def test_ilr():
"""Test ilr transformations."""
# Given
data = np.random.random([2, 3])
# When
data = coda.closure(data)
output_1 = coda.ilr_transformation(data)
output_2 = coda.inverse_ilr_transformation(output_1)
# Then
assert output_2 == pytest.approx(data)
# Plot related operations
p_mask = mask.reshape(dims[0] * dims[1] * dims[2])
p_comp = comp[p_mask > 0]
# Centering
center = tet.sample_center(p_comp)
# center = np.array([[ 0.06521165, 0.66942364, 0.26536471]]) # 0 noise center
print "Sample center: " + str(center)
c_temp = np.ones(p_comp.shape) * center
p_comp = tet.perturb(p_comp, c_temp**-1)
# Standardize
totvar = tet.sample_total_variance(p_comp, center)
p_comp = tet.power(p_comp, np.power(totvar, -1. / 2.))
# Isometric logratio transformation for plotting
ilr = tet.ilr_transformation(p_comp)
# Plot 2D histogram of ilr transformed data
plt.hist2d(
ilr[:, 0],
ilr[:, 1],
bins=2000,
norm=LogNorm(), # vmax=100,
cmap='inferno')
plt.xlabel('$v_1$')
plt.ylabel('$v_2$')
plt.axes().set_aspect('equal')
plt.axes().set_xlim([-3, 3])
plt.axes().set_ylim([-3, 3])
plt.colorbar()
# (optional) truncate and rescale
# for i in range(comp.shape[1]):
# temp = comp[:, i]
# temp = truncate_range(temp)
# temp = scale_range(temp, scale_factor=1000)
# comp[:, i] = temp
# Impute
comp[comp == 0] = 1.
# Closure
comp = coda.closure(comp)
# Isometric logratio transformation before any centering
ilr_orig = coda.ilr_transformation(np.copy(comp))
# Centering
center = coda.sample_center(comp)
print("Sample center: " + str(center))
c_temp = np.ones(comp.shape) * center
p_comp = coda.perturb(comp, c_temp**-1)
# Standardize
totvar = coda.sample_total_variance(comp, center)
comp = coda.power(comp, np.power(totvar, -1. / 2.))
# Isometric logratio transformation for plotting
ilr = coda.ilr_transformation(comp)
# Plots
fig = plt.figure()
import matplotlib.pyplot as plt
import seaborn
from compoda.core import closure, ilr_transformation
# create euclidean 3D lattice
parcels = 10
data = np.zeros([parcels**3, 3], dtype=float)
coords = np.linspace(1000, 2000, parcels)
x, y, z = np.meshgrid(coords, coords, coords)
data[:, 0] = x.flatten()
data[:, 1] = y.flatten()
data[:, 2] = z.flatten()
# isometric logratio transformation
bary = closure(np.copy(data))
ilr = ilr_transformation(bary)
# calculate intensity to demonstrate hexcone interpretation
inten = (np.max(data, axis=1) + np.min(data, axis=1)) / 2. # intensity
hexc = np.zeros(data.shape)
hexc[:, 0:2], hexc[:, 2] = ilr, inten
# Plots
fig = plt.figure()
ax_1 = plt.subplot(131, projection='3d')
ax_1.set_title('Euclidean space')
ax_1.set_aspect('equal')
ax_1.scatter(data[:, 0], data[:, 1], data[:, 2], color='k', s=3)
ax_2 = plt.subplot(132)
ax_2.scatter(ilr[:, 0], ilr[:, 1], color='k', s=3)
temp = truncate_range(temp)
temp = scale_range(temp, scale_factor=1000)
comp[:, i] = temp
# Impute
comp[comp == 0] = 1.
# Closure
comp = tet.closure(comp)
# Plot related operations
p_mask = mask.reshape(dims[0] * dims[1] * dims[2])
p_comp = comp[p_mask > 0]
# Isometric logratio transformation before any centering
ilr_orig = tet.ilr_transformation(np.copy(p_comp))
# Centering
center = tet.sample_center(p_comp)
print("Sample center: " + str(center))
c_temp = np.ones(p_comp.shape) * center
p_comp = tet.perturb(p_comp, c_temp**-1)
# Standardize
totvar = tet.sample_total_variance(p_comp, center)
p_comp = tet.power(p_comp, np.power(totvar, -1. / 2.))
# Isometric logratio transformation for plotting
ilr = tet.ilr_transformation(p_comp)
# Plots
fig = plt.figure()
data[650:660, 2] = temp[5::10]
# closure
data = tet.closure(data) # R^D
# alr
alr = tet.alr_transformation(data) # R^D to S^(D-1)
ialr = tet.inverse_alr_transformation(alr) # S^(D-1) to R^(D-1)
np.testing.assert_almost_equal(ialr, data, decimal=7, verbose=True)
# clr
clr = tet.clr_transformation(data) # R^D to S^D
iclr = tet.inverse_clr_transformation(clr) # S^D to R^D
# ilr
ilr = tet.ilr_transformation(data) # R^D to S^(D-1)
iilr = tet.inverse_ilr_transformation(ilr) # S^(D-1) to R^(D-1)
np.testing.assert_almost_equal(iilr, data, decimal=7, verbose=True)
# plots
fig = plt.figure()
ax_1 = plt.subplot(131)
ax_2 = plt.subplot(132, projection='3d')
ax_3 = plt.subplot(133)
ax_1.set_title('Additive log-ratio transformation\n(alr)')
ax_2.set_title('Centered log-ratio transformation\ntransformation(clr)')
ax_3.set_title('Isometric log-ratio transformation\ntransformation(ilr)')
ax_1.set_aspect('equal', 'datalim')
ax_2.set_aspect('equal')
ax_3.set_aspect('equal', 'datalim')
ax_1.scatter(alr[:, 0], alr[:, 1], color='red', s=2)