/// @ref gtc_matrix_inverse
/// @file glm/gtc/matrix_inverse.inl

namespace glm
{
	template<typename T, qualifier Q>
	GLM_FUNC_QUALIFIER mat<3, 3, T, Q> affineInverse(mat<3, 3, T, Q> const& m)
	{
		mat<2, 2, T, Q> const Inv(inverse(mat<2, 2, T, Q>(m)));

		return mat<3, 3, T, Q>(
			vec<3, T, Q>(Inv[0], static_cast<T>(0)),
			vec<3, T, Q>(Inv[1], static_cast<T>(0)),
			vec<3, T, Q>(-Inv * vec<2, T, Q>(m[2]), static_cast<T>(1)));
	}

	template<typename T, qualifier Q>
	GLM_FUNC_QUALIFIER mat<4, 4, T, Q> affineInverse(mat<4, 4, T, Q> const& m)
	{
		mat<3, 3, T, Q> const Inv(inverse(mat<3, 3, T, Q>(m)));

		return mat<4, 4, T, Q>(
			vec<4, T, Q>(Inv[0], static_cast<T>(0)),
			vec<4, T, Q>(Inv[1], static_cast<T>(0)),
			vec<4, T, Q>(Inv[2], static_cast<T>(0)),
			vec<4, T, Q>(-Inv * vec<3, T, Q>(m[3]), static_cast<T>(1)));
	}

	template<typename T, qualifier Q>
	GLM_FUNC_QUALIFIER mat<2, 2, T, Q> inverseTranspose(mat<2, 2, T, Q> const& m)
	{
		T Determinant = m[0][0] * m[1][1] - m[1][0] * m[0][1];

		mat<2, 2, T, Q> Inverse(
			+ m[1][1] / Determinant,
			- m[0][1] / Determinant,
			- m[1][0] / Determinant,
			+ m[0][0] / Determinant);

		return Inverse;
	}

	template<typename T, qualifier Q>
	GLM_FUNC_QUALIFIER mat<3, 3, T, Q> inverseTranspose(mat<3, 3, T, Q> const& m)
	{
		T Determinant =
			+ m[0][0] * (m[1][1] * m[2][2] - m[1][2] * m[2][1])
			- m[0][1] * (m[1][0] * m[2][2] - m[1][2] * m[2][0])
			+ m[0][2] * (m[1][0] * m[2][1] - m[1][1] * m[2][0]);

		mat<3, 3, T, Q> Inverse;
		Inverse[0][0] = + (m[1][1] * m[2][2] - m[2][1] * m[1][2]);
		Inverse[0][1] = - (m[1][0] * m[2][2] - m[2][0] * m[1][2]);
		Inverse[0][2] = + (m[1][0] * m[2][1] - m[2][0] * m[1][1]);
		Inverse[1][0] = - (m[0][1] * m[2][2] - m[2][1] * m[0][2]);
		Inverse[1][1] = + (m[0][0] * m[2][2] - m[2][0] * m[0][2]);
		Inverse[1][2] = - (m[0][0] * m[2][1] - m[2][0] * m[0][1]);
		Inverse[2][0] = + (m[0][1] * m[1][2] - m[1][1] * m[0][2]);
		Inverse[2][1] = - (m[0][0] * m[1][2] - m[1][0] * m[0][2]);
		Inverse[2][2] = + (m[0][0] * m[1][1] - m[1][0] * m[0][1]);
		Inverse /= Determinant;

