def NFW_fit(e, theta, Lambda, z, h=0.7):
a = np.linspace(-10, 10, 100)
x, y = np.meshgrid(a, a)
q = (1. - e) / (1. + e)
r = np.sqrt(q * (x**2) + (y**2) / q)
# SIMET RELATION FOR M200
M0 = (2.21e14) / h
alpha = 1.33
M200 = M0 * ((Lambda / 40.)**alpha)
# Compute cosmological parameters
cosmo = LambdaCDM(H0=h * 100, Om0=0.3, Ode0=0.7)
H = cosmo.H(z).value / (1.0e3 * pc) #H at z_pair s-1
roc = (3.0 *
(H**2.0)) / (8.0 * np.pi * G) #critical density at z_pair (kg.m-3)
roc_mpc = roc * ((pc * 1.0e6)**3.0)
# Compute R_200
R200 = r200_nfw(M200, roc_mpc)
# S_nfw R_200
S_nfw = SIGMA_nfw((r, sigma_c, z, h), R200)
x_rot = (x * np.cos(t) + y * np.sin(t))
y_rot = (-1. * x * np.sin(t) + y * np.cos(t))
w = np.ones(len(x_rot[mask]))
e, ang = momentos(x_rot[mask], y_rot[mask], w)
return e, np.rad2deg(ang)
class AstroPyCosmology(CLMMCosmology):
def __init__(self, **kwargs):
super(AstroPyCosmology, self).__init__(**kwargs)
# this tag will be used to check if the cosmology object is accepted by the modeling
self.backend = 'ct'
assert isinstance(self.be_cosmo, LambdaCDM)
def _init_from_cosmo(self, be_cosmo):
assert isinstance(be_cosmo, LambdaCDM)
self.be_cosmo = be_cosmo
def _init_from_params(self, H0, Omega_b0, Omega_dm0, Omega_k0):
Om0 = Omega_b0 + Omega_dm0
Ob0 = Omega_b0
self.be_cosmo = FlatLambdaCDM(H0=H0,
Om0=Om0,
Ob0=Ob0,
Tcmb0=2.7255,
Neff=3.046,
m_nu=([0.06, 0.0, 0.0] * units.eV))
if Omega_k0 != 0.0:
Ode0 = self.be_cosmo.Ode0 - Omega_k0
self.be_cosmo = LambdaCDM(H0=H0,
Om0=Om0,
Ob0=Ob0,
Ode0=Ode0,
Tcmb0=2.7255,
Neff=3.046,
m_nu=([0.06, 0.0, 0.0] * units.eV))
def _set_param(self, key, value):
raise NotImplementedError("Astropy do not support changing parameters")
def _get_param(self, key):
if key == "Omega_m0":
return self.be_cosmo.Om0
elif key == "Omega_b0":
return self.be_cosmo.Ob0
elif key == "Omega_dm0":
return self.be_cosmo.Odm0
elif key == "Omega_k0":
return self.be_cosmo.Ok0
elif key == 'h':
return self.be_cosmo.H0.to_value() / 100.0
elif key == 'H0':
return self.be_cosmo.H0.to_value()
else:
raise ValueError(f"Unsupported parameter {key}")
def get_Omega_m(self, z):
return self.be_cosmo.Om(z)
def get_E2Omega_m(self, z):
return self.be_cosmo.Om(z) * (self.be_cosmo.H(z) / self.be_cosmo.H0)**2
def eval_da_z1z2(self, z1, z2):
return self.be_cosmo.angular_diameter_distance_z1z2(z1, z2).to_value(
units.Mpc)
def eval_sigma_crit(self, z_len, z_src):
if np.any(np.array(z_src) <= z_len):
warnings.warn(
f'Some source redshifts are lower than the cluster redshift. Returning Sigma_crit = np.inf for those galaxies.'
)
# Constants
clight_pc_s = const.CLIGHT_KMS.value * 1000. / const.PC_TO_METER.value
gnewt_pc3_msun_s2 = const.GNEWT.value * const.SOLAR_MASS.value / const.PC_TO_METER.value**3
d_l = self.eval_da_z1z2(0, z_len)
d_s = self.eval_da_z1z2(0, z_src)
d_ls = self.eval_da_z1z2(z_len, z_src)
beta_s = np.maximum(0., d_ls / d_s)
return clight_pc_s**2 / (4.0 * np.pi *
gnewt_pc3_msun_s2) * 1 / d_l * np.divide(
1., beta_s) * 1.0e6
def main(sample='pru',N_min=0,N_max=1000.,
z_min = 0.0, z_max = 0.5,
conmin = 0.5, conmax = 5.0,
lMHmin = 11., lMHmax = 15.5,
odds_min=0.5, RIN = 100., ROUT =5000.,
ndots= 15,ncores=10,h=1.):
'''
INPUT
---------------------------------------------------------
sample (str) sample name
N_min (int) lower limit of galaxy members - >=
N_max (int) higher limit of galaxy members - <
z_min (float) lower limit for z - >=
z_max (float) higher limit for z - <
conmin (float) lower limit for C_BG - >=
conmax (float) higher limit for C_BG - <
lMHmin (float) lower limit for log(MHALO) - >=
lMHmax (float) higher limit for log(MHALO) - <
odds_min (float) cut in odds
RIN (float) Inner bin radius of profile
ROUT (float) Outer bin radius of profile
ndots (int) Number of bins of the profile
ncores (int) to run in parallel, number of cores
h (float) H0 = 100.*h
'''
cosmo = LambdaCDM(H0=100*h, Om0=0.3, Ode0=0.7)
tini = time.time()
print 'Using catalog gx_'+ncat+'_L_RM.fits'
print 'Sample ',sample
print 'Selecting groups with:'
print N_min,' <= N_GAL < ',N_max
print z_min,' <= z < ',z_max
print conmin,' <= C_BG < ',conmax
print lMHmin,' <= log(MH) < ',lMHmax
print 'Background galaxies with:'
print 'ODDS > ',odds_min
print 'Profile has ',ndots,'bins'
print 'from ',RIN,'kpc to ',ROUT,'kpc'
print 'h = ',h
# Defining radial bins
bines = np.logspace(np.log10(RIN),np.log10(ROUT),num=ndots+1)
R = (bines[:-1] + np.diff(bines)*0.5)*1.e-3
#reading cats
L=LensCat.Catalog.read_catalog(folder+'gx_'+ncat+'_L_RM.fits')
# L=LensCat.Catalog.read_catalog(folder+'gx_L_RM_FINAL.fits')
# L=LensCat.Catalog.read_catalog(folder+'gx_L_RM_FOF.fits')
mrich = (L.data.N_GAL >= N_min)*(L.data.N_GAL < N_max)
mz = (L.data.Z >= z_min)*(L.data.Z < z_max)
mcon = (L.data.C_BG >= conmin)*(L.data.C_BG < conmax)
mmass = (np.log10(L.data.MASS_HALO) >= lMHmin)*(np.log10(L.data.MASS_HALO) < lMHmax)
mlenses = mrich*mz*mcon*mmass
Nlenses = mlenses.sum()
if Nlenses < ncores:
ncores = Nlenses
print 'Nlenses',Nlenses
print 'CORRIENDO EN ',ncores,' CORES'
L.data = L.data[mlenses]
# SPLIT LENSING CAT
lbins = int(round(Nlenses/float(ncores), 0))
slices = ((np.arange(lbins)+1)*ncores).astype(int)
slices = slices[(slices < Nlenses)]
Lsplit = np.split(L.data.iloc[:],slices)
# WHERE THE SUMS ARE GOING TO BE SAVED
DSIGMAwsum_T = np.zeros(ndots)
DSIGMAwsum_X = np.zeros(ndots)
WEIGHTsum = np.zeros(ndots)
NGALsum = np.zeros(ndots)
Mwsum = np.zeros(ndots)
BOOTwsum_T = np.zeros((100,ndots))
BOOTwsum_X = np.zeros((100,ndots))
BOOTwsum = np.zeros((100,ndots))
Ntot = []
tslice = np.array([])
for l in range(len(Lsplit)):
print 'RUN ',l+1,' OF ',len(Lsplit)
t1 = time.time()
num = len(Lsplit[l])
rin = RIN*np.ones(num)
rout = ROUT*np.ones(num)
nd = ndots*np.ones(num)
h_a = h*np.ones(num)
if num == 1:
entrada = [Lsplit[l].CATID.iloc[0],Lsplit[l].RA_BG.iloc[0],
Lsplit[l].DEC_BG.iloc[0],Lsplit[l].Z.iloc[0],
RIN,ROUT,ndots,h]
salida = [partial_profile_unpack(entrada)]
else:
entrada = np.array([Lsplit[l].CATID.iloc[:],Lsplit[l].RA_BG,
Lsplit[l].DEC_BG,Lsplit[l].Z,rin,rout,nd,h_a]).T
pool = Pool(processes=(num))
salida = np.array(pool.map(partial_profile_unpack, entrada))
pool.terminate()
for profilesums in salida:
DSIGMAwsum_T += profilesums['DSIGMAwsum_T']
DSIGMAwsum_X += profilesums['DSIGMAwsum_X']
WEIGHTsum += profilesums['WEIGHTsum']
NGALsum += profilesums['NGAL']
Mwsum += profilesums['Mwsum']
BOOTwsum_T += profilesums['BOOTwsum_T']
BOOTwsum_X += profilesums['BOOTwsum_X']
BOOTwsum += profilesums['BOOTwsum']
Ntot = np.append(Ntot,profilesums['Ntot'])
t2 = time.time()
ts = (t2-t1)/60.
