---
name: "legfit"
section: "3m"
platform: "linux"
package: "iraf"
version: "2.11.3-2"
release: "Debian 3.0 (Woody)"
platforms: ["linux"]
url: "https://new.carta.tech/legfit"
---

# legfit(3m)

## 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