Compute polynomial coefficients that best fit input data in least-squares sense
Math Functions / Polynomial Functions
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
where ui is the ith element in the input column, and
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.
In the ex_leastsquarespolyfit_ref model below, the Polynomial Evaluation block uses the second-order polynomial
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
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.
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).
The order, n, of the polynomial to be used in constructing the best fit. The number of coefficients is n+1.
Double-precision floating point
Single-precision floating point