def test_2_random_vector_fields_svf(get_figures=False):
"""
The composition is not the identity since we are working in the tangent space.
"""
dec = 3
passe_partout = 5
omega = (10, 10)
svf_f = gen_id.id_lagrangian(omega=omega)
svf_f_inv = np.copy(-1 * svf_f)
f_o_f_inv = cp.lagrangian_dot_lagrangian(svf_f, svf_f_inv, add_right=True)
f_inv_o_f = cp.lagrangian_dot_lagrangian(svf_f_inv, svf_f, add_right=True)
svf_id = gen_id.id_lagrangian(omega=omega)
# # 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_id[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_id[passe_partout:-passe_partout,
passe_partout:-passe_partout, 0, 0, :],
decimal=dec)
if get_figures:
fields_at_the_window.see_field(svf_f, fig_tag=51)
fields_at_the_window.see_field(
svf_f_inv,
fig_tag=51,
input_color='r',
title_input='2 vector fields: f blue, g red')
fields_at_the_window.see_field(svf_f, fig_tag=52)
fields_at_the_window.see_field(svf_f_inv, fig_tag=52, input_color='r')
fields_at_the_window.see_field(
f_o_f_inv,
fig_tag=52,
input_color='g',
title_input='composition (f o f^(-1)) in green')
fields_at_the_window.see_field(svf_f, fig_tag=53)
fields_at_the_window.see_field(svf_f_inv, fig_tag=53, input_color='r')
fields_at_the_window.see_field(
f_inv_o_f,
fig_tag=53,
input_color='g',
title_input='composition (f^(-1) o f) in green')
plt.show()
def test_jacobian_toy_field_3():
clear_cache()
def field_f(t, x):
t = float(t)
x = [float(y) for y in x]
return x[0]**2 + 2 * x[0] + x[1], 3.0 * x[0] + 2.0
def jacobian_f(t, x):
t = float(t)
x = [float(y) for y in x]
return 2.0 * x[0] + 2.0, 1.0, 3.0, 0.0
svf_f = gen_id.id_lagrangian(omega=(30, 30))
jac_f_ground = jac.initialise_jacobian(svf_f)
for i in range(0, 30):
for j in range(0, 30):
svf_f[i, j, 0, 0, :] = field_f(1, [i, j])
jac_f_ground[i, j, 0, 0, :] = jacobian_f(1, [i, j])
jac_f_numeric = jac.compute_jacobian(svf_f)
pp = 2
assert_array_almost_equal(jac_f_ground[pp:-pp, pp:-pp, 0, 0, :],
jac_f_numeric[pp:-pp, pp:-pp, 0, 0, :])
def test_jacobian_toy_field_2():
clear_cache()
def field_f(t, x):
t = float(t)
x = [float(y) for y in x]
return 0.5 * x[0] + 0.6 * x[1], 0.8 * x[1]
def jacobian_f(t, x):
t = float(t)
x = [float(y) for y in x]
return 0.5, 0.6, 0.0, 0.8
svf_f = gen_id.id_lagrangian(omega=(20, 20))
jac_f_ground = jac.initialise_jacobian(svf_f)
for i in range(0, 20):
for j in range(0, 20):
svf_f[i, j, 0, 0, :] = field_f(1, [i, j])
jac_f_ground[i, j, 0, 0, :] = jacobian_f(1, [i, j])
jac_f_numeric = jac.compute_jacobian(svf_f)
square_size = range(0, 20)
assert_array_almost_equal(jac_f_ground[square_size, square_size, 0, 0, :],
jac_f_numeric[square_size, square_size, 0, 0, :])
def test_2_less_easy_vector_fields(get_figures=False):
dec = 1 # decimal for the error
passe_partout = 3
omega = (20, 20)
svf_zeros = gen_id.id_lagrangian(omega)
svf_f = gen_id.id_lagrangian(omega)
svf_f_inv = gen_id.id_lagrangian(omega)
