def debye_waller_factors(self,
miller_index=None,
miller_indices=None,
u_iso=None,
b_iso=None,
u_cart=None,
b_cart=None,
u_cif=None,
u_star=None,
exp_arg_limit=50,
truncate_exp_arg=False):
assert [miller_index, miller_indices].count(None) == 1
assert [u_iso, b_iso, u_cart, b_cart, u_cif, u_star].count(None) == 5
from cctbx import adptbx
h = miller_index
if (h is None): h = miller_indices
if (u_iso is not None):
b_iso = adptbx.u_as_b(u_iso)
if (b_iso is not None):
return adptbx.debye_waller_factor_b_iso(
self.stol_sq(h),
b_iso, exp_arg_limit, truncate_exp_arg)
if (b_cart is not None):
u_cart = adptbx.b_as_u(b_cart)
if (u_cart is not None):
u_star = adptbx.u_cart_as_u_star(self, u_cart)
if (u_cif is not None):
u_star = adptbx.u_cif_as_u_star(self, u_cif)
assert u_star is not None
return adptbx.debye_waller_factor_u_star(
h, u_star, exp_arg_limit, truncate_exp_arg)
def debye_waller_factors(self,
miller_index=None,
miller_indices=None,
u_iso=None,
b_iso=None,
u_cart=None,
b_cart=None,
u_cif=None,
u_star=None,
exp_arg_limit=50,
truncate_exp_arg=False):
assert [miller_index, miller_indices].count(None) == 1
assert [u_iso, b_iso, u_cart, b_cart, u_cif, u_star].count(None) == 5
from cctbx import adptbx
h = miller_index
if (h is None): h = miller_indices
if (u_iso is not None):
b_iso = adptbx.u_as_b(u_iso)
if (b_iso is not None):
return adptbx.debye_waller_factor_b_iso(
self.stol_sq(h),
b_iso, exp_arg_limit, truncate_exp_arg)
if (b_cart is not None):
u_cart = adptbx.b_as_u(b_cart)
if (u_cart is not None):
u_star = adptbx.u_cart_as_u_star(self, u_cart)
if (u_cif is not None):
u_star = adptbx.u_cif_as_u_star(self, u_cif)
assert u_star is not None
return adptbx.debye_waller_factor_u_star(
h, u_star, exp_arg_limit, truncate_exp_arg)
def d_dw_d_u_star_finite(h, u_star, eps=1.e-6):
result = flex.double()
for ip in xrange(len(u_star)):
vs = []
for signed_eps in [eps,-eps]:
u_star_eps = list(u_star)
u_star_eps[ip] += signed_eps
vs.append(adptbx.debye_waller_factor_u_star(h, u_star_eps))
result.append((vs[0]-vs[1])/(2*eps))
return result
def d_dw_d_u_indep_finite(adp_constraints, h, u_indep, eps=1.e-6):
result = flex.double()
for i_indep in xrange(len(u_indep)):
vs = []
for signed_eps in [eps,-eps]:
u_indep_eps = list(u_indep)
u_indep_eps[i_indep] += signed_eps
u_eps = adp_constraints.all_params(u_indep_eps)
vs.append(adptbx.debye_waller_factor_u_star(h, u_eps))
result.append((vs[0]-vs[1])/(2*eps))
return result
def p23_curv(h, u_star):
"""\
h = {h0,h1,h2}
u = {{u22,0,0},{0,u22,0},{0,0,u22}}
dw=Exp[mtps*h.u.h]
FortranForm[D[dw,u22,u22]/dw]
"""
dw = adptbx.debye_waller_factor_u_star(h, u_star)
h0, h1, h2 = h
u22 = u_star[2]
mtps = -2 * math.pi**2
return [[dw * ((h0**2 + h1**2 + h2**2)**2 * mtps**2)]]
def p23_curv(h, u_star):
"""\
h = {h0,h1,h2}
u = {{u22,0,0},{0,u22,0},{0,0,u22}}
dw=Exp[mtps*h.u.h]
FortranForm[D[dw,u22,u22]/dw]
"""
dw = adptbx.debye_waller_factor_u_star(h, u_star)
h0, h1, h2 = h
u22 = u_star[2]
mtps = -2*math.pi**2
return [
[dw * ((h0**2 + h1**2 + h2**2)**2*mtps**2)]]
def p2_curv(h, u_star):
"""\
h = {h0,h1,h2}
u = {{u00,0,u02},{0,u11,0},{u02,0,u22}}
dw=Exp[mtps*h.u.h]
FortranForm[D[dw,u00,u00]/dw]
FortranForm[D[dw,u00,u11]/dw]
FortranForm[D[dw,u00,u22]/dw]
FortranForm[D[dw,u00,u02]/dw]
FortranForm[D[dw,u11,u00]/dw]
FortranForm[D[dw,u11,u11]/dw]
FortranForm[D[dw,u11,u22]/dw]
FortranForm[D[dw,u11,u02]/dw]
FortranForm[D[dw,u22,u00]/dw]
FortranForm[D[dw,u22,u11]/dw]
FortranForm[D[dw,u22,u22]/dw]
