Parameters:#

• var_shape (tuple of ints) – The shape of the variables of the manifold. The length of var_shape should equal to $2$.

Attributes:#

A(x) (callable)

The constraint dissolving mapping $\mathcal{A}(x)$. A(X) is set as 1.5 * X - X @ (X.T @ X /2).

C(X) (callable)

Describe the constraints $c$. C(X) returns torch.matmul(X.transpose(-2,-1), X) - self.Ip.

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_autograd.

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_autograd.

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. $\underset{t\to 0}{lim}\frac{1}{t}(J_A(x+td)-J_A(x))$.

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., ${\mathrm{\nabla }}^{2}h(x)[d]$. beta is a float object that refers to the penalty parameter in the constraint dissolving function.