def test_fill_diagonal():
a = np.zeros((3, 3), int)
fill_diagonal(a, 5)
yield (assert_array_equal, a, np.array([[5, 0, 0], [0, 5, 0], [0, 0, 5]]))
#Test tall matrix
a = np.zeros((10, 3), int)
fill_diagonal(a, 5)
yield (assert_array_equal, a,
np.array([[5, 0, 0], [0, 5, 0], [0, 0, 5], [0, 0, 0], [0, 0, 0],
[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]))
#Test tall matrix wrap
a = np.zeros((10, 3), int)
fill_diagonal(a, 5, True)
yield (assert_array_equal, a,
np.array([[5, 0, 0], [0, 5, 0], [0, 0, 5], [0, 0, 0], [5, 0, 0],
[0, 5, 0], [0, 0, 5], [0, 0, 0], [5, 0, 0], [0, 5, 0]]))
#Test wide matrix
a = np.zeros((3, 10), int)
fill_diagonal(a, 5)
yield (assert_array_equal, a,
np.array([[5, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 5, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 5, 0, 0, 0, 0, 0, 0, 0]]))
# The same function can operate on a 4-d array:
a = np.zeros((3, 3, 3, 3), int)
fill_diagonal(a, 4)
i = np.array([0, 1, 2])
yield (assert_equal, np.where(a != 0), (i, i, i, i))
def test_tall_matrix_wrap(self):
a = np.zeros((10, 3), int)
fill_diagonal(a, 5, True)
assert_array_equal(
a,
np.array([[5, 0, 0], [0, 5, 0], [0, 0, 5], [0, 0, 0], [5, 0, 0],
[0, 5, 0], [0, 0, 5], [0, 0, 0], [5, 0, 0], [0, 5, 0]]))
def estimate_mmd(self, sample1, sample2, unbiased=False):
"""
Compute the MMD between two samples.
Parameters
----------
sample1 : array-like matrix, shape=(n_samples1, n_features)
sample2 : array-like matrix, shape=(n_samples2, n_features)
unbiased : boolean, optional
Default is False.
Returns
-------
estimated_mmd : float
"""
assert len(sample1.shape) == 2
assert len(sample2.shape) == 2
assert sample1.shape[1] == sample2.shape[1]
K11 = self.kernel(sample1, sample1)
K22 = self.kernel(sample2, sample2)
K12 = self.kernel(sample1, sample2)
if unbiased:
fill_diagonal(K11, 0.0)
fill_diagonal(K22, 0.0)
n = float(shape(K11)[0])
m = float(shape(K22)[0])
return (np.sum(K11) / (n**2 - n) + np.sum(K22) / (m**2 - m) -
2 * np.mean(K12))
else:
return np.mean(K11) + np.mean(K22) - 2 * np.mean(K12)
def test_basic(self):
a = np.zeros((3, 3), int)
fill_diagonal(a, 5)
assert_array_equal(
a, np.array([[5, 0, 0],
[0, 5, 0],
[0, 0, 5]])
)
def test_wide_matrix(self):
a = np.zeros((3, 10), int)
fill_diagonal(a, 5)
assert_array_equal(
a,
np.array([[5, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 5, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 5, 0, 0, 0, 0, 0, 0, 0]]))
def test_wide_matrix(self):
a = np.zeros((3, 10), int)
fill_diagonal(a, 5)
assert_array_equal(
a, np.array([[5, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 5, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 5, 0, 0, 0, 0, 0, 0, 0]])
)
def test_basic(self):
a = np.zeros((3, 3), int)
fill_diagonal(a, 5)
assert_array_equal(
a, np.array([[5, 0, 0],
[0, 5, 0],
[0, 0, 5]])
)
def unbiased_HSnorm_estimate_of_centred_operator(K):
'''returns an unbiased estimate of \sum_r \lambda_r^2 where \lambda_r are the
eigenvalues of the centred kernel operator'''
m = shape(K)[0]
fill_diagonal(K, 0.)
first_term = sum(K**2)
second_term = (sum(K)**2) / ((m - 1.) * (m - 2.))
