import type { Complex } from '../../treb-base-types/src';
export interface ComplexMatrixType {
    array: Complex[][];
    m: number;
    n: number;
    error?: boolean;
}
export interface RealMatrixType {
    array: number[][];
    m: number;
    n: number;
    error?: boolean;
}
export declare const PolarToRectangular: (a: {
    r: number;
    theta: number;
}) => Complex;
export declare const RectangularToPolar: (value: Complex) => {
    r: number;
    theta: number;
};
export declare const TanH: (z: Complex) => Complex;
export declare const Tan: (z: Complex) => Complex;
export declare const CosH: (z: Complex) => Complex;
export declare const Cos: (z: Complex) => {
    real: number;
    imaginary: number;
};
export declare const SinH: (z: Complex) => Complex;
export declare const Sin: (z: Complex) => {
    real: number;
    imaginary: number;
};
export declare const ASin: (cpx: Complex) => Complex;
export declare const ACos: (cpx: Complex) => {
    real: number;
    imaginary: number;
};
export declare const ATan: (cpx: Complex) => Complex;
export declare const ATan2: (y: Complex, x: Complex) => Complex | false;
export declare const Product: (...args: Complex[]) => Complex;
export declare const Multiply: (a: Complex, b: Complex) => Complex;
export declare const RealSum: (a: RealMatrixType, b: RealMatrixType) => RealMatrixType;
export declare const RealProduct: (a: RealMatrixType, b: RealMatrixType) => RealMatrixType;
export declare const ComplexProduct: (a: ComplexMatrixType, b: ComplexMatrixType) => Complex[][];
/**
 * this function DOES NOT check if the matrix is square, because it's
 * recursive and we don't want to do that every time. check before you
 * call it.
 */
export declare const ComplexDeterminant: (matrix: ComplexMatrixType) => Complex;
export declare const RealDeterminant: (matrix: RealMatrixType) => number;
export declare const RealInverse: (matrix: RealMatrixType) => RealMatrixType | undefined;
/**
 * returns the inverse of a complex matrix. the first step in this is
 * to split into {real, imaginary} and then invert the real matrix. we
 * can use that as a shortcut if there are no imaginary values, just return
 * the inverted real matrix (here converted to complex, but we don't necessarily
 * need to do that)
 *
 * @param a
 * @returns
 */
export declare const MatrixInverse: (a: ComplexMatrixType) => Complex[][] | undefined;
export declare const Divide: (a: Complex, b: Complex) => Complex;
export declare const Exp: (value: Complex) => Complex;
/**
 * from polar form, the principal value is
 * Log z = ln r + iθ
 */
export declare const Log: (value: Complex) => Complex;
/**
 * returns a^b where a and b are (possibly) complex
 */
export declare const Power: (a: Complex, b: Complex) => Complex;