Classes
struct	eig_genus
	Structure containing classification of eigenvalues. More...

Enumerations
enum	eig_case_t { safe_eig_case, negative_eig_case, both_eig_case }
	Classification of eigenvalues of a matrix. More...

Functions
template<typename LHS_T , typename RHS_T >
const RHS_T	kron (const LHS_T &lhs, const RHS_T &rhs)
	Kronecker tensor product of matrices - as per Matlab kron. More...

template<typename LHS_T , typename RHS_T >
const RHS_T	mono_kron (const LHS_T &lhs, const RHS_T &rhs)
	Sparse Kronecker tensor product of monomial matrices. More...

template<typename LHS_T , typename RHS_T >
const RHS_T	nork (const LHS_T &lhs, const RHS_T &rhs, const bool mono=true)
	Left inverse of Kronecker product. More...

template<typename LHS_T , typename RHS_T >
const RHS_T	signed_perm_nork (const LHS_T &lhs, const RHS_T &rhs)
	Left inverse of Kronecker product where lhs is a signed permutation matrix. More...

template<typename Matrix_T >
Matrix_T::size_type	nnz (const Matrix_T &m)
	Number of non-zeros. More...

template<typename Matrix_T >
bool	isnan (const Matrix_T &m)
	Not a Number. More...

template<typename Matrix_T >
const Matrix_T	unit (const typename Matrix_T::size_type n)
	Unit matrix - as per Matlab eye. More...

template<typename LHS_T , typename RHS_T >
const RHS_T::expression_type	mono_prod (const ublas::matrix_expression< LHS_T > &lhs, const ublas::matrix_expression< RHS_T > &rhs)
	Product of monomial matrices. More...

template<typename LHS_T , typename RHS_T >
const RHS_T::expression_type	sparse_prod (const ublas::matrix_expression< LHS_T > &lhs, const ublas::matrix_expression< RHS_T > &rhs)
	Product of sparse matrices. More...

template<typename LHS_T , typename RHS_T >
const RHS_T::expression_type	prod (const ublas::matrix_expression< LHS_T > &lhs, const ublas::matrix_expression< RHS_T > &rhs)
	Product of matrices. More...

template<typename Scalar_T , typename LHS_T , typename RHS_T >
Scalar_T	inner (const LHS_T &lhs, const RHS_T &rhs)
	Inner product: sum(x(i,j)*y(i,j))/x.nrows() More...

template<typename Matrix_T >
Matrix_T::value_type	norm_frob2 (const Matrix_T &val)
	Square of Frobenius norm. More...

template<typename Matrix_T >
Matrix_T::value_type	trace (const Matrix_T &val)
	Matrix trace. More...

template<typename Matrix_T >
ublas::vector< std::complex< double > >	eigenvalues (const Matrix_T &val)
	Eigenvalues of a matrix. More...

template<typename Matrix_T >
eig_genus< Matrix_T >	classify_eigenvalues (const Matrix_T &val)
	Classify the eigenvalues of a matrix. More...

template<typename LHS_T , typename RHS_T >
void	nork_range (RHS_T &result, const typename LHS_T::const_iterator2 lhs_it2, const RHS_T &rhs, const typename RHS_T::size_type res_s1, const typename RHS_T::size_type res_s2)
	Utility routine for nork: calculate result for a range of indices. More...

template<typename Matrix_T >
static ublas::matrix< double, ublas::column_major >	to_lapack (const Matrix_T &val)
	Convert matrix to LAPACK format. More...

Enumeration Type Documentation

◆ eig_case_t

enum glucat::matrix::eig_case_t

Classification of eigenvalues of a matrix.

Enumerator
safe_eig_case
negative_eig_case
both_eig_case

Definition at line 127 of file matrix.h.

Function Documentation

◆ classify_eigenvalues()

template<typename Matrix_T >

eig_genus< Matrix_T > glucat::matrix::classify_eigenvalues ( const Matrix_T & val )

Classify the eigenvalues of a matrix.

Definition at line 526 of file matrix_imp.h.

References glucat::abs(), both_eig_case, eigenvalues(), glucat::imag(), glucat::matrix::eig_genus< Matrix_T >::m_eig_case, glucat::matrix::eig_genus< Matrix_T >::m_safe_arg, negative_eig_case, glucat::norm(), glucat::numeric_traits< Scalar_T >::pi(), PyClical::pi, glucat::real(), and safe_eig_case.

Referenced by glucat::matrix_log(), and glucat::matrix_sqrt().

◆ eigenvalues()

template<typename Matrix_T >

ublas::vector< std::complex< double > > glucat::matrix::eigenvalues ( const Matrix_T & val )

Eigenvalues of a matrix.

Definition at line 493 of file matrix_imp.h.

References to_lapack().

Referenced by classify_eigenvalues().

◆ inner()

template<typename Scalar_T , typename LHS_T , typename RHS_T >

Scalar_T glucat::matrix::inner	(	const LHS_T &	lhs,
		const RHS_T &	rhs
	)

Inner product: sum(x(i,j)*y(i,j))/x.nrows()

Inner product: sum(lhs(i,j)*rhs(i,j))/lhs.nrows()

Definition at line 391 of file matrix_imp.h.

◆ isnan()

template<typename Matrix_T >

bool glucat::matrix::isnan ( const Matrix_T & m )

Not a Number.

