def _clear(self, name=None):
# NOTE the Diffraction calculator is expecting this object to exist in
# the long run. We can't remove this entire object, and recreate it.
# It also contains a required link to the angle calculator.
reflist = ReflectionList(self._geometry,
self._get_diffractometer_axes_names())
reference = YouReference(self._get_UB)
self._state = UBCalcState(name=name,
reflist=reflist,
reference=reference)
self._U = None
self._UB = None
self._state.configure_calc_type()
def _clear(self, name=None):
# NOTE the Diffraction calculator is expecting this object to exist in
# the long run. We can't remove this entire object, and recreate it.
# It also contains a required link to the angle calculator.
reflist = ReflectionList(self._geometry, self._diffractometer_axes_names)
self._state = UBCalcState(name=name, reflist=reflist)
self._U = None
self._UB = None
self._state.configure_calc_type()
def _clear(self, name=None):
# NOTE the Diffraction calculator is expecting this object to exist in
# the long run. We can't remove this entire object, and recreate it.
# It also contains a required link to the angle calculator.
reflist = ReflectionList(
settings.geometry,
self._get_diffractometer_axes_names(),
multiplier=settings.hardware.energyScannableMultiplierToGetKeV)
orientlist = OrientationList(settings.geometry,
self._get_diffractometer_axes_names())
reference = YouReference(self._get_UB)
reference._set_n_hkl_configured(settings.reference_vector)
surface = YouReference(self._get_UB)
surface._set_n_phi_configured(settings.surface_vector)
self._state = UBCalcState(name=name,
reflist=reflist,
orientlist=orientlist,
reference=reference,
surface=surface)
self._U = None
self._UB = None
self._state.configure_calc_type()
class UBCalculation:
"""A UB matrix calculation for an experiment.
Contains the parameters for the _crystal under test, a list of measured
reflections and, if its been calculated, a UB matrix to be used by the rest
of the code.
"""
def __init__(self,
persister,
strategy,
include_sigtau=True,
include_reference=True):
# The diffractometer geometry is required to map the internal angles
# into those used by this diffractometer (for display only)
self._persister = persister
self._strategy = strategy
self.include_sigtau = include_sigtau
self.include_reference = include_reference
try:
self._tobj = CoordinateConverter(
transform=settings.geometry.beamline_axes_transform)
except AttributeError:
self._tobj = CoordinateConverter(transform=None)
self._clear()
def _get_diffractometer_axes_names(self):
return settings.hardware.get_axes_names()
def _clear(self, name=None):
# NOTE the Diffraction calculator is expecting this object to exist in
# the long run. We can't remove this entire object, and recreate it.
# It also contains a required link to the angle calculator.
reflist = ReflectionList(
settings.geometry,
self._get_diffractometer_axes_names(),
multiplier=settings.hardware.energyScannableMultiplierToGetKeV)
orientlist = OrientationList(settings.geometry,
self._get_diffractometer_axes_names())
reference = YouReference(self._get_UB)
reference._set_n_hkl_configured(settings.reference_vector)
surface = YouReference(self._get_UB)
surface._set_n_phi_configured(settings.surface_vector)
self._state = UBCalcState(name=name,
reflist=reflist,
orientlist=orientlist,
reference=reference,
surface=surface)
self._U = None
self._UB = None
self._state.configure_calc_type()
### State ###
def start_new(self, name):
"""Start new UB matrix calculation.
Creates a new blank UB matrix calculation.
Parameters
----------
name: str
Name of a new UB matrix calculation
"""
# Create storage object if name does not exist (TODO)
self._clear(name)
self.save()
def load(self, name):
state = self._persister.load(name)
if isinstance(self._persister, UBCalculationJSONPersister):
self._state = self._persister.encoder.decode_ubcalcstate(
state, settings.geometry,
self._get_diffractometer_axes_names(),
settings.hardware.energyScannableMultiplierToGetKeV)
self._state.reference.get_UB = self._get_UB
self._state.surface.get_UB = self._get_UB
elif isinstance(self._persister, UBCalculationPersister):
self._state = state
else:
raise DiffcalcException('Unexpected persister type: ' +
str(self._persister))
if self._state.manual_U is not None:
self._U = self._state.manual_U
self._UB = self._U * self._state.crystal.B
self.save()
elif self._state.manual_UB is not None:
self._UB = self._state.manual_UB
self.save()
elif self._state.is_okay_to_autocalculate_ub:
try:
self.calculate_UB(self._state.or0, self._state.or1)
except Exception, e:
print e
else:
class UBCalculation:
"""A UB matrix calculation for an experiment.
Contains the parameters for the _crystal under test, a list of measured
reflections and, if its been calculated, a UB matrix to be used by the rest
of the code.
"""
def __init__(self,
hardware,
diffractometerPluginObject,
persister,
strategy,
include_sigtau=True,
include_reference=True):
# The diffractometer geometry is required to map the internal angles
# into those used by this diffractometer (for display only)
self._hardware = hardware
self._geometry = diffractometerPluginObject
self._persister = persister
self._strategy = strategy
self.include_sigtau = include_sigtau
self.include_reference = include_reference
self._clear()
def _get_diffractometer_axes_names(self):
return self._hardware.get_axes_names()
def _clear(self, name=None):
# NOTE the Diffraction calculator is expecting this object to exist in
# the long run. We can't remove this entire object, and recreate it.
# It also contains a required link to the angle calculator.
reflist = ReflectionList(self._geometry,
self._get_diffractometer_axes_names())
reference = YouReference(self._get_UB)
self._state = UBCalcState(name=name,
reflist=reflist,
reference=reference)
self._U = None
self._UB = None
self._state.configure_calc_type()
### State ###
def start_new(self, name):
"""start_new(name) --- creates a new blank ub calculation"""
# Create storage object if name does not exist (TODO)
if name in self._persister.list():
print(
"No UBCalculation started: There is already a calculation "
"called: " + name)
print "Saved calculations: " + repr(self._persister.list())
return
self._clear(name)
self.save()
def load(self, name):
state = self._persister.load(name)
if isinstance(self._persister, UBCalculationJSONPersister):
self._state = decode_ubcalcstate(
state, self._geometry, self._get_diffractometer_axes_names())
self._state.reference.get_UB = self._get_UB
elif isinstance(self._persister, UBCalculationPersister):
self._state = state
else:
raise Exception('Unexpected persister type: ' +
str(self._persister))
if self._state.manual_U is not None:
self.set_U_manually(self._state.manual_U)
elif self._state.manual_UB is not None:
self.set_UB_manually(self._state.manual_UB)
elif self._state.or0 is not None:
if self._state.or1 is None:
self.calculate_UB_from_primary_only()
else:
self.calculate_UB()
else:
pass
def save(self):
self.saveas(self._state.name)
def saveas(self, name):
self._state.name = name
self._persister.save(self._state, name)
def listub(self):
return self._persister.list()
def listub_metadata(self):
return self._persister.list_metadata()
def remove(self, name):
self._persister.remove(name)
if self._state == name:
self._clear(name)
def getState(self):
return self._state.getState()
def __str__(self):
if self._state.name is None:
return "<<< No UB calculation started >>>"
lines = []
lines.append(bold("UBCALC"))
lines.append("")
lines.append(" name:".ljust(WIDTH) + self._state.name.rjust(9))
if self.include_sigtau:
lines.append("")
lines.append(" sigma:".ljust(WIDTH) +
("% 9.5f" % self._state.sigma).rjust(9))
lines.append(" tau:".ljust(WIDTH) +
("% 9.5f" % self._state.tau).rjust(9))
if self.include_reference:
lines.append("")
ub_calculated = self._UB is not None
lines.extend(self._state.reference.repr_lines(
ub_calculated, WIDTH))
lines.append("")
lines.append(bold("CRYSTAL"))
lines.append("")
if self._state.crystal is None:
lines.append(" <<< none specified >>>")
else:
lines.extend(self._state.crystal.str_lines())
lines.append("")
lines.append(bold("UB MATRIX"))
lines.append("")
if self._UB is None:
lines.append(" <<< none calculated >>>")
else:
lines.extend(self.str_lines_u())
lines.append("")
lines.extend(self.str_lines_u_angle_and_axis())
lines.append("")
lines.extend(self.str_lines_ub())
lines.append("")
lines.append(bold("REFLECTIONS"))
lines.append("")
lines.extend(self._state.reflist.str_lines())
return '\n'.join(lines)
def str_lines_u(self):
lines = []
fmt = "% 9.5f % 9.5f % 9.5f"
U = self.U
lines.append(" U matrix:".ljust(WIDTH) + fmt %
(z(U[0, 0]), z(U[0, 1]), z(U[0, 2])))
lines.append(' ' * WIDTH + fmt % (z(U[1, 0]), z(U[1, 1]), z(U[1, 2])))
lines.append(' ' * WIDTH + fmt % (z(U[2, 0]), z(U[2, 1]), z(U[2, 2])))
return lines
def str_lines_u_angle_and_axis(self):
lines = []
fmt = "% 9.5f % 9.5f % 9.5f"
y = matrix('0; 0; 1')
rotation_axis = cross3(y, self.U * y)
if abs(norm(rotation_axis)) < SMALL:
lines.append(" U angle:".ljust(WIDTH) + " 0")
else:
rotation_axis = rotation_axis * (1 / norm(rotation_axis))
cos_rotation_angle = dot3(y, self.U * y)
rotation_angle = acos(cos_rotation_angle)
lines.append(" angle:".ljust(WIDTH) + "% 9.5f" %
(rotation_angle * TODEG))
lines.append(" axis:".ljust(WIDTH) +
fmt % tuple((rotation_axis.T).tolist()[0]))
return lines
def str_lines_ub(self):
lines = []
fmt = "% 9.5f % 9.5f % 9.5f"
UB = self.UB
lines.append(" UB matrix:".ljust(WIDTH) + fmt %
(z(UB[0, 0]), z(UB[0, 1]), z(UB[0, 2])))
lines.append(' ' * WIDTH + fmt %
(z(UB[1, 0]), z(UB[1, 1]), z(UB[1, 2])))
lines.append(' ' * WIDTH + fmt %
(z(UB[2, 0]), z(UB[2, 1]), z(UB[2, 2])))
return lines
@property
def name(self):
return self._state.name
### Lattice ###
def set_lattice(self, name, *shortform):
"""
Converts a list shortform crystal parameter specification to a six-long
tuple returned as . Returns None if wrong number of input args. See
set_lattice() for a description of the shortforms supported.
shortformLattice -- a tuple as follows:
[a] - assumes cubic
[a,b]) - assumes tetragonal
[a,b,c]) - assumes ortho
[a,b,c,gam]) - assumes mon/hex gam different from 90.