tslice = np.append(tslice,ts)
print 'TIME SLICE'
print ts
print 'Estimated ramaining time'
print (np.mean(tslice)*(len(Lsplit)-(l+1)))
# COMPUTING PROFILE
Mcorr = Mwsum/WEIGHTsum
DSigma_T = (DSIGMAwsum_T/WEIGHTsum)/(1+Mcorr)
DSigma_X = (DSIGMAwsum_X/WEIGHTsum)/(1+Mcorr)
eDSigma_T = np.std((BOOTwsum_T/BOOTwsum),axis=0)/(1+Mcorr)
eDSigma_X = np.std((BOOTwsum_X/BOOTwsum),axis=0)/(1+Mcorr)
# AVERAGE LENS PARAMETERS
zmean = np.average(L.data.Z,weights=Ntot)
Ngal_mean = np.average(L.data.N_GAL,weights=Ntot)
MH_mean = np.average(L.data.MASS_HALO,weights=Ntot)
MD_mean = np.average(L.data.MASS_DYN,weights=Ntot)
sigmaH_mean = np.average(L.data.VDISP_HALO,weights=Ntot)
sigmaD_mean = np.average(L.data.VDISP_DYN,weights=Ntot)
RH_mean = np.average(L.data.RADIUS_HALO,weights=Ntot)
# FITING AN NFW MODEL
H = cosmo.H(zmean).value/(1.0e3*pc) #H at z_pair s-1
roc = (3.0*(H**2.0))/(8.0*np.pi*G) #critical density at z_pair (kg.m-3)
roc_mpc = roc*((pc*1.0e6)**3.0)
try:
nfw = NFW_stack_fit(R,DSigma_T,eDSigma_T,zmean,roc)
except:
nfw = [0.01,0.,100.,[0.,0.],[0.,0.],-999.,0.]
M200_NFW = (800.0*np.pi*roc_mpc*(nfw[0]**3))/(3.0*Msun)
e_M200_NFW =((800.0*np.pi*roc_mpc*(nfw[0]**2))/(Msun))*nfw[1]
le_M200 = (np.log(10.)/M200_NFW)*e_M200_NFW
# WRITING OUTPUT FITS FILE
tbhdu = fits.BinTableHDU.from_columns(
[fits.Column(name='Rp', format='D', array=R),
fits.Column(name='DSigma_T', format='D', array=DSigma_T),
fits.Column(name='error_DSigma_T', format='D', array=eDSigma_T),
fits.Column(name='DSigma_X', format='D', array=DSigma_X),
fits.Column(name='error_DSigma_X', format='D', array=eDSigma_X),
fits.Column(name='NGAL', format='D', array=NGALsum),
fits.Column(name='NGAL_w', format='D', array=WEIGHTsum)])
h = tbhdu.header
h.append(('N_LENSES',np.int(Nlenses)))
h.append(('N_min',np.int(N_min)))
h.append(('N_max',np.int(N_max)))
h.append(('z_min',np.round(z_min,4)))
h.append(('z_max',np.round(z_max,4)))
h.append(('C_BG_min',np.round(conmin,4)))
h.append(('C_BG_max',np.round(conmax,4)))
h.append(('lMH_min',np.round(lMHmin,4)))
h.append(('lMH_max',np.round(lMHmax,4)))
h.append(('lM200_NFW',np.round(np.log10(M200_NFW),4)))
h.append(('elM200_NFW',np.round(le_M200,4)))
h.append(('CHI2_NFW',np.round(nfw[2],4)))
h.append(('N_GAL_mean',np.round(Ngal_mean,4)))
h.append(('lMASS_HALO_mean',np.round(np.log10(MH_mean),4)))
h.append(('VDISP_HALO_mean',np.round(sigmaH_mean,2)))
h.append(('VDISP_DYN_mean',np.round(sigmaD_mean,2)))
h.append(('RADIUS_HALO_mean',np.round(RH_mean,2)))
h.append(('z_mean',np.round(zmean,4)))
try:
h.append(('lMASS_DYN_mean',np.round(np.log10(MD_mean),4)))
except:
print 'NO DYN MASS'
tbhdu.writeto(folder+'profile_'+sample+'.fits',overwrite=True)
tfin = time.time()
print 'TOTAL TIME ',(tfin-tini)/60.
def multipole_shear(r,
M200=1.e14,
ellip=0.25,
z=0.2,
h=0.7,
misscentred=False,
s_off=0.4,
components=['t0', 't', 'tcos', 'xsin'],
verbose=True,
Yanmiss=False):
'''
Equations from van Uitert (vU, arXiv:1610.04226) for the
multipole expansion and from Ford et al. (F,2015) for
the misscentring
INPUTS:
r [Mpc] - Float or numpy_array
Distance to the centre of
the gravitational potential
OPTIONAL:
M200 [M_sun] - Float/ Cluster Mass
ellip Float / Halo ellipticity defined as
(1-q)/(1+q) where q is the semi-axis
ratio (q < 1)
z Float/ Lens redshift
zs Float/ Source redshift
h Float/ Cosmological quantity
misscentred Float/ If True computes de misscentred quantities
The misscentred is considered only in the
x - axis
s_off [Mpc h-1] Float/ sigma_offset width of the distribution
of cluster offsets (F_Eq11)
components List of misscentred components that are going
to be computed:
't0' -> Gt0_off
't' -> Gt_off
'tcos' -> Gt_off_cos
'xsin' -> Gx_off_sin
verbose Print time computing
Yanmiss if True use Eq 4 to model the miss of Yan et al. 2020
OUTPUT:
output Dictionary (the shear is scales with the
critical density Gamma_i = Sigma_cr*gamma_i
---------- vU_Eq18 ---------
Gt0: Shear monopole
Gt2: Tangential component for the quadrupole
Gx2: Cross component for the quadrupole
--------- Misscentred terms --------
Gt0_off: (ellip = 0) F_Eq14
Gt_off: Integrated tangential component (vU_Eq17)
for considering kappa_offset
Gt_off_cos: Integrated tangential component times
cos(2theta) (vU_Eq17) for considering kappa_offset
Gx_off_sin: Integrated cross component times
sin(2theta) (vU_Eq17) for considering kappa_offset
'''
if not verbose:
blockPrint()
# Check if r is float or numpy array
if not isinstance(r, (np.ndarray)):
r = np.array([r])
# Compute cosmological parameters
cosmo = LambdaCDM(H0=h * 100, Om0=0.3, Ode0=0.7)
H = cosmo.H(z).value / (1.0e3 * pc) #H at z_pair s-1
roc = (3.0 *
(H**2.0)) / (8.0 * np.pi * G) #critical density at z_pair (kg.m-3)
roc_mpc = roc * ((pc * 1.0e6)**3.0)
# Compute R_200
R200 = r200_nfw(M200, roc_mpc)
# Scaling sigma_off
s_off = s_off / h
#print '##################'
#print ' CENTRED '
#print '##################'
def Delta_Sigma(R):
'''
Density contraste for NFW
'''
#calculo de c usando la relacion de Duffy et al 2008
M = ((800.0 * np.pi * roc_mpc * (R200**3)) / (3.0 * Msun)) * h
c = 5.71 * ((M / 2.e12)**-0.084) * ((1. + z)**-0.47)
####################################################
deltac = (200. / 3.) * ((c**3) / (np.log(1. + c) - (c / (1 + c))))
x = np.round((R * c) / R200, 12)
m1 = x < 1.0
m2 = x > 1.0
m3 = (x == 1.0)
try:
jota = np.zeros(len(x))
atanh = np.arctanh(((1.0 - x[m1]) / (1.0 + x[m1]))**0.5)
jota[m1]=(4.0*atanh)/((x[m1]**2.0)*((1.0-x[m1]**2.0)**0.5)) \
+ (2.0*np.log(x[m1]/2.0))/(x[m1]**2.0) - 1.0/(x[m1]**2.0-1.0) \
+ (2.0*atanh)/((x[m1]**2.0-1.0)*((1.0-x[m1]**2.0)**0.5))
atan = np.arctan(((x[m2] - 1.0) / (1.0 + x[m2]))**0.5)
jota[m2]=(4.0*atan)/((x[m2]**2.0)*((x[m2]**2.0-1.0)**0.5)) \
+ (2.0*np.log(x[m2]/2.0))/(x[m2]**2.0) - 1.0/(x[m2]**2.0-1.0) \
+ (2.0*atan)/((x[m2]**2.0-1.0)**1.5)
jota[m3] = 2.0 * np.log(0.5) + 5.0 / 3.0
except:
if m1:
atanh = np.arctanh(((1.0 - x[m1]) / (1.0 + x[m1]))**0.5)
jota = (4.0*atanh)/((x[m1]**2.0)*((1.0-x[m1]**2.0)**0.5)) \
+ (2.0*np.log(x[m1]/2.0))/(x[m1]**2.0) - 1.0/(x[m1]**2.0-1.0) \
+ (2.0*atanh)/((x[m1]**2.0-1.0)*((1.0-x[m1]**2.0)**0.5))
if m2:
atan = np.arctan(((x[m2] - 1.0) / (1.0 + x[m2]))**0.5)
jota = (4.0*atan)/((x[m2]**2.0)*((x[m2]**2.0-1.0)**0.5)) \
+ (2.0*np.log(x[m2]/2.0))/(x[m2]**2.0) - 1.0/(x[m2]**2.0-1.0) \
+ (2.0*atan)/((x[m2]**2.0-1.0)**1.5)
if m3:
jota = 2.0 * np.log(0.5) + 5.0 / 3.0
rs_m = (R200 * 1.e6 * pc) / c
kapak = ((2. * rs_m * deltac * roc_mpc) *
(pc**2 / Msun)) / ((pc * 1.0e6)**3.0)
return kapak * jota
def monopole(R):
'''
Projected density for NFW
'''
if not isinstance(R, (np.ndarray)):
R = np.array([R])
