import type { FourDimensionalComponent, FourDimensionalIndex } from '../dimensions.ts';
import type { Pipeable } from '../utils.ts';
import type { Vector4 } from '../vector/vector4.ts';
import type { Matrix3x3 } from './matrix3x3.ts';
import type { Matrix4x4TypeId } from './matrix4x4.internal.ts';
/**
 * A coordinate in a 4x4 matrix.
 *
 * @since 1.0.0
 */
export type Matrix4x4Coordinate = FourDimensionalIndex | FourDimensionalComponent;
/**
 * A 4x4 matrix.
 *
 * All fields are readonly and immutable, and all operations create new instances.
 *
 * @since 1.0.0
 */
export interface Matrix4x4 extends Pipeable {
    readonly [Matrix4x4TypeId]: Matrix4x4TypeId;
    /**
     * The value of the first row and first column.
     */
    readonly m00: number;
    /**
     * The value of the first row and second column.
     */
    readonly m01: number;
    /**
     * The value of the first row and third column.
     */
    readonly m02: number;
    /**
     * The value of the first row and fourth column.
     */
    readonly m03: number;
    /**
     * The value of the second row and first column.
     */
    readonly m10: number;
    /**
     * The value of the second row and second column.
     */
    readonly m11: number;
    /**
     * The value of the second row and third column.
     */
    readonly m12: number;
    /**
     * The value of the second row and fourth column.
     */
    readonly m13: number;
    /**
     * The value of the third row and first column.
     */
    readonly m20: number;
    /**
     * The value of the third row and second column.
     */
    readonly m21: number;
    /**
     * The value of the third row and third column.
     */
    readonly m22: number;
    /**
     * The value of the third row and fourth column.
     */
    readonly m23: number;
    /**
     * The value of the fourth row and first column.
     */
    readonly m30: number;
    /**
     * The value of the fourth row and second column.
     */
    readonly m31: number;
    /**
     * The value of the fourth row and third column.
     */
    readonly m32: number;
    /**
     * The value of the fourth row and fourth column.
     */
    readonly m33: number;
}
/**
 * Checks if a value is a `Matrix4x4`.
 *
 * @param m - The value to check.
 * @returns `true` if the value is a `Matrix4x4`, `false` otherwise.
 * @since 1.0.0
 */
export declare const isMatrix4x4: (m: unknown) => m is Matrix4x4;
/**
 * The 4x4 identity matrix.
 *
 * @since 1.1.0
 */
export declare const identity: Matrix4x4;
export declare const equals: {
    /**
     * Checks if two `Matrix4x4` instances are approximately equal within the
     * default absolute tolerance ({@link EPSILON}).
     *
     * @param a - The first matrix.
     * @param b - The second matrix.
     * @returns `true` when each pair of components is within tolerance.
     * @since 1.1.0
     */
    (a: Matrix4x4, b: Matrix4x4): boolean;
    /**
     * Checks if two `Matrix4x4` instances are approximately equal within the
     * default absolute tolerance ({@link EPSILON}).
     *
     * @param b - The second matrix.
     * @returns A function that takes the first matrix and returns the comparison result.
     * @since 1.1.0
     */
    (b: Matrix4x4): (a: Matrix4x4) => boolean;
};
/**
 * Creates a new `Matrix4x4` instance.
 *
 * @param m00 - The value of the first row and first column.
 * @param m01 - The value of the first row and second column.
 * @param m02 - The value of the first row and third column.
 * @param m03 - The value of the first row and fourth column.
 * @param m10 - The value of the second row and first column.
 * @param m11 - The value of the second row and second column.
 * @param m12 - The value of the second row and third column.
 * @param m13 - The value of the second row and fourth column.
 * @param m20 - The value of the third row and first column.
 * @param m21 - The value of the third row and second column.
 * @param m22 - The value of the third row and third column.
 * @param m23 - The value of the third row and fourth column.
 * @param m30 - The value of the fourth row and first column.
 * @param m31 - The value of the fourth row and second column.
