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Abteilung Astronomie

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FLEGENDRE Source code in flegendre.pro

FLEGENDRE

Name
        FLEGENDRE
Purpose
       Compute the first M terms in a Legendre polynomial expansion.
Explanation
       Meant to be used as a supplied function to SVDFIT.
       This procedure became partially obsolete in IDL V5.0 with the
       introduction of the /LEGENDRE keyword to SVDFIT and the associated
       SVDLEG function.    However, note that, unlike SVDLEG, FLEGENDRE works
       on vector values of X.
Calling Sequence
       result = FLEGENDRE( X, M)
Input Parameters
       X - the value of the independent variable, scalar or vector
       M - number of term of the Legendre expansion to compute, integer scalar
Output Parameters
       result - (N,M) array, where N is the number of elements in X and M
               is the order.   Contains the value of each Legendre term for
               each value of X
Example
       (1) If x = 2.88 and M = 3 then
       IDL> print, flegendre(x,3)   ==>   [1.00, 2.88, 11.9416]
       This result can be checked by explicitly computing the first 3 Legendre
       terms, 1.0, x, 0.5*( 3*x^2 -1)
       (2) Find the coefficients to an M term Legendre polynomial that gives
               the best least-squares fit to a dataset (x,y)
               IDL> coeff = SVDFIT( x,y,M,func='flegendre')
           The coefficients can then be supplied to the function POLYLEG to
               compute the best YFIT values for any X.
Procedure
       The recurrence relation for the Legendre polynomials is used to compute
       each term.   Compare with the function FLEG in "Numerical Recipes"
       by Press et al. (1992), p. 674
Revision History
       Written     Wayne Landsman    Hughes STX      April 1995
       Converted to IDL V5.0   W. Landsman   September 1997

Last modified by pro2html on 2002 April 27 at 03:39 UTC

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Jörn Wilms (wilms@astro.uni-tuebingen.de)
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