Institut für Astronomie und AstrophysikAbteilung AstronomieSand 1, D-72076 Tübingen, GermanyNew Address! -- Neue Adresse! |
FLEGENDRE
Compute the first M terms in a Legendre polynomial expansion.
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.
result = FLEGENDRE( X, M)
X - the value of the independent variable, scalar or vector M - number of term of the Legendre expansion to compute, integer scalar
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
(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.
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
Written Wayne Landsman Hughes STX April 1995 Converted to IDL V5.0 W. Landsman September 1997
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