def plot_hist_and_fit_gauss(data_list,
binno=60,
normed=1,
facecolor="green",
linecolor='r--',
alpha=0.5):
"""
return (mu, sigma)
"""
# fit the data by maxwell-boltzmann distribution
# mawell.fit returns shape, loc, scale : tuple of floats
# MLEs for any shape statistics, followed by those for location and
# scale.
params = maxwell.fit(data_list)
print params
# plot the histogram of the data
#(n, bins, patches) = plt.hist(data_list, binno, range=(0, 50), normed=normed, facecolor=facecolor, alpha=alpha)
(n, bins, patches) = plt.hist(data_list,
binno,
normed=normed,
facecolor=facecolor,
alpha=alpha)
x = np.linspace(0, 25, 100)
# add a 'best fit' line
plt.plot(x, maxwell.pdf(x, *params), linecolor, lw=3)
print get_max_likelihood(data_list, params[0], params[1])
return params
def plot(p2D,pens,p2De,para,params_exp,thickness,tempres):
#print tempres
plt.subplot(511)
plt.hist(p2D[:,5], bins=20, normed=True)
x = np.linspace(0, 5, 80)
if para !=None :
plt.plot(x, maxwell.pdf(x, *para),'r',x,maxwell.cdf(x, *para), 'g')
plt.subplot(512)
plt.hist(pens, bins=20, normed=True)
z=np.linspace(0,500,200)
plt.xlim(0,2*thickness)
plt.plot(z, expon.pdf(z, *params_exp),'r')#plt.plot(z, expon.pdf(z, *params_exp),'r',z,expon.cdf(z, *params_exp), 'g')
plt.subplot(513)
plt.xlim(0,thickness+1)
plt.plot(p2D[:,0],p2D[:,1],'b.')
plt.subplot(514)
plt.ylim(-1*10**6,1*10**6)
plt.xlim(0,thickness+1)
plt.plot(p2De[:,0],p2De[:,1],'b.')
plt.subplot(515)
plt.plot(tempres[:,0],tempres[:,1],'r-')
plt.savefig()
plt.show()
return
def plot(p2D, pens, p2De, para, params_exp, thickness):
plt.subplot(411)
plt.hist(p2D[:, 5], bins=10, normed=True)
x = np.linspace(0, 5, 80)
plt.plot(x, maxwell.pdf(x, *para), 'r', x, maxwell.cdf(x, *para), 'g')
plt.subplot(412)
plt.hist(pens, bins=20, normed=True)
z = np.linspace(0, 500, 200)
plt.xlim(0, 2 * thickness)
plt.plot(
z, expon.pdf(z, *params_exp), 'r'
) #plt.plot(z, expon.pdf(z, *params_exp),'r',z,expon.cdf(z, *params_exp), 'g')
plt.subplot(413)
plt.xlim(0, thickness + 1)
plt.plot(p2D[:, 0], p2D[:, 1], 'b.')
plt.subplot(414)
plt.ylim(-1 * 10**6, 1 * 10**6)
plt.xlim(0, thickness + 1)
plt.plot(p2De[:, 0], p2De[:, 1], 'b.')
