FUNCTION lsqNormalFit, xin, yin , $
        plotx   = plotx , $
        oplotx  = oplotx, $
        worst   = worst , $
        xfit    = xfit  , $
        yfit    = yfit  , $
        _extra  = _extra
    @compile_opt.pro        ; On error, return to caller

InitVar, plotx  , /key
InitVar, oplotx , /key
InitVar, worst  , /key

n = n_elements(xin)
IF n_elements(yin) NE N THEN message, 'both arrays must have same size'

x   = xin
y   = yin

Vx  = total(x)/n
Vy  = total(y)/n

xx  = x-Vx
yy  = y-Vy
Dxx = sqrt( total(xx*xx)/n )
Dyy = sqrt( total(yy*yy)/n )

x   = x/Dxx
y   = y/Dyy

Tx  = total(x)/n
Ty  = total(y)/n

xx  = x-Tx
yy  = y-Ty
Rx  = total(xx*xx)/n
Ry  = total(yy*yy)/n
Rxy = total(xx*yy)/n

Rp  = (Rx+Ry)/2.
Rm  = (Rx-Ry)/2.

Zxy = (Rm*Rm+Rxy*Rxy) > 0
Zxy = sqrt(Zxy)
;print, rp,'  ',rm,'  ',zxy

; The equation for the fit is A*(x-Tx)+B*(y-Ty)=0

A1  = -Tx*Rxy+Ty*(Rm+Zxy)       ; Worst fit
B1  =  Ty*Rxy+Tx*(Rm-Zxy)
F1  = sqrt(Rp+Zxy)              ; Root of average of dist^2

A2  = -Tx*Rxy+Ty*(Rm-Zxy)       ; Best fit
B2  =  Ty*Rxy+Tx*(Rm+Zxy)
F2  = sqrt( (Rp-Zxy) > 0 )      ; Root of average of dist^2

d   = sort(x)                   ; Do not sort the arrays prior to the calculation.
x   = x[d]                      ; This destroys the symmetry between x and y.
y   = y[d]

;if plotx then plot, Dxx*x,Dyy*y, /ynozero, psym=2, _extra=_extra
IF plotx THEN plot, xin[d], yin[d], /ynozero, psym=2, _extra=_extra

IF plotx OR oplotx THEN BEGIN
    d  = 3.*sqrt(Rp)
    s  = sqrt(A2*A2+B2*B2)
    dx =  d*(b2/s)
    dy = -d*(a2/s)
    oplot, Dxx*(Tx+dx*[-1,1]), Dyy*(Ty+dy*[-1,1]), _extra=_extra
    IF worst AND (A1 NE 0 OR B1 NE 0) THEN BEGIN
        s  = sqrt(A1*A1+B1*B1)
        dx =  d*(b1/s)
        dy = -d*(a1/s)
        oplot, Dxx*(Tx+dx*[-1,1]), Dyy*(Ty+dy*[-1,1])
    ENDIF
    catch, ierr
    IF ierr EQ 0 THEN s = poly_fit(Dxx*x,Dyy*y,1,d)
    catch, /cancel
    ;oplot, Dxx*x, d, linestyle=3
ENDIF

yfit = Vy-(A2/B2)*(Dyy/Dxx)*(x-Vx)
xfit = Vx-(B2/A2)*(Dxx/Dyy)*(y-Vy)

RETURN, [[A2/Dxx,Vx,B2/Dyy,Vy,F2],[A1/Dxx,Vx,B1/Dyy,Vy,F1]]  &  END