def test_one_dimensional_line_integral_maker():
cuboid_coordinates = {
'x1': -1.5,
'x2': 1.5,
'y1': -1.5,
'y2': 1.5,
'z1': -1.5,
'z2': 1.5
}
steps = 3
points_cuboid = np.array([[[1, 6, 5], [4, 13, 19], [2.5, 7.3, 2.1]],
[[1.5, 60, 51], [32, 16, 19], [1.1, 1.3, 1.6]],
[[21, 0.9, 2.9], [1.6, 11.1, 0.2], [2.8, 4.4,
7]]])
x_cor, y_cor, z_cor = coordinate_discretization(cuboid_coordinates, steps)
dist = distance_creater(x_cor, y_cor, z_cor, steps)
dist_fru = dist_array_maker(dist)
integral_array = one_dimensional_line_integral_maker(
dist, dist_fru, points_cuboid)
integral_array_c = np.array([16, 136.4, 98.6, 44.3])
np.testing.assert_array_almost_equal(integral_array, integral_array_c)
def td_to_od_nonsymmetric(td, steps, cuboid_coordinates):
"""sums up all the values with the same distance"""
x_cor, y_cor, z_cor = coordinate_discretization(cuboid_coordinates, steps)
dist = distance_creater(x_cor, y_cor, z_cor, steps)
dist_fru = dist_array_maker(dist)
integral_array = np.zeros(dist_fru.size)
# need to round since we did it in the dist_array_maker
dist_r = np.round(dist, 6)
for i, j in enumerate(dist_fru):
d = (dist_r == j) * td
integral_array[i] = np.sum(d)
return integral_array
def compare_values_original_function(cuboid_coordinates, steps, inner_of_box):
"""
creates an array of the original value of the inner_of_box function for
comparisson
"""
x_cor, y_cor, z_cor = coordinate_discretization(cuboid_coordinates, steps)
dist = distance_creater(x_cor, y_cor, z_cor, steps)
dist_fru = dist_array_maker(dist)
compare_values = np.zeros(dist_fru.size)
for i in range(len(compare_values)):
compare_values[i] = inner_of_box(dist_fru[i], 0, 0)
return compare_values
def threed_to_oned(values, cuboid_coordinates, steps):
"""takes symmetric 3d value array and creates 1d array from it
this function was completly reworked in commit 53, 20.04.20
"""
x_cor, y_cor, z_cor = coordinate_discretization(cuboid_coordinates, steps)
dist = distance_creater(x_cor, y_cor, z_cor, steps)
dist_fru = dist_array_maker(dist)
values_oned = 0 * dist_fru
for j, i in enumerate(dist_fru):
x, y, z = np.where(np.round(dist, 6) == i)
values_oned[j] = values[x[0], y[0], z[0]]
return values_oned
def make_threed_back(array_oned, steps, cuboid_coordinates):
"""
create the 3D matrix again from the 1D array.
"""
x_cor, y_cor, z_cor = coordinate_discretization(cuboid_coordinates, steps)
dist = np.round(distance_creater(x_cor, y_cor, z_cor, steps), 6)
dist_fru = dist_array_maker(dist)
model_threed = np.zeros((steps, steps, steps))
for i in range(len(dist_fru)):
model_threed += (dist == dist_fru[i]) * array_oned[i]
return model_threed
def test_dist_array_maker():
cuboid_coordinates = {
'x1': -1.5,
'x2': 1.5,
'y1': -1.5,
'y2': 1.5,
'z1': -1.5,
'z2': 1.5
}
steps = 3
x_cor, y_cor, z_cor = coordinate_discretization(cuboid_coordinates, steps)
dist = distance_creater(x_cor, y_cor, z_cor, steps)
dist_fru = dist_array_maker(dist)
dist_fru_c = np.array([0, 1, np.sqrt(2), np.sqrt(3)])
np.testing.assert_array_almost_equal(dist_fru, dist_fru_c)
def test_dist_array_maker_2():
cuboid_coordinates2 = {
'x1': -2,
'x2': 2,
'y1': -2,
'y2': 2,
'z1': -2,
'z2': 2
}
steps2 = 4
x_cor2, y_cor2, z_cor2 = coordinate_discretization(cuboid_coordinates2,
steps2)
dist2 = distance_creater(x_cor2, y_cor2, z_cor2, steps2)
dist_fru2 = dist_array_maker(dist2)
dist_fru_c2 = np.array(
[np.sqrt(0.75),
np.sqrt(2.75),
np.sqrt(4.75),
np.sqrt(6.75)])
np.testing.assert_array_almost_equal(dist_fru2, dist_fru_c2)
def z_step(x, y, z):
z = z + y - x
return z
steps = 5
cuboid_coordinates = {'x1': -1, 'x2': 1, 'y1': -1, 'y2': 1, 'z1': -1, 'z2': 1}
x_cor, y_cor, z_cor = coordinate_discretization(cuboid_coordinates, steps)
dist = distance_creater(x_cor, y_cor, z_cor, steps)
