atlas::matrix Namespace Reference

Classes
class	atlas::matrix::Matrix< C >
Functions
template<typename C>
void	columnVectors (std::vector< std::vector< C > > &b, const Matrix< C > &m)
template<typename C>
Matrix< C > &	conjugate (Matrix< C > &, const Matrix< C > &)
template<typename C>
void	extractBlock (Matrix< C > &, const Matrix< C > &, size_t, size_t, size_t, size_t)
template<typename C>
void	extractMatrix (Matrix< C > &, const Matrix< C > &, const std::vector< size_t > &, const std::vector< size_t > &)
template<typename C>
void	identityMatrix (Matrix< C > &, size_t)
template<typename C>
void	initBasis (std::vector< std::vector< C > > &, size_t)
template<typename C>
Matrix< C > &	invConjugate (Matrix< C > &, const Matrix< C > &)
template<typename C>
void	blockReduce (Matrix< C > &, size_t, Matrix< C > &, Matrix< C > &)
template<typename C>
void	blockShape (Matrix< C > &, size_t, Matrix< C > &, Matrix< C > &)
template<typename C>
void	columnReduce (Matrix< C > &, size_t, size_t, Matrix< C > &)
template<typename C>
bool	hasBlockReduction (const Matrix< C > &, size_t)
template<typename C>
bool	hasReduction (const Matrix< C > &, size_t)
template<typename C>
Matrix< C >::index_pair	findBlockReduction (const Matrix< C > &, size_t)
template<typename C>
Matrix< C >::index_pair	findReduction (const Matrix< C > &, size_t)
template<typename C>
void	rowReduce (Matrix< C > &, size_t, size_t, Matrix< C > &)
template<typename C>
void	blockReduce (Matrix< C > &m, size_t d, Matrix< C > &r, Matrix< C > &c)
template<typename C>
void	blockShape (Matrix< C > &m, size_t d, Matrix< C > &r, Matrix< C > &c)
template<typename C>
void	columnReduce (Matrix< C > &m, size_t j, size_t d, Matrix< C > &c)
template<typename C>
Matrix< C >::index_pair	findBlockReduction (const Matrix< C > &m, size_t r)
template<typename C>
Matrix< C >::index_pair	findReduction (const Matrix< C > &m, size_t r)
template<typename C>
bool	hasBlockReduction (const Matrix< C > &m, size_t r)
template<typename C>
bool	hasReduction (const Matrix< C > &m, size_t r)
template<typename C>
void	rowReduce (Matrix< C > &m, size_t i, size_t d, Matrix< C > &r)

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Function Documentation

template<typename C> void blockReduce (  Matrix< C > &  m, size_t  d, Matrix< C > &  r, Matrix< C > &  c )  [static]

Ensures that m(d,d) divides the block from (d+1,d+1) down. Definition at line 1002 of file matrix_def.h. References blockShape(), columnReduce(), atlas::matrix::Matrix< C >::columnSize(), findBlockReduction(), findReduction(), hasBlockReduction(), hasReduction(), atlas::matrix::Matrix< C >::rowOperation(), rowReduce(), and atlas::matrix::Matrix< C >::rowSize().

template<typename C> void blockReduce (  Matrix< C > &  , size_t  , Matrix< C > &  , Matrix< C > &  )  [static]

Referenced by atlas::matrix::Matrix< C >::invert().

template<typename C> void blockShape (  Matrix< C > &  m, size_t  d, Matrix< C > &  r, Matrix< C > &  c )  [static]

Does the final reduction of m to block shape, recording row reductions in r and column reductions in c. Definition at line 1038 of file matrix_def.h. References atlas::matrix::Matrix< C >::columnOperation(), atlas::matrix::Matrix< C >::columnSize(), atlas::matrix::Matrix< C >::rowOperation(), and atlas::matrix::Matrix< C >::rowSize().

