import * as tf from '../backend/adapter';
export interface LanczosOptions {
    /** Maximum Lanczos subspace size before restart. Default: min(max(2k+20, 4k), n, 200) */
    max_subspace_size?: number;
    max_restarts?: number;
    convergence_tol?: number;
    /** Random seed for deterministic starting vector. Default: 42 */
    random_seed?: number;
    /** Whether the matrix is PSD (clamp negative eigenvalues to 0). Default: true */
    is_psd?: boolean;
}
export interface LanczosResult {
    eigenvalues: number[];
    eigenvectors: number[][];
}
export interface LanczosOperator {
    n: number;
    matvec: (vector: Float64Array) => Float64Array;
}
/**
 * Computes the k smallest eigenpairs of a symmetric matrix using the
 * Lanczos algorithm with full reorthogonalization.
 *
 * Standard Lanczos: applies A*v directly and extracts the k smallest
 * Ritz values from the tridiagonal eigenproblem. Uses simple restart
 * (best Ritz vector as new starting point) when the subspace reaches
 * its maximum size without convergence.
 *
 * Complexity: O(n² · m) where m is the Lanczos subspace size (typically 30–100),
 * versus O(n³) for Jacobi. For n=5000, k=5, this is ~1000x faster.
 *
 * @param matrix  Symmetric n×n matrix (typically a normalized Laplacian)
 */
export declare function lanczos_smallest_eigenpairs(matrix: tf.Tensor2D | LanczosOperator, k: number, options?: LanczosOptions): LanczosResult;