Legendre Module (numpy.polynomial.legendre)
New in version 1.6.0.
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).
Legendre Class
| Legendre(coef[, domain, window]) |
A Legendre series class. |
Basics
| legval(x, cs) |
Evaluate a Legendre series. |
| legval2d |
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| legval3d |
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| leggrid2d |
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| leggrid3d |
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| legroots(cs) |
Compute the roots of a Legendre series. |
| legfromroots(roots) |
Generate a Legendre series with the given roots. |
Fitting
| legfit(x, y, deg[, rcond, full, w]) |
Least squares fit of Legendre series to data. |
| legvander(x, deg) |
Vandermonde matrix of given degree. |
| legvander2d |
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| legvander3d |
|
Calculus
| legder(cs[, m, scl]) |
Differentiate a Legendre series. |
| legint(cs[, m, k, lbnd, scl]) |
Integrate a Legendre series. |
Algebra
| legadd(c1, c2) |
Add one Legendre series to another. |
| legsub(c1, c2) |
Subtract one Legendre series from another. |
| legmul(c1, c2) |
Multiply one Legendre series by another. |
| legmulx(cs) |
Multiply a Legendre series by x. |
| legdiv(c1, c2) |
Divide one Legendre series by another. |
| legpow(cs, pow[, maxpower]) |
Raise a Legendre series to a power. |
Miscellaneous
| legcompanion(cs) |
Return the scaled companion matrix of cs. |
| legdomain |
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| legzero |
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| legone |
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| legx |
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| legtrim(c[, tol]) |
Remove “small” “trailing” coefficients from a polynomial. |
| legline(off, scl) |
Legendre series whose graph is a straight line. |
| leg2poly(cs) |
Convert a Legendre series to a polynomial. |
| poly2leg(pol) |
Convert a polynomial to a Legendre series. |
