Legendre Series (`numpy.polynomial.legendre`)#

This module provides a number of objects (mostly functions) useful for dealing with Legendre series, including a Legendre class that encapsulates the usual arithmetic operations. (General information on how this module represents and works with such polynomials is in the docstring for its parent sub-package, numpy.polynomial).

Classes#

Legendre(coef[,domain,window,symbol])

A Legendre series class.

Constants#

`legdomain`	ndarray(shape, dtype=None, buffer=None, offset=0, strides=None, order=None)
`legzero`	ndarray(shape, dtype=None, buffer=None, offset=0, strides=None, order=None)
`legone`	ndarray(shape, dtype=None, buffer=None, offset=0, strides=None, order=None)
`legx`	ndarray(shape, dtype=None, buffer=None, offset=0, strides=None, order=None)

Arithmetic#

`legadd`(c1,c2)	Add one Legendre series to another.
`legsub`(c1,c2)	Subtract one Legendre series from another.
`legmulx`(c)	Multiply a Legendre series by x.
`legmul`(c1,c2)	Multiply one Legendre series by another.
`legdiv`(c1,c2)	Divide one Legendre series by another.
`legpow`(c,pow[,maxpower])	Raise a Legendre series to a power.
`legval`(x,c[,tensor])	Evaluate a Legendre series at points x.
`legval2d`(x,y,c)	Evaluate a 2-D Legendre series at points (x, y).
`legval3d`(x,y,z,c)	Evaluate a 3-D Legendre series at points (x, y, z).
`legvalnd`(pts,c)	Evaluate an N-D Legendre series at points.
`leggrid2d`(x,y,c)	Evaluate a 2-D Legendre series on the Cartesian product of x and y.
`leggrid3d`(x,y,z,c)	Evaluate a 3-D Legendre series on the Cartesian product of x, y, and z.

Calculus#

`legder`(c[,m,scl,axis])	Differentiate a Legendre series.
`legint`(c[,m,k,lbnd,scl,axis])	Integrate a Legendre series.

Misc Functions#

`legfromroots`(roots)	Generate a Legendre series with given roots.
`legroots`(c)	Compute the roots of a Legendre series.
`legvander`(x,deg)	Pseudo-Vandermonde matrix of given degree.
`legvander2d`(x,y,deg)	Pseudo-Vandermonde matrix of given degrees.
`legvander3d`(x,y,z,deg)	Pseudo-Vandermonde matrix of given degrees.
`leggauss`(deg)	Gauss-Legendre quadrature.
`legweight`(x)	Weight function of the Legendre polynomials.
`legcompanion`(c)	Return the scaled companion matrix of c.
`legfit`(x,y,deg[,rcond,full,w])	Least squares fit of Legendre series to data.
`legtrim`(c[,tol])	Remove "small" "trailing" coefficients from a polynomial.
`legline`(off,scl)	Legendre series whose graph is a straight line.
`leg2poly`(c)	Convert a Legendre series to a polynomial.
`poly2leg`(pol)	Convert a polynomial to a Legendre series.

Legendre Series (numpy.polynomial.legendre)#