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 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)
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)
def calculate_q_phi(self, pos):
[ALPHA, DELTA, GAMMA, OMEGA, CHI, PHI] = createVliegMatrices(
pos.alpha, pos.delta, pos.gamma, pos.omega, pos.chi, pos.phi)
u1a = (DELTA * GAMMA - ALPHA.I) * y
u1p = PHI.I * CHI.I * OMEGA.I * u1a
return u1p
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 _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 calculate_q_phi(self, pos):
[ALPHA, DELTA, GAMMA, OMEGA, CHI,
PHI] = createVliegMatrices(pos.alpha, pos.delta, pos.gamma, pos.omega,
pos.chi, pos.phi)
u1a = (DELTA * GAMMA - ALPHA.I) * y
u1p = PHI.I * CHI.I * OMEGA.I * u1a
return u1p
def try__findOmegaAndChiToRotateHchiIntoQalpha(self, omega, chi):
h_chi = matrix([[1], [1], [1]])
h_chi = h_chi * (1 / norm(h_chi))
[_, _, _, OMEGA, CHI, _] = createVliegMatrices(
None, None, None, omega * TORAD, chi * TORAD, None)
q_alpha = OMEGA * CHI * h_chi
try:
omega_calc, chi_calc = _findOmegaAndChiToRotateHchiIntoQalpha(
h_chi, q_alpha)
except ValueError, e:
raise ValueError(str(e) + "\n, resulting from test where omega:%f"
" chi%f" % (self.omega, self.chi))
def try__findOmegaAndChiToRotateHchiIntoQalpha(self, omega, chi):
h_chi = matrix([[1], [1], [1]])
h_chi = h_chi * (1 / norm(h_chi))
[_, _, _, OMEGA, CHI,
_] = createVliegMatrices(None, None, None, omega * TORAD, chi * TORAD,
None)
q_alpha = OMEGA * CHI * h_chi
try:
omega_calc, chi_calc = _findOmegaAndChiToRotateHchiIntoQalpha(
h_chi, q_alpha)
except ValueError, e:
raise ValueError(
str(e) + "\n, resulting from test where omega:%f"
" chi%f" % (self.omega, self.chi))
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 _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 vliegAnglesToHkl(pos, wavelength, UBMatrix):
"""
Returns hkl indices from pos object in radians.
"""
wavevector = 2 * pi / wavelength
# Create transformation matrices
[ALPHA, DELTA, GAMMA, OMEGA, CHI, PHI] = createVliegMatrices(
pos.alpha, pos.delta, pos.gamma, pos.omega, pos.chi, pos.phi)
# Create the plane normal vector in the alpha axis coordinate frame
qa = ((DELTA * GAMMA) - ALPHA.I) * matrix([[0], [wavevector], [0]])
# Transform the plane normal vector from the alpha frame to reciprical
# lattice frame.
hkl = UBMatrix.I * PHI.I * CHI.I * OMEGA.I * qa
return hkl[0, 0], hkl[1, 0], hkl[2, 0]
def vliegAnglesToHkl(pos, wavelength, UBMatrix):
"""
Returns hkl indices from pos object in radians.
"""
wavevector = 2 * pi / wavelength
# Create transformation matrices
[ALPHA, DELTA, GAMMA, OMEGA, CHI,
PHI] = createVliegMatrices(pos.alpha, pos.delta, pos.gamma, pos.omega,
pos.chi, pos.phi)
# Create the plane normal vector in the alpha axis coordinate frame
qa = ((DELTA * GAMMA) - ALPHA.I) * matrix([[0], [wavevector], [0]])
# Transform the plane normal vector from the alpha frame to reciprical
# lattice frame.
hkl = UBMatrix.I * PHI.I * CHI.I * OMEGA.I * qa
return hkl[0, 0], hkl[1, 0], hkl[2, 0]
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 armAnglesToLabVector(alpha, delta, gamma):
[ALPHA, DELTA, GAMMA, _, _, _] = createVliegMatrices(
alpha, delta, gamma, None, None, None)
return ALPHA * DELTA * GAMMA * y_vector
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 baseAnglesToLabVector(delta, gamma):
[_, DELTA, GAMMA, _, _, _] = createVliegMatrices(
None, delta, gamma, None, None, None)
return GAMMA * DELTA * y_vector
def armAnglesToLabVector(alpha, delta, gamma):
[ALPHA, DELTA, GAMMA, _, _,
_] = createVliegMatrices(alpha, delta, gamma, None, None, None)
return ALPHA * DELTA * GAMMA * y_vector
def baseAnglesToLabVector(delta, gamma):
[_, DELTA, GAMMA, _, _, _] = createVliegMatrices(None, delta, gamma, None,
None, None)
return GAMMA * DELTA * y_vector
class TestVliegCoreMathBits(object):
def setup_method(self):
self.many = [
-91, -90, -89, -46, -45, -44, -1, 0, 1, 44, 45, 46, 89, 90, 91
]
self.many = (self.many + map(lambda x: x + 180, self.many) +
map(lambda x: x - 180, self.many))
def test_check(self):
check(True, 'Should not throw')
with pytest.raises(Exception):
check(False, 'string')
with pytest.raises(DiffcalcException):
check(False, DiffcalcException('dce'))
def acallable(toPrint=None):
if toPrint is None:
print "Not throwing exception"
else:
print toPrint
check(False, acallable)
check(False, acallable, 'this should be printed')
# TODO: Removed 2017-03-06, deprecated started code failing -- RobW.
def SKIP__findOmegaAndChiToRotateHchiIntoQalpha_WithIntegerValues(self):
for omega in self.many:
for chi in self.many:
print str(omega), ",", str(chi)
self.try__findOmegaAndChiToRotateHchiIntoQalpha(omega, chi)
def SKIP_findOmegaAndChiToRotateHchiIntoQalpha_WithRandomValues(self):
for _ in range(10):
for omega in self.many:
for chi in self.many:
omega = omega + random.uniform(-.001, .001)
chi = chi + random.uniform(-.001, .001)
self.try__findOmegaAndChiToRotateHchiIntoQalpha(omega, chi)
#print str(omega), ",", str(chi)
def test__findOmegaAndChiToRotateHchiIntoQalpha_WithTrickyOnes(self):
tricky_ones = [(-45., -180.), (45., -180.), (135., -180.), (2000, 0.),
(225., 0.), (225., -180.), (-225., 0.), (-225., 0.),
(-225., -180.), (-135., -180.), (89.998894, -44.999218)]
for omega, chi in tricky_ones:
self.try__findOmegaAndChiToRotateHchiIntoQalpha(omega, chi)
def try__findOmegaAndChiToRotateHchiIntoQalpha(self, omega, chi):
h_chi = matrix([[1], [1], [1]])
h_chi = h_chi * (1 / norm(h_chi))
[_, _, _, OMEGA, CHI,
_] = createVliegMatrices(None, None, None, omega * TORAD, chi * TORAD,
None)
q_alpha = OMEGA * CHI * h_chi
try:
omega_calc, chi_calc = _findOmegaAndChiToRotateHchiIntoQalpha(
h_chi, q_alpha)
except ValueError, e:
raise ValueError(
str(e) + "\n, resulting from test where omega:%f"
" chi%f" % (self.omega, self.chi))
[_, _, _, OMEGA, CHI,
_] = createVliegMatrices(None, None, None, omega_calc, chi_calc, None)
self.assertArraysNearlyEqual(OMEGA * CHI * h_chi, q_alpha, .000001,
"omega: %f chi:%f" % (omega, chi))
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)
