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+;******************************************************************************
+;+
+;*NAME:
+;
+;    CHISQ    (General IDL Library 01)  JUNE,1984
+; 
+;*CLASS: 
+;
+;    Statistics
+;
+;*CATEGORY
+;  
+;*PURPOSE:   
+;
+;    To evaluate reduced chi-squared for a fit to data.
+; 
+;*CALLING SEQUENCE: 
+;
+;    CHISQ,Y,WEIGHT,YFIT,NFREE,CHISQ
+; 
+;*PARAMETERS:
+;
+;    Y       (REQ) (I) (1) (F D)
+;            Required input vector containing the measured data.
+;
+;    WEIGHT  (REQ) (I/O) (1) (F D)
+;            Required input vector containing the data point weights:
+;              for instrumental uncertainties use WEIGHT=1/sigmay^2,
+;              for statistical uncertaintities use WEIGHT=1/Y,
+;              if WEIGHT=1 then value returned = variance of fit,
+;              see BEVINGTON for further information.
+;
+;    YFIT    (REQ) (I) (1) (F D)
+;            Required input vector containing the calculated data based
+;            on some model or least squares fitting.
+;
+;    NFREE   (REQ) (I) (0) (I L F D)
+;            Required input scalar containing the number of degrees of 
+;            freedom.  This is equal to:
+;               number of data points - degree of polynomial - 1
+;
+;    CHISQ   (REQ) (O) (0) (F D)
+;            Required ouput scalar giving the reduced chi-squared statistic.
+;
+;*EXAMPLES:
+;
+;    To compute the chi-squared statistic for observed data YDATA and
+;    computed data YFIT, with uniform data weighting,
+;
+;       weight = 0 * ydata + 1.
+;       chisq,ydata,weight,yfit,nfree,chisq
+;
+;    To compute the reduced chi-squared statistic for observed data Y and
+;    computed data YF, where the weight = abs(1./y), Y has 100 points, YF
+;    is a third degree polynomial [i.e., yf = a(0) + a(1) * x + a(2) * x^2 +
+;    a(3) * x^3}:
+;
+;       chisq,y,abs(1./y),yf,n_elements(y)-3-1,chisq
+;
+;*SYSTEM VARIABLES USED:
+;
+;    none
+;
+;*INTERACTIVE INPUT:
+;
+;    none
+;
+;*SUBROUTINES CALLED:
+;
+;    PARCHECK
+;    PCHECK
+;
+;*FILES USED:
+;
+;    none
+;
+;*SIDE EFFECTS:
+;
+;    If WEIGHT
+;
+;*PROCEDURE: 
+;
+;    The procedure computes total(weight(y-yfit)^2)/nfree
+;                 (See Bevington [1969] p. 193-195 for weighting methods)
+;   
+;*NOTES:
+;
+;    If NFREE is < 0  or NPTS is < NFREE then CHISQ is set to 0
+;    and an error message will appear.
+;    Typing CHISQ without any parameters will display the procedure
+;    call statement.
+;
+; tested with IDL Version 2.1.0 (sunos sparc)   19 Jun 91
+; tested with IDL Version 2.1.0 (ultrix mispel) N/A
+; tested with IDL Version 2.1.0 (vms vax)       21 Jun 91
+; 
+;*MODIFICATION HISTORY:
+;
+;    July,  1981  TBA  GSFC add weighting
+;    June,  1984  NRE  GSFC change to 1/SIGMA^2 weighting, document
+;    Jul  5 1984  RWT  GSFC correct error in using WEIGHT and modify
+;                          documentation
+;    Sep  9 1987  RWT  GSFC add procedure call listing 
+;    Mar  8 1988  CAG  GSFC add VAX RDAF-style prolog.
+;    Jun 21 1991  PJL  GSFC cleaned up; tested on SUN and VAX; updated prolog
+;     6 May 94  PJL  added to prolog
+;    11 May 94  PJL  print a warning if any of the weights are negative
+;
+;-
+;******************************************************************************
+ pro chisq,y,weight,yfit,nfree,chisq
+;
+ npar = n_params(0)
+ if (npar eq 0) then begin
+    print,'CHISQ,Y,WEIGHT,YFIT,NFREE,CHISQ'
+    retall
+ endif  ; npar
+; parcheck,npar,5,'CHISQ'
+; pcheck,y,1,010,0011
+; pcheck,yfit,2,010,0011
+; pcheck,nfree,3,100,0010
+;
+;  print a warning if any of the weights are negative
+;
+ temp = where(weight lt 0,count)
+ if (count gt 0) then begin
+    print,' '
+    print,'WARNING:  ' + strtrim(count,2) + ' of the ' +   $
+       strtrim(n_elements(weight),2) + ' weight values are negative.'
+    print,'ACTION:  continuing'
+    print,' '
+ endif  ; count gt 0
+;
+ npts  = n_elements(y)
+;
+; if degrees of freedom positive, proceed
+;
+ if (nfree gt 0) and (npts gt nfree) then begin
+    chisq = total(weight*(y-yfit)*(y-yfit)) / nfree
+ endif else begin
+    print,'Error detected in CHISQ.'
+    print,'nfree = ',strtrim(nfree,2),'  npts = ',strtrim(npts,2)
+    chisq = 0
+ endelse  ; nfree
+;
+ return
+ end  ; chisq
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