plt.show()
return
def gibbsDist():
fig, ax = plt.subplots(1, 1)
mean, var, skew, kurt = maxwell.stats(moments='mvsk')
x = np.linspace(maxwell.ppf(0.01), maxwell.ppf(0.99), 100)
ax.plot(x, maxwell.pdf(x), 'r-', lw=5, alpha=0.6, label='maxwell pdf')
ax.legend(loc='best', frameon=False)
plt.show()
def quiver_desired_velocity(crStats\
,further_conditioning = None
,grid_x=40,grid_y=40,small_incr=.00001\
,qty='vel'
,spec_type='gt'
,img_format='png'
,**kw):
x_class_v,y_class_v,u_means,v_means,u_delta,v_delta,u_all,v_all =\
sub_eval_desired_velocity_qtys(crStats
,further_conditioning\
,grid_x,grid_y,small_incr\
,qty\
,spec_type)
plt.figure()
plt.hist2d(u_delta,v_delta,**hist2d_param)
plt.title('Overall noise distribution')
plt.savefig(PATH_PREFIX + 'total_noise_%s_%s.%s' % (qty,spec_type,img_format))
rv = maxwell()
speed_delta = np.sqrt(np.asarray(u_delta)**2 + np.asarray(v_delta)**2)
loc,scale = maxwell.fit(speed_delta)
plt.figure()
plt.hist(speed_delta,**hist_param_noLog)
x = np.linspace(0,2,100)
plt.plot(x,maxwell.pdf(x,scale=scale,loc=loc))
plt.title('Overall abs noise distribution')
plt.savefig(PATH_PREFIX + 'maxwellian_noise_%s_%s.%s' % (qty,spec_type,img_format))
temperature = np.sqrt( np.asarray([np.var(us) for us in u_all]) + np.asarray([np.var(vs) for vs in v_all]) )
speed = [np.mean(np.sqrt(np.asarray(us)**2 + np.asarray(vs)**2)) for us,vs in zip(u_all,v_all) ]
plt.figure()
plt.quiver(x_class_v,y_class_v,u_means,v_means,temperature,**kw)
plt.colorbar()
plt.title('cross-realization "thermal" noise [m/s]')
plt.xlabel('x [m]')
plt.ylabel('y [m]')
plt.savefig(PATH_PREFIX + 'quiver_thermal_noise_%s_%s.%s' % (qty,spec_type,img_format))
plt.figure()
plt.quiver(x_class_v,y_class_v,u_means,v_means,speed,**kw)
plt.colorbar()
plt.title('average speed')
plt.xlabel('x [m]')
plt.ylabel('y [m]')
plt.savefig(PATH_PREFIX + 'quiver_average_modulus_%s_%s.%s' % (qty,spec_type,img_format))
def plot(p2D, pens, p2De, para, params_exp, thickness, tempres, petest,
electron_affinity, finame):
#print tempres
plt.subplot(511)
plt.xlabel('thickness[nm]')
plt.ylabel('P')
plt.hist(p2D[:, 5], bins=20, normed=True)
x = np.linspace(0, 5, 80)
if para != None:
plt.plot(x, maxwell.pdf(x, *para), 'r', x, maxwell.cdf(x, *para), 'g')
plt.subplot(512)
plt.hist(pens, bins=20, normed=True)
z = np.linspace(0, 500, 200)
plt.xlabel('thickness[nm]')
plt.ylabel('P')
plt.xlim(0, 2 * thickness)
plt.plot(
z, expon.pdf(z, *params_exp), 'r'
) #plt.plot(z, expon.pdf(z, *params_exp),'r',z,expon.cdf(z, *params_exp), 'g')
plt.subplot(513)
plt.xlim(0, thickness + 1)
plt.xlabel('thickness[nm]')
plt.ylabel('size[nm]')
plt.plot(p2D[:, 0], p2D[:, 1], 'b,')
plt.subplot(514)
plt.ylim(-1 * 10**6, 1 * 10**6)
plt.xlim(0, thickness + 1)
plt.xlabel('thickness[nm]')
plt.ylabel('size[nm]')
plt.plot(p2De[:, 0], p2De[:, 1], 'b,')
plt.subplot(515)
plt.xlabel('Time[s]')
plt.ylabel('count[1]')
smooth = 80
for i in np.arange(0, len(tempres)):
tempres[i,
1] = (np.sum(tempres[i:i + smooth, 1]) / smooth).astype(float)
plt.ylim(0, tempres[1, 1] * 1.5)
plt.plot(tempres[:, 0], tempres[:, 1], 'r-')
plt.savefig(finame + 'full_tk_%dpe_%.3fea_%.3f.pdf' %
(thickness, petest, electron_affinity))
plt.show()
return
def ln_prior_v_kick(v_kick, sigma=c.v_kick_sigma):
"""
Return the natural log of the prior probability on the SN kick velocity: ln P(v_kick).
Args:
v_kick : float, SN kick velocity.
sigma : float (default: constants.v_kick_sigma), dispersion velocity for
the Maxwellian distribution of birth kick magnitudes.
