def check_vector_to_001(g):
assert approx_equal(abs(matrix.col(g)), 1)
r = matrix.sqr(vector_to_001(given_unit_vector=g))
assert approx_equal(r * matrix.col(g), (0, 0, 1))
assert approx_equal(r.determinant(), 1)
p = matrix.col(g).vector_to_001_rotation()
assert approx_equal(p * matrix.col(g), (0, 0, 1))
assert approx_equal(p.determinant(), 1)
assert approx_equal(p, r)
def check_vector_to_001(g): assert approx_equal(abs(matrix.col(g)), 1) r = matrix.sqr(vector_to_001(given_unit_vector=g)) assert approx_equal(r * matrix.col(g), (0,0,1)) assert approx_equal(r.determinant(), 1) p = matrix.col(g).vector_to_001_rotation() assert approx_equal(p * matrix.col(g), (0,0,1)) assert approx_equal(p.determinant(), 1) assert approx_equal(p, r)
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)