def power(ell, theta, clump=True):
eps_f = theta[0]
eps_DM = theta[1]
f_star = theta[2]
S_star = theta[3]
A_C = theta[4]
alpha0 = theta[5]
n_nt = theta[6]
beta = theta[7]
gamma_mod0 = theta[8]
gamma_mod_zslope = theta[9]
x_break = theta[10]
x_smooth = theta[11]
n_nt_mod = theta[12]
clump0 = theta[13]
clump_zslope = theta[14]
x_clump = theta[15]
alpha_clump1 = theta[16]
alpha_clump2 = theta[17]
xx_power.set_Flender_params(alpha0, n_nt, beta, eps_f * 1e-6, eps_DM,
f_star, S_star, A_C, gamma_mod0,
gamma_mod_zslope, x_break, x_smooth, n_nt_mod,
clump0, clump_zslope, x_clump, alpha_clump1,
alpha_clump2)
model = xx_power.return_yy_power(ell) # [erg cm^-2 s^-1 str^-1]^2
return model
def cxb(theta):
eps_f = theta[0]
eps_DM = theta[1]
f_star = theta[2]
S_star = theta[3]
A_C = theta[4]
alpha0 = theta[5]
n_nt = theta[6]
beta = theta[7]
gamma_mod0 = theta[8]
gamma_mod_zslope = theta[9]
x_break = theta[10]
x_smooth = theta[11]
n_nt_mod = theta[12]
clump0 = theta[13]
clump_zslope = theta[14]
x_clump = theta[15]
alpha_clump1 = theta[16]
alpha_clump2 = theta[17]
xx_power.set_Flender_params(alpha0, n_nt, beta, eps_f * 1e-6, eps_DM,
f_star, S_star, A_C, gamma_mod0,
gamma_mod_zslope, x_break, x_smooth, n_nt_mod,
clump0, clump_zslope, x_clump, alpha_clump1,
alpha_clump2)
return (xx_power.return_total_xsb() / (4.0 * math.pi))
def pressure_profile(x, mass, redshift, theta):
eps_f = theta[0]
eps_DM = theta[1]
f_star = theta[2]
S_star = theta[3]
A_C = theta[4]
A_nt = theta[5]
B_nt = theta[6]
gamma_nt = theta[7]
gamma_mod0 = theta[8]
gamma_mod_zslope = theta[9]
x_break = theta[10]
x_smooth = theta[11]
n_nt_mod = theta[12]
clump0 = theta[13]
alpha_clump = theta[14]
beta_clump = theta[15]
gamma_clump = theta[16]
xx_power.set_Flender_params(eps_f * 1e-6, eps_DM, f_star, S_star, A_C,
A_nt, B_nt, gamma_nt, gamma_mod0,
gamma_mod_zslope, x_break, x_smooth, n_nt_mod,
clump0, alpha_clump, beta_clump, gamma_clump)
#xx_power.set_Flender_params(alpha0, n_nt, beta, eps_f*1e-6, eps_DM, f_star, S_star, A_C, gamma_mod0, gamma_mod_zslope, x_break, x_smooth, n_nt_mod, clump0, clump_zslope, x_clump, alpha_clump1, alpha_clump2)
pressure = xx_power.return_pressure_profile(x, redshift, mass)
return pressure
def density_profile(x, mass, redshift, theta):
eps_f = theta[0]
eps_DM = theta[1]
f_star = theta[2]
S_star = theta[3]
A_C = theta[4]
A_nt = theta[5]
B_nt = theta[6]
gamma_nt = theta[7]
gamma_mod0 = theta[8]
gamma_mod_zslope = theta[9]
x_break = theta[10]
x_smooth = theta[11]
n_nt_mod = theta[12]
clump0 = theta[13]
alpha_clump = theta[14]
beta_clump = theta[15]
gamma_clump = theta[16]
xx_power.set_Flender_params(eps_f * 1e-6, eps_DM, f_star, S_star, A_C,
A_nt, B_nt, gamma_nt, gamma_mod0,
gamma_mod_zslope, x_break, x_smooth, n_nt_mod,
clump0, alpha_clump, beta_clump, gamma_clump)
density = xx_power.return_density_profile(x, redshift, mass) # in cm^-3
density = density * mmw * m_p # g cm^-3
