def test_beam_parameters():
from scitbx import matrix
from dxtbx.model import BeamFactory
from dials.algorithms.refinement.parameterisation.beam_parameters import (
BeamParameterisation,
)
from dials.algorithms.refinement.refinement_helpers import (
get_fd_gradients,
random_param_shift,
)
# make a random beam vector and parameterise it
bf = BeamFactory()
s0 = bf.make_beam(matrix.col.random(3, 0.5, 1.5), wavelength=1.2)
s0p = BeamParameterisation(s0)
# Let's do some basic tests. First, can we change parameter values and
# update the modelled vector s0?
s0_old = matrix.col(s0.get_s0())
s0p.set_param_vals([1000 * 0.1, 1000 * 0.1, 0.8])
assert matrix.col(s0.get_s0()).angle(s0_old) == pytest.approx(0.1413033, abs=1e-6)
assert matrix.col(s0.get_s0()).length() == pytest.approx(0.8, abs=1e-6)
# random initial orientations and wavelengths with a random parameter shifts
attempts = 1000
failures = 0
for i in range(attempts):
# make a random beam vector and parameterise it
s0 = bf.make_beam(
matrix.col.random(3, 0.5, 1.5), wavelength=random.uniform(0.8, 1.5)
)
s0p = BeamParameterisation(s0)
# apply a random parameter shift
p_vals = s0p.get_param_vals()
p_vals = random_param_shift(p_vals, [1000 * pi / 9, 1000 * pi / 9, 0.01])
s0p.set_param_vals(p_vals)
# compare analytical and finite difference derivatives
an_ds_dp = s0p.get_ds_dp()
fd_ds_dp = get_fd_gradients(s0p, [1.0e-5 * pi / 180, 1.0e-5 * pi / 180, 1.0e-6])
for j in range(3):
try:
assert list(fd_ds_dp[j] - an_ds_dp[j]) == pytest.approx(
(0, 0, 0), abs=1e-6
)
except Exception:
print("for try", i)
print("failure for parameter number", j)
print("with fd_ds_dp = ")
print(fd_ds_dp[j])
print("and an_ds_dp = ")
print(an_ds_dp[j])
print("so that difference fd_ds_dp - an_ds_dp =")
print(fd_ds_dp[j] - an_ds_dp[j])
raise
attempts = 1000
failures = 0
for i in range(attempts):
# make a random beam vector and parameterise it
s0 = bf.make_beam(matrix.col.random(3, 0.5, 1.5),
wavelength=random.uniform(0.8,1.5))
s0p = BeamParameterisation(s0)
# apply a random parameter shift
p_vals = s0p.get_param_vals()
p_vals = random_param_shift(p_vals, [1000*pi/9, 1000*pi/9, 0.01])
s0p.set_param_vals(p_vals)
# compare analytical and finite difference derivatives
an_ds_dp = s0p.get_ds_dp()
fd_ds_dp = get_fd_gradients(s0p, [1.e-5 * pi/180, 1.e-5 * pi/180, 1.e-6])
for j in range(3):
try:
assert(approx_equal((fd_ds_dp[j] - an_ds_dp[j]),
matrix.col((0., 0., 0.)), eps = 1.e-6))
except Exception:
failures += 1
print "for try", i
print "failure for parameter number", j
print "with fd_ds_dp = "
print fd_ds_dp[j]
print "and an_ds_dp = "
print an_ds_dp[j]
print "so that difference fd_ds_dp - an_ds_dp ="
def test_beam_parameters():
from dxtbx.model import BeamFactory
from dials.algorithms.refinement.parameterisation.beam_parameters import (
BeamParameterisation,
)
from dials.algorithms.refinement.refinement_helpers import (
get_fd_gradients,
random_param_shift,
)
# make a random beam vector and parameterise it
bf = BeamFactory()
s0 = bf.make_beam(matrix.col.random(3, 0.5, 1.5), wavelength=1.2)
s0p = BeamParameterisation(s0)