FortranForm[D[dw,u22,u02]/dw]
FortranForm[D[dw,u02,u00]/dw]
FortranForm[D[dw,u02,u11]/dw]
FortranForm[D[dw,u02,u22]/dw]
FortranForm[D[dw,u02,u02]/dw]
"""
dw = adptbx.debye_waller_factor_u_star(h, u_star)
h0, h1, h2 = h
u00 = u_star[0]
u11 = u_star[1]
u22 = u_star[2]
u02 = u_star[4]
mtps = -2 * math.pi**2
return [[
dw * (h0**4 * mtps**2), dw * (h0**2 * h1**2 * mtps**2),
dw * (h0**2 * h2**2 * mtps**2), dw * (2 * h0**3 * h2 * mtps**2)
],
[
dw * (h0**2 * h1**2 * mtps**2), dw * (h1**4 * mtps**2),
dw * (h1**2 * h2**2 * mtps**2),
dw * (2 * h0 * h1**2 * h2 * mtps**2)
],
[
dw * (h0**2 * h2**2 * mtps**2), dw * (h1**2 * h2**2 * mtps**2),
dw * (h2**4 * mtps**2), dw * (2 * h0 * h2**3 * mtps**2)
],
[
dw * (2 * h0**3 * h2 * mtps**2),
dw * (2 * h0 * h1**2 * h2 * mtps**2),
dw * (2 * h0 * h2**3 * mtps**2),
dw * (4 * h0**2 * h2**2 * mtps**2)
]]
def p2_curv(h, u_star):
"""\
h = {h0,h1,h2}
u = {{u00,0,u02},{0,u11,0},{u02,0,u22}}
dw=Exp[mtps*h.u.h]
FortranForm[D[dw,u00,u00]/dw]
FortranForm[D[dw,u00,u11]/dw]
FortranForm[D[dw,u00,u22]/dw]
FortranForm[D[dw,u00,u02]/dw]
FortranForm[D[dw,u11,u00]/dw]
FortranForm[D[dw,u11,u11]/dw]
FortranForm[D[dw,u11,u22]/dw]
FortranForm[D[dw,u11,u02]/dw]
FortranForm[D[dw,u22,u00]/dw]
FortranForm[D[dw,u22,u11]/dw]
FortranForm[D[dw,u22,u22]/dw]
FortranForm[D[dw,u22,u02]/dw]
FortranForm[D[dw,u02,u00]/dw]
FortranForm[D[dw,u02,u11]/dw]
FortranForm[D[dw,u02,u22]/dw]
FortranForm[D[dw,u02,u02]/dw]
"""
dw = adptbx.debye_waller_factor_u_star(h, u_star)
h0, h1, h2 = h
u00 = u_star[0]
u11 = u_star[1]
u22 = u_star[2]
u02 = u_star[4]
mtps = -2*math.pi**2
return [
[dw * (h0**4*mtps**2),
dw * (h0**2*h1**2*mtps**2),
dw * (h0**2*h2**2*mtps**2),
dw * (2*h0**3*h2*mtps**2)],
[dw * (h0**2*h1**2*mtps**2),
dw * (h1**4*mtps**2),
dw * (h1**2*h2**2*mtps**2),
dw * (2*h0*h1**2*h2*mtps**2)],
[dw * (h0**2*h2**2*mtps**2),
dw * (h1**2*h2**2*mtps**2),
dw * (h2**4*mtps**2),
dw * (2*h0*h2**3*mtps**2)],
[dw * (2*h0**3*h2*mtps**2),
dw * (2*h0*h1**2*h2*mtps**2),
dw * (2*h0*h2**3*mtps**2),
dw * (4*h0**2*h2**2*mtps**2)]]
def calc_debye_waller_factor(self, observations, b_cart):
#apply space-group constraints on B-tensor
space_group = self.observations.space_group()
adp_constraints = sgtbx.tensor_rank_2_constraints(
space_group=space_group, reciprocal_space=True)
#convert B tensor direct-space to reciprocal space
fmx = sqr(self.unit_cell.fractionalization_matrix())
u_cart = b_cart / (8 * math.pi**2)
u_star_mat = fmx * u_cart * fmx.transpose()
u_star = u_star_mat.as_sym_mat3()
u_star = space_group.average_u_star(u_star)
u_indep = adp_constraints.independent_params(all_params=u_star)
u_star = adp_constraints.all_params(independent_params=u_indep)
dw_c = adptbx.debye_waller_factor_u_star(observations.indices(),
u_star)
return dw_c
def p3_curv(h, u_star):
"""\
h = {h0,h1,h2}
u = {{2*u01,u01,0},{u01,2*u01,0},{0,0,u22}}
dw=Exp[mtps*h.u.h]
FortranForm[D[dw,u22,u22]/dw]
FortranForm[D[dw,u22,u01]/dw]
FortranForm[D[dw,u01,u22]/dw]
FortranForm[D[dw,u01,u01]/dw]
"""
dw = adptbx.debye_waller_factor_u_star(h, u_star)
h0, h1, h2 = h
u22 = u_star[2]
u01 = u_star[3]
mtps = -2*math.pi**2
return [
[dw * (h2**4*mtps**2),
dw * ((h0*(2*h0 + h1) + h1*(h0 + 2*h1))*h2**2*mtps**2)],
[dw * ((h0*(2*h0 + h1) + h1*(h0 + 2*h1))*h2**2*mtps**2),
dw * ((h0*(2*h0 + h1) + h1*(h0 + 2*h1))**2*mtps**2)]]
def structure_factors(self, d_min):
print "WARNING: RESULTS NOT VERIFIED" # XXX
miller_set = miller.build_set(
crystal_symmetry=self,
anomalous_flag=True, # XXX always True?
