glucat  0.8.2
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glucat::matrix_multi< Scalar_T, LO, HI > Class Template Reference

A matrix_multi<Scalar_T,LO,HI> is a matrix approximation to a multivector. More...

#include <framed_multi.h>

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Public Types

typedef matrix_multi multivector_t
 
typedef multivector_t matrix_multi_t
 
typedef Scalar_T scalar_t
 
typedef index_set< LO, HI > index_set_t
 
typedef std::pair< const index_set_t, Scalar_T > term_t
 
typedef std::vector< Scalar_T > vector_t
 
typedef error< multivector_terror_t
 
typedef framed_multi< Scalar_T, LO, HI > framed_multi_t
 
- Public Types inherited from glucat::clifford_algebra< Scalar_T, index_set< LO, HI >, matrix_multi< Scalar_T, LO, HI > >
typedef Scalar_T scalar_t
 
typedef index_set< LO, HI > index_set_t
 
typedef matrix_multi< Scalar_T, LO, HI > multivector_t
 
typedef std::pair< const index_set_t, Scalar_T > pair_t
 
typedef std::vector< Scalar_T > vector_t
 

Public Member Functions

 ~matrix_multi ()
 Destructor. More...
 
 matrix_multi ()
 Default constructor. More...
 
template<typename Other_Scalar_T >
 matrix_multi (const matrix_multi< Other_Scalar_T, LO, HI > &val)
 Construct a multivector from a multivector with a different scalar type. More...
 
template<typename Other_Scalar_T >
 matrix_multi (const matrix_multi< Other_Scalar_T, LO, HI > &val, const index_set_t frm, const bool prechecked=false)
 Construct a multivector, within a given frame, from a given multivector. More...
 
 matrix_multi (const multivector_t &val, const index_set_t frm, const bool prechecked=false)
 Construct a multivector, within a given frame, from a given multivector. More...
 
 matrix_multi (const index_set_t ist, const Scalar_T &crd=Scalar_T(1))
 Construct a multivector from an index set and a scalar coordinate. More...
 
 matrix_multi (const index_set_t ist, const Scalar_T &crd, const index_set_t frm, const bool prechecked=false)
 Construct a multivector, within a given frame, from an index set and a scalar coordinate. More...
 
 matrix_multi (const Scalar_T &scr, const index_set_t frm=index_set_t())
 Construct a multivector from a scalar (within a frame, if given) More...
 
 matrix_multi (const int scr, const index_set_t frm=index_set_t())
 Construct a multivector from an int (within a frame, if given) More...
 
 matrix_multi (const vector_t &vec, const index_set_t frm, const bool prechecked=false)
 Construct a multivector, within a given frame, from a given vector. More...
 
 matrix_multi (const std::string &str)
 Construct a multivector from a string: eg: "3+2{1,2}-6.1e-2{2,3}". More...
 
 matrix_multi (const std::string &str, const index_set_t frm, const bool prechecked=false)
 Construct a multivector, within a given frame, from a string: eg: "3+2{1,2}-6.1e-2{2,3}". More...
 
 matrix_multi (const char *str)
 Construct a multivector from a char*: eg: "3+2{1,2}-6.1e-2{2,3}". More...
 
 matrix_multi (const char *str, const index_set_t frm, const bool prechecked=false)
 Construct a multivector, within a given frame, from a char*: eg: "3+2{1,2}-6.1e-2{2,3}". More...
 
template<typename Other_Scalar_T >
 matrix_multi (const framed_multi< Other_Scalar_T, LO, HI > &val)
 Construct a multivector from a framed_multi_t. More...
 
template<typename Other_Scalar_T >
 matrix_multi (const framed_multi< Other_Scalar_T, LO, HI > &val, const index_set_t frm, const bool prechecked=false)
 Construct a multivector, within a given frame, from a framed_multi_t. More...
 
const matrix_multi_t fast_matrix_multi (const index_set_t frm) const
 Use generalized FFT to construct a matrix_multi_t. More...
 
template<typename Other_Scalar_T >
const framed_multi< Other_Scalar_T, LO, HI > fast_framed_multi () const
 Use inverse generalized FFT to construct a framed_multi_t. More...
 
