def branch_3_mn():
m = None
n = None
small = 1.e-15
for i in range(10000):
m2 = []
n2 = []
for i in range(4):
r1 = random.random()
r2 = random.random()
r3 = random.random()
if (r3 > 0.1):
r1 = r2
m2.append(r1)
n2.append(r2)
p1 = 0.5 * (m2[0] + m2[3] + math.sqrt(4 * m2[1] * m2[2] +
(m2[0] - m2[3])**2))
p2 = 0.5 * (m2[0] + m2[3] - math.sqrt(4 * m2[1] * m2[2] +
(m2[0] - m2[3])**2))
q1 = 0.5 * (n2[0] + m2[3] + math.sqrt(4 * n2[1] * n2[2] +
(n2[0] - n2[3])**2))
q2 = 0.5 * (n2[0] + m2[3] - math.sqrt(4 * n2[1] * n2[2] +
(n2[0] - n2[3])**2))
if (min(p1, p2) > 0.0 and min(q1, q2) > 0.0):
r = random.random()
if (r > 0.5):
r1 = r3
r2 = r2
m = [m2[0], m2[3], r1, m2[1], 0, 0]
n = [n2[0], n2[3], r2, n2[1], 0, 0]
if ([
adptbx.is_positive_definite(m),
adptbx.is_positive_definite(n)
].count(True) == 2):
esm = adptbx.eigensystem(m)
esn = adptbx.eigensystem(n)
vn = esn.values()
vm = esm.values()
mmin = flex.min(flex.double(vm))
nmin = flex.min(flex.double(vn))
if (abs(abs(mmin) - abs(nmin)) < small and mmin > 0.
and nmin > 0.):
for i, v in enumerate(vn):
if (abs(abs(nmin) - v) < small): break
for j, v in enumerate(vm):
if (abs(abs(mmin) - v) < small): break
vecn = flex.double(esn.vectors(i))
vecm = flex.double(esm.vectors(j))
if (flex.mean(vecm - vecn) < small): break
else:
m = None
n = None
assert [m, n] != [None, None]
assert [adptbx.is_positive_definite(m),
adptbx.is_positive_definite(n)].count(True) == 2
r = random.random()
if (r > 0.5):
m = adptbx.random_rotate_ellipsoid(u_cart=m)
n = adptbx.random_rotate_ellipsoid(u_cart=n)
return m, n
def branch_3_mn():
m = None
n = None
small = 1.e-15
for i in xrange(10000):
m2=[]
n2=[]
for i in xrange(4):
r1 = random.random()
r2 = random.random()
r3 = random.random()
if(r3 > 0.1):
r1 = r2
m2.append(r1)
n2.append(r2)
p1 = 0.5 * (m2[0]+m2[3] + math.sqrt(4*m2[1]*m2[2]+(m2[0]-m2[3])**2))
p2 = 0.5 * (m2[0]+m2[3] - math.sqrt(4*m2[1]*m2[2]+(m2[0]-m2[3])**2))
q1 = 0.5 * (n2[0]+m2[3] + math.sqrt(4*n2[1]*n2[2]+(n2[0]-n2[3])**2))
q2 = 0.5 * (n2[0]+m2[3] - math.sqrt(4*n2[1]*n2[2]+(n2[0]-n2[3])**2))
if(min(p1,p2) > 0.0 and min(q1,q2) > 0.0):
r = random.random()
if(r > 0.5):
r1 = r3
r2 = r2
m = [m2[0],m2[3],r1,m2[1],0,0]
n = [n2[0],n2[3],r2,n2[1],0,0]
if([adptbx.is_positive_definite(m),
adptbx.is_positive_definite(n)].count(True)==2):
esm = adptbx.eigensystem(m)
esn = adptbx.eigensystem(n)
vn = esn.values()
vm = esm.values()
mmin = flex.min(flex.double(vm))
nmin = flex.min(flex.double(vn))
if(abs(abs(mmin) - abs(nmin)) < small and mmin> 0. and nmin> 0.):
for i, v in enumerate(vn):
if(abs(abs(nmin) - v) < small): break
for j, v in enumerate(vm):
if(abs(abs(mmin) - v) < small): break
vecn = flex.double(esn.vectors(i))
vecm = flex.double(esm.vectors(j))
if(flex.mean(vecm-vecn) < small): break
else:
m = None
n = None
assert [m,n] != [None,None]
assert [adptbx.is_positive_definite(m),
adptbx.is_positive_definite(n)].count(True)==2
r = random.random()
if(r > 0.5):
m = adptbx.random_rotate_ellipsoid(u_cart = m)
n = adptbx.random_rotate_ellipsoid(u_cart = n)
return m,n
def run():
symmetry = crystal.symmetry(unit_cell=(10.67, 10.67, 4.68, 90, 90, 120),
space_group_symbol="P 3")
special_position_settings = crystal.special_position_settings(
crystal_symmetry=symmetry, min_distance_sym_equiv=0.5)
site = (0, 0, 0.236)
u_cif = ((0.17, 0.17, 0.19, 0.09, 0, 0))
site_symmetry = special_position_settings.site_symmetry(site)
print "Input Ucif:", u_cif
u_star = adptbx.u_cif_as_u_star(symmetry.unit_cell(), u_cif)
if (not site_symmetry.is_compatible_u_star(u_star)):
print "Warning: ADP tensor is incompatible with site symmetry."
