lambda_lanczos::util Namespace Reference

Classes
class	MapValueIterable
struct	realTypeMap
	Template class to map specific types. See real_t<T> for usage. More...
struct	realTypeMap< std::complex< T > >
class	TupleViewIterator
	Iterator for a container of tuples to iterate over the I-th tuple elements. More...
struct	TypedConjugate
	Complex conjugate template. More...
struct	TypedConjugate< std::complex< T > >

Typedefs
template<typename map_type >
using	MapValueIterator = TupleViewIterator< 1, map_type >
	Iterator for a map to iterate over its values. More...
template<typename T >
using	real_t = typename realTypeMap< T >::type
	Type mapper from T to real type of T. More...

Functions
template<typename T >
T	typed_conj (const T &val)
	Complex conjugate with type. This function returns the argument itself for real type, and returns its complex conjugate for complex type. More...
template<typename T >
T	inner_prod (const std::vector< T > &v1, const std::vector< T > &v2)
	Returns "mathematical" inner product of v1 and v2. More...
template<typename T >
real_t< T >	norm (const std::vector< T > &vec)
	Returns Euclidean norm of given vector. More...
template<typename T1 , typename T2 >
void	scalar_mul (T1 a, std::vector< T2 > &vec)
	Multiplies each element of vec by a. More...
template<typename T >
void	normalize (std::vector< T > &vec)
	Normalizes given vector. More...
template<typename T >
real_t< T >	l1_norm (const std::vector< T > &vec)
	Returns 1-norm of given vector. More...
template<typename ForwardIterator , typename T >
void	schmidt_orth (std::vector< T > &uorth, ForwardIterator first, ForwardIterator last)
	Orthogonalizes vector uorth with respect to orthonormal vectors defined by given iterators. More...
template<typename T >
void	initAsIdentity (std::vector< std::vector< T > > &a, size_t n)
	Initializes the given matrix a to an n by n identity matrix. More...
template<typename T >
void	sort_eigenpairs (std::vector< real_t< T > > &eigenvalues, std::vector< std::vector< T > > &eigenvectors, bool sort_eigenvector, const std::function< bool(real_t< T >, real_t< T >)> predicate=std::less< real_t< T > >())
	Sorts eigenvalues and eigenvectors with respect to given predicate. More...
template<typename T >
constexpr int	sig_decimal_digit ()
	Returns the significant decimal digits of type T. More...
template<typename T >
constexpr T	minimum_effective_decimal ()
template<typename T >
T	sgn (T val)
	Return the sign of given value. More...
template<typename T >
std::string	vectorToString (const std::vector< T > &vec, std::string delimiter=" ")
	Returns string representation of given vector. More...

Typedef Documentation

MapValueIterator

template<typename map_type >

using lambda_lanczos::util::MapValueIterator = typedef TupleViewIterator<1, map_type>

Iterator for a map to iterate over its values.

real_t

template<typename T >

using lambda_lanczos::util::real_t = typedef typename realTypeMap<T>::type

Type mapper from T to real type of T.

By default, real_t<T> returns T. However real_t<complex<T>> returns T. Usage example: This function returns a real number even if T is complex:

template <typename T>
inline real_t<T> norm(const std::vector<T>& vec);

Function Documentation

initAsIdentity()

template<typename T >

void lambda_lanczos::util::initAsIdentity	(	std::vector< std::vector< T > > &	a,
		size_t	n
	)

Initializes the given matrix a to an n by n identity matrix.

inner_prod()

template<typename T >

T lambda_lanczos::util::inner_prod ( const std::vector< T > &  v1, const std::vector< T > &  v2  )

inline

Returns "mathematical" inner product of v1 and v2.

This function is needed because std::inner_product calculates transpose(v1)*v2 instead of dagger(v1)*v2 for complex type.

l1_norm()

template<typename T >

real_t< T > lambda_lanczos::util::l1_norm ( const std::vector< T > &  vec )

inline

Returns 1-norm of given vector.

minimum_effective_decimal()

template<typename T >

constexpr T lambda_lanczos::util::minimum_effective_decimal ( )

inlineconstexpr

norm()

template<typename T >

real_t< T > lambda_lanczos::util::norm ( const std::vector< T > &  vec )

inline

Returns Euclidean norm of given vector.

normalize()

template<typename T >

void lambda_lanczos::util::normalize ( std::vector< T > &  vec )

inline

Normalizes given vector.

scalar_mul()

template<typename T1 , typename T2 >

void lambda_lanczos::util::scalar_mul ( T1  a, std::vector< T2 > &  vec  )

inline

Multiplies each element of vec by a.

schmidt_orth()

template<typename ForwardIterator , typename T >

void lambda_lanczos::util::schmidt_orth ( std::vector< T > &  uorth, ForwardIterator  first, ForwardIterator  last  )

inline

Orthogonalizes vector uorth with respect to orthonormal vectors defined by given iterators.

Vectors in u must be normalized, but uorth doesn't have to be.

sgn()

template<typename T >

T lambda_lanczos::util::sgn

(

T

val

)

Return the sign of given value.

If 0 is given, this function returns +1.

sig_decimal_digit()

template<typename T >

constexpr int lambda_lanczos::util::sig_decimal_digit ( )

inlineconstexpr

Returns the significant decimal digits of type T.

sort_eigenpairs()

template<typename T >

void lambda_lanczos::util::sort_eigenpairs ( std::vector< real_t< T > > &  eigenvalues, std::vector< std::vector< T > > &  eigenvectors, bool  sort_eigenvector, const std::function< bool(real_t< T >, real_t< T >)>  predicate = std::less<real_t<T>>()  )

inline

Sorts eigenvalues and eigenvectors with respect to given predicate.

Note

This function changes the memory location of the eigenpairs.

typed_conj()

template<typename T >

T lambda_lanczos::util::typed_conj ( const T &  val )

inline

Complex conjugate with type. This function returns the argument itself for real type, and returns its complex conjugate for complex type.

vectorToString()

template<typename T >

std::string lambda_lanczos::util::vectorToString	(	const std::vector< T > &	vec,
		std::string	delimiter = " "
	)

Returns string representation of given vector.