Returns:
ln_P_v_kick : float, natural logarithm of the prior on the SN kick velocity.
"""
if v_kick < 0.0: return -np.inf
return np.log(maxwell.pdf(v_kick, scale=sigma))
def plot_hist_and_fit_gauss(data_list, binno=60, normed=1, facecolor="green", linecolor='r--', alpha=0.5):
"""
return (mu, sigma)
"""
# fit the data by maxwell-boltzmann distribution
# mawell.fit returns shape, loc, scale : tuple of floats
# MLEs for any shape statistics, followed by those for location and
# scale.
params = maxwell.fit(data_list)
print params
# plot the histogram of the data
#(n, bins, patches) = plt.hist(data_list, binno, range=(0, 50), normed=normed, facecolor=facecolor, alpha=alpha)
(n, bins, patches) = plt.hist(data_list, binno, normed=normed, facecolor=facecolor, alpha=alpha)
x = np.linspace(0, 25, 100)
# add a 'best fit' line
plt.plot(x, maxwell.pdf(x, *params), linecolor, lw=3)
print get_max_likelihood(data_list, params[0], params[1])
return params
def vel_distribution(dm_p): #reads in particle class details (FROM ALAN AND CORRECT)
vrange = 10.**(np.linspace(1.,3.,num=100000.)) * units.km/units.s
print vrange
mass =10.*units.GeV/const.c**2
temp = (0.5 * dm_p.mass* (230. * units.km/units.s)**2)/const.k_B
print "Effective temp for DM particles moving at 230km/s ", temp.to(units.Kelvin)
a = np.sqrt(const.k_B * temp/mass)
print "Normalisation velocity ",a
scale = a
rv = maxwell.pdf(vrange, loc=0, scale=scale)
plt.plot(vrange,rv,'-',color='b') #rv instead of 3000
plt.title('Velocity Distribution')
#plt.show()
plt.clf()
#global v_values
v_values_i = maxwell.rvs(size=10000, loc=0, scale=scale) *units.m/units.s
v_values = ((v_values_i)*1000) / const.c
print("Velocity Values", v_values)
plt.hist(v_values,1000,color='b',normed=1)
plt.title('Velocity Samples')
#plt.show()
plt.clf()
return v_values
#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
Tracé d'une distribution de Maxwell
"""
__author__ = "Dominique Lefebvre"
__copyright__ = "Copyright 2019 - TangenteX.com"
__version__ = "1.0"
__date__ = "2 novembre 2019"
__email__ = "*****@*****.**"
from scipy import linspace
from matplotlib.pylab import figure, title, grid, xlim, xlabel, ylabel, plot
from scipy.stats import maxwell
# domaine
x_min = 0.0
x_max = 10.0
x = linspace(x_min, x_max, 500)
# calcul de la distribution de Maxwell
y = maxwell.pdf(x)
# tracé de la distribution
fig1 = figure(figsize=(10, 8))
plot(x, y, 'blue')
grid()
xlim(x_min, x_max)
title(u'Distribution de Maxwell', fontsize=14)
xlabel('x')
ylabel('y')
# In[8]:
temp = 400
kb = 1.380649e-23
# In[9]:
mean, var, skew, kurt = maxwell.stats(moments ='mvsk')
fig, ax = plt.subplots(1, 1)
x = np.linspace(maxwell.ppf(0.01),maxwell.ppf(0.99), 100)
ax.plot(x, maxwell.pdf(x), 'r-', lw=4, alpha=0.6, label='maxwell pdf')