[a,b,c,alp,bet,gam]) - for arbitrary
where all measurements in angstroms and angles in degrees
"""
self._set_lattice_without_saving(name, *shortform)
self.save()
def _set_lattice_without_saving(self, name, *shortform):
sf = shortform
if len(sf) == 1:
fullform = (sf[0], sf[0], sf[0], 90., 90., 90.) # cubic
elif len(sf) == 2:
fullform = (sf[0], sf[0], sf[1], 90., 90., 90.) # tetragonal
elif len(sf) == 3:
fullform = (sf[0], sf[1], sf[2], 90., 90., 90.) # ortho
elif len(sf) == 4:
fullform = (sf[0], sf[1], sf[2], 90., 90., sf[3]) # mon/hex gam
# not 90
elif len(sf) == 5:
raise ValueError("wrong length input to set_lattice")
elif len(sf) == 6:
fullform = sf # triclinic/arbitrary
else:
raise ValueError("wrong length input to set_lattice")
self._set_lattice(name, *fullform)
def _set_lattice(self, name, a, b, c, alpha, beta, gamma):
"""set lattice parameters in degrees"""
if self._state.name is None:
raise DiffcalcException(
"Cannot set lattice until a UBCalcaluation has been started "
"with newubcalc")
self._state.crystal = CrystalUnderTest(name, a, b, c, alpha, beta,
gamma)
# Clear U and UB if these exist
if self._U is not None: # (UB will also exist)
print "Warning: the old UB calculation has been cleared."
print " Use 'calcub' to recalculate with old reflections."
### Surface normal stuff ###
def _gettau(self):
"""
Returns tau (in degrees): the (minus) ammount of phi axis rotation ,
that together with some chi axis rotation (minus sigma) brings the
optical surface normal parallelto the omega axis.
"""
return self._state.tau
def _settau(self, tau):
self._state.tau = tau
self.save()
tau = property(_gettau, _settau)
def _getsigma(self):
"""
Returns sigma (in degrees): the (minus) ammount of phi axis rotation ,
that together with some phi axis rotation (minus tau) brings the
optical surface normal parallel to the omega axis.
"""
return self._state.sigma
def _setsigma(self, sigma):
self.state._sigma = sigma
self.save()
sigma = property(_getsigma, _setsigma)
### Reference vector ###
def _get_n_phi(self):
return self._state.reference.n_phi
n_phi = property(_get_n_phi)
def set_n_phi_configured(self, n_phi):
self._state.reference.n_phi_configured = n_phi
self.save()
def set_n_hkl_configured(self, n_hkl):
self._state.reference.n_hkl_configured = n_hkl
self.save()
def print_reference(self):
print '\n'.join(
self._state.reference.repr_lines(self.is_ub_calculated()))
### Reflections ###
def add_reflection(self, h, k, l, position, energy, tag, time):
"""add_reflection(h, k, l, position, tag=None) -- adds a reflection
position is in degrees and in the systems internal representation.
"""
if self._state.reflist is None:
raise DiffcalcException("No UBCalculation loaded")
self._state.reflist.add_reflection(h, k, l, position, energy, tag,
time)
self.save() # incase autocalculateUbAndReport fails
# If second reflection has just been added then calculateUB
if len(self._state.reflist) == 2:
self._autocalculateUbAndReport()
self.save()
def edit_reflection(self, num, h, k, l, position, energy, tag, time):
"""
edit_reflection(num, h, k, l, position, tag=None) -- adds a reflection
position is in degrees and in the systems internal representation.
"""
if self._state.reflist is None:
raise DiffcalcException("No UBCalculation loaded")
self._state.reflist.edit_reflection(num, h, k, l, position, energy,
tag, time)
# If first or second reflection has been changed and there are at least
# two reflections then recalculate UB
if (num == 1 or num == 2) and len(self._state.reflist) >= 2:
self._autocalculateUbAndReport()
self.save()
def get_reflection(self, num):
"""--> ( [h, k, l], position, energy, tag, time
num starts at 1, position in degrees"""
return self._state.reflist.getReflection(num)
def get_reflection_in_external_angles(self, num):
"""--> ( [h, k, l], position, energy, tag, time
num starts at 1, position in degrees"""
return self._state.reflist.get_reflection_in_external_angles(num)
def get_number_reflections(self):
return 0 if self._state.reflist is None else len(self._state.reflist)
def del_reflection(self, reflectionNumber):
self._state.reflist.removeReflection(reflectionNumber)
if ((reflectionNumber == 1 or reflectionNumber == 2)
and (self._U != None)):
self._autocalculateUbAndReport()
self.save()
def swap_reflections(self, num1, num2):
self._state.reflist.swap_reflections(num1, num2)
if ((num1 == 1 or num1 == 2 or num2 == 1 or num2 == 2)
and (self._U != None)):
self._autocalculateUbAndReport()
self.save()
def _autocalculateUbAndReport(self):
if len(self._state.reflist) < 2:
pass
elif self._state.crystal is None:
print(
"Not calculating UB matrix as no lattice parameters have "
"been specified.")
elif not self._state.is_okay_to_autocalculate_ub:
print(
"Not calculating UB matrix as it has been manually set. "
"Use 'calcub' to explicitly recalculate it.")
else: # okay to autocalculate
if self._UB is None:
print "Calculating UB matrix."
else:
print "Recalculating UB matrix."
self.calculate_UB()
# @property
# def reflist(self):
# return self._state.reflist
### Calculations ###
def set_U_manually(self, m):
"""Manually sets U. matrix must be 3*3 Jama or python matrix.
Turns off aution UB calcualtion."""
# Check matrix is a 3*3 Jama matrix
if m.__class__ != matrix:
m = matrix(m) # assume its a python matrix
if m.shape[0] != 3 or m.shape[1] != 3:
raise ValueError("Expects 3*3 matrix")
if self._UB is None:
print "Calculating UB matrix."
else:
print "Recalculating UB matrix."
self._state.configure_calc_type(manual_U=m)
self._U = m
if self._state.crystal is None:
raise DiffcalcException(
"A crystal must be specified before manually setting U")
self._UB = self._U * self._state.crystal.B
print(
"NOTE: A new UB matrix will not be automatically calculated "
"when the orientation reflections are modified.")
self.save()
def set_UB_manually(self, m):
"""Manually sets UB. matrix must be 3*3 Jama or python matrix.
Turns off aution UB calcualtion."""
# Check matrix is a 3*3 Jama matrix
if m.__class__ != matrix:
m = matrix(m) # assume its a python matrix
if m.shape[0] != 3 or m.shape[1] != 3:
raise ValueError("Expects 3*3 matrix")
self._state.configure_calc_type(manual_UB=m)
self._UB = m
self.save()
@property
def U(self):
if self._U is None:
raise DiffcalcException(
"No U matrix has been calculated during this ub calculation")
return self._U
@property
def UB(self):
return self._get_UB()
def is_ub_calculated(self):
return self._UB is not None
def _get_UB(self):
if not self.is_ub_calculated():
raise DiffcalcException(
"No UB matrix has been calculated during this ub calculation")
else:
return self._UB
def calculate_UB(self):
"""
Calculate orientation matrix. Uses first two orientation reflections
as in Busang and Levy, but for the diffractometer in Lohmeier and
Vlieg.
"""
# Major variables:
# h1, h2: user input reciprical lattice vectors of the two reflections
# h1c, h2c: user input vectors in cartesian crystal plane
# pos1, pos2: measured diffractometer positions of the two reflections
# u1a, u2a: measured reflection vectors in alpha frame
# u1p, u2p: measured reflection vectors in phi frame
# Get hkl and angle values for the first two refelctions
if self._state.reflist is None:
raise DiffcalcException("Cannot calculate a U matrix until a "
"UBCalculation has been started with "
"'newub'")
try:
(h1, pos1, _, _, _) = self._state.reflist.getReflection(1)
(h2, pos2, _, _, _) = self._state.reflist.getReflection(2)
except IndexError:
raise DiffcalcException(
"Two reflections are required to calculate a u matrix")
h1 = matrix([h1]).T # row->column
h2 = matrix([h2]).T
pos1.changeToRadians()
pos2.changeToRadians()
# Compute the two reflections' reciprical lattice vectors in the
# cartesian crystal frame
B = self._state.crystal.B
h1c = B * h1
h2c = B * h2
u1p = self._strategy.calculate_q_phi(pos1)
u2p = self._strategy.calculate_q_phi(pos2)
# Create modified unit vectors t1, t2 and t3 in crystal and phi systems
t1c = h1c
t3c = cross3(h1c, h2c)
t2c = cross3(t3c, t1c)
t1p = u1p # FIXED from h1c 9July08
t3p = cross3(u1p, u2p)
t2p = cross3(t3p, t1p)
# ...and nornmalise and check that the reflections used are appropriate
SMALL = 1e-4 # Taken from Vlieg's code
e = DiffcalcException("Invalid orientation reflection(s)")
def normalise(m):
d = norm(m)
if d < SMALL:
raise e
return m / d
t1c = normalise(t1c)
t2c = normalise(t2c)
t3c = normalise(t3c)
t1p = normalise(t1p)
t2p = normalise(t2p)
t3p = normalise(t3p)
Tc = hstack([t1c, t2c, t3c])
Tp = hstack([t1p, t2p, t3p])
self._state.configure_calc_type(or0=1, or1=2)
self._U = Tp * Tc.I
self._UB = self._U * B
self.save()
def calculate_UB_from_primary_only(self):
"""
Calculate orientation matrix with the shortest absolute angle change.