# m = R == 0.
# R[m] = 1.e-8
#calculo de c usando la relacion de Duffy et al 2008
M = ((800.0 * np.pi * roc_mpc * (R200**3)) / (3.0 * Msun)) * h
c = 5.71 * ((M / 2.e12)**-0.084) * ((1. + z)**-0.47)
####################################################
deltac = (200. / 3.) * ((c**3) / (np.log(1. + c) - (c / (1 + c))))
x = (R * c) / R200
m1 = x <= (1.0 - 1.e-12)
m2 = x >= (1.0 + 1.e-12)
m3 = (x == 1.0)
m4 = (~m1) * (~m2) * (~m3)
jota = np.zeros(len(x))
atanh = np.arctanh(np.sqrt((1.0 - x[m1]) / (1.0 + x[m1])))
jota[m1] = (1. /
(x[m1]**2 - 1.)) * (1. -
(2. / np.sqrt(1. - x[m1]**2)) * atanh)
atan = np.arctan(((x[m2] - 1.0) / (1.0 + x[m2]))**0.5)
jota[m2] = (1. /
(x[m2]**2 - 1.)) * (1. -
(2. / np.sqrt(x[m2]**2 - 1.)) * atan)
jota[m3] = 1. / 3.
x1 = 1. - 1.e-4
atanh1 = np.arctanh(np.sqrt((1.0 - x1) / (1.0 + x1)))
j1 = (1. / (x1**2 - 1.)) * (1. - (2. / np.sqrt(1. - x1**2)) * atanh1)
x2 = 1. + 1.e-4
atan2 = np.arctan(((x2 - 1.0) / (1.0 + x2))**0.5)
j2 = (1. / (x2**2 - 1.)) * (1. - (2. / np.sqrt(x2**2 - 1.)) * atan2)
jota[m4] = np.interp(x[m4].astype(float64), [x1, x2], [j1, j2])
rs_m = (R200 * 1.e6 * pc) / c
kapak = ((2. * rs_m * deltac * roc_mpc) *
(pc**2 / Msun)) / ((pc * 1.0e6)**3.0)
return kapak * jota
def quadrupole(R):
'''
Quadrupole term defined as (d(Sigma)/dr)*r
'''
m0p = derivative(monopole, R, dx=1e-5)
return m0p * R
def psi2(R):
'''
vU_Eq10
'''
argumento = lambda x: (x**3) * monopole(x)
integral = integrate.quad(argumento,
0,
R,
epsabs=1.e-01,
epsrel=1.e-01)[0]
return integral * (-2. / (R**2))
vecpsi2 = np.vectorize(psi2)
#print '##################'
#print ' MISCENTRED '
#print '##################'
def P_Roff(Roff):
if Yanmiss:
Poff = (Roff / s_off**2) * np.exp(-1. * (Roff / s_off))
else:
# F_Eq11
Poff = abs((Roff / s_off**2) * np.exp(-0.5 * (Roff / s_off)**2))
return Poff
def monopole_off(R, theta):
'''
F_Eq12
'''
def moff(x):
return monopole(np.sqrt(R**2 + x**2 - 2. * x * R *
np.cos(theta))) * P_Roff(x) * 0.5
argumento = lambda x: moff(x)
# integral1 = integrate.quad(argumento, -1.*np.inf, 0, epsabs=1.e-01, epsrel=1.e-01)[0]
integral1 = integrate.quad(argumento,
-1. * np.inf,
-100.,
epsabs=1.e-01,
epsrel=1.e-01)[0]
# integral2 = integrate.quad(argumento, 0., R, epsabs=1.e-01, epsrel=1.e-01)[0]
x = np.linspace(-100., 100., 5000)
integral2 = integrate.simps(moff(x), x, even='first')
# integral3 = integrate.quad(argumento, R, np.inf, epsabs=1.e-01, epsrel=1.e-01)[0]
integral3 = integrate.quad(argumento,
100.,
np.inf,
epsabs=1.e-01,
epsrel=1.e-01)[0]
return integral1 + integral2 + integral3
vec_moff = np.vectorize(monopole_off)
def Delta_Sigma_off(R, theta):
'''
F_Eq14
'''
argumento = lambda x: monopole_off(x, theta) * x
integral = integrate.quad(argumento,
0,
R,
epsabs=1.e-01,
epsrel=1.e-01)[0]
DS_off = (2. / R**2) * integral - monopole_off(R, theta)
return DS_off
def monopole_off0(R):
'''
F_Eq12
'''
def DS_RRs(Rs, R):
# F_Eq13
#argumento = lambda x: monopole(np.sqrt(R**2+Rs**2-2.*Rs*R*np.cos(x)))
#integral = integrate.quad(argumento, 0, 2.*np.pi, epsabs=1.e-01, epsrel=1.e-01)[0]
x = np.linspace(0., 2. * np.pi, 500)
integral = integrate.simps(monopole(
np.sqrt(R**2 + Rs**2 - 2. * Rs * R * np.cos(x))),
x,
even='first')
return integral / (2. * np.pi)
argumento = lambda x: DS_RRs(x, R) * P_Roff(x)
integral = integrate.quad(argumento,
0,
np.inf,
epsabs=1.e-02,
epsrel=1.e-02)[0]
return integral
def Delta_Sigma_off0(R):
'''
F_Eq14
'''
argumento = lambda x: monopole_off0(x) * x
integral = integrate.quad(argumento,
0,
R,
epsabs=1.e-02,
epsrel=1.e-02)[0]
DS_off = (2. / R**2) * integral - monopole_off0(R)
return DS_off
vec_DSoff0 = np.vectorize(Delta_Sigma_off0)
def quadrupole_off(R, theta):
def q_off(roff):
rp = np.sqrt(R**2 + roff**2 - 2 * roff * R * np.cos(theta))
return quadrupole(rp) * P_Roff(roff) * 0.5
argumento = lambda x: q_off(x)
# integral10 = integrate.quad(argumento, -1.*np.inf, 0, epsabs=1.e-01, epsrel=1.e-01)[0]
integral10 = integrate.quad(argumento,
-1. * np.inf,
-100.,
epsabs=1.e-01,
epsrel=1.e-01)[0]
# integral20 = integrate.quad(argumento, 0., R, epsabs=1.e-01, epsrel=1.e-01)[0]
x = np.linspace(-100., 100., 5000)
integral20 = integrate.simps(q_off(x), x, even='first')
# integral30 = integrate.quad(argumento, R, np.inf, epsabs=1.e-01, epsrel=1.e-01)[0]
integral30 = integrate.quad(argumento,
100.,
np.inf,
epsabs=1.e-01,
epsrel=1.e-01)[0]
return integral10 + integral20 + integral30
vec_qoff = np.vectorize(quadrupole_off)
def psi2_off(R, theta):
def arg(x):
return (x**3) * monopole_off(x, theta)
argumento = lambda x: arg(x)
integral = integrate.quad(argumento,
0,
R,
epsabs=1.e-01,
epsrel=1.e-01)[0]
return integral * (-2. / (R**2))
vecpsi2_off = np.vectorize(psi2_off)
def quantities_centred(r):
gt0 = Delta_Sigma(r)
monopole_r = monopole(r)
quadrupole_r = quadrupole(r)
print 'computing psi2 centred'
psi2_r = vecpsi2(r)
return gt0, monopole_r, quadrupole_r, psi2_r
def quantities_misscentred(r):
print 'computing misscentred profile'
gamma_t0_off = []
gamma_t_off0 = []
gamma_t_off = []
gamma_x_off = []
for R in r:
if 't0' in components:
print 'computing DS_t0_off'
t1 = time.time()
DSoff = Delta_Sigma_off0(R)
gamma_t0_off = np.append(gamma_t0_off, DSoff)
t2 = time.time()
print(t2 - t1) / 60.
def DS_t_off(theta):
gamma_t0 = []
gamma_t2 = []
for t in theta:
gamma_t0 = np.append(gamma_t0, Delta_Sigma_off(R, t))
gamma_t2 = np.append(
gamma_t2,
((-6 * psi2_off(R, t) / R**2) -
2. * monopole_off(R, t) + quadrupole_off(R, t)) *
np.cos(2. * t))
return gamma_t0 + ellip * gamma_t2
if 't' in components:
print 'computing DS_t_off'
t1 = time.time()
if ellip == 0.:
DSoff = Delta_Sigma_off0(R)
gamma_t_off0 = np.append(gamma_t_off0, DSoff)
else:
x = np.linspace(0., 2. * np.pi, 100)
integral = integrate.simps(DS_t_off(x), x, even='first')
gamma_t_off0 = np.append(gamma_t_off0,
integral / (2. * np.pi))
t2 = time.time()
print R, (t2 - t1) / 60.
if 'tcos' in components:
print 'computing DS_t_off_cos'
t1 = time.time()
x = np.linspace(0., 2. * np.pi, 100)
integral = integrate.simps(DS_t_off(x) * np.cos(2. * x),
x,
even='first')
gamma_t_off = np.append(gamma_t_off, integral / np.pi)
t2 = time.time()
print 'tcos', R, (t2 - t1) / 60.
if 'xsin' in components:
print 'computing DS_x_off_sin'
t1 = time.time()
def DS_x_off(theta):
gamma_x2 = ((-6 * psi2_off(R, theta) / R**2) -
4. * monopole_off(R, theta))
return ellip * gamma_x2 * np.sin(2. * theta)
argumento = lambda x: DS_x_off(x) * np.sin(2. * x)
integral = integrate.quad(argumento,
0,
2. * np.pi,
points=[np.pi],
epsabs=1.e-01,
epsrel=1.e-01)[0]
gamma_x_off = np.append(gamma_x_off, integral / np.pi)
t2 = time.time()
print 'xsin', R, (t2 - t1) / 60.
