Syntax

Description

y = polyval(p,x) returns the value of a polynomial of degree n evaluated at x. The input argument p is a vector of length n+1 whose elements are the coefficients in descending powers of the polynomial to be evaluated.

y = p₁xⁿ + p₂x^n–1 + … + p_nx + p_n+1

x can be a matrix or a vector. In either case, polyval evaluates p at each element of x.

[y,delta] = polyval(p,x,S) uses the optional output structure S generated by polyfit to generate error estimates delta. delta is an estimate of the standard deviation of the error in predicting a future observation at x by p(x). If the coefficients in p are least squares estimates computed by polyfit, and the errors in the data input to polyfit are independent, normal, and have constant variance, then y±delta contains at least 50% of the predictions of future observations at x.

y = polyval(p,x,[],mu) or [y,delta] = polyval(p,x,S,mu) use $$\widehat{x}=(x-{\mu }_1)/{\mu }_2$$ in place of x. In this equation, $${\mu }_1=\text{mean}(x)$$ and $${\mu }_2=\text{std}(x)$$. The centering and scaling parameters mu = [μ₁,μ₂] are optional output computed by polyfit.

Examples

The polynomial $$p(x)=3x^2+2x+1$$ is evaluated at x = 5, 7, and 9 with

p = [3 2 1];
polyval(p,[5 7 9])

which results in

ans =

    86   162   262

For another example, see polyfit.

See Also

polyder | polyfit | polyint | polyvalm