Table Of Contents
Curve Fitting (Logarithm) (G Dataflow)
Returns the logarithmic fit of a data set using a specific fitting method.
base
Base of the logarithm.
| Name | Value | Description |
|---|---|---|
| e | 2.71828 | Uses the natural logarithm. |
| 10 | 10 | Uses 10 as the base of the logarithm. |
| 2 | 2 | Uses 2 as the base of the logarithm. |
Default: e
y
Array of dependent values. The length of y must be greater than or equal to the number of unknown parameters.
x
Independent values. x must be the same size as y.
weight
Weights for the observations.
weight must be the same size as y. weight also must contain non-zero elements. If an element in weight is less than 0, this node uses the absolute value of the element. If you do not wire an input to weight, this node sets all elements of weight to 1.
tolerance
Value that determines when to stop the iterative adjustment of the amplitude and scale.
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 and scale in two successive iterations is less than tolerance, this node returns the resulting amplitude and scale.
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.
Default: No error
parameter bounds
Upper and lower constraints for the amplitude and scale. If you know the exact value of certain parameters, you can set the lower and upper bounds of those parameters equal to the known values.
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.
scale min
Lower bound for the scale.
Default: -Inf, which means no lower bound is imposed on the scale.
scale max
Upper bound for the scale.
Default: Inf, which means no upper bound is imposed on the scale.
method
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 and scale of the logarithmic 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
- wi is the ith element of weight
- fi is the ith element of best logarithm 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 and scale of the logarithmic 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
- wi is the ith element of weight
- fi is the ith element of best logarithm 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 and scale of the logarithmic model 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
- wi is the ith element of weight
- fi is the ith element of best logarithm fit
- yi is the ith element of y or the ith data value in a waveform.
Default: Least Square
best logarithm fit
Y-values of the fitted model.
amplitude
Amplitude of the fitted model.
scale
Scale of the fitted model.
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.
residue
Weighted mean error of the fitted model.
If method is Least Absolute Residual, residue is the weighted mean absolute error. Otherwise, residue is the weighted mean square error.
Algorithm for Calculating best logarithm fit
This node uses the iterative general least square method and the Levenberg-Marquardt method to fit data to a logarithmic function of the general form described by the following equation:
where
- x is the input sequence
- a is amplitude
- b is scale
- c is base
This node finds the values of a and b that best fit the observations (x, y).
The following equation describes the logarithm function resulting from the logarithm fit algorithm:
Where This Node Can Run:
Desktop OS: Windows
FPGA: This product does not support FPGA devices