def ismc(g, xdists, u_to_x, T, seed, maxitr, tol, ftol, eps):
"""
Importance sampling Monte Carlo.
"""
# Seed the random number generator if required
if seed == -1:
prng = RandomState()
else:
prng = RandomState(seed)
# Use FORM to get estimate of u*
u_beta = slsqp(g, xdists, u_to_x, T, maxitr, tol, ftol, eps)['u_beta']
# Generate standard normal samples centred at u*
covmat = eye(len(xdists))
v = prng.multivariate_normal(u_beta, covmat, size=maxitr).T
g_mc = g(u_to_x(v, xdists, T))
# Define importance sampling functions weighting functions
fv = multivariate_normal(zeros(len(xdists)), covmat).pdf
hv = multivariate_normal(u_beta, covmat).pdf
# Convert g-function output to pass/fail indicator function and estimate pf
g_mc[g_mc>0] = 0
g_mc[g_mc<0] = 1
indfunc = g_mc * fv(v.T)/hv(v.T)
mu_pf = indfunc.mean()
beta = -norm.ppf(mu_pf) if mu_pf < 0.5 else norm.ppf(mu_pf)
# Convergence metrics (standard deviation, standard error, CoV of s.e.)
std_pf = indfunc.std(ddof=1) # Calculate sample standard deviation
se_pf = std_pf/sqrt(maxitr)
cv_pf = se_pf/mu_pf
return {'vars': xdists, 'beta': beta, 'Pf': mu_pf, 'stderr': se_pf,
'stdcv': cv_pf}
def relython(inp):
"""
Main function.
"""
# Validate input
err = io.validinp(inp)
# Proceed if there are no validation errors
if len(err) == 0:
res = {}
# Parse and prepare input
print('Parsing input...')
gfuncs, xdists, cmat_x = io.parseinp(inp)
inp['xdists'] = xdists # So can show mus and sigs in pprint
# Convert correlation matrix from X- to U-space
print('Converting correlation matrix to U-space...')
cmat_u = tr.corrmat_u(cmat_x, xdists)
# Generate transformation matrix from standard to correlated U-space
print('Generating transformation from standard to correlated U...')
T = tr.utrans(cmat_u)
for i, g in enumerate(gfuncs):
res[i] = []
for j, slvr in enumerate(inp['solver']):
print('Solving: {0}...'.format(slvr))
# Direct estimation methods
if slvr.upper() == 'HLRF':
res[i].append(sl.hlrf(g, xdists, tr.u_to_x, T,
inp['maxitr'][j], inp['tol'],
inp['ftol'], inp['eps']))
elif slvr.upper() == 'IHLRF':
res[i].append(sl.ihlrf(g, xdists, tr.u_to_x, T,
inp['maxitr'][j], inp['tol'],
inp['ftol'], inp['eps']))
elif slvr.upper() == 'SLSQP':
res[i].append(sl.slsqp(g, xdists, tr.u_to_x, T,
inp['maxitr'][j], inp['tol'],
inp['ftol'], inp['eps']))
# Monte Carlo simulation methods
elif slvr.upper() == 'CMC':
res[i].append(sl.cmc(g, xdists, tr.u_to_x, T, inp['seed'],
inp['maxitr'][j]))
elif slvr.upper() == 'ISMC':
res[i].append(sl.ismc(g, xdists, tr.u_to_x, T, inp['seed'],
inp['maxitr'][j], inp['tol'],
inp['ftol'], inp['eps']))
elif slvr.upper() == 'DSIM':
res[i].append(sl.dsim(g, xdists, tr.u_to_x, T, inp['seed'],
inp['maxitr'][j], inp['tol'],
inp['ftol'], inp['eps']))
else:
continue
output = io.pprint(inp, cmat_x, cmat_u, res, __version__, __author__)
if 'outpath' in inp.keys():
try:
with open(inp['outpath'], 'w') as f:
f.write(output)
except:
print('\nUnable to write to {0}\n'.format(inp['outpath']))
print(output)
return res
else:
if inp['showresults'] == 1:
print('\nErrors:\n{0}'.format('\n'.join(err)))
return err
