import { ComplexDecimal } from './complex-decimal';
import { MultiArray } from './multi-array';
/**
 * # LinearAlgebra
 *
 * LinearAlgebra abstract class. Implements static methods related to linear algebra operations and algorithms.
 *
 * ## References
 *
 * * [Linear Algebra at Wolfram MathWorld](https://mathworld.wolfram.com/LinearAlgebra.html)
 * * [Fundamental Theorem of Linear Algebra at Wolfram MathWorld](https://mathworld.wolfram.com/FundamentalTheoremofLinearAlgebra.html)
 * * [Linear algebra at Wikipedia](https://en.wikipedia.org/wiki/Linear_algebra)
 */
export declare abstract class LinearAlgebra {
    /**
     * LinearAlgebra functions.
     */
    static functions: {
        [name: string]: Function;
    };
    /**
     * Identity matrix
     * @param args
     * * `eye(N)` - create identity N x N
     * * `eye(N,M)` - create identity N x M
     * * `eye([N,M])` - create identity N x M
     * @returns Identity matrix
     */
    static eye(...args: any): MultiArray | ComplexDecimal;
    /**
     * Sum of diagonal elements.
     * @param M Matrix.
     * @returns Trace of matrix.
     */
    static trace(M: MultiArray): ComplexDecimal;
    /**
     * Transpose and apply function.
     * @param M Matrix.
     * @returns Transpose matrix with `func` applied to each element.
     */
    private static applyTranspose;
    /**
     * Transpose.
     * @param M Matrix.
     * @returns Transpose matrix.
     */
    static transpose(M: MultiArray): MultiArray;
    /**
     * Complex conjugate transpose.
     * @param M Matrix.
     * @returns Complex conjugate transpose matrix.
     */
    static ctranspose(M: MultiArray): MultiArray;
    /**
     * Matrix product.
     * @param left Matrix.
     * @param right Matrix.
     * @returns left * right.
     */
    static mul(left: MultiArray, right: MultiArray): MultiArray;
    /**
     * Matrix power (multiple multiplication).
     * @param left
     * @param right
     * @returns
     */
    static power(left: MultiArray, right: ComplexDecimal): MultiArray;
    /**
     * Matrix determinant.
     * @param M Matrix.
     * @returns Matrix determinant.
     */
    static det(M: MultiArray): ComplexDecimal;
    /**
     * Returns the inverse of matrix `M`.
     * Source: http://blog.acipo.com/matrix-inversion-in-javascript/
     * This method uses Guassian Elimination to calculate the inverse:
     * (1) 'Augment' the matrix (M) by the identity (on the right).
     * (2) Turn the matrix on the M into the identity by elemetry row ops.
     * (3) The matrix on the right is the inverse (was the identity matrix).
     * There are 3 elemtary row ops: (b and c are combined in the code).
     * (a) Swap 2 rows.
     * (b) Multiply a row by a scalar.
     * (c) Add 2 rows.
     * @param M Matrix.
     * @returns Inverted matrix.
     */
    static inv(M: MultiArray): MultiArray;
    /**
     * Gaussian elimination algorithm for solving systems of linear equations.
     * Adapted from: https://github.com/itsravenous/gaussian-elimination
     * ## References
     * * https://mathworld.wolfram.com/GaussianElimination.html
     * @param M Matrix.
     * @param m Vector.
     * @returns Solution of linear system.
     */
    static gauss(M: MultiArray, m: MultiArray): MultiArray;
    /**
     * PLU matrix factorization.
     * @param M Matrix.
     * @returns L, U and P matrices as multiple output.
     * ## References
     * * https://www.codeproject.com/Articles/1203224/A-Note-on-PA-equals-LU-in-Javascript
     * * https://rosettacode.org/wiki/LU_decomposition#JavaScript
     */
    static lu(M: MultiArray): any;
}