/**
 * @license
 * Copyright (c) 2013, Brandon Jones, Colin MacKenzie IV. All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are met:
 *
 *   * Redistributions of source code must retain the above copyright notice,
 * this list of conditions and the following disclaimer.
 *   * Redistributions in binary form must reproduce the above copyright notice,
 * this list of conditions and the following disclaimer in the documentation
 * and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
 * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
 * POSSIBILITY OF SUCH DAMAGE.
 */
import { Mat2Array, Vec2Array } from './common';
export type { Mat2Array };
/**
 * Creates a new identity mat2
 *
 * @returns a new 2x2 matrix
 */
export declare function create(): Mat2Array;
/**
 * Creates a new mat2 initialized with values from an existing matrix
 *
 * @param a matrix to clone
 * @returns a new 2x2 matrix
 */
export declare function clone(a: Mat2Array): Mat2Array;
/**
 * Copy the values from one mat2 to another
 *
 * @param out the receiving matrix
 * @param a the source matrix
 * @returns out
 */
export declare function copy(out: Mat2Array, a: Mat2Array): Mat2Array;
/**
 * Set a mat2 to the identity matrix
 *
 * @param out the receiving matrix
 * @returns out
 */
export declare function identity(out: Mat2Array): Mat2Array;
/**
 * Transpose the values of a mat2
 *
 * @param out the receiving matrix
 * @param a the source matrix
 * @returns out
 */
export declare function transpose(out: Mat2Array, a: Mat2Array): Mat2Array;
/**
 * Inverts a mat2
 *
 * @param out the receiving matrix
 * @param a the source matrix
 * @returns out
 */
export declare function invert(out: Mat2Array, a: Mat2Array): Mat2Array | null;
/**
 * Calculates the adjugate of a mat2
 *
 * @param out the receiving matrix
 * @param a the source matrix
 * @returns out
 */
export declare function adjoint(out: Mat2Array, a: Mat2Array): Mat2Array;
/**
 * Calculates the determinant of a mat2
 *
 * @param a the source matrix
 * @returns determinant of a
 */
export declare function determinant(a: Mat2Array): number;
/**
 * Multiplies two mat2's
 *
 * @param out the receiving matrix
 * @param a the first operand
 * @param b the second operand
 * @returns out
 */
export declare function multiply(out: Mat2Array, a: Mat2Array, b: Mat2Array): Mat2Array;
/**
 * Alias for {@link mat2.multiply}
 * @function
 */
export declare const mul: typeof multiply;
/**
 * Rotates a mat2 by the given angle
 *
 * @param out the receiving matrix
 * @param a the matrix to rotate
 * @param rad the angle to rotate the matrix by
 * @returns out
 */
export declare function rotate(out: Mat2Array, a: Mat2Array, rad: number): Mat2Array;
/**
 * Scales the mat2 by the dimensions in the given vec2
 *
 * @param out the receiving matrix
 * @param a the matrix to rotate
 * @param {vec2} v the vec2 to scale the matrix by
 * @returns out
 **/
export declare function scale(out: Mat2Array, a: Mat2Array, v: Vec2Array): Mat2Array;
/**
 * Returns Frobenius norm of a mat2
 *
 * @param a the matrix to calculate Frobenius norm of
 * @returns Frobenius norm
 */
export declare function frob(a: Mat2Array): number;
/**
 * Returns L, D and U matrices (Lower triangular, Diagonal and Upper triangular) by factorizing the input matrix
 * @param L the lower triangular matrix
 * @param D the diagonal matrix
 * @param U the upper triangular matrix
 * @param a the input matrix to factorize
 */
export declare function LDU(L: Mat2Array, D: Mat2Array, U: Mat2Array, a: Mat2Array): Mat2Array[];