fiber_spaces Directory Reference

Files
file	any_lite.cc [code]
	Implementation for class any_lite.
file	any_lite.h [code]
	Interface for class any_lite.
file	at0.cc [code]
	Implementation for class at0.
file	at0.h [code]
	Interface for class at0.
file	at0.impl.h [code]
	Implementation for at0 facet function templates.
file	at1.cc [code]
	Implementation for class at1.
file	at1.h [code]
	Interface for class at1.
file	at1.impl.h [code]
	Implementation for at1 facet function templates.
file	at2.cc [code]
	Implementation for class at2.
file	at2.h [code]
	Interface for class at2.
file	at2.impl.h [code]
	Implementation for at2 facet function templates.
file	at2_e2.cc [code]
	Implementation for class at2_e2.
file	at2_e2.h [code]
	Interface for at2_e2 facet function templates.
file	at2_e2.impl.h [code]
	Implementation for class at2_e2.
file	at2_e3.cc [code]
	Implementation for class at2_e3.
file	at2_e3.h [code]
	Interface for class at2_e3.
file	at2_e3.impl.h [code]
	Implementation for class at2_e3.
file	at3.cc [code]
	Implementation for class at3.
file	at3.h [code]
	Interface for class at3.
file	at3.impl.h [code]
	Implementation for at3 facet function templates.
file	at3_e3.h [code]
	Interface for class at3_e3.
file	at3_e3.impl.h [code]
	Implementation for class at3_e3.
file	atp.cc [code]
	Implementation for class atp.
file	atp.h [code]
	Interface for class atp.
file	atp.impl.h [code]
	Implementation for atp facet function templates.
file	e1.cc [code]
	Implementation for class e1.
file	e1.h [code]
	Interface for class e1.
file	e1.impl.h [code]
	Implementation for class e1.
file	e2.cc [code]
	Implementation for class e2.
file	e2.h [code]
	Interface for class e2.
file	e2.impl.h [code]
	Implementation for e2 facet function templates.
file	e3.cc [code]
	Implementation for class e3.
file	e3.h [code]
	Interface for class e3.
file	e3.impl.h [code]
	Implementation for class e3.
file	e4.cc [code]
	Implementation for class e4.
file	e4.h [code]
	Interface for class e4.
file	e4.impl.h [code]
	Implementation for class e4.
file	ed.cc [code]
	Implementation for class ed.
file	ed.h [code]
	Interface for class ed.
file	ed.impl.h [code]
	Implementation for ed facet function templates.
file	gl2.cc [code]
	Implementation for class gl2.
file	gl2.h [code]
	Interface for class gl2.
file	gl2.impl.h [code]
	Implementation for class gl2.
file	gl3.cc [code]
	Implementation for class gl3.
file	gl3.h [code]
	Interface for class gl3.
file	gl3.impl.h [code]
	Implementation for class gl3.
file	gln.cc [code]
	Implementation for class gln.
file	gln.h [code]
	Interface for class gln.
file	gln.impl.h [code]
	Implementation for gln facet function templates.
file	gln_table_dofs_type.h [code]
	Interface for class gln_table_dofs_type.
file	group.cc [code]
	Implementation for class group.
file	group.h [code]
	Interface for abstract class group.
file	group.impl.h [code]
	Implementation for group facet function templates.
file	jcb.cc [code]
	Implementation for class jcb.
file	jcb.h [code]
	Interface for class jcb.
file	jcb.impl.h [code]
	Implementation for jcb facet function templates.
file	jcb_e13.cc [code]
	Implementation for class jcb_e13.
file	jcb_e13.h [code]
	Interface for class jcb_e13.
file	jcb_e13.impl.h [code]
	Implementation for class jcb_e13.
file	jcb_e23.cc [code]
	Implementation for class jcb_e23.
file	jcb_e23.h [code]
	Interface for class jcb_e23.
file	jcb_e23.impl.h [code]
	Implementation for class jcb_e23.
file	jcb_e33.cc [code]
	Implementation for class jcb_e33.
file	jcb_e33.h [code]
	Interface for class jcb_e33.
file	jcb_e33.impl.h [code]
	Implementation for class jcb_e33.
file	jcb_ed.cc [code]
	Implementation for class jcb_ed.
file	jcb_ed.h [code]
	Interface for class jcb_ed.
file	jcb_ed.impl.h [code]
	Implementation for jcb facet function templates.
