Classes
struct	MomentTensor
	Joint moment array of size (n_1+1)x...x(n_d+1), stored column major. More...

Enumerations
enum class	MomentEdge { FactorialFromRaw , RawFromFactorial , UpfactorialFromRaw , RawFromUpfactorial , BinomialFromFactorial , NegbinomialFromUpfactorial , FactorialFromBinomial , UpfactorialFromNegbinomial , FactorialFromUpfactorial , UpfactorialFromFactorial , NegbinomialFromBinomial , BinomialFromNegbinomial , BinomialFromTail , TailFromBinomial }
	Edge labels of the house of moments, one per MATLAB edge string. More...

Functions
template<class T>
std::vector< T >	apply_table (const Matrix< T > &A, const std::vector< T > &v)
	Apply a lower-triangular transform table to a moment vector.
template<class T>
std::vector< T >	moment_binomial_from_factorial (const std::vector< T > &f)
	b_i = f_i / i!
template<class T>
std::vector< T >	moment_binomial_from_negbinomial (const std::vector< T > &bm)
	b_0 = 1; b_i = sum_k (-1)^(i-k) C(i-1,k-1) bm_k for i >= 1.
template<class T>
std::vector< T >	moment_binotrans (const std::vector< T > &x)
	y_i = sum_k (-1)^(i-k) C(i,k) x_k.
template<class T>
std::vector< T >	moment_binotransinv (const std::vector< T > &y)
	x_i = sum_k C(i,k) y_k.
template<class T>
std::vector< T >	moment_central_from_raw (const std::vector< T > &m)
	mc_i = sum_k (-1)^(i-k) C(i,k) m_k m1^(i-k), with m1 = m[1].
template<class T>
std::vector< T >	moment_cumulant_from_raw (const std::vector< T > &m)
	kappa_i = m_i - sum_{k=1}^{i-1} C(i-1,k-1) kappa_k m_{i-k}.
template<class T>
std::vector< T >	moment_raw_from_cumulant (const std::vector< T > &kappa)
	mi = sum{k=1}^{i} C(i-1,k-1) kappa_k m_{i-k}, with m_0 = 1.
template<class T>
std::vector< T >	moment_factcumulant_from_factorial (const std::vector< T > &f)
	Factorial cumulants from factorial moments.
template<class T>
std::vector< T >	moment_factorial_from_factcumulant (const std::vector< T > &kappa)
	Factorial moments from factorial cumulants.
template<class T>
std::vector< T >	moment_factorial_from_binomial (const std::vector< T > &b)
	f_i = i!
template<class T>
std::vector< T >	moment_factorial_from_raw (const std::vector< T > &m)
	f = s * m, with s the signed Stirling numbers of the first kind.
template<class T>
std::vector< T >	moment_factorial_from_upfactorial (const std::vector< T > &fp)
	f_0 = 1; f_i = sum_k (-1)^(i-k) L(i,k) fp_k for i >= 1.
MomentEdge	moment_edge_from_string (const std::string &edge)
	Parses the MATLAB edge string into its label.
template<class T>
Matrix< T >	moment_housematrix (MomentEdge edge, int n)
	(n+1)x(n+1) conversion table of the given edge.
template<class T>
Matrix< T >	moment_housematrix (const std::string &edge, int n)
	String overload matching the MATLAB call signature.
template<class T>
std::vector< T >	moment_apply_full (const Matrix< T > &A, const std::vector< T > &v)
	Full matrix-vector product, needed because the tail edges are upper triangular.
template<class T>
MomentTensor< T >	moment_joint_binomial_from_factorial (const MomentTensor< T > &f)
	Joint binomial moments from joint factorial moments.
template<class T>
MomentTensor< T >	moment_joint_binomial_from_negbinomial (const MomentTensor< T > &bm)
	Joint binomial moments from joint negative-binomial moments.
template<class T>
MomentTensor< T >	moment_joint_binomial_from_tail (const MomentTensor< T > &t)
	Joint binomial moments from joint tail moments.
template<class T>
MomentTensor< T >	moment_joint_factorial_from_binomial (const MomentTensor< T > &b)
	Joint factorial moments from joint binomial moments.
template<class T>
MomentTensor< T >	moment_joint_factorial_from_raw (const MomentTensor< T > &m)
	Joint factorial moments from joint raw moments.
template<class T>
MomentTensor< T >	moment_joint_factorial_from_upfactorial (const MomentTensor< T > &fp)
	Joint factorial moments from joint upper-factorial moments.
template<class T>
MomentTensor< T >	moment_joint_negbinomial_from_binomial (const MomentTensor< T > &b)
	Joint negative-binomial moments from joint binomial moments.
template<class T>
MomentTensor< T >	moment_joint_negbinomial_from_upfactorial (const MomentTensor< T > &fp)
	Joint negative-binomial moments from joint upper-factorial moments.
template<class T>
MomentTensor< T >	moment_joint_raw_from_factorial (const MomentTensor< T > &f)
	Joint raw moments from joint factorial moments.
template<class T>
MomentTensor< T >	moment_joint_raw_from_upfactorial (const MomentTensor< T > &fp)
	Joint raw moments from joint upper-factorial moments.
template<class T>
MomentTensor< T >	moment_joint_tail_from_binomial (const MomentTensor< T > &b)