dist_array = dist_array_maker(dist)
dist_count_array = count_edges_for_reg(dist, dist_array)
different_lengths = len(dist_array)
number_ktrans = int(different_lengths * 10)
number_rays = {'dim_1': 5, 'dim_2': 5}
fineness = 10**3
radii = np.linspace(
2, 30, different_lengths) #[2.1, 2.3, 2.5, 2.7, 2.9, 3.1, 3.3, 3.5]
start_index = [i * int(number_ktrans / len(radii)) for i in range(len(radii))]
end_index = [
i * int(number_ktrans / len(radii)) for i in range(1,
len(radii) + 1)
def reconstruction(steps, alpha, letter="a"):
cuboid_coordinates = {
'x1': -1,
'x2': 1,
'y1': -1,
'y2': 1,
'z1': -1,
'z2': 1
}
x_cor, y_cor, z_cor = coordinate_discretization(cuboid_coordinates, steps)
dist = distance_creater(x_cor, y_cor, z_cor, steps)
dist_array = dist_array_maker(dist)
different_lengths = len(dist_array)
number_ktrans = int(different_lengths * 10)
number_rays = {'dim_1': 9, 'dim_2': 9}
fineness = 10**3
radii = np.linspace(
2, 30, different_lengths) #[2.1, 2.3, 2.5, 2.7, 2.9, 3.1, 3.3, 3.5]
start_index = [
i * int(number_ktrans / len(radii)) for i in range(len(radii))
]
end_index = [
i * int(number_ktrans / len(radii)) for i in range(1,
len(radii) + 1)
]
source_point_d = {}
################################################################################
for i, r in enumerate(radii):
new_source_points = create_source_point_d(r,
end_index[i],
perc_circle=0.125,
start_index=start_index[i])
source_point_d.update(new_source_points)
number_ktrans = len(source_point_d)
print("1/8")
rays_d = generate_rays_d(source_point_d, cuboid_coordinates, number_rays)
print("2/8")
if True:
liam_all = generate_all_line_integral_array_matrix(
rays_d, cuboid_coordinates, steps, fineness)
np.save("liam_all", liam_all)
print("3/8")
if True:
cont_results = create_con_results(rays_d, inner_of_box, fineness)
np.save("cont_results", cont_results)
print("4/8")
#compare_values = compare_values_original_function(cuboid_coordinates, steps, inner_of_box)
print("5/8")
x_cor, y_cor, z_cor = coordinate_discretization(cuboid_coordinates, steps)
print("6/8")
values = discretization_of_model(x_cor, y_cor, z_cor, inner_of_box, steps)
print("7/8")
x = np.ones(different_lengths)
y = np.ones(different_lengths)
z = np.ones(different_lengths)
alpha_not_normed = alpha
alpha /= x.size
gamma = 1
perc_noise = 0.01
cont_results = np.load("cont_results.npy")
liam_all = np.load("liam_all.npy")
print("8/8")
v1d = threed_to_oned(values, cuboid_coordinates, steps)
cont_results_noise = cont_results + perc_noise * np.max(
cont_results) * 2 * (np.random.random(number_ktrans) - 0.5)
################################################################################
####################### Make wD data for comparing##############################
################################################################################
x_comp = np.arange(-1, 1, 0.01)
y_comp = np.arange(-1, 1, 0.01)
cont = np.zeros((x_comp.size, y_comp.size))
for i in range(x_comp.size):
for j in range(y_comp.size):
cont[i, j] = inner_of_box(x_comp[i], y_comp[j], 0)
################################################################################
for i in range(5000):
x_old, y_old, z_old = x, y, z
x = x_step(x, y, z, alpha, gamma)
y = y_step(x, z, y, gamma, liam_all, cont_results_noise)
z = z_step(x, y, z)
tv_reg_value = get_tv(y)
f = open(
"logbook" + "-" + str(steps) + "-" + letter + "-" +
str(alpha_not_normed) + ".txt", "a+")
f.write(str(i).ljust(8) + str(tv_reg_value).ljust(20) + str(y) + "\n")
print(i, "--------", np.linalg.norm(y - y_old))
if i % 100 == 0:
results3d = make_threed_back(x, steps, cuboid_coordinates)
fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(7, 3.5))
ax[0].imshow(cont, vmin=0, vmax=1.2)
