def inner_product_embedding(C, ndim):
n = C.shape[0]
if ndim > n:
msg = 'Number of points: %s Dimensions: %s' % (n, ndim)
raise ValueError(msg)
eigvals = (n - ndim, n - 1)
print n, eigvals
S, V = eigh(C, eigvals=eigvals)
assert S[0] <= S[1] # eigh returns in ascending order
if np.any(S < 0):
msg = 'The cosine matrix singular values are not all positive: \n'
msg += formatm('S', S)
msg += 'I assume it is rounding error and approximate with:\n'
S[S < 0] = 0
msg += formatm('S\'', S)
logger.warning(msg)
assert V.shape == (n, ndim)
assert S.shape == (ndim,)
# check_multiple([('K', ndim),
# ('array[NxK]', V),
# ('array[K]', S)])
coords = V.T
for i in range(ndim):
assert S[i] >= 0
coords[i, :] = coords[i, :] * np.sqrt(S[i])
return coords
def inner_product_embedding(C, ndim):
n = C.shape[0]
if ndim > n:
msg = 'Number of points: %s Dimensions: %s' % (n, ndim)
raise ValueError(msg)
eigvals = (n - ndim, n - 1)
print n, eigvals
S, V = eigh(C, eigvals=eigvals)
assert S[0] <= S[1] # eigh returns in ascending order
if np.any(S < 0):
msg = 'The cosine matrix singular values are not all positive: \n'
msg += formatm('S', S)
msg += 'I assume it is rounding error and approximate with:\n'
S[S < 0] = 0
msg += formatm('S\'', S)
logger.warning(msg)
assert V.shape == (n, ndim)
assert S.shape == (ndim, )
# check_multiple([('K', ndim),
# ('array[NxK]', V),
# ('array[K]', S)])
coords = V.T
for i in range(ndim):
assert S[i] >= 0
coords[i, :] = coords[i, :] * np.sqrt(S[i])
return coords
def check_logmap3(M, a, b):
d = M.distance(a, b)
base, vel = M.logmap(a, b)
ratios = [0.5, 0.3]
for ratio in ratios:
b2 = M.expmap((base, vel * ratio))
d2 = M.distance(a, b2)
msg = "Checking that distance is consistent with logmap/expmap"
msg += formatm('a', a, 'b', b, 'd', d)
msg += formatm('base', base, 'vel', vel)
msg += formatm('b2', b2)
msg += formatm('d2', d2)
check_allclose(d * ratio, d2, atol=1e-7, err_msg=msg)
def check_logmap3(M, a, b):
d = M.distance(a, b)
base, vel = M.logmap(a, b)
ratios = [0.5, 0.3]
for ratio in ratios:
b2 = M.expmap((base, vel * ratio))
d2 = M.distance(a, b2)
msg = "Checking that distance is consistent with logmap/expmap"
msg += formatm('a', a, 'b', b, 'd', d)
msg += formatm('base', base, 'vel', vel)
msg += formatm('b2', b2)
msg += formatm('d2', d2)
check_allclose(d * ratio, d2, atol=1e-7, err_msg=msg)
def expect_shape(name, vector, shape):
if vector.shape != shape:
msg = ('Expected shape %s for %r but found %s' %
(shape, name, vector.shape))
if vector.size < 100:
msg += '\n' + formatm(vector)
raise ValueError(msg)
def check_logmap1(M, a, b):
''' This is a test that:
Exp_a( Log_a(b) ) = b
'''
check_logmap1.description = ('%s: Checking that logmap/expmap work. '
'(a: %s, b: %s)' %
(M, M.friendly(a), M.friendly(b)))
bv = M.logmap(a, b)
b2 = M.expmap(bv)
msg = ""
msg += formatm('a', a, 'b', b)
msg += formatm('M.logmap(a,b) base = ', bv[0], 'vel', bv[1])
msg += formatm('b2', b2)
check_allclose(M.distance(b, b2), 0, atol=1e-7, err_msg=msg)
def check_logmap1(M, a, b):
''' This is a test that:
Exp_a( Log_a(b) ) = b
'''
check_logmap1.description = (
'%s: Checking that logmap/expmap work. '
'(a: %s, b: %s)'
% (M, M.friendly(a), M.friendly(b)))
bv = M.logmap(a, b)
b2 = M.expmap(bv)
msg = ""
msg += formatm('a', a, 'b', b)
msg += formatm('M.logmap(a,b) base = ', bv[0], 'vel', bv[1])
msg += formatm('b2', b2)
check_allclose(M.distance(b, b2), 0, atol=1e-7, err_msg=msg)
def __str__(self):
try:
s = ''
if self.context is not None:
s += '%s\n' % self.context
s += ('%s: The point does not belong here:\n%s' %
(self.M, formatm('p', self.point)))
s += self.e
return s
except Exception as e:
return "(%s) %s: %s" % (e, self.M, self.point)
def __str__(self):
try:
s = ''
if self.context is not None:
s += '%s\n' % self.context
s += ('%s: The point does not belong here:\n%s' %
(self.M, formatm('p', self.point)))
s += self.e
return s
except Exception as e:
return "(%s) %s: %s" % (e, self.M, self.point)
def assert_close(self, a, b, atol=1e-8, msg=None):
'''
Asserts that two points on the manifold are close to the given
tolerance.
'''
distance = self.distance(a, b)
if msg is None:
msg = ""
if distance > atol:
msg += "\nThe two points should be the same:\n"
msg += "- a: %s\n" % self.friendly(a)
msg += "- b: %s\n" % self.friendly(b)
msg += formatm('a', a, 'b', b)
check_allclose(distance, 0, atol=atol, err_msg=msg)
return distance