def __init__(self, ubcalc, raiseExceptionsIfAnglesDoNotMapBackToHkl=True):
r = raiseExceptionsIfAnglesDoNotMapBackToHkl
HklCalculatorBase.__init__(self,
ubcalc,
raiseExceptionsIfAnglesDoNotMapBackToHkl=r)
self._gammaParameterName = ({
'arm': 'gamma',
'base': 'oopgamma'
}[settings.geometry.gamma_location])
self.mode_selector = ModeSelector(settings.geometry, None,
self._gammaParameterName)
self.parameter_manager = VliegParameterManager(
settings.geometry, settings.hardware, self.mode_selector,
self._gammaParameterName)
self.mode_selector.setParameterManager(self.parameter_manager)
def setup_method(self):
self.ms = ModeSelector(createMockDiffractometerGeometry(),
parameterManager=None)
self.pm = VliegParameterManager(createMockDiffractometerGeometry(),
None, self.ms)
self.ms.setParameterManager(self.pm)
def __init__(self, ubcalc, geometry, hardware,
raiseExceptionsIfAnglesDoNotMapBackToHkl=True):
r = raiseExceptionsIfAnglesDoNotMapBackToHkl
HklCalculatorBase.__init__(self, ubcalc, geometry, hardware,
raiseExceptionsIfAnglesDoNotMapBackToHkl=r)
self._gammaParameterName = ({'arm': 'gamma', 'base': 'oopgamma'}
[self._geometry.gamma_location])
self.mode_selector = ModeSelector(self._geometry, None,
self._gammaParameterName)
self.parameter_manager = VliegParameterManager(
self._geometry, self._hardware, self.mode_selector,
self._gammaParameterName)
self.mode_selector.setParameterManager(self.parameter_manager)
def setUp(self):
self.hw = createMockHardwareMonitor()
self.ms = ModeSelector(createMockDiffractometerGeometry())
self.pm = VliegParameterManager(createMockDiffractometerGeometry(),
self.hw, self.ms)
class TestParameterManager(unittest.TestCase):
def setUp(self):
self.hw = createMockHardwareMonitor()
self.ms = ModeSelector(createMockDiffractometerGeometry())
self.pm = VliegParameterManager(createMockDiffractometerGeometry(),
self.hw, self.ms)
def testDefaultParameterValues(self):
self.assertEqual(self.pm.get_constraint('alpha'), 0)
self.assertEqual(self.pm.get_constraint('gamma'), 0)
self.assertRaises(DiffcalcException, self.pm.get_constraint,
'not-a-parameter-name')
def testSetParameter(self):
self.pm.set_constraint('alpha', 10.1)
self.assertEqual(self.pm.get_constraint('alpha'), 10.1)
def testSetTrackParameter_isParameterChecked(self):
self.assertEqual(self.pm.isParameterTracked('alpha'), False)
self.pm.set_constraint('alpha', 9)
self.pm.setTrackParameter('alpha', True)
self.assertEqual(self.pm.isParameterTracked('alpha'), True)
self.assertRaises(DiffcalcException, self.pm.set_constraint, 'alpha', 10)
self.hw.get_position.return_value = 888, 11, 999
self.assertEqual(self.pm.get_constraint('alpha'), 11)
print self.pm.reportAllParameters()
print "**"
print self.ms.reportCurrentMode()
print self.pm.reportParametersUsedInCurrentMode()
self.pm.setTrackParameter('alpha', False)
self.assertEqual(self.pm.isParameterTracked('alpha'), False)
self.assertEqual(self.pm.get_constraint('alpha'), 11)
self.hw.get_position.return_value = 888, 12, 999
self.assertEqual(self.pm.get_constraint('alpha'), 11)
self.pm.set_constraint('alpha', 13)
self.assertEqual(self.pm.get_constraint('alpha'), 13)
class VliegHklCalculator(HklCalculatorBase):
def __init__(self, ubcalc, geometry, hardware,
raiseExceptionsIfAnglesDoNotMapBackToHkl=True):
r = raiseExceptionsIfAnglesDoNotMapBackToHkl
HklCalculatorBase.__init__(self, ubcalc, geometry, hardware,
raiseExceptionsIfAnglesDoNotMapBackToHkl=r)
self._gammaParameterName = ({'arm': 'gamma', 'base': 'oopgamma'}
[self._geometry.gamma_location])
self.mode_selector = ModeSelector(self._geometry, None,
self._gammaParameterName)
self.parameter_manager = VliegParameterManager(
self._geometry, self._hardware, self.mode_selector,
self._gammaParameterName)
self.mode_selector.setParameterManager(self.parameter_manager)
def __str__(self):
# should list paramemeters and indicate which are used in selected mode
result = "Available mode_selector:\n"
result += self.mode_selector.reportAvailableModes()
result += '\nCurrent mode:\n'
result += self.mode_selector.reportCurrentMode()
result += '\n\nParameters:\n'
result += self.parameter_manager.reportAllParameters()
return result
def _anglesToHkl(self, pos, wavelength):
"""
Return hkl tuple from VliegPosition in radians and wavelength in
Angstroms.
"""
return vliegAnglesToHkl(pos, wavelength, self._getUBMatrix())
def _anglesToVirtualAngles(self, pos, wavelength):
"""
Return dictionary of all virtual angles in radians from VliegPosition
object win radians and wavelength in Angstroms. The virtual angles are:
Bin, Bout, azimuth and 2theta.
"""
# Create transformation matrices
[ALPHA, DELTA, GAMMA, OMEGA, CHI, PHI] = createVliegMatrices(
pos.alpha, pos.delta, pos.gamma, pos.omega, pos.chi, pos.phi)
[SIGMA, TAU] = createVliegsSurfaceTransformationMatrices(
self._getSigma() * TORAD, self._getTau() * TORAD)
S = TAU * SIGMA
y_vector = matrix([[0], [1], [0]])
# Calculate Bin from equation 15:
surfacenormal_alpha = OMEGA * CHI * PHI * S * matrix([[0], [0], [1]])
incoming_alpha = ALPHA.I * y_vector
minusSinBetaIn = dot3(surfacenormal_alpha, incoming_alpha)
Bin = asin(bound(-minusSinBetaIn))
# Calculate Bout from equation 16:
# surfacenormal_alpha has just ben calculated
outgoing_alpha = DELTA * GAMMA * y_vector
sinBetaOut = dot3(surfacenormal_alpha, outgoing_alpha)
Bout = asin(bound(sinBetaOut))
# Calculate 2theta from equation 25:
cosTwoTheta = dot3(ALPHA * DELTA * GAMMA * y_vector, y_vector)
twotheta = acos(bound(cosTwoTheta))
psi = self._anglesToPsi(pos, wavelength)
return {'Bin': Bin, 'Bout': Bout, 'azimuth': psi, '2theta': twotheta}
def _hklToAngles(self, h, k, l, wavelength):
"""
Return VliegPosition and virtual angles in radians from h, k & l and
wavelength in Angstroms. The virtual angles are those fixed or
generated while calculating the position: Bin, Bout and 2theta; and
azimuth in four and five circle modes.