template<typename C> void blockShape (  Matrix< C > &  , size_t  , Matrix< C > &  , Matrix< C > &  )  [static]

Referenced by blockReduce(), and atlas::matrix::Matrix< C >::invert().

template<typename C> void columnReduce (  Matrix< C > &  m, size_t  j, size_t  d, Matrix< C > &  c )  [static]

Does the column reduction for m at place j, and does the same operation on r. The reduction consists in subtracting from column j the multiple of column d which leaves at (d,j) the remainder of the Euclidian division of m(d,j) by m(d,d), and then swapping columns j and d. Definition at line 1071 of file matrix_def.h. References atlas::matrix::Matrix< C >::columnOperation(), atlas::intutils::divide(), and atlas::matrix::Matrix< C >::swapColumns().

template<typename C> void columnReduce (  Matrix< C > &  , size_t  , size_t  , Matrix< C > &  )  [static]

Referenced by blockReduce(), and atlas::matrix::Matrix< C >::invert().

template<typename C> void atlas::matrix::columnVectors (  std::vector< std::vector< C > > &  b, const Matrix< C > &  m )

Synopsis: writes in b the list of column vectors of m. Definition at line 865 of file matrix_def.h. References atlas::matrix::Matrix< C >::column(), atlas::matrix::Matrix< C >::numColumns(), and atlas::matrix::Matrix< C >::resize(). Referenced by atlas::interpreter::root_datum_wrapper().

template<typename C> Matrix< C > & atlas::matrix::conjugate (  Matrix< C > &  m, const Matrix< C > &  p )

Conjugates m by p, i.e. transforms m into pmp^{-1}. It is assumed that p is invertible (over the quotient field of the coefficients), and that denominators cancel out. Definition at line 882 of file matrix_def.h. References atlas::matrix::Matrix< C >::inverse(), and atlas::matrix::Matrix< C >::swap().

template<typename C> void atlas::matrix::extractBlock (  Matrix< C > &  dest, const Matrix< C > &  source, size_t  firstRow, size_t  lastRow, size_t  firstColumn, size_t  lastColumn )

Synopsis: sets dest equal to the block [firstRow,lastRow[ x [firstColumn, lastColumn[ in source. Definition at line 900 of file matrix_def.h. References atlas::matrix::Matrix< C >::numColumns(), atlas::matrix::Matrix< C >::numRows(), and atlas::matrix::Matrix< C >::resize().

template<typename C> void atlas::matrix::extractMatrix (  Matrix< C > &  dest, const Matrix< C > &  source, const std::vector< size_t > &  r, const std::vector< size_t > &  c )

Synopsis: extracts the sub-matrix corresponding to the subsets r and c of the row and column indices respectively. Definition at line 919 of file matrix_def.h. References atlas::matrix::Matrix< C >::resize().

template<typename C> Matrix<C>::index_pair findBlockReduction (  const Matrix< C > &  m, size_t  r )  [static]

Returns the reduction point of m. Assumes that hasBlockReduction(m,r) has returned true. Definition at line 1094 of file matrix_def.h. References atlas::matrix::Matrix< C >::columnSize(), and atlas::matrix::Matrix< C >::rowSize().

template<typename C> Matrix<C>::index_pair findBlockReduction (  const Matrix< C > &  , size_t  )  [static]

Referenced by blockReduce().

template<typename C> Matrix<C>::index_pair findReduction (  const Matrix< C > &  m, size_t  r )  [static]

Returns the reduction point of m. Assumes that hasReduction(m,r) has returned true. Definition at line 1117 of file matrix_def.h. References atlas::matrix::Matrix< C >::columnSize(), and atlas::matrix::Matrix< C >::rowSize().

template<typename C> Matrix<C>::index_pair findReduction (  const Matrix< C > &  , size_t  )  [static]

Referenced by blockReduce(), and atlas::matrix::Matrix< C >::invert().