plt.title('1D Maxwell-Boltzmann Distribution')
plt.xlabel('Speed (m/s)') # fix this
plt.ylabel('Probability Density (s/m)')
# In[10]:
m = 2*kb*temp/(np.pi*float(mean)**2)
print('At STP, \nmass of particle = %s kg' % (m))
# In[11]:
def ln_priors(y):
""" Priors on the model parameters
Parameters
----------
y : ra, dec, M1, M2, A, ecc, v_k, theta, phi, ra_b, dec_b, t_b
Current HMXB location (ra, dec) and 10 model parameters
Returns
-------
lp : float
Natural log of the prior
"""
# M1, M2, A, v_k, theta, phi, ra_b, dec_b, t_b = y
ra, dec, M1, M2, A, ecc, v_k, theta, phi, ra_b, dec_b, t_b = y
lp = 0.0
# P(M1)
if M1 < c.min_mass or M1 > c.max_mass: return -np.inf
norm_const = (c.alpha+1.0) / (np.power(c.max_mass, c.alpha+1.0) - np.power(c.min_mass, c.alpha+1.0))
lp += np.log( norm_const * np.power(M1, c.alpha) )
# M1 must be massive enough to evolve off the MS by t_obs
if load_sse.func_sse_tmax(M1) > t_b: return -np.inf
# P(M2)
# Normalization is over full q in (0,1.0)
q = M2 / M1
if q < 0.3 or q > 1.0: return -np.inf
lp += np.log( (1.0 / M1 ) )
# P(ecc)
if ecc < 0.0 or ecc > 1.0: return -np.inf
lp += np.log(2.0 * ecc)
# P(A)
if A*(1.0-ecc) < c.min_A or A*(1.0+ecc) > c.max_A: return -np.inf
norm_const = np.log(c.max_A) - np.log(c.min_A)
lp += np.log( norm_const / A )
# A must avoid RLOF at ZAMS, by a factor of 2
r_1_roche = binary_evolve.func_Roche_radius(M1, M2, A*(1.0-ecc))
if 2.0 * load_sse.func_sse_r_ZAMS(M1) > r_1_roche: return -np.inf
# P(v_k)
if v_k < 0.0: return -np.inf
lp += np.log( maxwell.pdf(v_k, scale=c.v_k_sigma) )
# P(theta)
if theta <= 0.0 or theta >= np.pi: return -np.inf
lp += np.log(np.sin(theta) / 2.0)
# P(phi)
if phi < 0.0 or phi > np.pi: return -np.inf
lp += -np.log( np.pi )
# Get star formation history
sf_history.load_sf_history()
sfh = sf_history.get_SFH(ra_b, dec_b, t_b, sf_history.smc_coor, sf_history.smc_sfh)
if sfh <= 0.0: return -np.inf
# P(alpha, delta)
# From spherical geometric effect, we need to care about cos(declination)
lp += np.log(np.cos(c.deg_to_rad * dec_b) / 2.0)
##################################################################
# We add an additional prior that scales the RA and Dec by the
# area available to it, i.e. pi theta^2, where theta is the angle
# of the maximum projected separation over the distance.
#
# Still under construction
##################################################################
M1_b, M2_b, A_b = binary_evolve.func_MT_forward(M1, M2, A, ecc)
A_c, v_sys, ecc = binary_evolve.func_SN_forward(M1_b, M2_b, A_b, v_k, theta, phi)
if ecc < 0.0 or ecc > 1.0 or np.isnan(ecc): return -np.inf
# Ensure that we only get non-compact object companions
tobs_eff = binary_evolve.func_get_time(M1, M2, t_b)
M_tmp, M_dot_tmp, R_tmp, k_type = load_sse.func_get_sse_star(M2_b, tobs_eff)