'''
def DS_t_off(theta):
gamma_t0 = Delta_Sigma_off(R,theta)
gamma_t2 = ((-6*psi2_off(R,theta)/R**2)
- 2.*monopole_off(R,theta)
+ quadrupole_off(R,theta))
return gamma_t0 + ellip*gamma_t2*np.cos(2.*theta)
if 't' in components:
print 'computing DS_t_off'
t1 = time.time()
if ellip == 0.:
DSoff = Delta_Sigma_off0(R)
gamma_t_off0 = np.append(gamma_t_off0,DSoff)
else:
argumento = lambda x: DS_t_off(x)
integral = integrate.quad(argumento, 0., 2.*np.pi,points=[np.pi], epsabs=1.e-01, epsrel=1.e-01)[0]
gamma_t_off0 = np.append(gamma_t_off0,integral/(2.*np.pi))
t2 = time.time()
print (t2-t1)/60.
if 'tcos' in components:
print 'computing DS_t_off_cos'
t1 = time.time()
argumento = lambda x: DS_t_off(x)*np.cos(2.*x)
integral = integrate.quad(argumento, 0., 2.*np.pi,points=[np.pi], epsabs=1.e-01, epsrel=1.e-01)[0]
gamma_t_off = np.append(gamma_t_off,integral/np.pi)
t2 = time.time()
print (t2-t1)/60.
if 'xsin' in components:
print 'computing DS_x_off_sin'
t1 = time.time()
def DS_x_off(theta):
gamma_x2 = ((-6*psi2_off(R,theta)/R**2)
- 4.*monopole_off(R,theta))
return ellip*gamma_x2*np.sin(2.*theta)
argumento = lambda x: DS_x_off(x)*np.sin(2.*x)
integral = integrate.quad(argumento, 0, 2.*np.pi,points=[np.pi], epsabs=1.e-01, epsrel=1.e-01)[0]
gamma_x_off = np.append(gamma_x_off,integral/np.pi)
t2 = time.time()
print 'xsin',R,(t2-t1)/60.
'''
return gamma_t0_off, gamma_t_off0, gamma_t_off, gamma_x_off
gt0, m, q, p2 = quantities_centred(r)
'''
vU_Eq18
'''
gt2 = ellip * ((-6 * p2 / r**2) - 2. * m + q)
gx2 = ellip * ((-6 * p2 / r**2) - 4. * m)
output = {'Gt0': gt0, 'Gt2': gt2, 'Gx2': gx2}
if misscentred:
gt0_off, gt_off0, gt_off, gx_off = quantities_misscentred(r)
output.update({
'Gt0_off': gt0_off,
'Gt_off': gt_off0,
'Gt_off_cos': gt_off,
'Gx_off_sin': gx_off
})
enablePrint()
return output
def main(sample='pru',
l_min=20.,
l_max=150.,
z_min=0.1,
z_max=0.4,
RIN=100.,
ROUT=5000.,
proxy_angle='theta_sat_w1',
plim=0.,
Rn_min=0.,
Rn_max=1000.,
ndots=10,
ncores=10,
h=0.7):
'''
INPUT
---------------------------------------------------------
sample (str) sample name
l_min (int) lower limit of galaxy members - >=
l_max (int) higher limit of galaxy members - <
z_min (float) lower limit for z - >=
z_max (float) higher limit for z - <
RIN (float) Inner bin radius of profile
ROUT (float) Outer bin radius of profile
proxy_angle (str) proxy definition of the angle to compute the quadrupole
plim (float) Cut in centre probability - select clusters with Pcen > plim
Rn_min (float) Mpc - Select clusters with a distance to their neirest neighbour >= Rn_min
Rn_max (float) Mpc - Select clusters with a distance to their neirest neighbour < Rn_max
ndots (int) Number of bins of the profile
ncores (int) to run in parallel, number of cores
h (float) H0 = 100.*h
'''
cosmo = LambdaCDM(H0=100 * h, Om0=0.3, Ode0=0.7)
tini = time.time()
print('Sample ', sample)
print('Selecting groups with:')
print(l_min, ' <= Lambda < ', l_max)
print(z_min, ' <= z < ', z_max)
print(Rn_min, ' <= Rprox < ', Rn_max)
print('P_cen lim ', plim)
print('Profile has ', ndots, 'bins')
print('from ', RIN, 'kpc to ', ROUT, 'kpc')
print('Angle proxy ', proxy_angle)
print('h ', h)
# Defining radial bins
bines = np.logspace(np.log10(RIN), np.log10(ROUT), num=ndots + 1)
R = (bines[:-1] + np.diff(bines) * 0.5) * 1.e-3
#reading cats
L = Table(f[1].data).to_pandas()
angles = fits.open(folder + 'SAT_angles.fits')[1].data
borderid = np.loadtxt(folder + 'redMapperID_border.list')
zlambda = L.Z_LAMBDA
zspec = L.Z_SPEC
Z_c = zspec
Z_c[Z_c < 0] = zlambda[Z_c < 0]
L.Z_LAMBDA = Z_c
Pcen = angles.P_cen
Rprox = angles.Rprox
mrich = (L.LAMBDA >= l_min) * (L.LAMBDA < l_max)
mz = (L.Z_LAMBDA >= z_min) * (L.Z_LAMBDA < z_max)
mborder = (~np.in1d(L.ID, borderid))
mpcen = (Pcen > plim)
mprox = (Rprox >= Rn_min) * (Rprox < Rn_max)
mlenses = mrich * mz * mborder * mpcen * mprox
Nlenses = mlenses.sum()
if Nlenses < ncores:
ncores = Nlenses
print('Nlenses', Nlenses)
print('CORRIENDO EN ', ncores, ' CORES')
# A = fits.open('/mnt/clemente/lensing/RodriguezGroups/angle_Rgroups_FINAL.fits')[1].data
# theta = A.theta[mlenses]
L = L[mlenses]
if 'control' in proxy_angle:
theta = np.zeros(sum(mlenses))
print('entro en control')
else:
theta = angles[mlenses][proxy_angle]
# SPLIT LENSING CAT
lbins = int(round(Nlenses / float(ncores), 0))
slices = ((np.arange(lbins) + 1) * ncores).astype(int)
slices = slices[(slices < Nlenses)]
Lsplit = np.split(L.iloc[:], slices)
Tsplit = np.split(theta, slices)
# WHERE THE SUMS ARE GOING TO BE SAVED
DSIGMAwsum_T = np.zeros(ndots)
DSIGMAwsum_X = np.zeros(ndots)
WEIGHTsum = np.zeros(ndots)
Mwsum = np.zeros(ndots)
BOOTwsum_T = np.zeros((100, ndots))
BOOTwsum_X = np.zeros((100, ndots))
BOOTwsum = np.zeros((100, ndots))
GAMMATcos_wsum = np.zeros(ndots)
GAMMAXsin_wsum = np.zeros(ndots)
WEIGHTcos_sum = np.zeros(ndots)
WEIGHTsin_sum = np.zeros(ndots)
BOOTwsum_Tcos = np.zeros((100, ndots))
BOOTwsum_Xsin = np.zeros((100, ndots))
BOOTwsum_cos = np.zeros((100, ndots))
BOOTwsum_sin = np.zeros((100, ndots))
Ntot = []
tslice = np.array([])
for l in range(len(Lsplit)):
print('RUN ', l + 1, ' OF ', len(Lsplit))
t1 = time.time()
num = len(Lsplit[l])
rin = RIN * np.ones(num)
rout = ROUT * np.ones(num)
nd = ndots * np.ones(num)
if num == 1:
entrada = [
Lsplit[l].CATID.iloc[0], Lsplit[l].RA.iloc[0],
Lsplit[l].DEC.iloc[0], Lsplit[l].Z_LAMBDA.iloc[0],
Tsplit[l][0], RIN, ROUT, ndots
]
salida = [partial_profile_unpack(entrada)]
else:
entrada = np.array([
Lsplit[l].CATID.iloc[:], Lsplit[l].RA, Lsplit[l].DEC,
Lsplit[l].Z_LAMBDA, Tsplit[l][:], rin, rout, nd
]).T
pool = Pool(processes=(num))
salida = np.array(pool.map(partial_profile_unpack, entrada))
pool.terminate()
for profilesums in salida:
DSIGMAwsum_T += profilesums['DSIGMAwsum_T']
DSIGMAwsum_X += profilesums['DSIGMAwsum_X']
WEIGHTsum += profilesums['WEIGHTsum']
Mwsum += profilesums['Mwsum']
BOOTwsum_T += profilesums['BOOTwsum_T']
BOOTwsum_X += profilesums['BOOTwsum_X']
BOOTwsum += profilesums['BOOTwsum']
GAMMATcos_wsum += profilesums['GAMMATcos_wsum']
GAMMAXsin_wsum += profilesums['GAMMAXsin_wsum']
WEIGHTcos_sum += profilesums['WEIGHTcos_sum']
WEIGHTsin_sum += profilesums['WEIGHTsin_sum']
BOOTwsum_Tcos += profilesums['BOOTwsum_Tcos']
BOOTwsum_Xsin += profilesums['BOOTwsum_Xsin']
BOOTwsum_cos += profilesums['BOOTwsum_cos']
BOOTwsum_sin += profilesums['BOOTwsum_sin']
Ntot = np.append(Ntot, profilesums['Ntot'])
t2 = time.time()
ts = (t2 - t1) / 60.
