def generate_initial_velocities(atoms, m, T):
v = []
for n in range(len(atoms)):
a = np.sqrt((k[0] * T) / m[n])
transl_vec = np.full(3, maxwell(scale=a).stats('m') / 2)
distr = maxwell.rvs(scale=a, size=3)
v.append((distr - transl_vec) * 2)
return np.array(v)
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_velocity_distribution(snap, temp):
"""
Plots histogram of atomic speeds against analytical Maxwell-Boltzman
distribution for input temperature, ``temp``.
Parameters
----------
snap : :class:`mdhandle.snap.Snap`
:class:`~mdhandle.snap.Snap` object.
temp : float
Temperature for analytical Maxwell distribution
Returns
--------
0
Successfully completed velocity distribution plot.
-1
An error has occured and velocity distribution plot was not generated.
"""
kb = units.KBOLTZ[snap.meta['units']]
speed = vectors.magnitude(snap.get_vector(('vx', 'vy', 'vz')))*\
units.VELOCITY[snap.meta['units']]**2
if np.unique(snap.get_scalar('mass')).size > 1:
logger.warning('Cannot handle polyatomic system')
return -1
# Taking mass as constant based on value at index 0
mass = snap.get_scalar('mass')[0]*units.MASS[snap.meta['units']]
# See: <http://mathworld.wolfram.com/MaxwellDistribution.html>
# Energy factor is applied to bring to SI units for calculation.
# if metal or other unit system.
a = np.sqrt(kb*temp/mass * units.ENERGY[snap.meta['units']])
scale = 1 / np.sqrt(a)
# Maxwell-Boltzmann RV based on temperature
maxwell_rv = maxwell(loc=0, scale=scale)
x = np.linspace(0, np.minimum( maxwell_rv.dist.b, speed.max() ))
# Plotting
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(x, maxwell_rv.pdf(x), linewidth=2)
n, bins, patches = ax.hist(speed, 100, normed=True,
facecolor='red', alpha=0.75)
return 0
def maxwell_boltzmann(T, m, lengthscale=1):
# Mean molecular weight
if isinstance(m, numbers.Real):
m *= atomic_mass
# Temperature
if isinstance(T, numbers.Real):
T *= Kelvin
if isinstance(lengthscale, numbers.Real):
T *= meter
# Maxwell-Boltzmann velocity distribution
# velocity scale value in units of a per sec
vscale = (np.sqrt(k_B * T.si / m.si) / lengthscale.si).to('/s')
return maxwell(0, vscale.value)
def run():
min_long = np.pi / 12
max_long = 2 * np.pi - np.pi / 12
LongitudeGenerator = stats.uniform(loc=min_long, scale=max_long - min_long)
# Generate, then freeze the distribution:
min_lat = np.pi / 6
max_lat = np.pi / 4
LatitudeGenerator = math_operations.SphericalLatitudeGen(a=min_lat,
b=max_lat)()
n_points = 1000
theta_points = LongitudeGenerator.rvs(size=n_points)
phi_points = LatitudeGenerator.rvs(size=n_points)
points = math_operations.vect_from_spherical_coords(
theta_points, phi_points)
MyPointCloud = PointCloud(points,
point_color="k",
display_marker='.',
point_size=4,
linewidth=0,
name="Uniformly distributed points")
ax_dic = scatter_plot_3d(MyPointCloud, savefile='hold')
set_3d_axes_equal(ax_dic['ax'])
plt.legend()
plt.show()
# ============================================================= #
max_val = 100
rv_gen_1 = stats.uniform(0, 10)
random_walk_1 = math_operations.stochastic_flare_process(
stop_value=max_val, distribution=rv_gen_1)
plt.plot(random_walk_1, color='r', label="Uniform")
rv_gen_2 = stats.maxwell(0, 3)
random_walk_2 = math_operations.stochastic_flare_process(
stop_value=max_val, distribution=rv_gen_2)
plt.plot(random_walk_2, color='k', label='Maxwell')
plt.legend()
plt.show()
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:
r = maxwell.rvs(size=1000)
# And compare the histogram:
ax.hist(r, density=True, histtype='stepfilled', alpha=0.2)
# -*- coding: UTF-8 -*-
# Ejemplo de distrbuciones del módulo stats de Scipy
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import cauchy, gamma, maxwell, norm
SAMPLE_SIZE = 100
x = np.linspace(-5, 5, 1000)
# Inicializo las distribuciones
cauchy_dist = cauchy()
gamma_dist = gamma(1, scale=2.)