	Joint tail moments from joint binomial moments.
template<class T>
MomentTensor< T >	moment_joint_upfactorial_from_factorial (const MomentTensor< T > &f)
	Joint upper-factorial moments from joint factorial moments.
template<class T>
MomentTensor< T >	moment_joint_upfactorial_from_negbinomial (const MomentTensor< T > &bm)
	Joint upper-factorial moments from joint negative-binomial moments.
template<class T>
MomentTensor< T >	moment_joint_upfactorial_from_raw (const MomentTensor< T > &m)
	Joint upper-factorial moments from joint raw moments.
template<class T>
MomentTensor< T >	moment_joint_cumulant_from_raw (const MomentTensor< T > &m)
	Joint cumulants from joint raw moments.
template<class T>
MomentTensor< T >	moment_joint_raw_from_cumulant (const MomentTensor< T > &kappa)
	Joint raw moments from joint cumulants.
template<class T>
MomentTensor< T >	moment_joint_factcumulant_from_factorial (const MomentTensor< T > &f)
	Joint factorial cumulants from joint factorial moments.
template<class T>
MomentTensor< T >	moment_joint_factorial_from_factcumulant (const MomentTensor< T > &kappa)
	Joint factorial moments from joint factorial cumulants.
template<class T>
MomentTensor< T >	moment_joint_central_from_raw_mean (const MomentTensor< T > &m, const std::vector< T > &mu)
	Joint central moments from joint raw moments about a given mean vector.
template<class T>
MomentTensor< T >	moment_joint_central_from_raw (const MomentTensor< T > &m)
	Joint central moments from joint raw moments, reading the means off m.
template<class T>
MomentTensor< T >	moment_joint_raw_from_central (const MomentTensor< T > &mc, const std::vector< T > &mu)
	Joint raw moments from joint central moments about a given mean vector.
template<class T>
MomentTensor< T >	moment_joint_central_from_tail (const MomentTensor< T > &t)
	Joint central moments from joint tail moments.
template<class T>
std::vector< T >	moment_joint_aggregate (const MomentTensor< T > &F)
	Factorial moments of a total count from the joint factorial moments of its parts.
template<class T>
MomentTensor< T >	moment_joint_marking (const std::vector< T > &f, const std::vector< T > &p, const std::vector< std::size_t > &dims)
	Joint factorial moments of a multinomially marked count from the aggregate ones.
template<class T>
Matrix< T >	moment_lah (int n)
	L(i,j) = L(i-1,j-1) + (i+j-1) L(i-1,j), L(0,0) = 1.
template<class T>
std::vector< T >	moment_negbinomial_from_binomial (const std::vector< T > &b)
	bm_0 = 1; bm_i = sum_k C(i-1,k-1) b_k for i >= 1.
template<class T>
std::vector< T >	moment_negbinomial_from_upfactorial (const std::vector< T > &fp)
	bm_i = fp_i / i!
template<class T>
std::vector< T >	moment_raw_from_central (const std::vector< T > &mc, const T &m1)
	m_i = sum_k C(i,k) mc_k m1^(i-k).
template<class T>
std::vector< T >	moment_raw_from_factorial (const std::vector< T > &f)
	m = S * f.
template<class T>
std::vector< T >	moment_raw_from_upfactorial (const std::vector< T > &fp)
	m_i = sum_j (-1)^(i-j) S(i,j) fp_j.
template<class T>
Matrix< T >	moment_stirling1 (int n)
	s(i,j) = (-1)^(i-j) sigma(i,j).
template<class T>
Matrix< T >	moment_stirling2 (int n)
	S(i,j) = j S(i-1,j) + S(i-1,j-1), S(0,0) = 1.
template<class T>
Matrix< T >	moment_stirlingcycle (int n)
	sigma(i,j), (n+1) x (n+1) lower triangular, sigma(0,0) = 1.
template<class T>
std::vector< T >	moment_binomial_from_tail (const std::vector< T > &t)
	bi = sum{k>=i} C(k-1,i-1) t_k.
template<class T>
std::vector< T >	moment_tail_from_binomial (const std::vector< T > &b)
	ti = sum{k>=i} (-1)^(k-i) C(k-1,i-1) b_k.
template<class T>
std::vector< std::size_t >	moment_tensorsize (const MomentTensor< T > &A)
	Extents with the trailing singleton dimensions removed.
template<class T>
MomentTensor< T >	moment_tensortrans (const MomentTensor< T > &A, const Matrix< T > &Tm, std::size_t mode)
	Mode product: every fibre of A along dimension mode is replaced by Tm times that fibre.
template<class T>
MomentTensor< T >	moment_jointtrans (const MomentTensor< T > &A, MomentEdge edge)
	Applies the conversion matrix of one edge along every dimension of A.
template<class T>
MomentTensor< T >	moment_jointtrans (const MomentTensor< T > &A, const std::string &edge)
	String overload matching the MATLAB call signature.
template<class T>
std::vector< T >	moment_upfactorial_from_factorial (const std::vector< T > &f)
	fp_0 = 1; fp_i = sum_k L(i,k) f_k for i >= 1.
template<class T>
std::vector< T >	moment_upfactorial_from_negbinomial (const std::vector< T > &bm)
	fp_i = i!
template<class T>
std::vector< T >	moment_upfactorial_from_raw (const std::vector< T > &m)
	fp = sigma * m.