d_min=d_min)
f_calc = flex.complex_double()
for h in miller_set.indices():
fc = 0j
for scatterer in self.scatterers():
site_symmetry = self.site_symmetry(scatterer.site)
equiv_sites = sgtbx.sym_equiv_sites(site_symmetry)
sum_exp_j_two_pi_hx = 0j
for i_symop, x in enumerate(equiv_sites.coordinates()):
sum_hx = 0
for i in xrange(3):
sum_hx += h[i] * x[i]
phase = 2 * math.pi * sum_hx
exp_j_two_pi_hx = complex(math.cos(phase), math.sin(phase))
if (scatterer.anisotropic_flag):
r = self.space_group()(i_symop).r()
hr = h
dw = adptbx.debye_waller_factor_u_star(
hr, scatterer.u_star)
exp_j_two_pi_hx *= dw
sum_exp_j_two_pi_hx += exp_j_two_pi_hx
b_j = scatterer.scattering_info.bound_coh_scatt_length()
fc_site = scatterer.weight() * b_j * sum_exp_j_two_pi_hx
if (not scatterer.anisotropic_flag):
d_star_sq = self.unit_cell().d_star_sq(h)
dw = adptbx.debye_waller_factor_u_iso(
d_star_sq / 4, scatterer.u_iso)
fc_site *= dw
fc += fc_site
f_calc.append(fc)
return miller.array(miller_set=miller_set, data=f_calc)
def structure_factors(self, d_min):
print "WARNING: RESULTS NOT VERIFIED" # XXX
miller_set = miller.build_set(
crystal_symmetry=self,
anomalous_flag=True, # XXX always True?
d_min=d_min)
f_calc = flex.complex_double()
for h in miller_set.indices():
fc = 0j
for scatterer in self.scatterers():
site_symmetry = self.site_symmetry(scatterer.site)
equiv_sites = sgtbx.sym_equiv_sites(site_symmetry)
sum_exp_j_two_pi_hx = 0j
for i_symop,x in enumerate(equiv_sites.coordinates()):
sum_hx = 0
for i in xrange(3):
sum_hx += h[i] * x[i]
phase = 2 * math.pi * sum_hx
exp_j_two_pi_hx = complex(math.cos(phase), math.sin(phase))
if (scatterer.anisotropic_flag):
r = self.space_group()(i_symop).r()
hr = h
dw = adptbx.debye_waller_factor_u_star(hr, scatterer.u_star)
exp_j_two_pi_hx *= dw
sum_exp_j_two_pi_hx += exp_j_two_pi_hx
b_j = scatterer.scattering_info.bound_coh_scatt_length()
fc_site = scatterer.weight() * b_j * sum_exp_j_two_pi_hx
if (not scatterer.anisotropic_flag):
d_star_sq = self.unit_cell().d_star_sq(h)
dw = adptbx.debye_waller_factor_u_iso(d_star_sq/4, scatterer.u_iso)
fc_site *= dw
fc += fc_site
f_calc.append(fc)
return miller.array(
miller_set=miller_set,
data=f_calc)
def exercise_interface():
episq = 8 * (math.pi**2)
assert approx_equal(adptbx.u_as_b(2.3), 2.3 * episq)
assert approx_equal(adptbx.b_as_u(adptbx.u_as_b(2.3)), 2.3)
u = (3, 4, 9, 2, 1, 7)
assert approx_equal(adptbx.u_as_b(u), [x * episq for x in u])
assert approx_equal(adptbx.b_as_u(adptbx.u_as_b(u)), u)
uc = uctbx.unit_cell((5, 4, 7, 80, 110, 100))
for fw, bw in ((adptbx.u_cif_as_u_star, adptbx.u_star_as_u_cif),
(adptbx.u_cart_as_u_star, adptbx.u_star_as_u_cart),
(adptbx.u_cart_as_u_cif, adptbx.u_cif_as_u_cart),
(adptbx.u_cart_as_beta, adptbx.beta_as_u_cart),
(adptbx.u_cif_as_beta, adptbx.beta_as_u_cif)):
assert approx_equal(bw(uc, fw(uc, u)), u)
assert approx_equal(adptbx.beta_as_u_star(adptbx.u_star_as_beta(u)), u)
assert approx_equal(adptbx.u_cart_as_u_iso(adptbx.u_iso_as_u_cart(2.3)),
2.3)
for fw, bw in ((adptbx.u_iso_as_u_star, adptbx.u_star_as_u_iso),
(adptbx.u_iso_as_u_cif, adptbx.u_cif_as_u_iso),
(adptbx.u_iso_as_beta, adptbx.beta_as_u_iso)):
assert approx_equal(bw(uc, fw(uc, 2.3)), 2.3)
fc = adptbx.factor_u_cart_u_iso(u_cart=u)
assert approx_equal(fc.u_iso, adptbx.u_cart_as_u_iso(u))
assert approx_equal(fc.u_cart_minus_u_iso,
[uii - fc.u_iso for uii in u[:3]] + list(u[3:]))
f = adptbx.factor_u_star_u_iso(unit_cell=uc,
u_star=adptbx.u_cart_as_u_star(uc, u))
assert approx_equal(f.u_iso, fc.u_iso)
assert approx_equal(f.u_star_minus_u_iso,
adptbx.u_cart_as_u_star(uc, fc.u_cart_minus_u_iso))
f = adptbx.factor_u_cif_u_iso(unit_cell=uc,
u_cif=adptbx.u_cart_as_u_cif(uc, u))
assert approx_equal(f.u_iso, fc.u_iso)
assert approx_equal(f.u_cif_minus_u_iso,
adptbx.u_cart_as_u_cif(uc, fc.u_cart_minus_u_iso))
f = adptbx.factor_beta_u_iso(unit_cell=uc,
beta=adptbx.u_cart_as_beta(uc, u))
assert approx_equal(f.u_iso, fc.u_iso)
assert approx_equal(f.beta_minus_u_iso,
adptbx.u_cart_as_beta(uc, fc.u_cart_minus_u_iso))
assert approx_equal(adptbx.debye_waller_factor_b_iso(0.25, 2.3),
math.exp(-2.3 * 0.25))
assert approx_equal(adptbx.debye_waller_factor_u_iso(0.25, 2.3),
math.exp(-2.3 * episq * 0.25))
assert approx_equal(
