numpy.polynomial.legendre.legvander(x, deg)
[source]
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 Legendre polynomial.
If c
is a 1-D array of coefficients of length n + 1
and 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.
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 deg : int Degree of the resulting matrix. |
---|---|
Returns: |
vander : ndarray The pseudo-Vandermonde matrix. The shape of the returned matrix is |
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https://docs.scipy.org/doc/numpy-1.13.0/reference/generated/numpy.polynomial.legendre.legvander.html