Enumeration Type Documentation

◆ MomentEdge

enum class line::moment::MomentEdge

strong

Edge labels of the house of moments, one per MATLAB edge string.

Enumerator
FactorialFromRaw
RawFromFactorial
UpfactorialFromRaw
RawFromUpfactorial
BinomialFromFactorial
NegbinomialFromUpfactorial
FactorialFromBinomial
UpfactorialFromNegbinomial
FactorialFromUpfactorial
UpfactorialFromFactorial
NegbinomialFromBinomial
BinomialFromNegbinomial
BinomialFromTail
TailFromBinomial

Definition at line 44 of file moment_housematrix.h.

Function Documentation

◆ apply_table()

template<class T>

std::vector< T > line::moment::apply_table	(	const Matrix< T > &	A,
		const std::vector< T > &	v )

Apply a lower-triangular transform table to a moment vector.

Definition at line 32 of file moment_apply.h.

References apply_table().

Referenced by apply_table(), moment_factorial_from_raw(), moment_raw_from_factorial(), moment_raw_from_upfactorial(), and moment_upfactorial_from_raw().

◆ moment_apply_full()

template<class T>

std::vector< T > line::moment::moment_apply_full	(	const Matrix< T > &	A,
		const std::vector< T > &	v )

Full matrix-vector product, needed because the tail edges are upper triangular.

Definition at line 155 of file moment_housematrix.h.

References moment_apply_full().

Referenced by moment_apply_full(), moment_binomial_from_tail(), and moment_tail_from_binomial().

◆ moment_binomial_from_factorial()

template<class T>

std::vector< T > line::moment::moment_binomial_from_factorial ( const std::vector< T > & f )

b_i = f_i / i!

Definition at line 32 of file moment_binomial_from_factorial.h.

References moment_binomial_from_factorial(), and line::num_factorial().

Referenced by moment_binomial_from_factorial().

◆ moment_binomial_from_negbinomial()

template<class T>

std::vector< T > line::moment::moment_binomial_from_negbinomial ( const std::vector< T > & bm )

b_0 = 1; b_i = sum_k (-1)^(i-k) C(i-1,k-1) bm_k for i >= 1.

Definition at line 32 of file moment_binomial_from_negbinomial.h.

References moment_binomial_from_negbinomial(), and line::num_nck().

Referenced by moment_binomial_from_negbinomial().

◆ moment_binomial_from_tail()

template<class T>

std::vector< T > line::moment::moment_binomial_from_tail ( const std::vector< T > & t )

bi = sum{k>=i} C(k-1,i-1) t_k.

Definition at line 36 of file moment_tail.h.

References BinomialFromTail, line::InputError::InputError(), moment_apply_full(), moment_binomial_from_tail(), and moment_housematrix().

Referenced by moment_binomial_from_tail().

◆ moment_binotrans()

template<class T>

std::vector< T > line::moment::moment_binotrans ( const std::vector< T > & x )

y_i = sum_k (-1)^(i-k) C(i,k) x_k.

Definition at line 38 of file moment_binotrans.h.

References moment_binotrans(), and line::num_nck().

Referenced by moment_binotrans().

◆ moment_binotransinv()

template<class T>

std::vector< T > line::moment::moment_binotransinv ( const std::vector< T > & y )

x_i = sum_k C(i,k) y_k.

Definition at line 32 of file moment_binotransinv.h.

References moment_binotransinv(), and line::num_nck().

Referenced by moment_binotransinv().

◆ moment_central_from_raw()

template<class T>

std::vector< T > line::moment::moment_central_from_raw ( const std::vector< T > & m )

mc_i = sum_k (-1)^(i-k) C(i,k) m_k m1^(i-k), with m1 = m[1].

Definition at line 32 of file moment_central_from_raw.h.

References line::InputError::InputError(), moment_central_from_raw(), line::num_nck(), and line::num_pow_int().

Referenced by moment_central_from_raw().

◆ moment_cumulant_from_raw()

template<class T>

std::vector< T > line::moment::moment_cumulant_from_raw ( const std::vector< T > & m )

kappa_i = m_i - sum_{k=1}^{i-1} C(i-1,k-1) kappa_k m_{i-k}.

Definition at line 38 of file moment_cumulant.h.

References line::InputError::InputError(), moment_cumulant_from_raw(), and line::num_nck().

Referenced by moment_cumulant_from_raw(), and moment_factcumulant_from_factorial().

◆ moment_edge_from_string()

MomentEdge line::moment::moment_edge_from_string ( const std::string & edge )

inline

Parses the MATLAB edge string into its label.

Definition at line 62 of file moment_housematrix.h.

References BinomialFromFactorial, BinomialFromNegbinomial, BinomialFromTail, FactorialFromBinomial, FactorialFromRaw, FactorialFromUpfactorial, line::InputError::InputError(), moment_edge_from_string(), NegbinomialFromBinomial, NegbinomialFromUpfactorial, RawFromFactorial, RawFromUpfactorial, TailFromBinomial, UpfactorialFromFactorial, UpfactorialFromNegbinomial, and UpfactorialFromRaw.

Referenced by moment_edge_from_string(), moment_housematrix(), and moment_jointtrans().

