classmethod Legendre.fit(x, y, deg, domain=None, rcond=None, full=False, w=None, window=None) [source] Least squares fit to data. Return a series instance that is the least squares fit to the data y sampled at x. The domain of the returned instance can be specified and this will often result in a superior fit with less chance of ill conditioning. Parameters: x : array_like, shape (M,) x-coordinates of the M sample points (x[i], y[i]). y : array_like, shape (M,) or (M, K) y-coordinates o

Legendre.has_samecoef(other) [source] Check if coefficients match. New in version 1.6.0. Parameters: other : class instance The other class must have the coef attribute. Returns: bool : boolean True if the coefficients are the same, False otherwise.

classmethod Legendre.fromroots(roots, domain=[], window=None) [source] Return series instance that has the specified roots. Returns a series representing the product (x - r[0])*(x - r[1])*...*(x - r[n-1]), where r is a list of roots. Parameters: roots : array_like List of roots. domain : {[], None, array_like}, optional Domain for the resulting series. If None the domain is the interval from the smallest root to the largest. If [] the domain is the class domain. The default is []. wind

Legendre.cutdeg(deg) [source] Truncate series to the given degree. Reduce the degree of the series to deg by discarding the high order terms. If deg is greater than the current degree a copy of the current series is returned. This can be useful in least squares where the coefficients of the high degree terms may be very small. New in version 1.5.0. Parameters: deg : non-negative int The series is reduced to degree deg by discarding the high order terms. The value of deg must be a non-ne

Legendre.deriv(m=1) [source] Differentiate. Return a series instance of that is the derivative of the current series. Parameters: m : non-negative int Find the derivative of order m. Returns: new_series : series A new series representing the derivative. The domain is the same as the domain of the differentiated series.

Legendre.degree() [source] The degree of the series. New in version 1.5.0. Returns: degree : int Degree of the series, one less than the number of coefficients.

Legendre.convert(domain=None, kind=None, window=None) [source] Convert series to a different kind and/or domain and/or window. Parameters: domain : array_like, optional The domain of the converted series. If the value is None, the default domain of kind is used. kind : class, optional The polynomial series type class to which the current instance should be converted. If kind is None, then the class of the current instance is used. window : array_like, optional The window of the conver

Legendre.copy() [source] Return a copy. Returns: new_series : series Copy of self.

classmethod Legendre.cast(series, domain=None, window=None) [source] Convert series to series of this class. The series is expected to be an instance of some polynomial series of one of the types supported by by the numpy.polynomial module, but could be some other class that supports the convert method. New in version 1.7.0. Parameters: series : series The series instance to be converted. domain : {None, array_like}, optional If given, the array must be of the form [beg, end], where b

classmethod Legendre.basis(deg, domain=None, window=None) [source] Series basis polynomial of degree deg. Returns the series representing the basis polynomial of degree deg. New in version 1.7.0. Parameters: deg : int Degree of the basis polynomial for the series. Must be >= 0. domain : {None, array_like}, optional If given, the array must be of the form [beg, end], where beg and end are the endpoints of the domain. If None is given then the class domain is used. The default is Non