def projection(self, point):
"""Make a square matrix lower triangular by zeroing out other elements.
Parameters
----------
point : array-like, shape=[..., n, n]
Matrix.
Returns
-------
sym : array-like, shape=[..., n, n]
Symmetric matrix.
"""
return Matrices.to_lower_triangular(point)
def random_point(self, n_samples=1, bound=1.0):
"""Sample a lower triangular matrix with a uniform distribution in a box.
Parameters
----------
n_samples : int
Number of samples.
Optional, default: 1.
bound : float
Side of hypercube support of the uniform distribution.
Optional, default: 1.0.
Returns
-------
point : array-like, shape=[..., n, n]
Sample.
"""
sample = super(LowerTriangularMatrices, self).random_point(n_samples, bound)
return Matrices.to_lower_triangular(sample)
def projection(self, point):
"""Project a matrix to the Cholesksy space.
First it is projected to space lower triangular matrices
and then diagonal elements are exponentiated to make it positive.
Parameters
----------
point : array-like, shape=[..., n, n]
Matrix to project.
Returns
-------
projected: array-like, shape=[..., n, n]
SPD matrix.
"""
vec_diag = gs.abs(Matrices.diagonal(point) - 0.1) + 0.1
diag = gs.vec_to_diag(vec_diag)
strictly_lower_triangular = Matrices.to_lower_triangular(point)
projection = diag + strictly_lower_triangular
return projection
