/**
 * Various Matrix sub-types that are guarded by various constructors and branded-newtypes.
 * Allows for convenient inverses if the inverse need be applied to the diagonal of a
 * particular matrix, such as with the Pearson Correlation Matrix for multivariate samples.
 *
 * @since 1.0.0
 */
import * as Rng from 'fp-ts/Ring';
import * as Fld from 'fp-ts/Field';
import * as Mon from 'fp-ts/Monoid';
import * as O from 'fp-ts/Option';
import * as M from './Matrix';
import * as V from './Vector';
import * as Iso from './Iso';
declare const UpperTriangularSymbol: unique symbol;
declare type UpperTriangularSymbol = typeof UpperTriangularSymbol;
declare const LowerTriangularSymbol: unique symbol;
declare type LowerTriangularSymbol = typeof LowerTriangularSymbol;
declare const DiagonalSymbol: unique symbol;
declare type DiagonalSymbol = typeof DiagonalSymbol;
declare const OrthogonalSymbol: unique symbol;
declare type OrthogonalSymbol = typeof OrthogonalSymbol;
/**
 * Upper Triangular Matricies
 *
 * @since 1.0.0
 * @category Model
 */
export interface UpperTriangularMatrix<M, A> extends M.Mat<M, M, A> {
    _URI: UpperTriangularSymbol;
}
/**
 * Lower Triangular Matricies
 *
 * @since 1.0.0
 * @category Model
 */
export interface LowerTriangularMatrix<M, A> extends M.Mat<M, M, A> {
    _URI: LowerTriangularSymbol;
}
/**
 * Diagonal Matricies
 *
 * @since 1.0.0
 * @category Model
 */
export interface DiagonalMatrix<M, A> extends M.Mat<M, M, A> {
    _URI: DiagonalSymbol;
}
/**
 * Orthogonal Matricies
 *
 * @since 1.1.0
 * @category Model
 */
export interface OrthogonalMatrix<M, A> extends M.Mat<M, M, A> {
    _URI: OrthogonalSymbol;
}
/**
 * @since 1.0.0
 * @category Constructors
 */
export declare const fromMatrix: <A>(R: Rng.Ring<A>) => <M>(m: M.Mat<M, M, A>) => [LowerTriangularMatrix<M, A>, UpperTriangularMatrix<M, A>];
/**
 * @since 1.0.0
 * @category Constructors
 */
export declare const toMatrix: <M, A>([l, u]: [LowerTriangularMatrix<M, A>, UpperTriangularMatrix<M, A>]) => M.Mat<M, M, A>;
/**
 * @since 1.0.0
 * @category Constructors
 */
export declare const extractDiagonal: <A>(zero: A) => <M>(m: M.Mat<M, M, A>) => DiagonalMatrix<M, A>;
/**
 * @since 1.0.0
 * @category Isomorphisms
 */
export declare const getTransposeIso: <M extends number, A>() => Iso.Iso<LowerTriangularMatrix<M, A>, UpperTriangularMatrix<M, A>>;
/**
 * @since 1.0.0
 * @category Matrix Operations
 */
export declare const diagonalMap: <A>(f: (a: A) => A) => <M>(m: DiagonalMatrix<M, A>) => DiagonalMatrix<M, A>;
/**
 * @since 1.0.4
 * @category Matrix Operations
 */
export declare const diagonalFoldMap: <A>(Mn: Mon.Monoid<A>) => <M>(as: DiagonalMatrix<M, A>) => A;
/**
 * @since 1.0.0
 * @category Matrix Operations
 */
export declare const diagonalInverse: <A>(F: Fld.Field<A>) => <M>(m: DiagonalMatrix<M, A>) => DiagonalMatrix<M, A>;
/**
 * @since 1.1.0
 * @category Matrix Operations
 */
export declare const orthogonalInverse: <M extends number, A>(m: OrthogonalMatrix<M, A>) => OrthogonalMatrix<M, A>;
/**
 * See: Fundamentals of Matrix Computation, David S. Watkins, page 26. Returns O.none if
 * matrix is singular
 *
 * @since 1.1.0
 * @category Matrix Operations
 */
export declare const forwardSub: <M>(L: LowerTriangularMatrix<M, number>, b: V.Vec<M, number>) => O.Option<V.Vec<M, number>>;
/**
 * See: Fundamentals of Matrix Computation, David S. Watkins, page 30. Returns O.none if
 * matrix is singular
 *
 * @since 1.1.0
 * @category Matrix Operations
 */
export declare const backSub: <M extends number>(U: UpperTriangularMatrix<M, number>, y: V.Vec<M, number>) => O.Option<V.Vec<M, number>>;
export {};
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