def test_axis(self):
axis = (0.37394394059075464, 0.49642290523592875, 0.7834093619893614)
angle = flex.random_double() * math.pi
rotmat = scitbx.matrix.sqr(
scitbx.math.r3_rotation_axis_and_angle_as_matrix( axis, angle )
)
missets = [
scitbx.matrix.sqr(
scitbx.math.r3_rotation_axis_and_angle_as_matrix(
flex.random_double_point_on_sphere(),
( flex.random_double() - 0.5 )* self.MAX_ERROR,
)
)
for i in range( self.SAMPLE_SIZE )
]
matrices = [ misset * rotmat for misset in missets ]
aver_lie = scitbx.math.r3_rotation_average_rotation_via_lie_algebra(
matrices = matrices,
)
aver_quat = scitbx.matrix.sqr(
scitbx.math.r3_rotation_average_rotation_matrix_from_matrices(
*matrices
)
)
diff = aver_quat.transpose() * aver_lie
self.assertAlmostEqual( ( diff - TestElement.IDENTITY ).norm_sq(), 0, 7 )
def random_gonio():
# make a random rotation axis with a random setting matrix
axis = matrix.col(flex.random_double_point_on_sphere())
fixed_rotation = matrix.sqr((1, 0, 0, 0, 1, 0, 0, 0, 1))
setting_rotation = matrix.sqr(flex.random_double_r3_rotation_matrix())
goniometer = Goniometer(axis, fixed_rotation, setting_rotation)
return goniometer
def test_project_2d():
# The function project_2d should give the same results even if the
# detector is rotated in the laboratory frame
# Use a multipanel detector
detector = create_multipanel_detector(offset=0)
# Get 2D origin, fast and slow vectors for the detector
o, f, s = project_2d(detector)
# Now rotate the detector by 30 degrees around an arbitrary axis
h = detector.hierarchy()
fast = matrix.col(h.get_fast_axis())
slow = matrix.col(h.get_slow_axis())
origin = matrix.col(h.get_origin())
axis = matrix.col(flex.random_double_point_on_sphere())
rot = axis.axis_and_angle_as_r3_rotation_matrix(30, deg=True)
for panel in detector:
fast = matrix.col(panel.get_fast_axis())
slow = matrix.col(panel.get_slow_axis())
origin = matrix.col(panel.get_origin())
panel.set_frame(rot * fast, rot * slow, rot * origin)
# Get 2D origin, fast and slow vectors for the rotated detector
new_o, new_f, new_s = project_2d(detector)
for o1, o2 in zip(o, new_o):
assert o1 == pytest.approx(o2)
for f1, f2 in zip(f, new_f):
assert f1 == pytest.approx(f2)
for s1, s2 in zip(s, new_s):
assert s1 == pytest.approx(s2)
def test_random_matrices(self):
for i in range( self.SAMPLE_SIZE ):
axis = flex.random_double_point_on_sphere()
angle = flex.random_double() * ( math.pi - self.SINGULARITY_GUARD )
rotmat = scitbx.matrix.sqr(
scitbx.math.r3_rotation_axis_and_angle_as_matrix( axis, angle )
)
self.run_tests_with( matrix = rotmat )
def test_angle(self):
axis = scitbx.matrix.col( flex.random_double_point_on_sphere() )
centre = flex.random_double() * math.pi
errors = [ ( flex.random_double() - 0.5 )* self.MAX_ERROR
for i in range( self.SAMPLE_SIZE ) ]
average = scitbx.math.r3_rotation_average_rotation_via_lie_algebra(
matrices = [
scitbx.matrix.sqr(
scitbx.math.r3_rotation_axis_and_angle_as_matrix( axis, centre + e )
)
for e in errors
]
)
angle = centre + sum( errors ) / len( errors )
aaf = scitbx.math.r3_rotation_axis_and_angle_from_matrix( average )
alignment = axis.dot( scitbx.matrix.col( aaf.axis ) )
self.assertAlmostEqual( abs( alignment ), 1.0, 7 )
self.assertAlmostEqual( aaf.angle() / alignment, angle, 7 )
def exercise1(n_trials):
v = 1000
for i in range(n_trials):
for scale in [0.0000001, 0.0001, 1.]:
ri1 = random.randint(-v, v) * scale
ri2 = random.randint(-v, v) * scale
ri3 = random.randint(-v, v) * scale
ri = flex.double([ri1, ri2, ri3])
x = flex.double(flex.random_double_point_on_sphere()) * ri
a, b, c, d = abcd(x=x)
#
sol(x=x, a=a, b=b, c=c, d=d, check_roots=True)
