MatrixOps Namespace Reference

Functions
void	addMultipleTo (DMatZZpFFPACK &C, const DMatZZpFFPACK::ElementType &a, const DMatZZpFFPACK &A, const DMatZZpFFPACK &B)
void	addMultipleTo (DMatZZpFFPACK &C, const DMatZZpFFPACK &A, const DMatZZpFFPACK &B)
void	subtractMultipleTo (DMatZZpFFPACK &C, const DMatZZpFFPACK &A, const DMatZZpFFPACK &B)
void	mult (const DMatZZpFFPACK &A, const DMatZZpFFPACK &B, DMatZZpFFPACK &C)
template<typename RT>
bool	isZero (const DMat< RT > &A)
template<typename RT>
bool	isEqual (const DMat< RT > &A, const DMat< RT > &B)
template<typename RT>
void	scalarMultInPlace (DMat< RT > &A, const typename RT::ElementType &f)
template<typename RT>
void	negateInPlace (DMat< RT > &A)
template<typename RT>
void	addInPlace (DMat< RT > &A, const DMat< RT > &B)
template<typename RT>
void	subtractInPlace (DMat< RT > &A, const DMat< RT > &B)
template<typename RT>
void	transpose (const DMat< RT > &A, DMat< RT > &result)
template<typename RT>
void	setZero (DMat< RT > &A, MatrixWindow wA)
template<typename MatType>
void	setZero (SubMatrix< MatType > A)
template<typename RT>
void	set (DMat< RT > &A, MatrixWindow wA, const DMat< RT > &B, MatrixWindow wB)
template<typename RT>
void	addTo (DMat< RT > &A, MatrixWindow wA, const DMat< RT > &B, MatrixWindow wB)
template<typename RT>
void	addMultipleTo (DMat< RT > &A, MatrixWindow wA, const typename RT::ElementType &c, const DMat< RT > &B, MatrixWindow wB)
template<typename RT>
void	scalarMult (DMat< RT > &A, MatrixWindow wA, const typename RT::ElementType &c, const DMat< RT > &B, MatrixWindow wB)
template<typename RT>
void	scalarMultInPlace (DMat< RT > &A, MatrixWindow wA, const typename RT::ElementType &c)
template<typename RT>
bool	isZero (const SMat< RT > &A)
template<typename RT>
bool	isEqual (const SMat< RT > &A, const SMat< RT > &B)
template<typename RT>
void	scalarMultInPlace (SMat< RT > &A, const typename RT::ElementType &f)
template<typename RT>
void	negateInPlace (SMat< RT > &A)
template<typename RT>
void	addInPlace (SMat< RT > &A, const SMat< RT > &B)
template<typename RT>
void	subtractInPlace (SMat< RT > &A, const SMat< RT > &B)
template<typename RT>
void	transpose (const SMat< RT > &A, SMat< RT > &result)
template<typename Mat>
size_t	rank (const Mat &A)
	the rank of a matrix
template<typename Mat>
void	determinant (const Mat &A, typename Mat::ElementType &result_det)
	the determinant of a square matrix
template<typename Mat>
bool	inverse (const Mat &A, Mat &result_inv)
	the inverse of a square matrix
template<typename Mat>
size_t	rowReducedEchelonForm (const Mat &A, Mat &result_rref)
	the row reduced echelon form of a matrix over a field, or ZZ.
template<typename Mat>
void	mult (const Mat &A, const Mat &B, Mat &result_product)
	the product of two matrices
template<typename Mat>
size_t	nullSpace (const Mat &A, Mat &result_nullspace)
	the null space of a matrix
template<typename Mat>
bool	solveLinear (const Mat &A, const Mat &B, Mat &X)
	solve AX=B, return true if the system has a solution.
template<typename Mat>
bool	solveInvertible (const Mat &A, const Mat &B, Mat &X)
	solve AX=B, where A is a square (invertible) matrix.
