# set terminal pngcairo transparent enhanced fontscale 1.0 size 600, 400 # set output 'fit.24.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 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 "Pearson's data and York's weights\nfunction fit with no error terms" set xlabel "x" set xrange [ -1.00000 : 9.00000 ] noreverse nowriteback set ylabel "y" set yrange [ 0.00000 : 8.00000 ] noreverse nowriteback 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 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 myencoding = "utf8" y0 = 0.2 m = -0.000943519626924529 GPFUN_l = "l(x) = y0 + m*x" x = 0.0 FIT_CONVERGED = 1 FIT_NDF = 8 FIT_STDFIT = 0.316358878932538 FIT_WSSR = 0.80066352223562 FIT_P = 0.999221373947135 FIT_NITER = 3 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 = -0.162075247473126 GPFUN_phi = "phi(x)\t = (x - phi0)/360.0*2.0*pi" c11 = 5.3401473546286 c33 = 12.4010644097779 c44 = 1.0 GPFUN_main = "main(x) = c11*sin(phi(x))**2 + c33*cos(phi(x))**2 + c44" c13 = 4.0 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) = a1 + a2*x" c33_err = 0.0725104739381576 c11_err = 0.0461985530124751 c44_err = 0.0238549841497271 c13_err = 0.0822947518353551 phi0_err = 0.354321536370196 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 GPFUN_W = "W(x) = 1./(sqrt(2.*pi)*eta) * exp( -1. * x**2 / (2.*eta**2) )" GPFUN_Y = "Y(tc) = tc/sin(tb) * Fhkl * r0liV" GPFUN_Q = "Q(tc) = (r0*Fhkl/V)**2 * (lambda**3/sin(2.*tb)) * P * f(tc)" tc = 0.0020212816909931 GPFUN_a = "a(x) = W(x) * Q(tc) / mu" GPFUN_R = "R(x) = sinh(A*a(x)) * exp(-1.*A*(1.+a(x)))" FIT_LIMIT = 1e-08 eta_err = 3.18415875281773e-07 tc_err = 1.28183863917988e-05 a0 = 1.02179023689138 a1 = 5.76118519031632 a2 = -0.539577274953492 GPFUN_f1 = "f1(x,y)=a0/(1+a1*x**2+a2*y**2)" a0_err = 0.0141448466704434 a1_err = 0.189485195921111 a2_err = 0.0421265483886943 FIT_START_LAMBDA = 1.0 a1y = 5.0 a2y = -0.5 GPFUN_fy = "fy(x) = a1y + a2y*x" msg = "Press enter to fit the data using only the uncertainties of the y-values." ## Last datafile plotted: "$PearsonYork" plot $PearsonYork using 2:4:(sqrt(1./$3)):(sqrt(1./$5)) lt -1 with xyerrorbars title 'data', f(x) lw 2 lt 1 title 'fit using no error terms' ## fit f(x) $PearsonYork using 2:4 via a1, a2