ax[0].axis(False)
ax[1].imshow(results3d[int(steps / 2)], vmin=0, vmax=1.2)
ax[1].axis(False)
plt.savefig(letter + "-" + str(steps) + "-" +
str(alpha_not_normed) + "-" + str(i) + ".png")
plt.close()
def reconstruction(steps, alpha, perc_noise, obj):
cuboid_coordinates = {'x1': -1, 'x2': 1, 'y1': -1, 'y2': 1, 'z1': -1, 'z2': 1}
x_cor, y_cor, z_cor = coordinate_discretization(cuboid_coordinates, steps)
dist = distance_creater(x_cor, y_cor, z_cor, steps)
dist_array = dist_array_maker(dist)
different_lengths = len(dist_array)
number_ktrans = int(different_lengths*10)
number_rays = {'dim_1': 15, 'dim_2': 15}
fineness = 10**3
radii = np.linspace(2,30, different_lengths) #[2.1, 2.3, 2.5, 2.7, 2.9, 3.1, 3.3, 3.5]
start_index = [i * int(number_ktrans / len(radii)) for i in range(len(radii))]
end_index = [i * int(number_ktrans / len(radii)) for i in range(1, len(radii) + 1)]
source_point_d = {}
################################################################################
for i, r in enumerate(radii):
new_source_points = create_source_point_d(r, end_index[i], perc_circle=0.125, start_index=start_index[i])
source_point_d.update(new_source_points)
number_ktrans = len(source_point_d)
print("1/8")
rays_d = generate_rays_d(source_point_d, cuboid_coordinates, number_rays)
print("2/8")
if True:
liam_all = generate_all_line_integral_array_matrix(rays_d, cuboid_coordinates, steps, fineness)
np.save("liam_all", liam_all)
print("3/8")
if True:
if obj == 1:
cont_results = create_con_results(rays_d, inner_of_box_1, fineness)
if obj == 2:
cont_results = create_con_results(rays_d, inner_of_box_2, fineness)
if obj == 3:
cont_results = create_con_results(rays_d, inner_of_box_3, fineness)
np.save("cont_results", cont_results)
print("4/8")
#compare_values = compare_values_original_function(cuboid_coordinates, steps, inner_of_box)
print("5/8")
x_cor, y_cor, z_cor = coordinate_discretization(cuboid_coordinates, steps)
print("6/8")
if obj == 1:
values = discretization_of_model(x_cor, y_cor, z_cor, inner_of_box_1, steps)
if obj == 2:
values = discretization_of_model(x_cor, y_cor, z_cor, inner_of_box_2, steps)
if obj == 3:
values = discretization_of_model(x_cor, y_cor, z_cor, inner_of_box_3, steps)
print("7/8")
x = np.ones(different_lengths)
y = np.ones(different_lengths)
z = np.ones(different_lengths)
alpha_not_normed = alpha
alpha /= x.size
gamma = 1
#perc_noise = 0.01
cont_results = np.load("cont_results.npy")
liam_all = np.load("liam_all.npy")
print("8/8")
v1d = threed_to_oned(values, cuboid_coordinates, steps)
cont_results_noise = cont_results + perc_noise * np.max(cont_results) * 2 * (np.random.random(number_ktrans) - 0.5)
################################################################################
####################### Make wD data for comparing##############################
################################################################################
x_comp = np.arange(-1, 1, 0.01)
y_comp = np.arange(-1, 1, 0.01)
cont = np.zeros((x_comp.size, y_comp.size))
for i in range(x_comp.size):
for j in range(y_comp.size):
if obj == 1:
cont[i,j] = inner_of_box_1(x_comp[i], y_comp[j], 0)
if obj == 2:
cont[i,j] = inner_of_box_2(x_comp[i], y_comp[j], 0)
if obj == 3:
cont[i,j] = inner_of_box_3(x_comp[i], y_comp[j], 0)
################################################################################
f = open("logbook" + "-" + str(steps) + "-" + str(perc_noise) + "-" + str(alpha_not_normed) + ".txt", "a+")
f.write("discretization" + " , " + "perc_noise" + " , " + "alpha_not_normed" + ", " +
"step"+ " , " + "tv_reg_value" + " , " + "y" + " , " + "x" + "\n" )
for i in range(5001):
x_old, y_old, z_old = x, y, z
x = x_step(x, y, z, alpha, gamma)
y = y_step(x, z, y, gamma, liam_all, cont_results_noise)
