oblique_torch

oblique_torch#

CLASS oblique_torch(var_shape, device = torch.device('cpu'), dtype = torch.float64)

This manifold class defines the oblique manifold i.e.

\[ \{X \in \mathbb{R}^{n_1\times n_2\times \cdots n_k \times p}: \sum_i X_{n_1,...n_k,i}^2 = 1, \text{ for any} n_1,...,n_k \}. \]

Parameters:#

  • var_shape ( tuple of ints ) – The shape of the variables of the manifold. Its length must be no smaller than 2.

  • device (PyTorch device) – The object representing the device on which a torch.Tensor is or will be allocated.

  • dtype (PyTorch dtype) – The object that represents the data type of a torch.Tensor.

Attributes:#

A(x) (callable)

The constraint dissolving mapping \(\mathcal{A}(x)\). A(X) is set as (2*X)/( 1 + torch.sum( X * X, 1 )[:, None] ).

C(X) (callable)

Describe the constraints \(c\). C(X) returns torch.sum( X * X, 1 )[:, None] - 1.

_parameter() (OrdDict)

The ordered dictionary that contains all the variables that changes when device and dtype changes.

m2v(x) (callable)

Flatten the variable of the manifold.

v2m(x) (callable)

Recover flattened variables to its original shape as variable_shape.

Init_point(Xinit = None) (callable)

Generate the initial point.

tensor2array(x) (callable)

Transfer the variable of the manifold to the numpy Nd-array while keep its shape. Default settings are provided in the core.backbone_torch.

array2tensor(x) (callable)

Transfer the numpy Nd-array to the variable of the manifold while keep its shape. Default settings are provided in the core.backbone_torch.

JC(x, lambda) (callable)

The Jacobian of C(x).

JC_transpose(x, lambda) (callable)

The transpose of \(J_c(x)\), expressed by matrix-vector production.

JA(x, d) (callable)

The transposed Jacobian of \(\mathcal{A}(x)\).

JA_transpose(x, d) (callable)

The transpose (or adjoint) of JA(x), i.e. \(\lim_{t \to 0} \frac{1}{t}(J_A(x+td) -J_A(x)) \).

C_quad_penalty(x) (callable)

Returns the quadratical penalty term \(||c(x)||^2\).

hessA(X, U, D) (callable)

Returns the Hessian of \(\mathcal{A}(x)\) in a tensor-vector product form.

hess_feas(X, D) (callable)

Returns the hessian-vector product of \(\frac{1}{2} ||c(x)||^2\).

Feas_eval(X) (callable)

Returns the feasibility of \(x\), measured by value of \(||c(x)||\).

Post_process(X) (callable)

Return the post-processing for X to achieve a point with better feasibility.

generate_cdf_fun(obj_fun, beta) (callable)

Return the function value of the constraint dissolving function. obj_fun is a callable function that returns the value of \(f\) at \(x\). beta is a float object that refers to the penalty parameter in the constraint dissolving function.

generate_cdf_grad(obj_grad, beta) (callable)

Return the gradient of the constraint dissolving function. obj_grad is a callable function that returns the gradient of \(f\) at \(x\). beta is a float object that refers to the penalty parameter in the constraint dissolving function.

generate_cdf_hess(obj_grad, obj_hvp, beta) (callable)

Return the hessian of the constraint dissolving function. obj_grad is a callable function that returns the gradient of \(f\) at \(x\). obj_hvp is the hessian-vector product of \(f\) at \(x\), i.e., \(\nabla^2 h(x)[d]\). beta is a float object that refers to the penalty parameter in the constraint dissolving function.

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