Matrix.h File Reference

typedef and functions to augment Eigen's MatrixXd More...

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Namespaces
	gtsam
	Global functions in a separate testing namespace.

Typedefs
typedef Eigen::MatrixXd	gtsam::Matrix
typedef Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor >	gtsam::MatrixRowMajor
typedef Eigen::Matrix3d	gtsam::Matrix3
typedef Eigen::Matrix4d	gtsam::Matrix4
typedef Eigen::Matrix< double, 6, 6 >	gtsam::Matrix6
typedef Eigen::Block< Matrix >	gtsam::SubMatrix
typedef Eigen::Block< const Matrix >	gtsam::ConstSubMatrix

Functions
Matrix	gtsam::zeros (size_t m, size_t n)
	Creates an zeros matrix, with matlab-like syntax. More...
Matrix	gtsam::ones (size_t m, size_t n)
	Creates an ones matrix, with matlab-like syntax.
Matrix	gtsam::eye (size_t m, size_t n)
	Creates an identity matrix, with matlab-like syntax. More...
Matrix	gtsam::eye (size_t m)
	Creates a square identity matrix, with matlab-like syntax. More...
Matrix	gtsam::diag (const Vector &v)
template<class MATRIX >
bool	gtsam::equal_with_abs_tol (const Eigen::DenseBase< MATRIX > &A, const Eigen::DenseBase< MATRIX > &B, double tol=1e-9)
	equals with an tolerance
bool	gtsam::operator== (const Matrix &A, const Matrix &B)
	equality is just equal_with_abs_tol 1e-9 More...
bool	gtsam::operator!= (const Matrix &A, const Matrix &B)
	inequality
bool	gtsam::assert_equal (const Matrix &A, const Matrix &B, double tol=1e-9)
	equals with an tolerance, prints out message if unequal More...
bool	gtsam::assert_inequal (const Matrix &A, const Matrix &B, double tol=1e-9)
	inequals with an tolerance, prints out message if within tolerance More...
bool	gtsam::assert_equal (const std::list< Matrix > &As, const std::list< Matrix > &Bs, double tol=1e-9)
	equals with an tolerance, prints out message if unequal
bool	gtsam::linear_independent (const Matrix &A, const Matrix &B, double tol=1e-9)
	check whether the rows of two matrices are linear independent
bool	gtsam::linear_dependent (const Matrix &A, const Matrix &B, double tol=1e-9)
	check whether the rows of two matrices are linear dependent More...
void	gtsam::multiplyAdd (double alpha, const Matrix &A, const Vector &x, Vector &e)
	BLAS Level-2 style e <- e + alpha*A*x.
void	gtsam::multiplyAdd (const Matrix &A, const Vector &x, Vector &e)
	BLAS Level-2 style e <- e + A*x.
Vector	gtsam::operator^ (const Matrix &A, const Vector &v)
	overload ^ for trans(A)*v We transpose the vectors for speed.
void	gtsam::transposeMultiplyAdd (double alpha, const Matrix &A, const Vector &e, Vector &x)
	BLAS Level-2 style x <- x + alpha*A'*e.
void	gtsam::transposeMultiplyAdd (const Matrix &A, const Vector &e, Vector &x)
	BLAS Level-2 style x <- x + A'*e.
void	gtsam::transposeMultiplyAdd (double alpha, const Matrix &A, const Vector &e, SubVector x)
	BLAS Level-2 style x <- x + alpha*A'*e.
template<class MATRIX >
MATRIX	gtsam::prod (const MATRIX &A, const MATRIX &B)
	products using old-style format to improve compatibility
void	gtsam::print (const Matrix &A, const std::string &s="", std::ostream &stream=std::cout)
	print a matrix More...
void	gtsam::save (const Matrix &A, const std::string &s, const std::string &filename)
	save a matrix to file, which can be loaded by matlab More...
istream &	gtsam::operator>> (std::istream &inputStream, Matrix &destinationMatrix)
	Read a matrix from an input stream, such as a file. More...
template<class MATRIX >
Eigen::Block< const MATRIX >	gtsam::sub (const MATRIX &A, size_t i1, size_t i2, size_t j1, size_t j2)
	extract submatrix, slice semantics, i.e. More...
template<typename Derived1 , typename Derived2 >
void	gtsam::insertSub (Eigen::MatrixBase< Derived1 > &fullMatrix, const Eigen::MatrixBase< Derived2 > &subMatrix, size_t i, size_t j)
	insert a submatrix IN PLACE at a specified location in a larger matrix NOTE: there is no size checking More...
Matrix	gtsam::diag (const std::vector< Matrix > &Hs)
	Create a matrix with submatrices along its diagonal.
template<class MATRIX >
const MATRIX::ConstColXpr	gtsam::column (const MATRIX &A, size_t j)
	Extracts a column view from a matrix that avoids a copy. More...
template<class MATRIX >
const MATRIX::ConstRowXpr	gtsam::row (const MATRIX &A, size_t j)
	Extracts a row view from a matrix that avoids a copy. More...
void	gtsam::insertColumn (Matrix &A, const Vector &col, size_t j)
