polyval (Statistics Toolbox)

Polynomial evaluation.

Syntax

Y = polyval(p,X)
[Y,DELTA] = polyval(p,X,S)

Description

Y = polyval(p,X) returns the predicted value of a polynomial given its coefficients, p, at the values in X.

[Y,DELTA] = polyval(p,X,S) uses the optional output, S, generated by polyfit to generate error estimates, Y +/- DELTA. If the errors in the data input to polyfit are independent normal with constant variance, Y +/- DELTA contains at least 50% of the predictions.

If p is a vector whose elements are the coefficients of a polynomial in descending powers, then polyval(p,X) is the value of the polynomial evaluated at X. If X is a matrix or vector, the polynomial is evaluated at each of the elements.

Examples

Simulate the function y = x, adding normal random errors with a standard deviation of 0.1. Then use polyfit to estimate the polynomial coefficients. Note that tredicted Y values are within DELTA of the integer, X, in every case.

[p,S] = polyfit(1:10,(1:10) + normrnd(0,0.1,1,10),1);
X = magic(3);
[Y,D] = polyval(p,X,S)

Y =

    8.0696    1.0486    6.0636
    3.0546    5.0606    7.0666
    4.0576    9.0726    2.0516

D =

    0.0889    0.0951    0.0861
    0.0889    0.0861    0.0870
    0.0870    0.0916    0.0916