def ppf_phi ( x ):
return sin2x.ppf( x )
''' Created on 27.03.2012 @author: Axel ''' from stats.pdistrib.sin2x_distr import sin2x print sin2x.ppf(1)
# joint probability density function of embedded lengths and inclination angles
#e = make_ogrid([l, phi])
#m.surf(e[0], e[1], l*np.cos(phi[:,np.newaxis]))
#m.surf(e[0], e[1], 1./2*np.ones_like(l)*np.sin(2.*phi[:,np.newaxis]))
#m.show()
# exact solution of number of fibers with distance from crack
sim = 10000.
def mc(z, uhel, delka):
return np.sum(delka * np.cos(uhel) > z)/sim
n_list = []
z_arr = np.linspace(0,1,50)
for z in z_arr:
n_list.append(mc(z,sin2x.ppf(np.random.rand(sim)),
uniform(loc = 0, scale = 1).ppf(np.random.rand(sim))))
def exact(lf, z):
return (lf-2*z)**2/lf**2
def power(z):
return np.ones_like(z) - 2*z + z**2
plt.plot(z_arr,n_list, color = 'red', lw = 3, ls = 'dashed', label = 'MC')
plt.plot(z_arr,exact(2.,z_arr), color = 'black', lw = 1, label = 'analytical')
plt.plot(z_arr,power(z_arr), color = 'green', lw = 2, label = 'power series')
plt.legend(loc = 'best')
plt.ylim(0,1.1)
plt.show()
import numpy as np
from math import pi as Pi
from matplotlib import pyplot as plt
x = np.linspace( 0, Pi / 2 , 10000 )
pdf = sin2x.pdf( x )
sin2stats = sin2x.stats()
#plt.plot( x, y2 )
plt.fill( x, pdf, facecolor = 'red', alpha = 0.2 , hatch = '\\' )
plt.axvline( x = sin2stats[0] , linewidth = 2.0, color = 'red' )
plt.xlabel( '$\phi$ in [$Rad$]', fontsize = 20 )
plt.ylabel( '$f_\phi (\phi)$', fontsize = 22 )
plt.title( 'Dichtefunktion PDF $sin(2\phi)$' , fontsize = 20 )
plt.xlim( 0, Pi / 2 )
legend_names = ['Erwartungswert $E_\phi(\phi)$', 'Dichtefunktion $sin(x)$']
plt.legend( legend_names, 'upper left' )
plt.show()
ppf_x = np.linspace( 0, 1 , 10000 )
ppf = sin2x.ppf( ppf_x )
ppf[-1] = 0
nulls = np.zeros( len( ppf ) )
#plt.fill( x, ppf, facecolor = 'red', alpha = 0.2 , hatch = '/' )
plt.fill( ppf_x , ppf, facecolor = 'red', alpha = 0.2 , hatch = '\\' )
plt.title( 'Inverse Verteilungsfunktion PPF $sin(2\phi)$' , fontsize = 20 )
plt.xlabel( '$F_\phi(\phi)$', fontsize = 20 )
plt.ylabel( '$\phi$ in [$Rad$]', fontsize = 22 )
plt.axhline( y = sin2stats[0] , linewidth = 2.0, color = 'red' )
legend_names2 = ['Erwartungswert $E_\phi(\phi)$', 'Inverse Verteilungsfunktion $F_\phi^{-1}(\phi)$']
plt.legend( legend_names2, 'upper left' )
plt.show()