u_star = site_symmetry.average_u_star(u_star)
u_cif = adptbx.u_star_as_u_cif(symmetry.unit_cell(), u_star)
print "Averaged Ucif:", u_cif
u_cart = adptbx.u_star_as_u_cart(symmetry.unit_cell(), u_star)
eigenvalues = adptbx.eigenvalues(u_cart)
if (not adptbx.is_positive_definite(eigenvalues)):
print "ADP tensor is not positive definite."
print "Eigenvectors and values:"
eigensystem = adptbx.eigensystem(u_cart)
for i in xrange(3):
print " v=(%.5f %.5f %.5f) " % eigensystem.vectors(i),
print "lambda=%.4f" % (eigensystem.values()[i], )
def run():
symmetry = crystal.symmetry(
unit_cell=(10.67, 10.67, 4.68, 90, 90, 120),
space_group_symbol="P 3")
special_position_settings = crystal.special_position_settings(
crystal_symmetry=symmetry,
min_distance_sym_equiv=0.5)
site = (0, 0, 0.236)
u_cif = ((0.17, 0.17, 0.19, 0.09, 0, 0))
site_symmetry = special_position_settings.site_symmetry(site)
print "Input Ucif:", u_cif
u_star = adptbx.u_cif_as_u_star(symmetry.unit_cell(), u_cif)
if (not site_symmetry.is_compatible_u_star(u_star)):
print "Warning: ADP tensor is incompatible with site symmetry."
u_star = site_symmetry.average_u_star(u_star)
u_cif = adptbx.u_star_as_u_cif(symmetry.unit_cell(), u_star)
print "Averaged Ucif:", u_cif
u_cart = adptbx.u_star_as_u_cart(symmetry.unit_cell(), u_star)
eigenvalues = adptbx.eigenvalues(u_cart)
if (not adptbx.is_positive_definite(eigenvalues)):
print "ADP tensor is not positive definite."
print "Eigenvectors and values:"
eigensystem = adptbx.eigensystem(u_cart)
for i in xrange(3):
print " v=(%.5f %.5f %.5f) " % eigensystem.vectors(i),
print "lambda=%.4f" % (eigensystem.values()[i],)
def check_u_cart(axis, u_cart):
ev = adptbx.eigenvalues(u_cart)
assert ev[0] > 0
assert approx_equal(ev[1:], [0, 0])
es = adptbx.eigensystem(u_cart)
evs = es.vectors(0), es.vectors(1), es.vectors(2)
a1 = math.acos((axis[0]*evs[0][0]+axis[1]*evs[0][1]+axis[2]*evs[0][2])/ \
(evs[0][0]**2+evs[0][1]**2+evs[0][2]**2)) *180/math.pi
a2 = math.acos((axis[0]*evs[1][0]+axis[1]*evs[1][1]+axis[2]*evs[1][2])/ \
(evs[1][0]**2+evs[1][1]**2+evs[1][2]**2)) *180/math.pi
a3 = math.acos((axis[0]*evs[2][0]+axis[1]*evs[2][1]+axis[2]*evs[2][2])/ \
(evs[2][0]**2+evs[2][1]**2+evs[2][2]**2)) *180/math.pi
assert approx_equal(a1, 90.)
def check_u_cart(axis, u_cart):
ev = adptbx.eigenvalues(u_cart)
assert ev[0] > 0
assert approx_equal(ev[1:],[0,0])
es = adptbx.eigensystem(u_cart)
evs = es.vectors(0),es.vectors(1),es.vectors(2)
a1 = math.acos((axis[0]*evs[0][0]+axis[1]*evs[0][1]+axis[2]*evs[0][2])/ \
(evs[0][0]**2+evs[0][1]**2+evs[0][2]**2)) *180/math.pi
a2 = math.acos((axis[0]*evs[1][0]+axis[1]*evs[1][1]+axis[2]*evs[1][2])/ \
(evs[1][0]**2+evs[1][1]**2+evs[1][2]**2)) *180/math.pi
a3 = math.acos((axis[0]*evs[2][0]+axis[1]*evs[2][1]+axis[2]*evs[2][2])/ \
(evs[2][0]**2+evs[2][1]**2+evs[2][2]**2)) *180/math.pi
assert approx_equal(a1, 90.)
def exercise_eigen_core(diag):
u = adptbx.random_rotate_ellipsoid(diag + [0., 0., 0.])
