def update(self):
check_inputs_synchronized(self)
y_dot = self.input.y_dot
y = self.input.y
u = self.input.u
T = self.T
check_multiple([
('shape(x),(array[HxW]|array[N])', y),
('shape(x),(array[HxW]|array[N])', y_dot),
('array[K]', u),
('array[Kx2xHxW]|array[Kx1xN]', T), # TODO: use references
])
K = u.size
# update covariance of gradients
gy = generalized_gradient(y)
Tgy = np.tensordot([1, 1], T * gy , axes=(0, 1))
y_dot_pred = np.tensordot(u, Tgy, axes=(0, 0))
assert y_dot_pred.ndim == 2
error = np.maximum(0, -y_dot_pred * y_dot)
# error = np.abs(np.sign(y_dot_pred) - np.sign(y_dot))
self.output.y_dot_pred = y_dot_pred
self.output.error = error
self.output.error_sensel = np.sum(error, axis=0)
def inner_product_embedding_slow(C, ndim):
U, S, V = np.linalg.svd(C, full_matrices=0)
check_multiple([('array[NxN]', U), ('array[N]', S), ('array[NxN]', V)])
coords = V[:ndim, :]
for i in range(ndim):
coords[i, :] = coords[i, :] * np.sqrt(S[i])
return coords
def test_check_multiple_1(self):
data = [[1, 2, 3],
[4, 5, 6]]
row_labels = ['first season', 'second season']
col_labels = ['Team1', 'Team2', 'Team3']
spec = [('list[C](str),C>0', col_labels),
('list[R](str),R>0', row_labels),
('list[R](list[C])', data)]
check_multiple(spec)
# now with description
check_multiple(spec,
'I expect col_labels, row_labels, data to '
'have coherent dimensions.')
data = [[1, 2, 3], [1, 2]]
spec = [('list[C](str),C>0', col_labels),
('list[R](str),R>0', row_labels),
('list[R](list[C])', data)]
self.assertRaises(ContractNotRespected, check_multiple, spec)
self.assertRaises(ContractNotRespected, check_multiple, spec,
'my message')
def inner_product_embedding_slow(C, ndim):
U, S, V = np.linalg.svd(C, full_matrices=0)
check_multiple([('array[NxN]', U),
('array[N]', S),
('array[NxN]', V)])
coords = V[:ndim, :]
for i in range(ndim):
coords[i, :] = coords[i, :] * np.sqrt(S[i])
return coords
def inner_product_embedding_randomized(C, ndim):
'''
Best embedding of inner product matrix based on
randomized projections.
'''
U, S, V = truncated_svd_randomized(C, ndim) # @UnusedVariable.
check_multiple([('K', ndim), ('array[KxN]', V), ('array[K]', S)])
coords = V
for i in range(ndim):
coords[i, :] = coords[i, :] * np.sqrt(S[i])
return coords
def inner_product_embedding_randomized(C, ndim):
'''
Best embedding of inner product matrix based on
randomized projections.
'''
U, S, V = truncated_svd_randomized(C, ndim) # @UnusedVariable.
check_multiple([('K', ndim),
('array[KxN]', V),
('array[K]', S)])
coords = V
for i in range(ndim):
coords[i, :] = coords[i, :] * np.sqrt(S[i])
return coords
def test_check_multiple_1(self):
data = [[1, 2, 3], [4, 5, 6]]
row_labels = ['first season', 'second season']
col_labels = ['Team1', 'Team2', 'Team3']
spec = [('list[C](str),C>0', col_labels),
('list[R](str),R>0', row_labels), ('list[R](list[C])', data)]
check_multiple(spec)
# now with description
check_multiple(
spec, 'I expect col_labels, row_labels, data to '
'have coherent dimensions.')
