jem::numeric Namespace Reference

This namespace provides support for developing numerical algorithms and applications. More...

Namespaces
	ufunc

Classes
class	BandFilter
class	Cholesky
class	ConstantFunc
class	DataFunc
class	DiagonalFilter
class	EigenUtils
class	EqualFilter
class	FuncException
class	Function
class	GreaterFilter
class	LUSolver
class	MatmulChain
	Multiplies a series of matrices and vectors. More...
class	PassFilter
class	Quadrature
class	Quaternion
class	Reorder
class	SparseFilter
class	SparseFilterInterface
class	SparseFilters
class	SparseFilterWrapper
class	SparseILU
class	SparseLU
class	SparseMatrix
	Represents a sparse matrix. More...
class	SparseSelector
class	SparseSolver
class	SparseStructure
	Represents the structure of a sparse matrix. More...
class	SparseUtils
class	UserFunc

Functions
double	det (const Array< double, 2 > &a)
template<int N>
double	det (const Tuple< double, N, N > &a)
Array< double, 2 >	inverse (const Array< double, 2 > &a)
template<int N>
Tuple< double, N, N >	inverse (const Tuple< double, N, N > &a)
bool	invert (const Array< double, 2 > &a)
bool	invert (const Array< double, 2 > &a, double &d)
template<int N>
bool	invert (Tuple< double, N, N > &a)
template<int N>
bool	invert (Tuple< double, N, N > &a, double &d)
double	det (const Tuple< double, 1, 1 > &a)
double	det (const Tuple< double, 2, 2 > &a)
double	det (const Tuple< double, 3, 3 > &a)
bool	invert (Tuple< double, 1, 1 > &a, double &d)
bool	invert (Tuple< double, 2, 2 > &a, double &d)
bool	invert (Tuple< double, 3, 3 > &a, double &d)
template<class T >
void	matmul (const Array< T, 1 > &r, const Array< T, 2 > &a, const Array< T, 1 > &b)
	Computes the product of a matrix and a column vector. More...
template<class T >
Array< T, 1 >	matmul (const Array< T, 2 > &a, const Array< T, 1 > &b)
	Returns the product of a matrix and a column vector. More...
template<class T >
void	matmul (const Array< T, 1 > &r, const Array< T, 1 > &a, const Array< T, 2 > &b)
	Computes the product of a row vector and a matrix. More...
template<class T >
Array< T, 1 >	matmul (const Array< T, 1 > &a, const Array< T, 2 > &b)
	Returns the product of a row vector and a matrix. More...
template<class T >
void	matmul (const Array< T, 2 > &r, const Array< T, 1 > &a, const Array< T, 1 > &b)
	Computes the product of a column vector and a row vector. More...
template<class T >
Array< T, 2 >	matmul (const Array< T, 1 > &a, const Array< T, 1 > &b)
	Returns the product of a column vector and a row vector. More...
template<class T >
void	matmul (const Array< T, 2 > &r, const Array< T, 2 > &a, const Array< T, 2 > &b)
	Computes the product of two matrices. More...
template<class T , int M, int N, int P>
void	matmul (Tuple< T, M, P > &r, const Tuple< T, M, N > &a, const Tuple< T, N, P > &b)
	Computes the product of two matrices. More...
template<class T , int M, int P>
void	matmul (Tuple< T, M, P > &r, const Array< T, 2 > &a, const Array< T, 2 > &b)
	Computes the product of two matrices. More...
template<class T , int M, int N>
void	matmul (const Array< T, 2 > &r, const Tuple< T, M, N > &a, const Array< T, 2 > &b)
	Computes the product of two matrices. More...
template<class T , int N, int P>
void	matmul (const Array< T, 2 > &r, const Array< T, 2 > &a, const Tuple< T, N, P > &b)
	Computes the product of two matrices. More...
template<class T >
Array< T, 2 >	matmul (const Array< T, 2 > &a, const Array< T, 2 > &b)
	Returns the product of two matrices. More...
template<class T , int M, int N, int P>
Tuple< T, M, P >	matmul (const Tuple< T, M, N > &a, const Tuple< T, N, P > &b)
	Returns the product of two matrices. More...
template<class T , int M, int N>
Array< T, 2 >	matmul (const Tuple< T, M, N > &a, const Array< T, 2 > &b)
	Returns the product of two matrices. More...
template<class T , int N, int P>
Array< T, 2 >	matmul (const Array< T, 2 > &a, const Tuple< T, N, P > &b)
	Returns the product of two matrices. More...
template<class T , class E1 , class E2 >
Tuple< T, 3 >	crossProduct (const Tuple< T, 3, 1, E1 > &a, const Tuple< T, 3, 1, E2 > &b)
template<class T , class E1 , class E2 >
