import type { array, matrix } from "../types";
/**
 * Tracking Error (ex-post).
 *
 * Ex-post tracking error, which measures the standard deviation of the difference
 * between portfolio returns and benchmark returns.
 *
 * @param x Portfolio/asset returns
 * @param y Benchmark returns
 * @param dim Dimension to operate on (0: row-wise, 1: column-wise) (defaults to 0)
 * @returns Tracking error value(s)
 * @throws If input is a number or insufficient arguments provided
 *
 * @example Single asset tracking error
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * const x = [0.003, 0.026, 0.015, -0.009, 0.014, 0.024, 0.015, 0.066, -0.014, 0.039];
 * const z = [0.04, -0.022, 0.043, 0.028, -0.078, -0.011, 0.033, -0.049, 0.09, 0.087];
 * assertEquals(trackerr(x, z), 0.06843618276256436);
 *
 * ```
 *
 * @example Different portfolio tracking error
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * const z = [0.04, -0.022, 0.043, 0.028, -0.078, -0.011, 0.033, -0.049, 0.09, 0.087];
 *
 * const y = [-0.005, 0.081, 0.04, -0.037, -0.061, 0.058, -0.049, -0.021, 0.062, 0.058];
 * assertEquals(trackerr(y, z), 0.058621668348828156);
 *
 * ```
 *
 * @example Tracking error with different assets
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(trackerr([0.05, 0.03, 0.08], [0.04, 0.025, 0.075]), 0.0028867513459481294);
 * ```
 */
export default function trackerr(x: array, y: array, dim?: 0 | 1): number;
/**
 * Tracking Error (ex-post).
 *
 * Ex-post tracking error, which measures the standard deviation of the difference
 * between portfolio returns and benchmark returns.
 *
 * @param x Portfolio/asset returns
 * @param y Benchmark returns
 * @param dim Dimension to operate on (0: row-wise, 1: column-wise) (defaults to 0)
 * @returns Tracking error value(s)
 * @throws If input is a number or insufficient arguments provided
 *
 * @example Single asset tracking error
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * const x = [0.003, 0.026, 0.015, -0.009, 0.014, 0.024, 0.015, 0.066, -0.014, 0.039];
 * const z = [0.04, -0.022, 0.043, 0.028, -0.078, -0.011, 0.033, -0.049, 0.09, 0.087];
 * assertEquals(trackerr(x, z), 0.06843618276256436);
 *
 * ```
 *
 * @example Different portfolio tracking error
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * const z = [0.04, -0.022, 0.043, 0.028, -0.078, -0.011, 0.033, -0.049, 0.09, 0.087];
 *
 * const y = [-0.005, 0.081, 0.04, -0.037, -0.061, 0.058, -0.049, -0.021, 0.062, 0.058];
 * assertEquals(trackerr(y, z), 0.058621668348828156);
 *
 * ```
 *
 * @example Tracking error with different assets
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(trackerr([0.05, 0.03, 0.08], [0.04, 0.025, 0.075]), 0.0028867513459481294);
 * ```
 */
export default function trackerr(x: matrix, y: array, dim?: 0 | 1): array | matrix;
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