numpy.polynomial.laguerre.lagvander

numpy.polynomial.laguerre.lagvander(x, deg)

Vandermonde matrix of given degree.

Returns the Vandermonde matrix of degree deg and sample points x. This isn’t a true Vandermonde matrix because x can be an arbitrary ndarray and the Laguerre polynomials aren’t powers. If V is the returned matrix and x is a 2d array, then the elements of V are V[i,j,k] = P_k(x[i,j]), where P_k is the Laguerre polynomial of degree k.

Parameters :

x : array_like

Array of points. The values are converted to double or complex doubles. If x is scalar it is converted to a 1D array.

deg : integer

Degree of the resulting matrix.

Returns :

vander : Vandermonde matrix.

The shape of the returned matrix is x.shape + (deg+1,). The last index is the degree.

Examples

>>> 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]])

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