[Matrix-SIG] Re: cephesmodule

[Rob Managan]

Probably doesn't make much difference up to P5 but the polynomials should
be nested to help avoid cancelation problems.

At 4:01 PM -0600 3/10/99, Mike Miller wrote:
>>>>>> "Les" == Les Schaffer <godzilla@netmeg.net> writes:
>
>    >> Do you know of some code that computes them?  Isn't there
>    >> someway to write them as a hypergeometric functions?
>
>#!/usr/bin/env python
>#
># Legendre Polynomials.
>#
># Oct-25-1998
>#    M.A.Miller, NPL UIUC <miller5@uiuc.edu>
>
>"""
>class Legendre:  Legendre polynomials.  For n = 0-5, they are hard
>coded: P0(x), P1(x), P2(x), P3(x), P4(x), P5(x).  For n > 5, the
>recurrence relation is used: Pn(n,x).
>"""
>class Legendre:
>    def __init__(self):
>        pass
>
>    def P0(self,x):
>        result = 1.0
>        return result
>
>    def P1(self,x):
>        result = x
>        return result
>
>    def P2(self,x):
>        result = ( 3.0 * x**2 - 1 ) / 2.0
>        return result
>
>    def P3(self,x):
>        result = ( (5.0 * x*x - 3.0) * x ) / 2.0
>        return result
>
>    def P4(self,x):
>        result = ( (35.0 * x*x - 30.0) * x*x + 3.0 ) / 8.0
>        return result
>
>    def P5(self,x):
>        result = ( ((63.0 * x*x - 70.0) * x*x + 15.0) * x ) / 8.0
>        return result
>
>    def Pn(self,n,x):
>        if n == 0:
>            result = self.P0(x)
>        elif n == 1:
>            result = self.P1(x)
>        elif n == 2:
>            result = self.P2(x)
>        elif n == 3:
>            result = self.P3(x)
>        elif n == 4:
>            result = self.P4(x)
>        elif n == 5:
>            result = self.P5(x)
>        else:
>            result= ( ( 2.0 * n - 1.0 ) * x * self.Pn(n-1,x) -
>                      ( n - 1.0 ) * self.Pn(n-2,x) ) / n
>        return result
>
>def test():
>    import Numeric
>    L = Legendre()
>    for x in Numeric.arrayrange( -1.0, 1.0, 0.1 ):
>        print '%6.2f  %7.4f  %7.4f  %7.4f  %7.4f  %7.4f  %7.4f  %7.4f
>%7.4f' % \
>              ( x, L.P0(x), L.P1(x), L.P2(x), L.P3(x), L.P4(x), L.P5(x),
>                L.Pn(5,x), L.Pn(7,x) )
>
>if __name__ == '__main__':
>    test()
>
>_______________________________________________
>Matrix-SIG maillist  -  Matrix-SIG@python.org
>http://www.python.org/mailman/listinfo/matrix-sig

*-*-*-*-*-*-*-*-*-*-**-*-*-*-*-*-*-*-*-*-*-
Rob Managan       mailto://managan@llnl.gov
LLNL                      ph:  925-423-0903
P.O. Box 808, L-098       FAX: 925-423-5804
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