E = np.sqrt(Omega_m * (1 + redshift)**3 + Omega_l)
density /= rho_crit * E**2 # \rho/\rho_crit(z)
return density
def lnlike(theta, x, y, invcov):
'''
double alpha0; // fiducial : 0.18
double n_nt; // fiducial : 0.80
double beta; // fiducial : 0.50
double eps_f; // fiducial : 3.97e-6
double eps_DM; // fiducial : 0.00
double f_star; // fiducial : 0.026
double S_star; // fiducial : 0.12
double A_C; // fiducial : 1.00
double gamma_mod0; // fiducial : 0.10
double gamma_mod_zslope; // fiducial : 1.72
double x_break; // fiducial : 0.195
double x_smooth; // fiducial : 0.01
'''
eps_f, f_star, S_star, gamma_mod0, clump0, alpha_clump, beta_clump, gamma_clump = theta
eps_f = 10**eps_f
f_star = 10**f_star
S_star = 10**S_star
gamma_mod0 = 10**gamma_mod0
clump0 = 10**clump0
alpha_clump = 10**alpha_clump
beta_clump = 10**beta_clump
gamma_clump = 10**gamma_clump
#fix DM profile
eps_DM = 3e-5
A_C = 1.0
#fix non-thermal pressure term
A_nt = 0.452
B_nt = 0.841
gamma_nt = 1.628
x_smooth = 0.01
x_break = 0.195
#gamma_mod0 = 0.10
gamma_mod_zslope = 1.72
#S_star = 0.12
#clumping terms
#clump0 = 0.0
#alpha_clump = 1.0
#beta_clump = 6.0
#gamma_clump = 3.0
xx_power.set_Flender_params(eps_f * 1e-6, eps_DM, f_star, S_star, A_C,
A_nt, B_nt, gamma_nt, gamma_mod0,
gamma_mod_zslope, x_break, x_smooth, clump0,
alpha_clump, beta_clump, gamma_clump)
model = xx_power.return_xx_power_alt(x)
#sn = np.full(x.shape, 10.0**log_noise, dtype = np.float64)
#model += sn
#model /= beam(x)
diff = np.array(y - model, dtype=np.float64)
lnl = -0.5 * np.dot(diff, np.dot(invcov, np.transpose(diff)))
return lnl
def xray_flux(mass, redshift, theta):
eps_f = theta[0]
eps_DM = theta[1]
f_star = theta[2]
S_star = theta[3]
A_C = theta[4]
alpha0 = theta[5]
n_nt = theta[6]
beta = theta[7]
gamma_mod0 = theta[8]
gamma_mod_zslope = theta[9]
x_break = theta[10]
x_smooth = theta[11]
n_nt_mod = theta[12]
clump0 = theta[13]
alpha_clump = theta[14]
beta_clump = theta[15]
gamma_clump = theta[16]
xx_power.set_Flender_params(alpha0, n_nt, beta, eps_f * 1e-6, eps_DM,
f_star, S_star, A_C, gamma_mod0,
gamma_mod_zslope, x_break, x_smooth, n_nt_mod,
clump0, alpha_clump, beta_clump, gamma_clump)
flux = xx_power.return_flux(redshift, mass)
m500 = xx_power.Mvir_to_Mdeltac(redshift, mass, 500.0)
return flux, m500
def cxb(theta):
eps_f = theta[0]
eps_DM = theta[1]
f_star = theta[2]
S_star = theta[3]
A_C = theta[4]
A_nt = theta[5]
B_nt = theta[6]
gamma_nt = theta[7]
gamma_mod0 = theta[8]
gamma_mod_zslope = theta[9]
x_break = theta[10]
x_smooth = theta[11]
n_nt_mod = theta[12]
clump0 = theta[13]
alpha_clump = theta[14]
beta_clump = theta[15]
gamma_clump = theta[16]
xx_power.set_Flender_params(eps_f * 1e-6, eps_DM, f_star, S_star, A_C,
A_nt, B_nt, gamma_nt, gamma_mod0,
gamma_mod_zslope, x_break, x_smooth, n_nt_mod,
clump0, alpha_clump, beta_clump, gamma_clump)
return (xx_power.return_total_xsb())
def power(ell, theta, clump=True):
eps_f = theta[0]
eps_DM = theta[1]
f_star = theta[2]
