glucat  0.12.0
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glucat::matrix_multi< Scalar_T, LO, HI, Tune_P > Class Template Reference

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

#include <framed_multi.h>

Inheritance diagram for glucat::matrix_multi< Scalar_T, LO, HI, Tune_P >:
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Collaboration diagram for glucat::matrix_multi< Scalar_T, LO, HI, Tune_P >:
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Public Types

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

Public Member Functions

 ~matrix_multi () override=default
 Destructor. More...
 
 matrix_multi ()
 Default constructor. More...
 
template<typename Other_Scalar_T >
 matrix_multi (const matrix_multi< Other_Scalar_T, LO, HI, Tune_P > &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, Tune_P > &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, Tune_P > &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, Tune_P > &val, const index_set_t frm, const bool prechecked=false)
 Construct a multivector, within a given frame, from a framed_multi_t. More...
 
auto fast_matrix_multi (const index_set_t frm) const -> const matrix_multi_t
 Use generalized FFT to construct a matrix_multi_t. More...
 
template<typename Other_Scalar_T >
auto fast_framed_multi () const -> const framed_multi< Other_Scalar_T, LO, HI, Tune_P >
 Use inverse generalized FFT to construct a framed_multi_t. More...
 
_GLUCAT_CLIFFORD_ALGEBRA_OPERATIONS auto operator= (const multivector_t &rhs) -> multivector_t &
 Assignment operator. More...
 
auto operator+= (const term_t &rhs) -> multivector_t &
 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, Tune_P > >
virtual ~clifford_algebra ()=default
 
virtual auto operator== (const multivector_t &val) const -> bool=0
 Test for equality of multivectors. More...
 
virtual auto operator== (const Scalar_T &scr) const -> bool=0
 Test for equality of multivector and scalar. More...
 
virtual auto operator+= (const multivector_t &rhs) -> multivector_t &=0
 Geometric sum. More...
 
virtual auto operator+= (const Scalar_T &scr) -> multivector_t &=0
 Geometric sum of multivector and scalar. More...
 
virtual auto operator-= (const multivector_t &rhs) -> multivector_t &=0
 Geometric difference. More...
 
virtual auto operator-= (const Scalar_T &scr) -> multivector_t &=0
 Geometric difference of multivector and scalar. More...
 
virtual auto operator- () const -> const multivector_t=0
 Unary -. More...
 
virtual auto operator*= (const Scalar_T &scr) -> multivector_t &=0
 Product of multivector and scalar. More...
 
virtual auto operator*= (const multivector_t &rhs) -> multivector_t &=0
 Geometric product. More...
 
virtual auto operator%= (const multivector_t &rhs) -> multivector_t &=0
 Contraction. More...
 
virtual auto operator&= (const multivector_t &rhs) -> multivector_t &=0
 Inner product. More...
 
virtual auto operator^= (const multivector_t &rhs) -> multivector_t &=0
 Outer product. More...
 
virtual auto operator/= (const Scalar_T &scr) -> multivector_t &=0
 Quotient of multivector and scalar. More...
 
virtual auto operator/= (const multivector_t &rhs) -> multivector_t &=0
 Geometric quotient. More...
 
virtual auto operator|= (const multivector_t &rhs) -> multivector_t &=0
 Transformation via twisted adjoint action. More...
 
virtual auto inv () const -> const multivector_t=0
 Geometric multiplicative inverse. More...
 
virtual auto pow (int m) const -> const multivector_t=0
 *this to the m More...
 
virtual auto outer_pow (int m) const -> const multivector_t=0
 Outer product power. More...
 
virtual auto frame () const -> const index_set_t=0
 Subalgebra generated by all generators of terms of given multivector. More...
 
virtual auto grade () const -> index_t=0
 Maximum of the grades of each term. More...
 
virtual auto operator[] (const index_set_t ist) const -> Scalar_T=0
 Subscripting: map from index set to scalar coordinate. More...
 
virtual auto operator() (index_t grade) const -> const multivector_t=0
 Pure grade-vector part. More...
 
virtual auto scalar () const -> Scalar_T=0
 Scalar part. More...
 
virtual auto pure () const -> const multivector_t=0
 Pure part. More...
 
virtual auto even () const -> const multivector_t=0
 Even part of multivector, sum of even grade terms. More...
 
virtual auto odd () const -> const multivector_t=0
 Odd part of multivector, sum of odd grade terms. More...
 
virtual auto vector_part () const -> const vector_t=0
 Vector part of multivector, as a vector_t with respect to frame() More...
 
