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

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

/**
 * Matrix Operations Utilities
 *
 * Collection of utility functions for matrix operations commonly used in
 * mathematical optimization and portfolio analysis.
 */
/**
 * Multiply a matrix by a vector
 *
 * @param A - Matrix (m×n)
 * @param x - Vector (n×1)
 * @returns Result vector (m×1)
 *
 * @example
 * ```typescript
 * const A = [[1, 2], [3, 4]];
 * const x = [5, 6];
 * const result = matrixVectorMultiply(A, x); // [17, 39]
 * ```
 */
export declare function matrixVectorMultiply(A: number[][], x: number[]): number[];
/**
 * Calculate the transpose of a matrix
 *
 * @param A - Input matrix (m×n)
 * @returns Transpose matrix (n×m)
 *
 * @example
 * ```typescript
 * const A = [[1, 2, 3], [4, 5, 6]];
 * const At = matrixTranspose(A); // [[1, 4], [2, 5], [3, 6]]
 * ```
 */
export declare function matrixTranspose(A: number[][]): number[][];
/**
 * Multiply two matrices
 *
 * @param A - First matrix (m×k)
 * @param B - Second matrix (k×n)
 * @returns Result matrix (m×n)
 *
 * @example
 * ```typescript
 * const A = [[1, 2], [3, 4]];
 * const B = [[5, 6], [7, 8]];
 * const result = matrixMatrixMultiply(A, B); // [[19, 22], [43, 50]]
 * ```
 */
export declare function matrixMatrixMultiply(A: number[][], B: number[][]): number[][];
/**
 * Calculate the trace of a square matrix
 *
 * @param A - Square matrix (n×n)
 * @returns Trace (sum of diagonal elements)
 *
 * @example
 * ```typescript
 * const A = [[1, 2], [3, 4]];
 * const trace = matrixTrace(A); // 5
 * ```
 */
export declare function matrixTrace(A: number[][]): number;
/**
 * Check if a matrix is symmetric
 *
 * @param A - Matrix to check
 * @param tolerance - Tolerance for comparison (default: 1e-12)
 * @returns True if matrix is symmetric
 *
 * @example
 * ```typescript
 * const A = [[1, 2], [2, 3]];
 * const symmetric = isMatrixSymmetric(A); // true
 * ```
 */
export declare function isMatrixSymmetric(A: number[][], tolerance?: number): boolean;
/**
 * Check if a matrix is positive definite (simplified check)
 *
 * @param A - Square matrix to check
 * @returns True if matrix appears to be positive definite
 *
 * @example
 * ```typescript
 * const A = [[2, -1], [-1, 2]]; // Positive definite
 * const pd = isMatrixPositiveDefinite(A); // true
 * ```
 */
export declare function isMatrixPositiveDefinite(A: number[][]): boolean;
/**
 * Create an identity matrix of specified size
 *
 * @param size - Size of the identity matrix
 * @returns Identity matrix (n×n)
 *
 * @example
 * ```typescript
 * const I = createIdentityMatrix(3);
 * // [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
 * ```
 */
export declare function createIdentityMatrix(size: number): number[][];
/**
 * Create a zero matrix of specified dimensions
 *
 * @param rows - Number of rows
 * @param cols - Number of columns
 * @returns Zero matrix (m×n)
 *
 * @example
 * ```typescript
 * const Z = createZeroMatrix(2, 3);
 * // [[0, 0, 0], [0, 0, 0]]
 * ```
 */
export declare function createZeroMatrix(rows: number, cols: number): number[][];
/**
 * Extract diagonal elements from a square matrix
 *
 * @param A - Square matrix
 * @returns Array of diagonal elements
 *
 * @example
 * ```typescript
 * const A = [[1, 2, 3], [4, 5, 6], [7, 8, 9]];
 * const diag = matrixDiagonal(A); // [1, 5, 9]
 * ```
 */
export declare function matrixDiagonal(A: number[][]): number[];
/**
 * Calculate the Frobenius norm of a matrix
 *
 * @param A - Matrix
 * @returns Frobenius norm (square root of sum of squares of all elements)
 *
 * @example
 * ```typescript
 * const A = [[1, 2], [3, 4]];
 * const norm = matrixFrobeniusNorm(A); // √30 ≈ 5.477
 * ```
 */
export declare function matrixFrobeniusNorm(A: number[][]): number;