Version:

Last Modified: January 9, 2017

Finds the *k*-dimension linear curve values and the set of *k*-dimension linear fit coefficients, which describe the *k*-dimension linear curve that best represents the input data set using the Least Square, Least Absolute Residual, or Bisquare method.

Whether the node computes the covariance matrix.

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

do not compute Covariance | Does not compute the covariance matrix. |

compute Covariance | Computes the covariance matrix. |

**Default: **do not compute Covariance

Observed data set. The number of elements in **y** must equal the number of rows in **H**.

Matrix that represents the formula you use to fit the data set.

Example of Obtaining the Matrix *H*

Assume you have a set of observations (*x*, *y*). For example, you can obtain a set of observations through data acquisition. Also, assume you think the relationship between *x* and *y* is of the following form:

$y={a}_{0}{f}_{0}\left(x\right)+{a}_{1}{f}_{1}\left(x\right)+{a}_{2}{f}_{2}\left(x\right)+{a}_{3}{f}_{3}\left(x\right)+{a}_{4}{f}_{4}\left(x\right)$

where

- ${f}_{0}\left(x\right)=1.0$
- ${f}_{1}\left(x\right)=\mathrm{sin}\left({x}^{2}\right)$
- ${f}_{2}\left(x\right)=3\mathrm{cos}\left(x\right)$
- ${f}_{3}\left(x\right)=\frac{1}{x+1}$
- ${f}_{4}\left(x\right)={x}^{4}$

The following equation describes matrix *H*.

${H}_{ij}={f}_{j}\left({x}_{i}\right)$

where

*H*ij is element in the*i*^{th}column and*j*^{th}row of*H**f*_{j}(*x*_{i}) is the function value of the*i*^{th}element in*x*

In this example, the number of columns in *H* equals the number of elements in *x*. the number of rows in *H* equals 5.

Array of weights for the observations.

**weight** must be the same size as **y**. If you do not wire an input to **weight**, this node sets all elements of **weight** to 1. If an element in **weight** is less than 0, this node uses the absolute value of the element.

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.

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

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

**Default: **No error

Algorithm this node uses to compute the best fit.

Use the SVD for Rank Deficient H algorithm only if **H** is rank deficient or does not have a full rank and if all other algorithms are unsuccessful.

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

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. |

**Default: **Least Square

Fitted data.

Set of coefficients that minimize chi squared.

Matrix of covariance *C* with *k*-by-*k* elements. *c*_{jk} is the covariance between *a*_{i} and *a*_{k}. *c*_{jj} is the variance of *a*_{j}. This node uses the following equation to compute the covariance matrix *C*:

$C={\left({H}_{0}^{T}{H}_{0}\right)}^{-1}$

Actual weight of general linear fitting if the fitting method is Bisquare.

If the fitting method is Least Square or Least Absolute Residual, this output returns the value you enter for **weight**.

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.

The following linear data model demonstrates how to configure the input parameters and how to use this node to obtain the fitted values and the set of least square coefficients that best represents the relationship of observations (x, y):

$y=f(a,x)=\underset{i=0}{\overset{n-1}{\sum}}{a}_{i}{f}_{i}\left(x\right)={a}_{0}{f}_{0}\left(x\right)+{a}_{1}{f}_{1}\left(x\right)+\mathrm{...}+{a}_{n-1}{f}_{n-1}\left(x\right)$

where

*a*= {*a*_{0},*a*_{1},*a*_{2}, ...,*a*_{n - 1}}*n*is the total number of functions*f*_{i}(*x*) are modal functions

**Where This Node Can Run: **

Desktop OS: Windows

FPGA: Not supported