def bovy_dens2d(x,y, *args,**kwargs): ''' wrapper around bovy_dens2d hist_2d = bovy_dens2d(x,y, *args,**kwargs) ''' try: import bovy_plot except ImportError: print 'Import bovyplot failed' if kwargs.has_key('xrange'): xrange=kwargs['xrange'] kwargs.pop('xrange') else: xrange=[x.min(),x.max()] if kwargs.has_key('yrange'): yrange=kwargs['yrange'] kwargs.pop('yrange') else: yrange=[y.min(),y.max()] ndata= len(x) if kwargs.has_key('bins'): bins= kwargs['bins'] kwargs.pop('bins') else: bins= round(0.3*sc.sqrt(ndata)) if kwargs.has_key('aspect'): aspect= kwargs['aspect'] kwargs.pop('aspect') else: aspect= (xrange[1]-xrange[0])/(yrange[1]-yrange[0]) if kwargs.has_key('weights'): weights= kwargs['weights'] kwargs.pop('weights') else: weights= None if kwargs.has_key('levels'): levels= kwargs['levels'] kwargs.pop('levels') else: levels= special.erf(0.5*sc.arange(1,4)) hh_2d, edges= sc.histogramdd(sc.array([x, y]).T, bins=bins, range=[xrange ,yrange]) bovy_plot.bovy_dens2d(hh_2d.T, contours=True,levels=levels,cntrmass=True, cmap='gist_yarg',origin='lower', xrange=xrange, yrange=yrange, aspect=aspect, interpolation='nearest', retCumImage=True, **kwargs) return hh_2d
def exNew(exclude=sc.array([1,2,3,4]), plotfilename='exNew.png',nburn=20000,nsamples=200000, parsigma=[5,.075,.01,1,.1],dsigma=1.): """exMix1: solve the new exercise using MCMC sampling Input: exclude - ID numbers to exclude from the analysis (can be None) plotfilename - filename for the output plot nburn - number of burn-in samples nsamples - number of samples to take after burn-in parsigma - proposal distribution width (Gaussian) dsigma - divide uncertainties by this amount Output: plot History: 2010-04-28 - Written - Bovy (NYU) """ sc.random.seed(1) #In the interest of reproducibility (if that's a word) #Read the data data= read_data('data_yerr.dat') ndata= len(data) if not exclude == None: nsample= ndata- len(exclude) else: nsample= ndata #First find the chi-squared solution, which we will use as an #initial guess #Put the data in the appropriate arrays and matrices Y= sc.zeros(nsample) X= sc.zeros(nsample) A= sc.ones((nsample,2)) C= sc.zeros((nsample,nsample)) yerr= sc.zeros(nsample) jj= 0 for ii in range(ndata): if not exclude == None and sc.any(exclude == data[ii][0]): pass else: Y[jj]= data[ii][1][1] X[jj]= data[ii][1][0] A[jj,1]= data[ii][1][0] C[jj,jj]= data[ii][2]**2./dsigma**2. yerr[jj]= data[ii][2]/dsigma jj= jj+1 #Now compute the best fit and the uncertainties bestfit= sc.dot(linalg.inv(C),Y.T) bestfit= sc.dot(A.T,bestfit) bestfitvar= sc.dot(linalg.inv(C),A) bestfitvar= sc.dot(A.T,bestfitvar) bestfitvar= linalg.inv(bestfitvar) bestfit= sc.dot(bestfitvar,bestfit) initialguess= sc.array([bestfit[0],bestfit[1],0.,sc.mean(Y),m.log(sc.var(Y))])#(m,b,Pb,Yb,Vb) #With this initial guess start off the sampling procedure initialX= objective(initialguess,X,Y,yerr) currentX= initialX bestX= initialX bestfit= initialguess currentguess= initialguess naccept= 0 samples= [] samples.append(currentguess) for jj in range(nburn+nsamples): #Draw a sample from the proposal distribution