_GLUCAT_CLIFFORD_ALGEBRA_OPERATIONS multivector_toperator= (const multivector_t &rhs)
 Assignment operator. More...
 
multivector_toperator+= (const term_t &rhs)
 Add a term, if non-zero. More...
 
- Public Member Functions inherited from glucat::clifford_algebra< Scalar_T, index_set< LO, HI >, matrix_multi< Scalar_T, LO, HI > >
virtual ~clifford_algebra ()
 
virtual bool operator== (const multivector_t &val) const =0
 Test for equality of multivectors. More...
 
virtual bool operator== (const Scalar_T &scr) const =0
 Test for equality of multivector and scalar. More...
 
virtual multivector_toperator+= (const multivector_t &rhs)=0
 Geometric sum. More...
 
virtual multivector_toperator+= (const Scalar_T &scr)=0
 Geometric sum of multivector and scalar. More...
 
virtual multivector_toperator-= (const multivector_t &rhs)=0
 Geometric difference. More...
 
virtual const multivector_t operator- () const =0
 Unary -. More...
 
virtual multivector_toperator*= (const Scalar_T &scr)=0
 Product of multivector and scalar. More...
 
virtual multivector_toperator*= (const multivector_t &rhs)=0
 Geometric product. More...
 
virtual multivector_toperator%= (const multivector_t &rhs)=0
 Contraction. More...
 
virtual multivector_toperator&= (const multivector_t &rhs)=0
 Inner product. More...
 
virtual multivector_toperator^= (const multivector_t &rhs)=0
 Outer product. More...
 
virtual multivector_toperator/= (const Scalar_T &scr)=0
 Quotient of multivector and scalar. More...
 
virtual multivector_toperator/= (const multivector_t &rhs)=0
 Geometric quotient. More...
 
virtual multivector_toperator|= (const multivector_t &rhs)=0
 Transformation via twisted adjoint action. More...
 
virtual const multivector_t inv () const =0
 Geometric multiplicative inverse. More...
 
virtual const multivector_t pow (int m) const =0
 *this to the m More...
 
virtual const multivector_t outer_pow (int m) const =0
 Outer product power. More...
 
virtual const index_set_t frame () const =0
 Subalgebra generated by all generators of terms of given multivector. More...
 
virtual index_t grade () const =0
 Maximum of the grades of each term. More...
 
virtual Scalar_T operator[] (const index_set_t ist) const =0
 Subscripting: map from index set to scalar coordinate. More...
 
virtual const multivector_t operator() (index_t grade) const =0
 Pure grade-vector part. More...
 
virtual Scalar_T scalar () const =0
 Scalar part. More...
 
virtual const multivector_t pure () const =0
 Pure part. More...
 
virtual const multivector_t even () const =0
 Even part of multivector, sum of even grade terms. More...
 
virtual const multivector_t odd () const =0
 Odd part of multivector, sum of odd grade terms. More...
 
virtual const vector_t vector_part () const =0
 Vector part of multivector, as a vector_t with respect to frame() More...
 
virtual const vector_t vector_part (const index_set_t frm, const bool prechecked) const =0
 Vector part of multivector, as a vector_t with respect to frm. More...
 
virtual const multivector_t involute () const =0
 Main involution, each {i} is replaced by -{i} in each term, eg. {1} -> -{1}. More...
 
virtual const multivector_t reverse () const =0
 Reversion, eg. {1}*{2} -> {2}*{1}. More...
 
virtual const multivector_t conj () const =0
 Conjugation, reverse o involute == involute o reverse. More...
 
virtual Scalar_T quad () const =0
 Scalar_T quadratic form == (rev(x)*x)(0) More...
 
virtual Scalar_T norm () const =0
 Scalar_T norm == sum of norm of coordinates. More...
 
virtual Scalar_T max_abs () const =0
 Maximum of absolute values of components of multivector: multivector infinity norm. More...
 
virtual const multivector_t truncated (const Scalar_T &limit=Scalar_T(DEFAULT_TRUNCATION)) const =0
 Remove all terms with relative size smaller than limit. More...
 
virtual bool isnan () const =0
 Check if a multivector contains any IEEE NaN values. More...
 
virtual void write (const std::string &msg="") const =0
 Write formatted multivector to output. More...
 
virtual void write (std::ofstream &ofile, const std::string &msg="") const =0
 Write formatted multivector to file. More...
 

