def exercise_debye_waller():
ucell = uctbx.unit_cell((5,7,9,80,100,130))
assert abs(adptbx.debye_waller_factor_u_iso(ucell.d_star_sq((7,8,9))/4,0.025)
- 0.006625427) < 1.e-6
assert abs(adptbx.debye_waller_factor_u_iso(ucell, (7, 8, 9), 0.025)
- 0.006625427) < 1.e-6
u = (0.1, 0.2, 0.3, -0.04, 0.05, -0.06)
assert abs(adptbx.debye_waller_factor_u_cif(ucell, (1, 2, 3), u)
- 0.335822877927) < 1.e-6
#
u_star=(0.000002, 0.000001, 0.000003, 0.0000005, 0.0000004, 0.0000006)
assert approx_equal(
adptbx.debye_waller_factor_u_star_gradient_coefficients(h=(5,2,-1)),
[25, 4, 1, 20, -10, -4])
g = adptbx.debye_waller_factor_u_star_gradients(h=(5,2,-1), u_star=u_star)
assert approx_equal(g*1.e-3,
[-0.49289027387879081, -0.078862443820606531, -0.019715610955151633,
-0.39431221910303266, 0.19715610955151633, 0.078862443820606531])
assert approx_equal(
adptbx.debye_waller_factor_u_star_curvature_coefficients(h=(5,2,-1)),
[625,100,25,500,-250,-100,
16,4,80,-40,-16,
1,20,-10,-4,
400,-200,-80,
100,40,
16])
c = adptbx.debye_waller_factor_u_star_curvatures(h=(5,2,-1), u_star=u_star)
assert approx_equal(c*1.e-6,
[0.24323160081641265, 0.038917056130626029, 0.0097292640326565073,
0.1945852806531301, -0.097292640326565052, -0.038917056130626029,
0.006226728980900164, 0.001556682245225041, 0.031133644904500817,
-0.015566822452250408, -0.006226728980900164, 0.00038917056130626025,
0.0077834112261252041, -0.0038917056130626021, -0.001556682245225041,
0.15566822452250412, -0.077834112261252059, -0.031133644904500817,
0.038917056130626029, 0.015566822452250408, 0.006226728980900164])
def exercise_debye_waller():
ucell = uctbx.unit_cell((5, 7, 9, 80, 100, 130))
assert abs(adptbx.debye_waller_factor_u_iso(ucell.d_star_sq((7, 8, 9)) / 4, 0.025) - 0.006625427) < 1.0e-6
assert abs(adptbx.debye_waller_factor_u_iso(ucell, (7, 8, 9), 0.025) - 0.006625427) < 1.0e-6
u = (0.1, 0.2, 0.3, -0.04, 0.05, -0.06)
assert abs(adptbx.debye_waller_factor_u_cif(ucell, (1, 2, 3), u) - 0.335822877927) < 1.0e-6
#
u_star = (0.000002, 0.000001, 0.000003, 0.0000005, 0.0000004, 0.0000006)
assert approx_equal(adptbx.debye_waller_factor_u_star_gradient_coefficients(h=(5, 2, -1)), [25, 4, 1, 20, -10, -4])
g = adptbx.debye_waller_factor_u_star_gradients(h=(5, 2, -1), u_star=u_star)
assert approx_equal(
g * 1.0e-3,
[
-0.49289027387879081,
-0.078862443820606531,
-0.019715610955151633,
-0.39431221910303266,
0.19715610955151633,
0.078862443820606531,
],
)
assert approx_equal(
adptbx.debye_waller_factor_u_star_curvature_coefficients(h=(5, 2, -1)),
[625, 100, 25, 500, -250, -100, 16, 4, 80, -40, -16, 1, 20, -10, -4, 400, -200, -80, 100, 40, 16],
)
c = adptbx.debye_waller_factor_u_star_curvatures(h=(5, 2, -1), u_star=u_star)
assert approx_equal(
c * 1.0e-6,
[
0.24323160081641265,
0.038917056130626029,
0.0097292640326565073,
0.1945852806531301,
-0.097292640326565052,
-0.038917056130626029,
0.006226728980900164,
0.001556682245225041,
0.031133644904500817,
-0.015566822452250408,
-0.006226728980900164,
0.00038917056130626025,
0.0077834112261252041,
-0.0038917056130626021,
-0.001556682245225041,
0.15566822452250412,
-0.077834112261252059,
-0.031133644904500817,
0.038917056130626029,
0.015566822452250408,
0.006226728980900164,
],
)
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.")
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 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.")
