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 _verify_virtual_angles(self, h, k, l, wavelength, pos, virtualAngles):
# Check that the virtual angles calculated/fixed during the hklToAngles
# those read back from pos using anglesToVirtualAngles
virtualAnglesReadback = self.anglesToVirtualAngles(pos, wavelength)
for key, val in virtualAngles.items():
if val != None: # Some values calculated in some mode_selector
r = virtualAnglesReadback[key]
if ((differ(val, r, .00001) and differ(val, r + 360, .00001) and differ(val, r - 360, .00001))):
s = "ERROR: The angles calculated for hkl=(%f,%f,%f) with"\
" mode=%s were %s.\n" % (h, k, l, self.repr_mode(), str(pos))
s += "During verification the virtual angle %s resulting "\
"from (or set for) this calculation of %f" % (key, val)
s += "did not match that calculated by "\
"anglesToVirtualAngles of %f" % virtualAnglesReadback[key]
if self.raiseExceptionsIfAnglesDoNotMapBackToHkl:
raise DiffcalcException(s)
else:
print s
return virtualAnglesReadback
def _verify_virtual_angles(self, h, k, l, wavelength, pos, virtualAngles):
# Check that the virtual angles calculated/fixed during the hklToAngles
# those read back from pos using anglesToVirtualAngles
virtualAnglesReadback = self.anglesToVirtualAngles(pos, wavelength)
for key, val in virtualAngles.items():
if val != None: # Some values calculated in some mode_selector
r = virtualAnglesReadback[key]
if ((differ(val, r, .00001) and differ(val, r + 360, .00001) and differ(val, r - 360, .00001))):
s = "ERROR: The angles calculated for hkl=(%f,%f,%f) with"\
" mode=%s were %s.\n" % (h, k, l, self.repr_mode(), str(pos))
s += "During verification the virtual angle %s resulting "\
"from (or set for) this calculation of %f" % (key, val)
s += "did not match that calculated by "\
"anglesToVirtualAngles of %f" % virtualAnglesReadback[key]
if self.raiseExceptionsIfAnglesDoNotMapBackToHkl:
raise DiffcalcException(s)
else:
print(s)
return virtualAnglesReadback
def testDiffer(self):
assert not differ([1., 2., 3.], [1., 2., 3.], .0000000000000001)
assert not differ(1, 1.0, .000000000000000001)
assert (differ([2., 4., 6.], [1., 2., 3.], .1)
== '(2.0, 4.0, 6.0)!=(1.0, 2.0, 3.0)')
assert not differ(1., 1.2, .2)
assert differ(1., 1.2, .1999999999999) == '1.0!=1.2'
assert not differ(1., 1.2, 1.20000000000001)
def testDiffer(self):
assert not differ([1., 2., 3.], [1., 2., 3.], .0000000000000001)
assert not differ(1, 1.0, .000000000000000001)
assert (differ([2., 4., 6.], [1., 2., 3.],
.1) == '(2.0, 4.0, 6.0)!=(1.0, 2.0, 3.0)')
assert not differ(1., 1.2, .2)
assert differ(1., 1.2, .1999999999999) == '1.0!=1.2'
assert not differ(1., 1.2, 1.20000000000001)
def testDiffer(self):
self.assertFalse(differ([1., 2., 3.], [1., 2., 3.], .0000000000000001))
self.assertFalse(differ(1, 1.0, .000000000000000001))
self.assertEquals(differ([2., 4., 6.], [1., 2., 3.], .1),
'(2.0, 4.0, 6.0)!=(1.0, 2.0, 3.0)')
self.assertEquals(differ(1., 1.2, .2), False)
self.assertEquals(differ(1., 1.2, .1999999999999), '1.0!=1.2')
self.assertEquals(differ(1., 1.2, 1.20000000000001), False)
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)
