def demo():
m_la, std_la = 10., 1.0
m_xi, std_xi = 1.0, 0.1
# discretize the control variable (x-axis)
e_arr = np.linspace(0, 2.0, 80)
#===========================================================================
# Randomization
#===========================================================================
s = SPIRRID(
q=fiber_tt_2p(),
sampling_type='TGrid',
codegen_type='weave',
e_arr=e_arr,
n_int=10,
theta_vars=dict(la=RV('norm', m_la, std_la),
xi=RV('norm', m_xi, std_xi)),
)
#print current configuration of the integrator
#print s.__str__()
# print code of the weave (or cython) implementation
print s.codegen.code
def create_demo_object(fig_output_dir='fig'):
#===========================================================================
# Control variable
#===========================================================================
e_arr = np.linspace(0, 0.012, 80)
powers = np.linspace(1, math.log(20, 10), 6)
n_int_range = np.array(np.power(10, powers), dtype=int)
#===========================================================================
# Randomization
#===========================================================================
theta_vars = dict(
fu=RV('weibull_min', 1200.0e6, 200.),
qf=1500.0,
# qf = RV('uniform', 1500., 100.),
L=0.02, #
# L = RV('uniform', 0.02, 0.02 / 2.),
A=RV('norm', 5.30929158457e-10, .03 * 5.30929158457e-10),
E_mod=RV('uniform', 70.e9, 250.e9),
z=RV('uniform', 0.0, 0.03),
phi=0.0, #
# phi = RV('cos_distr', 0.0, 1.0),
# phi = RV('uniform', 0.0, 1.0),
f=RV('uniform', 0.0, 0.03))
#===========================================================================
# Integrator object
#===========================================================================
s = SPIRRID(
q=ConstantFrictionFiniteFiber(),
e_arr=e_arr,
n_int=10,
theta_vars=theta_vars,
)
#===========================================================================
# Lab
#===========================================================================
slab = SPIRRIDLAB(s=s,
save_output=False,
show_output=True,
dpi=300,
fig_output_dir=fig_output_dir,
qname='fiber_po_8p',
plot_mode='subplots',
n_int_range=n_int_range,
extra_compiler_args=True,
le_sampling_lst=['LHS', 'PGrid'],
le_n_int_lst=[10, 10],
plot_sampling_idx=[
0,
3,
])
return slab
def create_demo_object(fig_output_dir='fig'):
m_la, std_la = 10., 1.0
m_xi, std_xi = 1.0, 0.1
# discretize the control variable (x-axis)
e_arr = np.linspace(0, 2.0, 80)
# n_int range for sampling efficiency test
powers = np.linspace(1, math.log(500, 10), 50)
n_int_range = np.array(np.power(10, powers), dtype=int)
#===========================================================================
# Randomization
#===========================================================================
s = SPIRRID(
q=fiber_tt_2p(),
sampling_type='TGrid',
codegen_type='cython',
e_arr=e_arr,
n_int=10,
theta_vars=dict(la=RV('norm', m_la, std_la),
xi=RV('norm', m_xi, std_xi)),
)
#===========================================================================
# Exact solution
#===========================================================================
def mu_q_ex(e, m_xi, std_xi, m_la):
return e * (0.5 - 0.5 * erf(0.5 * math.sqrt(2) *
(e - m_xi) / std_xi)) * m_la
#===========================================================================
# Lab
#===========================================================================
slab = SPIRRIDLAB(s=s,
save_output=False,
show_output=True,
dpi=300,
fig_output_dir=fig_output_dir,
exact_arr=mu_q_ex(e_arr, m_xi, std_xi, m_la),
plot_mode='subplots',
n_int_range=n_int_range,
extra_compiler_args=True,
le_sampling_lst=['LHS', 'PGrid'],
le_n_int_lst=[440, 5000])
return slab
def run():
m_la, std_la = 10., 1.0
