Struct Problem 

pub struct Problem { /* private fields */ }

Represents an instance of the optimization problem.

The problem is defined as: $$\max_{c\in\mathbb{R}, B \in \mathbb{S}^n_+} c - \lambda \text{Tr}(B) + t \log \det (B) \qquad \text{s.t. }\quad f_i - c = \Phi_i^T B \Phi_i, \:\:\forall i\in[\![1, N]\!]$$ where:

• $\lambda$ is the trace penalty,
• $t$ is the relative precision, with $t = \varepsilon / n$,
• $x_i$ are the sample points,
• $f_i$ are the function values at the sample points,
• $\Phi$ is the features matrix derived from the kernel matrix $K$,
• $K$ is the kernel matrix computed from the sample points using a specified kernel function.

In practice, $K$ only is computed first, and $\Phi$ is optionally computed later.

Implementations

impl Problem

pub fn new( lambda: f64, t: f64, x_samples: Mat<f64>, f_samples: Mat<f64>, ) -> Result<Self, ProblemError>

Creates a new problem instance from samples and parameters.

The features matrix $\Phi$ and kernel matrix $K$ are not computed at this stage.

Arguments

• lambda - Trace penalty parameter.
• t - Relative precision parameter.
• x_samples - Sample points matrix of shape (n, d).
• f_samples - Function values at the sample points of shape (n, 1).

Note: this function does not compute the kernel matrix $K$ or the features matrix $\Phi$. To compute them, please call initialize_native_kernel and compute_phi respectively.

pub fn initialize_native_kernel( &mut self, kernel: Kernel, ) -> Result<(), ProblemError>

Initializes the kernel matrix $K$ using the specified native kernel.

This method computes the kernel matrix based on the provided kernel type and its parameters, and then derives the features matrix from the Cholesky decomposition of the kernel matrix.

Arguments

• kernel - The kernel type and its associated parameter (see Kernel enum).

Errors

Returns ProblemError::KernelAlreadyInitialized if the kernel has already been initialized. Returns a faer variant of ProblemError if there is an error during the Cholesky decomposition.

pub fn compute_phi(&mut self) -> Result<(), ProblemError>

Computes the features matrix $\Phi$ from the kernel matrix $K$ using Cholesky decomposition.

This function must be called after initialize_native_kernel.

Trait Implementations

impl Clone for Problem

fn clone(&self) -> Problem

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for Problem

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.