data = [[1, 2, 3], [1, 2]]
spec = [('list[C](str),C>0', col_labels),
('list[R](str),R>0', row_labels), ('list[R](list[C])', data)]
self.assertRaises(ContractNotRespected, check_multiple, spec)
self.assertRaises(ContractNotRespected, check_multiple, spec,
'my message')
def iteration(self, data):
""" Records one iteration of the algorithm """
for x in ['self']:
if x in data:
del data[x]
S = data['S']
check_multiple([('array[NxN]', self.R), ('array[*xN]', S)])
if self.is_spherical():
check('directions', S)
# Observable errors
C = cosines_from_directions(S)
C_order = scale_score(C)
data['spearman'] = correlation_coefficient(C_order, self.R_order)
valid = self.R_order > self.R.size * 0.6
data['spearman_robust'] = correlation_coefficient(C_order[valid],
self.R_order[valid])
data['diameter'] = compute_diameter(S)
data['diameter_deg'] = np.degrees(data['diameter'])
if self.is_euclidean():
D = euclidean_distances(S)
D_order = scale_score(D)
data['spearman'] = correlation_coefficient(-D_order, self.R_order)
valid = self.R_order > self.R.size * 0.6
data['spearman_robust'] = correlation_coefficient(-D_order[valid],
self.R_order[valid])
data['diameter'] = 2 * euclidean_distribution_radius(S)
data['diameter_deg'] = data['diameter']
data['robust'] = data['spearman_robust']
# These are unobservable statistics
if self.is_spherical() and self.true_S is not None:
# add more rows to S if necessary
K = S.shape[0]
if K != self.true_S.shape[0]:
newS = np.zeros(self.true_S.shape)
newS[:K, :] = S
newS[K:, :] = 0
S = newS
check('directions', S)
Rest = find_best_orthogonal_transform(S, self.true_S)
data['S_aligned'] = np.dot(Rest, S)
data['error'] = \
overlap_error_after_orthogonal_transform(S, self.true_S)
data['error_deg'] = np.degrees(data['error'])
data['rel_error'] = compute_relative_error(self.true_S, S, 10)
data['rel_error_deg'] = np.degrees(data['rel_error'])
# only valid in 2d
if K == 2:
true_angles_deg = \
np.degrees(angles_from_directions(self.true_S))
angles_deg = \
np.degrees(angles_from_directions(data['S_aligned']))
angles_deg = \
find_closest_multiple(angles_deg, true_angles_deg, 360)
data['angles_corr'] = \
correlation_coefficient(true_angles_deg, angles_deg)
D = distances_from_directions(S)
true_D = distances_from_directions(self.true_S)
scaled_rel_error, scaled_scale = scaled_error(D, true_D,
also_scale=True)
data['scaled_rel_error'] = scaled_rel_error
data['scaled_scale'] = scaled_scale
data['scaled_rel_error_deg'] = np.degrees(data['scaled_rel_error'])
if self.is_euclidean() and self.true_S is not None:
D = euclidean_distances(S)
true_D = euclidean_distances(self.true_S)
data['rel_error'] = np.abs(D - true_D).mean()
data['scaled_rel_error'], scale = scaled_error(D, true_D,
also_scale=True)
scaled_S = scale * S
def remove_mean(x):
k, n = x.shape
m = np.tile(x.mean(axis=1).reshape((k, 1)), (1, n))
assert m.shape == x.shape
return x - m
trans_scaled_S = remove_mean(scaled_S)
trans_true_S = remove_mean(self.true_S)
data['scaled_error'] = \
mean_euclidean_distance_after_orthogonal_transform(
trans_scaled_S, trans_true_S)
data['scaled_error_deg'] = np.rad2deg(data['scaled_error'])
data['error'] = \
mean_euclidean_distance_after_orthogonal_transform(
remove_mean(S), remove_mean(self.true_S))
def varstat(x, format='%.3f', #@ReservedAssignment
label=None, sign=(+1)):
if label is None:
label = x[:5]
if not x in data:
return ' %s: /' % label
current = data[x]
s = ' %s: %s' % (label, format % current)
if self.iterations:
all_previous = np.array([it[x] for it in self.iterations])
previous = all_previous[-1]
is_best = sign * current >= max(sign * all_previous)
if is_best:
mark = 'B'
else:
mark = '+' if sign * current > sign * previous else '-'
s += ' %s' % mark
return s
status = ('It: %2d' % len(self.iterations) +
varstat('diameter_deg', '%3d') +
varstat('spearman', '%.8f', label='spear') +
varstat('spearman_robust', '%.8f', label='sp_rob'))
if self.is_spherical():
status += (varstat('error_deg', '%5.3f', sign=(-1)) +
varstat('rel_error_deg', '%5.3f', sign=(-1)) +
varstat('scaled_rel_error_deg', '%5.3fd', sign=(-1),
label='s_r_err'))
if self.is_euclidean():
status += (
varstat('scaled_error', '%5.3f', sign=(-1), label='s_err') +
