def test_generate_from_matrix_from_algebra_element_3d_3d_matrix():
r = np.random.randn(3, 3)
m = np.eye(4)
m[:3, :3] = r
m[:3, 3] = np.array([3, 4, 5])
vf = gen.generate_from_matrix((10, 10, 5), m, t=1, structure='algebra')
vf_expected = np.zeros((10, 10, 5, 1, 3))
for x in range(10):
for y in range(10):
for z in range(5):
vf_expected[x, y, z, 0, :] = list(m.dot(np.array([x, y, z,
1])))[:3]
assert_array_equal(vf, vf_expected)
def test_generate_from_matrix_from_algebra_element_2d():
theta, tx, ty = np.pi / 8, 5, 5
a1 = [0, -theta, tx]
a2 = [theta, 0, ty]
a3 = [0, 0, 0]
m = np.array([a1, a2, a3])
vf = gen.generate_from_matrix((10, 10), m, t=1, structure='algebra')
vf_expected = np.zeros((10, 10, 1, 1, 2))
for x in range(10):
for y in range(10):
vf_expected[x, y, 0, 0, :] = m.dot(np.array([x, y, 1]))[:2]
assert_array_equal(vf, vf_expected)
def test_generate_from_matrix_from_group_element_2d():
theta, tx, ty = np.pi / 10, 5, 5
a1 = [np.cos(theta), -np.sin(theta), tx]
a2 = [np.sin(theta), np.cos(theta), ty]
a3 = [0, 0, 1]
m = np.array([a1, a2, a3])
vf = gen.generate_from_matrix((10, 10), m, t=1, structure='group')
vf_expected = np.zeros((10, 10, 1, 1, 2))
# move to lagrangian coordinates to compute the ground truth:
m = m - np.eye(3)
for x in range(10):
for y in range(10):
vf_expected[x, y, 0, 0, :] = m.dot(np.array([x, y, 1]))[:2]
assert_array_equal(vf, vf_expected)
def test_generate_from_matrix_from_group_element_3d_3d_matrix():
r = np.random.randn(3, 3)
m = np.eye(4)
m[:3, :3] = r
m[:3, 3] = np.array([3, 4, 5])
vf = gen.generate_from_matrix((10, 10, 5), m, t=1, structure='group')
vf_expected = np.zeros((10, 10, 5, 1, 3))
# move to lagrangian coordinates to compute the ground truth:
m = m - np.eye(4)
for x in range(10):
for y in range(10):
for z in range(5):
vf_expected[x, y, z, 0, :] = list(m.dot(np.array([x, y, z,
1])))[:3]
assert_array_equal(vf, vf_expected)
x_c, y_c = [c / 2 for c in omega]
theta = np.pi / 8
tx = (1 - np.cos(theta)) * x_c + np.sin(theta) * y_c
ty = -np.sin(theta) * x_c + (1 - np.cos(theta)) * y_c
m_0 = se2.Se2G(theta, tx, ty)
dm_0 = se2.se2g_log(m_0)
print(m_0.get_matrix)
print('')
print(dm_0.get_matrix)
# Generate subsequent vector fields
flow = gen.generate_from_matrix(list(omega)[::-1], m_0.get_matrix, structure='group')
svf_0 = gen.generate_from_matrix(list(omega)[::-1], dm_0.get_matrix, structure='algebra')
elif params['deformation_model'] == 'linear':
taste = 1
beta = 0.5
x_c, y_c = [c / 2 for c in omega]
dm = beta * linear.randomgen_linear_by_taste(1, taste, (x_c, y_c))
svf_0 = gen.generate_from_matrix(omega[::-1], dm, structure='algebra')
flow = l_exp.gss_aei(svf_0)
elif params['deformation_model'] == 'homography':
from calie.transformations import linear
from calie.fields import generate as gen
from calie.operations import lie_exp
# --- Linear example
beta = 0.1
omega = (10, 12, 13)