adptbx.debye_waller_factor_b_iso(uc, (1, 2, 3), 2.3),
adptbx.debye_waller_factor_u_iso(uc, (1, 2, 3), 2.3 / episq))
u_star = adptbx.u_cart_as_u_star(uc, u)
dw = adptbx.debye_waller_factor_u_star((1, 2, 3), u_star)
assert approx_equal(
dw,
adptbx.debye_waller_factor_beta((1, 2, 3),
adptbx.u_star_as_beta(u_star)))
assert approx_equal(
dw,
adptbx.debye_waller_factor_u_cif(uc, (1, 2, 3),
adptbx.u_star_as_u_cif(uc, u_star)))
assert approx_equal(
dw,
adptbx.debye_waller_factor_u_cart(uc, (1, 2, 3),
adptbx.u_star_as_u_cart(uc, u_star)))
for e in adptbx.eigenvalues(u):
check_eigenvalue(u, e)
assert not adptbx.is_positive_definite(adptbx.eigenvalues(u))
assert not adptbx.is_positive_definite(adptbx.eigenvalues(u), 0)
assert adptbx.is_positive_definite(adptbx.eigenvalues(u), 1.22)
assert not adptbx.is_positive_definite(u)
assert not adptbx.is_positive_definite(u, 0)
assert adptbx.is_positive_definite(u, 1.22)
up = (0.534, 0.812, 0.613, 0.0166, 0.134, -0.0124)
s = adptbx.eigensystem(up)
assert approx_equal(s.values(), (0.813132, 0.713201, 0.432668))
for i in xrange(3):
check_eigenvector(up, s.values()[i], s.vectors(i))
c = (1, 2, 3, 3, -4, 5, 4, 5, 6)
v = (198, 18, 1020, 116, 447, 269)
assert approx_equal(adptbx.c_u_c_transpose(c, u), v)
assert approx_equal(
adptbx.eigensystem(u).values(),
(14.279201519086316, 2.9369143826320214, -1.2161159017183376))
s = adptbx.eigensystem(up)
try:
s.vectors(4)
except RuntimeError, e:
assert str(e).endswith("Index out of range.")
def exercise_interface():
episq = 8 * (math.pi ** 2)
assert approx_equal(adptbx.u_as_b(2.3), 2.3 * episq)
assert approx_equal(adptbx.b_as_u(adptbx.u_as_b(2.3)), 2.3)
u = (3, 4, 9, 2, 1, 7)
assert approx_equal(adptbx.u_as_b(u), [x * episq for x in u])
assert approx_equal(adptbx.b_as_u(adptbx.u_as_b(u)), u)
uc = uctbx.unit_cell((5, 4, 7, 80, 110, 100))
for fw, bw in (
(adptbx.u_cif_as_u_star, adptbx.u_star_as_u_cif),
(adptbx.u_cart_as_u_star, adptbx.u_star_as_u_cart),
(adptbx.u_cart_as_u_cif, adptbx.u_cif_as_u_cart),
(adptbx.u_cart_as_beta, adptbx.beta_as_u_cart),
(adptbx.u_cif_as_beta, adptbx.beta_as_u_cif),
):
assert approx_equal(bw(uc, fw(uc, u)), u)
assert approx_equal(adptbx.beta_as_u_star(adptbx.u_star_as_beta(u)), u)
assert approx_equal(adptbx.u_cart_as_u_iso(adptbx.u_iso_as_u_cart(2.3)), 2.3)
for fw, bw in (
(adptbx.u_iso_as_u_star, adptbx.u_star_as_u_iso),
(adptbx.u_iso_as_u_cif, adptbx.u_cif_as_u_iso),
(adptbx.u_iso_as_beta, adptbx.beta_as_u_iso),
):
assert approx_equal(bw(uc, fw(uc, 2.3)), 2.3)
fc = adptbx.factor_u_cart_u_iso(u_cart=u)
assert approx_equal(fc.u_iso, adptbx.u_cart_as_u_iso(u))
assert approx_equal(fc.u_cart_minus_u_iso, [uii - fc.u_iso for uii in u[:3]] + list(u[3:]))
f = adptbx.factor_u_star_u_iso(unit_cell=uc, u_star=adptbx.u_cart_as_u_star(uc, u))
assert approx_equal(f.u_iso, fc.u_iso)
assert approx_equal(f.u_star_minus_u_iso, adptbx.u_cart_as_u_star(uc, fc.u_cart_minus_u_iso))
f = adptbx.factor_u_cif_u_iso(unit_cell=uc, u_cif=adptbx.u_cart_as_u_cif(uc, u))
assert approx_equal(f.u_iso, fc.u_iso)
assert approx_equal(f.u_cif_minus_u_iso, adptbx.u_cart_as_u_cif(uc, fc.u_cart_minus_u_iso))
f = adptbx.factor_beta_u_iso(unit_cell=uc, beta=adptbx.u_cart_as_beta(uc, u))
assert approx_equal(f.u_iso, fc.u_iso)
assert approx_equal(f.beta_minus_u_iso, adptbx.u_cart_as_beta(uc, fc.u_cart_minus_u_iso))
assert approx_equal(adptbx.debye_waller_factor_b_iso(0.25, 2.3), math.exp(-2.3 * 0.25))
assert approx_equal(adptbx.debye_waller_factor_u_iso(0.25, 2.3), math.exp(-2.3 * episq * 0.25))
assert approx_equal(
adptbx.debye_waller_factor_b_iso(uc, (1, 2, 3), 2.3),
adptbx.debye_waller_factor_u_iso(uc, (1, 2, 3), 2.3 / episq),
)
u_star = adptbx.u_cart_as_u_star(uc, u)
dw = adptbx.debye_waller_factor_u_star((1, 2, 3), u_star)
assert approx_equal(dw, adptbx.debye_waller_factor_beta((1, 2, 3), adptbx.u_star_as_beta(u_star)))
assert approx_equal(dw, adptbx.debye_waller_factor_u_cif(uc, (1, 2, 3), adptbx.u_star_as_u_cif(uc, u_star)))
assert approx_equal(dw, adptbx.debye_waller_factor_u_cart(uc, (1, 2, 3), adptbx.u_star_as_u_cart(uc, u_star)))
for e in adptbx.eigenvalues(u):
check_eigenvalue(u, e)
assert not adptbx.is_positive_definite(adptbx.eigenvalues(u))
assert not adptbx.is_positive_definite(adptbx.eigenvalues(u), 0)
