;+ ; NAME: ; LINFITEX ; ; AUTHOR: ; Craig B. Markwardt, NASA/GSFC Code 662, Greenbelt, MD 20770 ; craigm@lheamail.gsfc.nasa.gov ; UPDATED VERSIONs can be found on my WEB PAGE: ; http://cow.physics.wisc.edu/~craigm/idl/idl.html ; ; PURPOSE: ; Model function for fitting line with errors in X and Y ; ; MAJOR TOPICS: ; Curve and Surface Fitting ; ; CALLING SEQUENCE: ; parms = MPFIT('LINFITEX', start_parms, $ ; FUNCTARGS={X: X, Y: Y, SIGMA_X: SIGMA_X, SIGMA_Y: SIGMA_Y}, $ ; ...) ; ; DESCRIPTION: ; ; LINFITEX is a model function to be used with MPFIT in order to ; fit a line to data with errors in both "X" and "Y" directions. ; LINFITEX follows the methodology of Numerical Recipes, in the ; section entitled, "Straight-Line Data with Errors in Both ; Coordinates." ; ; The user is not meant to call LINFITEX directly. Rather, the ; should pass LINFITEX as a user function to MPFIT, and MPFIT will in ; turn call LINFITEX. ; ; Each data point will have an X and Y position, as well as an error ; in X and Y, denoted SIGMA_X and SIGMA_Y. The user should pass ; these values using the FUNCTARGS convention, as shown above. I.e. ; the FUNCTARGS keyword should be set to a single structure ; containing the fields "X", "Y", "SIGMA_X" and "SIGMA_Y". Each ; field should have a vector of the same length. ; ; Upon return from MPFIT, the best fit parameters will be, ; P[0] - Y-intercept of line on the X=0 axis. ; P[1] - slope of the line ; ; NOTE that LINFITEX requires that AUTODERIVATIVE=1, i.e. MPFIT ; should compute the derivatives associated with each parameter ; numerically. ; ; INPUTS: ; P - parameters of the linear model, as described above. ; ; KEYWORD INPUTS: ; (as described above, these quantities should be placed in ; a FUNCTARGS structure) ; X - vector, X position of each data point ; Y - vector, Y position of each data point ; SIGMA_X - vector, X uncertainty of each data point ; SIGMA_Y - vector, Y uncertainty of each data point ; ; RETURNS: ; Returns a vector of residuals, of the same size as X. ; ; EXAMPLE: ; ; ; X and Y values ; XS = [2.9359964E-01,1.0125043E+00,2.5900450E+00,2.6647639E+00,3.7756164E+00,4.0297413E+00,4.9227958E+00,6.4959011E+00] ; YS = [6.0932738E-01,1.3339731E+00,1.3525699E+00,1.4060204E+00,2.8321848E+00,2.7798350E+00,2.0494456E+00,3.3113062E+00] ; ; ; X and Y errors ; XE = [1.8218818E-01,3.3440986E-01,3.7536234E-01,4.5585755E-01,7.3387712E-01,8.0054945E-01,6.2370265E-01,6.7048335E-01] ; YE = [8.9751285E-01,6.4095122E-01,1.1858428E+00,1.4673588E+00,1.0045623E+00,7.8527629E-01,1.2574003E+00,1.0080348E+00] ; ; ; Best fit line ; p = mpfit('LINFITEX', [1d, 1d], $ ; FUNCTARGS={X: XS, Y: YS, SIGMA_X: XE, SIGMA_Y: YE}, $ ; perror=dp, bestnorm=chi2) ; yfit = p[0] + p[1]*XS ; ; ; REFERENCES: ; ; Press, W. H. 1992, *Numerical Recipes in C*, 2nd Ed., Cambridge ; University Press ; ; MODIFICATION HISTORY: ; Written, Feb 2009 ; Documented, 14 Apr 2009, CM ; $Id: linfitex.pro,v 1.3 2009/04/15 04:17:52 craigm Exp $ ; ;- ; Copyright (C) 2009, Craig Markwardt ; This software is provided as is without any warranty whatsoever. ; Permission to use, copy, modify, and distribute modified or ; unmodified copies is granted, provided this copyright and disclaimer ; are included unchanged. ;- ; function linfitex, p, $ x=x, y=y, sigma_x=sigma_x, sigma_y=sigma_y, $ _EXTRA=extra a = p[0] ;; Intercept b = p[1] ;; Slope f = a + b*x resid = (y - f)/sqrt(sigma_y^2 + (b*sigma_x)^2) return, resid end