def compare_analytical_and_finite(obs, hkl, d_star_sq, params, out):
grads_fin = d_target_d_params_finite(
obs=obs, hkl=hkl, d_star_sq=d_star_sq, params=params)
print >> out, "grads_fin:", pack_gradients(grads_fin)
sf = structure_factor(hkl=hkl, d_star_sq=d_star_sq, params=params)
target = least_squares(obs=obs, calc=sf.f())
grads_ana = sf.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, hkl=hkl, d_star_sq=d_star_sq, params=params)
print >> out, "curvs_fin:", curvs_fin
curvs_ana = sf.d2_target_d_params(target=target)
print >> out, "curvs_ana:", curvs_ana
assert approx_equal(curvs_ana, curvs_fin, 1.e-5)
print >> out
def compare_analytical_and_finite(obs, hkl, d_star_sq, params, out):
grads_fin = d_target_d_params_finite(obs=obs,
hkl=hkl,
d_star_sq=d_star_sq,
params=params)
print >> out, "grads_fin:", pack_gradients(grads_fin)
sf = structure_factor(hkl=hkl, d_star_sq=d_star_sq, params=params)
target = least_squares(obs=obs, calc=sf.f())
grads_ana = sf.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,
hkl=hkl,
d_star_sq=d_star_sq,
params=params)
print >> out, "curvs_fin:", curvs_fin
curvs_ana = sf.d2_target_d_params(target=target)
print >> out, "curvs_ana:", curvs_ana
assert approx_equal(curvs_ana, curvs_fin, 1.e-5)
print >> out
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 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