assert adptbx.is_positive_definite(adptbx.eigenvalues(u), 1.22)
assert not adptbx.is_positive_definite(u)
assert not adptbx.is_positive_definite(u, 0)
assert adptbx.is_positive_definite(u, 1.22)
up = (0.534, 0.812, 0.613, 0.0166, 0.134, -0.0124)
s = adptbx.eigensystem(up)
assert approx_equal(s.values(), (0.813132, 0.713201, 0.432668))
for i in xrange(3):
check_eigenvector(up, s.values()[i], s.vectors(i))
c = (1, 2, 3, 3, -4, 5, 4, 5, 6)
v = (198, 18, 1020, 116, 447, 269)
assert approx_equal(adptbx.c_u_c_transpose(c, u), v)
assert approx_equal(adptbx.eigensystem(u).values(), (14.279201519086316, 2.9369143826320214, -1.2161159017183376))
s = adptbx.eigensystem(up)
try:
s.vectors(4)
except RuntimeError, e:
assert str(e).endswith("Index out of range.")
def d_dw_d_u_star_analytical(h, u_star): dw = adptbx.debye_waller_factor_u_star(h, u_star) gc = flex.double(adptbx.debye_waller_factor_u_star_gradient_coefficients(h)) return -2*math.pi**2 * gc * dw
def d2_dw_d_u_star_d_u_star_analytical(h, u_star): dw = adptbx.debye_waller_factor_u_star(h, u_star) cc = flex.double(adptbx.debye_waller_factor_u_star_curvature_coefficients(h)) return 4*math.pi**4 * cc * dw
def exercise_interface():
episq = 8*(math.pi**2)
assert approx_equal(adptbx.u_as_b(2.3), 2.3*episq)
assert approx_equal(adptbx.b_as_u(adptbx.u_as_b(2.3)), 2.3)
u = (3,4,9, 2,1,7)
assert approx_equal(adptbx.u_as_b(u), [x*episq for x in u])
assert approx_equal(adptbx.b_as_u(adptbx.u_as_b(u)), u)
uc = uctbx.unit_cell((5,4,7,80,110,100))
for fw,bw in ((adptbx.u_cif_as_u_star, adptbx.u_star_as_u_cif),
(adptbx.u_cart_as_u_star, adptbx.u_star_as_u_cart),
(adptbx.u_cart_as_u_cif, adptbx.u_cif_as_u_cart),
(adptbx.u_cart_as_beta, adptbx.beta_as_u_cart),
(adptbx.u_cif_as_beta, adptbx.beta_as_u_cif)):
assert approx_equal(bw(uc, fw(uc, u)), u)
assert approx_equal(adptbx.beta_as_u_star(adptbx.u_star_as_beta(u)), u)
assert approx_equal(adptbx.u_cart_as_u_iso(adptbx.u_iso_as_u_cart(2.3)), 2.3)
for fw,bw in ((adptbx.u_iso_as_u_star, adptbx.u_star_as_u_iso),
(adptbx.u_iso_as_u_cif, adptbx.u_cif_as_u_iso),
(adptbx.u_iso_as_beta, adptbx.beta_as_u_iso)):
assert approx_equal(bw(uc, fw(uc, 2.3)), 2.3)
fc = adptbx.factor_u_cart_u_iso(u_cart=u)
assert approx_equal(fc.u_iso, adptbx.u_cart_as_u_iso(u))
assert approx_equal(
fc.u_cart_minus_u_iso,
[uii-fc.u_iso for uii in u[:3]]+list(u[3:]))
f = adptbx.factor_u_star_u_iso(
unit_cell=uc, u_star=adptbx.u_cart_as_u_star(uc, u))
assert approx_equal(f.u_iso, fc.u_iso)
assert approx_equal(
f.u_star_minus_u_iso,
adptbx.u_cart_as_u_star(uc, fc.u_cart_minus_u_iso))
f = adptbx.factor_u_cif_u_iso(
unit_cell=uc, u_cif=adptbx.u_cart_as_u_cif(uc, u))
assert approx_equal(f.u_iso, fc.u_iso)
assert approx_equal(
f.u_cif_minus_u_iso,
adptbx.u_cart_as_u_cif(uc, fc.u_cart_minus_u_iso))
f = adptbx.factor_beta_u_iso(
unit_cell=uc, beta=adptbx.u_cart_as_beta(uc, u))
assert approx_equal(f.u_iso, fc.u_iso)
assert approx_equal(
f.beta_minus_u_iso,
adptbx.u_cart_as_beta(uc, fc.u_cart_minus_u_iso))
assert approx_equal(adptbx.debye_waller_factor_b_iso(0.25,2.3),
math.exp(-2.3*0.25))
assert approx_equal(adptbx.debye_waller_factor_u_iso(0.25,2.3),
math.exp(-2.3*episq*0.25))
assert approx_equal(adptbx.debye_waller_factor_b_iso(uc, (1,2,3), 2.3),
adptbx.debye_waller_factor_u_iso(uc, (1,2,3), 2.3/episq))
u_star = adptbx.u_cart_as_u_star(uc, u)
dw = adptbx.debye_waller_factor_u_star((1,2,3), u_star)
assert approx_equal(dw, adptbx.debye_waller_factor_beta((1,2,3),
adptbx.u_star_as_beta(u_star)))
assert approx_equal(dw, adptbx.debye_waller_factor_u_cif(uc, (1,2,3),
adptbx.u_star_as_u_cif(uc, u_star)))
assert approx_equal(dw, adptbx.debye_waller_factor_u_cart(uc, (1,2,3),
adptbx.u_star_as_u_cart(uc, u_star)))
for e in adptbx.eigenvalues(u):
check_eigenvalue(u, e)
assert not adptbx.is_positive_definite(adptbx.eigenvalues(u))
assert not adptbx.is_positive_definite(adptbx.eigenvalues(u), 0)
assert adptbx.is_positive_definite(adptbx.eigenvalues(u), 1.22)
assert not adptbx.is_positive_definite(u)
assert not adptbx.is_positive_definite(u, 0)
assert adptbx.is_positive_definite(u, 1.22)
up = (0.534, 0.812, 0.613, 0.0166, 0.134, -0.0124)
s = adptbx.eigensystem(up)
assert approx_equal(s.values(), (0.813132, 0.713201, 0.432668))