# generate matrix
dm1 = beta * linear.randomgen_linear_by_taste(1, 1,
[int(c / 2) for c in omega])
m1 = scipy.linalg.expm(dm1)
# generate SVF
svf1 = gen.generate_from_matrix(omega, dm1, t=1, structure='algebra')
flow1_ground = gen.generate_from_matrix(omega, m1, t=1, structure='group')
quiver_3d(svf1, flow1_ground)
plt.show(block=False)
# --- Gaussian example
# generate SVF
svf1 = gen.generate_random(omega, 1, (1, 1))
l_exp = lie_exp.LieExp()
l_exp.s_i_o = 3
flow1_ground = l_exp.gss_aei(svf1)
theta = np.pi / 8
tx = (1 - np.cos(theta)) * x_c + np.sin(theta) * y_c
ty = -np.sin(theta) * x_c + (1 - np.cos(theta)) * y_c
passepartout = 2
m_0 = se2.Se2G(theta, tx, ty)
dm_0 = se2.se2g_log(m_0)
print(dm_0.get_matrix)
print(m_0.get_matrix)
# -> generate subsequent vector fields
svf_0 = gen.generate_from_matrix(omega,
dm_0.get_matrix,
structure='algebra')
sdisp_0 = gen.generate_from_matrix(omega,
m_0.get_matrix,
structure='group')
# -> compute exponential with different available methods:
spline_interpolation_order = 3
l_exp = lie_exp.LieExp()
l_exp.s_i_o = spline_interpolation_order
sdisp_ss = l_exp.scaling_and_squaring(svf_0)
sdisp_ss_pa = l_exp.gss_aei(svf_0)
sdisp_euler = l_exp.euler(svf_0)
if __name__ == '__main__':
pyplot.close('all')
l_exp = lie_exp.LieExp()
# ----------------------------
# ---- First example ---------
# ----------------------------
taste = 3
alpha = 1
beta = 0.1
dm = beta * linear.randomgen_linear_by_taste(1, taste, (20, 20))
svf = alpha * gen.generate_from_matrix((40, 40), dm, structure='algebra')
# get integral of the SVF with generalised scaling and squaring.
sdisp = l_exp.gss_aei(svf)
see_field(svf, subtract_id=False, input_color='r', fig_tag=1)
see_field(sdisp,
subtract_id=False,
input_color='b',
title_input='Unstable node exp',
fig_tag=1)
pyplot.show(block=False)
# get integral of the SVF with the matrix exponential
m = scipy.linalg.expm(dm)
sdisp_expm = alpha * gen.generate_from_matrix(
passepartout = 4
sio = 3 # spline interpolation order
# -> model <- #
m_0 = se2.Se2G(theta, tx, ty)
dm_0 = se2.se2g_log(m_0)
print(m_0.get_matrix)
print('')
print(dm_0.get_matrix)
# Generate subsequent vector fields
sdisp_0 = gen.generate_from_matrix(domain, m_0.get_matrix, structure='group')
svf_0 = gen.generate_from_matrix(domain, dm_0.get_matrix, structure='algebra')
# Compute exponential with different available methods:
l_exp = lie_exp.LieExp()
l_exp.s_i_o = sio
methods = [l_exp.euler,
l_exp.midpoint,
l_exp.scaling_and_squaring,
l_exp.gss_ei,
l_exp.gss_aei,
l_exp.trapeziod_euler,
l_exp.gss_trapezoid_euler,
l_exp.trapezoid_midpoint,
def test_visual_assessment_method_one_se2(show=False):
"""
:param show: to add the visualisation of a figure.
This test is for visual assessment. Please put show to True.
Aimed to test the prototyping of the computation of the exponential map
with some methods.
(Nothing is saved in external folder.)