"""
if self._getMode().group in ("fourc", "fivecFixedGamma",
"fivecFixedAlpha"):
return self._hklToAnglesFourAndFiveCirclesModes(h, k, l,
wavelength)
elif self._getMode().group == "zaxis":
return self._hklToAnglesZaxisModes(h, k, l, wavelength)
else:
raise RuntimeError(
'The current mode (%s) has an unrecognised group: %s.'
% (self._getMode().name, self._getMode().group))
def _hklToAnglesFourAndFiveCirclesModes(self, h, k, l, wavelength):
"""
Return VliegPosition and virtual angles in radians from h, k & l and
wavelength in Angstrom for four and five circle modes. The virtual
angles are those fixed or generated while calculating the position:
Bin, Bout, 2theta and azimuth.
"""
# Results in radians during calculations, returned in degreess
pos = VliegPosition(None, None, None, None, None, None)
# Normalise hkl
wavevector = 2 * pi / wavelength
hklNorm = matrix([[h], [k], [l]]) / wavevector
# Compute hkl in phi axis coordinate frame
hklPhiNorm = self._getUBMatrix() * hklNorm
# Determine Bin and Bout
if self._getMode().name == '4cPhi':
Bin = Bout = None
else:
Bin, Bout = self._determineBinAndBoutInFourAndFiveCirclesModes(
hklNorm)
# Determine alpha and gamma
if self._getMode().group == 'fourc':
pos.alpha, pos.gamma = \
self._determineAlphaAndGammaForFourCircleModes(hklPhiNorm)
else:
pos.alpha, pos.gamma = \
self._determineAlphaAndGammaForFiveCircleModes(Bin, hklPhiNorm)
if pos.alpha < -pi:
pos.alpha += 2 * pi
if pos.alpha > pi:
pos.alpha -= 2 * pi
# Determine delta
(pos.delta, twotheta) = self._determineDelta(hklPhiNorm, pos.alpha,
pos.gamma)
# Determine omega, chi & phi
pos.omega, pos.chi, pos.phi, psi = \
self._determineSampleAnglesInFourAndFiveCircleModes(
hklPhiNorm, pos.alpha, pos.delta, pos.gamma, Bin)
# (psi will be None in fixed phi mode)
# Ensure that by default omega is between -90 and 90, by possibly
# transforming the sample angles
if self._getMode().name != '4cPhi': # not in fixed-phi mode
if pos.omega < -pi / 2 or pos.omega > pi / 2:
pos = transformC.transform(pos)
# Gather up the virtual angles calculated along the way...
# -pi<psi<=pi
if psi is not None:
if psi > pi:
psi -= 2 * pi
if psi < (-1 * pi):
psi += 2 * pi
v = {'2theta': twotheta, 'Bin': Bin, 'Bout': Bout, 'azimuth': psi}
return pos, v
def _hklToAnglesZaxisModes(self, h, k, l, wavelength):
"""
Return VliegPosition and virtual angles in radians from h, k & l and
wavelength in Angstroms for z-axis modes. The virtual angles are those
fixed or generated while calculating the position: Bin, Bout, and
2theta.
"""
# Section 6:
# Results in radians during calculations, returned in degreess
pos = VliegPosition(None, None, None, None, None, None)
# Normalise hkl
wavevector = 2 * pi / wavelength
hkl = matrix([[h], [k], [l]])
hklNorm = hkl * (1.0 / wavevector)
# Compute hkl in phi axis coordinate frame
hklPhi = self._getUBMatrix() * hkl
hklPhiNorm = self._getUBMatrix() * hklNorm
# Determine Chi and Phi (Equation 29):
pos.phi = -self._getTau() * TORAD
pos.chi = -self._getSigma() * TORAD
# Equation 30:
[ALPHA, DELTA, GAMMA, OMEGA, CHI, PHI] = createVliegMatrices(
None, None, None, None, pos.chi, pos.phi)
del ALPHA, DELTA, GAMMA, OMEGA
Hw = CHI * PHI * hklPhi
# Determine Bin and Bout:
(Bin, Bout) = self._determineBinAndBoutInZaxisModes(
Hw[2, 0] / wavevector)
# Determine Alpha and Gamma (Equation 32):
pos.alpha = Bin
pos.gamma = Bout
# Determine Delta:
(pos.delta, twotheta) = self._determineDelta(hklPhiNorm, pos.alpha,
pos.gamma)
# Determine Omega:
delta = pos.delta
gamma = pos.gamma
d1 = (Hw[1, 0] * sin(delta) * cos(gamma) - Hw[0, 0] *
(cos(delta) * cos(gamma) - cos(pos.alpha)))
d2 = (Hw[0, 0] * sin(delta) * cos(gamma) + Hw[1, 0] *
(cos(delta) * cos(gamma) - cos(pos.alpha)))
if fabs(d2) < 1e-30:
pos.omega = sign(d1) * sign(d2) * pi / 2.0
else:
pos.omega = atan2(d1, d2)
# Gather up the virtual angles calculated along the way
return pos, {'2theta': twotheta, 'Bin': Bin, 'Bout': Bout}
###
def _determineBinAndBoutInFourAndFiveCirclesModes(self, hklNorm):
"""(Bin, Bout) = _determineBinAndBoutInFourAndFiveCirclesModes()"""
BinModes = ('4cBin', '5cgBin', '5caBin')
BoutModes = ('4cBout', '5cgBout', '5caBout')
BeqModes = ('4cBeq', '5cgBeq', '5caBeq')
azimuthModes = ('4cAzimuth')
fixedBusingAndLeviWmodes = ('4cFixedw')
# Calculate RHS of equation 20
# RHS (1/K)(S^-1*U*B*H)_3 where H/K = hklNorm
UB = self._getUBMatrix()
[SIGMA, TAU] = createVliegsSurfaceTransformationMatrices(
self._getSigma() * TORAD, self._getTau() * TORAD)
#S = SIGMA * TAU
S = TAU * SIGMA
RHS = (S.I * UB * hklNorm)[2, 0]
if self._getMode().name in BinModes:
