numpy.polyval#
- numpy.polyval(p, x)[source]#
Evaluate a polynomial at specific values.
Note
This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in
numpy.polynomial
is preferred. A summary of the differences can be found in the transition guide.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 ofx
. If x is another polynomial then the composite polynomialp(x(t))
is returned.- Parameters:
- parray_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.
- xarray_like or poly1d object
A number, an array of numbers, or an instance of poly1d, at which to evaluate p.
- Returns:
- valuesndarray 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 [1] is used to evaluate the polynomial. Even so, for polynomials of high degree the values may be inaccurate due to rounding errors. Use carefully.
If x is a subtype of
ndarray
the return value will be of the same type.References
[1]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])