numpy.polyval¶
- numpy.polyval(p, x)[source]¶
Evaluate a polynomial at specific values.
If p is of length N, this function returns the value:
p[0]*x**(N-1) + p[1]*x**(N-2) + ... + p[N-2]*x + p[N-1]If x is a sequence, then p(x) is returned for each element of x. If x is another polynomial then the composite polynomial p(x(t)) is returned.
Parameters: p : array_like or poly1d object
1D array of polynomial coefficients (including coefficients equal to zero) from highest degree to the constant term, or an instance of poly1d.
x : array_like or poly1d object
A number, a 1D array of numbers, or an instance of poly1d, “at” which to evaluate p.
Returns: values : ndarray or poly1d
If x is a poly1d instance, the result is the composition of the two polynomials, i.e., x is “substituted” in p and the simplified result is returned. In addition, the type of x - array_like or poly1d - governs the type of the output: x array_like => values array_like, x a poly1d object => values is also.
See also
- poly1d
- A polynomial class.
Notes
Horner’s scheme [R65] is used to evaluate the polynomial. Even so, for polynomials of high degree the values may be inaccurate due to rounding errors. Use carefully.
References
[R65] (1, 2) I. N. Bronshtein, K. A. Semendyayev, and K. A. Hirsch (Eng. trans. Ed.), Handbook of Mathematics, New York, Van Nostrand Reinhold Co., 1985, pg. 720. Examples
>>> np.polyval([3,0,1], 5) # 3 * 5**2 + 0 * 5**1 + 1 76 >>> np.polyval([3,0,1], np.poly1d(5)) poly1d([ 76.]) >>> np.polyval(np.poly1d([3,0,1]), 5) 76 >>> np.polyval(np.poly1d([3,0,1]), np.poly1d(5)) poly1d([ 76.])