◆ moment_factcumulant_from_factorial()

template<class T>

std::vector< T > line::moment::moment_factcumulant_from_factorial ( const std::vector< T > & f )

Factorial cumulants from factorial moments.

Definition at line 67 of file moment_cumulant.h.

References moment_cumulant_from_raw(), and moment_factcumulant_from_factorial().

Referenced by moment_factcumulant_from_factorial().

◆ moment_factorial_from_binomial()

template<class T>

std::vector< T > line::moment::moment_factorial_from_binomial ( const std::vector< T > & b )

f_i = i!

b_i.

Definition at line 32 of file moment_factorial_from_binomial.h.

References moment_factorial_from_binomial(), and line::num_factorial().

Referenced by moment_factorial_from_binomial().

◆ moment_factorial_from_factcumulant()

template<class T>

std::vector< T > line::moment::moment_factorial_from_factcumulant ( const std::vector< T > & kappa )

Factorial moments from factorial cumulants.

Definition at line 73 of file moment_cumulant.h.

References moment_factorial_from_factcumulant(), and moment_raw_from_cumulant().

Referenced by moment_factorial_from_factcumulant().

◆ moment_factorial_from_raw()

template<class T>

std::vector< T > line::moment::moment_factorial_from_raw ( const std::vector< T > & m )

f = s * m, with s the signed Stirling numbers of the first kind.

Definition at line 34 of file moment_factorial_from_raw.h.

References apply_table(), moment_factorial_from_raw(), and moment_stirling1().

Referenced by moment_factorial_from_raw().

◆ moment_factorial_from_upfactorial()

template<class T>

std::vector< T > line::moment::moment_factorial_from_upfactorial ( const std::vector< T > & fp )

f_0 = 1; f_i = sum_k (-1)^(i-k) L(i,k) fp_k for i >= 1.

Definition at line 33 of file moment_factorial_from_upfactorial.h.

References moment_factorial_from_upfactorial(), and moment_lah().

Referenced by moment_factorial_from_upfactorial().

◆ moment_housematrix() [1/2]

template<class T>

Matrix< T > line::moment::moment_housematrix	(	const std::string &	edge,
		int	n )

String overload matching the MATLAB call signature.

Definition at line 149 of file moment_housematrix.h.

References moment_edge_from_string(), and moment_housematrix().

◆ moment_housematrix() [2/2]

template<class T>

Matrix< T > line::moment::moment_housematrix	(	MomentEdge	edge,
		int	n )

(n+1)x(n+1) conversion table of the given edge.

Definition at line 82 of file moment_housematrix.h.

References BinomialFromFactorial, BinomialFromNegbinomial, BinomialFromTail, FactorialFromBinomial, FactorialFromRaw, FactorialFromUpfactorial, line::InputError::InputError(), moment_housematrix(), moment_lah(), moment_stirling1(), moment_stirling2(), moment_stirlingcycle(), NegbinomialFromBinomial, NegbinomialFromUpfactorial, line::num_factorial(), line::num_nck(), RawFromFactorial, RawFromUpfactorial, TailFromBinomial, UpfactorialFromFactorial, UpfactorialFromNegbinomial, and UpfactorialFromRaw.

Referenced by moment_binomial_from_tail(), moment_housematrix(), moment_housematrix(), moment_jointtrans(), and moment_tail_from_binomial().

◆ moment_joint_aggregate()

template<class T>

std::vector< T > line::moment::moment_joint_aggregate ( const MomentTensor< T > & F )

Factorial moments of a total count from the joint factorial moments of its parts.

Definition at line 301 of file moment_joint.h.

References line::moment::MomentTensor< T >::data, line::InputError::InputError(), moment_joint_aggregate(), line::num_factorial(), line::moment::MomentTensor< T >::numel(), line::moment::MomentTensor< T >::order(), and line::moment::MomentTensor< T >::sz.

Referenced by moment_joint_aggregate().

◆ moment_joint_binomial_from_factorial()

template<class T>

MomentTensor< T > line::moment::moment_joint_binomial_from_factorial ( const MomentTensor< T > & f )

Joint binomial moments from joint factorial moments.

Definition at line 45 of file moment_joint.h.

References BinomialFromFactorial, moment_joint_binomial_from_factorial(), and moment_jointtrans().

Referenced by moment_joint_binomial_from_factorial().

◆ moment_joint_binomial_from_negbinomial()

template<class T>

MomentTensor< T > line::moment::moment_joint_binomial_from_negbinomial ( const MomentTensor< T > & bm )

Joint binomial moments from joint negative-binomial moments.

Definition at line 51 of file moment_joint.h.

References BinomialFromNegbinomial, moment_joint_binomial_from_negbinomial(), and moment_jointtrans().

Referenced by moment_joint_binomial_from_negbinomial().

◆ moment_joint_binomial_from_tail()

template<class T>

MomentTensor< T > line::moment::moment_joint_binomial_from_tail ( const MomentTensor< T > & t )

Joint binomial moments from joint tail moments.

Definition at line 57 of file moment_joint.h.

References BinomialFromTail, moment_joint_binomial_from_tail(), and moment_jointtrans().

Referenced by moment_joint_binomial_from_tail(), and moment_joint_central_from_tail().

