import type { ThreeDimensionalComponent, ThreeDimensionalIndex } from '../dimensions.ts';
import type { Pipeable } from '../utils.ts';
import type { Vector3 } from '../vector/vector3.ts';
import type { Matrix2x2 } from './matrix2x2.ts';
import type { Matrix3x3TypeId } from './matrix3x3.internal.ts';
/**
 * A coordinate in a 3x3 matrix.
 *
 * @since 1.0.0
 */
export type Matrix3x3Coordinate = ThreeDimensionalIndex | ThreeDimensionalComponent;
/**
 * A 3x3 matrix.
 *
 * All fields are readonly and immutable, and all operations create new instances.
 *
 * @since 1.0.0
 */
export interface Matrix3x3 extends Pipeable {
    readonly [Matrix3x3TypeId]: Matrix3x3TypeId;
    /**
     * 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 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 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;
}
/**
 * Checks if a value is a `Matrix3x3`.
 *
 * @param m - The value to check.
 * @returns `true` if the value is a `Matrix3x3`, `false` otherwise.
 * @since 1.0.0
 */
export declare const isMatrix3x3: (m: unknown) => m is Matrix3x3;
export declare const equals: {
    /**
     * Checks if two `Matrix3x3` 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: Matrix3x3, b: Matrix3x3): boolean;
    /**
     * Checks if two `Matrix3x3` 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: Matrix3x3): (a: Matrix3x3) => boolean;
};
/**
 * Creates a new `Matrix3x3` 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 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 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.
 * @returns A new `Matrix3x3` instance.
 * @since 1.0.0
 */
export declare const make: (m00?: number, m01?: number, m02?: number, m10?: number, m11?: number, m12?: number, m20?: number, m21?: number, m22?: number) => Matrix3x3;
/**
 * Creates a new `Matrix3x3` instance from three row vectors.
 *
 * @param v0 - The first row vector.
 * @param v1 - The second row vector.
 * @param v2 - The third row vector.
 * @returns A new `Matrix3x3` instance.
 * @since 1.0.0
 */
export declare const fromRows: (v0: Vector3, v1: Vector3, v2: Vector3) => Matrix3x3;
/**
 * Creates a new `Matrix3x3` instance from three column vectors.
 *
 * @param v0 - The first column vector.
 * @param v1 - The second column vector.
 * @param v2 - The third column vector.
 * @returns A new `Matrix3x3` instance.
 * @since 1.0.0
 */
export declare const fromColumns: (v0: Vector3, v1: Vector3, v2: Vector3) => Matrix3x3;
export declare const setRow: {
    /**
     * Sets a row of the matrix to a new vector.
     *
     * @param m - The matrix to set the row of.
     * @param row - The row index to set.
     * @param v - The new vector for the row.
     * @returns A new matrix with the specified row set to the new vector.
     * @since 1.0.0
     */
    (m: Matrix3x3, row: Matrix3x3Coordinate, v: Vector3): Matrix3x3;
    /**
     * Sets a row of the matrix to a new vector.
     *
     * @param row - The row index to set.
     * @param v - The new vector for the row.
     * @returns A function that takes a matrix and returns a new matrix with the specified row set to the new vector.
     * @since 1.0.0
     */
    (row: Matrix3x3Coordinate, v: Vector3): (m: Matrix3x3) => Matrix3x3;
};
export declare const setColumn: {
    /**
     * Sets a column of the matrix to a new vector.
     *
     * @param m - The matrix to set the column of.
     * @param column - The column index to set.
     * @param v - The new vector for the column.
     * @returns A new matrix with the specified column set to the new vector.
     * @since 1.0.0
     */
    (m: Matrix3x3, column: Matrix3x3Coordinate, v: Vector3): Matrix3x3;
    /**
     * Sets a column of the matrix to a new vector.
     *
     * @param column - The column index to set.
     * @param v - The new vector for the column.
     * @returns A function that takes a matrix and returns a new matrix with the specified column set to the new vector.
     * @since 1.0.0
     */
    (column: Matrix3x3Coordinate, v: Vector3): (m: Matrix3x3) => Matrix3x3;
};
/**
 * Calculates the determinant of a 3x3 matrix.
 *
 * @param m - The matrix to calculate the determinant of.
 * @returns The determinant of the matrix.
 * @since 1.0.0
 */
export declare const determinant: (m: Matrix3x3) => number;
/**
 * Calculates the minor of a 3x3 matrix.
