def fig2():
'''
Plot histogram and solve characteristics of probability_cut_nooverlapsability, that we cut fibers.
Compare with binomial distribution.
Set n_sim >> 1
'''
figure( 2 )
delta = 0.
p = probability_cut_nooverlaps( spec.l_x, fib.lf, delta )
rvb = binom( fib.n, p )
rvp = poisson( fib.n * p )
rvn = norm( fib.n * p, sqrt( fib.n * p * ( 1 - p ) ) )
graph_from = floor( bin_mean - 4 * bin_stdv )
graph_to = floor( bin_mean + 4 * bin_stdv ) + 1
x = arange( graph_from , graph_to )
plot( x, n_sim * rvb.pmf( x ), color = 'red', linewidth = 2, label = 'Binomial' )
plot( x, n_sim * rvp.pmf( x ), color = 'green', linewidth = 2, label = 'Poisson' )
plot( x, n_sim * rvn.pdf( x ), color = 'blue', linewidth = 2, label = 'Normal' )
#plot( x, 20 * rv.pmf( x ) )
pdf, bins, patches = hist( v, n_sim, normed = 0 ) #, facecolor='green', alpha=1
#set_xlim( bin_mean - 2 * bin_stdv, bin_mean + 2 * bin_stdv )
#plot( sx, sy, 'rx' ) # centroids
#print sum( pdf * diff( bins ) )
legend()
draw()
def cut_fiber_distrib( L, l, phi ):
if L >= 2 * l:
return l * cos( phi ) * sin( phi ) / ( L - l * cos( phi ) ) / probability_cut_nooverlaps( L, l, 0 )
#if phi > 0 and phi < arccos( L / l / 2. ): #L > l and L < 2 * l * cos( phi ):
else:
return ( l * cos( phi ) * sin( phi ) / ( L - l * cos( phi ) ) / probability_cut_nooverlaps( L, l, 0 ) ) * Heaviside( phi - arccos( L / 2. / l ) ) * Heaviside( pi / 2. - phi ) + sin( phi ) / probability_cut_nooverlaps( L, l, 0 ) * Heaviside( phi ) * Heaviside( arccos( L / 2. / l ) - phi )
def cut_fibers():
'''
Plot cut fibers (only ellipses), solve mean value of area and embedded length of cut fibers.
Plot histogram of embedded length.
'''
mask = matrix( fib.cut_func( sx, lx, sec ).astype( 'bool' ) )
sx_cut = sx[ mask ]
sy_cut = sy[ mask ]
sz_cut = sz[ mask ]
phi_x_cut = phi_x[ mask ]
theta_cut = theta[ mask ]
def plot_cross_cut():
#plot cut plane with crossection of cut fibers
fig55 = figure( 55 )
title( 'Cut fibers area (ellipses)' )
ax55 = Axes( fig55, [.1, .1, .8, .8] )
fig55.add_axes( ax55 )
for i in range( 0, len( phi_x_cut ) ):
sy_c = sy_cut[i] + ( sec - sx_cut[i] ) / cos( phi_x_cut[i] ) * sin( phi_x_cut[i] ) * cos( theta_cut[i] )
sz_c = sz_cut[i] + ( sec - sx_cut[i] ) / cos( phi_x_cut[i] ) * sin( phi_x_cut[i] ) * sin( theta_cut[i] )
if ( 0 < phi_x_cut[i] < arctan( ( fib.lf ) / fib.df ) ) and ( sx_cut[i] - fib.lf / 2. * cos( phi_x_cut[i] ) + fib.df / 2. * sin( phi_x_cut[i] ) < sec < sx_cut[i] + fib.lf / 2. * cos( phi_x_cut[i] ) - fib.df / 2. * sin( phi_x_cut[i] ) ):
patch = Ellipse( [ sy_c, sz_c ] , fib.df, fib.df / cos( phi_x_cut[i] ), theta_cut[i] * 180 / pi , color = 'black' )
ax55.add_artist( patch )
ax55.set_xlim( -spec.l_y / 2., spec.l_y / 2. )
ax55.set_ylim( -spec.l_z / 2., spec.l_z / 2. )
#plot_cross_cut() #plot cut plane
A_cut = sum( cut_area_func( fib.df, fib.lf, sx_cut, phi_x_cut, sec ) )
le_cut = le_sim( phi_x_cut, abs( sx_cut - sec * ones_like( sx_cut ) ), fib.lf )
le_cut_null = le_sim( phi_x, abs( sx - sec * ones_like( sx ) ), fib.lf ) * fib.cut_func( sx, lx, sec )
