Pseudo-Vandermonde matrix of given degree.
Returns the pseudo-Vandermonde matrix of degree deg and sample points x. The pseudo-Vandermonde matrix is defined by
where 0 <= i <= deg. The leading indices of V index the elements of x and the last index is the degree of the Laguerre polynomial.
If c is a 1-D array of coefficients of length n + 1 and V is the array
V = lagvander(x, n), then
lagval(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 Laguerre series of the same degree and sample points.
- 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.
- vander : ndarray
The pseudo-Vandermonde matrix. The shape of the returned matrix is
x.shape + (deg + 1,), where The last index is the degree of the corresponding Laguerre polynomial. The dtype will be the same as the converted x.
>>> from numpy.polynomial.laguerre import lagvander >>> x = np.array([0, 1, 2]) >>> lagvander(x, 3) array([[ 1. , 1. , 1. , 1. ], [ 1. , 0. , -0.5 , -0.66666667], [ 1. , -1. , -1. , -0.33333333]])