 *
 * @param m - The matrix to calculate the minor of.
 * @param row - The row index of the element to calculate the minor for.
 * @param column - The column index of the element to calculate the minor for.
 * @returns The minor of the matrix at the specified row and column.
 * @since 1.0.0
 */
export declare const minor: (m: Matrix3x3, row: Matrix3x3Coordinate, column: Matrix3x3Coordinate) => Matrix2x2;
export declare const vectorProductLeft: {
    /**
     * Calculates the left vector product of a matrix and a vector.
     *
     * @example
     * ```ts
     * import * as Matrix3x3 from 'curvy/matrix3x3'
     * import * as Vector3 from 'curvy/vector3'
     *
     * const m = Matrix3x3.make(1, 2, 3, 4, 5, 6, 7, 8, 9)
     * const v = Vector3.vector3(10, 11, 12)
     *
     * // Performs:
     * // x = 1 * 10 + 2 * 11 + 3 * 12
     * // y = 4 * 10 + 5 * 11 + 6 * 12
     * // z = 7 * 10 + 8 * 11 + 9 * 12
     * const result = Matrix3x3.vectorProductLeft(m, v)
     * ```
     * @param m - The matrix to calculate the left vector product with.
     * @param v - The vector to calculate the left vector product with.
     * @returns The resulting vector from the left vector product.
     * @since 1.0.0
     */
    (m: Matrix3x3, v: Vector3): Vector3;
    /**
     * Calculates the left vector product of a matrix and a vector.
     *
     * @example
     * ```ts
     * import * as Matrix3x3 from 'curvy/matrix3x3'
     * import * as Vector3 from 'curvy/vector3'
     *
     * const m = Matrix3x3.make(1, 2, 3, 4, 5, 6, 7, 8, 9)
     * const v = Vector3.vector3(10, 11, 12)
     *
     * // Performs:
     * // x = 1 * 10 + 2 * 11 + 3 * 12
     * // y = 4 * 10 + 5 * 11 + 6 * 12
     * // z = 7 * 10 + 8 * 11 + 9 * 12
     * const result = Matrix3x3.vectorProductLeft(v)(m)
     * ```
     * @param v - The vector to calculate the left vector product with.
     * @returns A function that takes a matrix and returns the resulting vector from the left vector product.
     * @since 1.0.0
     */
    (v: Vector3): (m: Matrix3x3) => Vector3;
};
export declare const vectorProductRight: {
    /**
     * Calculates the right vector product of a matrix and a vector.
     *
     * @example
     * ```ts
     * import * as Matrix3x3 from 'curvy/matrix3x3'
     * import * as Vector3 from 'curvy/vector3'
     *
     * const m = Matrix3x3.make(1, 2, 3, 4, 5, 6, 7, 8, 9)
     * const v = Vector3.vector3(10, 11, 12)
     *
     * // Performs:
     * // x = 1 * 10 + 4 * 11 + 7 * 12
     * // y = 2 * 10 + 5 * 11 + 8 * 12
     * // z = 3 * 10 + 6 * 11 + 9 * 12
     * const result = Matrix3x3.vectorProductRight(m, v)
     * ```
     * @param m - The matrix to calculate the right vector product with.
     * @param v - The vector to calculate the right vector product with.
     * @returns The resulting vector from the right vector product.
     * @since 1.0.0
     */
    (m: Matrix3x3, v: Vector3): Vector3;
    /**
     * Calculates the right vector product of a matrix and a vector.
     *
     * @example
     * ```ts
     * import * as Matrix3x3 from 'curvy/matrix3x3'
     * import * as Vector3 from 'curvy/vector3'
     *
     * const m = Matrix3x3.make(1, 2, 3, 4, 5, 6, 7, 8, 9)
     * const v = Vector3.vector3(10, 11, 12)
     *
     * // Performs:
     * // x = 1 * 10 + 4 * 11 + 7 * 12
     * // y = 2 * 10 + 5 * 11 + 8 * 12
     * // z = 3 * 10 + 6 * 11 + 9 * 12
     * const result = Matrix3x3.vectorProductRight(v)(m)
     * ```
     * @param v - The vector to calculate the right vector product with.
     * @returns A function that takes a matrix and returns the resulting vector from the right vector product.
     * @since 1.0.0
     */
    (v: Vector3): (m: Matrix3x3) => Vector3;
};
export declare const solveSystem: {
    /**
     * Solves a system of equations represented by a matrix and a vector.
