# Curve Fitting (Logarithm) (G Dataflow)

Version:

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.

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.

### amp min

Lower bound for the amplitude.

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

### amp 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:

$\frac{1}{N}\underset{i=0}{\overset{N-1}{\sum }}{w}_{i}{\left({f}_{i}-{y}_{i}\right)}^{2}$

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 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:

$\frac{1}{N}\underset{i=0}{\overset{N-1}{\sum }}{w}_{i}|{f}_{i}-{y}_{i}|$

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 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:

$\frac{1}{N}\underset{i=0}{\overset{N-1}{\sum }}{w}_{i}{\left({f}_{i}-{y}_{i}\right)}^{2}$

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 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.

## 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:

$f=a{\mathrm{log}}_{c}\left(bx\right)$

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:

$y\left[i\right]=a{\mathrm{log}}_{c}\left(bx\left[i\right]\right)$

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

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported