import type { array, matrix } from "../types";
/**
 * Covariance matrix.
 *
 * Calculates the covariance matrix between arrays or matrices. For a single vector,
 * returns the variance. For two vectors, returns the 2x2 covariance matrix. For a matrix,
 * returns the covariance matrix between columns.
 *
 * @param x Input array or matrix
 * @param y Optional second input array or matrix, or flag value (0 or 1)
 * @param flag Optional Bessel's correction (0: population, 1: sample). Default is 1
 * @returns Covariance matrix or scalar variance
 * @throws When input dimensions do not agree
 *
 * @example Sample covariance (variance) of single array
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(cov([1, 2, 3]), 1);
 *
 * ```
 *
 * @example Population covariance with flag=0
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(cov([1, 2, 3], 0), 0.6666666666666666);
 *
 * ```
 *
 * @example Covariance matrix from 2x2 data matrix
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(cov([[1, 2], [3, 4]]), [[2, 2], [2, 2]]);
 * ```
 */
export default function cov(x: array): number;
/**
 * Covariance matrix.
 *
 * Calculates the covariance matrix between arrays or matrices. For a single vector,
 * returns the variance. For two vectors, returns the 2x2 covariance matrix. For a matrix,
 * returns the covariance matrix between columns.
 *
 * @param x Input array or matrix
 * @param y Optional second input array or matrix, or flag value (0 or 1)
 * @param flag Optional Bessel's correction (0: population, 1: sample). Default is 1
 * @returns Covariance matrix or scalar variance
 * @throws When input dimensions do not agree
 *
 * @example Sample covariance (variance) of single array
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(cov([1, 2, 3]), 1);
 *
 * ```
 *
 * @example Population covariance with flag=0
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(cov([1, 2, 3], 0), 0.6666666666666666);
 *
 * ```
 *
 * @example Covariance matrix from 2x2 data matrix
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(cov([[1, 2], [3, 4]]), [[2, 2], [2, 2]]);
 * ```
 */
export default function cov(x: array, flag: 0 | 1): number;
/**
 * Covariance matrix.
 *
 * Calculates the covariance matrix between arrays or matrices. For a single vector,
 * returns the variance. For two vectors, returns the 2x2 covariance matrix. For a matrix,
 * returns the covariance matrix between columns.
 *
 * @param x Input array or matrix
 * @param y Optional second input array or matrix, or flag value (0 or 1)
 * @param flag Optional Bessel's correction (0: population, 1: sample). Default is 1
 * @returns Covariance matrix or scalar variance
 * @throws When input dimensions do not agree
 *
 * @example Sample covariance (variance) of single array
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(cov([1, 2, 3]), 1);
 *
 * ```
 *
 * @example Population covariance with flag=0
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(cov([1, 2, 3], 0), 0.6666666666666666);
 *
 * ```
 *
 * @example Covariance matrix from 2x2 data matrix
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(cov([[1, 2], [3, 4]]), [[2, 2], [2, 2]]);
 * ```
 */
export default function cov(x: array, y: array, flag?: 0 | 1): matrix;
/**
 * Covariance matrix.
 *
 * Calculates the covariance matrix between arrays or matrices. For a single vector,
 * returns the variance. For two vectors, returns the 2x2 covariance matrix. For a matrix,
 * returns the covariance matrix between columns.
 *
 * @param x Input array or matrix
 * @param y Optional second input array or matrix, or flag value (0 or 1)
 * @param flag Optional Bessel's correction (0: population, 1: sample). Default is 1
 * @returns Covariance matrix or scalar variance
 * @throws When input dimensions do not agree
 *
 * @example Sample covariance (variance) of single array
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(cov([1, 2, 3]), 1);
 *
 * ```
 *
 * @example Population covariance with flag=0
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(cov([1, 2, 3], 0), 0.6666666666666666);
 *
 * ```
 *
 * @example Covariance matrix from 2x2 data matrix
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(cov([[1, 2], [3, 4]]), [[2, 2], [2, 2]]);
 * ```
 */
export default function cov(x: matrix, flag?: 0 | 1): matrix;
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