def display_solution(name, caption, R, S):
D = euclidean_distances(S)
sec = pub.section(name)
sec.text('info', caption)
with sec.plot('S') as pl:
pl.plot(S[0, :], S[1, :], 'k.')
if S.shape[0] == 3:
import mpl_toolkits.mplot3d.axes3d as p3
for angle in [0, 45, 90]:
with sec.plot('S3d%s' % angle) as pl:
fig = pl.gcf()
ax = p3.Axes3D(fig)
ax.view_init(30, angle)
col = S[2, :]
ax.scatter(S[0, :], S[1, :], S[2, :], c=col)
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
fig.add_axes(ax)
if False: # TODO: use cheaper solution for point cloud as in
# calib
with sec.plot('D_vs_R') as pl:
pl.plot(D.flat, R.flat, 'k.')
pl.xlabel('D')
pl.ylabel('R')
def euclidean_distances_test():
n = 5
P = np.random.rand(3, n)
D = euclidean_distances(P)
assert D.shape == (n, n)
for i, j in itertools.product(range(n), range(n)):
d = np.linalg.norm(P[:, i] - P[:, j])
assert_allclose(d, D[i, j])
def mds_test():
for n in [10, 100]:
for k in [3, 4, 5]:
P = np.random.rand(k, n)
D = euclidean_distances(P)
P2 = mds(D, ndim=k)
error = evaluate_error(P, P2)
assert_allclose(0, error, atol=1e-7)
def euclidean_distances_test():
n = 5
P = np.random.rand(3, n)
D = euclidean_distances(P)
assert D.shape == (n, n)
for i, j in itertools.product(range(n), range(n)):
d = np.linalg.norm(P[:, i] - P[:, j])
assert_allclose(d, D[i, j])
def mds_test():
for n in [10, 100]:
for k in [3, 4, 5]:
P = np.random.rand(k, n)
D = euclidean_distances(P)
P2 = mds(D, ndim=k)
error = evaluate_error(P, P2)
assert_allclose(0, error, atol=1e-7)
def rank_test():
''' Check that the double-centered matrix has small rank. '''
for n in range(5, 50, 5):
for k in range(1, 5):
P = np.random.rand(k, n)
D = euclidean_distances(P)
B = double_center(D * D)
w, v = eigh(B) #@UnusedVariable
w = w[::-1] # descending
# normalize
wn = w / w[0]
small = np.abs(wn[k])
assert_allclose(0, small, atol=1e-7)
def rank_test():
''' Check that the double-centered matrix has small rank. '''
for n in range(5, 50, 5):
for k in range(1, 5):
P = np.random.rand(k, n)
D = euclidean_distances(P)
B = double_center(D * D)
w, v = eigh(B) #@UnusedVariable
w = w[::-1] # descending
# normalize
wn = w / w[0]
small = np.abs(wn[k])
assert_allclose(0, small, atol=1e-7)
def mds_fast_test():
for n in [10, 100]:
for k in [2, 3]:
P = np.random.rand(k, n)
D = euclidean_distances(P)
for algo in [mds, mds_randomized]:
# t0 = time.clock()
P2 = algo(D, ndim=k)
# t1 = time.clock()
#t_mds = t1 - t0
# D2 = euclidean_distances(P2)
error = evaluate_error(P, P2)
assert_allclose(0, error, atol=1e-7)
def mds_fast_test():
for n in [10, 100]:
for k in [2, 3]:
P = np.random.rand(k, n)
D = euclidean_distances(P)
for algo in [mds, mds_randomized]:
# t0 = time.clock()
P2 = algo(D, ndim=k)
# t1 = time.clock()
#t_mds = t1 - t0
# D2 = euclidean_distances(P2)
error = evaluate_error(P, P2)
assert_allclose(0, error, atol=1e-7)
def evaluate_error(P1, P2):
D1 = euclidean_distances(P1)
D2 = euclidean_distances(P2)
return np.abs(D1 - D2).mean()
def evaluate_error(P1, P2):
D1 = euclidean_distances(P1)
D2 = euclidean_distances(P2)
return np.abs(D1 - D2).mean()
