def test_rt_transpose():
rt = Rototrans.from_random_data()
rt_t = Rototrans.from_transposed_rototrans(rt)
rt_t_expected = np.zeros((4, 4, rt.time.size))
rt_t_expected[3, 3, :] = 1
for row in range(rt.row.size):
for col in range(rt.col.size):
for frame in range(rt.time.size):
rt_t_expected[col, row, frame] = rt[row, col, frame]
for frame in range(rt.time.size):
rt_t_expected[:3, 3, frame] = -rt_t_expected[:3, :3, frame].dot(
rt[:3, 3, frame])
np.testing.assert_array_almost_equal(rt_t, rt_t_expected, decimal=10)
def test_average_rt():
# TODO: investigate why this does not work
# angles = Angles.from_random_data(size=(3, 1, 100))
# or
# angles = Angles(np.arange(300).reshape((3, 1, 100)))
angles = Angles(np.random.rand(3, 1, 100))
seq = "xyz"
rt = Rototrans.from_euler_angles(angles, seq)
rt_mean = Rototrans.from_averaged_rototrans(rt)
angles_mean = Angles.from_rototrans(rt_mean, seq).isel(time=0)
angles_mean_ref = Angles.from_rototrans(rt, seq).mean(dim="time")
np.testing.assert_array_almost_equal(angles_mean,
angles_mean_ref,
decimal=2)
def test_rototrans_creation():
dims = ("row", "col", "time")
array = Rototrans()
np.testing.assert_array_equal(x=array,
y=xr.DataArray(np.eye(4)[..., np.newaxis]))
assert array.dims == dims
array = Rototrans(MARKERS_DATA.values, time=MARKERS_DATA.time)
is_expected_array(array, **EXPECTED_VALUES[67])
size = 4, 4, 100
array = Rototrans.from_random_data(size=size)
assert array.shape == size
assert array.dims == dims
with pytest.raises(ValueError):
Angles(ANALOGS_DATA)
def test_average_rt():
seq = "xyz"
angles_size = (3, 1, 100)
ref_angles_from_rt_mean = [0.25265133, 0.57436872, 0.79133042]
restart_seed()
angles = Angles.from_random_data(size=angles_size)
# min-max normalization to keep the angles low
angles = angles.pipe(lambda x: (x - x.min()) / (x.max() - x.min()))
rt = Rototrans.from_euler_angles(angles, seq)
rt_mean = Rototrans.from_averaged_rototrans(rt)
angles_from_rt_mean = Angles.from_rototrans(rt_mean, seq)
np.testing.assert_almost_equal(angles_from_rt_mean.data.ravel(),
ref_angles_from_rt_mean,
decimal=4)
def test_rt_transpose():
n_frames = 10
angles = Angles.from_random_data(size=(3, 1, n_frames))
rt = Rototrans.from_euler_angles(angles, angle_sequence="xyz")
rt_t = Rototrans.from_transposed_rototrans(rt)
rt_t_expected = np.zeros((4, 4, n_frames))
rt_t_expected[3, 3, :] = 1
for row in range(rt.row.size):
for col in range(rt.col.size):
for frame in range(rt.time.size):
rt_t_expected[col, row, frame] = rt[row, col, frame]
for frame in range(rt.time.size):
rt_t_expected[:3, 3, frame] = -rt_t_expected[:3, :3, frame].dot(
rt[:3, 3, frame])
np.testing.assert_array_almost_equal(rt_t, rt_t_expected, decimal=10)
def test_euler2rot_rot2euleur(seq, angles=ANGLES, epsilon=EPSILON):
if seq == "zyzz":
angles_to_test = angles[:3, ...]
else:
angles_to_test = angles[:len(seq), ...]
r = Rototrans.from_euler_angles(angles=angles_to_test, angle_sequence=seq)
a = Angles.from_rototrans(rt=r, angle_sequence=seq)
np.testing.assert_array_less((a - angles_to_test).meca.abs().sum(),
epsilon)
def test_rototrans_creation():
dims = ("row", "col", "time")
array = Rototrans()
np.testing.assert_array_equal(x=array,
y=xr.DataArray(np.eye(4)[..., np.newaxis]))
assert array.dims == dims
data = Markers(MARKERS_DATA.values)
array = Rototrans.from_markers(
origin=data.isel(channel=[0]),
axis_1=data.isel(channel=[0, 1]),
axis_2=data.isel(channel=[0, 2]),
axes_name="xy",
axis_to_recalculate="y",
)
is_expected_array(array, **EXPECTED_VALUES[67])
size = 4, 4, 100
array = Rototrans.from_random_data(size=size)
assert array.shape == size
assert array.dims == dims
with pytest.raises(ValueError):
Angles(ANALOGS_DATA)
def test_rotate():
n_frames = 100
n_markers = 10
angles = Angles.from_random_data(size=(3, 1, n_frames))
rt = Rototrans.from_euler_angles(angles, "xyz")
markers = Markers.from_random_data(size=(3, n_markers, n_frames))
rotated_markers = Markers.from_rototrans(markers, rt)
expected_rotated_marker = np.ndarray((4, n_markers, n_frames))
for marker in range(n_markers):
for frame in range(n_frames):
expected_rotated_marker[:, marker, frame] = np.dot(
rt.isel(time=frame),
markers.isel(channel=marker, time=frame),
)
np.testing.assert_array_almost_equal(rotated_markers,
expected_rotated_marker,
decimal=10)
rotated_markers = Markers.from_rototrans(markers.isel(time=0),
rt.isel(time=0))
expected_rotated_marker = np.ndarray(rotated_markers.shape)
for marker in range(n_markers):
expected_rotated_marker[:, marker] = np.dot(
rt.isel(time=0), markers.isel(channel=marker, time=0))
np.testing.assert_array_almost_equal(rotated_markers,
expected_rotated_marker,
decimal=10)
rotated_markers = Markers.from_rototrans(markers, rt.isel(time=0))
expected_rotated_marker = np.ndarray(rotated_markers.shape)
for marker in range(n_markers):
expected_rotated_marker[:,
marker] = np.dot(rt.isel(time=0),
markers.isel(channel=marker))
np.testing.assert_array_almost_equal(rotated_markers,
expected_rotated_marker,
decimal=10)
with pytest.raises(ValueError):
Markers.from_rototrans(markers.isel(time=0), rt)
w = vertcat(transX, transY, transZ, angleX, angleY, angleZ)
prob = {'f': J, 'x': w}
options = {
'ipopt.hessian_approximation': "exact",
# 'ipopt.tol':1e-10,'ipopt.dual_inf_tol':1e-15
}
solver = nlpsol('solver', 'ipopt', prob, options)
w0 = np.zeros((6, 1))
# w0[0]= marker_model[0,0,0] - marker_treat[0,0,0]
# w0[1]= marker_model[1,0,0] - marker_treat[1,0,0]
# w0[2]= marker_model[2,0,0] - marker_treat[2,0,0]
solve = solver(x0=w0, lbx=-1000, ubx=10000)
w_opt = solve['x']
print(w_opt)
rt = Rototrans((RT(w_opt[0], w_opt[1], w_opt[2], w_opt[3], w_opt[4],
w_opt[5])))
# rt = Rototrans((RT(0.841114, 0.103637, -0.596597, -0.458244, 0.145129, 3.21253)))
marker_rotate = Markers.from_rototrans(marker_treat, rt)
# Data for three-dimensional scattered points
ax = plt.axes(projection='3d')
zdata = marker_rotate[2, :, 0]
xdata = marker_rotate[0, :, 0]
ydata = marker_rotate[1, :, 0]
ax.scatter3D(xdata, ydata, zdata, cmap='Greens')
zdata = marker_model[2, :, 0]
xdata = marker_model[0, :, 0]
ydata = marker_model[1, :, 0]
ax.scatter3D(xdata, ydata, zdata, edgecolors="red")
ax.view_init(60, 35)
plt.show()
def test_rt_from_markers():
all_m = Markers.from_random_data()
rt_xy = Rototrans.from_markers(
origin=all_m.isel(channel=[0]),
axis_1=all_m.isel(channel=[0, 1]),
axis_2=all_m.isel(channel=[0, 2]),
axes_name="xy",
axis_to_recalculate="y",
)
rt_yx = Rototrans.from_markers(
origin=all_m.isel(channel=[0]),
axis_1=all_m.isel(channel=[0, 2]),
axis_2=all_m.isel(channel=[0, 1]),
axes_name="yx",
axis_to_recalculate="y",
)
rt_xy_x_recalc = Rototrans.from_markers(
origin=all_m.isel(channel=[0]),
axis_1=all_m.isel(channel=[0, 1]),
axis_2=all_m.isel(channel=[0, 2]),
axes_name="yx",
axis_to_recalculate="x",
)
rt_xy_x_recalc = rt_xy_x_recalc.isel(col=[1, 0, 2, 3])
rt_xy_x_recalc[:, 2, :] = -rt_xy_x_recalc[:, 2, :]
rt_yz = Rototrans.from_markers(
origin=all_m.isel(channel=[0]),
axis_1=all_m.isel(channel=[0, 1]),
axis_2=all_m.isel(channel=[0, 2]),
axes_name="yz",
axis_to_recalculate="z",
)
rt_zy = Rototrans.from_markers(
origin=all_m.isel(channel=[0]),
axis_1=all_m.isel(channel=[0, 2]),
axis_2=all_m.isel(channel=[0, 1]),
axes_name="zy",
axis_to_recalculate="z",
)
rt_xy_from_yz = rt_yz.isel(col=[1, 2, 0, 3])
rt_xz = Rototrans.from_markers(
origin=all_m.isel(channel=[0]),
axis_1=all_m.isel(channel=[0, 1]),
axis_2=all_m.isel(channel=[0, 2]),
axes_name="xz",
axis_to_recalculate="z",
)
rt_zx = Rototrans.from_markers(
origin=all_m.isel(channel=[0]),
axis_1=all_m.isel(channel=[0, 2]),
axis_2=all_m.isel(channel=[0, 1]),
axes_name="zx",
axis_to_recalculate="z",
)
rt_xy_from_zx = rt_xz.isel(col=[0, 2, 1, 3])
rt_xy_from_zx[:, 2, :] = -rt_xy_from_zx[:, 2, :]
np.testing.assert_array_equal(rt_xy, rt_xy_x_recalc)
np.testing.assert_array_equal(rt_xy, rt_yx)
np.testing.assert_array_equal(rt_yz, rt_zy)
np.testing.assert_array_equal(rt_xz, rt_zx)
np.testing.assert_array_equal(rt_xy, rt_xy_from_yz)
np.testing.assert_array_equal(rt_xy, rt_xy_from_zx)
# Produce one that we know the solution
ref_m = Markers(
np.array(((1, 2, 3), (4, 5, 6), (6, 5, 4))).T[:, :, np.newaxis])
rt_xy_from_known_m = Rototrans.from_markers(
origin=ref_m.isel(channel=[0]),
axis_1=ref_m.isel(channel=[0, 1]),
axis_2=ref_m.isel(channel=[0, 2]),
axes_name="xy",
axis_to_recalculate="y",
)
rt_xy_expected = Rototrans(
np.array([
[0.5773502691896257, 0.7071067811865475, -0.408248290463863, 1.0],
[0.5773502691896257, 0.0, 0.816496580927726, 2.0],
[0.5773502691896257, -0.7071067811865475, -0.408248290463863, 3.0],
[0, 0, 0, 1.0],
]))
np.testing.assert_array_equal(rt_xy_from_known_m, rt_xy_expected)
exception_default_params = dict(
origin=all_m.isel(channel=[0]),
axis_1=all_m.isel(channel=[0, 1]),
axis_2=all_m.isel(channel=[0, 2]),
axes_name="xy",
axis_to_recalculate="y",
)
with pytest.raises(ValueError):
Rototrans.from_markers(**{
**exception_default_params,
**dict(origin=all_m.isel(channel=[0, 1]))
})
with pytest.raises(ValueError):
Rototrans.from_markers(**{
**exception_default_params,
**dict(axis_1=all_m.isel(channel=[0]))
})
with pytest.raises(ValueError):