maxwell_dist = maxwell()
norm_dist = norm()
# Calculo la funcion de densidad de probabilidad de cada distribucion
cauchy_pdf = cauchy_dist.pdf(x)
gamma_pdf = gamma_dist.pdf(x)
maxwell_pdf = maxwell_dist.pdf(x)
norm_pdf = norm_dist.pdf(x)
fig = plt.figure("Distribuciones")
sp1 = fig.add_subplot(221, title='Distribucion de Cauchy')
sp2 = fig.add_subplot(222, title='Distribucion Gamma')
sp3 = fig.add_subplot(223, title='Distribucion de Maxwell')
sp4 = fig.add_subplot(224, title='Distribucion Normal')
def all_dists():
# dists param were taken from scipy.stats official
# documentaion examples
# Total - 89
return {
"alpha":
stats.alpha(a=3.57, loc=0.0, scale=1.0),
"anglit":
stats.anglit(loc=0.0, scale=1.0),
"arcsine":
stats.arcsine(loc=0.0, scale=1.0),
"beta":
stats.beta(a=2.31, b=0.627, loc=0.0, scale=1.0),
"betaprime":
stats.betaprime(a=5, b=6, loc=0.0, scale=1.0),
"bradford":
stats.bradford(c=0.299, loc=0.0, scale=1.0),
"burr":
stats.burr(c=10.5, d=4.3, loc=0.0, scale=1.0),
"cauchy":
stats.cauchy(loc=0.0, scale=1.0),
"chi":
stats.chi(df=78, loc=0.0, scale=1.0),
"chi2":
stats.chi2(df=55, loc=0.0, scale=1.0),
"cosine":
stats.cosine(loc=0.0, scale=1.0),
"dgamma":
stats.dgamma(a=1.1, loc=0.0, scale=1.0),
"dweibull":
stats.dweibull(c=2.07, loc=0.0, scale=1.0),
"erlang":
stats.erlang(a=2, loc=0.0, scale=1.0),
"expon":
stats.expon(loc=0.0, scale=1.0),
"exponnorm":
stats.exponnorm(K=1.5, loc=0.0, scale=1.0),
"exponweib":
stats.exponweib(a=2.89, c=1.95, loc=0.0, scale=1.0),
"exponpow":
stats.exponpow(b=2.7, loc=0.0, scale=1.0),
"f":
stats.f(dfn=29, dfd=18, loc=0.0, scale=1.0),
"fatiguelife":
stats.fatiguelife(c=29, loc=0.0, scale=1.0),
"fisk":
stats.fisk(c=3.09, loc=0.0, scale=1.0),
"foldcauchy":
stats.foldcauchy(c=4.72, loc=0.0, scale=1.0),
"foldnorm":
stats.foldnorm(c=1.95, loc=0.0, scale=1.0),
# "frechet_r": stats.frechet_r(c=1.89, loc=0.0, scale=1.0),
# "frechet_l": stats.frechet_l(c=3.63, loc=0.0, scale=1.0),
"genlogistic":
stats.genlogistic(c=0.412, loc=0.0, scale=1.0),
"genpareto":
stats.genpareto(c=0.1, loc=0.0, scale=1.0),
"gennorm":
stats.gennorm(beta=1.3, loc=0.0, scale=1.0),
"genexpon":
stats.genexpon(a=9.13, b=16.2, c=3.28, loc=0.0, scale=1.0),
"genextreme":
stats.genextreme(c=-0.1, loc=0.0, scale=1.0),
"gausshyper":
stats.gausshyper(a=13.8, b=3.12, c=2.51, z=5.18, loc=0.0, scale=1.0),
"gamma":
stats.gamma(a=1.99, loc=0.0, scale=1.0),
"gengamma":
stats.gengamma(a=4.42, c=-3.12, loc=0.0, scale=1.0),
"genhalflogistic":
stats.genhalflogistic(c=0.773, loc=0.0, scale=1.0),
"gilbrat":
stats.gilbrat(loc=0.0, scale=1.0),
"gompertz":
stats.gompertz(c=0.947, loc=0.0, scale=1.0),
"gumbel_r":
stats.gumbel_r(loc=0.0, scale=1.0),
"gumbel_l":
stats.gumbel_l(loc=0.0, scale=1.0),
"halfcauchy":
stats.halfcauchy(loc=0.0, scale=1.0),
"halflogistic":
stats.halflogistic(loc=0.0, scale=1.0),
"halfnorm":
stats.halfnorm(loc=0.0, scale=1.0),
"halfgennorm":
stats.halfgennorm(beta=0.675, loc=0.0, scale=1.0),
"hypsecant":
stats.hypsecant(loc=0.0, scale=1.0),
"invgamma":
stats.invgamma(a=4.07, loc=0.0, scale=1.0),
"invgauss":
stats.invgauss(mu=0.145, loc=0.0, scale=1.0),
"invweibull":
stats.invweibull(c=10.6, loc=0.0, scale=1.0),
"johnsonsb":