Uses first orientation reflection
"""
# Algorithm from http://www.j3d.org/matrix_faq/matrfaq_latest.html
# Get hkl and angle values for the first two refelctions
if self._state.reflist is None:
raise DiffcalcException(
"Cannot calculate a u matrix until a UBCalcaluation has been "
"started with newub")
try:
(h, pos, _, _, _) = self._state.reflist.getReflection(1)
except IndexError:
raise DiffcalcException(
"One reflection is required to calculate a u matrix")
h = matrix([h]).T # row->column
pos.changeToRadians()
B = self._state.crystal.B
h_crystal = B * h
h_crystal = h_crystal * (1 / norm(h_crystal))
q_measured_phi = self._strategy.calculate_q_phi(pos)
q_measured_phi = q_measured_phi * (1 / norm(q_measured_phi))
rotation_axis = cross3(h_crystal, q_measured_phi)
rotation_axis = rotation_axis * (1 / norm(rotation_axis))
cos_rotation_angle = dot3(h_crystal, q_measured_phi)
rotation_angle = acos(cos_rotation_angle)
uvw = rotation_axis.T.tolist()[0] # TODO: cleanup
print "resulting U angle: %.5f deg" % (rotation_angle * TODEG)
u_repr = (', '.join(['% .5f' % el for el in uvw]))
print "resulting U axis direction: [%s]" % u_repr
u, v, w = uvw
rcos = cos(rotation_angle)
rsin = sin(rotation_angle)
m = [[0, 0, 0], [0, 0, 0], [0, 0, 0]] # TODO: tidy
m[0][0] = rcos + u * u * (1 - rcos)
m[1][0] = w * rsin + v * u * (1 - rcos)
m[2][0] = -v * rsin + w * u * (1 - rcos)
m[0][1] = -w * rsin + u * v * (1 - rcos)
m[1][1] = rcos + v * v * (1 - rcos)
m[2][1] = u * rsin + w * v * (1 - rcos)
m[0][2] = v * rsin + u * w * (1 - rcos)
m[1][2] = -u * rsin + v * w * (1 - rcos)
m[2][2] = rcos + w * w * (1 - rcos)
if self._UB is None:
print "Calculating UB matrix from the first reflection only."
else:
print "Recalculating UB matrix from the first reflection only."
print(
"NOTE: A new UB matrix will not be automatically calculated "
"when the orientation reflections are modified.")
self._state.configure_calc_type(or0=1)
self._U = matrix(m)
self._UB = self._U * B
self.save()
def get_hkl_plane_distance(self, hkl):
"""Calculates and returns the distance between planes"""
return self._state.crystal.get_hkl_plane_distance(hkl)
class UBCalculation:
"""A UB matrix calculation for an experiment.
Contains the parameters for the _crystal under test, a list of measured
reflections and, if its been calculated, a UB matrix to be used by the rest
of the code.
"""
def __init__(self, diffractometer_axes_names, diffractometerPluginObject, persister, strategy, include_sigtau=True):
# The diffractometer geometry is required to map the internal angles
# into those used by this diffractometer (for display only)
self._diffractometer_axes_names = diffractometer_axes_names
self._geometry = diffractometerPluginObject
self._persister = persister
self._strategy = strategy
self._include_sigtau = include_sigtau
self.reference = YouReference(self) # TODO: move into _state and persist
self._clear()
def _clear(self, name=None):
# NOTE the Diffraction calculator is expecting this object to exist in
# the long run. We can't remove this entire object, and recreate it.
# It also contains a required link to the angle calculator.
reflist = ReflectionList(self._geometry, self._diffractometer_axes_names)
self._state = UBCalcState(name=name, reflist=reflist)
self._U = None
self._UB = None
self._state.configure_calc_type()
### State ###
def start_new(self, name):
"""start_new(name) --- creates a new blank ub calculation"""
# Create storage object if name does not exist (TODO)
if name in self._persister.list():
print ("No UBCalculation started: There is already a calculation " "called: " + name)
print "Saved calculations: " + repr(self._persister.list())
return
self._clear(name)
self.save()
def load(self, name):
state = self._persister.load(name)
self._state = decode_ubcalcstate(state, self._geometry, self._diffractometer_axes_names)
if self._state.manual_U is not None:
self.set_U_manually(self._state.manual_U)
elif self._state.manual_UB is not None:
self.set_UB_manually(self._state.manual_UB)
elif self._state.or0 is not None:
if self._state.or1 is None:
self.calculate_UB_from_primary_only()
else:
self.calculate_UB()
else:
pass
def save(self):
self.saveas(self._state.name)
def saveas(self, name):
self._state.name = name
self._persister.save(self._state, name)
def listub(self):
return self._persister.list()
def remove(self, name):
self._persister.remove(name)
def getState(self):
return self._state.getState()
def __str__(self):
WIDTH = 13
if self._state.name is None:
return "<<< No UB calculation started >>>"
lines = []
lines.append("UBCALC")
lines.append("")
lines.append(" name:".ljust(WIDTH) + self._state.name.rjust(9))
if self._include_sigtau:
lines.append(" sigma:".ljust(WIDTH) + ("% 9.5f" % self._state.sigma).rjust(9))
lines.append(" tau:".ljust(WIDTH) + ("% 9.5f" % self._state.tau).rjust(9))
lines.append("")
lines.append("CRYSTAL")
lines.append("")
if self._state.crystal is None:
lines.append(" <<< none specified >>>")
else:
lines.extend(self._state.crystal.str_lines())
lines.append("")
lines.append("UB MATRIX")
lines.append("")
if self._UB is None:
lines.append(" <<< none calculated >>>")
else:
fmt = "% 9.5f % 9.5f % 9.5f"
U = self.U
UB = self.UB
lines.append(" U matrix:".ljust(WIDTH) + fmt % (U[0, 0], U[0, 1], U[0, 2]))
lines.append(" " * WIDTH + fmt % (U[1, 0], U[1, 1], U[1, 2]))
lines.append(" " * WIDTH + fmt % (U[2, 0], U[2, 1], U[2, 2]))
lines.append("")
lines.append(" UB matrix:".ljust(WIDTH) + fmt % (UB[0, 0], UB[0, 1], UB[0, 2]))
lines.append(" " * WIDTH + fmt % (UB[1, 0], UB[1, 1], UB[1, 2]))
lines.append(" " * WIDTH + fmt % (UB[2, 0], UB[2, 1], UB[2, 2]))
lines.append("")
lines.append("REFLECTIONS")
lines.append("")
lines.extend(self._state.reflist.str_lines())
return "\n".join(lines)
@property
def name(self):
return self._state.name
### Lattice ###
def set_lattice(self, name, *shortform):
"""
Converts a list shortform crystal parameter specification to a six-long
tuple returned as . Returns None if wrong number of input args. See
set_lattice() for a description of the shortforms supported.
shortformLattice -- a tuple as follows:
[a] - assumes cubic
[a,b]) - assumes tetragonal
[a,b,c]) - assumes ortho
[a,b,c,gam]) - assumes mon/hex gam different from 90.
[a,b,c,alp,bet,gam]) - for arbitrary
where all measurements in angstroms and angles in degrees
"""
self._set_lattice_without_saving(name, *shortform)
self.save()
def _set_lattice_without_saving(self, name, *shortform):
sf = shortform
if len(sf) == 1:
fullform = (sf[0], sf[0], sf[0], 90.0, 90.0, 90.0) # cubic
elif len(sf) == 2:
fullform = (sf[0], sf[0], sf[1], 90.0, 90.0, 90.0) # tetragonal
elif len(sf) == 3:
fullform = (sf[0], sf[1], sf[2], 90.0, 90.0, 90.0) # ortho
elif len(sf) == 4:
fullform = (sf[0], sf[1], sf[2], 90.0, 90.0, sf[3]) # mon/hex gam
# not 90
elif len(sf) == 5:
raise ValueError("wrong length input to set_lattice")
elif len(sf) == 6:
fullform = sf # triclinic/arbitrary
else:
raise ValueError("wrong length input to set_lattice")
self._set_lattice(name, *fullform)
def _set_lattice(self, name, a, b, c, alpha, beta, gamma):
"""set lattice parameters in degrees"""
if self._state.name is None:
raise DiffcalcException("Cannot set lattice until a UBCalcaluation has been started " "with newubcalc")
self._state.crystal = CrystalUnderTest(name, a, b, c, alpha, beta, gamma)
# Clear U and UB if these exist
if self._U != None: # (UB will also exist)
self._U = None
self._UB = None
print "Warning: the old UB calculation has been cleared."
print " Use 'calcub' to recalculate with old reflections."