Static Public Member Functions

static const std::string classname ()
 Class name used in messages. More...
 
static const matrix_multi_t random (const index_set_t frm, Scalar_T fill=Scalar_T(1))
 Random multivector within a frame. More...
 
- Static Public Member Functions inherited from glucat::clifford_algebra< Scalar_T, index_set< LO, HI >, matrix_multi< Scalar_T, LO, HI > >
static const std::string classname ()
 

Private Types

typedef ublas::row_major orientation_t
 
typedef ublas::compressed_matrix< int, orientation_tbasis_matrix_t
 
typedef ublas::compressed_matrix< Scalar_T, orientation_tmatrix_t
 
typedef matrix_t::size_type matrix_index_t
 

Private Member Functions

template<typename Matrix_T >
 matrix_multi (const Matrix_T &mtx, const index_set_t frm)
 Construct a multivector within a given frame from a given matrix. More...
 
 matrix_multi (const matrix_t &mtx, const index_set_t frm)
 Construct a multivector within a given frame from a given matrix. More...
 
const basis_matrix_t basis_element (const index_set< LO, HI > &ist) const
 Create a basis element matrix within the current frame. More...
 

Private Attributes

index_set_t m_frame
 Index set representing the frame for the subalgebra which contains the multivector. More...
 
matrix_t m_matrix
 Matrix value representing the multivector within the folded frame. More...
 

Friends

template<typename Other_Scalar_T , const index_t Other_LO, const index_t Other_HI>
class framed_multi
 
template<typename Other_Scalar_T , const index_t Other_LO, const index_t Other_HI>
class matrix_multi
 
const matrix_multi_t operator* (const matrix_multi_t &lhs, const matrix_multi_t &rhs)
 
const matrix_multi_t operator^ (const matrix_multi_t &lhs, const matrix_multi_t &rhs)
 
const matrix_multi_t operator& (const matrix_multi_t &lhs, const matrix_multi_t &rhs)
 
const matrix_multi_t operator% (const matrix_multi_t &lhs, const matrix_multi_t &rhs)
 
Scalar_T star (const matrix_multi_t &lhs, const matrix_multi_t &rhs)
 
const matrix_multi_t operator/ (const matrix_multi_t &lhs, const matrix_multi_t &rhs)
 
const matrix_multi_t operator| (const matrix_multi_t &lhs, const matrix_multi_t &rhs)
 
std::istream & operator>> (std::istream &s, multivector_t &val)
 
std::ostream & operator<< (std::ostream &os, const multivector_t &val)
 
std::ostream & operator<< (std::ostream &os, const term_t &term)
 
template<typename Other_Scalar_T , const index_t Other_LO, const index_t Other_HI>
const index_set< Other_LO, Other_HI > reframe (const matrix_multi< Other_Scalar_T, Other_LO, Other_HI > &lhs, const matrix_multi< Other_Scalar_T, Other_LO, Other_HI > &rhs, matrix_multi< Other_Scalar_T, Other_LO, Other_HI > &lhs_reframed, matrix_multi< Other_Scalar_T, Other_LO, Other_HI > &rhs_reframed)
 
template<typename Other_Scalar_T , const index_t Other_LO, const index_t Other_HI>
const matrix_multi< Other_Scalar_T, Other_LO, Other_HI > matrix_sqrt (const matrix_multi< Other_Scalar_T, Other_LO, Other_HI > &val, const matrix_multi< Other_Scalar_T, Other_LO, Other_HI > &i)
 
template<typename Other_Scalar_T , const index_t Other_LO, const index_t Other_HI>
const matrix_multi< Other_Scalar_T, Other_LO, Other_HI > matrix_log (const matrix_multi< Other_Scalar_T, Other_LO, Other_HI > &val, const matrix_multi< Other_Scalar_T, Other_LO, Other_HI > &i)
 

Detailed Description

template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI>
class glucat::matrix_multi< Scalar_T, LO, HI >

A matrix_multi<Scalar_T,LO,HI> is a matrix approximation to a multivector.

Definition at line 68 of file framed_multi.h.