if int(k_type) > 9: return -np.inf
# t_sn = (t_b - func_sse_tmax(M1)) * 1.0e6 * yr_to_sec # The time since the primary's core collapse
# theta_max = (v_sys * t_sn) / dist_LMC # Unitless
# area = np.pi * rad_to_dec(theta_max)**2
# lp += np.log(1.0 / area)
##################################################################
# Instead, let's estimate the number of stars formed within a cone
# around the observed position, over solid angle and time.
# Prior is in Msun/Myr/steradian
##################################################################
t_min = load_sse.func_sse_tmax(M1) * 1.0e6 * c.yr_to_sec
t_max = (load_sse.func_sse_tmax(M2_b) - binary_evolve.func_get_time(M1, M2, 0.0)) * 1.0e6 * c.yr_to_sec
if t_max-t_min < 0.0: return -np.inf
theta_C = (v_sys * (t_max - t_min)) / c.dist_SMC
stars_formed = get_stars_formed(ra, dec, t_min, t_max, v_sys, c.dist_SMC)
if stars_formed == 0.0: return -np.inf
volume_cone = (np.pi/3.0 * theta_C**2 * (t_max - t_min) / c.yr_to_sec / 1.0e6)
lp += np.log(sfh / stars_formed / volume_cone)
##################################################################
# # P(t_b | alpha, delta)
# sfh_normalization = 1.0e-6
# lp += np.log(sfh_normalization * sfh)
# Add a prior so that the post-MT secondary is within the correct bounds
M2_c = M1 + M2 - load_sse.func_sse_he_mass(M1)
if M2_c > c.max_mass or M2_c < c.min_mass: return -np.inf
# Add a prior so the effective time remains bounded
t_eff_obs = binary_evolve.func_get_time(M1, M2, t_b)
if t_eff_obs < 0.0: return -np.inf
if t_b * 1.0e6 * c.yr_to_sec < t_min: return -np.inf
if t_b * 1.0e6 * c.yr_to_sec > t_max: return -np.inf
return lp
def ln_priors_population(y):
""" Priors on the model parameters
Parameters
----------
y : M1, M2, A, ecc, v_k, theta, phi, ra_b, dec_b, t_b
10 model parameters
Returns
-------
lp : float
Natural log of the prior
"""
M1, M2, A, ecc, v_k, theta, phi, ra_b, dec_b, t_b = y
lp = 0.0
# P(M1)
if M1 < c.min_mass or M1 > c.max_mass: return -np.inf
norm_const = (c.alpha+1.0) / (np.power(c.max_mass, c.alpha+1.0) - np.power(c.min_mass, c.alpha+1.0))
lp += np.log( norm_const * np.power(M1, c.alpha) )
# M1 must be massive enough to evolve off the MS by t_obs
if load_sse.func_sse_tmax(M1) > t_b: return -np.inf
# P(M2)
# Normalization is over full q in (0,1.0)
q = M2 / M1
if q < 0.3 or q > 1.0: return -np.inf
lp += np.log( (1.0 / M1 ) )
# P(ecc)
if ecc < 0.0 or ecc > 1.0: return -np.inf
lp += np.log(2.0 * ecc)
# P(A)
if A*(1.0-ecc) < c.min_A or A*(1.0+ecc) > c.max_A: return -np.inf
norm_const = np.log(c.max_A) - np.log(c.min_A)
lp += np.log( norm_const / A )
# A must avoid RLOF at ZAMS, by a factor of 2
r_1_roche = binary_evolve.func_Roche_radius(M1, M2, A*(1.0-ecc))
if 2.0 * load_sse.func_sse_r_ZAMS(M1) > r_1_roche: return -np.inf
# P(v_k)
if v_k < 0.0: return -np.inf
lp += np.log( maxwell.pdf(v_k, scale=c.v_k_sigma) )
# P(theta)
if theta <= 0.0 or theta >= np.pi: return -np.inf
lp += np.log(np.sin(theta) / 2.0)
# P(phi)
if phi < 0.0 or phi > np.pi: return -np.inf
lp += -np.log( np.pi )
# Get star formation history
sfh = sf_history.get_SFH(ra_b, dec_b, t_b, sf_history.smc_coor, sf_history.smc_sfh)
if sfh <= 0.0: return -np.inf
lp += np.log(sfh)