◆ moment_joint_central_from_raw()

template<class T>

MomentTensor< T > line::moment::moment_joint_central_from_raw ( const MomentTensor< T > & m )

Joint central moments from joint raw moments, reading the means off m.

Definition at line 258 of file moment_joint.h.

References line::moment::MomentTensor< T >::data, line::InputError::InputError(), moment_joint_central_from_raw(), moment_joint_central_from_raw_mean(), line::moment::MomentTensor< T >::order(), line::moment::MomentTensor< T >::stride(), and line::moment::MomentTensor< T >::sz.

Referenced by moment_joint_central_from_raw(), and moment_joint_central_from_tail().

◆ moment_joint_central_from_raw_mean()

template<class T>

MomentTensor< T > line::moment::moment_joint_central_from_raw_mean	(	const MomentTensor< T > &	m,
		const std::vector< T > &	mu )

Joint central moments from joint raw moments about a given mean vector.

Definition at line 236 of file moment_joint.h.

References line::InputError::InputError(), moment_joint_central_from_raw_mean(), moment_tensortrans(), line::num_nck(), line::num_pow_int(), line::moment::MomentTensor< T >::order(), and line::moment::MomentTensor< T >::sz.

Referenced by moment_joint_central_from_raw(), and moment_joint_central_from_raw_mean().

◆ moment_joint_central_from_tail()

template<class T>

MomentTensor< T > line::moment::moment_joint_central_from_tail ( const MomentTensor< T > & t )

Joint central moments from joint tail moments.

Definition at line 293 of file moment_joint.h.

References moment_joint_binomial_from_tail(), moment_joint_central_from_raw(), moment_joint_central_from_tail(), moment_joint_factorial_from_binomial(), and moment_joint_raw_from_factorial().

Referenced by moment_joint_central_from_tail().

◆ moment_joint_cumulant_from_raw()

template<class T>

MomentTensor< T > line::moment::moment_joint_cumulant_from_raw ( const MomentTensor< T > & m )

Joint cumulants from joint raw moments.

Definition at line 208 of file moment_joint.h.

References line::moment::MomentTensor< T >::data, moment_joint_cumulant_from_raw(), and line::moment::MomentTensor< T >::sz.

Referenced by moment_joint_cumulant_from_raw(), and moment_joint_factcumulant_from_factorial().

◆ moment_joint_factcumulant_from_factorial()

template<class T>

MomentTensor< T > line::moment::moment_joint_factcumulant_from_factorial ( const MomentTensor< T > & f )

Joint factorial cumulants from joint factorial moments.

Definition at line 224 of file moment_joint.h.

References moment_joint_cumulant_from_raw(), and moment_joint_factcumulant_from_factorial().

Referenced by moment_joint_factcumulant_from_factorial().

◆ moment_joint_factorial_from_binomial()

template<class T>

MomentTensor< T > line::moment::moment_joint_factorial_from_binomial ( const MomentTensor< T > & b )

Joint factorial moments from joint binomial moments.

Definition at line 63 of file moment_joint.h.

References FactorialFromBinomial, moment_joint_factorial_from_binomial(), and moment_jointtrans().

Referenced by moment_joint_central_from_tail(), and moment_joint_factorial_from_binomial().

◆ moment_joint_factorial_from_factcumulant()

template<class T>

MomentTensor< T > line::moment::moment_joint_factorial_from_factcumulant ( const MomentTensor< T > & kappa )

Joint factorial moments from joint factorial cumulants.

Definition at line 230 of file moment_joint.h.

References moment_joint_factorial_from_factcumulant(), and moment_joint_raw_from_cumulant().

Referenced by moment_joint_factorial_from_factcumulant().

◆ moment_joint_factorial_from_raw()

template<class T>

MomentTensor< T > line::moment::moment_joint_factorial_from_raw ( const MomentTensor< T > & m )

Joint factorial moments from joint raw moments.

Definition at line 69 of file moment_joint.h.

References FactorialFromRaw, moment_joint_factorial_from_raw(), and moment_jointtrans().

Referenced by moment_joint_factorial_from_raw().

◆ moment_joint_factorial_from_upfactorial()

template<class T>

MomentTensor< T > line::moment::moment_joint_factorial_from_upfactorial ( const MomentTensor< T > & fp )

Joint factorial moments from joint upper-factorial moments.

Definition at line 75 of file moment_joint.h.

References FactorialFromUpfactorial, moment_joint_factorial_from_upfactorial(), and moment_jointtrans().

Referenced by moment_joint_factorial_from_upfactorial().

◆ moment_joint_marking()

template<class T>

MomentTensor< T > line::moment::moment_joint_marking	(	const std::vector< T > &	f,
		const std::vector< T > &	p,
		const std::vector< std::size_t > &	dims )

Joint factorial moments of a multinomially marked count from the aggregate ones.

Definition at line 326 of file moment_joint.h.

References line::moment::MomentTensor< T >::data, line::InputError::InputError(), moment_joint_marking(), line::num_pow_int(), and line::moment::MomentTensor< T >::numel().

Referenced by moment_joint_marking().

◆ moment_joint_negbinomial_from_binomial()

template<class T>

MomentTensor< T > line::moment::moment_joint_negbinomial_from_binomial ( const MomentTensor< T > & b )

Joint negative-binomial moments from joint binomial moments.