template<typename Mat>
M2_arrayintOrNull	rankProfile (const Mat &A, bool row_profile)
	Returns either the row or column rank profile of A.
template<typename Mat>
void	addMultipleTo (Mat &C, const Mat &A, const Mat &B)
	Set C += A*B.
template<typename Mat>
void	subtractMultipleTo (Mat &C, const Mat &A, const Mat &B)
	Set C -= A*B.
template<typename Mat>
M2_arrayintOrNull	LU (const Mat &A, Mat &L, Mat &U)
template<typename Mat>
M2_arrayintOrNull	LUincremental (std::vector< size_t > &P, Mat &LU, const Mat &v, int i)
template<typename Mat>
void	triangularSolve (Mat &Lv, Mat &x, int m, int strategy)
template<typename Mat, typename Mat2>
bool	eigenvalues (const Mat &A, Mat2 &eigenvals)
template<typename Mat, typename Mat2>
bool	eigenvaluesHermitian (const Mat &A, Mat2 &eigenvals)
template<typename Mat, typename Mat2, typename Mat3>
bool	eigenvectors (const Mat &A, Mat2 &eigenvals, Mat3 &eigenvecs)
template<typename Mat, typename Mat2, typename Mat3>
bool	eigenvectorsHermitian (const Mat &A, Mat2 &eigenvals, Mat3 &eigenvecs)
template<typename Mat>
bool	leastSquares (const Mat &A, const Mat &B, Mat &X, bool assume_full_rank)
template<typename Mat, typename Mat2>
bool	SVD (const Mat &A, Mat2 &Sigma, Mat &U, Mat &Vt, int strategy)
template<typename Mat, typename Mat2, typename Mat3>
bool	QR (const Mat &A, Mat2 &Q, Mat3 &R, bool return_QR)
template<typename T>
void	clean (gmp_RR epsilon, T &mat)
template<typename T>
void	increase_norm (gmp_RRmutable nm, const T &mat)
template<typename RT>
void	mult (const DMat< RT > &A, const DMat< RT > &B, DMat< RT > &result_product)
template<typename RT>
void	addMultipleTo (DMat< RT > &C, const DMat< RT > &A, const DMat< RT > &B)
template<typename RT>
void	subtractMultipleTo (DMat< RT > &C, const DMat< RT > &A, const DMat< RT > &B)
template<typename RT>
void	determinant (const DMat< RT > &A, typename RT::ElementType &result)
template<typename RT>
M2_arrayintOrNull	LU (const DMat< RT > &A, DMat< RT > &L, DMat< RT > &U)
template<typename RT>
void	triangularSolve (DMat< RT > &Lv, DMat< RT > &x, int m, int strategy)
template<typename RT>
M2_arrayintOrNull	LUincremental (std::vector< size_t > &P, DMat< RT > &LU, const DMat< RT > &v, int m)
template<typename RT>
size_t	rank (const DMat< RT > &A)
template<typename RT>
M2_arrayintOrNull	rankProfile (const DMat< RT > &A, bool row_profile)
template<typename RT>
bool	inverse (const DMat< RT > &A, DMat< RT > &result_inv)
template<typename RT>
size_t	nullSpace (const DMat< RT > &A, DMat< RT > &result_nullspace)
template<typename RT>
bool	solveLinear (const DMat< RT > &A, const DMat< RT > &B, DMat< RT > &X)
template<typename RT>
bool	solveInvertible (const DMat< RT > &A, const DMat< RT > &B, DMat< RT > &X)
M2_arrayintOrNull	LU (const DMatZZGMP &A, DMatZZGMP &L, DMatZZGMP &U)