### Surface normal stuff ###
def _gettau(self):
"""
Returns tau (in degrees): the (minus) ammount of phi axis rotation ,
that together with some chi axis rotation (minus sigma) brings the
optical surface normal parallelto the omega axis.
"""
return self._state.tau
def _settau(self, tau):
self._state.tau = tau
self.save()
tau = property(_gettau, _settau)
def _getsigma(self):
"""
Returns sigma (in degrees): the (minus) ammount of phi axis rotation ,
that together with some phi axis rotation (minus tau) brings the
optical surface normal parallelto the omega axis.
"""
return self._state.sigma
def _setsigma(self, sigma):
self.state._sigma = sigma
self.save()
sigma = property(_getsigma, _setsigma)
### Reflections ###
def add_reflection(self, h, k, l, position, energy, tag, time):
"""add_reflection(h, k, l, position, tag=None) -- adds a reflection
position is in degrees and in the systems internal representation.
"""
if self._state.reflist is None:
raise DiffcalcException("No UBCalculation loaded")
self._state.reflist.add_reflection(h, k, l, position, energy, tag, time)
self.save() # incase autocalculateUbAndReport fails
# If second reflection has just been added then calculateUB
if len(self._state.reflist) == 2:
self._autocalculateUbAndReport()
self.save()
def edit_reflection(self, num, h, k, l, position, energy, tag, time):
"""
edit_reflection(num, h, k, l, position, tag=None) -- adds a reflection
position is in degrees and in the systems internal representation.
"""
if self._state.reflist is None:
raise DiffcalcException("No UBCalculation loaded")
self._state.reflist.edit_reflection(num, h, k, l, position, energy, tag, time)
# If first or second reflection has been changed and there are at least
# two reflections then recalculate UB
if (num == 1 or num == 2) and len(self._state.reflist) >= 2:
self._autocalculateUbAndReport()
self.save()
def get_reflection(self, num):
"""--> ( [h, k, l], position, energy, tag, time
num starts at 1, position in degrees"""
return self._state.reflist.getReflection(num)
def get_reflection_in_external_angles(self, num):
"""--> ( [h, k, l], position, energy, tag, time
num starts at 1, position in degrees"""
return self._state.reflist.get_reflection_in_external_angles(num)
def get_number_reflections(self):
return 0 if self._state.reflist is None else len(self._state.reflist)
def del_reflection(self, reflectionNumber):
self._state.reflist.removeReflection(reflectionNumber)
if (reflectionNumber == 1 or reflectionNumber == 2) and (self._U != None):
self._autocalculateUbAndReport()
self.save()
def swap_reflections(self, num1, num2):
self._state.reflist.swap_reflections(num1, num2)
if (num1 == 1 or num1 == 2 or num2 == 1 or num2 == 2) and (self._U != None):
self._autocalculateUbAndReport()
self.save()
def _autocalculateUbAndReport(self):
if len(self._state.reflist) < 2:
pass
elif self._state.crystal is None:
print ("Not calculating UB matrix as no lattice parameters have " "been specified.")
elif not self._state.is_okay_to_autocalculate_ub:
print (
"Not calculating UB matrix as it has been manually set. " "Use 'calcub' to explicitly recalculate it."
)
else: # okay to autocalculate
if self._UB is None:
print "Calculating UB matrix."
else:
print "Recalculating UB matrix."
self.calculate_UB()
# @property
# def reflist(self):
# return self._state.reflist
### Calculations ###
def set_U_manually(self, m):
"""Manually sets U. matrix must be 3*3 Jama or python matrix.
Turns off aution UB calcualtion."""
# Check matrix is a 3*3 Jama matrix
if m.__class__ != matrix:
m = matrix(m) # assume its a python matrix
if m.shape[0] != 3 or m.shape[1] != 3:
raise ValueError("Expects 3*3 matrix")
if self._UB is None:
print "Calculating UB matrix."
else:
print "Recalculating UB matrix."
self._state.configure_calc_type(manual_U=m)
self._U = m
if self._state.crystal is None:
raise DiffcalcException("A crystal must be specified before manually setting U")
self._UB = self._U * self._state.crystal.B
print (
"NOTE: A new UB matrix will not be automatically calculated "
"when the orientation reflections are modified."
)
self.save()
def set_UB_manually(self, m):
"""Manually sets UB. matrix must be 3*3 Jama or python matrix.
Turns off aution UB calcualtion."""
# Check matrix is a 3*3 Jama matrix
if m.__class__ != matrix:
m = matrix(m) # assume its a python matrix
if m.shape[0] != 3 or m.shape[1] != 3:
raise ValueError("Expects 3*3 matrix")
self._state.configure_calc_type(manual_UB=m)
self._UB = m
self.save()
@property
def U(self):
if self._U is None:
raise DiffcalcException("No U matrix has been calculated during this ub calculation")
return self._U
@property
def UB(self):
if self._UB is None:
raise DiffcalcException("No UB matrix has been calculated during this ub calculation")
else:
return self._UB
def calculate_UB(self):
"""
Calculate orientation matrix. Uses first two orientation reflections
as in Busang and Levy, but for the diffractometer in Lohmeier and
Vlieg.
"""
# Major variables:
# h1, h2: user input reciprical lattice vectors of the two reflections
# h1c, h2c: user input vectors in cartesian crystal plane
# pos1, pos2: measured diffractometer positions of the two reflections
# u1a, u2a: measured reflection vectors in alpha frame
# u1p, u2p: measured reflection vectors in phi frame
# Get hkl and angle values for the first two refelctions
if self._state.reflist is None:
raise DiffcalcException(
"Cannot calculate a U matrix until a " "UBCalculation has been started with " "'newub'"
)
try:
(h1, pos1, _, _, _) = self._state.reflist.getReflection(1)
(h2, pos2, _, _, _) = self._state.reflist.getReflection(2)
except IndexError:
raise DiffcalcException("Two reflections are required to calculate a u matrix")
h1 = matrix([h1]).T # row->column
h2 = matrix([h2]).T
pos1.changeToRadians()
pos2.changeToRadians()
# Compute the two reflections' reciprical lattice vectors in the
# cartesian crystal frame
B = self._state.crystal.B
h1c = B * h1
h2c = B * h2
u1p = self._strategy.calculate_q_phi(pos1)
u2p = self._strategy.calculate_q_phi(pos2)
# Create modified unit vectors t1, t2 and t3 in crystal and phi systems
t1c = h1c
t3c = cross3(h1c, h2c)
t2c = cross3(t3c, t1c)
t1p = u1p # FIXED from h1c 9July08
t3p = cross3(u1p, u2p)
t2p = cross3(t3p, t1p)
# ...and nornmalise and check that the reflections used are appropriate
SMALL = 1e-4 # Taken from Vlieg's code
e = DiffcalcException("Invalid orientation reflection(s)")
def normalise(m):
d = norm(m)
if d < SMALL:
raise e
return m / d
t1c = normalise(t1c)
t2c = normalise(t2c)
t3c = normalise(t3c)
t1p = normalise(t1p)
t2p = normalise(t2p)
t3p = normalise(t3p)
Tc = hstack([t1c, t2c, t3c])
Tp = hstack([t1p, t2p, t3p])
self._state.configure_calc_type(or0=1, or1=2)
self._U = Tp * Tc.I
self._UB = self._U * B
self.save()
def calculate_UB_from_primary_only(self):
"""
Calculate orientation matrix with the shortest absolute angle change.
Uses first orientation reflection
"""
# Algorithm from http://www.j3d.org/matrix_faq/matrfaq_latest.html
# Get hkl and angle values for the first two refelctions
if self._state.reflist is None:
raise DiffcalcException("Cannot calculate a u matrix until a UBCalcaluation has been " "started with newub")
try:
(h, pos, _, _, _) = self._state.reflist.getReflection(1)
except IndexError:
raise DiffcalcException("One reflection is required to calculate a u matrix")
h = matrix([h]).T # row->column
pos.changeToRadians()
B = self._state.crystal.B
h_crystal = B * h
h_crystal = h_crystal * (1 / norm(h_crystal))
q_measured_phi = self._strategy.calculate_q_phi(pos)
q_measured_phi = q_measured_phi * (1 / norm(q_measured_phi))
rotation_axis = cross3(h_crystal, q_measured_phi)
rotation_axis = rotation_axis * (1 / norm(rotation_axis))
cos_rotation_angle = dot3(h_crystal, q_measured_phi)
rotation_angle = acos(cos_rotation_angle)
uvw = rotation_axis.T.tolist()[0] # TODO: cleanup
print "resulting U angle: %.5f deg" % (rotation_angle * TODEG)
u_repr = ", ".join(["% .5f" % el for el in uvw])
print "resulting U axis direction: [%s]" % u_repr
u, v, w = uvw
rcos = cos(rotation_angle)
rsin = sin(rotation_angle)
m = [[0, 0, 0], [0, 0, 0], [0, 0, 0]] # TODO: tidy
m[0][0] = rcos + u * u * (1 - rcos)
m[1][0] = w * rsin + v * u * (1 - rcos)
m[2][0] = -v * rsin + w * u * (1 - rcos)
m[0][1] = -w * rsin + u * v * (1 - rcos)
m[1][1] = rcos + v * v * (1 - rcos)
m[2][1] = u * rsin + w * v * (1 - rcos)
m[0][2] = v * rsin + u * w * (1 - rcos)
m[1][2] = -u * rsin + v * w * (1 - rcos)
m[2][2] = rcos + w * w * (1 - rcos)
if self._UB is None:
print "Calculating UB matrix from the first reflection only."
else:
print "Recalculating UB matrix from the first reflection only."
print (
"NOTE: A new UB matrix will not be automatically calculated "
"when the orientation reflections are modified."