Definition at line 81 of file moment_joint.h.

References moment_joint_negbinomial_from_binomial(), moment_jointtrans(), and NegbinomialFromBinomial.

Referenced by moment_joint_negbinomial_from_binomial().

◆ moment_joint_negbinomial_from_upfactorial()

template<class T>

MomentTensor< T > line::moment::moment_joint_negbinomial_from_upfactorial ( const MomentTensor< T > & fp )

Joint negative-binomial moments from joint upper-factorial moments.

Definition at line 87 of file moment_joint.h.

References moment_joint_negbinomial_from_upfactorial(), moment_jointtrans(), and NegbinomialFromUpfactorial.

Referenced by moment_joint_negbinomial_from_upfactorial().

◆ moment_joint_raw_from_central()

template<class T>

MomentTensor< T > line::moment::moment_joint_raw_from_central	(	const MomentTensor< T > &	mc,
		const std::vector< T > &	mu )

Joint raw moments from joint central moments about a given mean vector.

Definition at line 272 of file moment_joint.h.

References line::InputError::InputError(), moment_joint_raw_from_central(), moment_tensortrans(), line::num_nck(), and line::num_pow_int().

Referenced by moment_joint_raw_from_central().

◆ moment_joint_raw_from_cumulant()

template<class T>

MomentTensor< T > line::moment::moment_joint_raw_from_cumulant ( const MomentTensor< T > & kappa )

Joint raw moments from joint cumulants.

Definition at line 216 of file moment_joint.h.

References line::moment::MomentTensor< T >::data, moment_joint_raw_from_cumulant(), and line::moment::MomentTensor< T >::sz.

Referenced by moment_joint_factorial_from_factcumulant(), and moment_joint_raw_from_cumulant().

◆ moment_joint_raw_from_factorial()

template<class T>

MomentTensor< T > line::moment::moment_joint_raw_from_factorial ( const MomentTensor< T > & f )

Joint raw moments from joint factorial moments.

Definition at line 93 of file moment_joint.h.

References moment_joint_raw_from_factorial(), moment_jointtrans(), and RawFromFactorial.

Referenced by moment_joint_central_from_tail(), and moment_joint_raw_from_factorial().

◆ moment_joint_raw_from_upfactorial()

template<class T>

MomentTensor< T > line::moment::moment_joint_raw_from_upfactorial ( const MomentTensor< T > & fp )

Joint raw moments from joint upper-factorial moments.

Definition at line 99 of file moment_joint.h.

References moment_joint_raw_from_upfactorial(), moment_jointtrans(), and RawFromUpfactorial.

Referenced by moment_joint_raw_from_upfactorial().

◆ moment_joint_tail_from_binomial()

template<class T>

MomentTensor< T > line::moment::moment_joint_tail_from_binomial ( const MomentTensor< T > & b )

Joint tail moments from joint binomial moments.

Definition at line 105 of file moment_joint.h.

References moment_joint_tail_from_binomial(), moment_jointtrans(), and TailFromBinomial.

Referenced by moment_joint_tail_from_binomial().

◆ moment_joint_upfactorial_from_factorial()

template<class T>

MomentTensor< T > line::moment::moment_joint_upfactorial_from_factorial ( const MomentTensor< T > & f )

Joint upper-factorial moments from joint factorial moments.

Definition at line 111 of file moment_joint.h.

References moment_joint_upfactorial_from_factorial(), moment_jointtrans(), and UpfactorialFromFactorial.

Referenced by moment_joint_upfactorial_from_factorial().

◆ moment_joint_upfactorial_from_negbinomial()

template<class T>

MomentTensor< T > line::moment::moment_joint_upfactorial_from_negbinomial ( const MomentTensor< T > & bm )

Joint upper-factorial moments from joint negative-binomial moments.

Definition at line 117 of file moment_joint.h.

References moment_joint_upfactorial_from_negbinomial(), moment_jointtrans(), and UpfactorialFromNegbinomial.

Referenced by moment_joint_upfactorial_from_negbinomial().

◆ moment_joint_upfactorial_from_raw()

template<class T>

MomentTensor< T > line::moment::moment_joint_upfactorial_from_raw ( const MomentTensor< T > & m )

Joint upper-factorial moments from joint raw moments.

Definition at line 123 of file moment_joint.h.

References moment_joint_upfactorial_from_raw(), moment_jointtrans(), and UpfactorialFromRaw.

Referenced by moment_joint_upfactorial_from_raw().

◆ moment_jointtrans() [1/2]

template<class T>

MomentTensor< T > line::moment::moment_jointtrans	(	const MomentTensor< T > &	A,
		const std::string &	edge )

String overload matching the MATLAB call signature.

Definition at line 140 of file moment_tensor.h.

References moment_edge_from_string(), and moment_jointtrans().

◆ moment_jointtrans() [2/2]

template<class T>

MomentTensor< T > line::moment::moment_jointtrans	(	const MomentTensor< T > &	A,
		MomentEdge	edge )

Applies the conversion matrix of one edge along every dimension of A.

Definition at line 130 of file moment_tensor.h.

References moment_housematrix(), moment_jointtrans(), moment_tensortrans(), line::moment::MomentTensor< T >::order(), and line::moment::MomentTensor< T >::sz.