"""
##############
# controller #
##############
domain = (20, 20)
x_c = 10
y_c = 10
theta = np.pi / 8
tx = (1 - np.cos(theta)) * x_c + np.sin(theta) * y_c
ty = -np.sin(theta) * x_c + (1 - np.cos(theta)) * y_c
passepartout = 5
spline_interpolation_order = 3
l_exp = lie_exp.LieExp()
l_exp.s_i_o = spline_interpolation_order
methods_list = [
l_exp.scaling_and_squaring, l_exp.gss_ei, l_exp.gss_ei_mod,
l_exp.gss_aei, l_exp.midpoint, l_exp.series, l_exp.euler,
l_exp.euler_aei, l_exp.euler_mod, l_exp.heun, l_exp.heun_mod,
l_exp.rk4, l_exp.gss_rk4, l_exp.trapeziod_euler,
l_exp.trapezoid_midpoint, l_exp.gss_trapezoid_euler,
l_exp.gss_trapezoid_midpoint
]
# -----
# model
# -----
m_0 = se2.Se2G(theta, tx, ty)
dm_0 = se2.se2g_log(m_0)
# -- generate subsequent vector fields
svf_0 = gen.generate_from_matrix(domain,
dm_0.get_matrix,
structure='algebra')
sdisp_0 = gen.generate_from_matrix(domain,
m_0.get_matrix,
structure='group')
# -- compute exponential with different available methods:
sdisp_list = []
res_time = np.zeros(len(methods_list))
for num_met, met in enumerate(methods_list):
start = time.time()
sdisp_list.append(met(svf_0, input_num_steps=10))
res_time[num_met] = (time.time() - start)
# ----
# view
# ----
print('--------------------')
print('Norm of the svf: ')
print(qr.norm(svf_0, passe_partout_size=4))
print('--------------------')
print("Norm of the displacement field:")
print(qr.norm(sdisp_0, passe_partout_size=4))
print('--------------------')
print('Norm of the errors: ')
print('--------------------')
for num_met in range(len(methods_list)):
err = qr.norm(sdisp_list[num_met] - sdisp_0,
passe_partout_size=passepartout)
print('|{0:>22} - disp| = {1}'.format(methods_list[num_met].__name__,
err))
if methods_list[num_met].__name__ == 'euler':
assert err < 3
else:
assert err < 0.5
print('---------------------')
print('Computational Times: ')
print('---------------------')
if show:
title_input_l = ['Sfv Input', 'Ground Output'] + methods_list
fields_list = [svf_0, sdisp_0] + sdisp_list
list_fields_of_field = [[svf_0], [sdisp_0]]
list_colors = ['r', 'b']
for third_field in fields_list[2:]:
list_fields_of_field += [[svf_0, sdisp_0, third_field]]
list_colors += ['r', 'b', 'm']
fields_comparisons.see_n_fields_special(
list_fields_of_field,
fig_tag=50,
row_fig=5,
col_fig=5,
input_figsize=(14, 7),
colors_input=list_colors,
titles_input=title_input_l,
sample=(1, 1),
zoom_input=[0, 20, 0, 20],
window_title_input='matrix generated svf')
plt.show()
def test_generate_from_matrix_incompatible_matrix_omega_3d():
with assert_raises(IOError):
gen.generate_from_matrix((10, 10, 12), np.eye(5), t=1)
def test_generate_from_matrix_wrong_structure():
with assert_raises(IOError):
gen.generate_from_matrix((10, 11), np.eye(4), t=1, structure='spam')
def test_generate_from_matrix_wrong_timepoints():
with assert_raises(IndexError):
gen.generate_from_matrix((10, 11), np.eye(4), t=2)
d = 2
omega = (x_1, y_1)
shape = list(omega) + [1, 1, 2]
# center of the homography
x_c = x_1 / 2
y_c = y_1 / 2
z_c = 1
centre_hom = [x_c, y_c]
# generate matrices homography
scale_factor = 15. / (np.max(omega) * 10)
hom_attributes = [d, scale_factor, 1.3, special]
hom_a, hom_g = get_random_hom_matrices(d=hom_attributes[0],
scale_factor=hom_attributes[1],
sigma=hom_attributes[2],
special=hom_attributes[3],
projective_center=None)
# Generate SVF and flow
svf1 = gen.generate_from_matrix(omega, hom_a, t=1, structure='algebra')
flow1 = gen.generate_from_matrix(omega, hom_g, t=1, structure='group')
plt.close()
see_field(svf1, fig_tag=1, input_color='r')
see_field(flow1, fig_tag=1, input_color='b')
plt.show()