ev = list(adptbx.eigenvalues(u))
diag.sort()
ev.sort()
for i in xrange(3):
check_eigenvalue(u, ev[i])
for i in xrange(3):
assert abs(diag[i] - ev[i]) < 1.e-4
if (adptbx.is_positive_definite(ev)):
es = adptbx.eigensystem(u)
ev = list(es.values())
ev.sort()
for i in xrange(3):
check_eigenvalue(u, ev[i])
for i in xrange(3):
assert abs(diag[i] - ev[i]) < 1.e-4
evec = []
for i in xrange(3):
check_eigenvector(u, es.values()[i], es.vectors(i))
evec.extend(es.vectors(i))
return # XXX following tests disabled for the moment
# sometimes fail if eigenvalues are very similar but not identical
sqrt_eval = matrix.diag(flex.sqrt(flex.double(es.values())))
evec = matrix.sqr(evec).transpose()
sqrt_u = evec * sqrt_eval * evec.transpose()
u_full = matrix.sym(sym_mat3=u).elems
assert approx_equal(u_full, (sqrt_u.transpose() * sqrt_u).elems,
eps=1.e-3)
assert approx_equal(u_full, (sqrt_u * sqrt_u.transpose()).elems,
eps=1.e-3)
assert approx_equal(u_full, (sqrt_u * sqrt_u).elems, eps=1.e-3)
sqrt_u_plus_shifts = matrix.sym(sym_mat3=[
x + 10 * (random.random() - .5) for x in sqrt_u.as_sym_mat3()
])
sts = (sqrt_u_plus_shifts.transpose() *
sqrt_u_plus_shifts).as_sym_mat3()
ev = adptbx.eigenvalues(sts)
assert min(ev) >= 0
sts = (sqrt_u_plus_shifts *
sqrt_u_plus_shifts.transpose()).as_sym_mat3()
ev = adptbx.eigenvalues(sts)
assert min(ev) >= 0
sts = (sqrt_u_plus_shifts * sqrt_u_plus_shifts).as_sym_mat3()
ev = adptbx.eigenvalues(sts)
assert min(ev) >= 0
def principal_axes_of_inertia(real_map, site_cart, unit_cell, radius):
st = sphericity_tensor(map_data=real_map,
unit_cell=unit_cell,
radius=radius,
site_frac=unit_cell.fractionalize(site_cart))
es = adptbx.eigensystem(st)
def center_of_mass_():
return center_of_mass(map_data=real_map,
unit_cell=unit_cell,
cutoff=0.1)
def inertia_tensor():
return st
def eigensystem():
return es
return group_args(center_of_mass=center_of_mass_,
inertia_tensor=inertia_tensor,
eigensystem=eigensystem)
def exercise_eigen_core(diag):
u = adptbx.random_rotate_ellipsoid(diag + [0.0, 0.0, 0.0])
ev = list(adptbx.eigenvalues(u))
diag.sort()
ev.sort()
for i in xrange(3):
check_eigenvalue(u, ev[i])
for i in xrange(3):
assert abs(diag[i] - ev[i]) < 1.0e-4
if adptbx.is_positive_definite(ev):
es = adptbx.eigensystem(u)
ev = list(es.values())
ev.sort()
for i in xrange(3):
check_eigenvalue(u, ev[i])
for i in xrange(3):
assert abs(diag[i] - ev[i]) < 1.0e-4
evec = []
for i in xrange(3):
check_eigenvector(u, es.values()[i], es.vectors(i))
evec.extend(es.vectors(i))
return # XXX following tests disabled for the moment
# sometimes fail if eigenvalues are very similar but not identical
sqrt_eval = matrix.diag(flex.sqrt(flex.double(es.values())))
evec = matrix.sqr(evec).transpose()
sqrt_u = evec * sqrt_eval * evec.transpose()
u_full = matrix.sym(sym_mat3=u).elems
assert approx_equal(u_full, (sqrt_u.transpose() * sqrt_u).elems, eps=1.0e-3)
assert approx_equal(u_full, (sqrt_u * sqrt_u.transpose()).elems, eps=1.0e-3)
assert approx_equal(u_full, (sqrt_u * sqrt_u).elems, eps=1.0e-3)
sqrt_u_plus_shifts = matrix.sym(sym_mat3=[x + 10 * (random.random() - 0.5) for x in sqrt_u.as_sym_mat3()])
sts = (sqrt_u_plus_shifts.transpose() * sqrt_u_plus_shifts).as_sym_mat3()
ev = adptbx.eigenvalues(sts)
assert min(ev) >= 0
sts = (sqrt_u_plus_shifts * sqrt_u_plus_shifts.transpose()).as_sym_mat3()
ev = adptbx.eigenvalues(sts)
assert min(ev) >= 0
sts = (sqrt_u_plus_shifts * sqrt_u_plus_shifts).as_sym_mat3()
ev = adptbx.eigenvalues(sts)
assert min(ev) >= 0
def principal_axes_of_inertia (
real_map,
site_cart,
unit_cell,
radius):
st = sphericity_tensor(
map_data = real_map,
unit_cell = unit_cell,
radius = radius,
site_frac = unit_cell.fractionalize(site_cart))
es = adptbx.eigensystem(st)
def center_of_mass_():
return center_of_mass(
map_data=real_map, unit_cell=unit_cell, cutoff=0.1)
def inertia_tensor():
return st
def eigensystem():
return es
return group_args(
center_of_mass = center_of_mass_,
inertia_tensor = inertia_tensor,
eigensystem = eigensystem)
def get_anisotropy(u): esv = adptbx.eigensystem(u).values() return min(esv)/max(esv)
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.")