)
self._state.configure_calc_type(or0=1)
self._U = matrix(m)
self._UB = self._U * B
self.save()
def get_hkl_plane_distance(self, hkl):
"""Calculates and returns the distance between planes"""
return self._state.crystal.get_hkl_plane_distance(hkl)
class UBCalculation:
"""A UB matrix calculation for an experiment.
Contains the parameters for the _crystal under test, a list of measured
reflections and, if its been calculated, a UB matrix to be used by the rest
of the code.
"""
def __init__(self,
persister,
strategy,
include_sigtau=True,
include_reference=True):
# The diffractometer geometry is required to map the internal angles
# into those used by this diffractometer (for display only)
self._persister = persister
self._strategy = strategy
self.include_sigtau = include_sigtau
self.include_reference = include_reference
try:
self._tobj = CoordinateConverter(
transform=settings.geometry.beamline_axes_transform)
except AttributeError:
self._tobj = CoordinateConverter(transform=None)
self._clear()
def _get_diffractometer_axes_names(self):
return settings.hardware.get_axes_names()
def _clear(self, name=None):
# NOTE the Diffraction calculator is expecting this object to exist in
# the long run. We can't remove this entire object, and recreate it.
# It also contains a required link to the angle calculator.
reflist = ReflectionList(
settings.geometry,
self._get_diffractometer_axes_names(),
multiplier=settings.hardware.energyScannableMultiplierToGetKeV)
orientlist = OrientationList(settings.geometry,
self._get_diffractometer_axes_names())
reference = YouReference(self._get_UB)
reference._set_n_hkl_configured(settings.reference_vector)
surface = YouReference(self._get_UB)
surface._set_n_phi_configured(settings.surface_vector)
self._state = UBCalcState(name=name,
reflist=reflist,
orientlist=orientlist,
reference=reference,
surface=surface)
self._U = None
self._UB = None
self._state.configure_calc_type()
### State ###
def start_new(self, name):
"""Start new UB matrix calculation.
Creates a new blank UB matrix calculation.
Parameters
----------
name: str
Name of a new UB matrix calculation
"""
# Create storage object if name does not exist (TODO)
self._clear(name)
self.save()
def load(self, name):
state = self._persister.load(name)
if isinstance(self._persister, UBCalculationJSONPersister):
self._state = self._persister.encoder.decode_ubcalcstate(
state, settings.geometry,
self._get_diffractometer_axes_names(),
settings.hardware.energyScannableMultiplierToGetKeV)
self._state.reference.get_UB = self._get_UB
self._state.surface.get_UB = self._get_UB
elif isinstance(self._persister, UBCalculationPersister):
self._state = state
else:
raise DiffcalcException('Unexpected persister type: ' +
str(self._persister))
if self._state.manual_U is not None:
self._U = self._state.manual_U
self._UB = self._U * self._state.crystal.B
self.save()
elif self._state.manual_UB is not None:
self._UB = self._state.manual_UB
self.save()
elif self._state.is_okay_to_autocalculate_ub:
try:
self.calculate_UB(self._state.or0, self._state.or1)
except Exception as e:
print(e)
else:
print("Warning: No UB calculation loaded.")
def save(self):
"""Save current UB matrix calculation."""
if self._state.name:
self.saveas(self._state.name)
else:
print("Warning: No UB calculation defined.")
def saveas(self, name):
"""Save current UB matrix calculation.
Parameters
----------
name : str
Name for the saved UB matrix calculation.
"""
self._state.name = name
self._persister.save(self._state, name)
def listub(self):
"""List saved UB matrix calculations.
Returns:
:obj:`list` of :obj:`str`
List of names of the saved UB matrix calculations.
"""
return self._persister.list()
def listub_metadata(self):
return self._persister.list_metadata()
def remove(self, name):
"""Delete UB matrix calculation.
Parameters
----------
name : str
Name of the UB matrix calculation to be deleted.
"""
self._persister.remove(name)
if self._state.name == name:
self._clear()
def getState(self):
return self._state.getState()
def __str__(self):
if self._state.name is None:
return "<<< No UB calculation started >>>"
lines = []
lines.append(bold("UBCALC"))
lines.append("")
lines.append(" name:".ljust(WIDTH) + self._state.name.rjust(9))
if self.include_sigtau:
lines.append("")
lines.append(" sigma:".ljust(WIDTH) +
("% 9.5f" % self._state.sigma).rjust(9))
lines.append(" tau:".ljust(WIDTH) +
("% 9.5f" % self._state.tau).rjust(9))
_ub_calculated = self._UB is not None
if self.include_reference:
lines.append("")
lines.append(bold("REFERNCE"))
lines.append("")
lines.extend(
self._state.reference.repr_lines(_ub_calculated, WIDTH,
self._tobj))
lines.append("")
lines.append(bold("SURFACE NORMAL"))
lines.append("")
lines.extend(
self._state.surface.repr_lines(_ub_calculated, WIDTH, self._tobj))
lines.append("")
lines.append(bold("CRYSTAL"))
lines.append("")
if self._state.crystal is None:
lines.append(" <<< none specified >>>")
else:
lines.extend(self._state.crystal.str_lines(self._tobj))
lines.append("")
lines.append(bold("UB MATRIX"))
lines.append("")
if self._UB is None:
lines.append(" <<< none calculated >>>")
else:
lines.extend(self.str_lines_u(self.U))
lines.append("")
lines.extend(self.str_lines_ub_angle_and_axis(self.UB))
lines.append("")
lines.extend(self.str_lines_ub(self.UB))
lines.extend(self.str_lines_refl())
lines.extend(self.str_lines_orient())
return '\n'.join(lines)
def str_lines_u(self, umatrix):
lines = []
fmt = "% 9.5f % 9.5f % 9.5f"
U = self._tobj.transform(umatrix, True)
lines.append(" U matrix:".ljust(WIDTH) + fmt %
(z(U[0, 0]), z(U[0, 1]), z(U[0, 2])))
lines.append(' ' * WIDTH + fmt % (z(U[1, 0]), z(U[1, 1]), z(U[1, 2])))
lines.append(' ' * WIDTH + fmt % (z(U[2, 0]), z(U[2, 1]), z(U[2, 2])))
return lines
def str_lines_ub_angle_and_axis(self, ubmatrix):
lines = []
fmt = "% 9.5f % 9.5f % 9.5f"
rotation_angle, rotation_axis = self.get_miscut_angle_axis(ubmatrix)
if abs(norm(rotation_axis)) < SMALL:
lines.append(" miscut angle:".ljust(WIDTH) + " 0")
else:
lines.append(" miscut:")
lines.append(" angle:".ljust(WIDTH) +
"% 9.5f" % rotation_angle)
lines.append(" axis:".ljust(WIDTH) +
fmt % tuple((rotation_axis.T).tolist()[0]))
return lines
def str_lines_ub(self, ubmatrix):
lines = []
fmt = "% 9.5f % 9.5f % 9.5f"
if self._tobj.R is not None:
UB = self._tobj.R.I * ubmatrix
else:
UB = self.UB
lines.append(" UB matrix:".ljust(WIDTH) + fmt %
(z(UB[0, 0]), z(UB[0, 1]), z(UB[0, 2])))
lines.append(' ' * WIDTH + fmt %
(z(UB[1, 0]), z(UB[1, 1]), z(UB[1, 2])))
lines.append(' ' * WIDTH + fmt %
(z(UB[2, 0]), z(UB[2, 1]), z(UB[2, 2])))
return lines
def str_lines_refl(self):
lines = ["", bold("REFLECTIONS"), ""]
lines.extend(self._state.reflist.str_lines())
return lines
def str_lines_orient(self):
lines = ["", bold("CRYSTAL ORIENTATIONS"), ""]
lines.extend(self._state.orientlist.str_lines(self._tobj))
return lines
@property
def name(self):
"""str: Name of the current UB matrix calculation."""
return self._state.name
### Lattice ###
def set_lattice(self, name, *shortform):
"""
Converts a list shortform crystal parameter specification to a six-long
tuple. See setlat() for a description of the shortforms supported.
"""
if not shortform:
raise TypeError("Please specify unit cell parameters.")
elif allnum(shortform):
sf = shortform
if len(sf) == 1:
system = "Cubic"
elif len(sf) == 2:
system = "Tetragonal"
elif len(sf) == 3:
system = "Orthorhombic"
elif len(sf) == 4:
if abs(sf[0] - sf[1]) < SMALL and sf[3] == 120:
system = "Hexagonal"
else:
system = "Monoclinic"
elif len(sf) == 6:
system = "Triclinic"
else:
raise TypeError(
"Invalid number of input parameters to set unit lattice.")
fullform = (system, ) + shortform
else:
if not isinstance(shortform[0], str):
raise TypeError("Invalid unit cell parameters specified.")
fullform = shortform
if self._state.name is None:
raise DiffcalcException(
"Cannot set lattice until a UBCalcaluation has been started "
"with newubcalc")
self._state.crystal = CrystalUnderTest(name, *fullform)
# Clear U and UB if these exist
if self._U is not None: # (UB will also exist)
print("Warning: Setting new unit cell parameters.\n"
" The old UB calculation has been cleared.")
self.save()
### Surface normal stuff ###
def _gettau(self):
"""
Returns tau (in degrees): the (minus) ammount of phi axis rotation ,
that together with some chi axis rotation (minus sigma) brings the
optical surface normal parallel to the omega axis.