tslice = np.append(tslice, ts)
print('TIME SLICE')
print(ts)
print('Estimated ramaining time')
print(np.mean(tslice) * (len(Lsplit) - (l + 1)))
# COMPUTING PROFILE
Mcorr = Mwsum / WEIGHTsum
DSigma_T = (DSIGMAwsum_T / WEIGHTsum) / (1 + Mcorr)
DSigma_X = (DSIGMAwsum_X / WEIGHTsum) / (1 + Mcorr)
eDSigma_T = np.std((BOOTwsum_T / BOOTwsum), axis=0) / (1 + Mcorr)
eDSigma_X = np.std((BOOTwsum_X / BOOTwsum), axis=0) / (1 + Mcorr)
GAMMA_Tcos = (GAMMATcos_wsum / WEIGHTcos_sum) / (1 + Mcorr)
GAMMA_Xsin = (GAMMAXsin_wsum / WEIGHTsin_sum) / (1 + Mcorr)
eGAMMA_Tcos = np.std((BOOTwsum_Tcos / BOOTwsum_cos), axis=0) / (1 + Mcorr)
eGAMMA_Xsin = np.std((BOOTwsum_Xsin / BOOTwsum_sin), axis=0) / (1 + Mcorr)
# AVERAGE LENS PARAMETERS
zmean = np.average(L.Z_LAMBDA, weights=Ntot)
l_mean = np.average(L.LAMBDA, weights=Ntot)
# FITING AN NFW MODEL
H = cosmo.H(zmean).value / (1.0e3 * pc) #H at z_pair s-1
roc = (3.0 *
(H**2.0)) / (8.0 * np.pi * G) #critical density at z_pair (kg.m-3)
roc_mpc = roc * ((pc * 1.0e6)**3.0)
try:
nfw = NFW_stack_fit(R, DSigma_T, eDSigma_T, zmean, roc)
except:
nfw = [0.01, 0., 100., [0., 0.], [0., 0.], -999., 0.]
M200_NFW = (800.0 * np.pi * roc_mpc * (nfw[0]**3)) / (3.0 * Msun)
e_M200_NFW = ((800.0 * np.pi * roc_mpc * (nfw[0]**2)) / (Msun)) * nfw[1]
le_M200 = (np.log(10.) / M200_NFW) * e_M200_NFW
# WRITING OUTPUT FITS FILE
tbhdu = fits.BinTableHDU.from_columns([
fits.Column(name='Rp', format='D', array=R),
fits.Column(name='DSigma_T', format='D', array=DSigma_T),
fits.Column(name='error_DSigma_T', format='D', array=eDSigma_T),
fits.Column(name='DSigma_X', format='D', array=DSigma_X),
fits.Column(name='error_DSigma_X', format='D', array=eDSigma_X),
fits.Column(name='GAMMA_Tcos', format='D', array=GAMMA_Tcos),
fits.Column(name='error_GAMMA_Tcos', format='D', array=eGAMMA_Tcos),
fits.Column(name='GAMMA_Xsin', format='D', array=GAMMA_Xsin),
fits.Column(name='error_GAMMA_Xsin', format='D', array=eGAMMA_Xsin)
])
h = tbhdu.header
h.append(('N_LENSES', np.int(Nlenses)))
h.append(('l_min', np.int(l_min)))
h.append(('l_max', np.int(l_max)))
h.append(('z_min', np.round(z_min, 4)))
h.append(('z_max', np.round(z_max, 4)))
h.append(('Rn_min', np.round(Rn_min, 4)))
h.append(('Rn_max', np.round(Rn_max, 4)))
h.append(('plim', np.round(plim, 4)))
h.append(('lM200_NFW', np.round(np.log10(M200_NFW), 4)))
h.append(('elM200_NFW', np.round(le_M200, 4)))
h.append(('CHI2_NFW', np.round(nfw[2], 4)))
h.append(('l_mean', np.round(l_mean, 4)))
h.append(('z_mean', np.round(zmean, 4)))
tbhdu.writeto(folder + 'profile_' + sample + '.fits', overwrite=True)
tfin = time.time()
print('TOTAL TIME ', (tfin - tini) / 60.)
epcc_c = np.array([outc[15], outc[16]])
ratio_pcc, eratio_pcc = ratio(pcc_c, epcc_c, pcc, epcc)
ratio_pcc_T, eratio_pcc_T = ratio(pcc_cT, epcc_cT, pcc_T, epcc_T)
ratio_pcc = np.append(ratio_pcc, ratio_pcc_T)
eratio_pcc = np.append(eratio_pcc, eratio_pcc_T)
lMH2 = np.append(lMH, lMH_T)
N = out[3]
mN1 = N == 1
mN23 = (N > 1) * (N < 4)
mN4M = (N > 3)
H = cosmo.H(out[9][mN4M]).value / (1.0e3 * pc) #H at z_pair s-1
M200_SIS = ((2. * (sdisp * 1.e3)**3) / ((50**0.5) * G * H)) / (Msun)
lMdyn2 = np.log10(M200_SIS)
def y(x, alpha):
return np.log10(1.e14 * ((x / 500.)**(alpha)))
x = np.arange(250, 600, 20)
fig = plt.figure()
ax1 = fig.add_subplot(111)
# ax2 = ax1.twiny()
ax1.plot(sdisp, lM200[mN4M], 'C8s', ms=8)
ax1.errorbar(sdisp, lM200[mN4M], yerr=elM200[:, mN4M], fmt='none', ecolor='C8')
class MPShear:
"""
Equations from van Uitert (vU, arXiv:1610.04226) for the
multipole expansion and from Ford et al. (F,2015) for
the misscentring
INPUTS:
r [Mpc] - Float or numpy_array
Distance to the centre of
the gravitational potential
OPTIONAL:
M200 [M_sun] - Float/ Cluster Mass
ellip Float / Halo ellipticity defined as
(1-q)/(1+q) where q is the semi-axis
ratio (q < 1)
z Float/ Lens redshift
zs Float/ Source redshift
h Float/ Cosmological quantity
misscentred Float/ If True computes de misscentred quantities
The misscentred is considered only in the
x - axis
s_off [Mpc h-1] Float/ sigma_offset width of the distribution
of cluster offsets (F_Eq11)
components List of misscentred components that are going
to be computed:
't0' -> Gt0_off
't' -> Gt_off
'tcos' -> Gt_off_cos
'xsin' -> Gx_off_sin
verbose Print time computing
Yanmiss if True use Eq 4 to model the miss of Yan et al. 2020
OUTPUT:
output Dictionary (the shear is scales with the
critical density Gamma_i = Sigma_cr*gamma_i
---------- vU_Eq18 ---------
Gt0: Shear monopole
Gt2: Tangential component for the quadrupole
Gx2: Cross component for the quadrupole
--------- Misscentred terms --------
Gt0_off: (ellip = 0) F_Eq14
Gt_off: Integrated tangential component (vU_Eq17)
for considering kappa_offset
Gt_off_cos: Integrated tangential component times
cos(2theta) (vU_Eq17) for considering kappa_offset
Gx_off_sin: Integrated cross component times
sin(2theta) (vU_Eq17) for considering kappa_offset
"""
cvel = 299792458 # Speed of light (m.s-1)
G = 6.670e-11 # Gravitational constant (m3.kg-1.s-2)
pc = 3.085678e16 # 1 pc (m)
Msun = 1.989e30 # Solar mass (kg)
def __init__(self,
r,
M200=1.e14,
ellip=0.25,
z=0.2,
h=0.7,
misscentred=False,
s_off=0.4,
components=['t0', 't', 'tcos', 'xsin'],
verbose=True,
Yanmiss=False):
"""
init method, it sets up all variables
"""
if not isinstance(r, (np.ndarray)):
r = np.array([r])
self.r = r
self.M200 = M200
self.ellip = ellip
self.z = z
self.h = h
self.misscentred = misscentred
self.s_off = s_off
self.components = components
self.verbose = verbose
self.Yanmiss = Yanmiss
# Compute cosmological parameters
self.cosmo = LambdaCDM(H0=self.h * 100, Om0=0.3, Ode0=0.7)
# H at z_pair s-1
self.H = self.cosmo.H(self.z).value / (1.0e3 * self.pc)
# critical density at z_pair (kg.m-3)
self.roc = (3.0 * (self.H**2.0)) / (8.0 * np.pi * self.G)
self.roc_mpc = self.roc * ((self.pc * 1.0e6)**3.0)
# Compute R_200
self.R200 = profiles_fit.r200_nfw(self.M200, self.roc_mpc)
# Scaling sigma_off
self.s_off = self.s_off / self.h
print 'fitting monopole misscentred'
print folder
print file_name
profile = fits.open(folder + file_name)
h = profile[1].header
p = profile[1].data
zmean = h['Z_MEAN']
Mhalo = 10**h['lMASS_HALO_mean']
Rmean = h['RADIUS_HALO_mean']
ROUT = (2.5 * (2. * (Mhalo / 2.21e14)**0.75)**(1. / 3.)) / 0.7
# Compute cosmological parameters
cosmo = LambdaCDM(H0=0.7 * 100, Om0=0.3, Ode0=0.7)
H = cosmo.H(zmean).value / (1.0e3 * pc) #H at z_pair s-1