 * @param m32 - The value of the fourth row and third column.
 * @param m33 - The value of the fourth row and fourth column.
 * @returns A new `Matrix4x4` instance.
 * @since 1.0.0
 */
export declare const make: (m00?: number, m01?: number, m02?: number, m03?: number, m10?: number, m11?: number, m12?: number, m13?: number, m20?: number, m21?: number, m22?: number, m23?: number, m30?: number, m31?: number, m32?: number, m33?: number) => Matrix4x4;
/**
 * Creates a new `Matrix4x4` instance from four row vectors.
 *
 * @param v0 - The first row vector.
 * @param v1 - The second row vector.
 * @param v2 - The third row vector.
 * @param v3 - The fourth row vector.
 * @returns A new `Matrix4x4` instance.
 * @since 1.0.0
 */
export declare const fromRows: (v0: Vector4, v1: Vector4, v2: Vector4, v3: Vector4) => Matrix4x4;
/**
 * Creates a new `Matrix4x4` instance from four column vectors.
 *
 * @param v0 - The first column vector.
 * @param v1 - The second column vector.
 * @param v2 - The third column vector.
 * @param v3 - The fourth column vector.
 */
export declare const fromColumns: (v0: Vector4, v1: Vector4, v2: Vector4, v3: Vector4) => Matrix4x4;
export declare const setRow: {
    /**
     * Sets a row of a `Matrix4x4` to a new vector.
     *
     * @param m - The matrix to modify.
     * @param row - The row to set.
     * @param v - The new vector.
     * @returns A new `Matrix4x4` instance with the specified row set to the new vector.
     * @since 1.0.0
     */
    (m: Matrix4x4, row: Matrix4x4Coordinate, v: Vector4): Matrix4x4;
    /**
     * Sets a row of a `Matrix4x4` to a new vector.
     *
     * @param row - The row to set.
     * @param v - The new vector.
     * @returns A function that takes a matrix and returns a new `Matrix4x4` instance with the specified row set to the new vector.
     * @since 1.0.0
     */
    (row: Matrix4x4Coordinate, v: Vector4): (m: Matrix4x4) => Matrix4x4;
};
export declare const setColumn: {
    /**
     * Sets a column of a `Matrix4x4` to a new vector.
     *
     * @param m - The matrix to modify.
     * @param column - The column to set.
     * @param v - The new vector.
     * @returns A new `Matrix4x4` instance with the specified column set to the new vector.
     * @since 1.0.0
     */
    (m: Matrix4x4, column: Matrix4x4Coordinate, v: Vector4): Matrix4x4;
    /**
     * Sets a column of a `Matrix4x4` to a new vector.
     *
     * @param column - The column to set.
     * @param v - The new vector.
     * @returns A function that takes a matrix and returns a new `Matrix4x4` instance with the specified column set to the new vector.
     * @since 1.0.0
     */
    (column: Matrix4x4Coordinate, v: Vector4): (m: Matrix4x4) => Matrix4x4;
};
/**
 * Calculates the determinant of a `Matrix4x4`.
 *
 * @param m - The matrix to calculate the determinant of.
 * @returns The determinant of the matrix.
 * @since 1.0.0
 */
export declare const determinant: (m: Matrix4x4) => number;
/**
 * Calculates the minor of a `Matrix4x4` at a given row and column.
 *
 * @param m - The matrix to calculate the minor of.
 * @param row - The row to exclude.
 * @param column - The column to exclude.
 * @returns The minor of the matrix at the given row and column.
 */
export declare const minor: (m: Matrix4x4, row: Matrix4x4Coordinate, column: Matrix4x4Coordinate) => Matrix3x3;
export declare const vectorProductLeft: {
    /**
     * Calculates the left vector product of a `Matrix4x4` and a `Vector4`.