T	crossProduct (const Tuple< T, 2, 1, E1 > &a, const Tuple< T, 2, 1, E2 > &b)
template<class T , int N, class E1 , class E2 >
T	dotProduct (const Tuple< T, N, 1, E1 > &a, const Tuple< T, N, 1, E2 > &b)
template<class T , class E1 , class E2 >
T	dotProduct (const Array< T, 1, E1 > &a, const Array< T, 1, E2 > &b)
template<class T , int N, class E >
T	norm2 (const Tuple< T, N, 1, E > &v)
template<class T , class E >
T	norm2 (const Array< T, 1, E > &v)
template<class T , int N>
void	axpy (const Array< T, N > &r, T t, const Array< T, N > &b)
template<class T , int N>
void	axpy (const Array< T, N > &r, const Array< T, N > &a, T t, const Array< T, N > &b)
void	parseUserFunc (String &name, String &args, String &expr, const String &input)
template<class T >
void	matmul (const Array< T > &r, const SparseMatrix< T > &a, const Array< T > &b)
	Computes the product of a matrix and a column vector. More...
template<class T >
Array< T >	matmul (const SparseMatrix< T > &a, const Array< T > &b)
	Returns the product of a matrix and a column vector. More...
template<class T >
void	matmul (const Array< T > &r, const Array< T > &a, const SparseMatrix< T > &b)
	Computes the product of a row vector and a matrix. More...
template<class T >
Array< T >	matmul (const Array< T > &a, const SparseMatrix< T > &b)
	Returns the product of a row vector and a matrix. More...
template<class T >
SparseMatrix< T >	matmul (const SparseMatrix< T > &a, const SparseMatrix< T > &b)
	Returns the product of two sparse matrices. More...
template<class T , class F >
SparseMatrix< T >	matmul (const SparseMatrix< T > &a, const SparseMatrix< T > &b, const SparseFilter< T, F > &filter)
	Returns the filtered product of two sparse matrices. More...
template<class R , class C >
SparseStructure	select (const SparseStruct &src, const R &rows, const C &cols)
template<class T , class R , class C >
SparseMatrix< T >	select (const SparseMatrix< T > &src, const R &rows, const C &cols)
template<class T >
Array< T >	diag (const SparseMatrix< T > &a)
	Returns the diagonal values of a sparse matrix. More...
template<class T >
void	sortRows (SparseMatrix< T > &a)
	performs a jem::sort on each row of a sparse matrix More...
template<class T , class F >
SparseMatrix< T >	filter (const SparseMatrix< T > &a, const SparseFilter< T, F > &f)
	Returns a copy of a sparse matrix with certain elements filtered out. More...
template<class T , class A >
SparseMatrix< T >	toMatrix (const util::SparseArray< T, 2, A > &a)
	creates a sparse matrix from a two-dimensional sparse array. More...
template<class T , class A >
util::SparseArray< T, 2, A > &	toArray (util::SparseArray< T, 2, A > &out, const SparseMatrix< T > &in)
	creates a two-dimensional sparse array from a sparse matrix. More...
bool	testCancelled (lint &flopCount)
void	testCancelled (lint &flopCount, const char *where, const char *what)
short	abs (short s)
int	abs (int i)
lint	abs (lint l)
float	abs (float f)
double	abs (double d)
float	sqrt (float f)
double	sqrt (double d)
template<class T >
T	modulus (const T &a, const T &b)
float	modulus (float a, float b)
double	modulus (double a, double b)
template<class T >
T	sign (const T &a, const T &b)
template<class T >
void	addToSum (T &sum, T &err, const T &val)
template<class T >
void	closeSum (T &sum, const T &err)
template<class T >
void	closeSum (T &sum, const T &err, const T &val)
template<class T , class Op >
SparseMatrix< T >	unite (const SparseMatrix< T > &a, const SparseMatrix< T > &b, const Op &op)
	Brief explanation of this unite function. More...
template<class T , class Op , class F >
SparseMatrix< T >	unite (const SparseMatrix< T > &a, const SparseMatrix< T > &b, const Op &op, const SparseFilter< T, F > &filter)
	Brief explanation of this unite function. More...
template<class T , class Op >
SparseMatrix< T >	intersect (const SparseMatrix< T > &a, const SparseMatrix< T > &b, const Op &op)
	Brief explanation of this unite function. More...
template<class T , class Op , class F >
SparseMatrix< T >	intersect (const SparseMatrix< T > &a, const SparseMatrix< T > &b, const Op &op, const SparseFilter< T, F > &filter)
	Brief explanation of this unite function. More...

Detailed Description

The namespace jem::numeric provides support for developing numerical algorithms and applications.

All classes and functions in this namespace can be found in the package jem.numeric.

Function Documentation

double jem::numeric::det

(

const Array< double, 2 > &

a

)

template<int N>

double jem::numeric::det

(

const Tuple< double, N, N > &

a

)

Array<double,2> jem::numeric::inverse

(

const Array< double, 2 > &

a

)

template<int N>

Tuple< double, N, N > jem::numeric::inverse

(

const Tuple< double, N, N > &

a

)

bool jem::numeric::invert

(

const Array< double, 2 > &

a

)

bool jem::numeric::invert	(	const Array< double, 2 > &	a,
		double &	d
	)

template<int N>

bool jem::numeric::invert

(

Tuple< double, N, N > &

a

)

template<int N>

bool jem::numeric::invert	(	Tuple< double, N, N > &	a,
		double &	d
	)

double jem::numeric::det

(

const Tuple< double, 1, 1 > &

a

)

double jem::numeric::det

(

const Tuple< double, 2, 2 > &

a

)

double jem::numeric::det

(

const Tuple< double, 3, 3 > &

a

)

bool jem::numeric::invert	(	Tuple< double, 1, 1 > &	a,
		double &	d
	)

bool jem::numeric::invert	(	Tuple< double, 2, 2 > &	a,
		double &	d
	)

bool jem::numeric::invert	(	Tuple< double, 3, 3 > &	a,
		double &	d
	)

template<class T , class E1 , class E2 >

Tuple<T,3> jem::numeric::crossProduct	(	const Tuple< T, 3, 1, E1 > &	a,
		const Tuple< T, 3, 1, E2 > &	b
	)

template<class T , class E1 , class E2 >

T jem::numeric::crossProduct	(	const Tuple< T, 2, 1, E1 > &	a,
		const Tuple< T, 2, 1, E2 > &	b
	)

template<class T , int N, class E1 , class E2 >

T jem::numeric::dotProduct	(	const Tuple< T, N, 1, E1 > &	a,
		const Tuple< T, N, 1, E2 > &	b
	)

template<class T , class E1 , class E2 >

T jem::numeric::dotProduct	(	const Array< T, 1, E1 > &	a,
		const Array< T, 1, E2 > &	b
	)

template<class T , int N, class E >

T jem::numeric::norm2

(

const Tuple< T, N, 1, E > &

v

)

template<class T , class E >

T jem::numeric::norm2

(

const Array< T, 1, E > &

v

)

template<class T , int N>

void jem::numeric::axpy	(	const Array< T, N > &	r,
		T	t,
		const Array< T, N > &	b
	)

template<class T , int N>

void jem::numeric::axpy	(	const Array< T, N > &	r,
		const Array< T, N > &	a,
		T	t,
		const Array< T, N > &	b
	)

void jem::numeric::parseUserFunc	(	String &	name,
		String &	args,
		String &	expr,
		const String &	input
	)

template<class T , class Op >

SparseMatrix<T> jem::numeric::unite	(	const SparseMatrix< T > &	a,
		const SparseMatrix< T > &	b,
		const Op &	op
	)

More elaborate explanation of this unite function

Parameters

a	- a sparse matrix
b	- a sparse matrix
op	- the binary operation to be performed between elements of the two sparse matrices

Returns

SparseMatrix object

template<class T , class Op , class F >

SparseMatrix<T> jem::numeric::unite	(	const SparseMatrix< T > &	a,
		const SparseMatrix< T > &	b,
		const Op &	op,
		const SparseFilter< T, F > &	filter
	)

More elaborate explanation of this unite function

Parameters

a	- a sparse matrix
b	- a sparse matrix
op	- the binary operation to be performed between elements of the two sparse matrices
filter	- the filter that has to be applied on the result of the binary operation of the two elements

Returns

SparseMatrix object

template<class T , class Op >

SparseMatrix<T> jem::numeric::intersect	(	const SparseMatrix< T > &	a,
		const SparseMatrix< T > &	b,
		const Op &	op
	)

More elaborate explanation of this unite function

Parameters

a	- a sparse matrix
b	- a sparse matrix
op	- the binary operation to be performed between elements of the two sparse matrices

Returns

SparseMatrix object

template<class T , class Op , class F >

SparseMatrix<T> jem::numeric::intersect	(	const SparseMatrix< T > &	a,
		const SparseMatrix< T > &	b,
		const Op &	op,
		const SparseFilter< T, F > &	filter
	)

More elaborate explanation of this unite function

Parameters

a	- a sparse matrix
b	- a sparse matrix
op	- the binary operation to be performed between elements of the two sparse matrices
filter	- the filter that has to be applied on the result of the binary operation of the two elements

Returns

SparseMatrix object

template<class R , class C >

SparseStructure jem::numeric::select	(	const SparseStruct &	src,
		const R &	rows,
		const C &	cols
	)

template<class T , class R , class C >

SparseMatrix<T> jem::numeric::select	(	const SparseMatrix< T > &	src,
		const R &	rows,
		const C &	cols
	)

bool jem::numeric::testCancelled

(

lint &

flopCount

)

void jem::numeric::testCancelled	(	lint &	flopCount,
		const char *	where,
		const char *	what
	)

short jem::numeric::abs

(

short

s

)

int jem::numeric::abs

(

int

i

)

lint jem::numeric::abs

(

lint

l

)

float jem::numeric::abs

(

float

f

)

double jem::numeric::abs

(

double

d

)

float jem::numeric::sqrt

(

float

f

)

double jem::numeric::sqrt

(

double

d

)

template<class T >

T jem::numeric::modulus	(	const T &	a,
		const T &	b
	)

float jem::numeric::modulus	(	float	a,
		float	b
	)

double jem::numeric::modulus	(	double	a,
		double	b
	)

template<class T >

T jem::numeric::sign	(	const T &	a,
		const T &	b
	)

template<class T >

void jem::numeric::addToSum	(	T &	sum,
		T &	err,
		const T &	val
	)

template<class T >

void jem::numeric::closeSum	(	T &	sum,
		const T &	err
	)

template<class T >

void jem::numeric::closeSum	(	T &	sum,
		const T &	err,
		const T &	val
	)