Curve Fitting (Gaussian Peak) (G Dataflow)

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Last Modified: January 12, 2018

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

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.

initial amplitude

Initial guess of the amplitude.

Default: NaN

initial center

Initial guess of the center.

Default: NaN

initial standard deviation

Initial guess of the standard deviation.

Default: NaN

offset

Initial guess of the offset.

Default: NaN

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 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

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

parameter bounds

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

amplitude min

Lower bound for the amplitude.

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

amplitude max

Upper bound for the amplitude.

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

center min

Lower bound for the center.

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

center max

Upper bound for the center.

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

deviation min

Lower bound for the standard deviation.

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

deviation max

Upper bound for the standard deviation.

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

offset min

Lower bound for the offset.

Default: 0

offset max

Upper bound for the offset.

Default: 0

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:

\frac{1}{N} \sum_{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
w_i is the i^th element of weight
f_i is the i^th element of best Gaussian fit
y_i is the i^th element of y or the i^th 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:

\frac{1}{N} \sum_{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
w_i is the i^th element of weight
f_i is the i^th element of best Gaussian fit
y_i is the i^th element of y or the i^th 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:

\frac{1}{N} \sum_{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
w_i is the i^th element of weight
f_i is the i^th element of best Gaussian fit
y_i is the i^th element of y or the i^th data value in a waveform.

Default: Least Square

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.

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.

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.

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.

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.

error out

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

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.

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 \cdot \exp (- \frac{{(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 \cdot \exp (- \frac{{(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: Not supported

Web Server: Not supported in VIs that run in a web application

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Table Of Contents

initial guess

initial amplitude

initial center

initial standard deviation

offset

signal

y

x

weight

tolerance

error in

parameter bounds

amplitude min

amplitude max

center min

center max

deviation min

deviation max

offset min

offset max

method

offset

best Gaussian fit

amplitude

center

standard deviation

error out

residue

Algorithm for Calculating best Gaussian fit

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