Version:

Last Modified: January 9, 2017

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

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

Array of dependent values. The length of **y** must be greater than or equal to the number of unknown parameters.

Independent values. **x** must be the same size as **y**.

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.

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

**Default: **No error

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.

Lower bound for the amplitude.

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

Upper bound for the amplitude.

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

Lower bound for the scale.

**Default: **-Inf, which means no lower bound is imposed on the scale.

Upper bound for the scale.

**Default: **Inf, which means no upper bound is imposed on the scale.

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:

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

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 logarithm 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** 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*w*_{i}is the*i*^{th}element of**weight***f*_{i}is the*i*^{th}element of**best logarithm 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** 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:

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

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 logarithm fit***y*_{i}is the*i*^{th}element of**y**or the*i*^{th}data value in a waveform.

**Default: **Least Square

Y-values of the fitted model.

Amplitude of the fitted model.

Scale of the fitted model.

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.

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:

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

**Where This Node Can Run: **

Desktop OS: Windows

FPGA: Not supported