	inserts a column into a matrix IN PLACE NOTE: there is no size checking Alternate form allows for vectors smaller than the whole column to be inserted More...
void	gtsam::insertColumn (Matrix &A, const Vector &col, size_t i, size_t j)
Vector	gtsam::columnNormSquare (const Matrix &A)
template<class MATRIX >
void	gtsam::zeroBelowDiagonal (MATRIX &A, size_t cols=0)
	Zeros all of the elements below the diagonal of a matrix, in place. More...
Matrix	gtsam::trans (const Matrix &A)
	static transpose function, just calls Eigen transpose member function
void	gtsam::solve (Matrix &A, Matrix &B)
	solve AX=B via in-place Lu factorization and backsubstitution After calling, A contains LU, B the solved RHS vectors
Matrix	gtsam::inverse (const Matrix &A)
	invert A
pair< Matrix, Matrix >	gtsam::qr (const Matrix &A)
	Householder QR factorization, Golub & Van Loan p 224, explicit version. More...
template<class MATRIX >
void	gtsam::inplace_QR (MATRIX &A)
	QR factorization using Eigen's internal block QR algorithm. More...
list< boost::tuple< Vector, double, double > >	gtsam::weighted_eliminate (Matrix &A, Vector &b, const Vector &sigmas)
	Imperative algorithm for in-place full elimination with weights and constraint handling. More...
void	gtsam::householder_ (Matrix &A, size_t k, bool copy_vectors)
	Imperative version of Householder QR factorization, Golub & Van Loan p 224 version with Householder vectors below diagonal, as in GVL. More...
void	gtsam::householder (Matrix &A, size_t k)
	Householder tranformation, zeros below diagonal. More...
Vector	gtsam::backSubstituteUpper (const Matrix &U, const Vector &b, bool unit=false)
	backSubstitute U*x=b More...
Vector	gtsam::backSubstituteUpper (const Vector &b, const Matrix &U, bool unit=false)
	backSubstitute x'*U=b' More...
Vector	gtsam::backSubstituteLower (const Matrix &L, const Vector &b, bool unit=false)
	backSubstitute L*x=b More...
Matrix	gtsam::stack (size_t nrMatrices,...)
	create a matrix by stacking other matrices Given a set of matrices: A1, A2, A3... More...
Matrix	gtsam::stack (const std::vector< Matrix > &blocks)
Matrix	gtsam::collect (const std::vector< const Matrix * > &matrices, size_t m=0, size_t n=0)
	create a matrix by concatenating Given a set of matrices: A1, A2, A3... More...
Matrix	gtsam::collect (size_t nrMatrices,...)
void	gtsam::vector_scale_inplace (const Vector &v, Matrix &A, bool inf_mask=false)
	scales a matrix row or column by the values in a vector Arguments (Matrix, Vector) scales the columns, (Vector, Matrix) scales the rows More...
Matrix	gtsam::vector_scale (const Vector &v, const Matrix &A, bool inf_mask)
Matrix	gtsam::vector_scale (const Matrix &A, const Vector &v, bool inf_mask)
Matrix3	gtsam::skewSymmetric (double wx, double wy, double wz)
	skew symmetric matrix returns this: 0 -wz wy wz 0 -wx -wy wx 0 More...
template<class Derived >
Matrix3	gtsam::skewSymmetric (const Eigen::MatrixBase< Derived > &w)
Matrix	gtsam::inverse_square_root (const Matrix &A)
	Use Cholesky to calculate inverse square root of a matrix.
Matrix	gtsam::LLt (const Matrix &A)
	Calculate the LL^t decomposition of a S.P.D matrix.
Matrix	gtsam::RtR (const Matrix &A)
	Calculate the R^tR decomposition of a S.P.D matrix.
Matrix	gtsam::cholesky_inverse (const Matrix &A)
	Return the inverse of a S.P.D. More...
void	gtsam::svd (const Matrix &A, Matrix &U, Vector &S, Matrix &V)
	SVD computes economy SVD A=U*S*V'. More...
boost::tuple< int, double, Vector >	gtsam::DLT (const Matrix &A, double rank_tol=1e-9)
	Direct linear transform algorithm that calls svd to find a vector v that minimizes the algebraic error A*v. More...
Matrix	gtsam::expm (const Matrix &A, size_t K=7)
	Numerical exponential map, naive approach, not industrial strength !!! More...
Matrix	gtsam::Cayley (const Matrix &A)
	Cayley transform.
template<int N>
Eigen::Matrix< double, N, N >	gtsam::CayleyFixed (const Eigen::Matrix< double, N, N > &A)
	Implementation of Cayley transform using fixed size matrices to let Eigen do more optimization.
std::string	gtsam::formatMatrixIndented (const std::string &label, const Matrix &matrix, bool makeVectorHorizontal)
template<class Archive >
void	boost::serialization::save (Archive &ar, const gtsam::Matrix &m, unsigned int version)
template<class Archive >
void	boost::serialization::load (Archive &ar, gtsam::Matrix &m, unsigned int version)

Detailed Description

typedef and functions to augment Eigen's MatrixXd

Author

Christian Potthast

Kai Ni

Frank Dellaert

Alex Cunningham