#
sol(x=(x[0], x[0], x[0]), a=a, b=b, c=c, d=d, check_roots=False)
sol(x=(x[1], x[1], x[1]), a=a, b=b, c=c, d=d, check_roots=False)
sol(x=(x[2], x[2], x[2]), a=a, b=b, c=c, d=d, check_roots=False)
#
sol(x=(x[0], x[0], x[2]), a=a, b=b, c=c, d=d, check_roots=False)
sol(x=(x[0], x[2], x[2]), a=a, b=b, c=c, d=d, check_roots=False)
sol(x=(x[1], x[0], x[1]), a=a, b=b, c=c, d=d, check_roots=False)
sol(x=(x[1], x[1], x[2]), a=a, b=b, c=c, d=d, check_roots=False)
sol(x=(x[2], x[0], x[2]), a=a, b=b, c=c, d=d, check_roots=False)
def exercise1(n_trials):
v = 1000
for i in xrange(n_trials):
for scale in [0.0000001, 0.0001, 1.0]:
ri1 = random.randint(-v, v) * scale
ri2 = random.randint(-v, v) * scale
ri3 = random.randint(-v, v) * scale
ri = flex.double([ri1, ri2, ri3])
x = flex.double(flex.random_double_point_on_sphere()) * ri
a, b, c, d = abcd(x=x)
#
sol(x=x, a=a, b=b, c=c, d=d, check_roots=True)
#
sol(x=(x[0], x[0], x[0]), a=a, b=b, c=c, d=d, check_roots=False)
sol(x=(x[1], x[1], x[1]), a=a, b=b, c=c, d=d, check_roots=False)
sol(x=(x[2], x[2], x[2]), a=a, b=b, c=c, d=d, check_roots=False)
#
sol(x=(x[0], x[0], x[2]), a=a, b=b, c=c, d=d, check_roots=False)
sol(x=(x[0], x[2], x[2]), a=a, b=b, c=c, d=d, check_roots=False)
sol(x=(x[1], x[0], x[1]), a=a, b=b, c=c, d=d, check_roots=False)
sol(x=(x[1], x[1], x[2]), a=a, b=b, c=c, d=d, check_roots=False)
sol(x=(x[2], x[0], x[2]), a=a, b=b, c=c, d=d, check_roots=False)
def exercise_vector_to_vector(angle_exponent_step=10, n_trials=10):
principal_vectors = [
matrix.col(v) for v in ((1, 0, 0), (0, 1, 0), (0, 0, 1))
]
for g0 in principal_vectors:
for t0 in principal_vectors:
for g in [g0, -g0]:
for t in [t0, -t0]:
check_vector_to_vector(g=g, t=t)
if (sys.platform.startswith("osf")):
max_exp = 300
else:
max_exp = 340
for ig, g0 in enumerate(principal_vectors):
for it, t0 in enumerate(principal_vectors):
if (ig == it): continue
axis = g0.cross(t0)
for e in range(0, max_exp, angle_exponent_step):
angle = 10**(-e)
for angle in [angle, -angle]:
r = matrix.sqr(
scitbx.math.r3_rotation_axis_and_angle_as_matrix(
axis=axis, angle=angle))
for g in [g0, -g0]:
for t in [t0, -t0]:
check_vector_to_vector(g, r * t)
check_vector_to_vector(r * g, t)
check_vector_to_vector(r * g, r * t)
for i_trial in range(n_trials):
g = matrix.col(flex.random_double_point_on_sphere())
check_vector_to_vector(g, g)
check_vector_to_vector(g, -g)
t = matrix.col(flex.random_double_point_on_sphere())
check_vector_to_vector(g, t)
for e in range(0, max_exp, angle_exponent_step):
angle = 10**(-e)
for angle in [angle, -angle]:
rt = matrix.sqr(
scitbx.math.r3_rotation_axis_and_angle_as_matrix(
axis=g, angle=angle)) * t
check_vector_to_vector(rt, t)
check_vector_to_vector(rt, -t)
#
check_vector_to_001((0, 0, 1))
check_vector_to_001((0, 0, -1))
for e in range(0, max_exp, angle_exponent_step):
angle = 10**(-e)
for angle in [angle, -angle]:
rg = matrix.sqr(
scitbx.math.r3_rotation_axis_and_angle_as_matrix(
axis=(1, 1, 0), angle=angle)) * matrix.col((0, 0, 1))
check_vector_to_001(rg)
check_vector_to_001(-rg)
for i_trial in range(n_trials):
g = matrix.col(flex.random_double_point_on_sphere())
check_vector_to_001(g)
#
check_vector_to_010((0, 1, 0))
check_vector_to_010((0, -1, 0))
for e in range(0, max_exp, angle_exponent_step):
angle = 10**(-e)
for angle in [angle, -angle]:
rg = matrix.sqr(
scitbx.math.r3_rotation_axis_and_angle_as_matrix(
axis=(1, 0, 1), angle=angle)) * matrix.col((0, 1, 0))
check_vector_to_010(rg)
check_vector_to_010(-rg)
for i_trial in range(n_trials):
g = matrix.col(flex.random_double_point_on_sphere())
check_vector_to_010(g)
#
check_vector_to_100((1, 0, 0))
