plt.xlim([0, 20])
plt.ylim([0, 20])
plt.xlabel(r"$x$")
plt.ylabel(r"$y$")
plt.grid()
fields_comparisons.see_2_fields_separate_and_overlay(
disp_0,
svf_0,
fig_tag=2,
title_input_0='disp',
title_input_1='svf',
title_input_both='overlay')
# Initialize the displacement field that will be computed using the integral curves.
l_exp = lie_exp.LieExp()
disp_1 = l_exp.scaling_and_squaring(svf_0)
fields_comparisons.see_2_fields_separate_and_overlay(
disp_1,
svf_0,
fig_tag=3,
title_input_0='disp',
title_input_1='svf',
title_input_both='overlay',
window_title_input='embedded')
print('Showing outcome: ...')
plt.show()
def test_2_random_vector_fields_as_deformations(get_figures=False):
dec = 1
passe_partout = 3
omega = (15, 15)
sigma_init = 4
sigma_gaussian_filter = 2
svf_zeros = gen_id.id_lagrangian(omega)
svf_0 = gen.generate_random(omega,
parameters=(sigma_init, sigma_gaussian_filter))
l_exp = lie_exp.LieExp()
sdisp_0 = l_exp.scaling_and_squaring(svf_0)
sdisp_0_inv = l_exp.scaling_and_squaring(-1 * svf_0)
f_o_f_inv = cp.lagrangian_dot_lagrangian(sdisp_0,
sdisp_0_inv,
add_right=True)
f_inv_o_f = cp.lagrangian_dot_lagrangian(sdisp_0_inv,
sdisp_0,
add_right=True)
# results of a composition of 2 lagrangian must be a lagrangian zero field
assert_array_almost_equal(f_o_f_inv[passe_partout:-passe_partout,
passe_partout:-passe_partout, 0, 0, :],
svf_zeros[passe_partout:-passe_partout,
passe_partout:-passe_partout, 0, 0, :],
decimal=dec)
assert_array_almost_equal(f_inv_o_f[passe_partout:-passe_partout,
passe_partout:-passe_partout, 0, 0, :],
svf_zeros[passe_partout:-passe_partout,
passe_partout:-passe_partout, 0, 0, :],
decimal=dec)
if get_figures:
fields_at_the_window.see_field(sdisp_0, fig_tag=61)
fields_at_the_window.see_field(
sdisp_0_inv,
fig_tag=61,
input_color='r',
title_input='2 displacement fields: f blue, g red')
fields_at_the_window.see_field(sdisp_0, fig_tag=62)
fields_at_the_window.see_field(sdisp_0_inv,
fig_tag=62,
input_color='r')
fields_at_the_window.see_field(
f_o_f_inv,
fig_tag=62,
input_color='g',
title_input='composition (f o f^(-1)) in green')
fields_at_the_window.see_field(sdisp_0, fig_tag=63)
fields_at_the_window.see_field(sdisp_0_inv,
fig_tag=63,
input_color='r')
fields_at_the_window.see_field(
f_inv_o_f,
fig_tag=63,
input_color='g',
title_input='composition (f^(-1) o f) in green')
plt.show()
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()