"""
return self._state.tau
def _settau(self, tau):
self._state.tau = tau
self.save()
tau = property(_gettau, _settau)
def _getsigma(self):
"""
Returns sigma (in degrees): the (minus) ammount of phi axis rotation ,
that together with some phi axis rotation (minus tau) brings the
optical surface normal parallel to the omega axis.
"""
return self._state.sigma
def _setsigma(self, sigma):
self.state._sigma = sigma
self.save()
sigma = property(_getsigma, _setsigma)
### Reference vector ###
def _get_n_hkl(self):
return self._state.reference.n_hkl
def _get_n_phi(self):
return self._state.reference.n_phi
n_hkl = property(_get_n_hkl)
n_phi = property(_get_n_phi)
def set_n_phi_configured(self, n_phi):
self._state.reference.n_phi_configured = self._tobj.transform(n_phi)
self.save()
def set_n_hkl_configured(self, n_hkl):
self._state.reference.n_hkl_configured = n_hkl
self.save()
def print_reference(self):
print('\n'.join(
self._state.reference.repr_lines(self.is_ub_calculated(),
WIDTH=9,
conv=self._tobj)))
### Surface vector ###
def _get_surf_nhkl(self):
return self._state.surface.n_hkl
def _get_surf_nphi(self):
return self._state.surface.n_phi
surf_nhkl = property(_get_surf_nhkl)
surf_nphi = property(_get_surf_nphi)
def set_surf_nphi_configured(self, n_phi):
self._state.surface.n_phi_configured = self._tobj.transform(n_phi)
self.save()
def set_surf_nhkl_configured(self, n_hkl):
self._state.surface.n_hkl_configured = n_hkl
self.save()
def print_surface(self):
print('\n'.join(
self._state.surface.repr_lines(self.is_ub_calculated(),
WIDTH=9,
conv=self._tobj)))
### Reflections ###
def add_reflection(self, h, k, l, position, energy, tag, time):
"""Add a reference reflection.
Adds a reflection position in degrees and in the
systems internal representation.
Parameters
----------
h : number
h index of the reflection
k : number
k index of the reflection
l : number
l index of the reflection
position: :obj:`list` or :obj:`tuple` of numbers
list of diffractometer angles in internal representation in degrees
energy : float
energy of the x-ray beam
tag : str
identifying tag for the reflection
time : :obj:`datetime`
datetime object
"""
if self._state.reflist is None:
raise DiffcalcException("No UBCalculation loaded")
self._state.reflist.add_reflection(h, k, l, position, energy, tag,
time)
self.save() # incase autocalculateUbAndReport fails
# If second reflection has just been added then calculateUB
if self.get_reference_count() == 2:
self._autocalculateUbAndReport()
self.save()
def edit_reflection(self, idx, h, k, l, position, energy, tag, time):
"""Changes a reference reflection.
Changes a reflection position in degrees and in the
systems internal representation.
Parameters
----------
idx : str or int
index or tag of the reflection to be changed
h : number
h index of the reflection
k : number
k index of the reflection
l : number
l index of the reflection
position: :obj:`list` or :obj:`tuple` of numbers
list of diffractometer angles in internal representation in degrees
energy : float
energy of the x-ray beam
tag : str
identifying tag for the reflection
time : :obj:`datetime`
datetime object
"""
if self._state.reflist is None:
raise DiffcalcException("No UBCalculation loaded")
num = self.get_tag_refl_num(idx)
self._state.reflist.edit_reflection(num, h, k, l, position, energy,
tag, time)
# If first or second reflection has been changed and there are at least
# two reflections then recalculate UB
or12 = self.get_ub_references()
if idx in or12 or num in or12:
self._autocalculateUbAndReport()
self.save()
def get_reflection(self, idx):
"""Get a reference reflection.
Get a reflection position in degrees and in the
systems internal representation.
Parameters
----------
idx : str or int
index or tag of the reflection
"""
return self._state.reflist.getReflection(idx)
def get_reflection_in_external_angles(self, idx):
"""Get a reference reflection.
Get a reflection position in degrees and in the
external diffractometer representation.
Parameters
----------
idx : str or int
index or tag of the reflection
"""
return self._state.reflist.get_reflection_in_external_angles(idx)
def get_number_reflections(self):
"""Get a number of stored reference reflections.
Returns
-------
int:
Number of reference reflections.
"""
try:
return len(self._state.reflist)
except TypeError:
return 0
def get_tag_refl_num(self, tag):
"""Get a reference reflection index.
Get a reference reflection index for the
provided reflection tag.
Parameters
----------
tag : str
identifying tag for the reflection
Returns
-------
int:
Reference reflection index
"""
if tag is None:
raise IndexError("Reflection tag is None")
return self._state.reflist.get_tag_index(tag) + 1
def del_reflection(self, idx):
"""Delete a reference reflection.
Parameters
----------
idx : str or int
index or tag of the deleted reflection
"""
num = self.get_tag_refl_num(idx)
self._state.reflist.removeReflection(num)
or12 = self.get_ub_references()
if ((idx in or12 or num in or12) and (self._U is not None)):
self._autocalculateUbAndReport()
self.save()
def swap_reflections(self, idx1, idx2):
"""Swap indices of two reference reflections.
Parameters
----------
idx1 : str or int
index or tag of the first reflection to be swapped
idx2 : str or int
index or tag of the second reflection to be swapped
"""
num1 = self.get_tag_refl_num(idx1)
num2 = self.get_tag_refl_num(idx2)
self._state.reflist.swap_reflections(num1, num2)
or12 = self.get_ub_references()
if ((idx1 in or12 or idx2 in or12 or num1 in or12 or num2 in or12)
and (self._U is not None)):
self._autocalculateUbAndReport()
self.save()
def _autocalculateUbAndReport(self):
if self.get_reference_count() < 2:
pass
elif self._state.crystal is None:
print("Not calculating UB matrix as no lattice parameters have "
"been specified.")
elif not self._state.is_okay_to_autocalculate_ub:
print("Not calculating UB matrix as it has been manually set. "
"Use 'calcub' to explicitly recalculate it.")
else: # okay to autocalculate
if self._UB is None:
print("Calculating UB matrix.")
else:
print("Recalculating UB matrix.")
or12 = self.get_ub_references()
self.calculate_UB(*or12)
### Orientations ###
def add_orientation(self, h, k, l, x, y, z, position, tag, time):
"""Add a reference orientation.
Adds a reference orientation in the external diffractometer
coordinate system.
Parameters
----------
h : number
h index of the reference orientation
k : number
k index of the reference orientation
l : number
l index of the reference orientation
x : number
x coordinate of the reference orientation
y : number
x coordinate of the reference orientation
z : number
x coordinate of the reference orientation
position: :obj:`list` or :obj:`tuple` of numbers
list of diffractometer angles in internal representation in degrees
tag : str
identifying tag for the reflection
time : :obj:`datetime`
datetime object
"""
if self._state.orientlist is None:
raise DiffcalcException("No UBCalculation loaded")
xyz_tr = self._tobj.transform(matrix([[x], [y], [z]]))
xr, yr, zr = xyz_tr.T.tolist()[0]
self._state.orientlist.add_orientation(h, k, l, xr, yr, zr, position,
tag, time)
self.save() # in case autocalculateUbAndReport fails
# If second reflection has just been added then calculateUB
if self.get_reference_count() == 2:
self._autocalculateUbAndReport()
self.save()
def edit_orientation(self, idx, h, k, l, x, y, z, position, tag, time):
"""Change a reference orientation.
Changes a reference orientation in the external diffractometer
coordinate system.
Parameters
----------
idx : str or int
index or tag of the orientation to be changed
h : number
h index of the reference orientation
k : number
k index of the reference orientation
l : number
l index of the reference orientation
x : number
x coordinate of the reference orientation
y : number
x coordinate of the reference orientation
z : number
x coordinate of the reference orientation
position: :obj:`list` or :obj:`tuple` of numbers
list of diffractometer angles in internal representation in degrees
tag : str
identifying tag for the reflection
time : :obj:`datetime`
datetime object
"""
if self._state.orientlist is None:
raise DiffcalcException("No UBCalculation loaded")
num = self.get_tag_orient_num(idx)
xyz_tr = self._tobj.transform(matrix([[x], [y], [z]]))
xr, yr, zr = xyz_tr.T.tolist()[0]
self._state.orientlist.edit_orientation(num, h, k, l, xr, yr, zr,
position, tag, time)
# If first or second orientation has been changed and there are
# two orientations then recalculate UB
or12 = self.get_ub_references()
if idx in or12 or num in or12:
self._autocalculateUbAndReport()
self.save()
def get_orientation(self, idx, conv=False):
"""Get a reference orientation.
Get a reference orientation in the external diffractometer
coordinate system.
Parameters
----------
idx : str or int
index or tag of the reference orientation
"""
hkl, xyz, pos, tg, tm = self._state.orientlist.getOrientation(idx)
if conv:
xyz_rot = self._tobj.transform(
matrix([[xyz[0]], [xyz[1]], [xyz[2]]]), True)
xyz = xyz_rot.T.tolist()[0]
return hkl, xyz, pos, tg, tm
def get_orientation_in_external_angles(self, idx, conv=False):
"""Get a reference orientation.
Get a reference orientation in the external diffractometer
coordinate system with diffractometer position in external angles.
