@railpath/finance-toolkit/dist/utils/linearSystemSolver.d.ts

Production-ready finance library for portfolio construction, risk analytics, quantitative metrics, and ML-based regime detection

/**
 * Linear System Solver Utilities
 *
 * Collection of utility functions for solving linear systems of equations,
 * commonly used in mathematical optimization and portfolio analysis.
 */
/**
 * Solve a linear system Ax = b using Gaussian elimination with partial pivoting
 *
 * @param A - Coefficient matrix (n×n)
 * @param b - Right-hand side vector (n×1)
 * @returns Solution vector x
 *
 * @example
 * ```typescript
 * const A = [[2, 1], [1, 3]];
 * const b = [5, 8];
 * const x = solveLinearSystem(A, b); // [1, 3]
 * ```
 */
export declare function solveLinearSystem(A: number[][], b: number[]): number[];
/**
 * Solve multiple linear systems with the same coefficient matrix
 *
 * @param A - Coefficient matrix (n×n)
 * @param B - Matrix of right-hand sides (n×m)
 * @returns Matrix of solutions (n×m)
 *
 * @example
 * ```typescript
 * const A = [[2, 1], [1, 3]];
 * const B = [[5, 1], [8, 2]];
 * const X = solveMultipleLinearSystems(A, B);
 * ```
 */
export declare function solveMultipleLinearSystems(A: number[][], B: number[][]): number[][];
/**
 * Calculate the determinant of a square matrix using LU decomposition
 *
 * @param A - Square matrix (n×n)
 * @returns Determinant of the matrix
 *
 * @example
 * ```typescript
 * const A = [[2, 1], [1, 3]];
 * const det = matrixDeterminant(A); // 5
 * ```
 */
export declare function matrixDeterminant(A: number[][]): number;
/**
 * Perform LU decomposition of a matrix
 *
 * @param A - Square matrix (n×n)
 * @returns Object containing L, U matrices and permutation sign
 *
 * @example
 * ```typescript
 * const A = [[2, 1, 0], [1, 2, 1], [0, 1, 2]];
 * const { L, U, sign } = luDecomposition(A);
 * ```
 */
export declare function luDecomposition(A: number[][]): {
    L: number[][];
    U: number[][];
    sign: number;
};
/**
 * Check if a matrix is invertible (non-singular)
 *
 * @param A - Square matrix (n×n)
 * @param tolerance - Tolerance for determinant check (default: 1e-12)
 * @returns True if matrix is invertible
 *
 * @example
 * ```typescript
 * const A = [[2, 1], [1, 3]];
 * const invertible = isMatrixInvertible(A); // true
 * ```
 */
export declare function isMatrixInvertible(A: number[][], tolerance?: number): boolean;
/**
 * Calculate the condition number of a matrix (ratio of largest to smallest singular value)
 * Simplified implementation for 2x2 matrices
 *
 * @param A - Square matrix (n×n)
 * @returns Condition number
 *
 * @example
 * ```typescript
 * const A = [[2, 1], [1, 3]];
 * const cond = matrixConditionNumber(A);
 * ```
 */
export declare function matrixConditionNumber(A: number[][]): number;