glucat
0.8.4
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A matrix_multi<Scalar_T,LO,HI> is a matrix approximation to a multivector. More...
#include <framed_multi.h>
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_t > | error_t |
typedef framed_multi< Scalar_T, LO, HI > | framed_multi_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_t & | operator= (const multivector_t &rhs) |
Assignment operator. More... | |
multivector_t & | operator+= (const term_t &rhs) |
Add a term, if non-zero. 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... | |
Private Types | |
typedef ublas::row_major | orientation_t |
typedef ublas::compressed_matrix< int, orientation_t > | basis_matrix_t |
typedef ublas::compressed_matrix< Scalar_T, orientation_t > | matrix_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) |
A matrix_multi<Scalar_T,LO,HI> is a matrix approximation to a multivector.
Definition at line 68 of file framed_multi.h.
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Definition at line 181 of file matrix_multi.h.
typedef error<multivector_t> glucat::matrix_multi< Scalar_T, LO, HI >::error_t |
Definition at line 171 of file matrix_multi.h.
typedef framed_multi<Scalar_T,LO,HI> glucat::matrix_multi< Scalar_T, LO, HI >::framed_multi_t |
Definition at line 172 of file matrix_multi.h.
typedef index_set<LO,HI> glucat::matrix_multi< Scalar_T, LO, HI >::index_set_t |
Definition at line 168 of file matrix_multi.h.
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Definition at line 188 of file matrix_multi.h.
typedef multivector_t glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi_t |
Definition at line 166 of file matrix_multi.h.
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Definition at line 186 of file matrix_multi.h.
typedef matrix_multi glucat::matrix_multi< Scalar_T, LO, HI >::multivector_t |
Definition at line 165 of file matrix_multi.h.
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Definition at line 179 of file matrix_multi.h.
typedef Scalar_T glucat::matrix_multi< Scalar_T, LO, HI >::scalar_t |
Definition at line 167 of file matrix_multi.h.
typedef std::pair<const index_set_t, Scalar_T> glucat::matrix_multi< Scalar_T, LO, HI >::term_t |
Definition at line 169 of file matrix_multi.h.
typedef std::vector<Scalar_T> glucat::matrix_multi< Scalar_T, LO, HI >::vector_t |
Definition at line 170 of file matrix_multi.h.
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Destructor.
Definition at line 194 of file matrix_multi.h.
glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi |
Default constructor.
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 >::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 137 of file matrix_multi_imp.h.
References glucat::matrix_multi< Scalar_T, LO, HI >::m_matrix, and glucat::numeric_traits< Scalar_T >::to_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 |
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Construct a multivector, within a given frame, from a given multivector.
Definition at line 159 of file matrix_multi_imp.h.
References glucat::matrix_multi< Scalar_T, LO, HI >::m_frame, and glucat::matrix_multi< Scalar_T, LO, HI >::m_matrix.
glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi | ( | const multivector_t & | val, |
const index_set_t | frm, | ||
const bool | prechecked = false |
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Construct a multivector, within a given frame, from a given multivector.
Definition at line 187 of file matrix_multi_imp.h.
glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi | ( | const index_set_t | ist, |
const Scalar_T & | crd = Scalar_T(1) |
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Construct a multivector from an index set and a scalar coordinate.
Definition at line 199 of file matrix_multi_imp.h.
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 |
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Construct a multivector, within a given frame, from an index set and a scalar coordinate.
Definition at line 211 of file matrix_multi_imp.h.
References glucat::index_set< LO, HI >::count(), and glucat::matrix_multi< Scalar_T, LO, HI >::m_matrix.
glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi | ( | const Scalar_T & | scr, |
const index_set_t | frm = index_set_t() |
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Construct a multivector from a scalar (within a frame, if given)
Definition at line 225 of file matrix_multi_imp.h.
glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi | ( | const int | scr, |
const index_set_t | frm = index_set_t() |
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Construct a multivector from an int (within a frame, if given)
Definition at line 237 of file matrix_multi_imp.h.
glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi | ( | const vector_t & | vec, |
const index_set_t | frm, | ||
const bool | prechecked = false |
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Construct a multivector, within a given frame, from a given vector.