template<typename C> bool hasBlockReduction (  const Matrix< C > &  m, size_t  r )  [static]

Tells if there is an element in the block under (r,r) which is not divisible bu m(r,r) Definition at line 1143 of file matrix_def.h. References atlas::matrix::Matrix< C >::columnSize(), and atlas::matrix::Matrix< C >::rowSize().

template<typename C> bool hasBlockReduction (  const Matrix< C > &  , size_t  )  [static]

Referenced by blockReduce().

template<typename C> bool hasReduction (  const Matrix< C > &  m, size_t  r )  [static]

Tells if there is an element in the first row or column not divisible by m(r,r). Definition at line 1167 of file matrix_def.h. References atlas::matrix::Matrix< C >::columnSize(), and atlas::matrix::Matrix< C >::rowSize().

template<typename C> bool hasReduction (  const Matrix< C > &  , size_t  )  [static]

Referenced by blockReduce(), and atlas::matrix::Matrix< C >::invert().

template<typename C> void atlas::matrix::identityMatrix (  Matrix< C > &  m, size_t  n )

Synopsis: puts in q the identity matrix of size n. Definition at line 937 of file matrix_def.h. References atlas::matrix::Matrix< C >::resize(). Referenced by atlas::interpreter::check_involution(), atlas::interpreter::classify_involution(), atlas::tori::dualPi0(), atlas::interpreter::GL_wrapper(), atlas::interpreter::id_mat_wrapper(), atlas::rootdata::longest(), atlas::makeTopology(), atlas::interpreter::SL_wrapper(), and atlas::rootdata::toMatrix().

template<typename C> void atlas::matrix::initBasis (  std::vector< std::vector< C > > &  b, size_t  r )

Synopsis: sets b to the canonical basis in dimension r. Definition at line 953 of file matrix_def.h. Referenced by atlas::interpreter::annihilator_modulo(), atlas::abelian::basis(), atlas::interpreter::check_involution(), atlas::testrun::CoveringIterator::CoveringIterator(), atlas::rootdata::RootDatum::fillStatus(), atlas::fullMinusBasis(), atlas::fullPlusBasis(), atlas::interpreter::invfact_wrapper(), atlas::makeOrthogonal(), atlas::cartanclass::Fiber::makeRealFormPartition(), atlas::tori::minusBasis(), atlas::lattice::perp(), atlas::tori::plusBasis(), atlas::interpreter::Smith_basis_wrapper(), atlas::interpreter::Smith_wrapper(), atlas::interactive_lattice::smithBasis(), and atlas::interpreter::smithBasis().

template<typename C> Matrix< C > & atlas::matrix::invConjugate (  Matrix< C > &  m, const Matrix< C > &  p )

Conjugates m by p^{-1}, i.e. transforms m into p^{-1}mp. It is assumed that p is invertible (over the quotient field of the coefficients), and that denominators cancel out. Definition at line 970 of file matrix_def.h. References atlas::matrix::Matrix< C >::inverse(), and atlas::matrix::Matrix< C >::swap(). Referenced by atlas::interactive::getInnerClass(), and atlas::matrix::Matrix< C >::Matrix().

template<typename C> void rowReduce (  Matrix< C > &  m, size_t  i, size_t  d, Matrix< C > &  r )  [static]

Does the row reduction for m at place j, and does the same operation on r. The reduction consists in subtracting from row i the multiple of row d which leaves at (i,d) the remainder of the Euclidian division of m(d,j) by m(d,d), and then swapping rows i and d. Definition at line 1194 of file matrix_def.h. References atlas::intutils::divide(), atlas::matrix::Matrix< C >::rowOperation(), and atlas::matrix::Matrix< C >::swapRows().

template<typename C> void rowReduce (  Matrix< C > &  , size_t  , size_t  , Matrix< C > &  )  [static]

Referenced by blockReduce(), and atlas::matrix::Matrix< C >::invert().

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