Referenced by moment_joint_binomial_from_factorial(), moment_joint_binomial_from_negbinomial(), moment_joint_binomial_from_tail(), moment_joint_factorial_from_binomial(), moment_joint_factorial_from_raw(), moment_joint_factorial_from_upfactorial(), moment_joint_negbinomial_from_binomial(), moment_joint_negbinomial_from_upfactorial(), moment_joint_raw_from_factorial(), moment_joint_raw_from_upfactorial(), moment_joint_tail_from_binomial(), moment_joint_upfactorial_from_factorial(), moment_joint_upfactorial_from_negbinomial(), moment_joint_upfactorial_from_raw(), moment_jointtrans(), and moment_jointtrans().

◆ moment_lah()

template<class T>

Matrix< T > line::moment::moment_lah ( int n )

L(i,j) = L(i-1,j-1) + (i+j-1) L(i-1,j), L(0,0) = 1.

Definition at line 31 of file moment_lah.h.

References line::InputError::InputError(), and moment_lah().

Referenced by moment_factorial_from_upfactorial(), moment_housematrix(), moment_lah(), and moment_upfactorial_from_factorial().

◆ moment_negbinomial_from_binomial()

template<class T>

std::vector< T > line::moment::moment_negbinomial_from_binomial ( const std::vector< T > & b )

bm_0 = 1; bm_i = sum_k C(i-1,k-1) b_k for i >= 1.

Definition at line 32 of file moment_negbinomial_from_binomial.h.

References moment_negbinomial_from_binomial(), and line::num_nck().

Referenced by moment_negbinomial_from_binomial().

◆ moment_negbinomial_from_upfactorial()

template<class T>

std::vector< T > line::moment::moment_negbinomial_from_upfactorial ( const std::vector< T > & fp )

bm_i = fp_i / i!

Definition at line 32 of file moment_negbinomial_from_upfactorial.h.

References moment_negbinomial_from_upfactorial(), and line::num_factorial().

Referenced by moment_negbinomial_from_upfactorial().

◆ moment_raw_from_central()

template<class T>

std::vector< T > line::moment::moment_raw_from_central	(	const std::vector< T > &	mc,
		const T &	m1 )

m_i = sum_k C(i,k) mc_k m1^(i-k).

Definition at line 32 of file moment_raw_from_central.h.

References moment_raw_from_central(), line::num_nck(), and line::num_pow_int().

Referenced by moment_raw_from_central().

◆ moment_raw_from_cumulant()

template<class T>

std::vector< T > line::moment::moment_raw_from_cumulant ( const std::vector< T > & kappa )

mi = sum{k=1}^{i} C(i-1,k-1) kappa_k m_{i-k}, with m_0 = 1.

Definition at line 52 of file moment_cumulant.h.

References line::InputError::InputError(), and moment_raw_from_cumulant().

Referenced by moment_factorial_from_factcumulant(), and moment_raw_from_cumulant().

◆ moment_raw_from_factorial()

template<class T>

std::vector< T > line::moment::moment_raw_from_factorial ( const std::vector< T > & f )

m = S * f.

Definition at line 34 of file moment_raw_from_factorial.h.

References apply_table(), moment_raw_from_factorial(), and moment_stirling2().

Referenced by moment_raw_from_factorial().

◆ moment_raw_from_upfactorial()

template<class T>

std::vector< T > line::moment::moment_raw_from_upfactorial ( const std::vector< T > & fp )

m_i = sum_j (-1)^(i-j) S(i,j) fp_j.

Definition at line 34 of file moment_raw_from_upfactorial.h.

References apply_table(), moment_raw_from_upfactorial(), and moment_stirling2().

Referenced by moment_raw_from_upfactorial().

◆ moment_stirling1()

template<class T>

Matrix< T > line::moment::moment_stirling1 ( int n )

s(i,j) = (-1)^(i-j) sigma(i,j).

Definition at line 33 of file moment_stirling1.h.

References moment_stirling1(), and moment_stirlingcycle().

Referenced by moment_factorial_from_raw(), moment_housematrix(), and moment_stirling1().

◆ moment_stirling2()

template<class T>

Matrix< T > line::moment::moment_stirling2 ( int n )

S(i,j) = j S(i-1,j) + S(i-1,j-1), S(0,0) = 1.

Definition at line 31 of file moment_stirling2.h.

References line::InputError::InputError(), and moment_stirling2().

Referenced by moment_housematrix(), moment_raw_from_factorial(), moment_raw_from_upfactorial(), and moment_stirling2().

◆ moment_stirlingcycle()

template<class T>

Matrix< T > line::moment::moment_stirlingcycle ( int n )

sigma(i,j), (n+1) x (n+1) lower triangular, sigma(0,0) = 1.

Definition at line 31 of file moment_stirlingcycle.h.

References line::InputError::InputError(), and moment_stirlingcycle().

Referenced by moment_housematrix(), moment_stirling1(), moment_stirlingcycle(), and moment_upfactorial_from_raw().

◆ moment_tail_from_binomial()

template<class T>

std::vector< T > line::moment::moment_tail_from_binomial ( const std::vector< T > & b )

ti = sum{k>=i} (-1)^(k-i) C(k-1,i-1) b_k.

Definition at line 44 of file moment_tail.h.