# Let's do some basic tests. First, can we change parameter values and
# update the modelled vector s0?
s0_old = matrix.col(s0.get_s0())
s0p.set_param_vals([1000 * 0.1, 1000 * 0.1, 0.8])
assert matrix.col(s0.get_s0()).angle(s0_old) == pytest.approx(0.1413033, abs=1e-6)
assert matrix.col(s0.get_s0()).length() == pytest.approx(0.8, abs=1e-6)
# random initial orientations and wavelengths with a random parameter shifts
attempts = 1000
for i in range(attempts):
# make a random beam vector and parameterise it
sample_to_source = matrix.col.random(3, 0.5, 1.5).normalize()
beam = bf.make_beam(sample_to_source, wavelength=random.uniform(0.8, 1.5))
# Ensure consistent polarization (https://github.com/cctbx/dxtbx/issues/454)
beam.set_polarization_normal(sample_to_source.ortho().normalize())
s0p = BeamParameterisation(beam)
# apply a random parameter shift
p_vals = s0p.get_param_vals()
p_vals = random_param_shift(p_vals, [1000 * pi / 9, 1000 * pi / 9, 0.01])
s0p.set_param_vals(p_vals)
# compare analytical and finite difference derivatives
an_ds_dp = s0p.get_ds_dp()
fd_ds_dp = get_fd_gradients(s0p, [1.0e-5 * pi / 180, 1.0e-5 * pi / 180, 1.0e-6])
for j in range(3):
try:
assert list(fd_ds_dp[j] - an_ds_dp[j]) == pytest.approx(
(0, 0, 0), abs=1e-6
)
except Exception:
print("for try", i)
print("failure for parameter number", j)
print("with fd_ds_dp = ")
print(fd_ds_dp[j])
print("and an_ds_dp = ")
print(an_ds_dp[j])
print("so that difference fd_ds_dp - an_ds_dp =")
print(fd_ds_dp[j] - an_ds_dp[j])
raise
# Ensure the polarization normal vector remains orthogonal to the beam
# (https://github.com/dials/dials/issues/1939)
assert (
abs(
matrix.col(beam.get_unit_s0()).dot(
matrix.col(beam.get_polarization_normal())
)
)
< 1e-10
)
def tst_use_in_stills_parameterisation_for_beam(beam_param=0):
# test use of analytical expression in stills prediction parameterisation
from scitbx import matrix
from math import pi
import random
print
print "Test use of analytical expressions in stills prediction " + "parameterisation for beam parameters"
# beam model
from dxtbx.model.experiment import beam_factory
from dials.algorithms.refinement.parameterisation.beam_parameters import BeamParameterisation
beam = beam_factory().make_beam(matrix.col((0, 0, 1)), wavelength=1.1)
s0 = matrix.col(beam.get_s0())
s0u = matrix.col(beam.get_unit_s0())
# beam parameterisation
bp = BeamParameterisation(beam)
# choose the derivative with respect to a particular parameter. 0: mu1,
# 1: mu2, 2: nu.
ds0_dp = bp.get_ds_dp()[beam_param]
# pick a random point on (the positive octant of) the Ewald sphere to rotate
s1 = matrix.col((random.random(), random.random(), random.random())).normalize() * s0.length()
r = s1 - s0
r0 = r.normalize()
# calculate the axis of rotation
e1 = r0.cross(s0u).normalize()
# calculate c0, a vector orthogonal to s0u and e1
c0 = s0u.cross(e1).normalize()
# convert to derivative of the unit beam direction. This involves scaling
# by the wavelength, then projection back onto the Ewald sphere.
scaled = ds0_dp * beam.get_wavelength()
ds0u_dp = scaled.dot(c0) * c0 + scaled.dot(e1) * e1
# rotate relp off Ewald sphere a small angle (up to 1 deg)
DeltaPsi = random.uniform(-pi / 180, pi / 180)
q = r.rotate_around_origin(e1, -DeltaPsi)
q0 = q.normalize()
from libtbx.test_utils import approx_equal
assert approx_equal(q0.cross(s0u).normalize(), e1)
# use the fact that e1 == c0.cross(s0u) to redefine the derivative d[e1]/dp
# from Sauter et al. (2014) (A.3)
de1_dp = c0.cross(ds0u_dp)