roc = (3.0 *
(H**2.0)) / (8.0 * np.pi * G) #critical density at z_pair (kg.m-3)
roc_mpc = roc * ((pc * 1.0e6)**3.0)
def log_likelihood(data_model, r, Gamma, e_Gamma):
log_M200, pcc, soff = data_model
M200 = 10**log_M200
multipoles = multipole_shear_parallel(r,
M200=M200,
misscentred=True,
s_off=soff,
ellip=0,
z=zmean,
components=['t'],
def plt_map_fitted(samp, RIN, ROUT, fittype=''):
m_name = '../maps/map_' + samp + '.fits'
mapa = fits.open(folder + m_name)
p_name = 'profile_' + samp + '.fits'
profile = fits.open(folder + p_name)
print(p_name)
# '''
h = profile[0].header
p = profile[1].data
m = mapa[1].data
print(p_name)
cosmo = LambdaCDM(H0=100 * h['hcosmo'], Om0=0.25, Ode0=0.75)
'''
h = profile[1].header
p = profile[1].data
'''
zmean = h['z_mean']
q = np.round(h['q2d_mean'], 2)
qr = np.round(h['q2dr_mean'], 2)
print('mean q standard', q)
print('mean q reduced', qr)
e = (1 - q) / (1 + q)
er = (1 - qr) / (1 + qr)
H = cosmo.H(zmean).value / (1.0e3 * pc) #H at z_pair s-1
roc = (3.0 *
(H**2.0)) / (8.0 * np.pi * G) #critical density at z_pair (kg.m-3)
roc_mpc = roc * ((pc * 1.0e6)**3.0)
ndots = p.shape[0]
S = m.K
Sr = m.K_reduced
Sc = m.K_control
GT = m.GT
GTr = m.GT_reduced
GTc = m.GT_control
GX = m.GX
GXr = m.GX_reduced
GXc = m.GX_control
x = m.xmpc
y = m.ympc
theta = np.arctan2(m.ympc, m.xmpc)
r = np.sqrt(m.xmpc**2 + m.ympc**2)
# MCMC results
fitpar = fits.open(folder + 'fitresults' + fittype + '_' + str(int(RIN)) +
'_' + str(int(ROUT)) + '_' + p_name)[0].header
fitpar_red = fits.open(folder + 'fitresults' + fittype + '_' +
str(int(RIN)) + '_' + str(int(ROUT)) + '_reduced_' +
p_name)[0].header
efit = (1. - fitpar['q']) / (1. + fitpar['q'])
efit_red = (1. - fitpar_red['q']) / (1. + fitpar_red['q'])
R = r * np.sqrt(fitpar['q'] * (np.cos(theta))**2 +
(np.sin(theta))**2 / fitpar['q'])
Rr = r * np.sqrt(fitpar_red['q'] * (np.cos(theta))**2 +
(np.sin(theta))**2 / fitpar_red['q'])
S0_fit = Sigma_NFW(
r, zmean, M200=10**fitpar['lM200'], c200=fitpar['c200'],
cosmo=cosmo) / (1.e6**2)
Se_fit = Sigma_NFW(
R, zmean, M200=10**fitpar['lM200'], c200=fitpar['c200'],
cosmo=cosmo) / (1.e6**2)
Se_fit_red = Sigma_NFW(Rr,
zmean,
M200=10**fitpar_red['lM200'],
c200=fitpar_red['c200'],
cosmo=cosmo) / (1.e6**2)
S2_fit = quadrupole(r,
zmean,
M200=10**fitpar['lM200'],
c200=fitpar['c200'],
cosmo=cosmo)
gt0 = Delta_Sigma_NFW(r,
zmean,
M200=10**fitpar['lM200'],
c200=fitpar['c200'],
cosmo=cosmo)
gtc, gxs = GAMMA_components(r,
zmean,
ellip=efit,
M200=10**fitpar['lM200'],
c200=fitpar['c200'],
cosmo=cosmo)
gtc_red, gxs_red = GAMMA_components(r,
zmean,
ellip=efit_red,
M200=10**fitpar_red['lM200'],
c200=fitpar_red['c200'],
cosmo=cosmo)
GTfit = gt0 + gtc * np.cos(2 * theta)
GTfit_red = gt0 + gtc_red * np.cos(2 * theta)
GXfit = gxs * np.sin(2 * theta)
GXfit_red = gxs_red * np.sin(2 * theta)
Sfit = S0_fit + efit * S2_fit * np.cos(2 * theta)
Sfit_red = S0_fit + efit_red * S2_fit * np.cos(2 * theta)
print('Results standard fit')
print('log(M200) = ', fitpar['lM200'], ' c200 = ', fitpar['c200'], ' q ',
fitpar['q'])
print('Results reduced fit')
print('log(M200) = ', fitpar_red['lM200'], ' c200 = ', fitpar_red['c200'],
' q ', fitpar_red['q'])
##############
# SURFACE DENSITY PLOT
# JUST MONOPOLE
f, ax = plt.subplots(1, 2, figsize=(6.5, 3), sharex=True, sharey=True)
f.subplots_adjust(hspace=0, wspace=0)
im0 = ax[0].scatter(x, y, c=Sc, vmin=-10, cmap='cividis', vmax=50.)
ax[1].scatter(x, y, c=S0_fit, vmin=-10, cmap='cividis', vmax=50.)
ax[0].set_title('S0_MICE')
ax[1].set_title('S0_fit')
ax[0].set_ylabel('y [Mpc]')
ax[1].set_xlabel('x [Mpc]')
ax[0].set_xlabel('x [Mpc]')
f.colorbar(im0, ax=ax, orientation='vertical', fraction=.05)
f.savefig(folder + '../maps/plots/map_S0_' + samp + fittype + '.png',
bbox_inches='tight')
# Res
f, ax = plt.subplots(1, 1, figsize=(3.5, 3), sharex=True, sharey=True)
f.subplots_adjust(hspace=0, wspace=0)
im0 = ax.scatter(x, y, c=Sc - S0_fit, vmin=-10, cmap='cividis', vmax=10.)
ax.set_title('S0_MICE - S0_fit')
ax.set_ylabel('y [Mpc]')
ax.set_xlabel('x [Mpc]')
f.colorbar(im0, ax=ax, orientation='vertical', fraction=.05)
f.savefig(folder + '../maps/plots/map_S0_res_' + samp + fittype + '.png',
bbox_inches='tight')
# S(R)
f, ax = plt.subplots(2, 2, figsize=(6.5, 6), sharex=True, sharey=True)
f.subplots_adjust(hspace=0, wspace=0)
im0 = ax[0, 0].scatter(x, y, c=S, vmin=-10, cmap='cividis', vmax=50.)
ax[0, 1].scatter(x, y, c=Se_fit, vmin=-10, cmap='cividis', vmax=50.)
ax[1, 0].scatter(x, y, c=Sr, vmin=-10, cmap='cividis', vmax=50.)
ax[1, 1].scatter(x, y, c=Se_fit_red, vmin=-10, cmap='cividis', vmax=50.)
ax[0, 0].set_ylabel('y [Mpc]')
ax[1, 0].set_ylabel('y [Mpc]')
ax[1, 1].set_xlabel('x [Mpc]')
ax[1, 0].set_xlabel('x [Mpc]')
ax[0, 0].set_title('S_MICE')
ax[0, 1].set_title('S_fit(R)')
f.colorbar(im0, ax=ax, orientation='vertical', fraction=.05)
f.savefig(folder + '../maps/plots/map_SR_' + samp + fittype + '.png',
bbox_inches='tight')
# Res
f, ax = plt.subplots(2, figsize=(3.5, 6), sharex=True, sharey=True)
f.subplots_adjust(hspace=0, wspace=0)
im0 = ax[0].scatter(x, y, c=S - Se_fit, vmin=-10, cmap='cividis', vmax=10.)
ax[1].scatter(x, y, c=Sr - Se_fit_red, vmin=-10, cmap='cividis', vmax=10.)
ax[0].set_ylabel('y [Mpc]')
ax[1].set_ylabel('y [Mpc]')
ax[1].set_xlabel('x [Mpc]')
ax[0].set_title('S_MICE - S_fit(R)')
f.colorbar(im0, ax=ax, orientation='vertical', fraction=.05)
f.savefig(folder + '../maps/plots/map_SR_res_' + samp + fittype + '.png',
bbox_inches='tight')
# S(r) + S2
f, ax = plt.subplots(2, 2, figsize=(6.5, 6), sharex=True, sharey=True)
f.subplots_adjust(hspace=0, wspace=0)
im0 = ax[0, 0].scatter(x, y, c=S, vmin=-10, cmap='cividis', vmax=50.)
ax[0, 1].scatter(x, y, c=Sfit, vmin=-10, cmap='cividis', vmax=50.)
ax[1, 0].scatter(x, y, c=Sr, vmin=-10, cmap='cividis', vmax=50.)
ax[1, 1].scatter(x, y, c=Sfit_red, vmin=-10, cmap='cividis', vmax=50.)
ax[0, 0].set_ylabel('y [Mpc]')
ax[1, 0].set_ylabel('y [Mpc]')
ax[1, 1].set_xlabel('x [Mpc]')
ax[1, 0].set_xlabel('x [Mpc]')
ax[0, 0].set_title('S_MICE')
ax[0, 1].set_title('S0 + e*S2')
f.colorbar(im0, ax=ax, orientation='vertical', fraction=.05)
f.savefig(folder + '../maps/plots/map_S_' + samp + fittype + '.png',
bbox_inches='tight')
# Res
f, ax = plt.subplots(2, figsize=(3.5, 6), sharex=True, sharey=True)
f.subplots_adjust(hspace=0, wspace=0)
im0 = ax[0].scatter(x, y, c=S - Se_fit, vmin=-10, cmap='cividis', vmax=10.)