# P(alpha, delta)
# From spherical geometric effect, scale by cos(declination)
lp += np.log(np.cos(c.deg_to_rad*dec_b) / 2.0)
M1_b, M2_b, A_b = binary_evolve.func_MT_forward(M1, M2, A, ecc)
A_c, v_sys, ecc = binary_evolve.func_SN_forward(M1_b, M2_b, A_b, v_k, theta, phi)
if ecc < 0.0 or ecc > 1.0 or np.isnan(ecc): return -np.inf
# Ensure that we only get non-compact object companions
tobs_eff = binary_evolve.func_get_time(M1, M2, t_b)
M_tmp, M_dot_tmp, R_tmp, k_type = load_sse.func_get_sse_star(M2_b, tobs_eff)
if int(k_type) > 9: return -np.inf
# Add a prior so that the post-MT secondary is within the correct bounds
M2_c = M1 + M2 - load_sse.func_sse_he_mass(M1)
if M2_c > c.max_mass or M2_c < c.min_mass: return -np.inf
# Add a prior so the effective time remains bounded
t_eff_obs = binary_evolve.func_get_time(M1, M2, t_b)
if t_eff_obs < 0.0: return -np.inf
t_max = (load_sse.func_sse_tmax(M2_b) - binary_evolve.func_get_time(M1, M2, 0.0))
if t_b > t_max: return -np.inf
return lp
from scipy.stats import maxwell
import matplotlib.pyplot as plt
fig, ax = plt.subplots(1, 1)
# Calculate a few first moments:
mean, var, skew, kurt = maxwell.stats(moments='mvsk')
# Display the probability density function (``pdf``):
x = np.linspace(maxwell.ppf(0.01),
maxwell.ppf(0.99), 100)
ax.plot(x, maxwell.pdf(x),
'r-', lw=5, alpha=0.6, label='maxwell pdf')
# Alternatively, the distribution object can be called (as a function)
# to fix the shape, location and scale parameters. This returns a "frozen"
# RV object holding the given parameters fixed.
# Freeze the distribution and display the frozen ``pdf``:
rv = maxwell()
ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
# Check accuracy of ``cdf`` and ``ppf``:
vals = maxwell.ppf([0.001, 0.5, 0.999])
np.allclose([0.001, 0.5, 0.999], maxwell.cdf(vals))
# True
# Generate random numbers:
obj /= obj.max()
obj_samples.append(obj)
subplot(412)
grid(True)
axis([350,750,0,1.5])
xlabel('Wavelength $\lambda$ (nm)')
ylabel('Reflectance coefficient')
title(r'Sample reflectivity behaviour')
for obj in obj_samples:
plot(obj)
###############################
#### Black camera reflectivity
black_camera = maxwell.pdf(x, loc=350, scale=200,size=1000)
black_camera /= black_camera.max() * black_camera_absorbance
subplot(413)
grid(True)
axis([350,750,0,1.5])
xlabel('Wavelength $\lambda$ (nm)')
ylabel('Reflectance coefficient')
title(r'Black camera reflectivity behaviour')
plot(black_camera)
###############################
#### Reflected light from object and camera
subplot(414)
grid(True)
def get_max_likelihood(data_list, loc, scale, weight=45):
pdf_array = maxwell.pdf(data_list, loc, scale)
likelihood = 1
for item in pdf_array:
likelihood = item * weight * likelihood
return likelihood
'figure.subplot.left':0.15,
'figure.subplot.right':0.92}
hexcols = ['#332288', '#88CCEE', '#44AA99', '#117733', '#999933', '#DDCC77',\
'#CC6677', '#882255', '#AA4499', '#661100', '#6699CC', '#AA4466','#4477AA']
mpl.rcParams.update(params)
A=np.array([np.append([vkick],kicks.sample_kick_distribution_P(23,5.5,55,1.4,vdist=lambda x:[float(vkick)], num_v=5, num_theta=400,num_phi=100)) for vkick in range(0,701,5)])
print(A)
print(A[:,0])
print(A[:,1])
print(A[:,2])
fig, axes= plt.subplots(1)