Member Typedef Documentation

template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI>
typedef ublas::compressed_matrix< int, orientation_t > glucat::matrix_multi< Scalar_T, LO, HI >::basis_matrix_t
private

Definition at line 152 of file matrix_multi.h.

template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI>
typedef error<multivector_t> glucat::matrix_multi< Scalar_T, LO, HI >::error_t

Definition at line 142 of file matrix_multi.h.

template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI>
typedef framed_multi<Scalar_T,LO,HI> glucat::matrix_multi< Scalar_T, LO, HI >::framed_multi_t

Definition at line 143 of file matrix_multi.h.

template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI>
typedef index_set<LO,HI> glucat::matrix_multi< Scalar_T, LO, HI >::index_set_t

Definition at line 139 of file matrix_multi.h.

template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI>
typedef matrix_t::size_type glucat::matrix_multi< Scalar_T, LO, HI >::matrix_index_t
private

Definition at line 159 of file matrix_multi.h.

template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI>
typedef multivector_t glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi_t

Definition at line 137 of file matrix_multi.h.

template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI>
typedef ublas::compressed_matrix< Scalar_T, orientation_t > glucat::matrix_multi< Scalar_T, LO, HI >::matrix_t
private

Definition at line 157 of file matrix_multi.h.

template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI>
typedef matrix_multi glucat::matrix_multi< Scalar_T, LO, HI >::multivector_t

Definition at line 136 of file matrix_multi.h.

template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI>
typedef ublas::row_major glucat::matrix_multi< Scalar_T, LO, HI >::orientation_t
private

Definition at line 150 of file matrix_multi.h.

template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI>
typedef Scalar_T glucat::matrix_multi< Scalar_T, LO, HI >::scalar_t

Definition at line 138 of file matrix_multi.h.

template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI>
typedef std::pair<const index_set_t, Scalar_T> glucat::matrix_multi< Scalar_T, LO, HI >::term_t

Definition at line 140 of file matrix_multi.h.

template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI>
typedef std::vector<Scalar_T> glucat::matrix_multi< Scalar_T, LO, HI >::vector_t

Definition at line 141 of file matrix_multi.h.

Constructor & Destructor Documentation

template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI>
glucat::matrix_multi< Scalar_T, LO, HI >::~matrix_multi ( )
inline

Destructor.

Definition at line 165 of file matrix_multi.h.

References PyClical::ist, and glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi().

template<typename Scalar_T , const index_t LO, const index_t HI>
glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi ( )
template<typename Scalar_T , const index_t LO, const index_t HI>
template<typename Other_Scalar_T >
glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi ( const matrix_multi< Other_Scalar_T, LO, HI > &  val)

Construct a multivector from a multivector with a different scalar type.

Definition at line 106 of file matrix_multi_imp.h.

References glucat::matrix_multi< Scalar_T, LO, HI >::m_matrix, and glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi().

template<typename Scalar_T , const index_t LO, const index_t HI>
template<typename Other_Scalar_T >
glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi ( const matrix_multi< Other_Scalar_T, LO, HI > &  val,
const index_set_t  frm,
const bool  prechecked = false 
)

Construct a multivector, within a given frame, from a given multivector.

Definition at line 128 of file matrix_multi_imp.h.

References glucat::matrix_multi< Scalar_T, LO, HI >::m_frame, glucat::matrix_multi< Scalar_T, LO, HI >::m_matrix, and glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi().

template<typename Scalar_T , const index_t LO, const index_t HI>
glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi ( const multivector_t val,
const index_set_t  frm,
const bool  prechecked = false 
)

Construct a multivector, within a given frame, from a given multivector.

Definition at line 156 of file matrix_multi_imp.h.

References glucat::matrix_multi< Scalar_T, LO, HI >::m_frame, glucat::matrix_multi< Scalar_T, LO, HI >::m_matrix, and glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi().

template<typename Scalar_T , const index_t LO, const index_t HI>
glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi ( const index_set_t  ist,
const Scalar_T &  crd = Scalar_T(1) 
)

Construct a multivector from an index set and a scalar coordinate.

Definition at line 168 of file matrix_multi_imp.h.