Bin = self._getParameter('betain')
check(Bin != None, "The parameter betain must be set for mode %s" %
self._getMode().name)
Bin = Bin * TORAD
sinBout = RHS - sin(Bin)
check(fabs(sinBout) <= 1, "Could not compute Bout")
Bout = asin(sinBout)
elif self._getMode().name in BoutModes:
Bout = self._getParameter('betaout')
check(Bout != None, "The parameter Bout must be set for mode %s" %
self._getMode().name)
Bout = Bout * TORAD
sinBin = RHS - sin(Bout)
check(fabs(sinBin) <= 1, "Could not compute Bin")
Bin = asin(sinBin)
elif self._getMode().name in BeqModes:
sinBeq = RHS / 2
check(fabs(sinBeq) <= 1, "Could not compute Bin=Bout")
Bin = Bout = asin(sinBeq)
elif self._getMode().name in azimuthModes:
azimuth = self._getParameter('azimuth')
check(azimuth != None, "The parameter azimuth must be set for "
"mode %s" % self._getMode().name)
del azimuth
# TODO: codeit
raise NotImplementedError()
elif self._getMode().name in fixedBusingAndLeviWmodes:
bandlomega = self._getParameter('blw')
check(bandlomega != None, "The parameter abandlomega must be set "
"for mode %s" % self._getMode().name)
del bandlomega
# TODO: codeit
raise NotImplementedError()
else:
raise RuntimeError("AngleCalculator does not know how to handle "
"mode %s" % self._getMode().name)
return (Bin, Bout)
def _determineBinAndBoutInZaxisModes(self, Hw3OverK):
"""(Bin, Bout) = _determineBinAndBoutInZaxisModes(HwOverK)"""
BinModes = ('6czBin')
BoutModes = ('6czBout')
BeqModes = ('6czBeq')
if self._getMode().name in BinModes:
Bin = self._getParameter('betain')
check(Bin != None, "The parameter betain must be set for mode %s" %
self._getMode().name)
Bin = Bin * TORAD
# Equation 32a:
Bout = asin(Hw3OverK - sin(Bin))
elif self._getMode().name in BoutModes:
Bout = self._getParameter('betaout')
check(Bout != None, "The parameter Bout must be set for mode %s" %
self._getMode().name)
Bout = Bout * TORAD
# Equation 32b:
Bin = asin(Hw3OverK - sin(Bout))
elif self._getMode().name in BeqModes:
# Equation 32c:
Bin = Bout = asin(Hw3OverK / 2)
return (Bin, Bout)
###
def _determineAlphaAndGammaForFourCircleModes(self, hklPhiNorm):
if self._getMode().group == 'fourc':
alpha = self._getParameter('alpha') * TORAD
gamma = self._getParameter(self._getGammaParameterName()) * TORAD
check(alpha != None, "alpha parameter must be set in fourc modes")
check(gamma != None, "gamma parameter must be set in fourc modes")
return alpha, gamma
else:
raise RuntimeError(
"determineAlphaAndGammaForFourCirclesModes() "
"is not appropriate for %s modes" % self._getMode().group)
def _determineAlphaAndGammaForFiveCircleModes(self, Bin, hklPhiNorm):
## Solve equation 34 for one possible Y, Yo
# Calculate surface normal in phi frame
[SIGMA, TAU] = createVliegsSurfaceTransformationMatrices(
self._getSigma() * TORAD, self._getTau() * TORAD)
S = TAU * SIGMA
surfaceNormalPhi = S * matrix([[0], [0], [1]])
# Compute beta in vector
BetaVector = matrix([[0], [-sin(Bin)], [cos(Bin)]])
# Find Yo
Yo = self._findMatrixToTransformAIntoB(surfaceNormalPhi, BetaVector)
## Calculate Hv from equation 39
Z = matrix([[1, 0, 0],
[0, cos(Bin), sin(Bin)],
[0, -sin(Bin), cos(Bin)]])
Hv = Z * Yo * hklPhiNorm
# Fixed gamma:
if self._getMode().group == 'fivecFixedGamma':
gamma = self._getParameter(self._getGammaParameterName())
check(gamma != None,
"gamma parameter must be set in fivecFixedGamma modes")
gamma = gamma * TORAD
H2 = (hklPhiNorm[0, 0] ** 2 + hklPhiNorm[1, 0] ** 2 +
hklPhiNorm[2, 0] ** 2)
a = -(0.5 * H2 * sin(Bin) - Hv[2, 0])
b = -(1.0 - 0.5 * H2) * cos(Bin)
c = cos(Bin) * sin(gamma)
check((b * b + a * a - c * c) >= 0, 'Could not solve for alpha')
alpha = 2 * atan2(-(b + sqrt(b * b + a * a - c * c)), -(a + c))
# Fixed Alpha:
elif self._getMode().group == 'fivecFixedAlpha':
alpha = self._getParameter('alpha')
check(alpha != None,
"alpha parameter must be set in fivecFixedAlpha modes")
alpha = alpha * TORAD
H2 = (hklPhiNorm[0, 0] ** 2 + hklPhiNorm[1, 0] ** 2 +
hklPhiNorm[2, 0] ** 2)
t0 = ((2 * cos(alpha) * Hv[2, 0] - sin(Bin) * cos(alpha) * H2 +
cos(Bin) * sin(alpha) * H2 - 2 * cos(Bin) * sin(alpha)) /
(cos(Bin) * 2.0))
check(abs(t0) <= 1, "Cannot compute gamma: sin(gamma)>1")
gamma = asin(t0)
else:
raise RuntimeError(
"determineAlphaAndGammaInFiveCirclesModes() is not "
"appropriate for %s modes" % self._getMode().group)
return (alpha, gamma)
###
def _determineDelta(self, hklPhiNorm, alpha, gamma):
"""
(delta, twotheta) = _determineDelta(hklPhiNorm, alpha, gamma) --
computes delta for all modes. Also returns twotheta for sanity
checking. hklPhiNorm is a 3X1 matrix.
alpha, gamma & delta - in radians.
