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# numpy.polyval

numpy.polyval(p, x)

  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 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.

  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 [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

      >>> import numpy as np
      >>> 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])