numpy.polyval — NumPy v1.13 Manual (original) (raw)
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, an array of numbers, or an instance of poly1d, at which to evaluate p. |
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| 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
A polynomial class.
Notes
Horner’s scheme [R70] 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
| [R70] | (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. |
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Examples
np.polyval([3,0,1], 5) # 3 * 52 + 0 * 51 + 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.])