newsample= sc.zeros(5) newsample[0]= currentguess[0]+stats.norm.rvs()*parsigma[0] newsample[1]= currentguess[1]+stats.norm.rvs()*parsigma[1] #newsample[2]= stats.uniform.rvs() newsample[2]= currentguess[2]+stats.norm.rvs()*parsigma[2] newsample[3]= currentguess[3]+stats.norm.rvs()*parsigma[3] newsample[4]= currentguess[4]+stats.norm.rvs()*parsigma[4] #Calculate the objective function for the newsample newX= objective(newsample,X,Y,yerr) #Accept or reject #Reject with the appropriate probability u= stats.uniform.rvs() if u < m.exp(newX-currentX): #Accept currentX= newX currentguess= newsample naccept= naccept+1 if currentX > bestX: bestfit= currentguess bestX= currentX samples.append(currentguess) if double(naccept)/(nburn+nsamples) < .2 or double(naccept)/(nburn+nsamples) > .6: print "Acceptance ratio was "+str(double(naccept)/(nburn+nsamples)) samples= sc.array(samples).T[:,nburn:-1] print "Best-fit, overall" print bestfit, sc.mean(samples[2,:]), sc.median(samples[2,:]) histmb,edges= sc.histogramdd(samples.T[:,0:2],bins=round(sc.sqrt(nsamples)/5.)) indxi= sc.argmax(sc.amax(histmb,axis=1)) indxj= sc.argmax(sc.amax(histmb,axis=0)) print "Best-fit, marginalized" print edges[0][indxi-1], edges[1][indxj-1] print edges[0][indxi], edges[1][indxj] print edges[0][indxi+1], edges[1][indxj+1] #2D histogram plot.bovy_print() levels= special.erf(0.5*sc.arange(1,4)) #xrange=[edges[0][0],edges[0][-1]] #yrange=[edges[1][0],edges[1][-1]] xrange=[-120,120] yrange=[1.5,3.2] histmb,edges= sc.histogramdd(samples.T[:,0:2], range=[[-120,120],[1.5,3.2]], bins=(round(sc.sqrt(nsamples)/5.)/(edges[0][-1]-edges[0][0])*(xrange[1]-xrange[0]), round(sc.sqrt(nsamples)/5.)/(edges[1][-1]-edges[1][0])*(yrange[1]-yrange[0]))) aspect=(xrange[1]-xrange[0])/(yrange[1]-yrange[0]) plot.bovy_dens2d(histmb.T,origin='lower',cmap='gist_yarg', contours=True,cntrmass=True, xrange=xrange,yrange=yrange, levels=levels, aspect=aspect, xlabel=r'$b$',ylabel=r'$m$') if dsigma == 1.: plot.bovy_text(r'$\mathrm{using\ correct\ data\ uncertainties}$', top_right=True) else: plot.bovy_text(r'$\mathrm{using\ data\ uncertainties\ /\ 2}$', top_right=True) if dsigma == 1.: plot.bovy_end_print('exNew1a.png') else: plot.bovy_end_print('exNew2a.png') #Data with MAP line and sampling plot.bovy_print() bestb= edges[0][indxi] bestm= edges[1][indxj] xrange=[0,300] yrange=[0,700] plot.bovy_plot(xrange,bestm*sc.array(xrange)+bestb,'k-', xrange=xrange,yrange=yrange, xlabel=r'$x$',ylabel=r'$y$',zorder=2) errorbar(X,Y,yerr,color='k',marker='o',color='k',linestyle='None',zorder=1) for ii in range(10): #Random sample ransample= sc.floor((stats.uniform.rvs()*nsamples)) ransample= samples.T[ransample,0:2] bestb= ransample[0] bestm= ransample[1] plot.bovy_plot(xrange,bestm*sc.array(xrange)+bestb, overplot=True,xrange=xrange,yrange=yrange, xlabel=r'$x$',ylabel=r'$y$',color='0.75',zorder=1) if dsigma == 1.: plot.bovy_text(r'$\mathrm{using\ correct\ data\ uncertainties}$', top_right=True) else: plot.bovy_text(r'$\mathrm{using\ data\ uncertainties\ /\ 2}$', top_right=True) if dsigma == 1.: plot.bovy_end_print('exNew1b.png') else: plot.bovy_end_print('exNew2b.png') #Pb plot plot.bovy_print() plot.bovy_hist(samples.T[:,2],color='k',bins=round(sc.sqrt(nsamples)/5.), xlabel=r'$P_\mathrm{b}$',normed=True,histtype='step', range=[0,1]) if dsigma == 1.: plot.bovy_text(r'$\mathrm{using\ correct\ data\ uncertainties}$', top_right=True) else: plot.bovy_text(r'$\mathrm{using\ data\ uncertainties\ /\ 2}$', top_right=True) if dsigma == 1.: plot.bovy_end_print('exNew1c.png') else: plot.bovy_end_print('exNew2c.png') return