def function_f(t, x):
t = float(t)
x = [float(y) for y in x]
return np.array([np.sin(0.01 * x[1]), (3 * np.cos(x[0])) / (x[0] + 2)])
for x in range(20):
for y in range(20):
svf_f[x, y, 0, 0, :] = function_f(1, [x, y])
svf_f_inv[x, y, 0, 0, :] = -1 * function_f(1, [x, y])
f_o_f_inv = cp.lagrangian_dot_lagrangian(svf_f, svf_f_inv, add_right=True)
f_inv_o_f = cp.lagrangian_dot_lagrangian(svf_f_inv, svf_f, add_right=True)
assert_array_almost_equal(f_o_f_inv[10, 10, 0, 0, :], [.0, .0],
decimal=dec)
assert_array_almost_equal(f_inv_o_f[10, 10, 0, 0, :], [.0, .0],
decimal=dec)
# results of a composition
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(svf_f)
fields_at_the_window.see_field(
svf_f_inv,
input_color='r',
title_input='2 vector fields: f blue, g red')
fields_at_the_window.see_field(svf_f, fig_tag=2)
fields_at_the_window.see_field(svf_f_inv, fig_tag=2)
fields_at_the_window.see_field(
f_o_f_inv,
fig_tag=2,
input_color='g',
title_input='composition (f o f^(-1)) in green')
fields_at_the_window.see_field(svf_f, fig_tag=3)
fields_at_the_window.see_field(svf_f_inv, fig_tag=3, input_color='r')
fields_at_the_window.see_field(
f_inv_o_f,
fig_tag=3,
input_color='g',
title_input='composition (f^(-1) o f) in green')
plt.show()
def test_controlled_composition_of_two_closed_form_vector_fields_2d_1(
get_figures=False):
omega = (30, 30)
dec = 1
passe_partout = 10
def u(x, y):
return 0, 0
def v(x, y):
return 1, 1
def u_dot_v(x, y):
return 0, 0
def v_dot_u(x, y):
return 1, 1
svf_u = gen_id.id_lagrangian(omega=omega)
svf_v = gen_id.id_lagrangian(omega=omega)
svf_u_dot_v = gen_id.id_lagrangian(omega=omega)
svf_v_dot_u = gen_id.id_lagrangian(omega=omega)
for x in range(omega[0]):
for y in range(omega[1]):
svf_u[x, y, 0, 0, :] = u(x, y)
svf_v[x, y, 0, 0, :] = v(x, y)
svf_u_dot_v[x, y, 0, 0, :] = u_dot_v(x, y)
svf_v_dot_u[x, y, 0, 0, :] = v_dot_u(x, y)
svf_u_dot_v_numerical = cp.lagrangian_dot_lagrangian(svf_u,
svf_v,
add_right=False)
svf_v_dot_u_numerical = cp.lagrangian_dot_lagrangian(svf_v,
svf_u,
add_right=False)
if get_figures:
fields_at_the_window.see_field(svf_u, fig_tag=62)
fields_at_the_window.see_field(svf_v, fig_tag=62, input_color='r')
fields_at_the_window.see_field(svf_u_dot_v,
fig_tag=62,
input_color='g',
title_input='(u o v) closed form')
fields_at_the_window.see_field(svf_u, fig_tag=63)
fields_at_the_window.see_field(svf_v, fig_tag=63, input_color='r')
fields_at_the_window.see_field(svf_u_dot_v_numerical,
fig_tag=63,
input_color='g',
title_input='(u o v) numerical')
fields_at_the_window.see_field(svf_u, fig_tag=64)
fields_at_the_window.see_field(svf_v, fig_tag=64, input_color='r')
fields_at_the_window.see_field(
svf_v_dot_u,
fig_tag=64,
input_color='g',
title_input='composition v o u closed form')
fields_at_the_window.see_field(svf_u, fig_tag=65)
fields_at_the_window.see_field(svf_v, fig_tag=65, input_color='r')
fields_at_the_window.see_field(