References glucat::matrix_multi< Scalar_T, LO, HI >::m_frame, glucat::matrix_multi< Scalar_T, LO, HI >::m_matrix, and glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi().

template<typename Scalar_T , const index_t LO, const index_t HI>
glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi ( const index_set_t  ist,
const Scalar_T &  crd,
const index_set_t  frm,
const bool  prechecked = false 
)

Construct a multivector, within a given frame, from an index set and a scalar coordinate.

Definition at line 180 of file matrix_multi_imp.h.

References glucat::matrix_multi< Scalar_T, LO, HI >::m_matrix, and glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi().

template<typename Scalar_T , const index_t LO, const index_t HI>
glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi ( const Scalar_T &  scr,
const index_set_t  frm = index_set_t() 
)

Construct a multivector from a scalar (within a frame, if given)

Definition at line 194 of file matrix_multi_imp.h.

References glucat::matrix_multi< Scalar_T, LO, HI >::m_matrix, and glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi().

template<typename Scalar_T , const index_t LO, const index_t HI>
glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi ( const int  scr,
const index_set_t  frm = index_set_t() 
)

Construct a multivector from an int (within a frame, if given)

Definition at line 206 of file matrix_multi_imp.h.

References glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi().

template<typename Scalar_T , const index_t LO, const index_t HI>
glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi ( const vector_t vec,
const index_set_t  frm,
const bool  prechecked = false 
)
template<typename Scalar_T , const index_t LO, const index_t HI>
glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi ( const std::string &  str)

Construct a multivector from a string: eg: "3+2{1,2}-6.1e-2{2,3}".

Definition at line 239 of file matrix_multi_imp.h.

References glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi().

template<typename Scalar_T , const index_t LO, const index_t HI>
glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi ( const std::string &  str,
const index_set_t  frm,
const bool  prechecked = false 
)

Construct a multivector, within a given frame, from a string: eg: "3+2{1,2}-6.1e-2{2,3}".

Definition at line 245 of file matrix_multi_imp.h.

References glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi().

template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI>
glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi ( const char *  str)
inline

Construct a multivector from a char*: eg: "3+2{1,2}-6.1e-2{2,3}".

Definition at line 196 of file matrix_multi.h.

References glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi().

template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI>
glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi ( const char *  str,
const index_set_t  frm,
const bool  prechecked = false 
)
inline
template<typename Scalar_T , const index_t LO, const index_t HI>
template<typename Other_Scalar_T >
glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi ( const framed_multi< Other_Scalar_T, LO, HI > &  val)
template<typename Scalar_T , const index_t LO, const index_t HI>
template<typename Other_Scalar_T >
glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi ( const framed_multi< Other_Scalar_T, LO, HI > &  val,
const index_set_t  frm,
const bool  prechecked = false 
)
template<typename Scalar_T , const index_t LO, const index_t HI>
template<typename Matrix_T >
glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi ( const Matrix_T &  mtx,
const index_set_t  frm 
)
private

Construct a multivector within a given frame from a given matrix.

Definition at line 307 of file matrix_multi_imp.h.

References glucat::matrix_multi< Scalar_T, LO, HI >::m_matrix, and glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi().

template<typename Scalar_T , const index_t LO, const index_t HI>
glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi ( const matrix_t mtx,
const index_set_t  frm 
)
private

Construct a multivector within a given frame from a given matrix.

Definition at line 328 of file matrix_multi_imp.h.

References glucat::matrix_multi< Scalar_T, LO, HI >::operator=().

Member Function Documentation

template<typename Scalar_T , const index_t LO, const index_t HI>
const matrix_multi< Scalar_T, LO, HI >::basis_matrix_t glucat::matrix_multi< Scalar_T, LO, HI >::basis_element ( const index_set< LO, HI > &  ist) const
private
template<typename Scalar_T , const index_t LO, const index_t HI>
const std::string glucat::matrix_multi< Scalar_T, LO, HI >::classname ( )
static

Class name used in messages.