h k & l normalised to wavevector and in phi axis coordinates
"""
h = hklPhiNorm[0, 0]
k = hklPhiNorm[1, 0]
l = hklPhiNorm[2, 0]
# See Vlieg section 5 (with K=1)
cosdelta = ((1 + sin(gamma) * sin(alpha) - (h * h + k * k + l * l) / 2)
/ (cos(gamma) * cos(alpha)))
costwotheta = (cos(alpha) * cos(gamma) * bound(cosdelta) -
sin(alpha) * sin(gamma))
return (acos(bound(cosdelta)), acos(bound(costwotheta)))
def _determineSampleAnglesInFourAndFiveCircleModes(self, hklPhiNorm, alpha,
delta, gamma, Bin):
"""
(omega, chi, phi, psi)=determineNonZAxisSampleAngles(hklPhiNorm, alpha,
delta, gamma, sigma, tau) where hkl has been normalised by the
wavevector and is in the phi Axis coordinate frame. All angles in
radians. hklPhiNorm is a 3X1 matrix
"""
def equation49through59(psi):
# equation 49 R = (D^-1)*PI*D*Ro
PSI = createVliegsPsiTransformationMatrix(psi)
R = D.I * PSI * D * Ro
# eq 57: extract omega from R
if abs(R[0, 2]) < 1e-20:
omega = -sign(R[1, 2]) * sign(R[0, 2]) * pi / 2
else:
omega = -atan2(R[1, 2], R[0, 2])
# eq 58: extract chi from R
sinchi = sqrt(pow(R[0, 2], 2) + pow(R[1, 2], 2))
sinchi = bound(sinchi)
check(abs(sinchi) <= 1, 'could not compute chi')
# (there are two roots to this equation, but only the first is also
# a solution to R33=cos(chi))
chi = asin(sinchi)
# eq 59: extract phi from R
if abs(R[2, 0]) < 1e-20:
phi = sign(R[2, 1]) * sign(R[2, 1]) * pi / 2
else:
phi = atan2(-R[2, 1], -R[2, 0])
return omega, chi, phi
def checkSolution(omega, chi, phi):
_, _, _, OMEGA, CHI, PHI = createVliegMatrices(
None, None, None, omega, chi, phi)
R = OMEGA * CHI * PHI
RtimesH_phi = R * H_phi
print ("R*H_phi=%s, Q_alpha=%s" %
(R * H_phi.tolist(), Q_alpha.tolist()))
return not differ(RtimesH_phi, Q_alpha, .0001)
# Using Vlieg section 7.2
# Needed througout:
[ALPHA, DELTA, GAMMA, _, _, _] = createVliegMatrices(
alpha, delta, gamma, None, None, None)
## Find Ro, one possible solution to equation 46: R*H_phi=Q_alpha
# Normalise hklPhiNorm (As it is currently normalised only to the
# wavevector)
normh = norm(hklPhiNorm)
check(normh >= 1e-10, "reciprical lattice vector too close to zero")
H_phi = hklPhiNorm * (1 / normh)
# Create Q_alpha from equation 47, (it comes normalised)
Q_alpha = ((DELTA * GAMMA) - ALPHA.I) * matrix([[0], [1], [0]])
Q_alpha = Q_alpha * (1 / norm(Q_alpha))
if self._getMode().name == '4cPhi':
### Use the fixed value of phi as the final constraint ###
phi = self._getParameter('phi') * TORAD
PHI = calcPHI(phi)
H_chi = PHI * H_phi
omega, chi = _findOmegaAndChiToRotateHchiIntoQalpha(H_chi, Q_alpha)
return (omega, chi, phi, None) # psi = None as not calculated
else:
### Use Bin as the final constraint ###
# Find a solution Ro to Ro*H_phi=Q_alpha
Ro = self._findMatrixToTransformAIntoB(H_phi, Q_alpha)
## equation 50: Find a solution D to D*Q=norm(Q)*[[1],[0],[0]])
D = self._findMatrixToTransformAIntoB(
Q_alpha, matrix([[1], [0], [0]]))
## Find psi and create PSI
# eq 54: compute u=D*Ro*S*[[0],[0],[1]], the surface normal in
# psi frame
[SIGMA, TAU] = createVliegsSurfaceTransformationMatrices(
self._getSigma() * TORAD, self._getTau() * TORAD)
S = TAU * SIGMA
[u1], [u2], [u3] = (D * Ro * S * matrix([[0], [0], [1]])).tolist()
# TODO: If u points along 100, then any psi is a solution. Choose 0
if not differ([u1, u2, u3], [1, 0, 0], 1e-9):
psi = 0
omega, chi, phi = equation49through59(psi)
else:
# equation 53: V=A*(D^-1)
V = ALPHA * D.I
v21 = V[1, 0]
v22 = V[1, 1]
v23 = V[1, 2]
# equation 55
a = v22 * u2 + v23 * u3
b = v22 * u3 - v23 * u2
c = -sin(Bin) - v21 * u1 # TODO: changed sign from paper
# equation 44
# Try first root:
def myatan2(y, x):
if abs(x) < 1e-20 and abs(y) < 1e-20:
return pi / 2
else:
return atan2(y, x)
psi = 2 * myatan2(-(b - sqrt(b * b + a * a - c * c)), -(a + c))
#psi = -acos(c/sqrt(a*a+b*b))+atan2(b,a)# -2*pi
omega, chi, phi = equation49through59(psi)
# if u points along z axis, the psi could have been either 0 or 180
if (not differ([u1, u2, u3], [0, 0, 1], 1e-9) and
abs(psi - pi) < 1e-10):
# Choose 0 to match that read up by angles-to-virtual-angles
psi = 0.
# if u points a long
return (omega, chi, phi, psi)
def _anglesToPsi(self, pos, wavelength):
"""
pos assumed in radians. -180<= psi <= 180
"""
# Using Vlieg section 7.2
# Needed througout:
[ALPHA, DELTA, GAMMA, OMEGA, CHI, PHI] = createVliegMatrices(
pos.alpha, pos.delta, pos.gamma, pos.omega, pos.chi, pos.phi)
# Solve equation 49 for psi, the rotation of the a reference solution
# about Qalpha or H_phi##
# Find Ro, the reference solution to equation 46: R*H_phi=Q_alpha
# Create Q_alpha from equation 47, (it comes normalised)
Q_alpha = ((DELTA * GAMMA) - ALPHA.I) * matrix([[0], [1], [0]])
Q_alpha = Q_alpha * (1 / norm(Q_alpha))
# Finh H_phi
h, k, l = self._anglesToHkl(pos, wavelength)
H_phi = self._getUBMatrix() * matrix([[h], [k], [l]])
normh = norm(H_phi)
check(normh >= 1e-10, "reciprical lattice vector too close to zero")
H_phi = H_phi * (1 / normh)
# Find a solution Ro to Ro*H_phi=Q_alpha
# This the reference solution with zero azimuth (psi)
Ro = self._findMatrixToTransformAIntoB(H_phi, Q_alpha)
# equation 48:
R = OMEGA * CHI * PHI
## equation 50: Find a solution D to D*Q=norm(Q)*[[1],[0],[0]])
D = self._findMatrixToTransformAIntoB(Q_alpha, matrix([[1], [0], [0]]))
# solve equation 49 for psi
# D*R = PSI*D*Ro
# D*R*(D*Ro)^-1 = PSI
PSI = D * R * ((D * Ro).I)
# Find psi within PSI as defined in equation 51
PSI_23 = PSI[1, 2]
PSI_33 = PSI[2, 2]
psi = atan2(PSI_23, PSI_33)
#print "PSI: ", PSI.tolist()
return psi
def _findMatrixToTransformAIntoB(self, a, b):
"""
Finds a particular matrix Mo that transforms the unit vector a into the
unit vector b. Thats is it finds Mo Mo*a=b. a and b 3x1 matrixes and Mo
is a 3x3 matrix.
Throws an exception if this is not possible.