M2_arrayintOrNull	rankProfile (const DMatZZGMP &A, bool row_profile)
bool	inverse (const DMatZZGMP &A, DMatZZGMP &result_inv)
size_t	nullSpace (const DMatZZGMP &A, DMatZZGMP &result_nullspace)
bool	solveLinear (const DMatZZGMP &A, const DMatZZGMP &B, DMatZZGMP &X)
bool	solveInvertible (const DMatZZGMP &A, const DMatZZGMP &B, DMatZZGMP &X)
void	mult (const DMatZZGMP &A, const DMatZZGMP &B, DMatZZGMP &result_product)
void	addMultipleTo (DMatZZGMP &C, const DMatZZGMP &A, const DMatZZGMP &B)
void	subtractMultipleTo (DMatZZGMP &C, const DMatZZGMP &A, const DMatZZGMP &B)
size_t	rank (const DMatZZGMP &A)
void	determinant (const DMatZZGMP &A, M2::ARingZZGMP::ElementType &result_det)
size_t	rank (const DMatZZ &A)
void	determinant (const DMatZZ &A, M2::ARingZZ::ElementType &result_det)
bool	inverse (const DMatZZ &A, DMatZZ &result_inv)
void	mult (const DMatZZ &A, const DMatZZ &B, DMatZZ &result_product)
size_t	nullSpace (const DMatZZ &A, DMatZZ &result_nullspace)
bool	solveLinear (const DMatZZ &A, const DMatZZ &B, DMatZZ &X)
M2_arrayintOrNull	rankProfile (const DMatZZ &A, bool row_profile)
void	addMultipleTo (DMatZZ &C, const DMatZZ &A, const DMatZZ &B)
void	subtractMultipleTo (DMatZZ &C, const DMatZZ &A, const DMatZZ &B)
void	addMultipleTo (DMatZZpFlint &C, const DMatZZpFlint &A, const DMatZZpFlint &B)
void	subtractMultipleTo (DMatZZpFlint &C, const DMatZZpFlint &A, const DMatZZpFlint &B)
void	mult (const DMatZZpFlint &A, const DMatZZpFlint &B, DMatZZpFlint &result_product)
size_t	rowReducedEchelonForm (const DMatZZpFlint &A, DMatZZpFlint &result_rref)
void	addMultipleTo (DMatGFFlintBig &C, const DMatGFFlintBig &A, const DMatGFFlintBig &B)
void	subtractMultipleTo (DMatGFFlintBig &C, const DMatGFFlintBig &A, const DMatGFFlintBig &B)
void	mult (const DMatGFFlintBig &A, const DMatGFFlintBig &B, DMatGFFlintBig &result_product)
size_t	rowReducedEchelonForm (const DMatGFFlintBig &A, DMatGFFlintBig &result_rref)
void	addMultipleTo (DMatGFFlint &C, const DMatGFFlint &A, const DMatGFFlint &B)
void	subtractMultipleTo (DMatGFFlint &C, const DMatGFFlint &A, const DMatGFFlint &B)
void	mult (const DMatGFFlint &A, const DMatGFFlint &B, DMatGFFlint &result_product)
size_t	rowReducedEchelonForm (const DMatGFFlint &A, DMatGFFlint &result_rref)
void	mult (const DMatQQ &A, const DMatQQ &B, DMatQQ &result_product)
void	addMultipleTo (DMatQQ &C, const DMatQQ &A, const DMatQQ &B)
void	subtractMultipleTo (DMatQQ &C, const DMatQQ &A, const DMatQQ &B)
size_t	rowReducedEchelonForm (const DMatQQ &A, DMatQQ &result_rref)
size_t	rank (const DMatQQFlint &A)
void	determinant (const DMatQQFlint &A, M2::ARingQQFlint::ElementType &result_det)
bool	inverse (const DMatQQFlint &A, DMatQQFlint &result_inv)
size_t	rowReducedEchelonForm (const DMatQQFlint &A, DMatQQFlint &result_rref)