Definition at line 243 of file matrix_multi_imp.h.
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 270 of file matrix_multi_imp.h.
glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi | ( | const std::string & | str, |
const index_set_t | frm, | ||
const bool | prechecked = false |
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Construct a multivector, within a given frame, from a string: eg: "3+2{1,2}-6.1e-2{2,3}".
Definition at line 276 of file matrix_multi_imp.h.
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Construct a multivector from a char*: eg: "3+2{1,2}-6.1e-2{2,3}".
Definition at line 225 of file matrix_multi.h.
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Construct a multivector, within a given frame, from a char*: eg: "3+2{1,2}-6.1e-2{2,3}".
Definition at line 228 of file matrix_multi.h.
glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi | ( | const framed_multi< Other_Scalar_T, LO, HI > & | val | ) |
Construct a multivector from a framed_multi_t.
Definition at line 283 of file matrix_multi_imp.h.
References PyClical::e(), and glucat::tuning< Mult_Matrix_Threshold, Div_Max_Steps, Sqrt_Max_Steps, Log_Max_Outer_Steps, Log_Max_Inner_Steps, Basis_Max_Count, Fast_Size_Threshold, Inv_Fast_Dim_Threshold, Products_Size_Threshold, Function_Precision >::fast_size_threshold.
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 |
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Construct a multivector, within a given frame, from a framed_multi_t.
Definition at line 310 of file matrix_multi_imp.h.
References glucat::matrix_multi< Scalar_T, LO, HI >::m_matrix, and glucat::numeric_traits< Scalar_T >::to_scalar_t().
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Construct a multivector within a given frame from a given matrix.
Definition at line 338 of file matrix_multi_imp.h.
References glucat::matrix_multi< Scalar_T, LO, HI >::m_frame, and glucat::matrix_multi< Scalar_T, LO, HI >::m_matrix.
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Construct a multivector within a given frame from a given matrix.
Definition at line 359 of file matrix_multi_imp.h.
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Create a basis element matrix within the current frame.
Definition at line 1274 of file matrix_multi_imp.h.
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Class name used in messages.
Definition at line 100 of file matrix_multi_imp.h.
References glucat::matrix_multi< Scalar_T, LO, HI >::m_matrix.
const framed_multi< Other_Scalar_T, LO, HI > glucat::matrix_multi< Scalar_T, LO, HI >::fast_framed_multi |
Use inverse generalized FFT to construct a framed_multi_t.
Definition at line 1197 of file matrix_multi_imp.h.
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Use generalized FFT to construct a matrix_multi_t.
Definition at line 1184 of file matrix_multi_imp.h.
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Add a term, if non-zero.
Geometric sum.
Geometric sum of multivector and scalar.
Definition at line 501 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::reframe().
matrix_multi< Scalar_T, LO, HI > & glucat::matrix_multi< Scalar_T, LO, HI >::operator= | ( | const multivector_t & | rhs | ) |
Assignment operator.
Definition at line 367 of file matrix_multi_imp.h.
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Random multivector within a frame.
Definition at line 1027 of file matrix_multi_imp.h.
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Definition at line 174 of file matrix_multi.h.
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Definition at line 176 of file matrix_multi.h.
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Index set representing the frame for the subalgebra which contains the multivector.
Definition at line 304 of file matrix_multi.h.
Referenced by glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi(), and glucat::matrix_multi< Scalar_T, LO, HI >::operator+=().
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Matrix value representing the multivector within the folded frame.
Definition at line 306 of file matrix_multi.h.
Referenced by glucat::matrix_multi< Scalar_T, LO, HI >::classname(), glucat::framed_multi< Scalar_T, LO, HI >::framed_multi(), glucat::matrix_multi< Scalar_T, LO, HI >::matrix_multi(), glucat::offset_level(), and glucat::matrix_multi< Scalar_T, LO, HI >::operator+=().