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 _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 _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 _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 _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 _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 _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 _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)