ax[1].scatter(x, y, c=Sr - Se_fit_red, vmin=-10, cmap='cividis', vmax=10.)
ax[0].set_ylabel('y [Mpc]')
ax[1].set_ylabel('y [Mpc]')
ax[1].set_xlabel('x [Mpc]')
ax[0].set_title('S_MICE - (S0 + e*S2)')
f.colorbar(im0, ax=ax, orientation='vertical', fraction=.05)
f.savefig(folder + '../maps/plots/map_S_res_' + samp + fittype + '.png',
bbox_inches='tight')
# QUADRUPOLES
# GTcos
f, ax = plt.subplots(2, 2, figsize=(6.5, 6), sharex=True, sharey=True)
f.subplots_adjust(hspace=0, wspace=0)
im0 = ax[0, 0].scatter(x,
y,
c=GT - gt0,
vmin=-10,
cmap='cividis',
vmax=50.)
ax[0, 1].scatter(x,
y,
c=gtc * np.cos(2. * theta),
vmin=-10,
cmap='cividis',
vmax=50.)
ax[1, 0].scatter(x, y, c=GTr - gt0, vmin=-10, cmap='cividis', vmax=50.)
ax[1, 1].scatter(x,
y,
c=gtc_red * np.cos(2. * theta),
vmin=-10,
cmap='cividis',
vmax=50.)
ax[0, 0].set_ylabel('y [Mpc]')
ax[1, 0].set_ylabel('y [Mpc]')
ax[1, 1].set_xlabel('x [Mpc]')
ax[1, 0].set_xlabel('x [Mpc]')
ax[0, 0].set_title('GT_MICE')
ax[0, 1].set_title('GT_fit')
f.colorbar(im0, ax=ax, orientation='vertical', fraction=.05)
f.savefig(folder + '../maps/plots/map_GTcos_' + samp + fittype + '.png',
bbox_inches='tight')
f, ax = plt.subplots(2, 2, figsize=(6.5, 6), sharex=True, sharey=True)
f.subplots_adjust(hspace=0, wspace=0)
im0 = ax[0, 0].scatter(x, y, c=GT, vmin=-10, cmap='cividis', vmax=50.)
ax[0, 1].scatter(x, y, c=GTfit, vmin=-10, cmap='cividis', vmax=50.)
ax[1, 0].scatter(x, y, c=GTr, vmin=-10, cmap='cividis', vmax=50.)
ax[1, 1].scatter(x, y, c=GTfit_red, vmin=-10, cmap='cividis', vmax=50.)
ax[0, 0].set_ylabel('y [Mpc]')
ax[1, 0].set_ylabel('y [Mpc]')
ax[1, 1].set_xlabel('x [Mpc]')
ax[1, 0].set_xlabel('x [Mpc]')
ax[0, 0].set_title('GT_MICE')
ax[0, 1].set_title('GT_fit')
f.colorbar(im0, ax=ax, orientation='vertical', fraction=.05)
f.savefig(folder + '../maps/plots/map_GT_' + samp + fittype + '.png',
bbox_inches='tight')
# Res
f, ax = plt.subplots(2, figsize=(3.5, 6), sharex=True, sharey=True)
f.subplots_adjust(hspace=0, wspace=0)
im0 = ax[0].scatter(x, y, c=GT - GTfit, vmin=-10, cmap='cividis', vmax=10.)
ax[1].scatter(x, y, c=GTr - GTfit_red, vmin=-10, cmap='cividis', vmax=10.)
ax[0].set_ylabel('y [Mpc]')
ax[1].set_ylabel('y [Mpc]')
ax[1].set_xlabel('x [Mpc]')
ax[0].set_title('GT - (gt0 + e*gt2)')
f.colorbar(im0, ax=ax, orientation='vertical', fraction=.05)
f.savefig(folder + '../maps/plots/map_GT_res_' + samp + fittype + '.png',
bbox_inches='tight')
# QUADRUPOLES
# GX
f, ax = plt.subplots(2, 2, figsize=(6.5, 6), sharex=True, sharey=True)
f.subplots_adjust(hspace=0, wspace=0)
im0 = ax[0, 0].scatter(x, y, c=GX, vmin=-10, cmap='cividis', vmax=10.)
ax[0, 1].scatter(x, y, c=GXfit, vmin=-10, cmap='cividis', vmax=10.)
ax[1, 0].scatter(x, y, c=GXr, vmin=-10, cmap='cividis', vmax=10.)
ax[1, 1].scatter(x, y, c=GXfit_red, vmin=-10, cmap='cividis', vmax=10.)
ax[0, 0].set_ylabel('y [Mpc]')
ax[1, 0].set_ylabel('y [Mpc]')
ax[1, 1].set_xlabel('x [Mpc]')
ax[1, 0].set_xlabel('x [Mpc]')
ax[0, 0].set_title('GX_MICE')
ax[0, 1].set_title('GX_fit')
f.colorbar(im0, ax=ax, orientation='vertical', fraction=.05)
f.savefig(folder + '../maps/plots/map_GX_' + samp + fittype + '.png',
bbox_inches='tight')
# Res
f, ax = plt.subplots(2, figsize=(3.5, 6), sharex=True, sharey=True)
f.subplots_adjust(hspace=0, wspace=0)
im0 = ax[0].scatter(x, y, c=GX - GXfit, vmin=-10, cmap='cividis', vmax=10.)
ax[1].scatter(x, y, c=GXr - GXfit_red, vmin=-10, cmap='cividis', vmax=10.)
ax[0].set_ylabel('y [Mpc]')
ax[1].set_ylabel('y [Mpc]')
ax[1].set_xlabel('x [Mpc]')
ax[0].set_title('GX - (e*gx2)')
f.colorbar(im0, ax=ax, orientation='vertical', fraction=.05)
f.savefig(folder + '../maps/plots/map_GX_res_' + samp + fittype + '.png',
bbox_inches='tight')
def plt_profile_fitted_2h_2q(samp,
RIN,
ROUT,
fittype='_2h_2q',
substract=False,
component='',
terms='1h+2h',
pname='NFW'):
p_name = 'profile_' + samp + '.fits'
profile = fits.open(folder + p_name)
print(p_name)
# '''
h = profile[0].header
p = profile[1].data
cov = profile[2].data
cosmo = LambdaCDM(H0=100 * h['hcosmo'], Om0=0.25, Ode0=0.75)
params = {
'flat': True,
'H0': 70.0,
'Om0': 0.25,
'Ob0': 0.044,
'sigma8': 0.8,
'ns': 0.95
}
'''
h = profile[1].header
p = profile[1].data
'''
zmean = h['z_mean']
q = np.round(h['q2d_mean'], 2)
qr = np.round(h['q2dr_mean'], 2)
print('mean q standard', q)
print('mean q reduced', qr)
e = (1 - q) / (1 + q)
er = (1 - qr) / (1 + qr)
H = cosmo.H(zmean).value / (1.0e3 * pc) #H at z_pair s-1
roc = (3.0 *
(H**2.0)) / (8.0 * np.pi * G) #critical density at z_pair (kg.m-3)
roc_mpc = roc * ((pc * 1.0e6)**3.0)
ndots = p.shape[0]
GT = p.GAMMA_Tcos
GTr = p.GAMMA_Tcos_reduced
GTc = p.GAMMA_Tcos_control
GX = p.GAMMA_Xsin
GXr = p.GAMMA_Xsin_reduced
GXc = p.GAMMA_Xsin_control
# '''
CovDS = cov.COV_ST.reshape(len(GT), len(GT))
CovS = cov.COV_S.reshape(len(GT), len(GT))
CovGT = cov.COV_GT.reshape(len(GT), len(GT))
CovGTr = cov.COV_GT_reduced.reshape(len(GT), len(GT))
CovGTc = cov.COV_GT_control.reshape(len(GT), len(GT))
CovGX = cov.COV_GX.reshape(len(GT), len(GT))
CovGXr = cov.COV_GX_reduced.reshape(len(GT), len(GT))
CovGXc = cov.COV_GX_control.reshape(len(GT), len(GT))
rplot = np.round(p.Rp, 2)
# MCMC results
# fitpar = fits.open(folder+'fitresults_2h_250_2000_'+p_name)[0].header
# fitpar_red = fits.open(folder+'fitresults_2h_250_5000_reduced_'+p_name)[0].header
fitpar = fits.open(folder + 'fitresults' + fittype + component + '_' +
str(int(RIN)) + '_' + str(int(ROUT)) + '_' +
p_name)[0].header
fitpar_red = fits.open(folder + 'fitresults' + fittype + component + '_' +
str(int(RIN)) + '_' + str(int(ROUT)) + '_reduced_' +
p_name)[0].header
fitd = fits.open(folder + 'fitresults' + fittype + component + '_' +
str(int(RIN)) + '_' + str(int(ROUT)) + '_' +
p_name)[1].data
fitd_red = fits.open(folder + 'fitresults' + fittype + component + '_' +
str(int(RIN)) + '_' + str(int(ROUT)) + '_reduced_' +
p_name)[1].data
efit = (1. - fitpar['q']) / (1. + fitpar['q'])
