numpy.polynomial.legendre.legvander¶

numpy.polynomial.legendre.
legvander
(x, deg)[source]¶ PseudoVandermonde matrix of given degree.
Returns the pseudoVandermonde matrix of degree deg and sample points x. The pseudoVandermonde 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 Legendre polynomial.
If c is a 1D array of coefficients of length n + 1 and V is the array
V = legvander(x, n)
, thennp.dot(V, c)
andlegval(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 Legendre series 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 1D array.
deg : int
Degree of the resulting matrix.
Returns: vander : ndarray
The pseudoVandermonde matrix. The shape of the returned matrix is
x.shape + (deg + 1,)
, where The last index is the degree of the corresponding Legendre polynomial. The dtype will be the same as the converted x.