Parameters
----------
idx : str or int
index or tag of the reference orientation
"""
hkl, xyz, pos, tg, tm = self._state.orientlist.get_orientation_in_external_angles(
idx)
if conv:
xyz_rot = self._tobj.transform(
matrix([[xyz[0]], [xyz[1]], [xyz[2]]]), True)
xyz = xyz_rot.T.tolist()[0]
return hkl, xyz, pos, tg, tm
def get_number_orientations(self):
"""Get a number of stored reference orientations.
Returns
-------
int:
Number of reference orientations.
"""
try:
return len(self._state.orientlist)
except TypeError:
return 0
def get_tag_orient_num(self, tag):
"""Get a reference orientation index.
Get a reference orientation index for the
provided orientation tag.
Parameters
----------
tag : str
identifying tag for the orientation
Returns
-------
int:
Reference orientation index
"""
if tag is None:
raise IndexError("Orientations tag is None")
return self._state.orientlist.get_tag_index(tag) + 1
def del_orientation(self, idx):
"""Delete a reference orientation.
Parameters
----------
idx : str or int
index or tag of the deleted orientation
"""
orientationNumber = self.get_tag_orient_num(idx)
self._state.orientlist.removeOrientation(orientationNumber)
if ((orientationNumber == 2) and (self._U is not None)):
self._autocalculateUbAndReport()
self.save()
def swap_orientations(self, idx1, idx2):
"""Swap indices of two reference orientations.
Parameters
----------
idx1 : str or int
index or tag of the first orientation to be swapped
idx2 : str or int
index or tag of the second orientation to be swapped
"""
num1 = self.get_tag_orient_num(idx1)
num2 = self.get_tag_orient_num(idx2)
self._state.orientlist.swap_orientations(num1, num2)
if ((num1 == 1 or num1 == 2 or num2 == 1 or num2 == 2)
and (self._U is not None)):
self._autocalculateUbAndReport()
self.save()
def get_ub_references(self):
return (self._state.or0, self._state.or1)
def get_reference_count(self):
n_ref = self.get_number_reflections()
n_orient = self.get_number_orientations()
return n_ref + n_orient
# @property
# def reflist(self):
# return self._state.reflist
### Calculations ###
def set_U_manually(self, m, conv=True):
"""Manually sets U. matrix must be 3*3 Jama or python matrix.
Turns off aution UB calcualtion."""
# Check matrix is a 3*3 Jama matrix
if m.__class__ != matrix:
m = matrix(m) # assume its a python matrix
if m.shape[0] != 3 or m.shape[1] != 3:
raise ValueError("Expects 3*3 matrix")
if self._UB is None:
print("Calculating UB matrix.")
else:
print("Recalculating UB matrix.")
if conv:
self._U = self._tobj.transform(m)
else:
self._U = m
self._state.configure_calc_type(manual_U=self._U)
if self._state.crystal is None:
raise DiffcalcException(
"A crystal must be specified before manually setting U")
self._UB = self._U * self._state.crystal.B
self.save()
def set_UB_manually(self, m):
"""Manually sets UB. matrix must be 3*3 Jama or python matrix.
Turns off aution UB calcualtion."""
# Check matrix is a 3*3 Jama matrix
if m.__class__ != matrix:
m = matrix(m) # assume its a python matrix
if m.shape[0] != 3 or m.shape[1] != 3:
raise ValueError("Expects 3*3 matrix")
if self._tobj.R is not None:
self._UB = self._tobj.R * m
else:
self._UB = m
self._state.configure_calc_type(manual_UB=self._UB)
self.save()
@property
def U(self):
"""matrix: Returns U matrix."""
if self._U is None:
raise DiffcalcException(
"No U matrix has been calculated during this ub calculation")
return self._U
@property
def UB(self):
"""matrix: Returns UB matrix."""
return self._get_UB()
def is_ub_calculated(self):
return self._UB is not None
def _get_UB(self):
if not self.is_ub_calculated():
raise DiffcalcException(
"No UB matrix has been calculated during this ub calculation")
else:
return self._UB
def _calc_UB(self, h1, h2, u1p, u2p):
B = self._state.crystal.B
h1c = B * h1
h2c = B * h2
# Create modified unit vectors t1, t2 and t3 in crystal and phi systems
t1c = h1c
t3c = cross3(h1c, h2c)
t2c = cross3(t3c, t1c)
t1p = u1p # FIXED from h1c 9July08
t3p = cross3(u1p, u2p)
t2p = cross3(t3p, t1p)
# ...and nornmalise and check that the reflections used are appropriate
SMALL = 1e-4 # Taken from Vlieg's code
def normalise(m):
d = norm(m)
if d < SMALL:
raise DiffcalcException(
"Invalid UB reference data. Please check that the specified "
"reference reflections/orientations are not parallel.")
return m / d
t1c = normalise(t1c)
t2c = normalise(t2c)
t3c = normalise(t3c)
t1p = normalise(t1p)
t2p = normalise(t2p)
t3p = normalise(t3p)
Tc = hstack([t1c, t2c, t3c])
Tp = hstack([t1p, t2p, t3p])
self._U = Tp * Tc.I
self._UB = self._U * B
def calculate_UB(self, idx1=None, idx2=None):
"""Calculate UB matrix.
Calculate UB matrix using two reference reflections and/or
reference orientations.
By default use the first two reference reflections when provided.
If one or both reflections are not available use one or two reference
orientations to complement mission reflection data.
Parameters
----------
idx1: int or str, optional
The index or the tag of the first reflection or orientation.
idx2: int or str, optional
The index or the tag of the second reflection or orientation.
"""
# Major variables:
# h1, h2: user input reciprocal lattice vectors of the two reflections
# h1c, h2c: user input vectors in cartesian crystal plane
# pos1, pos2: measured diffractometer positions of the two reflections
# u1a, u2a: measured reflection vectors in alpha frame
# u1p, u2p: measured reflection vectors in phi frame
# Get hkl and angle values for the first two reflections
if self._state.reflist is None and self._state.orientlist is None:
raise DiffcalcException("Cannot calculate a U matrix until a "
"UBCalculation has been started with "
"'newub'")
if idx1 is not None and idx2 is None:
self.calculate_UB_from_primary_only(idx1)
return
elif idx1 is None and idx2 is None:
ref_data = []
for func, idx in product(
(self.get_reflection, self.get_orientation), (1, 2)):
try:
ref_data.append(func(idx))
except Exception:
pass
try:
ref1, ref2 = ref_data[:2]
except ValueError:
raise DiffcalcException(
"Cannot find calculate a U matrix. Please add "
"reference reflection and/or orientation data.")
else:
try:
ref1 = self.get_reflection(idx1)
except Exception:
try:
ref1 = self.get_orientation(idx1)
except Exception:
raise DiffcalcException(
"Cannot find first reflection or orientation with index %s"
% str(idx1))
try:
ref2 = self.get_reflection(idx2)
except Exception:
try:
ref2 = self.get_orientation(idx2)
except Exception:
raise DiffcalcException(
"Cannot find second reflection or orientation with index %s"
% str(idx2))
h1 = matrix([ref1[0]]).T # row->column
h2 = matrix([ref2[0]]).T
# Compute the two reflections' reciprocal lattice vectors in the
# cartesian crystal frame
try:
_, pos1, _ = ref1[:3]
pos1.changeToRadians()
u1p = self._strategy.calculate_q_phi(pos1)
except AttributeError:
_, r1, pos1 = ref1[:3]
pos1.changeToRadians()
[MU, _, _, ETA, CHI, PHI] = create_you_matrices(*pos1.totuple())
Z = PHI.I * CHI.I * ETA.I * MU.I
u1p = Z * matrix([r1]).T
try:
_, pos2, _ = ref2[:3]
pos2.changeToRadians()
u2p = self._strategy.calculate_q_phi(pos2)
except AttributeError:
_, r2, pos2 = ref2[:3]
pos2.changeToRadians()
[MU, _, _, ETA, CHI, PHI] = create_you_matrices(*pos2.totuple())
Z = PHI.I * CHI.I * ETA.I * MU.I
u2p = Z * matrix([r2]).T
self._calc_UB(h1, h2, u1p, u2p)
self._state.configure_calc_type(or0=idx1, or1=idx2)
self.save()
def calculate_UB_from_primary_only(self, idx=1):
"""
Calculate orientation matrix with the shortest absolute angle change.
Default: use first reflection.