efit_red = (1. - fitpar_red['q']) / (1. + fitpar_red['q'])
efit2h = (1. - fitpar['q2h']) / (1. + fitpar['q2h'])
efit_red2h = (1. - fitpar_red['q']) / (1. + fitpar_red['q'])
DS = Delta_Sigma_NFW_2h(rplot,
zmean,
M200=10**fitpar['lM200'],
c200=fitpar['c200'],
cosmo_params=params,
terms=terms)
DSr = DS
gt1h, gx1h = GAMMA_components(rplot,
zmean,
ellip=efit,
M200=10**fitpar['lM200'],
c200=fitpar['c200'],
cosmo_params=params,
terms='1h',
pname=pname)
gt1hr, gx1hr = GAMMA_components(rplot,
zmean,
ellip=efit_red,
M200=10**fitpar_red['lM200'],
c200=fitpar_red['c200'],
cosmo_params=params,
terms='1h',
pname=pname)
gt2h, gx2h = GAMMA_components(rplot,
zmean,
ellip=efit2h,
M200=10**fitpar['lM200'],
c200=fitpar['c200'],
cosmo_params=params,
terms='2h',
pname=pname)
gt2hr, gx2hr = GAMMA_components(rplot,
zmean,
ellip=efit_red2h,
M200=10**fitpar_red['lM200'],
c200=fitpar_red['c200'],
cosmo_params=params,
terms='2h',
pname=pname)
gt = gt1h + gt2h
gtr = gt1hr + gt2hr
gx = gx1h + gx2h
gxr = gx1hr + gx2hr
print('Results standard fit')
print('log(M200) = ', fitpar['lM200'], ' c200 = ', fitpar['c200'], ' q ',
fitpar['q'])
print('Results reduced fit')
print('log(M200) = ', fitpar_red['lM200'], ' c200 = ', fitpar_red['c200'],
' q ', fitpar_red['q'])
##############
mass = str(np.round(fitpar['lM200'], 2))
c200 = str(np.round(fitpar['c200'], 2))
qfit = str(np.round(fitpar['q'], 2))
qfit2h = str(np.round(fitpar['q2h'], 2))
mass_red = str(np.round(fitpar_red['lM200'], 2))
c200_red = str(np.round(fitpar_red['c200'], 2))
qfit_red = str(np.round(fitpar_red['q'], 2))
qfit2h_red = str(np.round(fitpar_red['q2h'], 2))
f, ax_all = plt.subplots(2, 2, figsize=(12, 8), sharex=True)
f.subplots_adjust(hspace=0)
ax, ax1, ax2, ax3 = ax_all[0, 0], ax_all[0, 1], ax_all[1, 0], ax_all[1, 1]
if substract:
GT = GT - GTc
GTr = GTr - GTc
GX = GX - GXc
GXr = GXr - GXc
p.DSigma_T = p.DSigma_T - p.DSigma_X
ax.set_title(p_name + fittype + component)
ax.plot(p.Rp, p.DSigma_T, 'C1')
ax.plot(rplot,
DS,
'C3',
label='$\log M_{200}=$' + mass + ', $c_{200} = $' + c200)
ax.plot(rplot,
DSr,
'C3--',
label='$\log M_{200}=$' + mass_red + ', $c_{200} = $' + c200_red)
ax.fill_between(p.Rp,
p.DSigma_T + np.diag(CovDS),
p.DSigma_T - np.diag(CovDS),
color='C1',
alpha=0.4)
ax.set_xscale('log')
ax.set_yscale('log')
ax.set_ylabel(r'$\Delta\Sigma$')
ax.set_xlabel('r [$h^{-1}$ Mpc]')
ax.set_ylim(2, 200)
ax.set_xlim(0.1, 10)
ax.xaxis.set_ticks([0.1, 1, 5, 7])
ax.set_xticklabels([0.1, 1, 5, 7])
ax.yaxis.set_ticks([5, 10, 100])
ax.set_yticklabels([5, 10, 100])
ax.axvline(RIN / 1000., color='C7')
ax.axvline(ROUT / 1000., color='C7')
ax.legend(loc=3, frameon=False)
# ax1.plot(RMt[0]*0.7,RMt[1]/0.7,'k',label='redMaPPer')
# ax1.errorbar(RMt[0]*0.7,RMt[1]/0.7,yerr=RMt[2]/0.7,fmt = 'none',ecolor='0.5')
ax1.plot(p.Rp, GT, 'C4')
ax1.plot(p.Rp, GTr, 'C0--')
ax1.plot(rplot,
gt,
'C3',
label='$q_{fit} = $' + qfit + ', $q_{2h} = $' + qfit2h +
', $q = $' + str(q))
ax1.plot(rplot,
gtr,
'C3--',
label='$q_{fit} = $' + qfit_red + ', $q_{2h} = $' + qfit2h_red +
', $q = $' + str(qr))
# ax1.plot(rplot,gt1h,'C2',lw=2)
# ax1.plot(rplot,gt2h,'C2',lw=1)
# ax1.plot(rplot,gt1hr,'C2--',lw=2)
# ax1.plot(rplot,gt2hr,'C2--',lw=1)
ax1.legend(loc=3, frameon=False)
ax1.fill_between(p.Rp,
GT + np.diag(CovGT),
GT - np.diag(CovGT),
color='C4',
alpha=0.4)
ax1.fill_between(p.Rp,
GTr + np.diag(CovGTr),
GTr - np.diag(CovGTr),
color='C0',
alpha=0.4)
ax1.set_xscale('log')
ax1.set_yscale('log')
ax1.set_xlabel('r [$h^{-1}$ Mpc]')
ax1.set_ylabel(r'$\Gamma_T$')
ax1.set_ylim(1, 100)
ax1.set_xlim(0.1, 10)
ax1.xaxis.set_ticks([0.1, 1, 5, 7])
ax1.set_xticklabels([0.1, 1, 5, 7])
ax1.yaxis.set_ticks([0.3, 10, 100])
ax1.set_yticklabels([0.3, 10, 100])
ax1.axvline(RIN / 1000., color='C7')
ax1.axvline(ROUT / 1000., color='C7')
# ax2.plot(RMt[0]*0.7,RMt[3]/0.7,'k',label='redMaPPer')
# ax2.errorbar(RMt[0]*0.7,RMt[3]/0.7,yerr=RMt[4]/0.7,fmt = 'none',ecolor='0.5')
ax2.plot([0, 10], [0, 0], 'C7')
ax2.plot(p.Rp, GX, 'C2')
ax2.plot(p.Rp, GXr, 'C5--')
ax2.plot(rplot, gx, 'C3')
ax2.plot(rplot, gxr, 'C3--')
# ax2.plot(rplot,gx1h,'C2',lw=2)
# ax2.plot(rplot,gx2h,'C2',lw=1)
# ax2.plot(rplot,gx1hr,'C2--',lw=2)
# ax2.plot(rplot,gx2hr,'C2--',lw=1)
ax2.axvline(RIN / 1000., color='C7')
ax2.axvline(ROUT / 1000., color='C7')
ax2.fill_between(p.Rp,
GX + np.diag(CovGX),
GX - np.diag(CovGX),
color='C2',
alpha=0.4)
ax2.fill_between(p.Rp,
GXr + np.diag(CovGXr),
GXr - np.diag(CovGXr),
color='C5',
alpha=0.4)
ax2.set_xlabel('r [$h^{-1}$ Mpc]')
ax2.set_ylabel(r'$\Gamma_\times$')
ax2.set_xscale('log')
ax2.set_xlim(0.1, 10)
ax2.set_ylim(-20, 16)
ax2.xaxis.set_ticks([0.1, 1, 5, 7])
ax2.set_xticklabels([0.1, 1, 5, 7])
ax3.plot([0, 10], [0, 0], 'C7')
ax3.plot(p.Rp, GTc, 'k', label='GT control')
ax3.plot(p.Rp, GXc, 'C8--', label='GX control')
ax3.fill_between(p.Rp,
GXc + np.diag(CovGXc),
GXc - np.diag(CovGXc),
color='C8',
alpha=0.4)
ax3.fill_between(p.Rp,
GTc + np.diag(CovGTc),
GTc - np.diag(CovGTc),
color='C7',
alpha=0.4)
ax3.set_xlabel('r [$h^{-1}$ Mpc]')
ax3.set_xscale('log')
ax3.set_xlim(0.1, 10)
ax3.set_ylim(-20, 16)
ax3.xaxis.set_ticks([0.1, 1, 5, 7])
ax3.set_xticklabels([0.1, 1, 5, 7])
ax3.legend(frameon=False)
if substract == True:
f.savefig(folder + 'plots/profile_' + samp + '_2q_+' + fittype +
component + '_substracted.png',
bbox_inches='tight')
else:
f.savefig(folder + 'plots/profile_' + samp + '_2q_+' + fittype +
component + '.png',
bbox_inches='tight')
f, ax = plt.subplots(2, 1, figsize=(12, 4), sharex=True)
f.subplots_adjust(hspace=0)
ax[0].plot(fitd.q2h, 'C7', alpha=0.7, label='2h')
ax[0].plot(fitd.q, 'C6', alpha=0.7, label='1h')
ax[1].plot(fitd_red.q2h, 'C7', alpha=0.7, label='2h')
ax[1].plot(fitd_red.q, 'C6', alpha=0.7, label='1h')
ax[0].legend(frameon=False, loc=1)
ax[0].set_ylabel('$q$')
ax[1].set_ylabel('$q_r$')
ax[1].set_xlabel('$N$')
f.savefig(folder + 'plots/fit_2q_' + samp + '.png', bbox_inches='tight')