Least Squares Polynomial Fit

Compute polynomial coefficients that best fit input data in least-squares sense

Library

Math Functions / Polynomial Functions

dsppolyfun

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Description

The Least Squares Polynomial Fit block computes the coefficients of the nth order polynomial that best fits the input data in the least-squares sense, where you specify n in the Polynomial order parameter. A distinct set of n+1 coefficients is computed for each column of the M-by-N input, u.

For a given input column, the block computes the set of coefficients, c₁, c₂, ..., c_n+1, that minimizes the quantity

$${\displaystyle \sum _{i=1}^M{(u_i-{\widehat{u}}_i)}^2}$$

where u_i is the ith element in the input column, and

$${\widehat{u}}_i=f\left(x_i\right)=c_1{x}_i^n+c_2{x}_i^{n-1}+\mathrm{...}+c_{n+1}$$

The values of the independent variable, x₁, x₂, ..., x_M, are specified as a length-M vector by the Control points parameter. The same M control points are used for all N polynomial fits, and can be equally or unequally spaced. The equivalent MATLAB^® code is shown below.

c = polyfit(x,u,n)						% Equivalent MATLAB code 

For convenience, the block treats length-M unoriented vector input as an M-by-1 matrix.

Each column of the (n+1)-by-N output matrix, c, represents a set of n+1 coefficients describing the best-fit polynomial for the corresponding column of the input. The coefficients in each column are arranged in order of descending exponents, c₁, c₂, ..., c_n+1.

Parameters

Control points

The values of the independent variable to which the data in each input column correspond. For an M-by-N input, this parameter must be a length-M vector. Tunable (Simulink).

Polynomial order

The order, n, of the polynomial to be used in constructing the best fit. The number of coefficients is n+1.

Supported Data Types

• Double-precision floating point

• Single-precision floating point

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using Simulink® Coder™.

Generated code relies on the memcpy or memset function (string.h) under certain conditions.

Version History

Introduced before R2006a