m_xi, std_xi = 1.0, 0.1
# discretize the control variable (x-axis)
e_arr = np.linspace(0, 2.0, 80)
#===========================================================================
# Randomization
#===========================================================================
s = SPIRRID(
q=fiber_tt_2p(),
e_arr=e_arr,
n_int=10,
theta_vars=dict(
la=m_la,
#la = RV('norm', m_la, std_la),
#xi = m_xi,
xi=RV('norm', m_xi, std_xi)),
sampling_type='MCS',
codegen_type='numpy',
)
p.plot(e_arr, s.mu_q_arr, 'b-x')
s.codegen_type = 'weave'
p.plot(e_arr, s.mu_q_arr, 'r-')
p.show()
def _redraw(self):
s = SPIRRID(
q=self.rf,
sampling_type='LHS',
e_arr=self.e_arr,
n_int=self.n_G_ipts,
theta_vars=dict(tau_fr=2.6,
l=0.0,
d=25.5e-3,
E_mod=72.0e3,
theta=0.0,
xi=0.0179,
phi=1.,
L=30.0),
# codegen_type='weave'
)
# construct the random variables
if self.pdf_xi_on:
s.theta_vars['xi'] = RV(
'weibull_min', shape=4.54, scale=0.017
) # RV( pd = self.pdf_xi, name = 'xi', n_int = self.n_G_ipts )
print self.pdf_theta.interp_ppf([0.01, 0.02])
print YMB_RV('theta', distr=self.pdf_theta,
n_int=self.n_G_ipts).distr.interp_ppf([0.01, 0.02])
if self.pdf_theta_on:
s.theta_vars['theta'] = YMB_RV('theta',
distr=self.pdf_theta,
n_int=self.n_G_ipts)
if self.pdf_l_on:
s.theta_vars['l'] = YMB_RV('l',
distr=self.pdf_l,
n_int=self.n_G_ipts)
if self.pdf_phi_on:
s.theta_vars['phi'] = YMB_RV('phi',
distr=self.pdf_phi,
n_int=self.n_G_ipts)
# print 'checking unity', s.mu_q_arr()
mu = s.mu_q_arr
axes = self.figure.axes[0]
# TODO:
axes.plot(self.e_arr, mu * self.n_f, linewidth=2, label=self.lab)
axes.set_xlabel('crack opening w[mm]')
axes.set_ylabel('force P[N]')
axes.legend(loc='best')
self.data_changed = True
def create_demo_object():
#===========================================================================
# Control variable
#===========================================================================
e_arr = np.linspace(0, 0.012, 80)
#===========================================================================
# Randomization
#===========================================================================
theta_vars = dict(#fu = 1200.0e6,
fu = RV('weibull_min', 1200.0e6, 200.),
qf = RV('uniform', 1500., 100.),
#qf = 1500.0,
L = 0.02, #
# L = RV('uniform', 0.02, 0.02 / 2.),
A = 5.30929158457e-10,
#A = RV('norm', 5.30929158457e-10, .03 * 5.30929158457e-10),
E_mod = 70.0e9,
#E_mod = RV('uniform', 70.e9, 250.e9),
z = 0,
#z = RV('uniform', 0.0, 0.03),
phi = 0.0, #
# phi = RV('cos_distr', 0.0, 1.0),
# phi = RV('uniform', 0.0, 1.0),
f = 0.01,
#f = RV('uniform', 0.0, 0.03),
)
#===========================================================================
# Integrator object
#===========================================================================
s = SPIRRID(q = ConstantFrictionFiniteFiber(),
e_arr = e_arr,
n_int = 10,
theta_vars = theta_vars,
)
import pylab as p
p.plot(e_arr, s.mu_q_arr)
p.show()
def setup_class(cls):
np.random.seed(2356)
#===========================================================================
# Control variable
#===========================================================================
e_arr = np.linspace(0, 0.012, 80)
cls.m_la, cls.std_la = 10., 1.0
cls.m_xi, cls.std_xi = 1.0, 0.1
#===========================================================================
# Randomization
#===========================================================================
cls.s = SPIRRID(q = fiber_tt_2p(),
eps_vars = {'e':e_arr},
codegen_type = 'numpy',
n_int = 10,
theta_vars = dict(la = RV('norm', cls.m_la, cls.std_la),
xi = RV('norm', cls.m_xi, cls.std_xi)
),
)
def create_demo_object(fig_output_dir='fig'):
D = 26 * 1.0e-6 # m
A = (D / 2.0)**2 * math.pi
# set the mean and standard deviation of the two random variables
la_mean, la_stdev = 0.0, 0.2
xi_mean, xi_stdev = 0.019027, 0.0022891
E_mean, E_stdev = 70.0e+9, 15.0e+9
th_mean, th_stdev = 0.0, 0.01
A_mean, A_stdev = A * 0.3, 0.7 * A
do = 'norm'
if do == 'general':
# set the mean and standard deviation of the two random variables
la_mean, la_stdev = 0.0, 0.2
xi_mean, xi_stdev = 0.019027, 0.0022891
E_mean, E_stdev = 70.0e+9, 15.0e+9
th_mean, th_stdev = 0.0, 0.01
A_mean, A_stdev = A * 0.3, 0.7 * A
# construct the normal distributions and get the methods
# for the evaluation of the probability density functions
g_la = RV('uniform', la_mean, la_stdev)
g_xi = RV('norm', xi_mean, xi_stdev)
g_E = RV('uniform', E_mean, E_stdev)
g_th = RV('uniform', th_mean, th_stdev)
g_A = RV('uniform', A_mean, A_stdev)
mu_ex_file = 'fiber_tt_5p_30.txt'
delimiter = ','
elif do == 'uniform':
# set the mean and standard deviation of the two random variables
la_mean, la_stdev = 0.0, 0.2
xi_mean, xi_stdev = 0.01, 0.02
E_mean, E_stdev = 70.0e+9, 15.0e+9
th_mean, th_stdev = 0.0, 0.01
A_mean, A_stdev = A * 0.3, 0.7 * A
# construct the uniform distributions and get the methods
# for the evaluation of the probability density functions
g_la = RV('uniform', la_mean, la_stdev)
g_xi = RV('uniform', xi_mean, xi_stdev)
g_E = RV('uniform', E_mean, E_stdev)
g_th = RV('uniform', th_mean, th_stdev)
g_A = RV('uniform', A_mean, A_stdev)
mu_ex_file = 'fiber_tt_5p_n_int_40_norm_exact.txt' # 'fiber_tt_5p_40_unif.txt'
delimiter = ' '
elif do == 'norm':
# set the mean and standard deviation of the two random variables
la_mean, la_stdev = 0.1, 0.02
xi_mean, xi_stdev = 0.019027, 0.0022891
E_mean, E_stdev = 70.0e+9, 15.0e+9
th_mean, th_stdev = 0.005, 0.001
A_mean, A_stdev = 5.3e-10, 1.0e-11
# construct the normal distributions and get the methods
# for the evaluation of the probability density functions
g_la = RV('norm', la_mean, la_stdev)
g_xi = RV('norm', xi_mean, xi_stdev)
g_E = RV('norm', E_mean, E_stdev)
g_th = RV('norm', th_mean, th_stdev)
g_A = RV('norm', A_mean, A_stdev)
mu_ex_file = os.path.join(file_dir,
'fiber_tt_5p_n_int_40_norm_exact.txt')
delimiter = ' '
# discretize the control variable (x-axis)
e_arr = np.linspace(0, 0.04, 40)
# n_int range for sampling efficiency test
powers = np.linspace(1, math.log(20, 10), 10)
n_int_range = np.array(np.power(10, powers), dtype=int)
#===========================================================================
# Randomization
#===========================================================================
s = SPIRRID(
q=fiber_tt_5p(),
codegen_type='cython',
e_arr=e_arr,
n_int=10,
theta_vars=dict(lambd=g_la, xi=g_xi, E_mod=g_E, theta=g_th, A=g_A),
)
# Exact solution
def mu_q_ex(e):
data = np.loadtxt(mu_ex_file, delimiter=delimiter)
x, y = data[:, 0], data[:, 1]
f = interp1d(x, y, kind='linear')
return f(e)
#===========================================================================
# Lab
#===========================================================================
slab = SPIRRIDLAB(s=s,
save_output=False,
show_output=True,
dpi=300,
fig_output_dir=fig_output_dir,
exact_arr=mu_q_ex(e_arr),
plot_mode='subplots',
n_int_range=n_int_range,
extra_compiler_args=True,
le_sampling_lst=['LHS', 'PGrid'],
le_n_int_lst=[25, 30])
return slab
def main():
#===========================================================================
# Response function
#===========================================================================
class fiber_tt_5p_np(RF):
''' Response function of a single fiber '''
implements(IRF)
title = Str('brittle filament')
def __call__(self, eps, lambd, xi, E_mod, theta, A):
'''
Implements the response function with arrays as variables.
