diff options
Diffstat (limited to 'numpy/polynomial/legendre.py')
| -rw-r--r-- | numpy/polynomial/legendre.py | 25 |
1 files changed, 11 insertions, 14 deletions
diff --git a/numpy/polynomial/legendre.py b/numpy/polynomial/legendre.py index f09f3dc17..9aec256cd 100644 --- a/numpy/polynomial/legendre.py +++ b/numpy/polynomial/legendre.py @@ -21,6 +21,7 @@ Arithmetic - `legsub` -- subtract one Legendre series from another. - `legmul` -- multiply two Legendre series. - `legdiv` -- divide one Legendre series by another. +- `legpow` -- raise a Legendre series to an positive integer power - `legval` -- evaluate a Legendre series at given points. Calculus @@ -35,7 +36,7 @@ Misc Functions - `legvander` -- Vandermonde-like matrix for Legendre polynomials. - `legfit` -- least-squares fit returning a Legendre series. - `legtrim` -- trim leading coefficients from a Legendre series. -- `legline` -- Legendre series of given straight line. +- `legline` -- Legendre series representing given straight line. - `leg2poly` -- convert a Legendre series to a polynomial. - `poly2leg` -- convert a polynomial to a Legendre series. @@ -51,9 +52,10 @@ See also from __future__ import division __all__ = ['legzero', 'legone', 'legx', 'legdomain', 'legline', - 'legadd', 'legsub', 'legmulx', 'legmul', 'legdiv', 'legval', - 'legder', 'legint', 'leg2poly', 'poly2leg', 'legfromroots', - 'legvander', 'legfit', 'legtrim', 'legroots', 'Legendre'] + 'legadd', 'legsub', 'legmulx', 'legmul', 'legdiv', 'legpow', + 'legval', 'legder', 'legint', 'leg2poly', 'poly2leg', + 'legfromroots', 'legvander', 'legfit', 'legtrim', 'legroots', + 'Legendre'] import numpy as np import numpy.linalg as la @@ -65,8 +67,6 @@ legtrim = pu.trimcoef def poly2leg(pol) : """ - poly2leg(pol) - Convert a polynomial to a Legendre series. Convert an array representing the coefficients of a polynomial (relative @@ -463,7 +463,7 @@ def legmulx(cs): .. math:: - xP_i(x) = ((i + 1)*P_{i + 1}(x) + i*P_{i - 1}(x))/(2i + 1) + xP_i(x) = ((i + 1)*P_{i + 1}(x) + i*P_{i - 1}(x))/(2i + 1) """ # cs is a trimmed copy @@ -564,12 +564,12 @@ def legdiv(c1, c2): Parameters ---------- c1, c2 : array_like - 1-d arrays of Legendre series coefficients ordered from low to + 1-D arrays of Legendre series coefficients ordered from low to high. Returns ------- - [quo, rem] : ndarrays + quo, rem : ndarrays Of Legendre series coefficients representing the quotient and remainder. @@ -683,8 +683,8 @@ def legder(cs, m=1, scl=1) : Parameters ---------- - cs: array_like - 1-d array of Legendre series coefficients ordered from low to high. + cs : array_like + 1-D array of Legendre series coefficients ordered from low to high. m : int, optional Number of derivatives taken, must be non-negative. (Default: 1) scl : scalar, optional @@ -887,9 +887,6 @@ def legval(x, cs): -------- legfit - Examples - -------- - Notes ----- The evaluation uses Clenshaw recursion, aka synthetic division. |