Documentation

This is machine translation

Translated by Microsoft
Mouse over text to see original. Click the button below to return to the English verison of the page.

Least Squares Polynomial Fit

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

Library

Math Functions / Polynomial Functions

dsppolyfun

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, ..., cn+1, that minimizes the quantity

i=1M(uiu^i)2

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

u^i=f(xi)=c1xin+c2xin1+ ... +cn+1

The values of the independent variable, x1, x2, ..., xM, 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, ..., cn+1.

Examples

In the ex_leastsquarespolyfit_ref model below, the Polynomial Evaluation block uses the second-order polynomial

y=2u2+3

to generate four values of dependent variable y from four values of independent variable u, received at the top port. The polynomial coefficients are supplied in the vector [-2 0 3] at the bottom port. Note that the coefficient of the first-order term is zero.

The Control points parameter of the Least Squares Polynomial Fit block is configured with the same four values of independent variable u that are used as input to the Polynomial Evaluation block, [1 2 3 4]. The Least Squares Polynomial Fit block uses these values together with the input values of dependent variable y to reconstruct the original polynomial coefficients.

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.

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

See Also

DetrendDSP System Toolbox
Polynomial EvaluationDSP System Toolbox
Polynomial Stability TestDSP System Toolbox
polyfitMATLAB

Introduced before R2006a


Was this topic helpful?