S_star = theta[3]
A_C = theta[4]
A_nt = theta[5]
B_nt = theta[6]
gamma_nt = theta[7]
gamma_mod0 = theta[8]
gamma_mod_zslope = theta[9]
x_break = theta[10]
x_smooth = theta[11]
n_nt_mod = theta[12]
clump0 = theta[13]
alpha_clump = theta[14]
beta_clump = theta[15]
gamma_clump = theta[16]
xx_power.set_Flender_params(eps_f * 1e-6, eps_DM, f_star, S_star, A_C,
A_nt, B_nt, gamma_nt, gamma_mod0,
gamma_mod_zslope, x_break, x_smooth, n_nt_mod,
clump0, alpha_clump, beta_clump, gamma_clump)
#model = xx_power.return_xx_power(ell) # [erg cm^-2 s^-1 str^-1]^2
model_alt = xx_power.return_xx_power_alt(ell) # [erg cm^-2 s^-1 str^-1]^2
return model_alt
def lnlike(theta, x, y, invcov):
'''
double alpha0; // fiducial : 0.18
double n_nt; // fiducial : 0.80
double beta; // fiducial : 0.50
double eps_f; // fiducial : 3.97e-6
double eps_DM; // fiducial : 0.00
double f_star; // fiducial : 0.026
double S_star; // fiducial : 0.12
double A_C; // fiducial : 1.00
double gamma_mod0; // fiducial : 0.10
double gamma_mod_zslope; // fiducial : 1.72
double x_break; // fiducial : 0.195
double x_smooth; // fiducial : 0.01
double n_nt_mod; // fiducial : 0.80
'''
#alpha0, n_nt, beta, eps_f, eps_DM, f_star, S_star, A_C, gamma_mod0, gamma_mod_zslope, x_break, x_smooth, n_nt_mod = theta
#xx_power.set_Flender_params(alpha0, n_nt, beta, eps_f*1e-6, eps_DM, f_star, S_star, A_C, gamma_mod0, gamma_mod_zslope, x_break, x_smooth, n_nt_mod)
#eps_f, f_star, S_star, gamma_mod0, gamma_mod_zslope, clump0, clump_zslope = theta
log_noise = theta
#fix DM profile
eps_DM = 0.006
A_C = 1.0
eps_f = 5.0
f_star = 0.026
S_star = 0.12
#fix non-thermal pressure term
alpha0 = 0.18
n_nt = 0.80
beta = 0.50
x_smooth = 0.01
n_nt_mod = 0.80
x_break = 0.195
gamma_mod0 = 0.10
gamma_mod_zslope = 1.72
#clumping terms
clump0 = 0.0
clump_zslope = 0.0
x_clump = 1.23
alpha_clump1 = 0.88
alpha_clump2 = 3.85
xx_power.set_Flender_params(alpha0, n_nt, beta, eps_f*1e-6, eps_DM, f_star, S_star, A_C, gamma_mod0, gamma_mod_zslope, x_break, x_smooth, n_nt_mod, clump0, clump_zslope, x_clump, alpha_clump1, alpha_clump2 )
model = xx_power.return_xx_power(x) # [erg cm^-2 s^-1 str^-1]^2
sn = np.full(x.shape, 10.0**log_noise, dtype = np.float64)
model = sn
diff = np.array(y-model, dtype=np.float64)
lnl = -0.5*np.dot(diff, np.dot(invcov, np.transpose(diff)))
return lnl
def power_spectrum(x, *theta):
'''
double alpha0; // fiducial : 0.18
double n_nt; // fiducial : 0.80
double beta; // fiducial : 0.50
double eps_f; // fiducial : 3.97e-6
double eps_DM; // fiducial : 0.00
double f_star; // fiducial : 0.026
double S_star; // fiducial : 0.12
double A_C; // fiducial : 1.00
double gamma_mod0; // fiducial : 0.10
double gamma_mod_zslope; // fiducial : 1.72
double x_break; // fiducial : 0.195
double x_smooth; // fiducial : 0.01
double n_nt_mod; // fiducial : 0.80
'''
#alpha0, n_nt, beta, eps_f, eps_DM, f_star, S_star, A_C, gamma_mod0, gamma_mod_zslope, x_break, x_smooth, n_nt_mod = theta
