Last Modified: March 30, 2017

Finds the set of polynomial fit coefficients that best represents an input signal or input data set using a specific fitting method.

Constraints on the polynomial coefficients of a certain order.

Use this input if you know the exact values of certain polynomial coefficients.

This input is available only if you wire one of the following data types to **signal** or **y**:

Constrained order.

**Default: **0

Coefficient of the specific order.

**Default: **0

Order of the polynomial.

**polynomial order** must be greater than or equal to 0. If **polynomial order** is less than zero, this node sets **polynomial coefficients** to an empty array and returns an error. In real applications, **polynomial order** is less than 10. If **polynomial order** is greater than 25, the node sets **polynomial coefficients** to zero and returns a warning.

**Default: **2

Dependent values representing the *y*-values of the data set.

This input accepts a double-precision, floating-point number or a 1D array of double-precision, floating-point numbers.

This input changes to **signal** when the data type is a waveform or a 1D array of waveforms.

Independent values representing the *x*-values of the data set.

This input accepts a double-precision, floating-point number or a 1D array of double-precision, floating-point numbers.

This input is available only if you wire a double-precision, floating-point number or a 1D array of double-precision, floating-point numbers to **y** or **signal**.

Value that determines when to stop the iterative adjustment of coefficients when you use the Least Absolute Residual or Bisquare methods.

If **tolerance** is less than or equal to 0, this node sets **tolerance** to 0.0001.

This input is available only if you wire one of the following data types to **signal** or **y**.

How tolerance Affects the Outputs with Different Fitting Methods

For the Least Absolute Residual method, if the relative difference of the weighted mean error of the polynomial fit in two successive iterations is less than **tolerance**, this node returns resulting **polynomial coefficients**. For the Bisquare method, if any relative difference between **polynomial coefficients** in two successive iterations is less than **tolerance**, this node returns the resulting **polynomial coefficients**.

**Default: **0.0001

Length of each set of data. The node performs computation for each set of data.

When you set **block size** to zero, the node calculates a cumulative solution for the input data from the time that you called or initialized the node. When **block size** is greater than zero, the node calculates the solution for only the newest set of input data.

This input is available only if you wire a double-precision, floating-point number to **signal** or **y**.

**Default: **100

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

Algorithm this node uses to compute the polynomial curve that best fits the input values.

Name | Value | Description |
---|---|---|

SVD | 0 | Uses the SVD algorithm. |

Givens | 1 | Uses the Givens algorithm. |

Givens2 | 2 | Uses the Givens2 algorithm. |

Householder | 3 | Uses the Householder algorithm. |

LU Decomposition | 4 | Uses the LU Decomposition algorithm. |

Cholesky | 5 | Uses the Cholesky algorithm. |

SVD for Rank Deficient H | 6 | Uses the SVD for Rank Deficient H algorithm. |

**Default: **SVD

Method of fitting data to a polynomial curve.

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 finds the polynomial coefficients of the polynomial model by minimizing the 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 polynomial 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 polynomial coefficients of the polynomial model by minimizing the 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 polynomial 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 finds the polynomial coefficients 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 polynomial fit***y*_{i}is the*i*^{th}element of**y**or the*i*^{th}data value in a waveform

**Default: **Least Square

Coefficients of the fitted model in ascending order of power. The total number of elements in polynomial coefficients is *m* + 1, where* m* is **polynomial order**.

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

**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.

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 **residue** When the Input Signal is a Double-Precision, Floating-Point Number

When the input signal is a double-precision, floating-point number, this node calculates **residue** according to the following equation:

$\mathrm{residue}=\text{\hspace{0.17em}}\frac{1}{N}\underset{i=0}{\overset{N-1}{\sum}}{({f}_{i}-{y}_{i})}^{2}$

where

*N*is the number of elements in the data set*f*_{i}is the*i*^{th}element of**best linear fit***y*_{i}is the**y**component of the*i*^{th}input data point

This node fits data to a polynomial function of the general form described by the following equation:

${f}_{i}=\underset{j=0}{\overset{m}{\sum}}{a}_{j}{x}_{i}^{j}$

where

*f*is the output sequence**best polynomial fit***x*is the input sequence calculated from the**dt**component of the input signal*a*is**polynomial coefficients***m*is**polynomial order**

This node finds the value of *a* that best fits the observations (X, Y). When the input signal is an array of double-precision, floating-point numbers, X is the **x** component of the input signal and Y is **y** component of the input signal. When the input signal is a waveform or an array of waveforms, X is the input sequence calculated from the start time of the waveform and Y is the data values in the waveform.

The following equation describes the polynomial curve resulting from the general polynomial fit algorithm:

$y\left[i\right]=\underset{j=0}{\overset{m}{\sum}}{a}_{j}{(x[i])}^{j}$

**Where This Node Can Run: **

Desktop OS: Windows

FPGA: DAQExpress does not support FPGA devices