for i in xrange(3):
check_eigenvector(up, s.values()[i], s.vectors(i))
c = (1,2,3, 3,-4,5, 4,5,6)
v = (198,18,1020,116,447,269)
assert approx_equal(adptbx.c_u_c_transpose(c, u), v)
assert approx_equal(adptbx.eigensystem(u).values(),
(14.279201519086316, 2.9369143826320214, -1.2161159017183376))
s = adptbx.eigensystem(up)
try: s.vectors(4)
except RuntimeError, e: assert str(e).endswith("Index out of range.")
else: raise Exception_expected
uf = adptbx.eigenvalue_filtering(u_cart=u, u_min=0)
assert approx_equal(uf, (3.0810418, 4.7950710, 9.3400030,
1.7461615, 1.1659954, 6.4800706))
uf = adptbx.eigenvalue_filtering(u_cart=u, u_min=0, u_max=3)
assert approx_equal(uf, (2.7430890, 1.0378360, 2.1559895,
0.6193215, -0.3921632, 1.2846854))
uf = adptbx.eigenvalue_filtering(u_cart=u, u_min=0, u_max=3)
assert approx_equal(scitbx.linalg.eigensystem.real_symmetric(u).values(),
(14.2792015, 2.9369144, -1.2161159))
assert approx_equal(scitbx.linalg.eigensystem.real_symmetric(uf).values(),
(3, 2.9369144, 0))
uf = adptbx.eigenvalue_filtering(up)
assert approx_equal(uf, up)
def compute_map_coefficients(self):
f_obs = self.f_obs_complete.select(self.f_obs_complete.d_spacings().data() >= self.d_min)
f_calc = f_obs.structure_factors_from_map(self.map, use_sg=True)
f_obs_active = f_obs.select_indices(self.active_indices)
minimized = relative_scaling.ls_rel_scale_driver(
f_obs_active,
f_calc.as_amplitude_array().select_indices(self.active_indices),
use_intensities=False,
use_weights=False)
#minimized.show()
f_calc = f_calc.customized_copy(data=f_calc.data()\
* math.exp(-minimized.p_scale)\
* adptbx.debye_waller_factor_u_star(
f_calc.indices(), minimized.u_star))
f_calc_active = f_calc.common_set(f_obs_active)
matched_indices = f_obs.match_indices(self.f_obs_active)
lone_indices_selection = matched_indices.single_selection(0)
from mmtbx.max_lik import maxlik
alpha_beta_est = maxlik.alpha_beta_est_manager(
f_obs=f_obs_active,
f_calc=f_calc_active,
free_reflections_per_bin=140,
flags=flex.bool(f_obs_active.size()),
interpolation=True,
epsilons=f_obs_active.epsilons().data().as_double())
alpha, beta = alpha_beta_est.alpha_beta_for_each_reflection(
f_obs=self.f_obs_complete.select(self.f_obs_complete.d_spacings().data() >= self.d_min))
f_obs.data().copy_selected(
lone_indices_selection.iselection(), flex.abs(f_calc.data()))
t = maxlik.fo_fc_alpha_over_eps_beta(
f_obs=f_obs,
f_model=f_calc,
alpha=alpha,
beta=beta)
hl_coeff = flex.hendrickson_lattman(
t * flex.cos(f_calc.phases().data()),
t * flex.sin(f_calc.phases().data()))
dd = alpha.data()
#
hl_array = f_calc.array(
data=self.hl_coeffs_start.common_set(f_calc).data()+hl_coeff)
self.compute_phase_source(hl_array)
fom = flex.abs(self.phase_source.data())
mFo = hl_array.array(data=f_obs.data()*self.phase_source.data())
DFc = hl_array.array(data=dd*f_calc.as_amplitude_array().phase_transfer(
self.phase_source).data())
centric_flags = f_obs.centric_flags().data()
acentric_flags = ~centric_flags
fo_scale = flex.double(centric_flags.size())
fc_scale = flex.double(centric_flags.size())
fo_scale.set_selected(acentric_flags, 2)
fo_scale.set_selected(centric_flags, 1)
fc_scale.set_selected(acentric_flags, 1)
fc_scale.set_selected(centric_flags, 0)
fo_scale.set_selected(lone_indices_selection, 0)
fc_scale.set_selected(lone_indices_selection, -1)
self.map_coeffs = hl_array.array(
data=mFo.data()*fo_scale - DFc.data()*fc_scale)
self.fom = hl_array.array(data=fom)
self.hl_coeffs = hl_array
# statistics
self.r1_factor = f_obs_active.r1_factor(f_calc_active)
fom = fom.select(matched_indices.pair_selection(0))
self.r1_factor_fom = flex.sum(
fom * flex.abs(f_obs_active.data() - f_calc_active.as_amplitude_array().data())) \
/ flex.sum(fom * f_obs_active.data())
phase_source, phase_source_previous = self.phase_source.common_sets(
self.phase_source_previous)
self.mean_delta_phi = phase_error(
flex.arg(phase_source.data()), flex.arg(phase_source_previous.data()))
phase_source, phase_source_initial = self.phase_source.common_sets(
self.phase_source_initial)
self.mean_delta_phi_initial = phase_error(
flex.arg(phase_source.data()), flex.arg(phase_source_initial.data()))
self.mean_fom = flex.mean(fom)
fom = f_obs_active.array(data=fom)