#xx_power.set_Flender_params(alpha0, n_nt, beta, eps_f*1e-6, eps_DM, f_star, S_star, A_C, gamma_mod0, gamma_mod_zslope, x_break, x_smooth, n_nt_mod)
#eps_f, f_star, S_star, gamma_mod0, gamma_mod_zslope, clump0, clump_zslope = theta
eps_f, f_star, S_star, clump0, clump_zslope = theta
#fix DM profile
eps_DM = 0.006
A_C = 1.0
#fix non-thermal pressure term
alpha0 = 0.18
n_nt = 0.80
beta = 0.50
x_smooth = 0.01
n_nt_mod = 0.80
x_break = 0.195
gamma_mod0 = 0.10
gamma_mod_zslope = 1.72
#clumping terms
#clump0 = 0.0
#clump_zslope = 0.0
x_clump = 1.23
alpha_clump1 = 0.88
alpha_clump2 = 3.85
xx_power.set_Flender_params(alpha0, n_nt, beta, eps_f * 1e-6, eps_DM,
f_star, S_star, A_C, gamma_mod0,
gamma_mod_zslope, x_break, x_smooth, n_nt_mod,
clump0, clump_zslope, x_clump, alpha_clump1,
alpha_clump2)
model = xx_power.return_xx_power(x, flux_lim) # [erg cm^-2 s^-1 str^-1]^2
return model
def power(ell):
'''
double alpha0; // fiducial : 0.18
double n_nt; // fiducial : 0.80
double beta; // fiducial : 0.50
double eps_f; // fiducial : 3.97e-6
double eps_DM; // fiducial : 0.00
double f_star; // fiducial : 0.026
double S_star; // fiducial : 0.12
double A_C; // fiducial : 1.00
double gamma_mod0; // fiducial : 0.10
double gamma_mod_zslope; // fiducial : 1.72
double x_break; // fiducial : 0.195
double x_smooth; // fiducial : 0.01
double n_nt_mod; // fiducial : 0.80
'''
#Shaw model param
eps_f = 3.97e-6
eps_DM = 0.00
f_star = 0.026
S_star = 0.12
A_C = 1.00
gamma_mod0 = 0.10
gamma_mod_zslope = 1.72
#fix non-thermal pressure term
alpha0 = 0.18
n_nt = 0.80
beta = 0.50
x_smooth = 0.01
n_nt_mod = 0.80
x_break = 0.1
#clumping terms
clump0 = 0.0
clump_zslope = 0.0
x_clump = 1.0
alpha_clump1 = 0.0
alpha_clump2 = 0.0
xx_power.set_Flender_params(alpha0, n_nt, beta, eps_f * 1.e-6, eps_DM,
f_star, S_star, A_C, gamma_mod0,
gamma_mod_zslope, x_break, x_smooth, n_nt_mod,
clump0, clump_zslope, x_clump, alpha_clump1,
alpha_clump2)
model = xx_power.return_xx_power(ell,
flux_lim) # [erg cm^-2 s^-1 str^-1]^2
#model = xx_power.return_xx_power(ell) # [erg cm^-2 s^-1 str^-1]^2
return model
def ysz_m(mass, redshift, theta):
eps_f = theta[0]
eps_DM = theta[1]
f_star = theta[2]
S_star = theta[3]
A_C = theta[4]
alpha0 = theta[5]
n_nt = theta[6]
beta = theta[7]
gamma_mod0 = theta[8]
gamma_mod_zslope = theta[9]
x_break = theta[10]
x_smooth = theta[11]
n_nt_mod = theta[12]
clump0 = theta[13]
alpha_clump = theta[14]
beta_clump = theta[15]
gamma_clump = theta[16]
xx_power.set_Flender_params(alpha0, n_nt, beta, eps_f * 1e-6, eps_DM,
f_star, S_star, A_C, gamma_mod0,
gamma_mod_zslope, x_break, x_smooth, n_nt_mod,
clump0, alpha_clump, beta_clump, gamma_clump)
ysz = []
m500 = []
for m in mass:
ysz.append(yy_power.return_Ysz(redshift, m))
m500.append(xx_power.Mvir_to_Mdeltac(redshift, m, 500.0))
ysz = np.array(ysz)
m500 = np.array(m500)
E = np.sqrt(Omega_m * (1 + redshift)**3 + Omega_l)
ysz = ysz * E**(-2. / 3.)