# unlike the previous definition this *is* orthogonal to e1, as expected.
print "[e1].(d[e1]/dp) = {0} (should be 0.0)".format(e1.dot(de1_dp))
# calculate (d[r]/d[e1])(d[e1]/dp) analytically
from scitbx.array_family import flex
from dials_refinement_helpers_ext import dRq_de
dr_de1 = matrix.sqr(dRq_de(flex.double([DeltaPsi]), flex.vec3_double([e1]), flex.vec3_double([q]))[0])
print "Analytical calculation for (d[r]/d[e1])(d[e1]/dp):"
print dr_de1 * de1_dp
# now calculate using finite differences.
dp = 1.0e-8
del_e1 = de1_dp * dp
e1f = e1 + del_e1 * 0.5
rfwd = q.rotate_around_origin(e1f, DeltaPsi)
e1r = e1 - del_e1 * 0.5
rrev = q.rotate_around_origin(e1r, DeltaPsi)
print "Finite difference estimate for (d[r]/d[e1])(d[e1]/dp):"
print (rfwd - rrev) * (1 / dp)
print "These are now the same :-)"
def tst_use_in_stills_parameterisation_for_beam(beam_param=0):
# test use of analytical expression in stills prediction parameterisation
from scitbx import matrix
from math import pi
import random
print()
print("Test use of analytical expressions in stills prediction " +
"parameterisation for beam parameters")
# beam model
from dxtbx.model.experiment import beam_factory
from dials.algorithms.refinement.parameterisation.beam_parameters import (
BeamParameterisation, )
beam = beam_factory().make_beam(matrix.col((0, 0, 1)), wavelength=1.1)
s0 = matrix.col(beam.get_s0())
s0u = matrix.col(beam.get_unit_s0())
# beam parameterisation
bp = BeamParameterisation(beam)
# choose the derivative with respect to a particular parameter. 0: mu1,
# 1: mu2, 2: nu.
ds0_dp = bp.get_ds_dp()[beam_param]
# pick a random point on (the positive octant of) the Ewald sphere to rotate
s1 = (matrix.col(
(random.random(), random.random(), random.random())).normalize() *
s0.length())
r = s1 - s0
r0 = r.normalize()
# calculate the axis of rotation
e1 = r0.cross(s0u).normalize()
# calculate c0, a vector orthogonal to s0u and e1
c0 = s0u.cross(e1).normalize()
# convert to derivative of the unit beam direction. This involves scaling
# by the wavelength, then projection back onto the Ewald sphere.
scaled = ds0_dp * beam.get_wavelength()
ds0u_dp = scaled.dot(c0) * c0 + scaled.dot(e1) * e1
# rotate relp off Ewald sphere a small angle (up to 1 deg)
DeltaPsi = random.uniform(-pi / 180, pi / 180)
q = r.rotate_around_origin(e1, -DeltaPsi)
q0 = q.normalize()
from libtbx.test_utils import approx_equal
assert approx_equal(q0.cross(s0u).normalize(), e1)
# use the fact that e1 == c0.cross(s0u) to redefine the derivative d[e1]/dp
# from Sauter et al. (2014) (A.3)
de1_dp = c0.cross(ds0u_dp)
# unlike the previous definition this *is* orthogonal to e1, as expected.
print("[e1].(d[e1]/dp) = {0} (should be 0.0)".format(e1.dot(de1_dp)))
# calculate (d[r]/d[e1])(d[e1]/dp) analytically
from scitbx.array_family import flex
from dials_refinement_helpers_ext import dRq_de
dr_de1 = matrix.sqr(
dRq_de(flex.double([DeltaPsi]), flex.vec3_double([e1]),
flex.vec3_double([q]))[0])
print("Analytical calculation for (d[r]/d[e1])(d[e1]/dp):")
print(dr_de1 * de1_dp)
# now calculate using finite differences.
dp = 1.0e-8
del_e1 = de1_dp * dp
e1f = e1 + del_e1 * 0.5
rfwd = q.rotate_around_origin(e1f, DeltaPsi)
e1r = e1 - del_e1 * 0.5
rrev = q.rotate_around_origin(e1r, DeltaPsi)
print("Finite difference estimate for (d[r]/d[e1])(d[e1]/dp):")
print((rfwd - rrev) * (1 / dp))
print("These are now the same :-)")