		return Inverse;
	}

	template<typename T, qualifier Q>
	GLM_FUNC_QUALIFIER mat<4, 4, T, Q> inverseTranspose(mat<4, 4, T, Q> const& m)
	{
		T SubFactor00 = m[2][2] * m[3][3] - m[3][2] * m[2][3];
		T SubFactor01 = m[2][1] * m[3][3] - m[3][1] * m[2][3];
		T SubFactor02 = m[2][1] * m[3][2] - m[3][1] * m[2][2];
		T SubFactor03 = m[2][0] * m[3][3] - m[3][0] * m[2][3];
		T SubFactor04 = m[2][0] * m[3][2] - m[3][0] * m[2][2];
		T SubFactor05 = m[2][0] * m[3][1] - m[3][0] * m[2][1];
		T SubFactor06 = m[1][2] * m[3][3] - m[3][2] * m[1][3];
		T SubFactor07 = m[1][1] * m[3][3] - m[3][1] * m[1][3];
		T SubFactor08 = m[1][1] * m[3][2] - m[3][1] * m[1][2];
		T SubFactor09 = m[1][0] * m[3][3] - m[3][0] * m[1][3];
		T SubFactor10 = m[1][0] * m[3][2] - m[3][0] * m[1][2];
		T SubFactor11 = m[1][1] * m[3][3] - m[3][1] * m[1][3];
		T SubFactor12 = m[1][0] * m[3][1] - m[3][0] * m[1][1];
		T SubFactor13 = m[1][2] * m[2][3] - m[2][2] * m[1][3];
		T SubFactor14 = m[1][1] * m[2][3] - m[2][1] * m[1][3];
		T SubFactor15 = m[1][1] * m[2][2] - m[2][1] * m[1][2];
		T SubFactor16 = m[1][0] * m[2][3] - m[2][0] * m[1][3];
		T SubFactor17 = m[1][0] * m[2][2] - m[2][0] * m[1][2];
		T SubFactor18 = m[1][0] * m[2][1] - m[2][0] * m[1][1];

		mat<4, 4, T, Q> Inverse;
		Inverse[0][0] = + (m[1][1] * SubFactor00 - m[1][2] * SubFactor01 + m[1][3] * SubFactor02);
		Inverse[0][1] = - (m[1][0] * SubFactor00 - m[1][2] * SubFactor03 + m[1][3] * SubFactor04);
		Inverse[0][2] = + (m[1][0] * SubFactor01 - m[1][1] * SubFactor03 + m[1][3] * SubFactor05);
		Inverse[0][3] = - (m[1][0] * SubFactor02 - m[1][1] * SubFactor04 + m[1][2] * SubFactor05);

		Inverse[1][0] = - (m[0][1] * SubFactor00 - m[0][2] * SubFactor01 + m[0][3] * SubFactor02);
		Inverse[1][1] = + (m[0][0] * SubFactor00 - m[0][2] * SubFactor03 + m[0][3] * SubFactor04);
		Inverse[1][2] = - (m[0][0] * SubFactor01 - m[0][1] * SubFactor03 + m[0][3] * SubFactor05);
		Inverse[1][3] = + (m[0][0] * SubFactor02 - m[0][1] * SubFactor04 + m[0][2] * SubFactor05);

		Inverse[2][0] = + (m[0][1] * SubFactor06 - m[0][2] * SubFactor07 + m[0][3] * SubFactor08);
		Inverse[2][1] = - (m[0][0] * SubFactor06 - m[0][2] * SubFactor09 + m[0][3] * SubFactor10);
		Inverse[2][2] = + (m[0][0] * SubFactor11 - m[0][1] * SubFactor09 + m[0][3] * SubFactor12);
		Inverse[2][3] = - (m[0][0] * SubFactor08 - m[0][1] * SubFactor10 + m[0][2] * SubFactor12);

		Inverse[3][0] = - (m[0][1] * SubFactor13 - m[0][2] * SubFactor14 + m[0][3] * SubFactor15);
		Inverse[3][1] = + (m[0][0] * SubFactor13 - m[0][2] * SubFactor16 + m[0][3] * SubFactor17);
		Inverse[3][2] = - (m[0][0] * SubFactor14 - m[0][1] * SubFactor16 + m[0][3] * SubFactor18);
		Inverse[3][3] = + (m[0][0] * SubFactor15 - m[0][1] * SubFactor17 + m[0][2] * SubFactor18);

		T Determinant =
			+ m[0][0] * Inverse[0][0]
			+ m[0][1] * Inverse[0][1]
			+ m[0][2] * Inverse[0][2]
			+ m[0][3] * Inverse[0][3];

		Inverse /= Determinant;

		return Inverse;
	}
}//namespace glm