def exercise(args):
verbose = "--verbose" in args
if (not verbose):
out = StringIO()
else:
out = sys.stdout
for n_params in xrange(2,5):
for i_trial in xrange(5):
params = []
for i in xrange(n_params):
params.append(parameters(
g=(random.random()-0.5)*2,
ffp=(random.random()-0.5)*2,
fdp=(random.random()-0.5)*2,
alpha=2*math.pi*random.random()))
exp_sum = g_exp_i_alpha_sum(params=params)
obs = abs(exp_sum.f())
compare_analytical_and_finite(
obs=obs,
params=params,
out=out)
compare_analytical_and_finite(
obs=obs*(random.random()+0.5),
params=params,
out=out)
print "OK"
def as_exp_i_sum(self):
params = []
for scatterer in self.scatterers:
params.append(
scatterer_as_g_alpha(scatterer=scatterer,
hkl=self.hkl,
d_star_sq=self.d_star_sq))
return g_exp_i_alpha_derivatives.g_exp_i_alpha_sum(params=params)
def compare_analytical_and_finite(obs, params, out):
grads_fin = d_target_d_params_finite(obs=obs, params=params)
print("grads_fin:", pack_gradients(grads_fin), file=out)
exp_sum = g_exp_i_alpha_sum(params=params)
target = least_squares(obs=obs, calc=exp_sum.f())
grads_ana = exp_sum.d_target_d_params(target=target)
print("grads_ana:", pack_gradients(grads_ana), file=out)
assert approx_equal(pack_gradients(grads_ana), pack_gradients(grads_fin))
curvs_fin = d2_target_d_params_finite(obs=obs, params=params)
print("curvs_fin:", curvs_fin, file=out)
curvs_ana = list(exp_sum.d2_target_d_params(target=target))
print("curvs_ana:", curvs_ana, file=out)
assert approx_equal(curvs_ana, curvs_fin)
print(file=out)
def compare_analytical_and_finite(obs, params, out): grads_fin = d_target_d_params_finite(obs=obs, params=params) print >> out, "grads_fin:", pack_gradients(grads_fin) exp_sum = g_exp_i_alpha_sum(params=params) target = least_squares(obs=obs, calc=exp_sum.f()) grads_ana = exp_sum.d_target_d_params(target=target) print >> out, "grads_ana:", pack_gradients(grads_ana) assert approx_equal(pack_gradients(grads_ana), pack_gradients(grads_fin)) curvs_fin = d2_target_d_params_finite(obs=obs, params=params) print >> out, "curvs_fin:", curvs_fin curvs_ana = list(exp_sum.d2_target_d_params(target=target)) print >> out, "curvs_ana:", curvs_ana assert approx_equal(curvs_ana, curvs_fin) print >> out
def d2_target_d_params_finite(obs, params, eps=1.e-8):
result = []
params_eps = copy.deepcopy(params)
for i_param in xrange(len(params)):
for ix in xrange(4):
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)
exp_sum = g_exp_i_alpha_sum(params=params_eps)
target = least_squares(obs=obs, calc=exp_sum.f())
dp = exp_sum.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 d2_target_d_params_finite(obs, params, eps=1.e-8):
result = []
params_eps = copy.deepcopy(params)
for i_param in range(len(params)):
for ix in range(4):
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)
exp_sum = g_exp_i_alpha_sum(params=params_eps)
target = least_squares(obs=obs, calc=exp_sum.f())
dp = exp_sum.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, params, eps=1.e-8):
result = []
params_eps = copy.deepcopy(params)
for i_param in range(len(params)):
dx = []
for ix in range(4):
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)
exp_sum = g_exp_i_alpha_sum(params=params_eps)
target = least_squares(obs=obs, calc=exp_sum.f())
ts.append(target.f())
dx.append((ts[0] - ts[1]) / (2 * eps))
result.append(gradients(*dx))
params_eps[i_param] = params[i_param]
return result
def d_target_d_params_finite(obs, params, eps=1.e-8):
result = []
params_eps = copy.deepcopy(params)
for i_param in xrange(len(params)):
dx = []
for ix in xrange(4):
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)
exp_sum = g_exp_i_alpha_sum(params=params_eps)
target = least_squares(obs=obs, calc=exp_sum.f())
ts.append(target.f())
dx.append((ts[0]-ts[1])/(2*eps))
result.append(gradients(*dx))
params_eps[i_param] = params[i_param]
return result
def exercise(args):
verbose = "--verbose" in args
if (not verbose):
out = StringIO()
else:
out = sys.stdout
for n_params in range(2, 5):
for i_trial in range(5):
params = []
for i in range(n_params):
params.append(
parameters(g=(random.random() - 0.5) * 2,
ffp=(random.random() - 0.5) * 2,
fdp=(random.random() - 0.5) * 2,
alpha=2 * math.pi * random.random()))
exp_sum = g_exp_i_alpha_sum(params=params)
obs = abs(exp_sum.f())
compare_analytical_and_finite(obs=obs, params=params, out=out)
compare_analytical_and_finite(obs=obs * (random.random() + 0.5),
params=params,
out=out)
print("OK")
def as_exp_i_sum(self):
return g_exp_i_alpha_derivatives.g_exp_i_alpha_sum(
params=[p.as_g_alpha(hkl=self.hkl, d_star_sq=self.d_star_sq) for p in self.params]
)
def as_exp_i_sum(self):
return g_exp_i_alpha_derivatives.g_exp_i_alpha_sum(params=[
p.as_g_alpha(hkl=self.hkl, d_star_sq=self.d_star_sq)
for p in self.params
])
def as_exp_i_sum(self):
params = []
for scatterer in self.scatterers:
params.append(scatterer_as_g_alpha(
scatterer=scatterer, hkl=self.hkl, d_star_sq=self.d_star_sq))
return g_exp_i_alpha_derivatives.g_exp_i_alpha_sum(params=params)
