//--------------------------------------------------------------------------------------

//

//  File: Matrix3.h

//

//  Abstract: Template class for 3x3 matrix operations, where matrix elements

//            are real numbers.

//

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//------------------------------------------------------------------------------------

#ifndef _MATRIX_3x3_H_

#define _MATRIX_3x3_H_

#ifdef __cplusplus

#import "Vector.h"

namespace Math

{

    template <typename Type>

    class Matrix3

    {

    public:

        Matrix3();

        Matrix3(const bool &bIsRowMajor,

                const Type * const pMatrix);

        Matrix3(const bool &bIsRowMajor,

                const Vector3<Type> &rVec1,

                const Vector3<Type> &rVec2,

                const Vector3<Type> &rVec3);

        Matrix3(const bool &bIsRowMajor,

                const Vector2<Type> &rVec1,

                const Vector2<Type> &rVec2,

                const Vector2<Type> &rVec3);

        Matrix3(const Matrix3<Type> &rMatrix);

        Matrix3(const Matrix3<Type> * const pMatrix);

        virtual ~Matrix3();

        Matrix3<Type> &operator=(const Matrix3<Type> &rMatrix);

        const Vector3<Type> GetColumn(const std::size_t &nCol) const;

        const Vector3<Type> GetRow(const std::size_t &nRow)    const;

        const Type  GetTolerance() const;

        void SetColumn(const std::size_t &nCol, const Vector3<Type> &rVec);

        void SetRow(const std::size_t &nRow, const Vector3<Type> &rVec);

        void SetMatrix(const bool &bIsRowMajor,

                       const Type * const pMatrix);

        void SetMatrix(const bool &bIsRowMajor,

                       const Vector3<Type> &rVec1,

                       const Vector3<Type> &rVec2,

                       const Vector3<Type> &rVec3);

        void SetTolerance(const Type &nTolerance);

        const Vector3<Type> operator[](const std::size_t &nRow) const;

        const Matrix3<Type> operator+(const Matrix3<Type> &rMatrix) const;

        const Matrix3<Type> operator-(const Matrix3<Type> &rMatrix) const;

        const Matrix3<Type> operator*(const Matrix3<Type> &rMatrix) const;

        Matrix3<Type> &operator+=(const Matrix3<Type> &rMatrix);

        Matrix3<Type> &operator-=(const Matrix3<Type> &rMatrix);

        Matrix3<Type> &operator*=(const Matrix3<Type> &rMatrix);

        const Matrix3<Type> operator+(const Type &k) const;

        const Matrix3<Type> operator-(const Type &k) const;

        const Matrix3<Type> operator*(const Type &k) const;

        const Matrix3<Type> operator/(const Type &k) const;

        Matrix3<Type> &operator+=(const Type &k);

        Matrix3<Type> &operator-=(const Type &k);

        Matrix3<Type> &operator*=(const Type &k);

        Matrix3<Type> &operator/=(const Type &k);

        Type &operator()(const std::size_t &nRow, const std::size_t &nColumn);

        Type  operator()(const std::size_t &nRow, const std::size_t &nColumn) const;

        friend Vector3<Type> operator*(const Matrix3<Type> &rMatrix, const Vector3<Type> &rVector);

        friend Vector3<Type> operator*(const Vector3<Type> &rVector, const Matrix3<Type> &rMatrix);

    public:

        union

        {

            Type matrix[10];

            struct

            {

                Type m_11, m_12, m_13;

                Type m_21, m_22, m_23;

                Type m_31, m_32, m_33;

                Type eps;

            }; // struct

        }; // union

    }; // Matrix3

    // Compute determinant of a 3x3 matrix.

    double det(const Matrix3<double> &rMatrix);

    float  det(const Matrix3<float>  &rMatrix);

    // Construct a diagonal 3x3 matrix.

    // Can be used to create identity and scalar matrices.

    Matrix3<double> diag(const Vector3<double> &rScalar);

    Matrix3<float>  diag(const Vector3<float>  &rScalar);

    // Compute matrix inverse of a 3x3 matrix.

    Matrix3<double> inv(const Matrix3<double> &rMatrix);

    Matrix3<float>  inv(const Matrix3<float>  &rMatrix);

    // Compute transpose of a 3x3 matrix.

    Matrix3<double> tr(const Matrix3<double> &rMatrix);

    Matrix3<float>  tr(const Matrix3<float>  &rMatrix);

    // Orthonormalize a 3x3 matrix.

    Matrix3<double> orthn(const Matrix3<double> &rMatrix);

    Matrix3<float>  orthn(const Matrix3<float>  &rMatrix);

    // Solve a 3x3 system of linear equations.

    Vector3<double> solve(const Vector3<double> &rColVecB, const Matrix3<double> &rMatrix);

    Vector3<float>  solve(const Vector3<float>  &rColVecB, const Matrix3<float>  &rMatrix);

} // Math

#endif

#endif