virtual auto vector_part (const index_set_t frm, const bool prechecked) const -> const vector_t=0
 Vector part of multivector, as a vector_t with respect to frm. More...
 
virtual auto involute () const -> const multivector_t=0
 Main involution, each {i} is replaced by -{i} in each term, eg. {1} -> -{1}. More...
 
virtual auto reverse () const -> const multivector_t=0
 Reversion, eg. {1}*{2} -> {2}*{1}. More...
 
virtual auto conj () const -> const multivector_t=0
 Conjugation, reverse o involute == involute o reverse. More...
 
virtual auto quad () const -> Scalar_T=0
 Scalar_T quadratic form == (rev(x)*x)(0) More...
 
virtual auto norm () const -> Scalar_T=0
 Scalar_T norm == sum of norm of coordinates. More...
 
virtual auto max_abs () const -> Scalar_T=0
 Maximum of absolute values of components of multivector: multivector infinity norm. More...
 
virtual auto truncated (const Scalar_T &limit=default_truncation) const -> const multivector_t=0
 Remove all terms with relative size smaller than limit. More...
 
virtual auto isinf () const -> bool=0
 Check if a multivector contains any infinite values. More...
 
virtual auto isnan () const -> bool=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 auto classname () -> const std::string
 Class name used in messages. More...
 
static auto random (const index_set_t frm, Scalar_T fill=Scalar_T(1)) -> const matrix_multi_t
 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, Tune_P > >
static auto classname () -> const std::string
 

Private Types

using orientation_t = ublas::row_major
 
using basis_matrix_t = ublas::compressed_matrix< int, orientation_t >
 
using matrix_t = ublas::matrix< Scalar_T, orientation_t >
 
using matrix_index_t = typename matrix_t::size_type
 

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...
 
auto basis_element (const index_set< LO, HI > &ist) const -> const basis_matrix_t
 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, typename Other_Tune_P >
class framed_multi
 
template<typename Other_Scalar_T , const index_t Other_LO, const index_t Other_HI, typename Other_Tune_P >
class matrix_multi
 
auto operator* (const matrix_multi_t &lhs, const matrix_multi_t &rhs) -> const matrix_multi_t
 
auto operator^ (const matrix_multi_t &lhs, const matrix_multi_t &rhs) -> const matrix_multi_t
 
auto operator & (const matrix_multi_t &lhs, const matrix_multi_t &rhs) -> const matrix_multi_t
 
auto operator% (const matrix_multi_t &lhs, const matrix_multi_t &rhs) -> const matrix_multi_t
 
auto star (const matrix_multi_t &lhs, const matrix_multi_t &rhs) -> Scalar_T
 
auto operator/ (const matrix_multi_t &lhs, const matrix_multi_t &rhs) -> const matrix_multi_t
 
auto operator| (const matrix_multi_t &lhs, const matrix_multi_t &rhs) -> const matrix_multi_t
 
auto operator>> (std::istream &s, multivector_t &val) -> std::istream &
 
auto operator<< (std::ostream &os, const multivector_t &val) -> std::ostream &
 
template<typename Other_Scalar_T , const index_t Other_LO, const index_t Other_HI, typename Other_Tune_P >
auto reframe (const matrix_multi< Other_Scalar_T, Other_LO, Other_HI, Other_Tune_P > &lhs, const matrix_multi< Other_Scalar_T, Other_LO, Other_HI, Other_Tune_P > &rhs, matrix_multi< Other_Scalar_T, Other_LO, Other_HI, Other_Tune_P > &lhs_reframed, matrix_multi< Other_Scalar_T, Other_LO, Other_HI, Other_Tune_P > &rhs_reframed) -> const index_set< Other_LO, Other_HI >
 
template<typename Other_Scalar_T , const index_t Other_LO, const index_t Other_HI, typename Other_Tune_P >
auto matrix_sqrt (const matrix_multi< Other_Scalar_T, Other_LO, Other_HI, Other_Tune_P > &val, const matrix_multi< Other_Scalar_T, Other_LO, Other_HI, Other_Tune_P > &i, const index_t level) -> const matrix_multi< Other_Scalar_T, Other_LO, Other_HI, Other_Tune_P >
 
template<typename Other_Scalar_T , const index_t Other_LO, const index_t Other_HI, typename Other_Tune_P >
auto matrix_log (const matrix_multi< Other_Scalar_T, Other_LO, Other_HI, Other_Tune_P > &val, const matrix_multi< Other_Scalar_T, Other_LO, Other_HI, Other_Tune_P > &i, const index_t level) -> const matrix_multi< Other_Scalar_T, Other_LO, Other_HI, Other_Tune_P >
 

Additional Inherited Members

- Static Public Attributes inherited from glucat::clifford_algebra< Scalar_T, index_set< LO, HI >, matrix_multi< Scalar_T, LO, HI, Tune_P > >
static const index_t v_lo
 
static const index_t v_hi
 
static const Scalar_T default_truncation
 Default for truncation. More...
 