     *
     * @example
     * ```ts
     * import * as Matrix4x4 from 'curvy/matrix4x4'
     * import * as Vector4 from 'curvy/vector4'
     *
     * const m = Matrix4x4.make(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16)
     * const v = Vector4.make(17, 18, 19, 20)
     *
     * // Result:
     * // x = 1 * 17 + 2 * 18 + 3 * 19 + 4 * 20
     * // y = 5 * 17 + 6 * 18 + 7 * 19 + 8 * 20
     * // z = 9 * 17 + 10 * 18 + 11 * 19 + 12 * 20
     * // w = 13 * 17 + 14 * 18 + 15 * 19 + 16 * 20
     * const result = Matrix4x4.vectorProductLeft(m, v)
     * ```
     * @param m - The matrix to multiply.
     * @param v - The vector to multiply.
     * @returns The resulting vector.
     * @since 1.0.0
     */
    (m: Matrix4x4, v: Vector4): Vector4;
    /**
     * Calculates the left vector product of a `Matrix4x4` and a `Vector4`.
     *
     * @example
     * ```ts
     * import * as Matrix4x4 from 'curvy/matrix4x4'
     * import * as Vector4 from 'curvy/vector4'
     *
     * const m = Matrix4x4.make(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16)
     * const v = Vector4.make(17, 18, 19, 20)
     *
     * // Result:
     * // x = 1 * 17 + 2 * 18 + 3 * 19 + 4 * 20
     * // y = 5 * 17 + 6 * 18 + 7 * 19 + 8 * 20
     * // z = 9 * 17 + 10 * 18 + 11 * 19 + 12 * 20
     * // w = 13 * 17 + 14 * 18 + 15 * 19 + 16 * 20
     * const result = Matrix4x4.vectorProductLeft(v)(m)
     * ```
     * @since 1.0.0
     */
    (v: Vector4): (m: Matrix4x4) => Vector4;
};
export declare const vectorProductRight: {
    /**
     * Calculates the right vector product of a `Matrix4x4` and a `Vector4`.
     *
     * @example
     * ```ts
     * import * as Matrix4x4 from 'curvy/matrix4x4'
     * import * as Vector4 from 'curvy/vector4'
     *
     * const m = Matrix4x4.make(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16)
     * const v = Vector4.make(17, 18, 19, 20)
     *
     * // Result:
     * // x = 1 * 17 + 5 * 18 + 9 * 19 + 13 * 20
     * // y = 2 * 17 + 6 * 18 + 10 * 19 + 14 * 20
     * // z = 3 * 17 + 7 * 18 + 11 * 19 + 15 * 20
     * // w = 4 * 17 + 8 * 18 + 12 * 19 + 16 * 20
     * const result = Matrix4x4.vectorProductRight(m, v)
     * ```
     * @since 1.0.0
     */
    (m: Matrix4x4, v: Vector4): Vector4;
    /**
     * Calculates the right vector product of a `Matrix4x4` and a `Vector4`.
     *
     * @example
     * ```ts
     * import * as Matrix4x4 from 'curvy/matrix4x4'
     * import * as Vector4 from 'curvy/vector4'
     *
     * const m = Matrix4x4.make(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16)
     * const v = Vector4.make(17, 18, 19, 20)
     *
     * // Result:
     * // x = 1 * 17 + 5 * 18 + 9 * 19 + 13 * 20
     * // y = 2 * 17 + 6 * 18 + 10 * 19 + 14 * 20
     * // z = 3 * 17 + 7 * 18 + 11 * 19 + 15 * 20
     * // w = 4 * 17 + 8 * 18 + 12 * 19 + 16 * 20
     * const result = Matrix4x4.vectorProductRight(v)(m)
     * ```
     * @since 1.0.0
     */
    (v: Vector4): (m: Matrix4x4) => Vector4;
};
export declare const multiply: {
    /**
     * Multiplies two `Matrix4x4` instances. Result is `a · b`.
     *
     * @param a - The left-hand matrix.
     * @param b - The right-hand matrix.
     * @returns The product matrix.
     * @since 1.1.0
     */
    (a: Matrix4x4, b: Matrix4x4): Matrix4x4;
    /**
     * Multiplies two `Matrix4x4` instances. Result is `a · b`.
