def exercise(args):
verbose = "--verbose" in args
if (not verbose):
out = StringIO()
else:
out = sys.stdout
hkl = (1, 2, 3)
d_star_sq = 1e-3
for n_params in xrange(2, 5):
for i_trial in xrange(5):
params = []
for i in xrange(n_params):
params.append(
parameters(xyz=[random.random() for i in xrange(3)],
u=random.random() * 0.1,
w=random.random(),
fp=(random.random() - 0.5) * 2,
fdp=(random.random() - 0.5) * 2))
sf = structure_factor(hkl=hkl, d_star_sq=d_star_sq, params=params)
obs = abs(sf.f())
compare_analytical_and_finite(obs=obs,
hkl=hkl,
d_star_sq=d_star_sq,
params=params,
out=out)
compare_analytical_and_finite(obs=obs * (random.random() + 0.5),
hkl=hkl,
d_star_sq=d_star_sq,
params=params,
out=out)
print "OK"
def exercise(args):
verbose = "--verbose" in args
if (not verbose):
out = StringIO()
else:
out = sys.stdout
hkl = (1,2,3)
d_star_sq = 1e-3
for n_params in xrange(2,5):
for i_trial in xrange(5):
params = []
for i in xrange(n_params):
params.append(parameters(
xyz=[random.random() for i in xrange(3)],
u=random.random()*0.1,
w=random.random(),
fp=(random.random()-0.5)*2,
fdp=(random.random()-0.5)*2))
sf = structure_factor(hkl=hkl, d_star_sq=d_star_sq, params=params)
obs = abs(sf.f())
compare_analytical_and_finite(
obs=obs,
hkl=hkl,
d_star_sq=d_star_sq,
params=params,
out=out)
compare_analytical_and_finite(
obs=obs*(random.random()+0.5),
hkl=hkl,
d_star_sq=d_star_sq,
params=params,
out=out)
print "OK"
def d2_target_d_params_finite(obs, hkl, d_star_sq, params, eps=1.e-8):
result = []
params_eps = copy.deepcopy(params)
for i_param in xrange(len(params)):
for ix in xrange(7):
gs = []
for signed_eps in [eps, -eps]:
pi_eps = params[i_param].as_list()
pi_eps[ix] += signed_eps
params_eps[i_param] = parameters(pi_eps[:3], *pi_eps[3:])
sf = structure_factor(hkl=hkl, d_star_sq=d_star_sq, params=params_eps)
target = least_squares(obs=obs, calc=sf.f())
dp = sf.d_target_d_params(target=target)
gs.append(pack_gradients(dp))
result.append([(gp-gm)/(2*eps) for gp,gm in zip(gs[0],gs[1])])
params_eps[i_param] = params[i_param]
return result
def d_target_d_params_finite(obs, hkl, d_star_sq, params, eps=1.e-8):
result = []
params_eps = copy.deepcopy(params)
for i_param in xrange(len(params)):
dx = []
for ix in xrange(7):
ts = []
for signed_eps in [eps, -eps]:
pi_eps = params[i_param].as_list()
pi_eps[ix] += signed_eps
params_eps[i_param] = parameters(pi_eps[:3], *pi_eps[3:])
sf = structure_factor(hkl=hkl, d_star_sq=d_star_sq, params=params_eps)
target = least_squares(obs=obs, calc=sf.f())
ts.append(target.f())
dx.append((ts[0]-ts[1])/(2*eps))
result.append(gradients(dx[:3], *dx[3:]))
params_eps[i_param] = params[i_param]
return result
def d2_target_d_params_finite(obs, hkl, d_star_sq, params, eps=1.e-8):
result = []
params_eps = copy.deepcopy(params)
for i_param in xrange(len(params)):
for ix in xrange(7):
gs = []
for signed_eps in [eps, -eps]:
pi_eps = params[i_param].as_list()
pi_eps[ix] += signed_eps
params_eps[i_param] = parameters(pi_eps[:3], *pi_eps[3:])
sf = structure_factor(hkl=hkl,
d_star_sq=d_star_sq,
params=params_eps)
target = least_squares(obs=obs, calc=sf.f())
dp = sf.d_target_d_params(target=target)
gs.append(pack_gradients(dp))
result.append([(gp - gm) / (2 * eps)
for gp, gm in zip(gs[0], gs[1])])
params_eps[i_param] = params[i_param]
return result
def d_target_d_params_finite(obs, hkl, d_star_sq, params, eps=1.e-8):
result = []
params_eps = copy.deepcopy(params)
for i_param in xrange(len(params)):
dx = []
for ix in xrange(7):
ts = []
for signed_eps in [eps, -eps]:
pi_eps = params[i_param].as_list()
pi_eps[ix] += signed_eps
params_eps[i_param] = parameters(pi_eps[:3], *pi_eps[3:])
sf = structure_factor(hkl=hkl,
d_star_sq=d_star_sq,
params=params_eps)
target = least_squares(obs=obs, calc=sf.f())
ts.append(target.f())
dx.append((ts[0] - ts[1]) / (2 * eps))
result.append(gradients(dx[:3], *dx[3:]))
params_eps[i_param] = params[i_param]
return result