svf_v_dot_u_numerical,
fig_tag=65,
input_color='g',
title_input='composition v o u numerical')
plt.show()
assert_array_almost_equal(
svf_u_dot_v[passe_partout:-passe_partout, passe_partout:-passe_partout,
0, 0, :],
svf_u_dot_v_numerical[passe_partout:-passe_partout,
passe_partout:-passe_partout, 0, 0, :],
decimal=dec)
assert_array_almost_equal(
svf_v_dot_u[passe_partout:-passe_partout, passe_partout:-passe_partout,
0, 0, :],
svf_v_dot_u_numerical[passe_partout:-passe_partout,
passe_partout:-passe_partout, 0, 0, :],
decimal=dec)
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_less_easy_composition_with_identity(get_figures=False):
dec = 0 # decimal for the error
passe_partout = 4
omega = (20, 25)
svf_zeros = gen_id.id_lagrangian(omega=omega)
svf_f = gen_id.id_lagrangian(omega=omega)
svf_id = gen_id.id_lagrangian(omega=omega)
def function_f(t, x):
t = float(t)
x = [float(y) for y in x]
return np.array([np.sin(0.01 * x[1]), (3 * np.cos(x[0])) / (x[0] + 2)])
for x in range(20):
for y in range(20):
svf_f[x, y, 0, 0, :] = function_f(1, [x, y])
f_o_id = cp.lagrangian_dot_lagrangian(svf_f, svf_id, add_right=True)
id_o_f = cp.lagrangian_dot_lagrangian(svf_id, svf_f, add_right=True)
# test if the compositions are still in lagrangian coordinates, as attributes and as shape
assert_array_almost_equal(f_o_id[5, 5, 0, 0, :],
function_f(1, [5, 5]),
decimal=dec)
assert_array_almost_equal(id_o_f[5, 5, 0, 0, :],
function_f(1, [5, 5]),
decimal=dec)
# results of a composition of 2 lagrangian must be a lagrangian zero field
assert_array_almost_equal(f_o_id[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(id_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(svf_f, fig_tag=41)
fields_at_the_window.see_field(
svf_id,
fig_tag=41,
input_color='r',
title_input='2 vector fields: f blue, g red')
fields_at_the_window.see_field(svf_f, fig_tag=42)
fields_at_the_window.see_field(svf_id, fig_tag=42, input_color='r')
fields_at_the_window.see_field(
f_o_id,
fig_tag=42,
input_color='g',
title_input='composition (f o id) in green')
fields_at_the_window.see_field(svf_f, fig_tag=43)
fields_at_the_window.see_field(svf_id, fig_tag=43, input_color='r')
fields_at_the_window.see_field(
id_o_f,
fig_tag=43,
input_color='g',
title_input='composition (id o f) in green')
plt.show()
def test_easy_composition_with_identity(get_figures=False):
dec = 6
passe_partout = 0
omega = (10, 10)
svf_zeros = gen_id.id_lagrangian(omega)
svf_f = gen_id.id_lagrangian(omega)
svf_id = gen_id.id_lagrangian(
omega) # id in lagrangian coordinates is the zero field
def function_f(t, x):
t = float(t)
x = [float(y) for y in x]
return np.array([0, 0.3])
for x in range(10):
for y in range(10):
svf_f[x, y, 0, 0, :] = function_f(1, [x, y])
f_o_id = cp.lagrangian_dot_lagrangian(svf_f, svf_id, add_right=True)
id_o_f = cp.lagrangian_dot_lagrangian(svf_id, svf_f, add_right=True)
