def to_strictly_lower_triangular(cls, mat):
"""Make a matrix strictly lower triangular.
Make a matrix stricly lower triangular by zeroing
out upper and diagonal elements.
Parameters
----------
mat : array-like, shape=[..., n, n]
Matrix.
Returns
-------
tril : array-like, shape=[..., n, n]
Lower triangular matrix.
"""
return gs.tril(mat, k=-1)
def to_lower_triangular(cls, mat):
"""Make a matrix lower triangular.
Make a matrix lower triangular by zeroing
out upper elements.
Parameters
----------
mat : array-like, shape=[..., n, n]
Matrix.
Returns
-------
tril : array-like, shape=[..., n, n]
Lower triangular matrix.
"""
return gs.tril(mat)
def is_strictly_lower_triangular(cls, mat, atol=gs.atol):
"""Check if a matrix is strictly lower triangular.
Parameters
----------
mat : array-like, shape=[..., n, n]
Matrix.
atol : float
Absolute tolerance.
Optional, default : backend atol.
Returns
-------
is_strictly_tril : array-like, shape=[...,]
Boolean evaluating if the matrix is strictly lower triangular
"""
is_square = cls.is_square(mat)
if not is_square:
is_vectorized = gs.ndim(gs.array(mat)) == 3
return gs.array([False] * len(mat)) if is_vectorized else False
return cls.equal(mat, gs.tril(mat, k=-1), atol)
def load_connectomes(as_vectors=False):
"""Load data from brain connectomes.
Load the correlation data from the kaggle MSLP 2014 Schizophrenia
Challenge. The original data came as flattened vectors, but if `raw=True`
is passed, the correlation values are reshaped as symmetric matrices with
ones on the diagonal.
Parameters
----------
as_vectors : bool
Whether to return raw data as vectors or as symmetric matrices.
Optional, default: False
Returns
-------
mat : array-like, shape=[86, {[28, 28], 378}
Connectomes.
patient_id : array-like, shape=[86,]
Patient unique identifiers
target : array-like, shape=[86,]
Labels, whether patients belong to the diseased class (1) or control
(0).
"""
with open(CONNECTOMES_PATH) as csvfile:
data_list = list(csv.reader(csvfile))
patient_id = gs.array([int(row[0]) for row in data_list[1:]])
data = gs.array([[float(value) for value in row[1:]]
for row in data_list[1:]])
with open(CONNECTOMES_LABELS_PATH) as csvfile:
labels = list(csv.reader(csvfile))
target = gs.array([int(row[1]) for row in labels[1:]])
if as_vectors:
return data, patient_id, target
mat = SkewSymmetricMatrices(28).matrix_representation(data)
mat = gs.eye(28) - gs.transpose(gs.tril(mat), (0, 2, 1))
mat = 1.0 / 2.0 * (mat + gs.transpose(mat, (0, 2, 1)))
return mat, patient_id, target