fig6 = figure( 6 )
ax6 = Axes( fig6, [.1, .1, .8, .8] )
hist( le_cut, 50, normed = 0 )
#hist( le_cut_null[0], 50, normed=0 )
title( 'Embedded length l_e' )
figure( 8 )
n_mask = 10
title( 'Histograms of $\phi$ fraction = $\pi/%i$' % n_mask )
for i in range( 0, n_mask ):
mask1 = phi_x_cut > i * pi / 2. / n_mask
mask2 = phi_x_cut < ( i + 1 ) * pi / 2. / n_mask
pdf, bins, patches = hist( le_cut[mask1 * mask2], 50 , histtype = 'step', label = '%i' % i )
legend()
#print mean( pdf )
figure( 9 )
title( 'Histogram of cut fibers angle' )
xx = linspace( 0, pi / 2., 100 )
hist( phi_x_cut, 50, normed = 1 )
plot( xx, sin( 2 * xx ), color = 'red', linewidth = 4, label = 'overlaps' )
plot( xx, cut_fiber_distrib( spec.l_x, fib.lf, xx ), color = 'green', linewidth = 4, label = 'nooverlaps' )
legend()
fig10 = figure( 10 )
title( '2D histogram of le and phi_x' )
ax10 = Axes3D( fig10 )
bin = 20
H, xedges, yedges = histogram2d( le_cut, phi_x_cut, ( bin, bin ), normed = 1 )
#extent = [xedges[0] * 100, xedges[-1] * 100, yedges[0], yedges[-1]] #[xedges[0], xedges[-1], yedges[0], yedges[-1]]
#im = imshow( H )#'binary', cmap='jet' , extent=extent
#im.set_interpolation( 'bilinear' )
#colorbar()
x = ( xedges[range( 0, len( xedges ) - 1 )] + xedges[range( 1, len( xedges ) )] ) / 2.
y = ( yedges[range( 0, len( yedges ) - 1 )] + yedges[range( 1, len( yedges ) )] ) / 2.
#ax10.scatter3D( xedges.ravel(), yedges.ravel(), H.ravel() )
xx = outer( x, ones( len( y ) ) )
yy = outer( ones( len( x ) ), y )
z = outer( ones( len( y ) ), sin( 2 * y ) ) / fib.lf * 2# * probability_cut_nooverlaps( spec.l_x, fib.lf, 0 )#* fib.n
zz = outer( ones( len( y ) ), cut_fiber_distrib( spec.l_x, fib.lf, y ) / fib.lf * 2 )
ax10.plot_wireframe( xx, yy, H )#, rstride=1, cstride=1
ax10.plot_wireframe( xx, yy, z , color = 'red', label = 'overlaps' )
ax10.plot_wireframe( xx, yy, zz , color = 'green', label = 'nooverlaps' )
legend()
print '%%%%%%%%%%%%%%%%%%%'
print '%%Embedded length%%'
print '%%%%%%%%%%%%%%%%%%%'
print 'probability cut fibers', probability_cut_nooverlaps( spec.l_x, fib.lf, 0. )
print 'le_mean cut fibers (int/p) \t', le( spec.l_x, fib.lf ) / probability_cut_nooverlaps( spec.l_x, fib.lf, 0. )
print 'le_mean of cut fibers (sim) \t', mean( le_cut ), '\t |\t standard deviation \t', std( le_cut )
print 'include nulls (sim) \t\t', mean( le_cut_null )
print 'E[le] (int) \t\t\t', le( spec.l_x, fib.lf )
print 'cut fibers area', A_cut, 'Ac', spec._get_cross_area(), 'af', A_cut / spec._get_cross_area()*100, '%'
print 'mean P and var P', mean( P ) #print 'number of cut fibers', v p = probability_cut_nooverlaps( spec.l_x, fib.lf, sec ) bin_mean = fib.n * p bin_stdv = sqrt( bin_mean * ( 1 - p ) ) bin_skew = ( 1 - 2 * p ) / bin_stdv poiss_lambda = fib.n * p poiss_mean = poiss_lambda poiss_stdv = poiss_lambda ** ( 1 / 2. ) poiss_skew = poiss_lambda ** ( -1 / 2. ) # Volume fraction Vf = fib._get_volume() Vc = spec._get_volume() vol_frac_V = Vf / Vc * 100 * fib.n #vol_frac_A = mean( v_vol_frac_A ) / Ac * 100