third_term = -2. * sum(K.dot(K)) / (m - 2.)
return (first_term + second_term + third_term) / (m * (m - 3.))
def test_fill_diagonal():
a = np.zeros((3, 3), int)
fill_diagonal(a, 5)
yield (assert_array_equal, a,
np.array([[5, 0, 0],
[0, 5, 0],
[0, 0, 5]]))
#Test tall matrix
a = np.zeros((10, 3), int)
fill_diagonal(a, 5)
yield (assert_array_equal, a,
np.array([[5, 0, 0],
[0, 5, 0],
[0, 0, 5],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0]]))
#Test tall matrix wrap
a = np.zeros((10, 3), int)
fill_diagonal(a, 5, True)
yield (assert_array_equal, a,
np.array([[5, 0, 0],
[0, 5, 0],
[0, 0, 5],
[0, 0, 0],
[5, 0, 0],
[0, 5, 0],
[0, 0, 5],
[0, 0, 0],
[5, 0, 0],
[0, 5, 0]]))
#Test wide matrix
a = np.zeros((3, 10), int)
fill_diagonal(a, 5)
yield (assert_array_equal, a,
np.array([[5, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 5, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 5, 0, 0, 0, 0, 0, 0, 0]]))
# The same function can operate on a 4-d array:
a = np.zeros((3, 3, 3, 3), int)
fill_diagonal(a, 4)
i = np.array([0, 1, 2])
yield (assert_equal, np.where(a != 0), (i, i, i, i))
def test_tall_matrix_wrap(self):
a = np.zeros((10, 3), int)
fill_diagonal(a, 5, True)
assert_array_equal(
a, np.array([[5, 0, 0],
[0, 5, 0],
[0, 0, 5],
[0, 0, 0],
[5, 0, 0],
[0, 5, 0],
[0, 0, 5],
[0, 0, 0],
[5, 0, 0],
[0, 5, 0]])
)
def estimateMMD(self,sample1,sample2,unbiased=False):
"""
Compute the MMD between two samples
"""
K11 = self.kernel(sample1,sample1)
K22 = self.kernel(sample2,sample2)
K12 = self.kernel(sample1,sample2)
if unbiased:
fill_diagonal(K11,0.0)
fill_diagonal(K22,0.0)
n=float(shape(K11)[0])
m=float(shape(K22)[0])
return sum(sum(K11))/(pow(n,2)-n) + sum(sum(K22))/(pow(m,2)-m) - 2*mean(K12[:])
else:
return mean(K11[:])+mean(K22[:])-2*mean(K12[:])
def test_tall_matrix(self):
a = np.zeros((10, 3), int)
fill_diagonal(a, 5)
assert_array_equal(
a,
np.array([
[5, 0, 0],
[0, 5, 0],
[0, 0, 5],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
]),
)
def test_hetero_shape_handling(self):
# raise error with high dimensionality and
# shape mismatch
a = np.zeros((3, 3, 7, 3), int)
with assert_raises_regex(ValueError, "equal length"):
fill_diagonal(a, 2)
def test_low_dim_handling(self):
# raise error with low dimensionality
a = np.zeros(3, int)
with assert_raises_regex(ValueError, "at least 2-d"):
fill_diagonal(a, 5)
def test_operate_4d_array(self):
a = np.zeros((3, 3, 3, 3), int)
fill_diagonal(a, 4)
i = np.array([0, 1, 2])
assert_equal(np.where(a != 0), (i, i, i, i))
def test_low_dim_handling(self):
# raise error with low dimensionality
a = np.zeros(3, int)
with assert_raises_regex(ValueError, "at least 2-d"):
fill_diagonal(a, 5)
def test_hetero_shape_handling(self):
# raise error with high dimensionality and
# shape mismatch
a = np.zeros((3,3,7,3), int)
with assert_raises_regex(ValueError, "equal length"):
fill_diagonal(a, 2)
def test_operate_4d_array(self):
a = np.zeros((3, 3, 3, 3), int)
fill_diagonal(a, 4)
i = np.array([0, 1, 2])
assert_equal(np.where(a != 0), (i, i, i, i))