return ysz, m500
def xxpower(ell, theta, survey=None):
eps_f = theta[0]
eps_DM = theta[1]
f_star = theta[2]
S_star = theta[3]
A_C = theta[4]
alpha0 = theta[5]
n_nt = theta[6]
beta = theta[7]
gamma_mod0 = theta[8]
gamma_mod_zslope = theta[9]
x_break = theta[10]
x_smooth = theta[11]
n_nt_mod = theta[12]
clump0 = theta[13]
clump_zslope = theta[14]
x_clump = theta[15]
alpha_clump1 = theta[16]
alpha_clump2 = theta[17]
xx_power.set_Flender_params(alpha0, n_nt, beta, 1e-6 * eps_f, eps_DM,
f_star, S_star, A_C, gamma_mod0,
gamma_mod_zslope, x_break, x_smooth, n_nt_mod,
clump0, clump_zslope, x_clump, alpha_clump1,
alpha_clump2)
cl = xx_power.return_xx_power(ell) # [erg cm^-2 s^-1 str^-1]^2
if survey == None:
psn = 0
else:
psn = beam(ell, fwhm=survey_fwhm[survey]) * survey_psn[survey]
var = (2. / ((2. * ell + 1) * survey_fsky[survey])) * (cl)**2
return cl, var
def tx_m(mass, redshift, theta):
eps_f = theta[0]
eps_DM = theta[1]
f_star = theta[2]
S_star = theta[3]
A_C = theta[4]
alpha0 = theta[5]
n_nt = theta[6]
beta = theta[7]
gamma_mod0 = theta[8]
gamma_mod_zslope = theta[9]
x_break = theta[10]
x_smooth = theta[11]
n_nt_mod = theta[12]
clump0 = theta[13]
alpha_clump = theta[14]
beta_clump = theta[15]
gamma_clump = theta[16]
xx_power.set_Flender_params(alpha0, n_nt, beta, eps_f * 1e-6, eps_DM,
f_star, S_star, A_C, gamma_mod0,
gamma_mod_zslope, x_break, x_smooth, n_nt_mod,
clump0, alpha_clump, beta_clump, gamma_clump)
tx = []
m500 = []
for m in mass:
tx.append(xx_power.return_Tx(redshift, m))
m500.append(xx_power.Mvir_to_Mdeltac(redshift, m, 500.0))
tx = np.array(tx)
m500 = np.array(m500)
return tx, m500
def mgas_m(mass, redshift, theta):
eps_f = theta[0]
eps_DM = theta[1]
f_star = theta[2]
S_star = theta[3]
A_C = theta[4]
A_nt = theta[5]
B_nt = theta[6]
gamma_nt = theta[7]
gamma_mod0 = theta[8]
gamma_mod_zslope = theta[9]
x_break = theta[10]
x_smooth = theta[11]
n_nt_mod = theta[12]
clump0 = theta[13]
alpha_clump = theta[14]
beta_clump = theta[15]
gamma_clump = theta[16]
xx_power.set_Flender_params(eps_f * 1e-6, eps_DM, f_star, S_star, A_C,
A_nt, B_nt, gamma_nt, gamma_mod0,
gamma_mod_zslope, x_break, x_smooth, n_nt_mod,
clump0, alpha_clump, beta_clump, gamma_clump)
mgas = []
m500 = []
for m in mass:
mgas.append(xx_power.return_Mgas(redshift, m))
m500.append(xx_power.Mvir_to_Mdeltac(redshift, m, 500.0))
mgas = np.array(mgas)
m500 = np.array(m500)
return mgas, m500
def power_model (x, params) :
# set cosmology and linear power spectrum
H0=70.000000
Omega_M=0.279000
Omega_b=0.046100
w0=-1.000000
Omega_k=0.000000
n_s=0.972000
nH = 1.e22
inputPk="../input_pk/wmap9_fid_matterpower_z0.dat"
xx_power.init_cosmology(H0, Omega_M, Omega_b, w0, Omega_k, n_s, nH, inputPk)
'''
double alpha0; // fiducial : 0.18
double n_nt; // fiducial : 0.80
double beta; // fiducial : 0.50
double eps_f; // fiducial : 3.97e-6
double eps_DM; // fiducial : 0.00
double f_star; // fiducial : 0.026
double S_star; // fiducial : 0.12
double A_C; // fiducial : 1.00
double gamma_mod0; // fiducial : 0.10
