hp.gnomview(output_map, rot=[0,90], reso=0.3, xsize=600,title='Output Map')
# get theta
iprings=np.arange(12*nside**2)
vecs=hp.pix2vec(int(nside),iprings[~mask])
vec0=hp.pix2vec(int(nside),0)
angles=np.arccos(np.dot(np.transpose(vec0),vecs))
themap=output_map[~mask]
clf()
plot(angles*180/np.pi,themap,'b.')
xlim(0,10)
yscale('log')
from Homogeneity import fitting
def radgauss(x,pars):
return(pars[0]/(2*np.pi*pars[1]**2)*np.exp(-0.5*(x/pars[1])**2))
angmax=1.6
ok=angles*180/np.pi < angmax
clf()
plot(angles*180/np.pi,themap,'b,')
#plot(angles[ok]*180/np.pi,themap[ok],'r,')
yscale('log')
xlabel('Angle w.r.t. point source position (deg.)')
ylabel('Map value')
bla=fitting.dothefit(angles[ok]*180/np.pi,themap[ok],themap[ok]*0+0.01,np.array([0.004,0.275]),functname=radgauss,method='mpfit')
title('Fit value : 37.1 arcmin FWHM')
xx=linspace(0,angmax,1000)
plot(xx,radgauss(xx,bla[1]),'r',lw=1)
# study covariance matrix
# 1/ it is extremely diagonal => the map making does not correlate pixels significantly... weird
from Homogeneity import fitting
def ffunc(x,pars):
return(pars[0]*x**pars[1])
npix=diag(covmc).size
clf()
plot(signoise**2/coverage[~mask],diag(covmc),'r.')
bla=fitting.dothefit(signoise**2/coverage[~mask],diag(covmc),ones(npix),[7500.,1.],functname=ffunc,method='minuit')
xlabel('naive diag covariance matrix')
ylabel('MC diag covariance matrix')
xx=linspace(0,0.001,10000)
plot(xx,xx,'k--')
plot(xx,ffunc(xx,bla[1]),lw=3)
clf()
plot(bla[1][0]*(signoise**2/coverage[~mask])**bla[1][1],diag(covmc),'r.')
xlabel('Model Diag Covariance Matrix from Coverage')
ylabel('MC Diag Covariance Matrix')
xx=linspace(0,0.06,10000)
plot(xx,xx,'g--',lw=3)
drh_m = err_on_funct / deriv_spl(rh)
clf()
xv = linspace(min(thex), max(thex), 1000)
xlabel('$r [h^{-1}.\mathrm{Mpc}]$')
ylabel('$d_2(r)$')
plot(arange(200), zeros(200) + 2.97, '--')
errorbar(thex, they, yerr=theyerr, fmt='ko')
plot(xv, spl(xv), label='Spline Fit (with covariance)', color='b')
errorbar(rh_m,
2.97,
xerr=drh_m,
label='$R_H$ = ' + str('%.1f' % rh_m) + ' $\pm$ ' +
str('%.1f' % drh_m) + ' $h^{-1}.\mathrm{Mpc}$',
fmt='ro')
legend(loc='lower right')
##### test
from Homogeneity import fitting
import numpy as np
import numpy.random as npr
npr.seed(0)
x = linspace(0, 10, 20)
y = 3 * x**2 + 15 + randn(20)
err = np.array([1] * 20)
errorbar(x, y, err, fmt='.')
