def run(mu, cov, plot = True):
# discretize the control variable (x-axis)
x_arr = np.linspace(0, 10.0, 1000)[1:]
#===========================================================================
# Randomization
#===========================================================================
s = SPIRRID(q = BasicPDF(),
e_arr = x_arr,
n_int = 100,
tvars = dict(mu = mu,
cov = cov
),
sampling_type = 'TGrid',
codegen_type = 'numpy',
)
#s.codegen.cached_dG = False
#s.codegen.compiled_eps_loop = False
#===========================================================================
# Calculate
#===========================================================================
# calculate compounded distribution values
cpd_pdf = s.mu_q_arr
cpd_cdf = np.cumsum(cpd_pdf) * np.diff(x_arr)[0]
# calculate first raw moment
raw_1 = np.trapz(cpd_pdf * x_arr, x_arr)
# calculate second raw moment
raw_2 = np.trapz(cpd_pdf * x_arr ** 2, x_arr)
std = np.sqrt(raw_2 - raw_1 ** 2)
# calculate values of lognormal distrib
lognorm_pdf = lognormal_pdf(x_arr, raw_1, std)
lognorm_cdf = lognormal_cdf(x_arr, raw_1, std)
# calculate error
rms_err = rms_error(lognorm_pdf, cpd_pdf)
max_err = max_error(lognorm_pdf, cpd_pdf)
chi_err = chi_error(lognorm_pdf, cpd_pdf)
ks_err = ks_error(lognorm_cdf, cpd_cdf)
# generate samples
samples = s.sampling.get_samples(50)
sample_args = [ sam[:, np.newaxis] for sam in samples]
q_arr = s.q(x_arr[None, :], *sample_args)
emp_data = np.loadtxt('data_emp.txt', delimiter = '\t')
#===========================================================================
# Print
#===========================================================================
print 'check unity\t', np.trapz(cpd_pdf, x_arr)
print 'mean\t\t', raw_1
print 'std\t\t', std
print 'rms error\t', rms_err
print 'max error\t', max_err
print 'chi error\t', chi_err
print 'ks error\t', ks_err
#===========================================================================
# Plot
#===========================================================================
if plot:
p.figure()
p.title(mu.type)
# plot samples
#p.plot(x_arr, q_arr.T, color = 'gray')
for s in q_arr:
p.plot(x_arr, s, color = 'gray', linewidth = mu.pdf((s * x_arr).sum() / 100.) * 5)
# plot compounded distribution
p.plot(x_arr, cpd_pdf, 'b-', label = 'cpd')
# plot lognormal distribution, method of moments
p.plot(x_arr, lognorm_pdf, color = 'red', linewidth = 2, label = 'lognorm')
p.plot(x_arr, lognormal_pdf(x_arr, np.mean(emp_data[:, 0]), np.std(emp_data[:, 0])), color = 'cyan', linewidth = 2, label = 'lognorm_data')
p.plot(x_arr, mu.pdf(x_arr), color = 'green', label = 'mu_dist')
p.legend(loc = 0)
p.figure()
p.title(mu.type)
p.plot(emp_data[:, 0], emp_data[:, 1], 'k-', linewidth = 3, label = 'emp')
p.plot(x_arr, cpd_cdf, 'b-', label = 'cpd')
# plot lognormal CDF, method of moments
p.plot(x_arr, lognorm_cdf, color = 'red', linewidth = 2, label = 'lognorm')
p.plot(x_arr, lognormal_cdf(x_arr, np.mean(emp_data[:, 0]), np.std(emp_data[:, 0])), color = 'cyan', linewidth = 2, label = 'lognorm_data')
p.legend(loc = 0)
p.figure()
p.title(mu.type)
p.loglog(emp_data[:, 0], emp_data[:, 1], 'k-', linewidth = 3, label = 'emp')
p.loglog(x_arr, cpd_cdf, 'b-', label = 'cpd')
p.loglog(x_arr, lognorm_cdf, color = 'red', linewidth = 2, label = 'lognorm')
p.loglog(x_arr, lognormal_cdf(x_arr, np.mean(emp_data[:, 0]), np.std(emp_data[:, 0])), color = 'cyan', linewidth = 2, label = 'lognorm_data')
p.ylim(1e-4, 1)
p.xlim(1, 10)
p.legend(loc = 0)
#p.show()
return rms_err
def run():
m_mu, std_mu = 3., 0.68
m_cov, std_cov = 0.18, 0.067
# discretize the control variable (x-axis)
x_arr = np.linspace(0, 6.0, 1000)[1:]
#===========================================================================
# Randomization
#===========================================================================
s = SPIRRID(q = BasicPDF(),
e_arr = x_arr,
n_int = 100,
tvars = dict(mu = RV('norm', m_mu, std_mu), #RV('beta', m_cov, std_cov),#BETA('beta', mu = m_mu, sig = std_mu, a = a, b = b),
cov = RV('norm', m_cov, std_cov)
),
sampling_type = 'TGrid',
codegen_type = 'numpy',
)
#===========================================================================
# Calculate
#===========================================================================
# calculate compounded distribution values
cpd_pdf = s.mu_q_arr
cpd_cdf = np.cumsum(cpd_pdf) * np.diff(x_arr)[0]
# calculate first raw moment
raw_1 = np.trapz(cpd_pdf * x_arr, x_arr)
# calculate second raw moment
raw_2 = np.trapz(cpd_pdf * x_arr ** 2, x_arr)
std = np.sqrt(raw_2 - raw_1 ** 2)
# calculate values of lognormal distrib
lognorm_pdf = lognormal_pdf(x_arr, raw_1, std)
lognorm_cdf = lognormal_cdf(x_arr, raw_1, std)
# calculate error
rms_err = rms_error(lognorm_pdf, cpd_pdf)
max_err = max_error(lognorm_pdf, cpd_pdf)
chi_err = chi_error(lognorm_pdf, cpd_pdf)
# generate samples
samples = s.sampling.get_samples(20)
sample_args = [ sam[:, np.newaxis] for sam in samples]
q_arr = s.q(x_arr[None, :], *sample_args)
#===========================================================================
# Print
#===========================================================================
print 'check unity\t', np.trapz(cpd_pdf, x_arr)
print 'mean\t\t', raw_1
print 'std\t\t', std
print 'rms error\t', rms_err
print 'max error\t', max_err
print 'chi error\t', chi_err
#===========================================================================
# Plot
#===========================================================================
p.figure()
# plot samples
#p.plot(x_arr, q_arr.T, color = 'gray')
# plot compounded distribution
p.plot(x_arr, cpd_pdf, 'b-')
# plot lognormal distribution, method of moments
p.plot(x_arr, lognorm_pdf, color = 'red', linewidth = 2)
data = np.loadtxt('maple_cpd.txt', delimiter = ',')
p.plot(data[:, 0], data[:, 1], color = 'violet')
p.figure()
p.plot(x_arr, cpd_cdf, 'b-')
# plot lognormal CDF, method of moments
p.plot(x_arr, lognorm_cdf, color = 'red', linewidth = 2)
p.show()