Detailed Description

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

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

Definition at line 59 of file framed_multi.h.

Member Typedef Documentation

◆ basis_matrix_t

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

Definition at line 157 of file matrix_multi.h.

◆ error_t

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

Definition at line 148 of file matrix_multi.h.

◆ framed_multi_t

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

Definition at line 149 of file matrix_multi.h.

◆ index_set_t

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

Definition at line 145 of file matrix_multi.h.

◆ matrix_index_t

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

Definition at line 159 of file matrix_multi.h.

◆ matrix_multi_t

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

Definition at line 142 of file matrix_multi.h.

◆ matrix_t

template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI, typename Tune_P = tuning<>>
using glucat::matrix_multi< Scalar_T, LO, HI, Tune_P >::matrix_t = ublas::matrix<Scalar_T, orientation_t>
private

Definition at line 158 of file matrix_multi.h.

◆ multivector_t

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

Definition at line 141 of file matrix_multi.h.

◆ orientation_t

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

Definition at line 156 of file matrix_multi.h.

◆ scalar_t

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

Definition at line 143 of file matrix_multi.h.

◆ term_t

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

Definition at line 146 of file matrix_multi.h.

◆ tune_p

template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI, typename Tune_P = tuning<>>
using glucat::matrix_multi< Scalar_T, LO, HI, Tune_P >::tune_p = Tune_P

Definition at line 144 of file matrix_multi.h.

◆ vector_t

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

Definition at line 147 of file matrix_multi.h.

Constructor & Destructor Documentation

◆ ~matrix_multi()

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

Destructor.

◆ matrix_multi() [1/17]

template<typename Scalar_T , const index_t LO, const index_t HI, typename Tune_P >
glucat::matrix_multi< Scalar_T, LO, HI, Tune_P >::matrix_multi ( )

◆ matrix_multi() [2/17]

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

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

Definition at line 116 of file matrix_multi_imp.h.

References glucat::matrix_multi< Scalar_T, LO, HI, Tune_P >::m_matrix.

◆ matrix_multi() [3/17]

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

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

Definition at line 135 of file matrix_multi_imp.h.

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

◆ matrix_multi() [4/17]

template<typename Scalar_T , const index_t LO, const index_t HI, typename Tune_P >
glucat::matrix_multi< Scalar_T, LO, HI, Tune_P >::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 160 of file matrix_multi_imp.h.

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

◆ matrix_multi() [5/17]

template<typename Scalar_T , const index_t LO, const index_t HI, typename Tune_P >
glucat::matrix_multi< Scalar_T, LO, HI, Tune_P >::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 172 of file matrix_multi_imp.h.

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

◆ matrix_multi() [6/17]

template<typename Scalar_T , const index_t LO, const index_t HI, typename Tune_P >
glucat::matrix_multi< Scalar_T, LO, HI, Tune_P >::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 184 of file matrix_multi_imp.h.

References PyClical::ist, and glucat::matrix_multi< Scalar_T, LO, HI, Tune_P >::m_matrix.

◆ matrix_multi() [7/17]

template<typename Scalar_T , const index_t LO, const index_t HI, typename Tune_P >
glucat::matrix_multi< Scalar_T, LO, HI, Tune_P >::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 198 of file matrix_multi_imp.h.

References glucat::matrix_multi< Scalar_T, LO, HI, Tune_P >::m_matrix.

◆ matrix_multi() [8/17]

template<typename Scalar_T , const index_t LO, const index_t HI, typename Tune_P >
glucat::matrix_multi< Scalar_T, LO, HI, Tune_P >::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 210 of file matrix_multi_imp.h.

◆ matrix_multi() [9/17]

template<typename Scalar_T , const index_t LO, const index_t HI, typename Tune_P >
glucat::matrix_multi< Scalar_T, LO, HI, Tune_P >::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.

Definition at line 216 of file matrix_multi_imp.h.

References glucat::index_set< LO, HI >::count(), glucat::matrix_multi< Scalar_T, LO, HI, Tune_P >::m_matrix, glucat::index_set< LO, HI >::max(), and glucat::index_set< LO, HI >::min().

◆ matrix_multi() [10/17]

template<typename Scalar_T , const index_t LO, const index_t HI, typename Tune_P >
glucat::matrix_multi< Scalar_T, LO, HI, Tune_P >::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 241 of file matrix_multi_imp.h.