Rototrans.from_markers(**{
**exception_default_params,
**dict(axis_2=all_m.isel(channel=[0]))
})
with pytest.raises(ValueError):
Rototrans.from_markers(
**{
**exception_default_params,
**dict(axis_1=all_m.isel(channel=[0, 1], time=slice(None, 50))),
})
with pytest.raises(ValueError):
Rototrans.from_markers(**{
**exception_default_params,
**dict(axes_name="yyz")
})
with pytest.raises(ValueError):
Rototrans.from_markers(**{
**exception_default_params,
**dict(axes_name="xxz")
})
with pytest.raises(ValueError):
Rototrans.from_markers(**{
**exception_default_params,
**dict(axes_name="zzz")
})
with pytest.raises(ValueError):
Rototrans.from_markers(**{
**exception_default_params,
**dict(axis_to_recalculate="h")
})
def test_construct_rt():
eye = Rototrans()
np.testing.assert_equal(eye.time.size, 1)
np.testing.assert_equal(eye.sel(time=0), np.eye(4))
eye = Rototrans.from_euler_angles()
np.testing.assert_equal(eye.time.size, 1)
np.testing.assert_equal(eye.sel(time=0), np.eye(4))
# Test the way to create a rt, but not when providing bot angles and sequence
nb_frames = 10
random_vector = Angles(np.random.rand(3, 1, nb_frames))
# with angles
rt_random_angles = Rototrans.from_euler_angles(angles=random_vector,
angle_sequence="xyz")
np.testing.assert_equal(rt_random_angles.time.size, nb_frames)
np.testing.assert_equal(rt_random_angles[:-1, -1:, :],
np.zeros((3, 1, nb_frames))) # Translation is 0
# with translation
rt_random_translation = Rototrans.from_euler_angles(
translations=random_vector)
np.testing.assert_equal(rt_random_translation.time.size, nb_frames)
np.testing.assert_equal(
rt_random_translation[:3, :3, :],
np.repeat(np.eye(3)[:, :, np.newaxis], nb_frames, axis=2),
) # rotation is eye3
np.arange(0, rt_random_angles.time.size / 0.5, 1 / 0.5)
rt_with_time = Rototrans(
rt_random_angles,
time=np.arange(0, rt_random_angles.time.size / 100, 1 / 100),
)
assert rt_with_time.time[-1] == 0.09
with pytest.raises(IndexError):
Rototrans(data=np.zeros(1))
with pytest.raises(IndexError):
Rototrans.from_euler_angles(
angles=random_vector[..., :5],
translations=random_vector,
angle_sequence="x",
)
with pytest.raises(IndexError):
Rototrans.from_euler_angles(angles=random_vector, angle_sequence="x")
with pytest.raises(ValueError):
Rototrans.from_euler_angles(angles=random_vector, angle_sequence="nop")
vtkModelMid = VtkModel(vtkWindow,
markers_color=(0, 0, 1),
markers_size=10.0,
markers_opacity=0.5,
rt_length=100)
vtkModelFromC3d = VtkModel(vtkWindow,
markers_color=(0, 1, 0),
markers_size=10.0,
markers_opacity=0.5,
rt_length=100)
# Create some RotoTrans attached to the first model
all_rt_real = []
all_rt_real.append(
Rototrans.from_euler_angles(angles=Angles(np.zeros((3, 1, 1))),
angle_sequence="yxz",
translations=d[:, [0], [0]]))
all_rt_real.append(
Rototrans.from_euler_angles(angles=Angles(np.zeros((3, 1, 1))),
angle_sequence="yxz",
translations=d[:, [0], [0]]))
# Create some Rototrans attached to the second model
one_rt = Rototrans.from_markers(
origin=d[:, [3, 5], :].mean("channel", keepdims=True),
axis_1=d[:, [4, 3], :],
axis_2=d[:, [4, 5], :],
axes_name="zx",
axis_to_recalculate="z",
)