first extract the variable discretizations from the orthogonal grid.
'''
eps_ = (eps - theta * (1 + lambd)) / ((1 + theta) * (1 + lambd))
eps_ *= Heaviside(eps_)
eps_grid = eps_ * Heaviside(xi - eps_)
q_grid = E_mod * A * eps_grid
return q_grid
class fiber_tt_5p_ne(RF):
''' Response function of a single fiber '''
implements(IRF)
title = Str('brittle filament')
def __call__(self, eps, lambd, xi, E_mod, theta, A):
'''
Implements the response function with arrays as variables.
first extract the variable discretizations from the orthogonal grid.
'''
eps_ = ne.evaluate(
"((eps - theta * (1 + lambd)) / ((1 + theta) * (1 + lambd)))")
tmp = Heaviside_ne(eps_)
eps_ = ne.evaluate('eps_*tmp')
tmp = Heaviside_ne(ne.evaluate("(xi - eps_)"))
eps_grid = ne.evaluate("eps_ * tmp")
q_grid = ne.evaluate("E_mod * A * eps_grid")
return q_grid
# all in one row, slower alternative
#return ne.evaluate("E_mod * A *((eps - theta * (1 + lambd)) / ((1 + theta) * (1 + lambd))) * (((eps - theta * (1 + lambd)) / ((1 + theta) * (1 + lambd)))>=0) * ((xi-((eps - theta * (1 + lambd)) / ((1 + theta) * (1 + lambd))))>=0)")
# set the mean and standard deviation of the two random variables
la_mean, la_stdev = 0.1, 0.02
xi_mean, xi_stdev = 0.019027, 0.0022891
E_mean, E_stdev = 70.0e+9, 15.0e+9
th_mean, th_stdev = 0.005, 0.001
A_mean, A_stdev = 5.3e-10, 1.0e-11
# construct the normal distributions and get the methods
# for the evaluation of the probability density functions
g_la = RV('norm', la_mean, la_stdev)
g_xi = RV('norm', xi_mean, xi_stdev)
g_E = RV('norm', E_mean, E_stdev)
g_th = RV('norm', th_mean, th_stdev)
g_A = RV('norm', A_mean, A_stdev)
# discretize the control variable (x-axis)
e_arr = np.linspace(0, 0.04, 80)
#===========================================================================
# Randomization
#===========================================================================
s_ne = SPIRRID(
q=fiber_tt_5p_ne(),
e_arr=e_arr,
n_int=10,
theta_vars=dict(lambd=g_la, xi=g_xi, E_mod=g_E, theta=g_th, A=g_A),
)
s_np = SPIRRID(
q=fiber_tt_5p_np(),
e_arr=e_arr,
n_int=10,
theta_vars=dict(lambd=g_la, xi=g_xi, E_mod=g_E, theta=g_th, A=g_A),
)
print 'Evaluation using NumPy'
print 'numpy time', s_np.exec_time
print 'Evaluation using numexpr'
print 'numexpr time', s_ne.exec_time
p.plot(e_arr, s_np.mu_q_arr, label='numpy')
p.plot(e_arr, s_ne.mu_q_arr, label='numexpr')
p.legend()
p.show()