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LINFITEX

LINFITEX

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 $



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