toto = fitting.dothefit(x, y, err, [0, 0, 0], functname=fitting.thepolynomial)
plot(x, fitting.thepolynomial(x, toto[1]))
rh_m=rh
drh_m=err_on_funct/deriv_spl(rh)
clf()
xv=linspace(min(thex),max(thex),1000)
xlabel('$r [h^{-1}.\mathrm{Mpc}]$')
ylabel('$d_2(r)$')
plot(arange(200),zeros(200)+2.97,'--')
errorbar(thex,they,yerr=theyerr,fmt='ko')
plot(xv,spl(xv),label='Spline Fit (with covariance)',color='b')
errorbar(rh_m,2.97,xerr=drh_m,label='$R_H$ = '+str('%.1f'%rh_m)+' $\pm$ '+str('%.1f'%drh_m)+' $h^{-1}.\mathrm{Mpc}$',fmt='ro')
legend(loc='lower right')
##### test
from Homogeneity import fitting
import numpy as np
import numpy.random as npr
npr.seed(0)
x = linspace(0,10,20)
y = 3*x**2+15+ randn(20)
err = np.array([1]*20)
errorbar(x,y,err,fmt='.');
toto=fitting.dothefit(x,y,err,[0,0,0],functname=fitting.thepolynomial)
plot(x,fitting.thepolynomial(x,toto[1]))
cho = np.linalg.cholesky(cov)
corr_data = np.dot(cho.T,data)
##### see if cholesky is correct:
print 'Accuracy of Cholesky Decomposition'
print np.dot(cho,cho.T.conj()) == cov
def model(x,pars):
f=np.poly1d(pars)
return(f(x))
guess1 = [np.mean(data),np.mean(data)]
guess2 = [np.mean(corr_data),np.mean(corr_data)]
res = fitting.dothefit(x,data,cov,guess1,functname=model,method='minuit')
corr_res = fitting.dothefit(x,corr_data,cov,guess2,functname=model,method='minuit')
plt.figure()
plt.errorbar(x,data,yerr=np.diag(cov),color='b',fmt='o-',label='data' )
plt.errorbar(x,corr_data,yerr=np.diag(cov),color='g',fmt='o-',label='corr data')
plt.plot(x,model(x,res[1]),'r-')
plt.plot(x,model(x,corr_res[1]),'r--')
plt.legend(loc=2,numpoints=1)
plt.show()
dphi=np.random.randn(npoints)*sigptg[j]/3600/np.sin(true_pointings[:,0]*np.pi/180)
new_pointings[:,0]=true_pointings[:,0]+dtheta
new_pointings[:,1]=true_pointings[:,1]+dphi
new_pointings[:,2]=true_pointings[:,2]+0
# maps
maptrueptg,masktrue,cctrue=TOD2map(tod,true_pointings,nside,disp=False,covmin=100)
map,mask,cc=TOD2map(tod,new_pointings,nside,disp=False,covmin=100)
mm=mask+masktrue
mask[mm]=np.nan
masktrue[mm]=np.nan
allressig[i]=np.std(map[~mm]-maptrueptg[~mm])
cltrueptg=hp.anafast(nan_to_num(maptrueptg))
cl=hp.anafast(nan_to_num(map))
allratios[i,j,:]=cl/cltrueptg
l=np.arange(3*nside)
fit=fitting.dothefit(l,cl/cltrueptg,np.ones(3*nside),[np.radians(sigptg[j]/3600),0.,0.],functname=fct,method='mpfit')
clf()
plot(l,cl/cltrueptg)
plot(l,fct(l,fit[1]))
draw()
sigrec[n,i,j]=fit[1][0]
sigma[n,j]=np.mean(allressig)
dsigma[n,j]=np.std(allressig)
dictio[nside]=allratios
clf()
xlim(np.min(sigptg)/2,np.max(sigptg)*2)
xscale('log')
