# set terminal pngcairo  transparent enhanced fontscale 1.0 size 600, 400 
# set output 'fit.23.png'
set title "Pearson's data and York's weights\noriginal data and the initial function" 
set trange [ * : * ] noreverse nowriteback
set urange [ * : * ] noreverse nowriteback
set vrange [ * : * ] noreverse nowriteback
set xlabel "x" 
set xrange [ -1.00000 : 9.00000 ] noreverse nowriteback
set x2range [ * : * ] noreverse writeback
set ylabel "y" 
set yrange [ 0.00000 : 8.00000 ] noreverse nowriteback
set y2range [ * : * ] noreverse writeback
set zrange [ * : * ] noreverse writeback
set cbrange [ * : * ] noreverse writeback
set rrange [ * : * ] noreverse writeback
set colorbox vertical origin screen 0.9, 0.2 size screen 0.05, 0.6 front  noinvert bdefault
set fit brief errorvariables nocovariancevariables noerrorscaling prescale limit 1e-08 start_lambda 1 nowrap v5
l(x) = y0 + m*x
high(x) = mh*(x-Tc) + dens_Tc
lowlin(x)  = ml*(x-Tc) + dens_Tc
curve(x) = b*tanh(g*(Tc-x))
density(x) = x < Tc ? curve(x)+lowlin(x) : high(x)
h(x,y) = sqrt(r*r - (abs(x-x0))**2.2 - (abs(y-y0))**1.8) + z0
phi(x)	    = (x - phi0)/360.0*2.0*pi
main(x)     = c11*sin(phi(x))**2 + c33*cos(phi(x))**2 + c44
mixed(x)    = sqrt( ((c11-c44)*sin(phi(x))**2				                    +(c44-c33)*cos(phi(x))**2)**2                     +(2.0*(c13+c44)*sin(phi(x))*cos(phi(x)))**2 )
vlong(x)    = sqrt(1.0/2.0/rho*1e9*(main(x) + mixed(x)))
vtrans(x)   = sqrt(1.0/2.0/rho*1e9*(main(x) - mixed(x)))
f(x)  = a1 + a2*x
W(x) = 1./(sqrt(2.*pi)*eta) * exp( -1. * x**2 / (2.*eta**2) )
Y(tc) = tc/sin(tb) * Fhkl * r0liV
Q(tc) = (r0*Fhkl/V)**2 * (lambda**3/sin(2.*tb)) * P * f(tc)
a(x) = W(x) * Q(tc) / mu
R(x) = sinh(A*a(x)) * exp(-1.*A*(1.+a(x)))
f1(x,y)=a0/(1+a1*x**2+a2*y**2)
fy(x) = a1y + a2y*x
NO_ANIMATION = 1
myencoding = "utf8"
y0 = 0.2
m = -0.000943519626924529
FIT_CONVERGED = 1
FIT_NDF = 480
FIT_STDFIT = 0.0975475561571701
FIT_WSSR = 4.5674523418734
FIT_P = 1.0
FIT_NITER = 5
y0_err = 0.000473544839558266
m_err = 3.15383626024729e-05
FIT_ERROR = 0
FIT_COV_y0_y0 = 2.20240170189915e-06
FIT_COV_m_y0 = -4.67890413749725e-08
FIT_COV_y0_m = -4.67890413749725e-08
FIT_COV_m_m = 9.9466831564506e-10
ml = -0.00103152542276233
mh = -0.0008340717673769
dens_Tc = 1.02499621370905
Tc = 46.0665367045608
g = 6.92493866108287
b = 0.00139548391000006
ml_err = 1.62623230565094e-05
mh_err = 3.737890801507e-06
dens_Tc_err = 7.27819513635249e-06
Tc_err = 0.00159887430059728
g_err = 0.429342070879149
b_err = 5.81804522574664e-05
r = 0.5
x0 = 0.1
z0 = 0.3
r_err = 0.000364063036551252
x0_err = 0.000392881045330412
z0_err = 0.00152588271551626
rho = 1000.0
phi0 = -0.162075247526506
c11 = 5.34014735462853
c33 = 12.4010644097762
c44 = 1.0
c13 = 4.0
c33_err = 0.0725104739377388
c11_err = 0.046198553012484
c44_err = 0.0238549841497308
c13_err = 0.0822947518354354
phi0_err = 0.354321536364052
mu = 0.113046900551349
t0 = 0.18
tb = 0.199278608299778
A = 0.020759275611633
P = 0.924693446208538
Fhkl = 3.42318325539711
r0 = 2.81794092e-13
lambda = 7.09338062818239e-09
V = 1.62253546981499e-23
r0liV = 123.194394853936
eta = 0.000100781677728629
tc = 0.0020212816909931
FIT_LIMIT = 1e-08
eta_err = 3.18415875281718e-07
tc_err = 1.28183863918037e-05
a0 = 1.02179023689138
a1 = 5.0
a2 = -0.5
a0_err = 0.0141448466704402
a1_err = 0.0176570664021064
a2_err = 0.0173713660669036
FIT_START_LAMBDA = 1.0
a1y = 5.0
a2y = -0.5
msg = "Press enter to fit the data using no error values"
## Last fit command: "fit f(x,y,t) 'fit3.dat' u 1:2:3:4 via a0,a1,a2"
## Last datafile plotted: "$PearsonYork"
plot   $PearsonYork using 2:4:(sqrt(1./$3)):(sqrt(1./$5)) with xyerrorbars lt -1 title 'data',   f(x) lw 2 lt 1 title 'initial function'