Version:

Last Modified: June 25, 2019

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 | Value | 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**.

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

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}(*x*_{i})

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.

Weights for the observations.

**weight** must be the same size as **y**. The elements in **weight** cannot be 0. 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 in **weight** to 1.

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 a 1D array of double-precision, floating-point number to **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 **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 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**, **weight out** returns the value you enter for **weight**.

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

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.

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):

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

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

Web Server: Not supported in VIs that run in a web application