legvander(x, deg)
Returns the pseudo-Vandermonde matrix of degree :None:None:`deg` and sample points x. The pseudo-Vandermonde matrix is defined by
where :None:None:`0 <= i <= deg`. The leading indices of :None:None:`V` index the elements of x and the last index is the degree of the Legendre polynomial.
If :None:None:`c` is a 1-D array of coefficients of length :None:None:`n + 1` and :None:None:`V` is the array V = legvander(x, n)
, then np.dot(V, c)
and legval(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.
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 Legendre polynomial. The dtype will be the same as the converted x.
Pseudo-Vandermonde matrix of given degree.
The following pages refer to to this document either explicitly or contain code examples using this.
numpy.polynomial.legendre.legvander3d
numpy.polynomial.legendre.legvander2d
numpy.polynomial.legendre.legfit
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