"""
# Maths from the appendix of "Angle caluculations
# for a 5-circle diffractometer used for surface X-ray diffraction",
# E. Vlieg, J.F. van der Veen, J.E. Macdonald and M. Miller, J. of
# Applied Cryst. 20 (1987) 330.
# - courtesy of Elias Vlieg again
# equation A2: compute angle xi between vectors a and b
cosxi = dot3(a, b)
try:
cosxi = bound(cosxi)
except ValueError:
raise Exception("Could not compute cos(xi), vectors a=%f and b=%f "
"must be of unit length" % (norm(a), norm(b)))
xi = acos(cosxi)
# Mo is identity matrix if xi zero (math below would blow up)
if abs(xi) < 1e-10:
return I
# equation A3: c=cross(a,b)/sin(xi)
c = cross3(a, b) * (1 / sin(xi))
# equation A4: find D matrix that transforms a into the frame
# x = a; y = c x a; z = c. */
a1 = a[0, 0]
a2 = a[1, 0]
a3 = a[2, 0]
c1 = c[0, 0]
c2 = c[1, 0]
c3 = c[2, 0]
D = matrix([[a1, a2, a3],
[c2 * a3 - c3 * a2, c3 * a1 - c1 * a3, c1 * a2 - c2 * a1],
[c1, c2, c3]])
# equation A5: create Xi to rotate by xi about z-axis
XI = matrix([[cos(xi), -sin(xi), 0],
[sin(xi), cos(xi), 0],
[0, 0, 1]])
# eq A6: compute Mo
return D.I * XI * D
class VliegHklCalculator(HklCalculatorBase):
def __init__(self,
ubcalc,
geometry,
hardware,
raiseExceptionsIfAnglesDoNotMapBackToHkl=True):
r = raiseExceptionsIfAnglesDoNotMapBackToHkl
HklCalculatorBase.__init__(self,
ubcalc,
geometry,
hardware,
raiseExceptionsIfAnglesDoNotMapBackToHkl=r)
self._gammaParameterName = ({
'arm': 'gamma',
'base': 'oopgamma'
}[self._geometry.gamma_location])
self.mode_selector = ModeSelector(self._geometry, None,
self._gammaParameterName)
self.parameter_manager = VliegParameterManager(
self._geometry, self._hardware, self.mode_selector,
self._gammaParameterName)
self.mode_selector.setParameterManager(self.parameter_manager)
def __str__(self):
# should list paramemeters and indicate which are used in selected mode
result = "Available mode_selector:\n"
result += self.mode_selector.reportAvailableModes()
result += '\nCurrent mode:\n'
result += self.mode_selector.reportCurrentMode()
result += '\n\nParameters:\n'
result += self.parameter_manager.reportAllParameters()
return result
def _anglesToHkl(self, pos, wavelength):
"""
Return hkl tuple from VliegPosition in radians and wavelength in
Angstroms.
"""
return vliegAnglesToHkl(pos, wavelength, self._getUBMatrix())
def _anglesToVirtualAngles(self, pos, wavelength):
"""
Return dictionary of all virtual angles in radians from VliegPosition
object win radians and wavelength in Angstroms. The virtual angles are:
Bin, Bout, azimuth and 2theta.
"""
# Create transformation matrices
[ALPHA, DELTA, GAMMA, OMEGA, CHI,
PHI] = createVliegMatrices(pos.alpha, pos.delta, pos.gamma, pos.omega,
pos.chi, pos.phi)
[SIGMA, TAU] = createVliegsSurfaceTransformationMatrices(
self._getSigma() * TORAD,
self._getTau() * TORAD)
S = TAU * SIGMA
y_vector = matrix([[0], [1], [0]])
# Calculate Bin from equation 15:
surfacenormal_alpha = OMEGA * CHI * PHI * S * matrix([[0], [0], [1]])
incoming_alpha = ALPHA.I * y_vector
minusSinBetaIn = dot3(surfacenormal_alpha, incoming_alpha)
Bin = asin(bound(-minusSinBetaIn))
# Calculate Bout from equation 16:
# surfacenormal_alpha has just ben calculated
outgoing_alpha = DELTA * GAMMA * y_vector
sinBetaOut = dot3(surfacenormal_alpha, outgoing_alpha)
Bout = asin(bound(sinBetaOut))
# Calculate 2theta from equation 25:
cosTwoTheta = dot3(ALPHA * DELTA * GAMMA * y_vector, y_vector)
twotheta = acos(bound(cosTwoTheta))
psi = self._anglesToPsi(pos, wavelength)
return {'Bin': Bin, 'Bout': Bout, 'azimuth': psi, '2theta': twotheta}
def _hklToAngles(self, h, k, l, wavelength):
"""
Return VliegPosition and virtual angles in radians from h, k & l and
wavelength in Angstroms. The virtual angles are those fixed or
generated while calculating the position: Bin, Bout and 2theta; and
azimuth in four and five circle modes.
"""
if self._getMode().group in ("fourc", "fivecFixedGamma",
"fivecFixedAlpha"):
return self._hklToAnglesFourAndFiveCirclesModes(
h, k, l, wavelength)
elif self._getMode().group == "zaxis":
return self._hklToAnglesZaxisModes(h, k, l, wavelength)
else:
raise RuntimeError(
'The current mode (%s) has an unrecognised group: %s.' %
(self._getMode().name, self._getMode().group))
def _hklToAnglesFourAndFiveCirclesModes(self, h, k, l, wavelength):
"""
Return VliegPosition and virtual angles in radians from h, k & l and
wavelength in Angstrom for four and five circle modes. The virtual
angles are those fixed or generated while calculating the position:
Bin, Bout, 2theta and azimuth.
"""
# Results in radians during calculations, returned in degreess
pos = VliegPosition(None, None, None, None, None, None)
# Normalise hkl
wavevector = 2 * pi / wavelength
hklNorm = matrix([[h], [k], [l]]) / wavevector
# Compute hkl in phi axis coordinate frame
hklPhiNorm = self._getUBMatrix() * hklNorm
# Determine Bin and Bout
if self._getMode().name == '4cPhi':
Bin = Bout = None
else:
Bin, Bout = self._determineBinAndBoutInFourAndFiveCirclesModes(
hklNorm)
# Determine alpha and gamma
if self._getMode().group == 'fourc':
pos.alpha, pos.gamma = \
self._determineAlphaAndGammaForFourCircleModes(hklPhiNorm)
else:
pos.alpha, pos.gamma = \
self._determineAlphaAndGammaForFiveCircleModes(Bin, hklPhiNorm)
if pos.alpha < -pi:
pos.alpha += 2 * pi
if pos.alpha > pi:
pos.alpha -= 2 * pi
# Determine delta
(pos.delta, twotheta) = self._determineDelta(hklPhiNorm, pos.alpha,
pos.gamma)
# Determine omega, chi & phi
pos.omega, pos.chi, pos.phi, psi = \
self._determineSampleAnglesInFourAndFiveCircleModes(
hklPhiNorm, pos.alpha, pos.delta, pos.gamma, Bin)
# (psi will be None in fixed phi mode)
# Ensure that by default omega is between -90 and 90, by possibly
# transforming the sample angles
if self._getMode().name != '4cPhi': # not in fixed-phi mode
if pos.omega < -pi / 2 or pos.omega > pi / 2:
pos = transformC.transform(pos)
# Gather up the virtual angles calculated along the way...
# -pi<psi<=pi
if psi is not None:
if psi > pi:
psi -= 2 * pi
if psi < (-1 * pi):
psi += 2 * pi
v = {'2theta': twotheta, 'Bin': Bin, 'Bout': Bout, 'azimuth': psi}
return pos, v
def _hklToAnglesZaxisModes(self, h, k, l, wavelength):
"""
Return VliegPosition and virtual angles in radians from h, k & l and
wavelength in Angstroms for z-axis modes. The virtual angles are those
fixed or generated while calculating the position: Bin, Bout, and
2theta.