stats.johnsonsb(a=4.32, b=3.18, loc=0.0, scale=1.0),
"johnsonsu":
stats.johnsonsu(a=2.55, b=2.25, loc=0.0, scale=1.0),
"ksone":
stats.ksone(n=1e03, loc=0.0, scale=1.0),
"kstwobign":
stats.kstwobign(loc=0.0, scale=1.0),
"laplace":
stats.laplace(loc=0.0, scale=1.0),
"levy":
stats.levy(loc=0.0, scale=1.0),
"levy_l":
stats.levy_l(loc=0.0, scale=1.0),
"levy_stable":
stats.levy_stable(alpha=0.357, beta=-0.675, loc=0.0, scale=1.0),
"logistic":
stats.logistic(loc=0.0, scale=1.0),
"loggamma":
stats.loggamma(c=0.414, loc=0.0, scale=1.0),
"loglaplace":
stats.loglaplace(c=3.25, loc=0.0, scale=1.0),
"lognorm":
stats.lognorm(s=0.954, loc=0.0, scale=1.0),
"lomax":
stats.lomax(c=1.88, loc=0.0, scale=1.0),
"maxwell":
stats.maxwell(loc=0.0, scale=1.0),
"mielke":
stats.mielke(k=10.4, s=3.6, loc=0.0, scale=1.0),
"nakagami":
stats.nakagami(nu=4.97, loc=0.0, scale=1.0),
"ncx2":
stats.ncx2(df=21, nc=1.06, loc=0.0, scale=1.0),
"ncf":
stats.ncf(dfn=27, dfd=27, nc=0.416, loc=0.0, scale=1.0),
"nct":
stats.nct(df=14, nc=0.24, loc=0.0, scale=1.0),
"norm":
stats.norm(loc=0.0, scale=1.0),
"pareto":
stats.pareto(b=2.62, loc=0.0, scale=1.0),
"pearson3":
stats.pearson3(skew=0.1, loc=0.0, scale=1.0),
"powerlaw":
stats.powerlaw(a=1.66, loc=0.0, scale=1.0),
"powerlognorm":
stats.powerlognorm(c=2.14, s=0.446, loc=0.0, scale=1.0),
"powernorm":
stats.powernorm(c=4.45, loc=0.0, scale=1.0),
"rdist":
stats.rdist(c=0.9, loc=0.0, scale=1.0),
"reciprocal":
stats.reciprocal(a=0.00623, b=1.01, loc=0.0, scale=1.0),
"rayleigh":
stats.rayleigh(loc=0.0, scale=1.0),
"rice":
stats.rice(b=0.775, loc=0.0, scale=1.0),
"recipinvgauss":
stats.recipinvgauss(mu=0.63, loc=0.0, scale=1.0),
"semicircular":
stats.semicircular(loc=0.0, scale=1.0),
"t":
stats.t(df=2.74, loc=0.0, scale=1.0),
"triang":
stats.triang(c=0.158, loc=0.0, scale=1.0),
"truncexpon":
stats.truncexpon(b=4.69, loc=0.0, scale=1.0),
"truncnorm":
stats.truncnorm(a=0.1, b=2, loc=0.0, scale=1.0),
"tukeylambda":
stats.tukeylambda(lam=3.13, loc=0.0, scale=1.0),
"uniform":
stats.uniform(loc=0.0, scale=1.0),
"vonmises":
stats.vonmises(kappa=3.99, loc=0.0, scale=1.0),
"vonmises_line":
stats.vonmises_line(kappa=3.99, loc=0.0, scale=1.0),
"wald":
stats.wald(loc=0.0, scale=1.0),
"weibull_min":
stats.weibull_min(c=1.79, loc=0.0, scale=1.0),
"weibull_max":
stats.weibull_max(c=2.87, loc=0.0, scale=1.0),
"wrapcauchy":
stats.wrapcauchy(c=0.0311, loc=0.0, scale=1.0),
}
# Ejemplo de distrbuciones del módulo stats de Scipy
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import cauchy, gamma, maxwell, norm
SAMPLE_SIZE = 100
x = np.linspace(-5,5,1000)
# Inicializo las distribuciones
cauchy_dist = cauchy()
gamma_dist = gamma(1, scale=2.)
maxwell_dist = maxwell()
norm_dist = norm()
# Calculo la funcion de densidad de probabilidad de cada distribucion
cauchy_pdf = cauchy_dist.pdf(x)
gamma_pdf = gamma_dist.pdf(x)
maxwell_pdf = maxwell_dist.pdf(x)
norm_pdf = norm_dist.pdf(x)
fig = plt.figure("Distribuciones")
sp1 = fig.add_subplot(221, title='Distribucion de Cauchy')
sp2 = fig.add_subplot(222, title='Distribucion Gamma')
sp3 = fig.add_subplot(223, title='Distribucion de Maxwell')
sp4 = fig.add_subplot(224, title='Distribucion Normal')