numpy.polynomial.polynomial.polyvander — NumPy v1.11 Manual (original) (raw)
numpy.polynomial.polynomial.polyvander(x, deg)[source]¶
Vandermonde matrix of given degree.
Returns the Vandermonde matrix of degree deg and sample points_x_. The Vandermonde matrix is defined by
![V[..., i] = x^i,](http://docs.scipy.org/doc/numpy-1.11.0/_images/math/28e864b2645803a0e21b2fff9d13ff8b5252b9c9.png)
where 0 <= i <= deg. The leading indices of V index the elements of_x_ and the last index is the power of x.
If c is a 1-D array of coefficients of length n + 1 and V is the matrix V = polyvander(x, n), then np.dot(V, c) andpolyval(x, c) are the same up to roundoff. This equivalence is useful both for least squares fitting and for the evaluation of a large number of polynomials of the same degree and sample points.
| Parameters: | x : array_like Array of points. The dtype is converted to float64 or complex128 depending on whether any of the elements are complex. If x is scalar it is converted to a 1-D array. deg : int Degree of the resulting matrix. |
|---|---|
| Returns: | vander : ndarray. The Vandermonde matrix. The shape of the returned matrix isx.shape + (deg + 1,), where the last index is the power of x. The dtype will be the same as the converted x. |