"""
# Section 6:
# Results in radians during calculations, returned in degreess
pos = VliegPosition(None, None, None, None, None, None)
# Normalise hkl
wavevector = 2 * pi / wavelength
hkl = matrix([[h], [k], [l]])
hklNorm = hkl * (1.0 / wavevector)
# Compute hkl in phi axis coordinate frame
hklPhi = self._getUBMatrix() * hkl
hklPhiNorm = self._getUBMatrix() * hklNorm
# Determine Chi and Phi (Equation 29):
pos.phi = -self._getTau() * TORAD
pos.chi = -self._getSigma() * TORAD
# Equation 30:
[ALPHA, DELTA, GAMMA, OMEGA, CHI,
PHI] = createVliegMatrices(None, None, None, None, pos.chi, pos.phi)
del ALPHA, DELTA, GAMMA, OMEGA
Hw = CHI * PHI * hklPhi
# Determine Bin and Bout:
(Bin,
Bout) = self._determineBinAndBoutInZaxisModes(Hw[2, 0] / wavevector)
# Determine Alpha and Gamma (Equation 32):
pos.alpha = Bin
pos.gamma = Bout
# Determine Delta:
(pos.delta, twotheta) = self._determineDelta(hklPhiNorm, pos.alpha,
pos.gamma)
# Determine Omega:
delta = pos.delta
gamma = pos.gamma
d1 = (Hw[1, 0] * sin(delta) * cos(gamma) - Hw[0, 0] *
(cos(delta) * cos(gamma) - cos(pos.alpha)))
d2 = (Hw[0, 0] * sin(delta) * cos(gamma) + Hw[1, 0] *
(cos(delta) * cos(gamma) - cos(pos.alpha)))
if fabs(d2) < 1e-30:
pos.omega = sign(d1) * sign(d2) * pi / 2.0
else:
pos.omega = atan2(d1, d2)
# Gather up the virtual angles calculated along the way
return pos, {'2theta': twotheta, 'Bin': Bin, 'Bout': Bout}
###
def _determineBinAndBoutInFourAndFiveCirclesModes(self, hklNorm):
"""(Bin, Bout) = _determineBinAndBoutInFourAndFiveCirclesModes()"""
BinModes = ('4cBin', '5cgBin', '5caBin')
BoutModes = ('4cBout', '5cgBout', '5caBout')
BeqModes = ('4cBeq', '5cgBeq', '5caBeq')
azimuthModes = ('4cAzimuth')
fixedBusingAndLeviWmodes = ('4cFixedw')
# Calculate RHS of equation 20
# RHS (1/K)(S^-1*U*B*H)_3 where H/K = hklNorm
UB = self._getUBMatrix()
[SIGMA, TAU] = createVliegsSurfaceTransformationMatrices(
self._getSigma() * TORAD,
self._getTau() * TORAD)
#S = SIGMA * TAU
S = TAU * SIGMA
RHS = (S.I * UB * hklNorm)[2, 0]
if self._getMode().name in BinModes:
Bin = self._getParameter('betain')
check(
Bin != None, "The parameter betain must be set for mode %s" %
self._getMode().name)
Bin = Bin * TORAD
sinBout = RHS - sin(Bin)
check(fabs(sinBout) <= 1, "Could not compute Bout")
Bout = asin(sinBout)
elif self._getMode().name in BoutModes:
Bout = self._getParameter('betaout')
check(
Bout != None, "The parameter Bout must be set for mode %s" %
self._getMode().name)
Bout = Bout * TORAD
sinBin = RHS - sin(Bout)
check(fabs(sinBin) <= 1, "Could not compute Bin")
Bin = asin(sinBin)
elif self._getMode().name in BeqModes:
sinBeq = RHS / 2
check(fabs(sinBeq) <= 1, "Could not compute Bin=Bout")
Bin = Bout = asin(sinBeq)
elif self._getMode().name in azimuthModes:
azimuth = self._getParameter('azimuth')
check(
azimuth != None, "The parameter azimuth must be set for "
"mode %s" % self._getMode().name)
del azimuth
# TODO: codeit
raise NotImplementedError()
elif self._getMode().name in fixedBusingAndLeviWmodes:
bandlomega = self._getParameter('blw')
check(
bandlomega != None, "The parameter abandlomega must be set "
"for mode %s" % self._getMode().name)
del bandlomega
# TODO: codeit
raise NotImplementedError()
else:
raise RuntimeError("AngleCalculator does not know how to handle "
"mode %s" % self._getMode().name)
return (Bin, Bout)
def _determineBinAndBoutInZaxisModes(self, Hw3OverK):
"""(Bin, Bout) = _determineBinAndBoutInZaxisModes(HwOverK)"""
BinModes = ('6czBin')
BoutModes = ('6czBout')
BeqModes = ('6czBeq')
if self._getMode().name in BinModes:
Bin = self._getParameter('betain')
check(
Bin != None, "The parameter betain must be set for mode %s" %
self._getMode().name)
Bin = Bin * TORAD
# Equation 32a:
Bout = asin(Hw3OverK - sin(Bin))
elif self._getMode().name in BoutModes:
Bout = self._getParameter('betaout')
check(
Bout != None, "The parameter Bout must be set for mode %s" %
self._getMode().name)
Bout = Bout * TORAD
# Equation 32b:
Bin = asin(Hw3OverK - sin(Bout))
elif self._getMode().name in BeqModes:
# Equation 32c:
Bin = Bout = asin(Hw3OverK / 2)
return (Bin, Bout)
###
def _determineAlphaAndGammaForFourCircleModes(self, hklPhiNorm):
if self._getMode().group == 'fourc':
alpha = self._getParameter('alpha') * TORAD
gamma = self._getParameter(self._getGammaParameterName()) * TORAD
check(alpha != None, "alpha parameter must be set in fourc modes")
check(gamma != None, "gamma parameter must be set in fourc modes")
return alpha, gamma
else:
raise RuntimeError("determineAlphaAndGammaForFourCirclesModes() "
"is not appropriate for %s modes" %
self._getMode().group)
def _determineAlphaAndGammaForFiveCircleModes(self, Bin, hklPhiNorm):
## Solve equation 34 for one possible Y, Yo
# Calculate surface normal in phi frame
[SIGMA, TAU] = createVliegsSurfaceTransformationMatrices(
self._getSigma() * TORAD,
self._getTau() * TORAD)
S = TAU * SIGMA
surfaceNormalPhi = S * matrix([[0], [0], [1]])
# Compute beta in vector
BetaVector = matrix([[0], [-sin(Bin)], [cos(Bin)]])
# Find Yo
Yo = self._findMatrixToTransformAIntoB(surfaceNormalPhi, BetaVector)
## Calculate Hv from equation 39
Z = matrix([[1, 0, 0], [0, cos(Bin), sin(Bin)],
[0, -sin(Bin), cos(Bin)]])
Hv = Z * Yo * hklPhiNorm
# Fixed gamma:
if self._getMode().group == 'fivecFixedGamma':
gamma = self._getParameter(self._getGammaParameterName())
check(gamma != None,
