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# numpy.polynomial.polynomial.polyval

polynomial.polynomial.polyval(x, c, tensor=True)

  Evaluate a polynomial at points x.

  If c is of length `n + 1`, this function returns the value

  \[p(x) = c_0 + c_1 * x + ... + c_n * x^n\]

  The parameter x is converted to an array only if it is a tuple or a list, otherwise it is treated as a scalar. In either case, either x or its elements must support multiplication and addition both with themselves and with the elements of c.

  If c is a 1-D array, then `p(x)` will have the same shape as x. If c is multidimensional, then the shape of the result depends on the value of tensor. If tensor is true the shape will be c.shape[1:] + x.shape. If tensor is false the shape will be c.shape[1:]. Note that scalars have shape (,).

  Trailing zeros in the coefficients will be used in the evaluation, so they should be avoided if efficiency is a concern.

  Parameters:
    x array_like, compatible object

      If x is a list or tuple, it is converted to an ndarray, otherwise it is left unchanged and treated as a scalar. In either case, x or its elements must support addition and multiplication with with themselves and with the elements of c.

    c array_like

      Array of coefficients ordered so that the coefficients for terms of degree n are contained in c[n]. If c is multidimensional the remaining indices enumerate multiple polynomials. In the two dimensional case the coefficients may be thought of as stored in the columns of c.

    tensor boolean, optional

      If True, the shape of the coefficient array is extended with ones on the right, one for each dimension of x. Scalars have dimension 0 for this action. The result is that every column of coefficients in c is evaluated for every element of x. If False, x is broadcast over the columns of c for the evaluation. This keyword is useful when c is multidimensional. The default value is True.

  Returns:
    values ndarray, compatible object

      The shape of the returned array is described above.

  See also

  `polyval2d`, `polygrid2d`, `polyval3d`, `polygrid3d`

  Notes

  The evaluation uses Horner’s method.

  When using coefficients from polynomials created with `Polynomial.fit()`, use `p(x)` or `polyval(x, p.convert().coef)` to handle domain/window scaling correctly, not `polyval(x, p.coef)`.

  Examples

      >>> import numpy as np
      >>> from numpy.polynomial.polynomial import polyval
      >>> polyval(1, [1,2,3])
      6.0
      >>> a = np.arange(4).reshape(2,2)
      >>> a
      array([[0, 1],
             [2, 3]])
      >>> polyval(a, [1, 2, 3])
      array([[ 1.,   6.],
             [17.,  34.]])
      >>> coef = np.arange(4).reshape(2, 2)  # multidimensional coefficients
      >>> coef
      array([[0, 1],
             [2, 3]])
      >>> polyval([1, 2], coef, tensor=True)
      array([[2.,  4.],
             [4.,  7.]])
      >>> polyval([1, 2], coef, tensor=False)
      array([2.,  7.])