 1D array of double-precision, floating-point numbers.

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    standard deviation

    Standard deviation of the fitted model.

    This output can return a double-precision, floating-point number or a 1D array of double-precision, floating-point numbers.

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    error out

    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.

    error in does not contain an error error in contains an error
    If no error occurred before the node runs, the node begins execution normally.

    If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

    If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.
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    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 best Gaussian fit

    This node uses the iterative general least square method and the Levenberg-Marquardt method to fit data to a Gaussian curve of the general form described by the following equation:

    f = a exp ( ( x μ ) 2 2 σ 2 ) + c

    where

    • x is the input sequence
    • a is amplitude
    • μ is center
    • σ is standard deviation
    • c is offset

    This node finds the values of a, μ , σ , and c that best fit the observations (x, y).

    The following equation specifically describes the Gaussian curve resulting from the Gaussian fit algorithm:

    y [ i ] = a exp ( ( x [ i ] μ ) 2 2 σ 2 ) + c

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

    Where This Node Can Run:

    Desktop OS: Windows

    FPGA: This product does not support FPGA devices


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