     *
     * @param b - The right-hand matrix.
     * @returns A function that takes the left-hand matrix and returns the product.
     * @since 1.1.0
     */
    (b: Matrix4x4): (a: Matrix4x4) => Matrix4x4;
};
/**
 * Returns the inverse of a `Matrix4x4`.
 *
 * Throws when the matrix is singular (determinant is zero).
 *
 * @param m - The matrix to invert.
 * @returns The inverse matrix.
 * @since 1.1.0
 */
export declare const inverse: (m: Matrix4x4) => Matrix4x4;
export declare const solveSystem: {
    /**
     * Solves a system of linear equations represented by a `Matrix4x4` and a `Vector4`.
     *
     * @param m - The matrix representing the coefficients of the equations.
     * @param v - The vector representing the constants of the equations.
     * @returns The solution vector.
     * @since 1.0.0
     */
    (m: Matrix4x4, v: Vector4): Vector4;
    /**
     * Solves a system of linear equations represented by a `Matrix4x4` and a `Vector4`.
     *
     * @param v - The vector representing the constants of the equations.
     * @returns A function that takes a matrix and returns the solution vector.
     * @since 1.0.0
     */
    (v: Vector4): (m: Matrix4x4) => Vector4;
};
/**
 * Returns the rows of a `Matrix4x4` as an array of vectors.
 *
 * @param m - The matrix to convert.
 * @returns An array of vectors representing the rows of the matrix.
 * @since 1.0.0
 */
export declare const toRows: (m: Matrix4x4) => [Vector4, Vector4, Vector4, Vector4];
/**
 * Returns the columns of a `Matrix4x4` as an array of vectors.
 *
 * @param m - The matrix to convert.
 * @returns An array of vectors representing the columns of the matrix.
 * @since 1.0.0
 */
export declare const toColumns: (m: Matrix4x4) => [Vector4, Vector4, Vector4, Vector4];
export declare const rowVector: {
    /**
     * Returns a row vector from a `Matrix4x4`.
     *
     * @param m - The matrix to get the row vector from.
     * @param row - The row index.
     * @returns The row vector.
     * @since 1.0.0
     */
    (m: Matrix4x4, row: Matrix4x4Coordinate): Vector4;
    /**
     * Returns a row vector from a `Matrix4x4`.
     *
     * @param row - The row index.
     * @returns A function that takes a matrix and returns the row vector.
     * @since 1.0.0
     */
    (row: Matrix4x4Coordinate): (m: Matrix4x4) => Vector4;
};
export declare const columnVector: {
    /**
     * Returns a column vector from a `Matrix4x4`.
     *
     * @param m - The matrix to get the column vector from.
     * @param column - The column index.
     * @returns The column vector.
     * @since 1.0.0
     */
    (m: Matrix4x4, column: Matrix4x4Coordinate): Vector4;
    /**
     * Returns a column vector from a `Matrix4x4`.
     *
     * @param column - The column index.
     * @returns A function that takes a matrix and returns the column vector.
     * @since 1.0.0
     */
    (column: Matrix4x4Coordinate): (m: Matrix4x4) => Vector4;
};
/**
 * Transposes a `Matrix4x4`.
 *
 * @param m - The matrix to transpose.
 * @returns The transposed matrix.
 * @since 1.0.0
 */
export declare const transpose: (m: Matrix4x4) => Matrix4x4;
/**
 * Reverses the rows of a `Matrix4x4`.
 *
 * @param m - The matrix to reverse the rows of.
 * @returns The matrix with the rows reversed.
 * @since 1.0.0
 */
export declare const reverseRows: (m: Matrix4x4) => Matrix4x4;
/**
 * Reverses the columns of a `Matrix4x4`.
 *
 * @param m - The matrix to reverse the columns of.
 * @returns The matrix with the columns reversed.
 * @since 1.0.0
 */
export declare const reverseColumns: (m: Matrix4x4) => Matrix4x4;