Definition at line 292 of file matrix_imp.h.

Referenced by glucat::matrix_log(), and glucat::operator/().

◆ kron()

template<typename LHS_T , typename RHS_T >

const RHS_T glucat::matrix::kron	(	const LHS_T &	lhs,
		const RHS_T &	rhs
	)

Kronecker tensor product of matrices - as per Matlab kron.

Definition at line 73 of file matrix_imp.h.

Referenced by glucat::framed_multi< Scalar_T, LO, HI >::fast().

◆ mono_kron()

template<typename LHS_T , typename RHS_T >

const RHS_T glucat::matrix::mono_kron	(	const LHS_T &	lhs,
		const RHS_T &	rhs
	)

Sparse Kronecker tensor product of monomial matrices.

Definition at line 116 of file matrix_imp.h.

Referenced by glucat::gen::generator_table< Matrix_T >::gen_from_pm1_qm1().

◆ mono_prod()

template<typename LHS_T , typename RHS_T >

const RHS_T::expression_type glucat::matrix::mono_prod	(	const ublas::matrix_expression< LHS_T > &	lhs,
		const ublas::matrix_expression< RHS_T > &	rhs
	)

Product of monomial matrices.

Definition at line 326 of file matrix_imp.h.

Referenced by glucat::matrix_multi< Scalar_T, LO, HI >::basis_element(), glucat::gen::generator_table< Matrix_T >::gen_from_pm4_qp4(), glucat::gen::generator_table< Matrix_T >::gen_from_pp4_qm4(), and glucat::gen::generator_table< Matrix_T >::gen_from_qp1_pm1().

◆ nnz()

template<typename Matrix_T >

Matrix_T::size_type glucat::matrix::nnz ( const Matrix_T & m )

Number of non-zeros.

Definition at line 269 of file matrix_imp.h.

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

◆ nork()

template<typename LHS_T , typename RHS_T >

const RHS_T glucat::matrix::nork	(	const LHS_T &	lhs,
		const RHS_T &	rhs,
		const bool	mono = `true`
	)

Left inverse of Kronecker product.

Definition at line 188 of file matrix_imp.h.

References norm_frob2().

◆ nork_range()

template<typename LHS_T , typename RHS_T >

void glucat::matrix::nork_range	(	RHS_T &	result,
		const typename LHS_T::const_iterator2	lhs_it2,
		const RHS_T &	rhs,
		const typename RHS_T::size_type	res_s1,
		const typename RHS_T::size_type	res_s2
	)

Utility routine for nork: calculate result for a range of indices.

Definition at line 155 of file matrix_imp.h.

References glucat::numeric_traits< Scalar_T >::to_scalar_t().

◆ norm_frob2()

template<typename Matrix_T >

Matrix_T::value_type glucat::matrix::norm_frob2 ( const Matrix_T & val )

Square of Frobenius norm.

Definition at line 413 of file matrix_imp.h.

Referenced by nork().

◆ prod()

template<typename LHS_T , typename RHS_T >

const RHS_T::expression_type glucat::matrix::prod	(	const ublas::matrix_expression< LHS_T > &	lhs,
		const ublas::matrix_expression< RHS_T > &	rhs
	)

inline

Product of matrices.

Definition at line 373 of file matrix_imp.h.

◆ signed_perm_nork()

template<typename LHS_T , typename RHS_T >

const RHS_T glucat::matrix::signed_perm_nork	(	const LHS_T &	lhs,
		const RHS_T &	rhs
	)

Left inverse of Kronecker product where lhs is a signed permutation matrix.

Definition at line 237 of file matrix_imp.h.

Referenced by glucat::fast().

◆ sparse_prod()

template<typename LHS_T , typename RHS_T >

const RHS_T::expression_type glucat::matrix::sparse_prod	(	const ublas::matrix_expression< LHS_T > &	lhs,
		const ublas::matrix_expression< RHS_T > &	rhs
	)

inline

Product of sparse matrices.

Definition at line 362 of file matrix_imp.h.

◆ to_lapack()

template<typename Matrix_T >

static ublas::matrix<double, ublas::column_major> glucat::matrix::to_lapack ( const Matrix_T & val )

static

Convert matrix to LAPACK format.

Definition at line 461 of file matrix_imp.h.

Referenced by eigenvalues().

◆ trace()

template<typename Matrix_T >

Matrix_T::value_type glucat::matrix::trace ( const Matrix_T & val )

Matrix trace.

Definition at line 437 of file matrix_imp.h.

References glucat::numeric_traits< Scalar_T >::NaN().

◆ unit()

template<typename Matrix_T >

const Matrix_T glucat::matrix::unit ( const typename Matrix_T::size_type n )

inline

Unit matrix - as per Matlab eye.

Definition at line 317 of file matrix_imp.h.

Classes

Enumerations

Functions

Enumeration Type Documentation

◆ eig_case_t

Function Documentation

◆ classify_eigenvalues()

◆ eigenvalues()

◆ inner()

◆ isnan()

◆ kron()

◆ mono_kron()

◆ mono_prod()

◆ nnz()

◆ nork()

◆ nork_range()

◆ norm_frob2()

◆ prod()

◆ signed_perm_nork()

◆ sparse_prod()

◆ to_lapack()

◆ trace()

◆ unit()