pl.show() pl.figure(2) pl.clf() pl.plot(sigmas, lognormalmass_integrals) pl.xlabel(r'$\sigma_s$') pl.ylabel(r'$\int P_M(s)$') pl.figure(3) pl.clf() fits = [] for s in sigmas[::10]: distr = lognormal_massweighted(rho, 1, s) L, = pl.loglog(rho,distr, label=r'$\sigma_s=%f' % s, linewidth=3, alpha=0.5) (fitted_rho0,fitted_s),cov = curve_fit(lognormal, rho, distr, p0=[np.exp(s**2),s]) fitted_distr = lognormal(rho, fitted_rho0, fitted_s) pl.loglog(rho,fitted_distr,color=L.get_color(), linestyle='--') fits.append((fitted_rho0,fitted_s)) fits = np.array(fits) pl.xlabel(r'$\rho$') pl.ylabel(r'$P_M(s)$') pl.axis([1e-10,1e30,1e-10,1]) pl.figure(4) pl.clf() pl.plot(meanrhos, lognormal_integrals_rho) pl.xlabel(r'$\rho_0$') pl.ylabel(r'$\int P_V(s)$') pl.show()
pl.figure(3) pl.clf() fits = [] for s in sigmas[::10]: distr = lognormal_massweighted(rho, 1, s) L, = pl.loglog(rho, distr, label=r'$\sigma_s=%f' % s, linewidth=3, alpha=0.5) (fitted_rho0, fitted_s), cov = curve_fit(lognormal, rho, distr, p0=[np.exp(s**2), s]) fitted_distr = lognormal(rho, fitted_rho0, fitted_s) pl.loglog(rho, fitted_distr, color=L.get_color(), linestyle='--') fits.append((fitted_rho0, fitted_s)) fits = np.array(fits) pl.xlabel(r'$\rho$') pl.ylabel(r'$P_M(s)$') pl.axis([1e-10, 1e30, 1e-10, 1]) pl.figure(4) pl.clf() pl.plot(meanrhos, lognormal_integrals_rho) pl.xlabel(r'$\rho_0$') pl.ylabel(r'$\int P_V(s)$') pl.show()
import pylab as pl import numpy as np import hopkins_pdf from turbulent_pdfs import lognormal def normalize(arr, normfunc=np.sum): return arr/normfunc(arr) pl.rc('font',size=24) meandens_4 = 15 xdens = np.linspace(-6,10,1000) for fignum,sigma in enumerate((0.5,1,1.5,2.0,2.5)): rho = 10**xdens distr = lognormal(dens=rho, meandens=meandens_4, sigma=sigma) pl.figure(fignum) pl.clf() #pl.plot(rho,distr_mass,label='Mass-weighted PDF',linewidth=2.0) pl.plot(rho,normalize(distr), label='Lognormal $P_V$',color='k', linestyle='-') pl.plot(rho,normalize(rho*distr),label='Lognormal $P_M$',color='k', linestyle='--') #pl.plot(10**(xdens+log(10)),distr_mass,":",label='Volume-weighted PDF scaled') #pl.plot(rho,massgauss,'--',label='Mass gaussian') #pl.plot(rho,taildens,'k--',label='with High Tail') #pl.plot(rho,taildenspower,'k:',label='with powerlaw Tail') #pl.plot(rho,powertail,label='powerlaw Tail') #pl.plot(rho,tail,label='High Tail') #pl.loglog(rho,hightail_distr(meandens_4,sigma,dens=xdens),label='High Tail',linewidth=2, alpha=0.5) #pl.loglog(rho,lowtail_distr(meandens_4,sigma,dens=xdens),label='Low Tail',linewidth=2, alpha=0.5) #pl.loglog(rho,compressive_distr(meandens_4,sigma,dens=xdens),label='Compressive',linewidth=2, alpha=0.5) #pl.loglog(rho,compressive_distr(meandens_4,sigma,dens=xdens,sigma2=sigma*0.6,secondscale=1.2,offset=1.9),label='Compressive2',linewidth=3, alpha=0.5)