def exMix1( exclude=None, plotfilenameA="exMix1a.png", plotfilenameB="exMix1b.png", plotfilenameC="exMix1c.png", nburn=20000, nsamples=1000000, parsigma=[5, 0.075, 0.2, 1, 0.1], dsigma=1.0, bovyprintargs={}, sampledata=None, ): """exMix1: solve exercise 5 (mixture model) using MCMC sampling Input: exclude - ID numbers to exclude from the analysis (can be None) plotfilename* - filenames for the output plot nburn - number of burn-in samples nsamples - number of samples to take after burn-in parsigma - proposal distribution width (Gaussian) dsigma - divide uncertainties by this amount Output: plot History: 2010-04-28 - Written - Bovy (NYU) """ sc.random.seed(-1) # In the interest of reproducibility (if that's a word) # Read the data data = read_data("data_yerr.dat") ndata = len(data) if not exclude == None: nsample = ndata - len(exclude) else: nsample = ndata # First find the chi-squared solution, which we will use as an # initial guess # Put the data in the appropriate arrays and matrices Y = sc.zeros(nsample) X = sc.zeros(nsample) A = sc.ones((nsample, 2)) C = sc.zeros((nsample, nsample)) yerr = sc.zeros(nsample) jj = 0 for ii in range(ndata): if not exclude == None and sc.any(exclude == data[ii][0]): pass else: Y[jj] = data[ii][1][1] X[jj] = data[ii][1][0] A[jj, 1] = data[ii][1][0] C[jj, jj] = data[ii][2] ** 2.0 / dsigma ** 2.0 yerr[jj] = data[ii][2] / dsigma jj = jj + 1 brange = [-120, 120] mrange = [1.5, 3.2] # This matches the order of the parameters in the "samples" vector mbrange = [brange, mrange] if sampledata is None: sampledata = runSampler(X, Y, A, C, yerr, nburn, nsamples, parsigma, mbrange) (histmb, edges, mbsamples, pbhist, pbedges) = sampledata # Hack -- produce fake Pbad samples from Pbad histogram. pbsamples = hstack([array([x] * N) for x, N in zip((pbedges[:-1] + pbedges[1:]) / 2, pbhist)]) indxi = sc.argmax(sc.amax(histmb, axis=1)) indxj = sc.argmax(sc.amax(histmb, axis=0)) print "Best-fit, marginalized" print edges[0][indxi - 1], edges[1][indxj - 1] print edges[0][indxi], edges[1][indxj] print edges[0][indxi + 1], edges[1][indxj + 1] # 2D histogram plot.bovy_print(**bovyprintargs) levels = special.erf(0.5 * sc.arange(1, 4)) xe = [edges[0][0], edges[0][-1]] ye = [edges[1][0], edges[1][-1]] aspect = (xe[1] - xe[0]) / (ye[1] - ye[0]) plot.bovy_dens2d( histmb.T, origin="lower", cmap=cm.gist_yarg, interpolation="nearest", contours=True, cntrmass=True, extent=xe + ye, levels=levels, aspect=aspect, xlabel=r"$b$", ylabel=r"$m$", ) xlim(brange) ylim(mrange) plot.bovy_end_print(plotfilenameA) # Data with MAP line and sampling plot.bovy_print(**bovyprintargs) bestb = edges[0][indxi] bestm = edges[1][indxj] xrange = [0, 300] yrange = [0, 700] plot.bovy_plot( xrange, bestm * sc.array(xrange) + bestb, "k-", xrange=xrange, yrange=yrange, xlabel=r"$x$", ylabel=r"$y$", zorder=2, ) errorbar(X, Y, yerr, marker="o", color="k", linestyle="None", zorder=1) for m, b in mbsamples: plot.bovy_plot( xrange, m * sc.array(xrange) + b, overplot=True, xrange=xrange, yrange=yrange, xlabel=r"$x$", ylabel=r"$y$", color="0.75", zorder=1, ) plot.bovy_end_print(plotfilenameB) # Pb plot if not "text_fontsize" in bovyprintargs: bovyprintargs["text_fontsize"] = 11 plot.bovy_print(**bovyprintargs) plot.bovy_hist( pbsamples, bins=round(sc.sqrt(nsamples) / 5.0), xlabel=r"$P_\mathrm{b}$", normed=True, histtype="step", range=[0, 1], edgecolor="k", ) ylim(0, 4.0) if dsigma == 1.0: plot.bovy_text(r"$\mathrm{using\ correct\ data\ uncertainties}$", top_right=True) else: plot.bovy_text(r"$\mathrm{using\ data\ uncertainties\ /\ 2}$", top_left=True) plot.bovy_end_print(plotfilenameC) return sampledata
def bar_detectability_convolve(parser,nconvsamples=1000, dx=_XWIDTH/20.,dy=_YWIDTH/20., nx=100,ny=20, ngrid=201,rrange=[0.7,1.3], phirange=[-m.pi/2.,m.pi/2.], saveDir='../bar/1dLarge/', saveDirConv='../bar/1dLargeConv/'): """ NAME: bar_detectability_convolve PURPOSE: analyze the detectability of the Hercules moving group in the los-distribution around the Galaxy, convolving with distance uncertainties INPUT: parser - from optparse nconvsamples - number of samples to take to perform the convolution nx - number of plots in the x-direction ny - number of plots in the y direction dx - x-spacing dy - y-spacing ngrid - number of gridpoints to evaluate the density on rrange - range of Galactocentric radii to consider phirange - range of Galactic azimuths to consider saveDir - directory to save the pickles in OUTPUT: plot in plotfilename HISTORY: 2010-05-09 - Written - Bovy (NYU) """ (options,args)= parser.parse_args() if len(args) == 0: parser.print_help() return vloslinspace= (-.9,.9,ngrid) vloss= sc.linspace(*vloslinspace) picklebasename= '1d_%i_%i_%i_%.1f_%.1f_%.1f_%.1f' % (nx,ny,ngrid,rrange[0],rrange[1],phirange[0],phirange[1]) #First load all of the precalculated velocity distributions phis= sc.zeros(nx) rs= sc.zeros(ny) bisplphis= sc.zeros(nx*ny) bisplrs= sc.zeros(nx*ny) vlosds= sc.zeros((nx*ny,ngrid)) axivlosds= sc.zeros((nx*ny,ngrid)) for ii in range(nx): for jj in range(ny): thisR= (rrange[0]+(rrange[1]-rrange[0])/ (ny*_YWIDTH+(ny-1)*dy)*(jj*(_YWIDTH+dy)+_YWIDTH/2.)) thisphi= (phirange[0]+(phirange[1]-phirange[0])/ (nx*_XWIDTH+(nx-1)*dx)*(ii*(_XWIDTH+dx)+_XWIDTH/2.)) phis[ii]= thisphi rs[jj]= thisR bisplphis[ii*ny+jj]= thisphi bisplrs[ii*ny+jj]= thisR thissavefilename= os.path.join(saveDir,picklebasename+'_%i_%i.sav' %(ii,jj)) if os.path.exists(thissavefilename): print "Restoring los-velocity distribution at %.2f, %.2f ..." %(thisR,thisphi) savefile= open(thissavefilename,'r') vlosd= pickle.load(savefile) axivlosd= pickle.load(savefile) savefile.close() vlosds[ii*ny+jj,:]= vlosd axivlosds[ii*ny+jj,:]= axivlosd else: print "Did not find the los-velocity distribution at at %.2f, %.2f ..." %(thisR,thisphi) print "returning ..." return #Now convolve and calculate Kullback-Leibler divergence picklebasename= '1d_%i_%i_%i_%.1f_%.1f_%.1f_%.1f_%.1f' % (nx,ny,ngrid,rrange[0],rrange[1],phirange[0],phirange[1],options.convolve) detect= sc.zeros((nx,ny)) losd= sc.zeros((nx,ny)) for ii in range(nx): for jj in range(ny): if ii == 45 and jj == 13: continue#BOVY: FIX FOR NOW thisR= rs[jj] thisphi= phis[ii] thissavefilename= os.path.join(saveDirConv,picklebasename+'_%i_%i.sav' %(ii,jj)) if os.path.exists(thissavefilename): print "Restoring convolved los-velocity distribution at %.2f, %.2f ..." %(thisR,thisphi) savefile= open(thissavefilename,'r') convvlosd= pickle.load(savefile) convaxivlosd= pickle.load(savefile) savefile.close() else: print "Calculating convolved los-velocity distribution at %.2f, %.2f ..." %(thisR,thisphi) #los distance losd[ii,jj]= m.sqrt(thisR**2.+1.-2.*thisR*m.cos(thisphi)) thislosd= losd[ii,jj] #Galactic longitude if 1./m.cos(thisphi) < thisR and m.cos(thisphi) > 0.: thisl= m.pi-m.asin(thisR/thislosd*m.sin(thisphi)) else: thisl= m.asin(thisR/thislosd*m.sin(thisphi)) convvlosd= sc.zeros(ngrid) convaxivlosd= sc.zeros(ngrid) broke= False for kk in range(ngrid): weights= invdist2(bisplrs[ii*ny+jj],bisplphis[ii*ny+jj], bisplrs,bisplphis) weights[sc.isinf(weights)]= sc.amax(weights[sc.isfinite(weights)]) splindx= (weights > 1./(thislosd*options.convolve*5.)**2.) try: tck= interpolate.bisplrep(bisplphis[splindx], bisplrs[splindx], vlosds[splindx,kk], w=weights[splindx]) except TypeError: #Trye interp2d? broke= True break except ValueError: splindx= (weights > 1./(2.*thislosd*options.convolve*5.)**2.) try: tck= interpolate.bisplrep(bisplphis[splindx], bisplrs[splindx], vlosds[splindx,kk], w=weights[splindx]) except TypeError: broke= True break except ValueError: broke= True break #Now convolve thisnsamples= 0 for ll in range(nconvsamples): samplelosd= thislosd+stats.norm.rvs()*thislosd*options.convolve sampleR, samplephi= dlToRphi(samplelosd,thisl) addvlos= interpolate.bisplev(samplephi,sampleR,tck) convvlosd[kk]+= addvlos if not addvlos == 0.: thisnsamples+= 1 convvlosd[kk]/= thisnsamples try: tck= interpolate.bisplrep(bisplphis[splindx], bisplrs[splindx], axivlosds[splindx,kk], w=weights[splindx]) except TypeError: broke= True break except ValueError: splindx= (weights > 1./(2.*thislosd*options.convolve*5.)**2.) try: tck= interpolate.bisplrep(bisplphis[splindx], bisplrs[splindx], axivlosds[splindx,kk], w=weights[splindx]) except TypeError: broke= True break except ValueError: broke= True break #Now convolve thisnsamples= 0 for ll in range(nconvsamples): samplelosd= thislosd+stats.norm.rvs()*thislosd*options.convolve sampleR, samplephi= dlToRphi(samplelosd,thisl) addvlos= interpolate.bisplev(samplephi,sampleR,tck) convaxivlosd[kk]+= addvlos if not addvlos == 0.: thisnsamples+= 1 convaxivlosd[kk]/= thisnsamples savefile= open(thissavefilename,'w') pickle.dump(convvlosd,savefile) pickle.dump(convaxivlosd,savefile) savefile.close() if broke: continue#BOVY: FIX FOR NOW ddx= 1./sc.sum(axivlosd) #skipCenter if not options.skipCenter == 0.: skipIndx= (sc.fabs(vloss) < options.skipCenter) indx= (sc.fabs(vloss) >= options.skipCenter) convvlosd= convvlosd/sc.sum(convvlosd[indx])/ddx convaxivlosd= convaxivlosd/sc.sum(convaxivlosd[indx])/ddx convvlosd[skipIndx]= 1. convaxivlosd[skipIndx]= 1. convvlosd_zeroindx= (convvlosd == 0.) convaxivlosd_zeroindx= (convaxivlosd == 0.) convvlosd[convvlosd_zeroindx]= 1. convaxivlosd[convvlosd_zeroindx]= 1. convvlosd[convaxivlosd_zeroindx]= 1. convaxivlosd[convaxivlosd_zeroindx]= 1. detect[ii,jj]= probDistance.kullbackLeibler(convvlosd,convaxivlosd, ddx,nan=True) detect[(detect < 0)]= 0. detect[(detect > 0.07)]= 0. #Now plot plot.bovy_print() plot.bovy_dens2d(detect.T,origin='lower',#interpolation='nearest', xlabel=r'$\mathrm{Galactocentric\ azimuth}\ [\mathrm{deg}]$', ylabel=r'$\mathrm{Galactocentric\ radius}\ /R_0$', cmap='gist_yarg',xrange=sc.array(phirange)*_RADTODEG, yrange=rrange, aspect=(phirange[1]-phirange[0])*_RADTODEG/(rrange[1]-rrange[0])) #contour the los distance levels= [2/8.2*(ii+1/2.) for ii in range(10)] contour(losd.T,levels,colors='0.25',origin='lower',linestyles='--', aspect=(phirange[1]-phirange[0])*_RADTODEG/(rrange[1]-rrange[0]), extent=(phirange[0]*_RADTODEG,phirange[1]*_RADTODEG, rrange[0],rrange[1])) plot.bovy_end_print(args[0])
def bar_detectability(parser, dx=_XWIDTH/20.,dy=_YWIDTH/20., nx=100,ny=20, ngrid=201,rrange=[0.7,1.3], phirange=[-m.pi/2.,m.pi/2.], saveDir='../bar/1dLarge/'): """ NAME: bar_detectability PURPOSE: analyze the detectability of the Hercules moving group in the los-distribution around the Galaxy INPUT: nx - number of plots in the x-direction ny - number of plots in the y direction dx - x-spacing dy - y-spacing ngrid - number of gridpoints to evaluate the density on rrange - range of Galactocentric radii to consider phirange - range of Galactic azimuths to consider saveDir - directory to save the pickles in OUTPUT: plot in plotfilename HISTORY: 2010-05-09 - Written - Bovy (NYU) """ (options,args)= parser.parse_args() if len(args) == 0: parser.print_help() return if not options.convolve == None: bar_detectability_convolve(parser,dx=dx,dy=dy,nx=nx,ny=ny,ngrid=ngrid, rrange=rrange,phirange=phirange, saveDir=saveDir) return vloslinspace= (-.9,.9,ngrid) vloss= sc.linspace(*vloslinspace) picklebasename= '1d_%i_%i_%i_%.1f_%.1f_%.1f_%.1f' % (nx,ny,ngrid,rrange[0],rrange[1],phirange[0],phirange[1]) detect= sc.zeros((nx,ny)) losd= sc.zeros((nx,ny)) gall= sc.zeros((nx,ny)) for ii in range(nx): for jj in range(ny): thisR= (rrange[0]+(rrange[1]-rrange[0])/ (ny*_YWIDTH+(ny-1)*dy)*(jj*(_YWIDTH+dy)+_YWIDTH/2.)) thisphi= (phirange[0]+(phirange[1]-phirange[0])/ (nx*_XWIDTH+(nx-1)*dx)*(ii*(_XWIDTH+dx)+_XWIDTH/2.)) thissavefilename= os.path.join(saveDir,picklebasename+'_%i_%i.sav' %(ii,jj)) if os.path.exists(thissavefilename): print "Restoring los-velocity distribution at %.2f, %.2f ..." %(thisR,thisphi) savefile= open(thissavefilename,'r') vlosd= pickle.load(savefile) axivlosd= pickle.load(savefile) savefile.close() else: print "Did not find the los-velocity distribution at at %.2f, %.2f ..." %(thisR,thisphi) print "returning ..." return ddx= 1./sc.sum(axivlosd) #skipCenter if not options.skipCenter == 0.: skipIndx= (sc.fabs(vloss) < options.skipCenter) indx= (sc.fabs(vloss) >= options.skipCenter) vlosd= vlosd/sc.sum(vlosd[indx])/ddx axivlosd= axivlosd/sc.sum(axivlosd[indx])/ddx vlosd[skipIndx]= 1. axivlosd[skipIndx]= 1. vlosd_zeroindx= (vlosd == 0.) axivlosd_zeroindx= (axivlosd == 0.) vlosd[vlosd_zeroindx]= 1. axivlosd[vlosd_zeroindx]= 1. vlosd[axivlosd_zeroindx]= 1. axivlosd[axivlosd_zeroindx]= 1. detect[ii,jj]= probDistance.kullbackLeibler(vlosd,axivlosd,ddx,nan=True) #los distance and Galactic longitude d= m.sqrt(thisR**2.+1.-2.*thisR*m.cos(thisphi)) losd[ii,jj]= d if 1./m.cos(thisphi) < thisR and m.cos(thisphi) > 0.: l= m.pi-m.asin(thisR/d*m.sin(thisphi)) else: l= m.asin(thisR/d*m.sin(thisphi)) gall[ii,jj]= l #Find maximum, further than 3 kpc away detectformax= detect.flatten() detectformax[losd.flatten() < 3./8.2]= 0. x= sc.argmax(detectformax) indx = sc.unravel_index(x,detect.shape) maxR= (rrange[0]+(rrange[1]-rrange[0])/ (ny*_YWIDTH+(ny-1)*dy)*(indx[1]*(_YWIDTH+dy)+_YWIDTH/2.)) maxphi= (phirange[0]+(phirange[1]-phirange[0])/ (nx*_XWIDTH+(nx-1)*dx)*(indx[0]*(_XWIDTH+dx)+_XWIDTH/2.)) print maxR, maxphi, losd[indx[0],indx[1]], detect[indx[0],indx[1]], gall[indx[0],indx[1]]*180./sc.pi #Now plot plot.bovy_print() plot.bovy_dens2d(detect.T,origin='lower',#interpolation='nearest', xlabel=r'$\mathrm{Galactocentric\ azimuth}\ [\mathrm{deg}]$', ylabel=r'$\mathrm{Galactocentric\ radius}\ /R_0$', cmap='gist_yarg',xrange=sc.array(phirange)*_RADTODEG, yrange=rrange, aspect=(phirange[1]-phirange[0])*_RADTODEG/(rrange[1]-rrange[0])) #contour the los distance and gall #plot.bovy_text(-22.,1.1,r'$\mathrm{apogee}$',color='w', # rotation=105.) plot.bovy_text(-18.,1.1,r'$\mathrm{APOGEE}$',color='w', rotation=285.) levels= [2/8.2*(ii+1/2.) for ii in range(10)] contour(losd.T,levels,colors='0.25',origin='lower',linestyles='--', aspect=(phirange[1]-phirange[0])*_RADTODEG/(rrange[1]-rrange[0]), extent=(phirange[0]*_RADTODEG,phirange[1]*_RADTODEG, rrange[0],rrange[1])) gall[gall < 0.]+= sc.pi*2. levels= [0.,sc.pi/2.,sc.pi,3.*sc.pi/2.] contour(gall.T,levels,colors='w',origin='lower',linestyles='--', aspect=(phirange[1]-phirange[0])*_RADTODEG/(rrange[1]-rrange[0]), extent=(phirange[0]*_RADTODEG,phirange[1]*_RADTODEG, rrange[0],rrange[1])) levels= [-5/180.*sc.pi,250/180.*sc.pi] contour(gall.T,levels,colors='w',origin='lower',linestyles='-.', aspect=(phirange[1]-phirange[0])*_RADTODEG/(rrange[1]-rrange[0]), extent=(phirange[0]*_RADTODEG,phirange[1]*_RADTODEG, rrange[0],rrange[1])) if options.skipCenter == 0.: plot.bovy_text(r'$\mathrm{KL\ divergence\ / \ all}\ v_{\mathrm{los}}$', title=True) else: plot.bovy_text(r'$\mathrm{KL\ divergence\ / }\ |v_{\mathrm{los}}| \geq %.2f \ v_0$' % options.skipCenter, title=True) plot.bovy_end_print(args[0])
def exMix1(exclude=None, plotfilenameA='exMix1a.png', plotfilenameB='exMix1b.png', plotfilenameC='exMix1c.png', nburn=20000, nsamples=1000000, parsigma=[5, .075, .2, 1, .1], dsigma=1., bovyprintargs={}, sampledata=None): """exMix1: solve exercise 5 (mixture model) using MCMC sampling Input: exclude - ID numbers to exclude from the analysis (can be None) plotfilename* - filenames for the output plot nburn - number of burn-in samples nsamples - number of samples to take after burn-in parsigma - proposal distribution width (Gaussian) dsigma - divide uncertainties by this amount Output: plot History: 2010-04-28 - Written - Bovy (NYU) """ sc.random.seed(-1) #In the interest of reproducibility (if that's a word) #Read the data data = read_data('data_yerr.dat') ndata = len(data) if not exclude == None: nsample = ndata - len(exclude) else: nsample = ndata #First find the chi-squared solution, which we will use as an #initial guess #Put the data in the appropriate arrays and matrices Y = sc.zeros(nsample) X = sc.zeros(nsample) A = sc.ones((nsample, 2)) C = sc.zeros((nsample, nsample)) yerr = sc.zeros(nsample) jj = 0 for ii in range(ndata): if not exclude == None and sc.any(exclude == data[ii][0]): pass else: Y[jj] = data[ii][1][1] X[jj] = data[ii][1][0] A[jj, 1] = data[ii][1][0] C[jj, jj] = data[ii][2]**2. / dsigma**2. yerr[jj] = data[ii][2] / dsigma jj = jj + 1 brange = [-120, 120] mrange = [1.5, 3.2] # This matches the order of the parameters in the "samples" vector mbrange = [brange, mrange] if sampledata is None: sampledata = runSampler(X, Y, A, C, yerr, nburn, nsamples, parsigma, mbrange) (histmb, edges, mbsamples, pbhist, pbedges) = sampledata # Hack -- produce fake Pbad samples from Pbad histogram. pbsamples = hstack([ array([x] * N) for x, N in zip((pbedges[:-1] + pbedges[1:]) / 2, pbhist) ]) indxi = sc.argmax(sc.amax(histmb, axis=1)) indxj = sc.argmax(sc.amax(histmb, axis=0)) print "Best-fit, marginalized" print edges[0][indxi - 1], edges[1][indxj - 1] print edges[0][indxi], edges[1][indxj] print edges[0][indxi + 1], edges[1][indxj + 1] #2D histogram plot.bovy_print(**bovyprintargs) levels = special.erf(0.5 * sc.arange(1, 4)) xe = [edges[0][0], edges[0][-1]] ye = [edges[1][0], edges[1][-1]] aspect = (xe[1] - xe[0]) / (ye[1] - ye[0]) plot.bovy_dens2d(histmb.T, origin='lower', cmap=cm.gist_yarg, interpolation='nearest', contours=True, cntrmass=True, extent=xe + ye, levels=levels, aspect=aspect, xlabel=r'$b$', ylabel=r'$m$') xlim(brange) ylim(mrange) plot.bovy_end_print(plotfilenameA) #Data with MAP line and sampling plot.bovy_print(**bovyprintargs) bestb = edges[0][indxi] bestm = edges[1][indxj] xrange = [0, 300] yrange = [0, 700] plot.bovy_plot(xrange, bestm * sc.array(xrange) + bestb, 'k-', xrange=xrange, yrange=yrange, xlabel=r'$x$', ylabel=r'$y$', zorder=2) errorbar(X, Y, yerr, marker='o', color='k', linestyle='None', zorder=1) for m, b in mbsamples: plot.bovy_plot(xrange, m * sc.array(xrange) + b, overplot=True, xrange=xrange, yrange=yrange, xlabel=r'$x$', ylabel=r'$y$', color='0.75', zorder=1) plot.bovy_end_print(plotfilenameB) #Pb plot if not 'text_fontsize' in bovyprintargs: bovyprintargs['text_fontsize'] = 11 plot.bovy_print(**bovyprintargs) plot.bovy_hist(pbsamples, bins=round(sc.sqrt(nsamples) / 5.), xlabel=r'$P_\mathrm{b}$', normed=True, histtype='step', range=[0, 1], edgecolor='k') ylim(0, 4.) if dsigma == 1.: plot.bovy_text(r'$\mathrm{using\ correct\ data\ uncertainties}$', top_right=True) else: plot.bovy_text(r'$\mathrm{using\ data\ uncertainties\ /\ 2}$', top_left=True) plot.bovy_end_print(plotfilenameC) return sampledata