check_vector_to_100((-1, 0, 0))
for e in range(0, max_exp, angle_exponent_step):
angle = 10**(-e)
for angle in [angle, -angle]:
rg = matrix.sqr(
scitbx.math.r3_rotation_axis_and_angle_as_matrix(
axis=(0, 1, 1), angle=angle)) * matrix.col((1, 0, 0))
check_vector_to_100(rg)
check_vector_to_100(-rg)
for i_trial in range(n_trials):
g = matrix.col(flex.random_double_point_on_sphere())
check_vector_to_100(g)
#
rvv = vector_to_vector((0, 0, -1), (0, 0, 1))
rv1 = vector_to_001((0, 0, -1))
assert approx_equal(rv1, rvv)
rvv = vector_to_vector((0, -1, 0), (0, 1, 0))
rv1 = vector_to_010((0, -1, 0))
assert approx_equal(rv1, rvv)
rvv = vector_to_vector((-1, 0, 0), (1, 0, 0))
rv1 = vector_to_100((-1, 0, 0))
assert approx_equal(rv1, rvv)
def exercise_vector_to_vector(angle_exponent_step=10, n_trials=10):
principal_vectors = [matrix.col(v) for v in (1,0,0), (0,1,0), (0,0,1)]
for g0 in principal_vectors:
for t0 in principal_vectors:
for g in [g0, -g0]:
for t in [t0, -t0]:
check_vector_to_vector(g=g, t=t)
if (sys.platform.startswith("osf")):
max_exp = 300
else:
max_exp = 340
for ig,g0 in enumerate(principal_vectors):
for it,t0 in enumerate(principal_vectors):
if (ig == it): continue
axis = g0.cross(t0)
for e in xrange(0, max_exp, angle_exponent_step):
angle = 10**(-e)
for angle in [angle, -angle]:
r = matrix.sqr(scitbx.math.r3_rotation_axis_and_angle_as_matrix(
axis=axis,
angle=angle))
for g in [g0, -g0]:
for t in [t0, -t0]:
check_vector_to_vector(g, r*t)
check_vector_to_vector(r*g, t)
check_vector_to_vector(r*g, r*t)
for i_trial in xrange(n_trials):
g = matrix.col(flex.random_double_point_on_sphere())
check_vector_to_vector(g, g)
check_vector_to_vector(g, -g)
t = matrix.col(flex.random_double_point_on_sphere())
check_vector_to_vector(g, t)
for e in xrange(0, max_exp, angle_exponent_step):
angle = 10**(-e)
for angle in [angle, -angle]:
rt = matrix.sqr(scitbx.math.r3_rotation_axis_and_angle_as_matrix(
axis=g,
angle=angle)) * t
check_vector_to_vector(rt, t)
check_vector_to_vector(rt, -t)
#
check_vector_to_001((0,0,1))
check_vector_to_001((0,0,-1))
for e in xrange(0, max_exp, angle_exponent_step):
angle = 10**(-e)
for angle in [angle, -angle]:
rg = matrix.sqr(scitbx.math.r3_rotation_axis_and_angle_as_matrix(
axis=(1,1,0),
angle=angle)) * matrix.col((0,0,1))
check_vector_to_001(rg)
check_vector_to_001(-rg)
for i_trial in xrange(n_trials):
g = matrix.col(flex.random_double_point_on_sphere())
check_vector_to_001(g)
#
check_vector_to_010((0,1,0))
check_vector_to_010((0,-1,0))
for e in xrange(0, max_exp, angle_exponent_step):
angle = 10**(-e)
for angle in [angle, -angle]:
rg = matrix.sqr(scitbx.math.r3_rotation_axis_and_angle_as_matrix(
axis=(1,0,1),
angle=angle)) * matrix.col((0,1,0))
check_vector_to_010(rg)
check_vector_to_010(-rg)
for i_trial in xrange(n_trials):
g = matrix.col(flex.random_double_point_on_sphere())
check_vector_to_010(g)
#
check_vector_to_100((1,0,0))
check_vector_to_100((-1,0,0))
for e in xrange(0, max_exp, angle_exponent_step):
angle = 10**(-e)
for angle in [angle, -angle]:
rg = matrix.sqr(scitbx.math.r3_rotation_axis_and_angle_as_matrix(
axis=(0,1,1),
angle=angle)) * matrix.col((1,0,0))
check_vector_to_100(rg)
check_vector_to_100(-rg)
for i_trial in xrange(n_trials):
g = matrix.col(flex.random_double_point_on_sphere())
check_vector_to_100(g)
#
rvv = vector_to_vector((0,0,-1), (0,0,1))
rv1 = vector_to_001((0,0,-1))
assert approx_equal(rv1, rvv)
rvv = vector_to_vector((0,-1,0), (0,1,0))
rv1 = vector_to_010((0,-1,0))
assert approx_equal(rv1, rvv)
rvv = vector_to_vector((-1,0,0), (1,0,0))
rv1 = vector_to_100((-1,0,0))
assert approx_equal(rv1, rvv)