◆ matrix_multi() [11/17]

template<typename Scalar_T , const index_t LO, const index_t HI, typename Tune_P >
glucat::matrix_multi< Scalar_T, LO, HI, Tune_P >::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 247 of file matrix_multi_imp.h.

◆ matrix_multi() [12/17]

template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI, typename Tune_P = tuning<>>
glucat::matrix_multi< Scalar_T, LO, HI, Tune_P >::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, Tune_P >::matrix_multi().

◆ matrix_multi() [13/17]

template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI, typename Tune_P = tuning<>>
glucat::matrix_multi< Scalar_T, LO, HI, Tune_P >::matrix_multi ( const char *  str,
const index_set_t  frm,
const bool  prechecked = false 
)
inline

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

Definition at line 199 of file matrix_multi.h.

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

◆ matrix_multi() [14/17]

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

◆ matrix_multi() [15/17]

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

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

Definition at line 278 of file matrix_multi_imp.h.

References PyClical::e(), and glucat::clifford_algebra< Scalar_T, index_set< LO, HI >, framed_multi< Scalar_T, LO, HI, Tune_P > >::truncated().

◆ matrix_multi() [16/17]

template<typename Scalar_T , const index_t LO, const index_t HI, typename Tune_P >
template<typename Matrix_T >
glucat::matrix_multi< Scalar_T, LO, HI, Tune_P >::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 304 of file matrix_multi_imp.h.

References glucat::matrix_multi< Scalar_T, LO, HI, Tune_P >::m_matrix.

◆ matrix_multi() [17/17]

template<typename Scalar_T , const index_t LO, const index_t HI, typename Tune_P >
glucat::matrix_multi< Scalar_T, LO, HI, Tune_P >::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 323 of file matrix_multi_imp.h.

Member Function Documentation

◆ basis_element()

template<typename Scalar_T , const index_t LO, const index_t HI, typename Tune_P >
auto glucat::matrix_multi< Scalar_T, LO, HI, Tune_P >::basis_element ( const index_set< LO, HI > &  ist) const -> const basis_matrix_t
private

◆ classname()

template<typename Scalar_T , const index_t LO, const index_t HI, typename Tune_P >
auto glucat::matrix_multi< Scalar_T, LO, HI, Tune_P >::classname ( ) -> const std::string
static

Class name used in messages.

Definition at line 79 of file matrix_multi_imp.h.

◆ fast_framed_multi()

template<typename Scalar_T , const index_t LO, const index_t HI, typename Tune_P >
template<typename Other_Scalar_T >
auto glucat::matrix_multi< Scalar_T, LO, HI, Tune_P >::fast_framed_multi ( ) const -> const framed_multi<Other_Scalar_T,LO,HI,Tune_P>

◆ fast_matrix_multi()

template<typename Scalar_T , const index_t LO, const index_t HI, typename Tune_P >
auto glucat::matrix_multi< Scalar_T, LO, HI, Tune_P >::fast_matrix_multi ( const index_set_t  frm) const -> const matrix_multi_t
inline

Use generalized FFT to construct a matrix_multi_t.

Definition at line 1097 of file matrix_multi_imp.h.

◆ operator+=()

template<typename Scalar_T , const index_t LO, const index_t HI, typename Tune_P >
auto glucat::matrix_multi< Scalar_T, LO, HI, Tune_P >::operator+= ( const term_t rhs) -> multivector_t&
inline

Add a term, if non-zero.

Geometric sum.

Geometric sum of multivector and scalar.

Definition at line 417 of file matrix_multi_imp.h.

◆ operator=()

template<typename Scalar_T , const index_t LO, const index_t HI, typename Tune_P >
auto glucat::matrix_multi< Scalar_T, LO, HI, Tune_P >::operator= ( const multivector_t rhs) -> multivector_t&

Assignment operator.

Definition at line 331 of file matrix_multi_imp.h.

References PyClical::rhs.

◆ random()

template<typename Scalar_T , const index_t LO, const index_t HI, typename Tune_P >
auto glucat::matrix_multi< Scalar_T, LO, HI, Tune_P >::random ( const index_set_t  frm,
Scalar_T  fill = Scalar_T(1) 
) -> const matrix_multi_t
static

Random multivector within a frame.

Definition at line 927 of file matrix_multi_imp.h.

References PyClical::fill, and glucat::framed_multi< Scalar_T, LO, HI, Tune_P >::random().

Friends And Related Function Documentation

◆ framed_multi

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

Definition at line 151 of file matrix_multi.h.

