NAME
legfit
DESCRIPTION
subroutine legfit.f
source
Bevington, pages 155-157.
purpose
make least-squares fit to data with a Legendre polynomial
y = a(1) + a(2)*x + a(3)*(3x**2-1)/2 + ...
= a(1) * (1. + b(2)*x + b(3)*(3x**2-1)/2 + ... )
where x = cos(theta)
usage
call legfit (theta, y, sigmay, npts, norder, neven, mode,
ftest, yfit, a, sigmaa, b, sigmab, chisqr)
description of parameters
theta - array of angles (in degrees) of the data points
y - array of data points for dependent variable
sigmay - array of standard deivations for y data points
npts - number of pairs of data points
norder - highest order of polynomial (number of terms - 1)
neven - determines odd or even character of polynomial
+1 fits only to even terms
0 fits to all terms
-1 fits only to odd terms (plus constant term)
mode - determines mode of weighting least-squares fit
+1 (instrumental) weight(i) = 1./sigmay(i)**2
0 (no weighting) weight(i) = 1.
-1 (statistical) weight(i) = 1./y(i)
ftest - array of values of f(l) for an f test
yfit - array of calculated values of y
a - array of coefficients of polynomial
sigmaa - array of standard deviations for coefficients
b - array of normalized relative coefficients
sigmab - array of std. deviations of relative coefficients
chisqr - reduced chi square for fit
subroutines and function subprograms required
matinv (array, nterms, det)
inverts symmetric two-dimension matrix of degree nterms
and calculates its determinant
comments
valid for npts up to 100 and order up to 9
one source line modified - cos substituted for dcos