numpy.polynomial.legendre.legzero = array([0])

numpy.polynomial.legendre.legx = array([0, 1])

numpy.polynomial.legendre.legweight(x) [source] Weight function of the Legendre polynomials. The weight function is and the interval of integration is . The Legendre polynomials are orthogonal, but not normalized, with respect to this weight function. Parameters: x : array_like Values at which the weight function will be computed. Returns: w : ndarray The weight function at x. Notes

numpy.polynomial.legendre.legvander3d(x, y, z, deg) [source] Pseudo-Vandermonde matrix of given degrees. Returns the pseudo-Vandermonde matrix of degrees deg and sample points (x, y, z). If l, m, n are the given degrees in x, y, z, then The pseudo-Vandermonde matrix is defined by where 0 <= i <= l, 0 <= j <= m, and 0 <= j <= n. The leading indices of V index the points (x, y, z) and the last index encodes the degrees of the Legendre polynomials. If V = legvander3d(x, y,

numpy.polynomial.legendre.legvander2d(x, y, deg) [source] Pseudo-Vandermonde matrix of given degrees. Returns the pseudo-Vandermonde matrix of degrees deg and sample points (x, y). The pseudo-Vandermonde matrix is defined by where 0 <= i <= deg[0] and 0 <= j <= deg[1]. The leading indices of V index the points (x, y) and the last index encodes the degrees of the Legendre polynomials. If V = legvander2d(x, y, [xdeg, ydeg]), then the columns of V correspond to the elements of a

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

numpy.polynomial.legendre.legval3d(x, y, z, c) [source] Evaluate a 3-D Legendre series at points (x, y, z). This function returns the values: The parameters x, y, and z are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars and they must have the same shape after conversion. In either case, either x, y, and z or their elements must support multiplication and addition both with themselves and with the elements of c. If c has fewer than 3 dimens

numpy.polynomial.legendre.legval2d(x, y, c) [source] Evaluate a 2-D Legendre series at points (x, y). This function returns the values: The parameters x and y are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars and they must have the same shape after conversion. In either case, either x and y or their elements must support multiplication and addition both with themselves and with the elements of c. If c is a 1-D array a one is implicitly ap

numpy.polynomial.legendre.legval(x, c, tensor=True) [source] Evaluate a Legendre series at points x. If c is of length n + 1, this function returns the value: The parameter x is converted to an array only if it is a tuple or a list, otherwise it is treated as a scalar. In either case, either x or its elements must support multiplication and addition both with themselves and with the elements of c. If c is a 1-D array, then p(x) will have the same shape as x. If c is multidimensional, the

numpy.polynomial.legendre.legtrim(c, tol=0) [source] Remove ?small? ?trailing? coefficients from a polynomial. ?Small? means ?small in absolute value? and is controlled by the parameter tol; ?trailing? means highest order coefficient(s), e.g., in [0, 1, 1, 0, 0] (which represents 0 + x + x**2 + 0*x**3 + 0*x**4) both the 3-rd and 4-th order coefficients would be ?trimmed.? Parameters: c : array_like 1-d array of coefficients, ordered from lowest order to highest. tol : number, optional T