res = hist(xvalues, bins=100, range = [-10,15]) xcenter = (res[1][:-1]+res[1][1:])/2 yvals = res[0] errors = np.sqrt(yvals) def mygaussian(x,pars): return(pars[0]*np.exp(-(x-pars[1])**2/(2*pars[2]**2))) avguess = np.sum(xcenter*yvals)/np.sum(yvals) av2guess = np.sum(xcenter**2*yvals)/np.sum(yvals) varguess = av2guess-avguess**2 guess = [np.max(yvals), avguess, np.sqrt(varguess)] ok = errors != 0 result_minuit = fitting.dothefit(xcenter[ok],yvals[ok],errors[ok],guess,functname=mygaussian,method='minuit') result_mpfit = fitting.dothefit(xcenter[ok],yvals[ok],errors[ok],guess,functname=mygaussian,method='mpfit') result_mcmc = fitting.dothefit(xcenter[ok],yvals[ok],errors[ok],guess,functname=mygaussian,method='mcmc') clf() errorbar(xcenter,yvals,yerr=errors,fmt='ro') xxx = np.linspace(-10,15,1000) plot(xxx, mygaussian(xxx, result_minuit[1])) plot(xxx, mygaussian(xxx, result_mpfit[1])) plot(xxx, mygaussian(xxx, result_mcmc[1]))
def toto(x, pars):
return (newtt * pars[0] + pars[2]) * np.exp((x / pars[1]))
guess = np.array([1.0 / 10000000, 100, 5.5e-4])
clf()
ii = 0
errorbar(ellbins, clbb[ii], yerr=errclbb[ii])
thesig = sigmas[ii]
plot(ellbins, toto(ellbins, guess))
bla = fitting.dothefit(ellbins, clbb[ii], errclbb[ii], guess, functname=toto)
clf()
errorbar(ellbins, clbb[ii], yerr=errclbb[ii])
plot(ellbins, toto(ellbins, bla[1]))
clf()
ellscale = np.zeros(len(sigmas))
normalisation = np.zeros(len(sigmas))
err_ellscale = np.zeros(len(sigmas))
err_normalisation = np.zeros(len(sigmas))
for i in xrange(len(sigmas)):
subplot(3, 3, i + 1)
thesig = sigmas[i]
bla = fitting.dothefit(ellbins, clbb[i], errclbb[i], guess, functname=toto)
plot(lll,clBBl,'g',alpha=0.5) plot(ll,clBB*2,'b',alpha=0.5) plot(ll,clBBl+clBB*2,'r') #### adding noise residuals and try fitting def functsum(x,pars): bla = pars[0] * np.interp(x, ll, clBB) + pars[1] * np.interp(x, ll, clBBl) + pars[2]**2 * x * (x + 1) / 2 / np.pi return bla def functsum2(x,pars): bla = pars[0] * np.interp(x, ll, clBB) + pars[1] * np.interp(x, ll, clBBl) return bla guess = [2., 1., np.sqrt(1e6)] fit = fitting.dothefit(lcenter, BB, dBB, guess, functname = functsum, method = 'minuit') res = fit[1] guess2 = [2., 1.] fit2 = fitting.dothefit(lcenter, BB, dBB, guess2, functname = functsum2, method = 'minuit') res2 = fit2[1] #### adding noise clnoise = res[2]**2 pownoise = clnoise*ll*(ll+1)/2/np.pi clf() xlim(0,500) ylim(-0.01,0.055) errorbar(lcenter,BB,fmt='ro',xlolims=lmin,xuplims=lmax,yerr=dBB) plot(lll,clBBl * res[1],'g',alpha=0.5)
errors = np.sqrt(yvals)
def mygaussian(x, pars):
return (pars[0] * np.exp(-(x - pars[1])**2 / (2 * pars[2]**2)))
avguess = np.sum(xcenter * yvals) / np.sum(yvals)
av2guess = np.sum(xcenter**2 * yvals) / np.sum(yvals)
varguess = av2guess - avguess**2
guess = [np.max(yvals), avguess, np.sqrt(varguess)]
ok = errors != 0
result_minuit = fitting.dothefit(xcenter[ok],
yvals[ok],
errors[ok],
guess,
functname=mygaussian,
method='minuit')
result_mpfit = fitting.dothefit(xcenter[ok],
yvals[ok],
errors[ok],
guess,
functname=mygaussian,
method='mpfit')
result_mcmc = fitting.dothefit(xcenter[ok],
yvals[ok],
errors[ok],
guess,
functname=mygaussian,
method='mcmc')
#### simulated data
nbpts = 25
signoise = 3.
err = np.linspace(0.7, 1.3, nbpts)*signoise
#signoise = 1.