"gamma parameter must be set in fivecFixedGamma modes")
gamma = gamma * TORAD
H2 = (hklPhiNorm[0, 0]**2 + hklPhiNorm[1, 0]**2 +
hklPhiNorm[2, 0]**2)
a = -(0.5 * H2 * sin(Bin) - Hv[2, 0])
b = -(1.0 - 0.5 * H2) * cos(Bin)
c = cos(Bin) * sin(gamma)
check((b * b + a * a - c * c) >= 0, 'Could not solve for alpha')
alpha = 2 * atan2(-(b + sqrt(b * b + a * a - c * c)), -(a + c))
# Fixed Alpha:
elif self._getMode().group == 'fivecFixedAlpha':
alpha = self._getParameter('alpha')
check(alpha != None,
"alpha parameter must be set in fivecFixedAlpha modes")
alpha = alpha * TORAD
H2 = (hklPhiNorm[0, 0]**2 + hklPhiNorm[1, 0]**2 +
hklPhiNorm[2, 0]**2)
t0 = ((2 * cos(alpha) * Hv[2, 0] - sin(Bin) * cos(alpha) * H2 +
cos(Bin) * sin(alpha) * H2 - 2 * cos(Bin) * sin(alpha)) /
(cos(Bin) * 2.0))
check(abs(t0) <= 1, "Cannot compute gamma: sin(gamma)>1")
gamma = asin(t0)
else:
raise RuntimeError(
"determineAlphaAndGammaInFiveCirclesModes() is not "
"appropriate for %s modes" % self._getMode().group)
return (alpha, gamma)
###
def _determineDelta(self, hklPhiNorm, alpha, gamma):
"""
(delta, twotheta) = _determineDelta(hklPhiNorm, alpha, gamma) --
computes delta for all modes. Also returns twotheta for sanity
checking. hklPhiNorm is a 3X1 matrix.
alpha, gamma & delta - in radians.
h k & l normalised to wavevector and in phi axis coordinates
"""
h = hklPhiNorm[0, 0]
k = hklPhiNorm[1, 0]
l = hklPhiNorm[2, 0]
# See Vlieg section 5 (with K=1)
cosdelta = ((1 + sin(gamma) * sin(alpha) -
(h * h + k * k + l * l) / 2) / (cos(gamma) * cos(alpha)))
costwotheta = (cos(alpha) * cos(gamma) * bound(cosdelta) -
sin(alpha) * sin(gamma))
return (acos(bound(cosdelta)), acos(bound(costwotheta)))
def _determineSampleAnglesInFourAndFiveCircleModes(self, hklPhiNorm, alpha,
delta, gamma, Bin):
"""
(omega, chi, phi, psi)=determineNonZAxisSampleAngles(hklPhiNorm, alpha,
delta, gamma, sigma, tau) where hkl has been normalised by the
wavevector and is in the phi Axis coordinate frame. All angles in
radians. hklPhiNorm is a 3X1 matrix
"""
def equation49through59(psi):
# equation 49 R = (D^-1)*PI*D*Ro
PSI = createVliegsPsiTransformationMatrix(psi)
R = D.I * PSI * D * Ro
# eq 57: extract omega from R
if abs(R[0, 2]) < 1e-20:
omega = -sign(R[1, 2]) * sign(R[0, 2]) * pi / 2
else:
omega = -atan2(R[1, 2], R[0, 2])
# eq 58: extract chi from R
sinchi = sqrt(pow(R[0, 2], 2) + pow(R[1, 2], 2))
sinchi = bound(sinchi)
check(abs(sinchi) <= 1, 'could not compute chi')
# (there are two roots to this equation, but only the first is also
# a solution to R33=cos(chi))
chi = asin(sinchi)
# eq 59: extract phi from R
if abs(R[2, 0]) < 1e-20:
phi = sign(R[2, 1]) * sign(R[2, 1]) * pi / 2
else:
phi = atan2(-R[2, 1], -R[2, 0])
return omega, chi, phi
def checkSolution(omega, chi, phi):
_, _, _, OMEGA, CHI, PHI = createVliegMatrices(
None, None, None, omega, chi, phi)
R = OMEGA * CHI * PHI
RtimesH_phi = R * H_phi
print("R*H_phi=%s, Q_alpha=%s" %
(R * H_phi.tolist(), Q_alpha.tolist()))
return not differ(RtimesH_phi, Q_alpha, .0001)
# Using Vlieg section 7.2
# Needed througout:
[ALPHA, DELTA, GAMMA, _, _,
_] = createVliegMatrices(alpha, delta, gamma, None, None, None)
## Find Ro, one possible solution to equation 46: R*H_phi=Q_alpha
# Normalise hklPhiNorm (As it is currently normalised only to the
# wavevector)
normh = norm(hklPhiNorm)
check(normh >= 1e-10, "reciprical lattice vector too close to zero")
H_phi = hklPhiNorm * (1 / normh)
# Create Q_alpha from equation 47, (it comes normalised)
Q_alpha = ((DELTA * GAMMA) - ALPHA.I) * matrix([[0], [1], [0]])
Q_alpha = Q_alpha * (1 / norm(Q_alpha))
if self._getMode().name == '4cPhi':
### Use the fixed value of phi as the final constraint ###
phi = self._getParameter('phi') * TORAD
PHI = calcPHI(phi)
H_chi = PHI * H_phi
omega, chi = _findOmegaAndChiToRotateHchiIntoQalpha(H_chi, Q_alpha)
return (omega, chi, phi, None) # psi = None as not calculated
else:
### Use Bin as the final constraint ###
# Find a solution Ro to Ro*H_phi=Q_alpha
Ro = self._findMatrixToTransformAIntoB(H_phi, Q_alpha)
## equation 50: Find a solution D to D*Q=norm(Q)*[[1],[0],[0]])
D = self._findMatrixToTransformAIntoB(Q_alpha,
matrix([[1], [0], [0]]))
## Find psi and create PSI
# eq 54: compute u=D*Ro*S*[[0],[0],[1]], the surface normal in
# psi frame
[SIGMA, TAU] = createVliegsSurfaceTransformationMatrices(
self._getSigma() * TORAD,
self._getTau() * TORAD)
S = TAU * SIGMA
[u1], [u2], [u3] = (D * Ro * S * matrix([[0], [0], [1]])).tolist()
# TODO: If u points along 100, then any psi is a solution. Choose 0
if not differ([u1, u2, u3], [1, 0, 0], 1e-9):
psi = 0
omega, chi, phi = equation49through59(psi)
else:
# equation 53: V=A*(D^-1)
V = ALPHA * D.I
v21 = V[1, 0]
v22 = V[1, 1]
v23 = V[1, 2]
# equation 55
a = v22 * u2 + v23 * u3
b = v22 * u3 - v23 * u2
c = -sin(Bin) - v21 * u1 # TODO: changed sign from paper
# equation 44
# Try first root:
def myatan2(y, x):
if abs(x) < 1e-20 and abs(y) < 1e-20:
return pi / 2
else:
return atan2(y, x)
psi = 2 * myatan2(-(b - sqrt(b * b + a * a - c * c)), -(a + c))
#psi = -acos(c/sqrt(a*a+b*b))+atan2(b,a)# -2*pi
omega, chi, phi = equation49through59(psi)
# if u points along z axis, the psi could have been either 0 or 180
if (not differ([u1, u2, u3], [0, 0, 1], 1e-9)
and abs(psi - pi) < 1e-10):
# Choose 0 to match that read up by angles-to-virtual-angles
psi = 0.
