# set terminal pngcairo  transparent enhanced fontscale 1.0 size 600, 400 
# set output 'fit.9.png'
set key bmargin center horizontal Right noreverse enhanced autotitle nobox
set title "sound data, and model with initial parameters" 
set trange [ * : * ] noreverse nowriteback
set urange [ * : * ] noreverse nowriteback
set vrange [ * : * ] noreverse nowriteback
set xrange [ * : * ] noreverse writeback
set x2range [ * : * ] noreverse writeback
set yrange [ * : * ] noreverse writeback
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 errorscaling noprescale 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,y)	=  y==1  ?  vlong(x)  :  vtrans(x)
NO_ANIMATION = 1
myencoding = "utf8"
y0 = 0.2
m = -0.000943519626924529
FIT_CONVERGED = 1
FIT_NDF = 245
FIT_STDFIT = 0.0180887832084143
FIT_WSSR = 0.0801649991004476
FIT_P = 1.0
FIT_NITER = 50
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 = 20.0
c11 = 6
c33 = 9
c44 = 1
c13 = 4
## Last fit command: "fit h(x,y) 'hemisphr.dat' using 1:2:3 via r, x0, y0, z0"
## Last datafile plotted: "soundvel.dat"
plot 'soundvel.dat', vlong(x), vtrans(x)