size_t	nullSpace (const DMatQQFlint &A, DMatQQFlint &result_nullspace)
bool	solveLinear (const DMatQQFlint &A, const DMatQQFlint &B, DMatQQFlint &X)
M2_arrayintOrNull	rankProfile (const DMatQQFlint &A, bool row_profile)
void	addMultipleTo (DMatQQFlint &C, const DMatQQFlint &A, const DMatQQFlint &B)
void	subtractMultipleTo (DMatQQFlint &C, const DMatQQFlint &A, const DMatQQFlint &B)
void	mult (const DMatQQFlint &A, const DMatQQFlint &B, DMatQQFlint &result_product)
bool	eigenvaluesHermitian (const DMatRR &A, DMatRR &eigenvals)
bool	eigenvalues (const DMatRR &A, DMatCC &eigenvals)
bool	eigenvectorsHermitian (const DMatRR &A, DMatRR &eigenvals, DMatRR &eigenvecs)
bool	eigenvectors (const DMatRR &A, DMatCC &eigenvals, DMatCC &eigenvecs)
bool	leastSquares (const DMatRR &A, const DMatRR &B, DMatRR &X, bool assume_full_rank)
bool	SVD (const DMatRR &A, DMatRR &Sigma, DMatRR &U, DMatRR &Vt, int strategy)
bool	QR (const DMatRR &A, DMatRR &Q, DMatRR &R, bool return_QR)
bool	QR (const DMatCC &A, DMatCC &Q, DMatCC &R, bool return_QR)
void	clean (gmp_RR epsilon, DMatRR &mat)
void	increase_norm (gmp_RRmutable norm, const DMatRR &mat)
bool	eigenvaluesHermitian (const DMatCC &A, DMatRR &eigenvals)
bool	eigenvalues (const DMatCC &A, DMatCC &eigenvals)
bool	eigenvectorsHermitian (const DMatCC &A, DMatRR &eigenvals, DMatCC &eigenvecs)
bool	eigenvectors (const DMatCC &A, DMatCC &eigenvals, DMatCC &eigenvecs)
bool	leastSquares (const DMatCC &A, const DMatCC &B, DMatCC &X, bool assume_full_rank)
bool	SVD (const DMatCC &A, DMatRR &Sigma, DMatCC &U, DMatCC &Vt, int strategy)
void	clean (gmp_RR epsilon, DMatCC &mat)
void	increase_norm (gmp_RRmutable norm, const DMatCC &mat)
bool	eigenvaluesHermitian (const DMatRRR &A, DMatRRR &eigenvals)
bool	eigenvalues (const DMatRRR &A, DMatCCC &eigenvals)
bool	eigenvectorsHermitian (const DMatRRR &A, DMatRRR &eigenvals, DMatRRR &eigenvecs)
bool	eigenvectors (const DMatRRR &A, DMatCCC &eigenvals, DMatCCC &eigenvecs)
bool	leastSquares (const DMatRRR &A, const DMatRRR &B, DMatRRR &X, bool assume_full_rank)
bool	SVD (const DMatRRR &A, DMatRRR &Sigma, DMatRRR &U, DMatRRR &Vt, int strategy)
void	clean (gmp_RR epsilon, DMatRRR &mat)
void	increase_norm (gmp_RRmutable norm, const DMatRRR &mat)
bool	eigenvaluesHermitian (const DMatCCC &A, DMatRRR &eigenvals)
bool	eigenvalues (const DMatCCC &A, DMatCCC &eigenvals)
bool	eigenvectorsHermitian (const DMatCCC &A, DMatRRR &eigenvals, DMatCCC &eigenvecs)
bool	eigenvectors (const DMatCCC &A, DMatCCC &eigenvals, DMatCCC &eigenvecs)
bool	leastSquares (const DMatCCC &A, const DMatCCC &B, DMatCCC &X, bool assume_full_rank)
bool	SVD (const DMatCCC &A, DMatRRR &Sigma, DMatCCC &U, DMatCCC &Vt, int strategy)
void	clean (gmp_RR epsilon, DMatCCC &mat)
void	increase_norm (gmp_RRmutable norm, const DMatCCC &mat)