# if u points a long
return (omega, chi, phi, psi)
def _anglesToPsi(self, pos, wavelength):
"""
pos assumed in radians. -180<= psi <= 180
"""
# Using Vlieg section 7.2
# Needed througout:
[ALPHA, DELTA, GAMMA, OMEGA, CHI,
PHI] = createVliegMatrices(pos.alpha, pos.delta, pos.gamma, pos.omega,
pos.chi, pos.phi)
# Solve equation 49 for psi, the rotation of the a reference solution
# about Qalpha or H_phi##
# Find Ro, the reference solution to equation 46: R*H_phi=Q_alpha
# Create Q_alpha from equation 47, (it comes normalised)
Q_alpha = ((DELTA * GAMMA) - ALPHA.I) * matrix([[0], [1], [0]])
Q_alpha = Q_alpha * (1 / norm(Q_alpha))
# Finh H_phi
h, k, l = self._anglesToHkl(pos, wavelength)
H_phi = self._getUBMatrix() * matrix([[h], [k], [l]])
normh = norm(H_phi)
check(normh >= 1e-10, "reciprical lattice vector too close to zero")
H_phi = H_phi * (1 / normh)
# Find a solution Ro to Ro*H_phi=Q_alpha
# This the reference solution with zero azimuth (psi)
Ro = self._findMatrixToTransformAIntoB(H_phi, Q_alpha)
# equation 48:
R = OMEGA * CHI * PHI
## equation 50: Find a solution D to D*Q=norm(Q)*[[1],[0],[0]])
D = self._findMatrixToTransformAIntoB(Q_alpha, matrix([[1], [0], [0]]))
# solve equation 49 for psi
# D*R = PSI*D*Ro
# D*R*(D*Ro)^-1 = PSI
PSI = D * R * ((D * Ro).I)
# Find psi within PSI as defined in equation 51
PSI_23 = PSI[1, 2]
PSI_33 = PSI[2, 2]
psi = atan2(PSI_23, PSI_33)
#print "PSI: ", PSI.tolist()
return psi
def _findMatrixToTransformAIntoB(self, a, b):
"""
Finds a particular matrix Mo that transforms the unit vector a into the
unit vector b. Thats is it finds Mo Mo*a=b. a and b 3x1 matrixes and Mo
is a 3x3 matrix.
Throws an exception if this is not possible.
"""
# Maths from the appendix of "Angle caluculations
# for a 5-circle diffractometer used for surface X-ray diffraction",
# E. Vlieg, J.F. van der Veen, J.E. Macdonald and M. Miller, J. of
# Applied Cryst. 20 (1987) 330.
# - courtesy of Elias Vlieg again
# equation A2: compute angle xi between vectors a and b
cosxi = dot3(a, b)
try:
cosxi = bound(cosxi)
except ValueError:
raise Exception("Could not compute cos(xi), vectors a=%f and b=%f "
"must be of unit length" % (norm(a), norm(b)))
xi = acos(cosxi)
# Mo is identity matrix if xi zero (math below would blow up)
if abs(xi) < 1e-10:
return I
# equation A3: c=cross(a,b)/sin(xi)
c = cross3(a, b) * (1 / sin(xi))
# equation A4: find D matrix that transforms a into the frame
# x = a; y = c x a; z = c. */
a1 = a[0, 0]
a2 = a[1, 0]
a3 = a[2, 0]
c1 = c[0, 0]
c2 = c[1, 0]
c3 = c[2, 0]
D = matrix([[a1, a2, a3],
[c2 * a3 - c3 * a2, c3 * a1 - c1 * a3, c1 * a2 - c2 * a1],
[c1, c2, c3]])
# equation A5: create Xi to rotate by xi about z-axis
XI = matrix([[cos(xi), -sin(xi), 0], [sin(xi), cos(xi), 0], [0, 0, 1]])
# eq A6: compute Mo
return D.I * XI * D
def setup_method(self):
self.hw = createMockHardwareMonitor()
self.ms = ModeSelector(createMockDiffractometerGeometry())
self.pm = VliegParameterManager(createMockDiffractometerGeometry(),
self.hw, self.ms)
class TestParameterManager(object):
def setup_method(self):
self.hw = createMockHardwareMonitor()
self.ms = ModeSelector(createMockDiffractometerGeometry())
self.pm = VliegParameterManager(createMockDiffractometerGeometry(),
self.hw, self.ms)
def testDefaultParameterValues(self):
assert self.pm.get_constraint('alpha') == 0
assert self.pm.get_constraint('gamma') == 0
with pytest.raises(DiffcalcException):
self.pm.get_constraint('not-a-parameter-name')
def testSetParameter(self):
self.pm.set_constraint('alpha', 10.1)
assert self.pm.get_constraint('alpha') == 10.1
def testSetTrackParameter_isParameterChecked(self):
assert not self.pm.isParameterTracked('alpha')
self.pm.set_constraint('alpha', 9)
self.pm.setTrackParameter('alpha', True)
assert self.pm.isParameterTracked('alpha') == True
with pytest.raises(DiffcalcException):
self.pm.set_constraint('alpha', 10)
self.hw.get_position.return_value = 888, 11, 999
assert self.pm.get_constraint('alpha') == 11
print self.pm.reportAllParameters()
print "**"
print self.ms.reportCurrentMode()
print self.pm.reportParametersUsedInCurrentMode()
self.pm.setTrackParameter('alpha', False)
assert not self.pm.isParameterTracked('alpha')
assert self.pm.get_constraint('alpha') == 11
self.hw.get_position.return_value = 888, 12, 999
assert self.pm.get_constraint('alpha') == 11
self.pm.set_constraint('alpha', 13)
assert self.pm.get_constraint('alpha') == 13