The value of a polynomial represented by the vector c can be evaluated at the point x very easily, as the following example shows:
N = length (c) - 1; val = dot (x.^(N:-1:0), c);
While the above example shows how easy it is to compute the value of a
polynomial, it isn’t the most stable algorithm. With larger polynomials
you should use more elegant algorithms, such as Horner’s Method,
which is exactly what the Octave function polyval does.
In the case where x is a square matrix, the polynomial given by
c is still well-defined. As when x is a scalar the obvious
implementation is easily expressed in Octave, but also in this case
more elegant algorithms perform better. The polyvalm function
provides such an algorithm.
y = polyval (p, x) ¶y = polyval (p, x, [], mu) ¶[y, dy] = polyval (p, x, s) ¶[y, dy] = polyval (p, x, s, mu) ¶Evaluate the polynomial p at the specified values of x.
If x is a vector or matrix, the polynomial is evaluated for each of the elements of x.
When mu is present, evaluate the polynomial for (x - mu(1)) / mu(2).
In addition to evaluating the polynomial, the second output represents the
prediction interval, y +/- dy, which contains at least 50% of
the future predictions. To calculate the prediction interval, the
structured variable s, originating from polyfit, must be
supplied.
See also: polyvalm, polyaffine, polyfit, roots, poly.
y = polyvalm (c, x) ¶Evaluate a polynomial in the matrix sense.
polyvalm (c, x) will evaluate the polynomial in the
matrix sense, i.e., matrix multiplication is used instead of element by
element multiplication as used in polyval.
The argument x must be a square matrix.