References line::InputError::InputError(), moment_apply_full(), moment_housematrix(), moment_tail_from_binomial(), and TailFromBinomial.

Referenced by moment_tail_from_binomial().

◆ moment_tensorsize()

template<class T>

std::vector< std::size_t > line::moment::moment_tensorsize ( const MomentTensor< T > & A )

Extents with the trailing singleton dimensions removed.

Definition at line 96 of file moment_tensor.h.

References moment_tensorsize(), and line::moment::MomentTensor< T >::sz.

Referenced by moment_tensorsize().

◆ moment_tensortrans()

template<class T>

MomentTensor< T > line::moment::moment_tensortrans	(	const MomentTensor< T > &	A,
		const Matrix< T > &	Tm,
		std::size_t	mode )

Mode product: every fibre of A along dimension mode is replaced by Tm times that fibre.

Definition at line 102 of file moment_tensor.h.

References line::Matrix< T >::cols(), line::moment::MomentTensor< T >::data, line::InputError::InputError(), moment_tensortrans(), line::moment::MomentTensor< T >::numel(), line::moment::MomentTensor< T >::order(), line::Matrix< T >::rows(), line::moment::MomentTensor< T >::stride(), and line::moment::MomentTensor< T >::sz.

Referenced by moment_joint_central_from_raw_mean(), moment_joint_raw_from_central(), moment_jointtrans(), and moment_tensortrans().

◆ moment_upfactorial_from_factorial()

template<class T>

std::vector< T > line::moment::moment_upfactorial_from_factorial ( const std::vector< T > & f )

fp_0 = 1; fp_i = sum_k L(i,k) f_k for i >= 1.

Definition at line 33 of file moment_upfactorial_from_factorial.h.

References moment_lah(), and moment_upfactorial_from_factorial().

Referenced by moment_upfactorial_from_factorial().

◆ moment_upfactorial_from_negbinomial()

template<class T>

std::vector< T > line::moment::moment_upfactorial_from_negbinomial ( const std::vector< T > & bm )

fp_i = i!

bm_i.

Definition at line 32 of file moment_upfactorial_from_negbinomial.h.

References moment_upfactorial_from_negbinomial(), and line::num_factorial().

Referenced by moment_upfactorial_from_negbinomial().

◆ moment_upfactorial_from_raw()

template<class T>

std::vector< T > line::moment::moment_upfactorial_from_raw ( const std::vector< T > & m )

fp = sigma * m.

Definition at line 34 of file moment_upfactorial_from_raw.h.

References apply_table(), moment_stirlingcycle(), and moment_upfactorial_from_raw().

Referenced by moment_upfactorial_from_raw().

Classes

Enumerations

Functions

Enumeration Type Documentation

◆ MomentEdge

Function Documentation

◆ apply_table()

◆ moment_apply_full()

◆ moment_binomial_from_factorial()

◆ moment_binomial_from_negbinomial()

◆ moment_binomial_from_tail()

◆ moment_binotrans()

◆ moment_binotransinv()

◆ moment_central_from_raw()

◆ moment_cumulant_from_raw()

◆ moment_edge_from_string()

◆ moment_factcumulant_from_factorial()

◆ moment_factorial_from_binomial()

◆ moment_factorial_from_factcumulant()

◆ moment_factorial_from_raw()

◆ moment_factorial_from_upfactorial()

◆ moment_housematrix() [1/2]

◆ moment_housematrix() [2/2]

◆ moment_joint_aggregate()

◆ moment_joint_binomial_from_factorial()

◆ moment_joint_binomial_from_negbinomial()

◆ moment_joint_binomial_from_tail()

◆ moment_joint_central_from_raw()

◆ moment_joint_central_from_raw_mean()

◆ moment_joint_central_from_tail()

◆ moment_joint_cumulant_from_raw()

◆ moment_joint_factcumulant_from_factorial()

◆ moment_joint_factorial_from_binomial()

◆ moment_joint_factorial_from_factcumulant()

◆ moment_joint_factorial_from_raw()

◆ moment_joint_factorial_from_upfactorial()

◆ moment_joint_marking()

◆ moment_joint_negbinomial_from_binomial()

◆ moment_joint_negbinomial_from_upfactorial()

◆ moment_joint_raw_from_central()

◆ moment_joint_raw_from_cumulant()

◆ moment_joint_raw_from_factorial()

◆ moment_joint_raw_from_upfactorial()

◆ moment_joint_tail_from_binomial()

◆ moment_joint_upfactorial_from_factorial()

◆ moment_joint_upfactorial_from_negbinomial()

◆ moment_joint_upfactorial_from_raw()

◆ moment_jointtrans() [1/2]

◆ moment_jointtrans() [2/2]

◆ moment_lah()

◆ moment_negbinomial_from_binomial()

◆ moment_negbinomial_from_upfactorial()

◆ moment_raw_from_central()

◆ moment_raw_from_cumulant()

◆ moment_raw_from_factorial()

◆ moment_raw_from_upfactorial()

◆ moment_stirling1()

◆ moment_stirling2()

◆ moment_stirlingcycle()

◆ moment_tail_from_binomial()

◆ moment_tensorsize()

◆ moment_tensortrans()

◆ moment_upfactorial_from_factorial()

◆ moment_upfactorial_from_negbinomial()

◆ moment_upfactorial_from_raw()