Routines for 3x3 matrices. More...

#include <FastMatrixMathHelper.h>

Inheritance diagram for lar::util::details::FastMatrixOperations< T, 3 >:

Public Types
using	Base_t = FastMatrixOperationsBase< T, 3 >

using	Data_t = typename Base_t::Data_t

using	Matrix_t = typename Base_t::Matrix_t

Public Types inherited from lar::util::details::FastMatrixOperationsBase< T, 3 >
using	Data_t = T

using	Matrix_t = std::array< Data_t, Dim *Dim >

using	Vector_t = std::array< Data_t, Dim >

Static Public Member Functions
static Data_t	Determinant (Matrix_t const &mat)
	Computes the determinant of a matrix. More...

static Matrix_t	InvertMatrix (Matrix_t const &mat, Data_t det)
	Computes the determinant of a matrix, using the provided determinant. More...

static Matrix_t	InvertSymmetricMatrix (Matrix_t const &mat, Data_t det)

static Matrix_t	InvertMatrix (Matrix_t const &mat)
	Computes the determinant of a matrix. More...

static Matrix_t	InvertSymmetricMatrix (Matrix_t const &mat)
	Computes the determinant of a matrix. More...

Static Public Member Functions inherited from lar::util::details::FastMatrixOperationsBase< T, 3 >
static Vector_t	MatrixVectorProduct (Matrix_t const &mat, Vector_t const &vec)
	Returns the product of a square matrix times a column vector. More...

static constexpr Data_t	sqr (Data_t v)

Static Public Attributes
static constexpr unsigned int	Dim = Base_t::Dim

Static Public Attributes inherited from lar::util::details::FastMatrixOperationsBase< T, 3 >
static constexpr unsigned int	Dim
	matrix dimensions More...

Detailed Description

template<typename T>
struct lar::util::details::FastMatrixOperations< T, 3 >

Routines for 3x3 matrices.

Definition at line 286 of file FastMatrixMathHelper.h.

Member Typedef Documentation

template<typename T >

using lar::util::details::FastMatrixOperations< T, 3 >::Base_t = FastMatrixOperationsBase<T, 3>

Definition at line 289 of file FastMatrixMathHelper.h.

template<typename T >

using lar::util::details::FastMatrixOperations< T, 3 >::Data_t = typename Base_t::Data_t

Definition at line 291 of file FastMatrixMathHelper.h.

template<typename T >

using lar::util::details::FastMatrixOperations< T, 3 >::Matrix_t = typename Base_t::Matrix_t

Definition at line 292 of file FastMatrixMathHelper.h.

Member Function Documentation

template<typename T >

static Data_t lar::util::details::FastMatrixOperations< T, 3 >::Determinant ( Matrix_t const & mat )

inlinestatic

Computes the determinant of a matrix.

Definition at line 295 of file FastMatrixMathHelper.h.

           {
             return
               DeterminantHelper<T, Dim, 0, 1, 2, 0, 1, 2>::compute(mat.data());
           }

template<typename T >

auto lar::util::details::FastMatrixOperations< T, 3 >::InvertMatrix	(	Matrix_t const &	mat,
		Data_t	det
	)

static

Computes the determinant of a matrix, using the provided determinant.

Definition at line 405 of file FastMatrixMathHelper.h.

 {
   Data_t const* data = mat.data();
   Matrix_t Inverse;
   //
   // Basically using Cramer's rule;
   // each element [r,c] gets assigned the determinant of the submatrix
   //   after removing c from the rows and r from the columns
   //   (effectively assigning the transpose of the minor matrix)
   //   with the usual sign -1^(r+c)
   //
   //
   Inverse[0 * Dim + 0] =  DeterminantHelper<T, 3, 1, 2, 1, 2>::compute(data)/det;
   Inverse[0 * Dim + 1] = -DeterminantHelper<T, 3, 0, 2, 1, 2>::compute(data)/det;
   Inverse[0 * Dim + 2] =  DeterminantHelper<T, 3, 0, 1, 1, 2>::compute(data)/det;
   Inverse[1 * Dim + 0] = -DeterminantHelper<T, 3, 1, 2, 0, 2>::compute(data)/det;
   Inverse[1 * Dim + 1] =  DeterminantHelper<T, 3, 0, 2, 0, 2>::compute(data)/det;
   Inverse[1 * Dim + 2] = -DeterminantHelper<T, 3, 0, 1, 0, 2>::compute(data)/det;
   Inverse[2 * Dim + 0] =  DeterminantHelper<T, 3, 1, 2, 0, 1>::compute(data)/det;
   Inverse[2 * Dim + 1] = -DeterminantHelper<T, 3, 0, 2, 0, 1>::compute(data)/det;
   Inverse[2 * Dim + 2] =  DeterminantHelper<T, 3, 0, 1, 0, 1>::compute(data)/det;
   return Inverse;
 } // FastMatrixOperations<T, 3>::InvertMatrix()

template<typename T >

static Matrix_t lar::util::details::FastMatrixOperations< T, 3 >::InvertMatrix ( Matrix_t const & mat )

inlinestatic

Computes the determinant of a matrix.

Definition at line 309 of file FastMatrixMathHelper.h.

310 { return InvertMatrix(mat, Determinant(mat)); }

lar::util::details::FastMatrixOperations< T, 3 >::InvertMatrix

static Matrix_t InvertMatrix(Matrix_t const &mat, Data_t det)

Computes the determinant of a matrix, using the provided determinant.

Definition: FastMatrixMathHelper.h:405

lar::util::details::FastMatrixOperations< T, 3 >::Determinant

static Data_t Determinant(Matrix_t const &mat)

Computes the determinant of a matrix.

Definition: FastMatrixMathHelper.h:295

template<typename T >

auto lar::util::details::FastMatrixOperations< T, 3 >::InvertSymmetricMatrix	(	Matrix_t const &	mat,
		Data_t	det
	)

static

Computes the determinant of a symmatric matrix, using the provided determinant

Definition at line 432 of file FastMatrixMathHelper.h.

 {
   //
   // Same algorithm as InvertMatrix(), but use the fact that the result is
   // also symmetric
   //
   Data_t const* data = mat.data();
   Matrix_t Inverse;
   Inverse[0 * Dim + 0] =  DeterminantHelper<T, 3, 1, 2, 1, 2>::compute(data)/det;
   Inverse[0 * Dim + 1] =
   Inverse[1 * Dim + 0] = -DeterminantHelper<T, 3, 1, 2, 0, 2>::compute(data)/det;
   Inverse[0 * Dim + 2] =
   Inverse[2 * Dim + 0] =  DeterminantHelper<T, 3, 1, 2, 0, 1>::compute(data)/det;
   Inverse[1 * Dim + 1] =  DeterminantHelper<T, 3, 0, 2, 0, 2>::compute(data)/det;
   Inverse[1 * Dim + 2] =
   Inverse[2 * Dim + 1] = -DeterminantHelper<T, 3, 0, 2, 0, 1>::compute(data)/det;
   Inverse[2 * Dim + 2] =  DeterminantHelper<T, 3, 0, 1, 0, 1>::compute(data)/det;
   return Inverse;
 } // FastMatrixOperations<T, 3>::InvertSymmetricMatrix()