double gamma_mod_zslope; // fiducial : 1.72
double x_break; // fiducial : 0.195
double x_smooth; // fiducial : 0.01
double n_nt_mod; // fiducial : 0.80
'''
#alpha0, n_nt, beta, eps_f, eps_DM, f_star, S_star, A_C, gamma_mod0, gamma_mod_zslope, x_break, x_smooth, n_nt_mod = theta
#xx_power.set_Flender_params(alpha0, n_nt, beta, eps_f*1e-6, eps_DM, f_star, S_star, A_C, gamma_mod0, gamma_mod_zslope, x_break, x_smooth, n_nt_mod)
#eps_f, f_star, S_star, gamma_mod0, gamma_mod_zslope, clump0, clump_zslope = theta
eps_f, f_star, S_star, clump0, noise = params[0], params[1], params[2], params[3], param[4]
#fix DM profile
eps_DM = 0.006
A_C = 1.0
#fix non-thermal pressure term
alpha0 = 0.18
n_nt = 0.80
beta = 0.50
x_smooth = 0.01
n_nt_mod = 0.80
x_break = 0.195
gamma_mod0 = 0.10
gamma_mod_zslope = 1.72
#clumping terms
#clump0 = 0.0
clump_zslope = 0.0
x_clump = 1.23
alpha_clump1 = 0.88
alpha_clump2 = 3.85
xx_power.set_Flender_params(alpha0, n_nt, beta, eps_f*1e-6, eps_DM, f_star, S_star, A_C, gamma_mod0, gamma_mod_zslope, x_break, x_smooth, n_nt_mod, clump0, clump_zslope, x_clump, alpha_clump1, alpha_clump2, noise)
model = xx_power.return_xx_power(x) # [erg cm^-2 s^-1 str^-1]^2
return model
def lnlike(theta, x, y, invcov):
'''
double alpha0; // fiducial : 0.18
double n_nt; // fiducial : 0.80
double beta; // fiducial : 0.50
double eps_f; // fiducial : 3.97e-6
double eps_DM; // fiducial : 0.00
double f_star; // fiducial : 0.026
double S_star; // fiducial : 0.12
double A_C; // fiducial : 1.00
double gamma_mod0; // fiducial : 0.10
double gamma_mod_zslope; // fiducial : 1.72
double x_break; // fiducial : 0.195
double x_smooth; // fiducial : 0.01
double n_nt_mod; // fiducial : 0.80
'''
#alpha0, n_nt, beta, eps_f, eps_DM, f_star, S_star, A_C, gamma_mod0, gamma_mod_zslope, x_break, x_smooth, n_nt_mod = theta
#xx_power.set_Flender_params(alpha0, n_nt, beta, eps_f*1e-6, eps_DM, f_star, S_star, A_C, gamma_mod0, gamma_mod_zslope, x_break, x_smooth, n_nt_mod)
#eps_f, f_star, S_star, gamma_mod0, gamma_mod_zslope, clump0, clump_zslope = theta
clump0, alpha_clump, beta_clump, gamma_clump = theta
eps_f = 3.97
f_star = 0.026
clump0 = 10**clump0
S_star = 0.12
alpha_clump = 10**alpha_clump
beta_clump = 10**beta_clump
gamma_clump = 10**gamma_clump
#fix DM profile
eps_DM = 3e-5
A_C = 1.0
#fix non-thermal pressure term
alpha0 = 0.18
n_nt = 0.80
beta = 0.50
x_smooth = 0.01
n_nt_mod = 0.80
x_break = 0.195
gamma_mod0 = 0.10
gamma_mod_zslope = 1.72
#S_star = 0.12
#clumping terms
#clump0 = 0.0
#alpha_clump = 1.0
#beta_clump = 6.0
#gamma_clump = 3.0
xx_power.set_Flender_params(alpha0, n_nt, beta, eps_f * 1.e-6, eps_DM,
f_star, S_star, A_C, gamma_mod0,
gamma_mod_zslope, x_break, x_smooth, n_nt_mod,
clump0, alpha_clump, beta_clump, gamma_clump)
model = xx_power.return_xx_power_alt(x) # [erg cm^-2 s^-1 str^-1]^2
#sn = np.full(x.shape, 10.0**log_noise, dtype = np.float64)
#model += sn
#model /= beam(x)
diff = np.array(y - model, dtype=np.float64)
lnl = -0.5 * np.dot(diff, np.dot(invcov, np.transpose(diff)))
return lnl