# sfv_0 is provided in Lagrangian coordinates!
if get_figures:
fields_at_the_window.see_field(svf_f, fig_tag=21)
fields_at_the_window.see_field(
svf_id,
fig_tag=21,
input_color='r',
title_input='2 vector fields: f blue, g red')
fields_at_the_window.see_field(svf_f, fig_tag=22)
fields_at_the_window.see_field(svf_id, fig_tag=22, input_color='r')
fields_at_the_window.see_field(
f_o_id,
fig_tag=22,
input_color='g',
title_input='composition (f o id) in green')
fields_at_the_window.see_field(svf_f, fig_tag=23)
fields_at_the_window.see_field(svf_id, fig_tag=23, input_color='r')
fields_at_the_window.see_field(
id_o_f,
fig_tag=23,
input_color='g',
title_input='composition (id o f) in green')
plt.show()
# test if the compositions are still in lagrangian coordinates, as attributes and as shape
assert_array_almost_equal(f_o_id[5, 5, 0, 0, :],
function_f(1, [5, 5]),
decimal=dec)
assert_array_almost_equal(id_o_f[5, 5, 0, 0, :],
function_f(1, [5, 5]),
decimal=dec)
# results of a composition of 2 lagrangian must be a lagrangian zero field
assert_array_almost_equal(f_o_id[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(id_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)
def see_one_slice(input_vf,
anatomical_plane='axial',
h_slice=0,
sample=(1, 1),
window_title_input='quiver',
title_input='2d vector field',
long_title=False,
fig_tag=1,
scale=1,
subtract_id=False,
input_color='b',
annotate=None,
annotate_position=(1, 1)):
qr.check_is_vf(input_vf)
d = input_vf.shape[-1]
if not d == 2:
raise TypeError('See field 2d works only for 2d to 2d fields.')
id_field = gen_id.id_lagrangian(list(input_vf.shape[:d]))
fig = plt.figure(fig_tag)
ax0 = fig.add_subplot(111)
fig.canvas.set_window_title(window_title_input)
input_field_copy = copy.deepcopy(input_vf)
if subtract_id:
input_field_copy -= id_field
if anatomical_plane == 'axial':
ax0.quiver(id_field[::sample[0], ::sample[1], h_slice, 0, 0],
id_field[::sample[0], ::sample[1], h_slice, 0, 1],
input_field_copy[::sample[0], ::sample[1], h_slice, 0, 0],
input_field_copy[::sample[0], ::sample[1], h_slice, 0, 1],
color=input_color,
linewidths=0.01,
width=0.03,
scale=scale,
scale_units='xy',
units='xy',
angles='xy')
ax0.set_xlabel('x')
ax0.set_ylabel('y')
elif anatomical_plane == 'sagittal':
ax0.quiver(id_field[::sample[0], h_slice, ::sample[1], 0, 0],
id_field[::sample[0], h_slice, ::sample[1], 0, 1],
input_field_copy[::sample[0], h_slice, ::sample[1], 0, 0],
input_field_copy[::sample[0], h_slice, ::sample[1], 0, 1],
color=input_color,
linewidths=0.01,
width=0.03,
units='xy',
angles='xy',
scale=scale,
scale_units='xy')
elif anatomical_plane == 'coronal':
ax0.quiver(id_field[h_slice, ::sample[0], ::sample[1], 0, 0],
id_field[h_slice, ::sample[0], ::sample[1], 0, 1],
input_field_copy[h_slice, ::sample[0], ::sample[1], 0, 0],
input_field_copy[h_slice, ::sample[0], ::sample[1], 0, 1],
color=input_color,
linewidths=0.01,
width=0.03,
units='xy',
angles='xy',
scale=scale,
scale_units='xy')
else:
raise TypeError('Anatomical_plane must be axial, sagittal or coronal')
ax0.xaxis.grid(True,
linestyle='-',
which='major',
color='lightgrey',
alpha=0.5)
ax0.yaxis.grid(True,
linestyle='-',
which='major',
color='lightgrey',
alpha=0.5)
ax0.set_axisbelow(True)
if long_title:
ax0.set_title(title_input + ', ' + str(anatomical_plane) +
' plane, slice ' + str(h_slice))
else:
ax0.set_title(title_input)
if annotate is not None:
ax0.text(annotate_position[0], annotate_position[1], annotate)
plt.axes().set_aspect('equal', 'datalim')
return fig
def test_vf_identity_lagrangian_ok_3d_timepoints():
assert_array_equal(gen_id.id_lagrangian((50, 49, 48), t=3),
np.zeros((50, 49, 48, 3, 3)))
def test_vf_identity_lagrangian_ok_3d():
assert_array_equal(gen_id.id_lagrangian((50, 49, 48)),
np.zeros((50, 49, 48, 1, 3)))
def test_vf_identity_lagrangian_ok_2d():
assert_array_equal(gen_id.id_lagrangian((50, 50)),
np.zeros((50, 50, 1, 1, 2)))
def test_vf_identity_lagrangian_bad_input():
with assert_raises(IOError):
gen_id.id_lagrangian((50, 50, 1, 1))
def generate_from_projective_matrix(omega, input_h, t=1, structure='algebra'):
"""
:param omega: domain of the vector field.
