projnormal.classes.constraints

Constraints to keep the distribution parameters in a valid region.

Classes

ConstrainedSPD([diag, rank, fixed_diag])	Constrain matrix \(M\) to be \(M = d \cdot I_n + W\), where \(d>0\) is a scalar, \(I_n\) is the identity matrix, and \(W\) is a symmetric positive semi-definite matrix of rank at most k.
Diagonal(*args, **kwargs)	Diagonal matrix with positive diagonal entries.
Isotropic([n_dim])	Constrain matrix to be \(M = \lambda \cdot I_n\), where \(\lambda>0\) and \(I_n\) is the identity matrix.
Positive(*args, **kwargs)	Positive value constraint.
PositiveOffset([offset])	Positive and larger than offset value constraint.
Sphere(*args, **kwargs)	Unit norm constraint.

class ConstrainedSPD(diag=1.0, rank=1, fixed_diag=False)

Bases: Module

Constrain matrix \(M\) to be \(M = d \cdot I_n + W\), where \(d>0\) is a scalar, \(I_n\) is the identity matrix, and \(W\) is a symmetric positive semi-definite matrix of rank at most k.

forward(vecs)

Generate a constrained SPD matrix as eye + vecs @ vecs.T.

Parameters:

vecs (torch.Tensor (n_dim, rank).) – Input vectors in euclidean space.

Returns:

Constrained SPD matrix.

Return type:

torch.Tensor (n_dim, n_dim).

right_inverse(M)

Initialize the vectors to a set of k random vectors.

class Diagonal(*args, **kwargs)

Bases: Module

Diagonal matrix with positive diagonal entries.

forward(diagonal)

Transform the input vector into matrix.

Parameters:

diagonal (torch.Tensor (n_dim,).) – Input vector in the real line.

Returns:

Diagonal matrix with positive diagonal of shape

Return type:

torch.Tensor (n_dim, n_dim).

right_inverse(M)

Assign as diagonal vector the diagonal entries of M.

Parameters:

M (torch.Tensor) – Input matrix. Must have positive diagonal entries.

Returns:

Vector with diagonal entries of M.

Return type:

torch.Tensor (n_dim,).

class Isotropic(n_dim=None)

Bases: Module

Constrain matrix to be \(M = \lambda \cdot I_n\), where \(\lambda>0\) and \(I_n\) is the identity matrix.

forward(val)

Transform the input number into an isotropic matrix.

Parameters:

val (torch.Tensor, shape (1,).) – Input number in the real line.

Returns:

Isotropic matrix with positive diagonal

Return type:

torch.Tensor, shape (n_dim, n_dim)

right_inverse(M)

Assign as val tr(M)/n_dim.

Parameters:

M (torch.Tensor, shape (n_dim, n_dim).) – Input isotropic matrix.

Returns:

Scalar value.

Return type:

torch.Tensor, shape (1,).

class Positive(*args, **kwargs)

Bases: Module

Positive value constraint.

forward(X)

Transform the input tensor to a positive number.

Parameters:

X (torch.Tensor, shape (...)) – Input vector in the real line

Returns:

Positive vector.

Return type:

torch.Tensor, shape (…)

right_inverse(P)

Inverse of the function to convert positive number to scalar.

Parameters:

P (torch.Tensor, shape (...)) – Input positive vector

Returns:

Scalar

Return type:

torch.Tensor, shape (…)

class PositiveOffset(offset=1.0)

Bases: Module

Positive and larger than offset value constraint.

forward(X)

Transform the input tensor to a positive number.

Parameters:

X (torch.Tensor, shape (...)) – Input number in the real line

Returns:

Positive number

Return type:

torch.Tensor, shape (…)

right_inverse(P)

Inverse of the function to convert positive number to scalar.

Parameters:

P (torch.Tensor, shape (...)) – Input positive number

Returns:

Real number

Return type:

torch.Tensor, shape (…)

class Sphere(*args, **kwargs)

Bases: Module

Unit norm constraint.

forward(X)

Normalize the input tensor so that it lies on the sphere.

Parameters:

X (torch.Tensor, shape (..., n_dim)) – Input tensor in Euclidean space.

Returns:

Normalized tensor lying on the sphere with shape.

Return type:

torch.Tensor, shape (…, n_dim)

right_inverse(S)

Identity function to assign to parametrization.

Parameters:

S (torch.Tensor, shape (..., n_dim)) – Input tensor. Should be different from zero.

Returns:

Returns the input tensor S.

Return type:

torch.Tensor, shape (…, n_dim)