Definition at line 69 of file matrix_multi_imp.h.

template<typename Scalar_T , const index_t LO, const index_t HI>
template<typename Other_Scalar_T >
const framed_multi< Other_Scalar_T, LO, HI > glucat::matrix_multi< Scalar_T, LO, HI >::fast_framed_multi ( ) const
template<typename Scalar_T , const index_t LO, const index_t HI>
const matrix_multi< Scalar_T, LO, HI > glucat::matrix_multi< Scalar_T, LO, HI >::fast_matrix_multi ( const index_set_t  frm) const
inline
template<typename Scalar_T , const index_t LO, const index_t HI>
matrix_multi< Scalar_T, LO, HI > & glucat::matrix_multi< Scalar_T, LO, HI >::operator+= ( const term_t rhs)
inline
template<typename Scalar_T , const index_t LO, const index_t HI>
matrix_multi< Scalar_T, LO, HI > & glucat::matrix_multi< Scalar_T, LO, HI >::operator= ( const multivector_t rhs)
template<typename Scalar_T , const index_t LO, const index_t HI>
const matrix_multi< Scalar_T, LO, HI > glucat::matrix_multi< Scalar_T, LO, HI >::random ( const index_set_t  frm,
Scalar_T  fill = Scalar_T(1) 
)
static

Friends And Related Function Documentation

template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI>
template<typename Other_Scalar_T , const index_t Other_LO, const index_t Other_HI>
friend class framed_multi
friend

Definition at line 145 of file matrix_multi.h.

template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI>
template<typename Other_Scalar_T , const index_t Other_LO, const index_t Other_HI>
const matrix_multi<Other_Scalar_T,Other_LO,Other_HI> matrix_log ( const matrix_multi< Other_Scalar_T, Other_LO, Other_HI > &  val,
const matrix_multi< Other_Scalar_T, Other_LO, Other_HI > &  i 
)
friend
template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI>
template<typename Other_Scalar_T , const index_t Other_LO, const index_t Other_HI>
friend class matrix_multi
friend

Definition at line 147 of file matrix_multi.h.

template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI>
template<typename Other_Scalar_T , const index_t Other_LO, const index_t Other_HI>
const matrix_multi<Other_Scalar_T,Other_LO,Other_HI> matrix_sqrt ( const matrix_multi< Other_Scalar_T, Other_LO, Other_HI > &  val,
const matrix_multi< Other_Scalar_T, Other_LO, Other_HI > &  i 
)
friend
template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI>
const matrix_multi_t operator% ( const matrix_multi_t lhs,
const matrix_multi_t rhs 
)
friend
template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI>
const matrix_multi_t operator& ( const matrix_multi_t lhs,
const matrix_multi_t rhs 
)
friend
template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI>
const matrix_multi_t operator* ( const matrix_multi_t lhs,
const matrix_multi_t rhs 
)
friend
template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI>
const matrix_multi_t operator/ ( const matrix_multi_t lhs,
const matrix_multi_t rhs 
)
friend
template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI>
std::ostream& operator<< ( std::ostream &  os,
const multivector_t val 
)
friend
template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI>
std::ostream& operator<< ( std::ostream &  os,
const term_t term 
)
friend
template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI>
std::istream& operator>> ( std::istream &  s,
multivector_t val 
)
friend
template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI>
const matrix_multi_t operator^ ( const matrix_multi_t lhs,
const matrix_multi_t rhs 
)
friend
template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI>
const matrix_multi_t operator| ( const matrix_multi_t lhs,
const matrix_multi_t rhs 
)
friend
template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI>
template<typename Other_Scalar_T , const index_t Other_LO, const index_t Other_HI>
const index_set<Other_LO,Other_HI> reframe ( const matrix_multi< Other_Scalar_T, Other_LO, Other_HI > &  lhs,
const matrix_multi< Other_Scalar_T, Other_LO, Other_HI > &  rhs,
matrix_multi< Other_Scalar_T, Other_LO, Other_HI > &  lhs_reframed,
matrix_multi< Other_Scalar_T, Other_LO, Other_HI > &  rhs_reframed 
)
friend
template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI>
Scalar_T star ( const matrix_multi_t lhs,
const matrix_multi_t rhs 
)
friend

Member Data Documentation

template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI>
index_set_t glucat::matrix_multi< Scalar_T, LO, HI >::m_frame
private
template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI>
matrix_t glucat::matrix_multi< Scalar_T, LO, HI >::m_matrix
private

The documentation for this class was generated from the following files: