polyval(x, c, tensor=True)[source]¶
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.
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.
New in version 1.7.0.
values : ndarray, compatible object
The shape of the returned array is described above.
The evaluation uses Horner’s method.
>>> 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.])