maxw = axes.fill_between(A[:,0],0,maxwell.pdf(A[:,0], scale=265.)/max(maxwell.pdf(A[:,0],scale=265.)),color="b", alpha=0.2, label="Maxwellian, $\\sigma=265~\\rm km~s^{-1}$")
merge, = axes.plot(A[:,0],10*A[:,1], color=hexcols[2],label="GW merge fraction $\\times$ 10")
disrupt, = axes.plot(A[:,0],A[:,2], color=hexcols[8],ls="--", label="Disrupt fraction")
axes.set_xlabel("$v_{\\rm kick}~\\rm[km~s^{-1}]$")
axes.set_ylabel("fraction")
#axes.set_xlim([0,50])
axes.set_ylim([0,1.19])
axes.legend([maxw,merge,disrupt],["Maxwellian, $\\sigma=265~\\rm km~s^{-1}$", "GW merge fraction $\\times$ 10", "Disrupt fraction"], loc="upper left", fontsize=7)
plt.savefig("kick_dist.pdf")
#plt.clf()
#plt.close(plt.gcf())
M = 66.9792e6 #keV: Mass of Nucleus
M_det = 5.60959e32 #keV: Mass of Detector 1kg
#NSI parameters: 0
from scipy.integrate import quad
from scipy.stats import maxwell
flux_1m = 1.511067123220e12 #/cm^2/s at 1m
flux_r = lambda r: flux_1m / (r * r) #r in meters
total_flux = flux_r(L) #/cm^2/s at 1m
#np.arange(1e2,20e3,1e2)#E=100keV - 20MeV with 100keV step
form_n_flux = lambda En: maxwell.pdf((En + 1.9e3) / 1.7e3) #En in keV
total = quad(lambda En: form_n_flux(En), 0, np.inf)[0]
norm_n_flux = lambda En: form_n_flux(En) / total
total_norm_n_flux = quad(norm_n_flux, 0, np.inf)[0]
n_flux = lambda En: total_flux * norm_n_flux(En)
total_n = quad(n_flux, 0, np.inf)[0]
#t=1#second
Gf2 = (1.16637e-17)**2 #keV-4
#area_det=34.322512#cm^2 /((4)*math.pi*100*100)
C_T = lambda En, T: (Gf2 * M / (2 * math.pi)) * (((G_V + G_A)**2) + ((
(G_V - G_A)**2) * ((1 - (T / En))**2)) - (((G_V**2) - (G_A**2)) *
(M * T / (En * En))))
def get_max_likelihood(data_list, loc, scale, weight=45):
pdf_array = maxwell.pdf(data_list, loc, scale)
likelihood = 1
for item in pdf_array:
likelihood = item * weight * likelihood
return likelihood
from scipy.stats import maxwell import numpy as np import matplotlib.pyplot as plt fig, ax = plt.subplots(1, 1) mean, var, skew, kurt = maxwell.stats(moments='mvsk') x = np.linspace(maxwell.ppf(0.01), maxwell.ppf(0.99), 10000) ax.plot(x, maxwell.pdf(x), 'r-', lw=5.5, alpha=0.6) vals = maxwell.ppf([0.001, 0.5, 0.999]) np.allclose([0.001, 0.5, 0.999], maxwell.cdf(vals)) r = maxwell.rvs(size=1000) ax.hist(r, density=True, histtype='stepfilled', alpha=0.2) ax.legend(loc='best', frameon=False) plt.show() print(mean, var, skew, kurt)
return args
args = parse_arguments()
option = args['option']
data_name = args['dataname']
# --------------------------------------------------------- #
# Import Data! (3/4) #
# --------------------------------------------------------- #
mean, var, skew, kurt = maxwell.stats(moments='mvsk')
if 0:
x = np.linspace(maxwell.ppf(0.0001), maxwell.ppf(0.9999), 1000)
y = 16 * maxwell.pdf(x)
else:
a = 1
x = np.linspace(0.00001, 4.9, 1000)
y2 = -1 * a * x**2
yf = a * x**2
y = yf * np.exp(y2)
x = np.linspace(1, 250000, 1000)
# y1 = x**2
# ye = np.exp((-1 * y1) * 0.5)
# y = np.sqrt(((2/math.pi) * y1)) * ye
mb = ax1.plot(x, y, 'r-', lw=5, alpha=0.6, label='maxwell pdf')
ax1.fill_between(x,
0,
def adjustar_Maxwell(mid_pointa, histoa):
a_ajustar_ray = lambda x,l,s: maxwell.pdf(x, l, s)
popt_wei, pcov = curve_fit(a_ajustar_ray, mid_pointa, histoa)
print(popt_wei, pcov)
ajustado_ray = a_ajustar_ray(mid_pointa, popt_wei[0], popt_wei[1])
return(ajustado_ray)