import * as tf from '../backend/adapter';
import { LanczosOperator } from './lanczos';
/**
 * Returns the `k` smallest eigenvectors AND eigenvalues of the provided symmetric matrix.
 * This is needed for spectral embedding normalization (dividing by D^{1/2}).
 *
 * Automatically selects the best eigensolver:
 * - n <= 100: Jacobi (full decomposition, proven accurate)
 * - n > 100: Lanczos (iterative, O(n²·m) vs O(n³))
 */
export declare function smallest_eigenvectors_with_values(matrix: tf.Tensor2D | LanczosOperator, k: number): {
    eigenvectors: tf.Tensor2D;
    eigenvalues: tf.Tensor1D;
};