if fom.data().size()<1000: # 2013-12-14 was hard-wired at 1000 tt
reflections_per_bin=fom.data().size()
else:
reflections_per_bin=1000
fom.setup_binner(reflections_per_bin=reflections_per_bin)
self.mean_fom_binned = fom.mean(use_binning=True)
def compute_map_coefficients(self):
f_obs = self.f_obs_complete.select(
self.f_obs_complete.d_spacings().data() >= self.d_min)
f_calc = f_obs.structure_factors_from_map(self.map, use_sg=True)
f_obs_active = f_obs.select_indices(self.active_indices)
minimized = relative_scaling.ls_rel_scale_driver(
f_obs_active,
f_calc.as_amplitude_array().select_indices(self.active_indices),
use_intensities=False,
use_weights=False)
#minimized.show()
f_calc = f_calc.customized_copy(data=f_calc.data()\
* math.exp(-minimized.p_scale)\
* adptbx.debye_waller_factor_u_star(
f_calc.indices(), minimized.u_star))
f_calc_active = f_calc.common_set(f_obs_active)
matched_indices = f_obs.match_indices(self.f_obs_active)
lone_indices_selection = matched_indices.single_selection(0)
from mmtbx.max_lik import maxlik
alpha_beta_est = maxlik.alpha_beta_est_manager(
f_obs=f_obs_active,
f_calc=f_calc_active,
free_reflections_per_bin=140,
flags=flex.bool(f_obs_active.size()),
interpolation=True,
epsilons=f_obs_active.epsilons().data().as_double())
alpha, beta = alpha_beta_est.alpha_beta_for_each_reflection(
f_obs=self.f_obs_complete.select(
self.f_obs_complete.d_spacings().data() >= self.d_min))
f_obs.data().copy_selected(lone_indices_selection.iselection(),
flex.abs(f_calc.data()))
t = maxlik.fo_fc_alpha_over_eps_beta(f_obs=f_obs,
f_model=f_calc,
alpha=alpha,
beta=beta)
hl_coeff = flex.hendrickson_lattman(
t * flex.cos(f_calc.phases().data()),
t * flex.sin(f_calc.phases().data()))
dd = alpha.data()
#
hl_array = f_calc.array(
data=self.hl_coeffs_start.common_set(f_calc).data() + hl_coeff)
self.compute_phase_source(hl_array)
fom = flex.abs(self.phase_source.data())
mFo = hl_array.array(data=f_obs.data() * self.phase_source.data())
DFc = hl_array.array(data=dd *
f_calc.as_amplitude_array().phase_transfer(
self.phase_source).data())
centric_flags = f_obs.centric_flags().data()
acentric_flags = ~centric_flags
fo_scale = flex.double(centric_flags.size())
fc_scale = flex.double(centric_flags.size())
fo_scale.set_selected(acentric_flags, 2)
fo_scale.set_selected(centric_flags, 1)
fc_scale.set_selected(acentric_flags, 1)
fc_scale.set_selected(centric_flags, 0)
fo_scale.set_selected(lone_indices_selection, 0)
fc_scale.set_selected(lone_indices_selection, -1)
self.map_coeffs = hl_array.array(data=mFo.data() * fo_scale -
DFc.data() * fc_scale)
self.fom = hl_array.array(data=fom)
self.hl_coeffs = hl_array
# statistics
self.r1_factor = f_obs_active.r1_factor(f_calc_active)
fom = fom.select(matched_indices.pair_selection(0))
self.r1_factor_fom = flex.sum(
fom * flex.abs(f_obs_active.data() - f_calc_active.as_amplitude_array().data())) \
/ flex.sum(fom * f_obs_active.data())
phase_source, phase_source_previous = self.phase_source.common_sets(
self.phase_source_previous)
self.mean_delta_phi = phase_error(
flex.arg(phase_source.data()),
flex.arg(phase_source_previous.data()))
phase_source, phase_source_initial = self.phase_source.common_sets(
self.phase_source_initial)
self.mean_delta_phi_initial = phase_error(
flex.arg(phase_source.data()),
flex.arg(phase_source_initial.data()))
self.mean_fom = flex.mean(fom)
fom = f_obs_active.array(data=fom)
if fom.data().size() < 1000: # 2013-12-14 was hard-wired at 1000 tt
reflections_per_bin = fom.data().size()
else:
reflections_per_bin = 1000
fom.setup_binner(reflections_per_bin=reflections_per_bin)
self.mean_fom_binned = fom.mean(use_binning=True)
def run():
#
# try these Hall symbols:
# "P 1", "P 2", "P 3", "P 3*", "P 4", "P 6", "P 2 2 3"
#
space_group = sgtbx.space_group("P 3*") # Hall symbol
#
# initialization of space group symmetry constraints
#
adp_constraints = sgtbx.tensor_rank_2_constraints(space_group=space_group,
reciprocal_space=True)
#
# number of independent u_star parameters
#
n_indep = adp_constraints.n_independent_params()
#
# arbitrary Miller index and u_star tensor
#
h = (3, 1, 2)
u_star = (0.000004, 0.000004, 0.000007, 0.000002, 0.0000000, 0.0000000)
# optional: enforce symmetry at the beginning
u_star = space_group.average_u_star(u_star)
