ts-quantum/dist/quantum/src/utils/math.d.ts

TypeScript library for quantum mechanics calculations and utilities

/**
 * Math utilities for quantum operations
 */
import { Complex } from '../core/types';
/**
 * Computes log(n!) avoiding overflow using summation of logs
 * Uses caching for efficiency
 *
 * @param n Input number (must be non-negative integer)
 * @returns log(n!)
 */
export declare function logFactorial(n: number): number;
/**
 * Computes n! using cached log factorial
 *
 * @param n Input number (must be non-negative integer)
 * @returns n!
 */
export declare function factorial(n: number): number;
/**
 * Computes double factorial n!! = n * (n-2) * (n-4) * ...
 * Uses caching for efficiency
 *
 * @param n Input number (must be non-negative integer)
 * @returns n!!
 */
export declare function doubleFactorial(n: number): number;
/**
 * Computes Legendre polynomial P_n(x) using recursion
 *
 * @param n Degree of polynomial (must be non-negative integer)
 * @param x Argument (-1 <= x <= 1)
 * @returns P_n(x)
 */
/**
 * Calculates triangle coefficient for three angular momenta
 * Delta(a,b,c) = sqrt((a+b-c)!(a-b+c)!(-a+b+c)!/(a+b+c+1)!)
 *
 * @param a First angular momentum
 * @param b Second angular momentum
 * @param c Third angular momentum
 * @returns Triangle coefficient
 */
export declare function triangleCoefficient(a: number, b: number, c: number): number;
/**
 * Computes Legendre polynomial P_n(x) using recursion
 *
 * @param n Degree of polynomial (must be non-negative integer)
 * @param x Argument (-1 <= x <= 1)
 * @returns P_n(x)
 */
export declare function legendrePolynomial(n: number, x: number): number;
/**
 * Computes matrix exponential using Taylor series
 */
export declare function matrixExponential(matrix: Complex[][], terms?: number): Complex[][];
/**
 * Multiplies two complex matrices
 */
export declare function multiplyMatrices(a: Complex[][], b: Complex[][]): Complex[][];
/**
 * Computes the singular value decomposition of a matrix
 * Note: This is a placeholder for a proper SVD implementation
 */
export declare function singularValueDecomposition(matrix: Complex[][]): {
    U: Complex[][];
    S: number[];
    V: Complex[][];
};