Struct LinearSystemSolver 

pub struct LinearSystemSolver;

Linear system of ODEs solver

Solves systems dx/dt = Ax where A is a constant coefficient matrix.

Implementations

impl LinearSystemSolver

pub fn solve( &self, coefficient_matrix: &Matrix, independent_var: &Symbol, initial_conditions: Option<Vec<Expression>>, ) -> Result<Vec<Expression>, ODEError>

Solve linear system dx/dt = Ax

Uses eigenvalue-eigenvector method. For an n×n system:

• Compute eigenvalues λ₁, λ₂, …, λₙ and eigenvectors v₁, v₂, …, vₙ
• General solution: x(t) = c₁e^(λ₁t)v₁ + c₂e^(λ₂t)v₂ + … + cₙe^(λₙt)vₙ

Complexity

• Time: O(n³) for eigenvalue decomposition of n×n matrix
• Space: O(n²) for storing eigenvectors and intermediate results

Arguments

• coefficient_matrix - The constant coefficient matrix A
• independent_var - The independent variable (typically t)
• initial_conditions - Optional initial state vector x(t₀) = x₀

Returns

Vector of expressions representing the solution [x₁(t), x₂(t), …, xₙ(t)]

Examples

use mathhook_core::calculus::ode::systems::LinearSystemSolver;
use mathhook_core::matrices::Matrix;
use mathhook_core::{symbol, expr};

let t = symbol!(t);

// 2×2 system: dx/dt = [1 0; 0 2]x
let matrix = Matrix::diagonal(vec![expr!(1), expr!(2)]);

let solver = LinearSystemSolver;
let solution = solver.solve(&matrix, &t, None);

pub fn solve_2x2( &self, a11: &Expression, a12: &Expression, a21: &Expression, a22: &Expression, independent_var: &Symbol, ) -> Result<Vec<Expression>, ODEError>

Solve 2×2 linear system dx/dt = Ax

Specialized solver for 2×2 systems with explicit formulas.

Complexity

• Time: O(1) for 2×2 eigenvalue computation (quadratic formula)
• Space: O(1) for storing solution components

Arguments

• a11, a12, a21, a22 - Matrix coefficients [a11 a12; a21 a22]
• independent_var - The independent variable (typically t)

Returns

Vector [x₁(t), x₂(t)] representing the solution

Examples

use mathhook_core::calculus::ode::systems::LinearSystemSolver;
use mathhook_core::{symbol, expr};

let t = symbol!(t);

// dx/dt = [1 0; 0 2]x
let solver = LinearSystemSolver;
let solution = solver.solve_2x2(
    &expr!(1), &expr!(0),
    &expr!(0), &expr!(2),
    &t
);

pub fn solve_3x3( &self, matrix_entries: &[Expression; 9], independent_var: &Symbol, ) -> Result<Vec<Expression>, ODEError>

Solve 3×3 linear system dx/dt = Ax

Specialized solver for 3×3 systems.

Complexity

• Time: O(1) for 3×3 eigenvalue computation (cubic formula)
• Space: O(1) for storing solution components

Arguments

• matrix_entries - Flattened 3×3 matrix entries [a11, a12, a13, a21, a22, a23, a31, a32, a33]
• independent_var - The independent variable (typically t)

Returns

Vector [x₁(t), x₂(t), x₃(t)] representing the solution

Examples

use mathhook_core::calculus::ode::systems::LinearSystemSolver;
use mathhook_core::{symbol, expr};

let t = symbol!(t);

// dx/dt = [1 0 0; 0 2 0; 0 0 3]x (diagonal)
let solver = LinearSystemSolver;
let solution = solver.solve_3x3(
    &[expr!(1), expr!(0), expr!(0),
      expr!(0), expr!(2), expr!(0),
      expr!(0), expr!(0), expr!(3)],
    &t
);