def scatterer_as_g_alpha(scatterer, hkl, d_star_sq):
return g_exp_i_alpha_derivatives.parameters(
g=scatterer.occupancy *
math.exp(-2 * math.pi**2 * scatterer.u_iso * d_star_sq),
ffp=1 + scatterer.fp,
fdp=scatterer.fdp,
alpha=2 * math.pi * matrix.col(scatterer.site).dot(matrix.col(hkl)))
def as_g_alpha(self, hkl, d_star_sq):
return g_exp_i_alpha_derivatives.parameters(
g=self.w * math.exp(-2 * math.pi ** 2 * self.u * d_star_sq),
ffp=1 + self.fp,
fdp=self.fdp,
alpha=2 * math.pi * matrix.col(self.xyz).dot(matrix.col(hkl)),
)
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 scatterer_as_g_alpha(scatterer, hkl, d_star_sq):
return g_exp_i_alpha_derivatives.parameters(
g = scatterer.occupancy
* math.exp(-2 * math.pi**2 * scatterer.u_iso * d_star_sq),
ffp = 1 + scatterer.fp,
fdp = scatterer.fdp,
alpha = 2 * math.pi * matrix.col(scatterer.site).dot(matrix.col(hkl)))
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_g_alpha(self, hkl, d_star_sq):
return g_exp_i_alpha_derivatives.parameters(
g=self.w * math.exp(-2 * math.pi**2 * self.u * d_star_sq),
ffp=1 + self.fp,
fdp=self.fdp,
alpha=2 * math.pi * matrix.col(self.xyz).dot(matrix.col(hkl)))