def run():
# Quantities for the response function
# and randomization
#
E_mod = 70 * 1e+9 # Pa
sig_u = 1.25 * 1e+9 # Pa
D = 26 * 1.0e-6 # m
A = (D / 2.0)**2 * pi
xi_u = sig_u / E_mod
# construct a default response function for a single filament
rf = Filament(E_mod=70.e9, xi=0.02, A=A, theta=0, lambd=0)
# construct the integrator and provide it with the response function.
s = SPIRRID(rf=rf, min_eps=0.00, max_eps=0.05, n_eps=20)
# construct the random variables
n_int = 40
s.add_rv('xi',
distribution='weibull_min',
scale=0.02,
shape=10.,
n_int=n_int)
s.add_rv('E_mod',
distribution='uniform',
loc=70e+9,
scale=15e+9,
n_int=n_int)
s.add_rv('theta', distribution='uniform', loc=0.0, scale=0.01, n_int=n_int)
s.add_rv('lambd', distribution='uniform', loc=0.0, scale=.2, n_int=n_int)
s.add_rv('A',
distribution='uniform',
loc=A * 0.3,
scale=0.7 * A,
n_int=n_int)
# define a tables with the run configurations to start in a batch
run_list = [
({
'cached_dG': False,
'compiled_QdG_loop': True,
'compiled_eps_loop': True
}, 'bx-',
'$\mathrm{C}_{e,\\theta} ( q(e,\\theta) \cdot g[\\theta_1] g[\\theta_2] \dots g[\\theta_n] ) $ - %4.2f sec'
),
(
{
'cached_dG': False,
'compiled_QdG_loop': True,
'compiled_eps_loop': False
},
'r-2',
'$\mathrm{P}_{e} ( \mathrm{C}_{\\theta} ( q(e,\\theta) \cdot g[\\theta_1] g[\\theta_2] \dots g[\\theta_n] ) ) $ - %4.2f sec',
),
(
{
'cached_dG': True,
'compiled_QdG_loop': True,
'compiled_eps_loop': True
},
'go-',
'$\mathrm{C}_{e,\\theta} ( q(e,\\theta) \cdot G[\\theta] ) $ - %4.2f sec',
),
({
'cached_dG': True,
'compiled_QdG_loop': False,
'compiled_eps_loop': False
}, 'y--',
'$\mathrm{P}_{e} ( \mathrm{N}_{\\theta} ( q(e,\\theta) \cdot G[\\theta] ) ) $ - %4.2f sec'
),
]
legend = []
for idx, run in enumerate(run_list):
run_options, plot_options, legend_string = run
print 'run', idx,
s.set(**run_options)
print 'xdata', s.mean_curve.xdata
print 'ydata', s.mean_curve.ydata
s.mean_curve.plot(plt, plot_options)
print 'integral of the pdf theta', s.eval_i_dG_grid()
print 'execution time', s.exec_time
legend.append(legend_string % s.exec_time)
plt.xlabel('strain [-]')
plt.ylabel('stress')
plt.legend(legend)
plt.title(s.rf.title)
plt.show()
def run():
# Quantities for the response function
# and randomization
#
E_mod = 70 * 1e+9 # Pa
sig_u = 1.25 * 1e+9 # Pa
D = 26 * 1.0e-6 # m
A = ( D / 2.0 ) ** 2 * pi
xi_u = sig_u / E_mod
# construct a default response function for a single filament
rf = Filament( E_mod = 70.e9, xi = 0.02, A = A, theta = 0, lambd = 0 )
# construct the integrator and provide it with the response function.
s = SPIRRID( rf = rf,
min_eps = 0.00, max_eps = 0.05, n_eps = 20 )
# construct the random variables
n_int = 40
s.add_rv( 'xi', distribution = 'weibull_min', scale = 0.02, shape = 10., n_int = n_int )
s.add_rv( 'E_mod', distribution = 'uniform', loc = 70e+9, scale = 15e+9, n_int = n_int )
s.add_rv( 'theta', distribution = 'uniform', loc = 0.0, scale = 0.01, n_int = n_int )
s.add_rv( 'lambd', distribution = 'uniform', loc = 0.0, scale = .2, n_int = n_int )
s.add_rv( 'A', distribution = 'uniform', loc = A * 0.3, scale = 0.7 * A, n_int = n_int )
# define a tables with the run configurations to start in a batch
run_list = [
(
{'cached_dG' : False,
'compiled_QdG_loop' : True,
'compiled_eps_loop' : True },
'bx-',
'$\mathrm{C}_{e,\\theta} ( q(e,\\theta) \cdot g[\\theta_1] g[\\theta_2] \dots g[\\theta_n] ) $ - %4.2f sec'
),
(
{'cached_dG' : False,
'compiled_QdG_loop' : True,
'compiled_eps_loop' : False },
'r-2',
'$\mathrm{P}_{e} ( \mathrm{C}_{\\theta} ( q(e,\\theta) \cdot g[\\theta_1] g[\\theta_2] \dots g[\\theta_n] ) ) $ - %4.2f sec',
),
(
{'cached_dG' : True,
'compiled_QdG_loop' : True,
'compiled_eps_loop' : True },
'go-',
'$\mathrm{C}_{e,\\theta} ( q(e,\\theta) \cdot G[\\theta] ) $ - %4.2f sec',
),
(
{'cached_dG' : True,
'compiled_QdG_loop' : False,
'compiled_eps_loop' : False },
'y--',
'$\mathrm{P}_{e} ( \mathrm{N}_{\\theta} ( q(e,\\theta) \cdot G[\\theta] ) ) $ - %4.2f sec'
),
]
legend = []
for idx, run in enumerate( run_list ):
run_options, plot_options, legend_string = run
print 'run', idx,
s.set( **run_options )
print 'xdata', s.mean_curve.xdata
print 'ydata', s.mean_curve.ydata
s.mean_curve.plot( plt, plot_options )
print 'integral of the pdf theta', s.eval_i_dG_grid()
print 'execution time', s.exec_time
legend.append( legend_string % s.exec_time )
plt.xlabel( 'strain [-]' )
plt.ylabel( 'stress' )
plt.legend( legend )
plt.title( s.rf.title )
plt.show()