z = z_step(x, y, z)
tv_reg_value = get_tv(y)
f.write(str(steps) + " , " + str(perc_noise) + " , " + str(alpha_not_normed) + ", " +
str(i)+ " , " + str(tv_reg_value) + " , " + str(y) + " , " + str(x) + "\n" )
print(i, "--------", np.linalg.norm(y - y_old))
def run_example(steps, lamb):
""" runs a full reconstruction"""
cuboid_coordinates = {'x1': -1, 'x2': 1, 'y1': -1, 'y2': 1, 'z1': -1, 'z2': 1}
x_cor, y_cor, z_cor = coordinate_discretization(cuboid_coordinates, steps)
dist = distance_creater(x_cor, y_cor, z_cor, steps)
dist_array = dist_array_maker(dist)
different_lengths = len(dist_array)
number_ktrans = different_lengths * 2
number_rays = {'dim_1': 7, 'dim_2': 7}
fineness = 10**3
radius = 3
################################################################################
source_point_d = create_source_point_d(radius, number_ktrans, perc_circle=0.125)
print("1/8")
rays_d = generate_rays_d(source_point_d, cuboid_coordinates, number_rays)
print("2/8")
liam_all = generate_all_line_integral_array_matrix(rays_d, cuboid_coordinates, steps, fineness)
np.save("liam_all", liam_all)
#liam_all = np.load("liam_all.npy")
print("3/8")
cont_results = create_con_results(rays_d, inner_of_box, fineness)
np.save("cont_results", cont_results)
# cont_results = np.load("cont_results.npy")
print("4/8")
compare_values = compare_values_original_function(cuboid_coordinates, steps, inner_of_box)
print("5/8")
x_cor, y_cor, z_cor = coordinate_discretization(cuboid_coordinates, steps)
print("6/8")
values = discretization_of_model(x_cor, y_cor, z_cor, inner_of_box, steps)
print("7/8")
# discrete_model = discretization_of_model(x_cor, y_cor, z_cor, inner_of_box, steps)
# one_d_model = threed_to_oned(discrete_model, cuboid_coordinates, steps)
# dis_results = k_trafo_one_dim_all(liam_all, one_d_model)
#cont_results = dis_results
#np.save("cont_results", cont_results)
perc_noise = 0.0
# rho = 0.001
rho = 2*lamb
cont_results_noise = (np.load("cont_results.npy") +
2 * perc_noise * (np.random.random(number_ktrans) - 0.5))
v1d = threed_to_oned(values, cuboid_coordinates, steps)
################################################################################
u = np.zeros(different_lengths)
letter = "z"
if lamb == 0.01:
letter = "a"
if lamb == 0.05:
letter = "b"
if lamb == 0.1:
letter = "c"
if lamb == 0.2:
letter = "d"
if lamb == 0.3:
letter = "e"
if lamb == 0.5:
letter = "f"
if lamb == 1.0:
letter = "g"
for i in range(1001):
print(str(i) + "/ 1000")
################################################################################
######################### U STEP #############################################
################################################################################
if i > 0:
x = tv_denoising_algorithm(v.x, lamb )
################################################################################
######################### V STEP #############################################
################################################################################
v = scipy.optimize.minimize(
v_step_function,
u,
args = (liam_all,
cont_results_noise,
steps,
cuboid_coordinates,
rho,
u),
method = 'L-BFGS-B',
bounds = scipy.optimize.Bounds(0,1),
options = {'disp': False,
'maxcor': 10,
'ftol': 10**-20,
'gtol': 10**-20,
'eps': 10**-8, # if to high stops fast
'maxiter': 10**7,
'maxls': 100,
'maxfun': 10**7})
old_solution = v.x
tv_reg_value = get_tv(v.x)
f = open("logbook" + "-" + str(steps) + "-" + letter + "-" + str(lamb) + ".txt", "a+")
f.write(str(i).ljust(8) + str(tv_reg_value).ljust(20) + str(v.x) + "\n" )
if i % 50 == 0:
plt.plot(v1d, "-o")
plt.plot(v.x, "-o")
plt.savefig(str(steps) + "-" + letter + "-" + str(lamb) + "-" + str(i) + ".png")
plt.close()