◆ matrix_log

template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI, typename Tune_P = tuning<>>
template<typename Other_Scalar_T , const index_t Other_LO, const index_t Other_HI, typename Other_Tune_P >
auto matrix_log ( const matrix_multi< Other_Scalar_T, Other_LO, Other_HI, Other_Tune_P > &  val,
const matrix_multi< Other_Scalar_T, Other_LO, Other_HI, Other_Tune_P > &  i,
const index_t  level 
) -> const matrix_multi< Other_Scalar_T, Other_LO, Other_HI, Other_Tune_P >
friend

◆ matrix_multi

template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI, typename Tune_P = tuning<>>
template<typename Other_Scalar_T , const index_t Other_LO, const index_t Other_HI, typename Other_Tune_P >
friend class matrix_multi
friend

Definition at line 153 of file matrix_multi.h.

◆ matrix_sqrt

template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI, typename Tune_P = tuning<>>
template<typename Other_Scalar_T , const index_t Other_LO, const index_t Other_HI, typename Other_Tune_P >
auto matrix_sqrt ( const matrix_multi< Other_Scalar_T, Other_LO, Other_HI, Other_Tune_P > &  val,
const matrix_multi< Other_Scalar_T, Other_LO, Other_HI, Other_Tune_P > &  i,
const index_t  level 
) -> const matrix_multi< Other_Scalar_T, Other_LO, Other_HI, Other_Tune_P >
friend

◆ operator &

template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI, typename Tune_P = tuning<>>
auto operator& ( const matrix_multi_t lhs,
const matrix_multi_t rhs 
) -> const matrix_multi_t
friend

◆ operator%

template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI, typename Tune_P = tuning<>>
auto operator% ( const matrix_multi_t lhs,
const matrix_multi_t rhs 
) -> const matrix_multi_t
friend

◆ operator*

template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI, typename Tune_P = tuning<>>
auto operator* ( const matrix_multi_t lhs,
const matrix_multi_t rhs 
) -> const matrix_multi_t
friend

◆ operator/

template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI, typename Tune_P = tuning<>>
auto operator/ ( const matrix_multi_t lhs,
const matrix_multi_t rhs 
) -> const matrix_multi_t
friend

◆ operator<<

template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI, typename Tune_P = tuning<>>
auto operator<< ( std::ostream &  os,
const multivector_t val 
) -> std::ostream &
friend

◆ operator>>

template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI, typename Tune_P = tuning<>>
auto operator>> ( std::istream &  s,
multivector_t val 
) -> std::istream &
friend

◆ operator^

template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI, typename Tune_P = tuning<>>
auto operator^ ( const matrix_multi_t lhs,
const matrix_multi_t rhs 
) -> const matrix_multi_t
friend

◆ operator|

template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI, typename Tune_P = tuning<>>
auto operator| ( const matrix_multi_t lhs,
const matrix_multi_t rhs 
) -> const matrix_multi_t
friend

◆ reframe

template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI, typename Tune_P = tuning<>>
template<typename Other_Scalar_T , const index_t Other_LO, const index_t Other_HI, typename Other_Tune_P >
auto reframe ( const matrix_multi< Other_Scalar_T, Other_LO, Other_HI, Other_Tune_P > &  lhs,
const matrix_multi< Other_Scalar_T, Other_LO, Other_HI, Other_Tune_P > &  rhs,
matrix_multi< Other_Scalar_T, Other_LO, Other_HI, Other_Tune_P > &  lhs_reframed,
matrix_multi< Other_Scalar_T, Other_LO, Other_HI, Other_Tune_P > &  rhs_reframed 
) -> const index_set< Other_LO, Other_HI >
friend

◆ star

template<typename Scalar_T = double, const index_t LO = DEFAULT_LO, const index_t HI = DEFAULT_HI, typename Tune_P = tuning<>>
auto star ( const matrix_multi_t lhs,
const matrix_multi_t rhs 
) -> Scalar_T
friend

Member Data Documentation

◆ m_frame

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

Index set representing the frame for the subalgebra which contains the multivector.

Definition at line 278 of file matrix_multi.h.

Referenced by glucat::matrix_multi< Scalar_T, LO, HI, Tune_P >::matrix_multi().

◆ m_matrix

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

Matrix value representing the multivector within the folded frame.

Definition at line 280 of file matrix_multi.h.

Referenced by glucat::framed_multi< Scalar_T, LO, HI, Tune_P >::framed_multi(), and glucat::matrix_multi< Scalar_T, LO, HI, Tune_P >::matrix_multi().


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