#err = np.zeros(nbpts)+signoise
x = np.linspace(0,10,nbpts)
y = thefct(x, partrue) + randn(nbpts)*signoise
clf()
errorbar(x,y,err,fmt='.');
xlim(-0.2,10.2)
############### Fitting
initpar = np.array([10.,1.])
#### Minuit
toto_minuit=fitting.dothefit(x,y,err,initpar,functname=thefct)
#### MPFit (Fast Levenberg-Markardt minimizer)
toto_mpfit=fitting.dothefit(x,y,err,initpar,functname=thefct, method='mpfit')
#### MCMC [slow !!]
toto_mcmc=fitting.dothefit(x,y,err,initpar,functname=thefct, method='mcmc')
clf()
xx = np.linspace(0,10,1000)
plot(xx,thefct(xx,toto_mcmc[1]), label='MCMC')
chains = toto_mcmc[0]
for i in xrange(len(chains)/100):
plot(xx,thefct(xx,chains[i,:]), color='b', alpha=0.01,lw=2)
errorbar(x,y,err,fmt='.');
plot(xx,thefct(xx,toto_minuit[1]), label='Minuit', lw=2)
plot(xx,thefct(xx,toto_mpfit[1]), label='MPFit', lw=2)
legend()
def thegaussian(x,pars): return(pars[0]*np.exp(-(x-pars[1])**2/(2*pars[2]**2))) clf() uu=0 allx0 = np.zeros(nsub) for i in np.arange(nsub)+1: uu += 1 subplot(3,3,uu) mm = np.abs(freq-i*xm) < 0.3 plot(freq[mm]/i, smoothedps[mm]) ampguess = np.max(smoothedps[mm]) x0guess = np.sum(freq[mm]/i*smoothedps[mm])/np.sum(smoothedps[mm]) x02guess = np.sum((freq[mm]/i)**2*smoothedps[mm])/np.sum(smoothedps[mm]) sigguess = np.sqrt(x02guess-x0guess**2) res = fitting.dothefit(freq[mm]/i, smoothedps[mm],freq[mm]*0+1,[ampguess,x0guess,sigguess], functname=thegaussian) plot([res[1][1],res[1][1]],[0, np.max(smoothedps[mm])],'r:') plot(freq[mm]/i, thegaussian(freq[mm]/i, res[1])) allx0[i-1]=res[1][1] xm = np.mean(allx0) noire = 1/xm ixm = np.int(xm/framerate*len(signal)) inoire = np.int(noire * framerate) ########## trace tempo stability size = inoire*16
cosmo=cosmolopy.fidcosmo.copy()
if min(pars) <= 0:
return(np.zeros(x.size)-1)
cosmo['h']=pars[0]
cosmo['omega_M_0']=pars[1]
cosmo['omega_lambda_0']=pars[2]
dlum=cosmolopy.distance.luminosity_distance(x,**cosmo)*1e6
if min(dlum) > 0:
return(5*np.log10(dlum)-5)
else:
return(np.zeros(x.size)-1)
from Homogeneity import fitting
### ne marche pas
a=fitting.dothefit(zsn,musn,dmusn,np.array([0.7,0.3,0.7]),themusn1a,method='mpfit')
### OK
a=fitting.dothefit(zsn,musn,dmusn,np.array([0.7,0.3,0.7]),themusn1a,method='minuit')
### ne marche pas...
a=fitting.dothefit(zsn,musn,dmusn,np.array([0.7,0.3,0.7]),themusn1a,method='mcmc')
chain=a[0]
clf()
ylim(0,2)
xlim(0,1)
plot(chain[:,1],chain[:,2],',')
#### essai avec pymc