"""
# Algorithm from http://www.j3d.org/matrix_faq/matrfaq_latest.html
# Get hkl and angle values for the first two reflections
if self._state.reflist is None:
raise DiffcalcException(
"Cannot calculate a u matrix until a UBCalcaluation has been "
"started with newub")
try:
(h, pos, _, _, _) = self.get_reflection(idx)
except IndexError:
raise DiffcalcException(
"One reflection is required to calculate a u matrix")
h = matrix([h]).T # row->column
pos.changeToRadians()
B = self._state.crystal.B
h_crystal = B * h
h_crystal = h_crystal * (1 / norm(h_crystal))
q_measured_phi = self._strategy.calculate_q_phi(pos)
q_measured_phi = q_measured_phi * (1 / norm(q_measured_phi))
rotation_axis = cross3(h_crystal, q_measured_phi)
rotation_axis = rotation_axis * (1 / norm(rotation_axis))
cos_rotation_angle = dot3(h_crystal, q_measured_phi)
rotation_angle = acos(cos_rotation_angle)
uvw = rotation_axis.T.tolist()[0] # TODO: cleanup
print("resulting U angle: %.5f deg" % (rotation_angle * TODEG))
u_repr = (', '.join(['% .5f' % el for el in uvw]))
print("resulting U axis direction: [%s]" % u_repr)
u, v, w = uvw
rcos = cos(rotation_angle)
rsin = sin(rotation_angle)
m = [[0, 0, 0], [0, 0, 0], [0, 0, 0]] # TODO: tidy
m[0][0] = rcos + u * u * (1 - rcos)
m[1][0] = w * rsin + v * u * (1 - rcos)
m[2][0] = -v * rsin + w * u * (1 - rcos)
m[0][1] = -w * rsin + u * v * (1 - rcos)
m[1][1] = rcos + v * v * (1 - rcos)
m[2][1] = u * rsin + w * v * (1 - rcos)
m[0][2] = v * rsin + u * w * (1 - rcos)
m[1][2] = -u * rsin + v * w * (1 - rcos)
m[2][2] = rcos + w * w * (1 - rcos)
if self._UB is None:
print("Calculating UB matrix from the first reflection only.")
else:
print("Recalculating UB matrix from the first reflection only.")
print("NOTE: A new UB matrix will not be automatically calculated "
"when the orientation reflections are modified.")
self._U = matrix(m)
self._UB = self._U * B
self._state.configure_calc_type(manual_U=self._U, or0=idx)
self.save()
def fit_ub_matrix(self, *args):
if args is None:
raise DiffcalcException(
"Please specify list of reference reflection indices.")
if len(args) < 3:
raise DiffcalcException(
"Need at least 3 reference reflections to fit UB matrix.")
if len(self._state.crystal.get_lattice_params()[1]) == 6:
new_u, uc_params = self._fit_ub_matrix_uncon(*args)
else:
refl_list = []
for idx in args:
try:
hkl_vals, pos, en, _, _ = self.get_reflection(idx)
pos.changeToRadians()
refl_list.append((
hkl_vals,
pos,
en,
))
except IndexError:
raise DiffcalcException(
"Cannot read reflection data for index %s" % str(idx))
print("Fitting crystal lattice parameters...")
new_lattice = fit_crystal(self._state.crystal, refl_list)
print("Fitting orientation matrix...")
new_u = fit_u_matrix(self._U, new_lattice, refl_list)
uc_params = (self._state.crystal.getLattice()[0],
) + new_lattice.getLattice()[1:]
return new_u, uc_params
def _fit_ub_matrix_uncon(self, *args):
if args is None:
raise DiffcalcException(
"Please specify list of reference reflection indices.")
if len(args) < 3:
raise DiffcalcException(
"Need at least 3 reference reflections to fit UB matrix.")
x = []
y = []
for idx in args:
try:
hkl_vals, pos, en, _, _ = self.get_reflection(idx)
except IndexError:
raise DiffcalcException(
"Cannot read reflection data for index %s" % str(idx))
pos.changeToRadians()
x.append(hkl_vals)
wl = 12.3984 / en
y_tmp = self._strategy.calculate_q_phi(pos) * 2. * pi / wl
y.append(y_tmp.T.tolist()[0])
xm = matrix(x)
ym = matrix(y)
b = (xm.T * xm).I * xm.T * ym
b1, b2, b3 = matrix(b.tolist()[0]), matrix(b.tolist()[1]), matrix(
b.tolist()[2])
e1 = b1 / norm(b1)
e2 = b2 - e1 * dot3(b2.T, e1.T)
e2 = e2 / norm(e2)
e3 = b3 - e1 * dot3(b3.T, e1.T) - e2 * dot3(b3.T, e2.T)
e3 = e3 / norm(e3)
new_umatrix = matrix(e1.tolist() + e2.tolist() + e3.tolist()).T
V = dot3(cross3(b1.T, b2.T), b3.T)
a1 = cross3(b2.T, b3.T) * 2 * pi / V
a2 = cross3(b3.T, b1.T) * 2 * pi / V
a3 = cross3(b1.T, b2.T) * 2 * pi / V
ax, bx, cx = norm(a1), norm(a2), norm(a3)
alpha = acos(dot3(a2, a3) / (bx * cx)) * TODEG
beta = acos(dot3(a1, a3) / (ax * cx)) * TODEG
gamma = acos(dot3(a1, a2) / (ax * bx)) * TODEG
lattice_name = self._state.crystal.getLattice()[0]
return new_umatrix, (lattice_name, ax, bx, cx, alpha, beta, gamma)
def set_miscut(self, xyz, angle, add_miscut=False):
"""Calculate U matrix using a miscut axis and an angle"""
if xyz is None:
rot_matrix = xyz_rotation([0, 1, 0], angle)
else:
rot_matrix = self._tobj.transform(xyz_rotation(xyz, angle))
if self.is_ub_calculated() and add_miscut:
new_U = rot_matrix * self._U
else:
new_U = rot_matrix
self.set_U_manually(new_U, False)
self.print_surface()
self.save()
def get_hkl_plane_distance(self, hkl):
"""Calculates and returns the distance between planes"""
return self._state.crystal.get_hkl_plane_distance(hkl)
def get_hkl_plane_angle(self, hkl1, hkl2):
"""Calculates and returns the angle between planes"""
return self._state.crystal.get_hkl_plane_angle(hkl1, hkl2)
def rescale_unit_cell(self, h, k, l, pos):
"""
Calculate unit cell scaling parameter that matches
given hkl position and diffractometer angles
"""
q_vec = self._strategy.calculate_q_phi(pos)
q_hkl = norm(q_vec) / settings.hardware.get_wavelength()
d_hkl = self._state.crystal.get_hkl_plane_distance([h, k, l])
sc = 1 / (q_hkl * d_hkl)
name, a1, a2, a3, alpha1, alpha2, alpha3 = self._state.crystal.getLattice(
)
if abs(sc - 1.) < SMALL:
return None, None
ref_a1 = sc * a1 if abs(h) > SMALL else a1
ref_a2 = sc * a2 if abs(k) > SMALL else a2
ref_a3 = sc * a3 if abs(l) > SMALL else a3
return sc, (name, ref_a1, ref_a2, ref_a3, alpha1, alpha2, alpha3)
def calc_miscut(self, h, k, l, pos):
"""
Calculate miscut angle and axis that matches
given hkl position and diffractometer angles
"""
q_vec = self._strategy.calculate_q_phi(pos)
hkl_nphi = self._UB * matrix([[h], [k], [l]])
axis = self._tobj.transform(cross3(q_vec, hkl_nphi), True)
norm_axis = norm(axis)
if norm_axis < SMALL:
return None, None
axis = axis / norm(axis)
try:
miscut = acos(
bound(dot3(q_vec, hkl_nphi) /
(norm(q_vec) * norm(hkl_nphi)))) * TODEG
except AssertionError:
return None, None
return miscut, axis.T.tolist()[0]
def get_miscut_angle_axis(self, ubmatrix):
y = self._get_surf_nphi()
l = ubmatrix * y
rotation_axis = self._tobj.transform(cross3(y, l), True)
if abs(norm(rotation_axis)) < SMALL:
rotation_axis = matrix('0; 0; 0')
rotation_angle = 0
else:
rotation_axis = rotation_axis * (1 / norm(rotation_axis))
cos_rotation_angle = bound(dot3(y, l) / norm(l))
rotation_angle = acos(cos_rotation_angle) * TODEG
return rotation_angle, rotation_axis
def calc_hkl_offset(self, h, k, l, pol, az):
"""
Calculate hkl orientation values that are related to
the input hkl values by rotation with a given polar
and azimuthal angles
"""
hkl_nphi = self._UB * matrix([[h], [k], [l]])
y_axis = cross3(hkl_nphi, matrix('0; 1; 0'))
if norm3(y_axis) < SMALL:
y_axis = cross3(hkl_nphi, matrix('0; 0; 1'))
rot_polar = xyz_rotation(y_axis.T.tolist()[0], pol)
rot_azimuthal = xyz_rotation(hkl_nphi.T.tolist()[0], az)
hklrot_nphi = rot_azimuthal * rot_polar * hkl_nphi
hklrot = self._UB.I * hklrot_nphi
hkl_list = hklrot.T.tolist()[0]
return hkl_list
def calc_offset_for_hkl(self, hkl_offset, hkl_ref):
"""
Calculate polar and azimuthal angles and scaling factor
relating offset and reference hkl values
"""
d_ref = self._state.crystal.get_hkl_plane_distance(hkl_ref)
hklref_nphi = self._UB * matrix([[hkl_ref[0]], [hkl_ref[1]],
[hkl_ref[2]]])
d_offset = self._state.crystal.get_hkl_plane_distance(hkl_offset)
hkloff_nphi = self._UB * matrix([[hkl_offset[0]], [hkl_offset[1]],
[hkl_offset[2]]])
sc = d_ref / d_offset
par_ref_off = cross3(hklref_nphi, hkloff_nphi)
if norm3(par_ref_off) < SMALL:
return 0, float('nan'), sc
y_axis = cross3(hklref_nphi, matrix('0; 1; 0'))
if norm3(y_axis) < SMALL:
y_axis = cross3(hklref_nphi, matrix('0; 0; 1'))
x_axis = cross3(y_axis, hklref_nphi)
x_coord = cos(angle_between_vectors(hkloff_nphi, x_axis))
y_coord = cos(angle_between_vectors(hkloff_nphi, y_axis))
pol = angle_between_vectors(hklref_nphi, hkloff_nphi)
if abs(y_coord) < SMALL and abs(x_coord) < SMALL:
# Set azimuthal rotation matrix to identity
az = 0
else:
az = atan2(y_coord, x_coord)
return pol, az, sc