Struct LpSensitivity 

pub struct LpSensitivity {
    pub basis: Vec<usize>,
    pub x_basic: Vec<f64>,
    pub dual: Vec<f64>,
    pub b_inv: Vec<Vec<f64>>,
}

Exact sensitivity analysis for LP in standard form.

For the LP:

min cᵀx s.t. Ax = b, x ≥ 0

at an optimal basic feasible solution with basis B (indices of basic variables), the optimal basic variable values are x_B = B⁻¹ b, and the sensitivity is:

dx_B*/dc_B = -B⁻¹ (from KKT optimality conditions) dx_B*/db = B⁻¹ (from primal feasibility) dx_N*/dc = 0 (nonbasic variables at zero)

Fields

basis: Vec<usize>

Optimal basis indices (into the original variable vector).

x_basic: Vec<f64>

Optimal basic variable values x_B = B⁻¹ b.

dual: Vec<f64>

Optimal dual variables (shadow prices): y = (B⁻¹)ᵀ c_B.

b_inv: Vec<Vec<f64>>

Inverse of the basis matrix B⁻¹.

Implementations

impl LpSensitivity

pub fn new( a: &[Vec<f64>], b_rhs: &[f64], c: &[f64], basis: Vec<usize>, ) -> OptimizeResult<Self>

Compute LP sensitivity at a given basic feasible solution.

Arguments

• a – equality constraint matrix (p×n).
• b_rhs – equality rhs (p).
• c – cost vector (n).
• basis – indices of basic variables (length p).

pub fn dl_dc(&self, n: usize, dl_dx: &[f64]) -> Vec<f64>

Compute dL/dc_B given upstream gradient dL/dx_B.

From the KKT conditions, dx_B*/dc_B = -B⁻¹, so: dL/dc_B_j = -Σ_i (B⁻¹)_{ij} * dL/dx_B_i

Arguments

• n – total number of variables.
• dl_dx – upstream gradient (length n).

pub fn dl_db(&self, dl_dx: &[f64]) -> Vec<f64>

Compute dL/db given upstream gradient dL/dx_B.

From primal feasibility, dx_B*/db = B⁻¹, so: dL/db_k = Σ_i (B⁻¹)_{ik} * dL/dx_B_i

pub fn reduced_costs(&self, a: &[Vec<f64>], c: &[f64]) -> Vec<f64>

Compute reduced costs: c_N - y A_N ≥ 0 at optimality.

Returns a vector of length n with reduced costs for all variables (0 for basic, actual reduced cost for nonbasic).

Trait Implementations

impl Clone for LpSensitivity

fn clone(&self) -> LpSensitivity

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for LpSensitivity

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

Formats the value using the given formatter.