numpy.polynomial.laguerre.
lagvander
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
System Message: WARNING/2 (V[..., i] = L_i(x) )
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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 np.dot(V, c) and 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.
V = lagvander(x, n)
np.dot(V, c)
lagval(x, c)
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.
Degree of the resulting matrix.
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.
x.shape + (deg + 1,)
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]])