:param input_h: matrix representing an element form the homography group.
:param t: number of timepoints.
:param structure: can be 'algebra' or 'group'.
:return: vector field with the given input parameters.
"""
if t > 1: # TODO
raise IndexError('Random generator not defined (yet) for multiple time points')
d = qr.check_omega(omega)
if structure == 'algebra':
if d == 2:
idd = gen_id.id_eulerian(omega)
vf = gen_id.id_lagrangian(omega)
idd = coord.affine_to_homogeneous(idd)
x_intervals, y_intervals = omega
for i in range(x_intervals):
for j in range(y_intervals):
vf[i, j, 0, 0, 0] = input_h[0, :].dot(idd[i, j, 0, 0, :]) - i * input_h[2, :].dot(idd[i, j, 0, 0, :])
vf[i, j, 0, 0, 1] = input_h[1, :].dot(idd[i, j, 0, 0, :]) - j * input_h[2, :].dot(idd[i, j, 0, 0, :])
return vf
elif d == 3:
idd = gen_id.id_eulerian(omega)
vf = gen_id.id_lagrangian(omega)
idd = coord.affine_to_homogeneous(idd)
x_intervals, y_intervals, z_intervals = omega
for i in range(x_intervals):
for j in range(y_intervals):
for k in range(z_intervals):
vf[i, j, k, 0, 0] = input_h[0, :].dot(idd[i, j, k, 0, :]) - i * input_h[3, :].dot(idd[i, j, k, 0, :])
vf[i, j, k, 0, 1] = input_h[1, :].dot(idd[i, j, k, 0, :]) - j * input_h[3, :].dot(idd[i, j, k, 0, :])
vf[i, j, k, 0, 2] = input_h[2, :].dot(idd[i, j, k, 0, :]) - k * input_h[3, :].dot(idd[i, j, k, 0, :])
return vf
elif structure == 'group':
if d == 2:
vf = gen_id.id_lagrangian(omega)
x_intervals, y_intervals = omega
for i in range(x_intervals):
for j in range(y_intervals):
s = input_h.dot(np.array([i, j, 1]))[:]
if abs(s[2]) > 1e-5:
# subtract the id to have the result in displacement coordinates
vf[i, j, 0, 0, :] = (s[0:2] / float(s[2])) - np.array([i, j])
return vf
elif d == 3:
vf = gen_id.id_lagrangian(omega)
x_intervals, y_intervals, z_intervals = omega
for i in range(x_intervals):
for j in range(y_intervals):
for k in range(z_intervals):
s = input_h.dot(np.array([i, j, k, 1]))[:]
if abs(s[3]) > 1e-5:
vf[i, j, k, 0, :] = (s[0:3] / float(s[3])) - np.array([i, j, k])
return vf
else:
raise IOError("structure can be only 'algebra' or 'group' corresponding to the algebraic structure.")