varstat('scaled_rel_error_deg', '%5.3fd',
sign=(-1), label='s_r_err'))
print(status)
self.iterations.append(data)
def iteration(self, data):
""" Records one iteration of the algorithm """
for x in ['self']:
if x in data:
del data[x]
S = data['S']
check_multiple([('array[NxN]', self.R), ('array[*xN]', S)])
if self.is_spherical():
check('directions', S)
# Observable errors
C = cosines_from_directions(S)
C_order = scale_score(C)
data['spearman'] = correlation_coefficient(C_order, self.R_order)
valid = self.R_order > self.R.size * 0.6
data['spearman_robust'] = correlation_coefficient(
C_order[valid], self.R_order[valid])
data['diameter'] = compute_diameter(S)
data['diameter_deg'] = np.degrees(data['diameter'])
if self.is_euclidean():
D = euclidean_distances(S)
D_order = scale_score(D)
data['spearman'] = correlation_coefficient(-D_order, self.R_order)
valid = self.R_order > self.R.size * 0.6
data['spearman_robust'] = correlation_coefficient(
-D_order[valid], self.R_order[valid])
data['diameter'] = 2 * euclidean_distribution_radius(S)
data['diameter_deg'] = data['diameter']
data['robust'] = data['spearman_robust']
# These are unobservable statistics
if self.is_spherical() and self.true_S is not None:
# add more rows to S if necessary
K = S.shape[0]
if K != self.true_S.shape[0]:
newS = np.zeros(self.true_S.shape)
newS[:K, :] = S
newS[K:, :] = 0
S = newS
check('directions', S)
Rest = find_best_orthogonal_transform(S, self.true_S)
data['S_aligned'] = np.dot(Rest, S)
data['error'] = \
overlap_error_after_orthogonal_transform(S, self.true_S)
data['error_deg'] = np.degrees(data['error'])
data['rel_error'] = compute_relative_error(self.true_S, S, 10)
data['rel_error_deg'] = np.degrees(data['rel_error'])
# only valid in 2d
if K == 2:
true_angles_deg = \
np.degrees(angles_from_directions(self.true_S))
angles_deg = \
np.degrees(angles_from_directions(data['S_aligned']))
angles_deg = \
find_closest_multiple(angles_deg, true_angles_deg, 360)
data['angles_corr'] = \
correlation_coefficient(true_angles_deg, angles_deg)
D = distances_from_directions(S)
true_D = distances_from_directions(self.true_S)
scaled_rel_error, scaled_scale = scaled_error(D,
true_D,
also_scale=True)
data['scaled_rel_error'] = scaled_rel_error
data['scaled_scale'] = scaled_scale
data['scaled_rel_error_deg'] = np.degrees(data['scaled_rel_error'])
if self.is_euclidean() and self.true_S is not None:
D = euclidean_distances(S)
true_D = euclidean_distances(self.true_S)
data['rel_error'] = np.abs(D - true_D).mean()
data['scaled_rel_error'], scale = scaled_error(D,
true_D,
also_scale=True)
scaled_S = scale * S
def remove_mean(x):
k, n = x.shape
m = np.tile(x.mean(axis=1).reshape((k, 1)), (1, n))
assert m.shape == x.shape
return x - m
trans_scaled_S = remove_mean(scaled_S)
trans_true_S = remove_mean(self.true_S)
data['scaled_error'] = \
mean_euclidean_distance_after_orthogonal_transform(
trans_scaled_S, trans_true_S)
data['scaled_error_deg'] = np.rad2deg(data['scaled_error'])
data['error'] = \
mean_euclidean_distance_after_orthogonal_transform(
remove_mean(S), remove_mean(self.true_S))
def varstat(
x,
format='%.3f', #@ReservedAssignment
label=None,
sign=(+1)):
if label is None:
label = x[:5]
if not x in data:
return ' %s: /' % label
current = data[x]
s = ' %s: %s' % (label, format % current)
if self.iterations:
all_previous = np.array([it[x] for it in self.iterations])
previous = all_previous[-1]
is_best = sign * current >= max(sign * all_previous)
if is_best:
mark = 'B'
else:
mark = '+' if sign * current > sign * previous else '-'
s += ' %s' % mark
return s
status = ('It: %2d' % len(self.iterations) +
varstat('diameter_deg', '%3d') +
varstat('spearman', '%.8f', label='spear') +
varstat('spearman_robust', '%.8f', label='sp_rob'))
if self.is_spherical():
status += (varstat('error_deg', '%5.3f', sign=(-1)) +
varstat('rel_error_deg', '%5.3f', sign=(-1)) +
varstat('scaled_rel_error_deg',
'%5.3fd',
sign=(-1),
label='s_r_err'))
if self.is_euclidean():
status += (
varstat('scaled_error', '%5.3f', sign=(-1), label='s_err') +
varstat('scaled_rel_error_deg',
'%5.3fd',
sign=(-1),
label='s_r_err'))
print(status)
self.iterations.append(data)