# set terminal pngcairo  transparent enhanced fontscale 1.0 size 600, 400 
# set output 'fit.9.png'
set bar 1.000000 front
set style circle radius graph 0.02, first 0.00000, 0.00000 
set style ellipse size graph 0.05, 0.03, first 0.00000 angle 0 units xy
set key bmargin center horizontal Right noreverse enhanced autotitle nobox
set style textbox transparent margins  1.0,  1.0 border
unset logscale
unset paxis 1 tics
unset paxis 2 tics
unset paxis 3 tics
unset paxis 4 tics
unset paxis 5 tics
unset paxis 6 tics
unset paxis 7 tics
set title "sound data, and model with initial parameters" 
set paxis 1 range [ * : * ] noreverse nowriteback
set paxis 2 range [ * : * ] noreverse nowriteback
set paxis 3 range [ * : * ] noreverse nowriteback
set paxis 4 range [ * : * ] noreverse nowriteback
set paxis 5 range [ * : * ] noreverse nowriteback
set paxis 6 range [ * : * ] noreverse nowriteback
set paxis 7 range [ * : * ] noreverse nowriteback
set colorbox vertical origin screen 0.9, 0.2, 0 size screen 0.05, 0.6, 0 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)
myencoding = "utf8"
y0 = 0.2
m = -0.000943519626924529
GPFUN_l = "l(x) = y0 + m*x"
x = 0.0
FIT_CONVERGED = 1
FIT_NDF = 245
FIT_STDFIT = 0.0180887832084403
FIT_WSSR = 0.0801649991006786
FIT_P = 1.0
FIT_NITER = 50
y0_err = 0.000473544839517863
m_err = 3.15383626024729e-05
ml = -0.00103152542276233
mh = -0.0008340717673769
dens_Tc = 1.02499621370905
Tc = 46.0665367045608
g = 6.92493866108287
b = 0.00139548391000006
GPFUN_high = "high(x) = mh*(x-Tc) + dens_Tc"
GPFUN_lowlin = "lowlin(x)  = ml*(x-Tc) + dens_Tc"
GPFUN_curve = "curve(x) = b*tanh(g*(Tc-x))"
GPFUN_density = "density(x) = x < Tc ? curve(x)+lowlin(x) : high(x)"
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
GPFUN_h = "h(x,y) = sqrt(r*r - (abs(x-x0))**2.2 - (abs(y-y0))**1.8) + z0"
r_err = 0.000364063036513251
x0_err = 0.000392881045327825
z0_err = 0.00152588271554302
rho = 1000.0
phi0 = 20.0
GPFUN_phi = "phi(x)\t    = (x - phi0)/360.0*2.0*pi"
c11 = 6
c33 = 9
c44 = 1
GPFUN_main = "main(x)     = c11*sin(phi(x))**2 + c33*cos(phi(x))**2 + c44"
c13 = 4
GPFUN_mixed = "mixed(x)    = sqrt( ((c11-c44)*sin(phi(x))**2\t\t\t\t                    +(c44-c33)*cos(phi(x))**2)**2                     +(2.0*(c13+c44)*sin(phi(x))*cos(phi(x)))**2 )"
GPFUN_vlong = "vlong(x)    = sqrt(1.0/2.0/rho*1e9*(main(x) + mixed(x)))"
GPFUN_vtrans = "vtrans(x)   = sqrt(1.0/2.0/rho*1e9*(main(x) - mixed(x)))"
GPFUN_f = "f(x,y)\t=  y==1  ?  vlong(x)  :  vtrans(x)"
## Last datafile plotted: "soundvel.dat"
plot 'soundvel.dat', vlong(x), vtrans(x)
## fit h(x,y) 'hemisphr.dat' using 1:2:3 via r, x0, y0, z0