def test_rotation_matrix():
sample_count = 10
vec_len_range = 10000
theta_range = pi # if > pi, may cause test fail, but don't worry.
tol = 1e-4
for i in xrange(sample_count):
axis_dir = random_vec(vec_len_range)
vec_to_rotate = random_vec(vec_len_range)
theta = random_float(theta_range)
mat = rotation_array(theta, axis_dir)
rotated_vec = mat.dot(vec_to_rotate)
rotated_vec2 = mat.dot(rotated_vec)
act_theta = intersec_angle(projection_to_plan(vec_to_rotate,
axis_dir),
projection_to_plan(rotated_vec,
axis_dir))
act_theta *= cmp(np.dot(np.cross(vec_to_rotate, rotated_vec),
axis_dir), 0)
feqok_(act_theta, theta, tol)
if theta < pi * tol:
continue
feqok_(vec_len(vec_to_rotate), vec_len(rotated_vec), tol)
(r, center) = circum(vec_to_rotate, rotated_vec, rotated_vec2)
feqok_(vec_len(np.cross(center, axis_dir)), 0, tol
* max(vec_len(axis_dir), vec_len(center)))
ok_(cmp(np.dot(center, axis_dir), 0)
== cmp(np.dot(vec_to_rotate, axis_dir), 0))
def _search_root_on_plane(self, p_init, plane_norm, normed=True):
# MARK: alpha_n_assuming see also self.edge_polygon
# in Cermak2005 it is not directly presented
# that grd should in the circle plan,
# but the Neighborhood test in S7.1 assumed that.
if not normed:
plane_norm = norm_vec(plane_norm)
grd = self.func_gd(p_init)
grd = projection_to_plan(grd, plane_norm)
func_val = self.func(p_init)
delta = self.line_search_dlt * -cmp(func_val, 0)
delta = delta * grd
pnew2 = p_init + delta
func_val2 = self.func(pnew2)
pnew = p_init
while func_val * func_val2 > 0:
pnew = pnew2
pnew2 = pnew + delta
func_val = func_val2
func_val2 = self.func(pnew2)
rslt = brentq(lambda t: self.func(pnew * (1 - t) + pnew2 * t),
0, 1)
pnew = pnew * (1 - rslt) + pnew2 * rslt
return pnew