     *
     * @example
     * ```ts
     * import * as Matrix3x3 from 'curvy/matrix3x3'
     * import * as Vector3 from 'curvy/vector3'
     *
     * const m = Matrix3x3.make(1, 2, 3, 4, 5, 6, 7, 8, 9)
     * const v = Vector3.vector3(10, 11, 12)
     *
     * // Performs:
     * // x = m00 * x + m01 * y + m02 * z
     * // y = m10 * x + m11 * y + m12 * z
     * // z = m20 * x + m21 * y + m22 * z
     * const result = Matrix3x3.solveSystem(m, v)
     * ```
     * @since 1.0.0
     */
    (m: Matrix3x3, v: Vector3): Vector3;
    /**
     * Solves a system of equations represented by a matrix and a vector.
     *
     * @example
     * ```ts
     * import * as Matrix3x3 from 'curvy/matrix3x3'
     * import * as Vector3 from 'curvy/vector3'
     *
     * const m = Matrix3x3.make(1, 2, 3, 4, 5, 6, 7, 8, 9)
     * const v = Vector3.vector3(10, 11, 12)
     *
     * // Performs:
     * // x = m00 * x + m01 * y + m02 * z
     * // y = m10 * x + m11 * y + m12 * z
     * // z = m20 * x + m21 * y + m22 * z
     * const result = Matrix3x3.solveSystem(v)(m)
     * ```
     * @since 1.0.0
     */
    (v: Vector3): (m: Matrix3x3) => Vector3;
};
/**
 * Returns the rows of a `Matrix3x3` as an array of vectors.
 *
 * @param m - The matrix to get the rows from.
 * @returns An array of vectors representing the rows of the matrix.
 * @since 1.0.0
 */
export declare const toRows: (m: Matrix3x3) => [Vector3, Vector3, Vector3];
/**
 * Returns the columns of a `Matrix3x3` as an array of vectors.
 *
 * @param m - The matrix to get the columns from.
 * @returns An array of vectors representing the columns of the matrix.
 * @since 1.0.0
 */
export declare const toColumns: (m: Matrix3x3) => [Vector3, Vector3, Vector3];
export declare const rowVector: {
    /**
     * Gets a row vector from the matrix.
     *
     * @param m - The matrix to get the row vector from.
     * @param row - The row index to get the vector from.
     * @returns The row vector at the specified index.
     * @since 1.0.0
     */
    (m: Matrix3x3, row: Matrix3x3Coordinate): Vector3;
    /**
     * Gets a row vector from the matrix.
     *
     * @param row - The row index to get the vector from.
     * @returns A function that takes a matrix and returns the row vector at the specified index.
     * @since 1.0.0
     */
    (row: Matrix3x3Coordinate): (m: Matrix3x3) => Vector3;
};
export declare const columnVector: {
    /**
     * Gets a column vector from the matrix.
     *
     * @param m - The matrix to get the column vector from.
     * @param column - The column index to get the vector from.
     * @returns The column vector at the specified index.
     * @since 1.0.0
     */
    (m: Matrix3x3, column: Matrix3x3Coordinate): Vector3;
    /**
     * Gets a column vector from the matrix.
     *
     * @param column - The column index to get the vector from.
     * @returns A function that takes a matrix and returns the column vector at the specified index.
     * @since 1.0.0
     */
    (column: Matrix3x3Coordinate): (m: Matrix3x3) => Vector3;
};
/**
 * Transposes a `Matrix3x3`.
 *
 * @param m - The matrix to transpose.
 * @returns A new `Matrix3x3` instance that is the transpose of the input matrix.
 * @since 1.0.0
 */
export declare const transpose: (m: Matrix3x3) => Matrix3x3;
/**
 * Reverses the rows of a `Matrix3x3`.
 *
 * @param m - The matrix to reverse the rows of.
 * @returns A new `Matrix3x3` instance with the rows reversed.
 * @since 1.0.0
 */
export declare const reverseRows: (m: Matrix3x3) => Matrix3x3;
/**
 * Reverses the columns of a `Matrix3x3`.
 *
 * @param m - The matrix to reverse the columns of.
 * @returns A new `Matrix3x3` instance with the columns reversed.
 * @since 1.0.0
 */
export declare const reverseColumns: (m: Matrix3x3) => Matrix3x3;