#
# pass u_indep to the minimizer
#
u_indep = adp_constraints.independent_params(all_params=u_star)
assert len(u_indep) == n_indep
#
# "expand" the independent parameters modified by the minimizer
#
u_star = adp_constraints.all_params(independent_params=u_indep)
assert len(u_star) == 6
#
# these calculations are completely independent of the symmetry
#
dwf = adptbx.debye_waller_factor_u_star(h, u_star)
gc = adptbx.debye_waller_factor_u_star_gradient_coefficients(h)
# all_gradients is an array of six values
all_gradients = [-2 * math.pi**2 * dwf * c for c in gc]
assert len(all_gradients) == 6
cc = adptbx.debye_waller_factor_u_star_curvature_coefficients(h)
# all_curvatures is an array of 21 values (upper triangle of 6x6 matrix)
all_curvatures = (-2 * math.pi**2)**2 * dwf * cc
assert len(all_curvatures) == 6 * (6 + 1) // 2
#
# here we apply the symmetry constraints to the gradients and curvatures
#
# g_indep is an array of n_indep values
g_indep = adp_constraints.independent_gradients(
all_gradients=all_gradients)
assert len(g_indep) == n_indep
# c_indep is an array of n_indep*(n_indep+1)/2 values (upper triangle)
c_indep = adp_constraints.independent_curvatures(
all_curvatures=all_curvatures)
assert len(c_indep) == n_indep * (n_indep + 1) // 2
# feed g_indep and c_indep to the minimizer
#
# initialization of site symmetry constraints
# (for sites on special positions)
#
unit_cell = uctbx.unit_cell((12, 12, 15, 90, 90, 120))
space_group = sgtbx.space_group_info("P 6").group()
site_symmetry = sgtbx.site_symmetry(
unit_cell=unit_cell,
space_group=space_group,
original_site=(1 / 3., 2 / 3., 0), # site on 3-fold axis
min_distance_sym_equiv=0.5)
assert len(site_symmetry.matrices()) == 3
adp_constraints = site_symmetry.adp_constraints()
# use adp_constraints as before
print("OK")
def run():
#
# try these Hall symbols:
# "P 1", "P 2", "P 3", "P 3*", "P 4", "P 6", "P 2 2 3"
#
space_group = sgtbx.space_group("P 3*") # Hall symbol
#
# initialization of space group symmetry constraints
#
adp_constraints = sgtbx.tensor_rank_2_constraints(
space_group=space_group,
reciprocal_space=True)
#
# number of independent u_star parameters
#
n_indep = adp_constraints.n_independent_params()
#
# arbitrary Miller index and u_star tensor
#
h = (3,1,2)
u_star=(0.000004, 0.000004, 0.000007, 0.000002, 0.0000000, 0.0000000)
# optional: enforce symmetry at the beginning
u_star = space_group.average_u_star(u_star)
#
# pass u_indep to the minimizer
#
u_indep = adp_constraints.independent_params(all_params=u_star)
assert len(u_indep) == n_indep
#
# "expand" the independent parameters modified by the minimizer
#
u_star = adp_constraints.all_params(independent_params=u_indep)
assert len(u_star) == 6
#
# these calculations are completely independent of the symmetry
#
dwf = adptbx.debye_waller_factor_u_star(h, u_star)
gc = adptbx.debye_waller_factor_u_star_gradient_coefficients(h)
# all_gradients is an array of six values
all_gradients = [-2*math.pi**2 * dwf * c for c in gc]
assert len(all_gradients) == 6
cc = adptbx.debye_waller_factor_u_star_curvature_coefficients(h)
# all_curvatures is an array of 21 values (upper triangle of 6x6 matrix)
all_curvatures = (-2*math.pi**2)**2 * dwf * cc
assert len(all_curvatures) == 6*(6+1)//2
#
# here we apply the symmetry constraints to the gradients and curvatures
#
# g_indep is an array of n_indep values
g_indep = adp_constraints.independent_gradients(
all_gradients=all_gradients)
assert len(g_indep) == n_indep
# c_indep is an array of n_indep*(n_indep+1)/2 values (upper triangle)
c_indep = adp_constraints.independent_curvatures(
all_curvatures=all_curvatures)
assert len(c_indep) == n_indep*(n_indep+1)//2
# feed g_indep and c_indep to the minimizer
#
# initialization of site symmetry constraints
# (for sites on special positions)
#
unit_cell = uctbx.unit_cell((12,12,15,90,90,120))
space_group = sgtbx.space_group_info("P 6").group()
site_symmetry = sgtbx.site_symmetry(
unit_cell=unit_cell,
space_group=space_group,
original_site=(1/3.,2/3.,0), # site on 3-fold axis
min_distance_sym_equiv=0.5)
assert len(site_symmetry.matrices()) == 3
adp_constraints = site_symmetry.adp_constraints()
# use adp_constraints as before
print "OK"