file	jcb_table_dofs_type.h [code]
	Interface for class jcb_table_dofs_type.
file	met.cc [code]
	Implementation for class met.
file	met.h [code]
	Interface for class met.
file	met.impl.h [code]
	Implementation for met facet function templates.
file	met_e1.cc [code]
	Implementation for class met_e1.
file	met_e1.h [code]
	Interface for class met_e1.
file	met_e1.impl.h [code]
	Implementation for class met_e1.
file	met_e2.cc [code]
	Implementation for class met_e2.
file	met_e2.h [code]
	Interface for class met_e2.
file	met_e2.impl.h [code]
	Implementation for class met_e2.
file	met_e3.cc [code]
	Implementation for class met_e3.
file	met_e3.h [code]
	Interface for class met_e3.
file	met_e3.impl.h [code]
	Implementation for class met_e3.
file	met_ed.cc [code]
	Implementation for class met_ed.
file	met_ed.h [code]
	Interface for class met_ed.
file	met_ed.impl.h [code]
	Implementation for met_ed facet function templates.
file	st2.cc [code]
	Implementation for class st2.
file	st2.h [code]
	Interface for class st2.
file	st2.impl.h [code]
	Implementation for st2 facet function templates.
file	st2_e2.cc [code]
	Implementation for class st2_e2.
file	st2_e2.h [code]
	Interface for class st2_e2.
file	st2_e2.impl.h [code]
	Implementation for st2_e2 facet function templates.
file	st2_e3.cc [code]
	Implementation for class st2_e3.
file	st2_e3.h [code]
	Interface for class st2_e3.
file	st2_e3.impl.h [code]
	Implementation for class st2_e3.
file	st3.cc [code]
	Implementation for class st3.
file	st3.h [code]
	Interface for class st3.
file	st3.impl.h [code]
	Implementation for st3 facet function templates.
file	st3_e3.h [code]
	Interface for class st3_e3.
file	st3_e3.impl.h [code]
	Implementation for class st3_e3.
file	st4.cc [code]
	Implementation for class st4.
file	st4.h [code]
	Interface for class st4.
file	st4_e2.cc [code]
	Implementation for class st4_e2.
file	st4_e2.h [code]
	Interface for class st4_e2.
file	st4_e2.impl.h [code]
	Implementation for class st4_e2.
file	st4_e3.h [code]
	Interface for class st4_e3.
file	st4_e3.impl.h [code]
	Implementation for class st4_e3.
file	stp.cc [code]
	Implementation for class stp.
file	stp.h [code]
	Interface for class stp.
file	stp.impl.h [code]
	Implementation for stp facet function templates.
file	t2.cc [code]
	Implementation for class t2.
file	t2.h [code]
	Interface for class t2.
file	t2_e2.cc [code]
	Implementation for class t2_e2.
file	t2_e2.h [code]
	Interface for class t2_e2.
file	t2_e2.impl.h [code]
	Implementation for t2_e2 facet function templates.
file	t2_e3.cc [code]
	Implementation for class t2_e3.
file	t2_e3.h [code]
	Interface for class t2_e3.
file	t2_e3.impl.h [code]
	Implementation for class t2_e3.
file	t3.cc [code]
	Implementation for class t3.
file	t3.h [code]
	Interface for class t3.
file	t3_e3.cc [code]
	Implementation for class t3_e3.
file	t3_e3.h [code]
	Interface for class t3_e3.
file	t3_e3.impl.h [code]
	Implementation for class t3_e3.
file	t4.cc [code]
	Implementation for class t4.
file	t4.h [code]
	Interface for class t4.
file	t4_e2.cc [code]
	Implementation for class t4_e2.
file	t4_e2.h [code]
	Interface for class t4_e2.
file	t4_e2.impl.h [code]
	Implementation for class t4_e2.
file	t4_e3.cc [code]
	Implementation for class t4_e3.
file	t4_e3.h [code]
	Interface for class t4_e3.
file	t4_e3.impl.h [code]
	Implementation for class t4_e3.
file	tensor_variance.cc [code]
	Implementation for class tensor_variance.
file	tensor_variance.h [code]
	Interface for class tensor_variance.
file	tp.cc [code]
	Implementation for class tp.
file	tp.h [code]
	Interface for class tp.
file	tp.impl.h [code]
	Implementation for tp facet function templates.
file	tp_table_dofs_type.h [code]
	Interface for class tp_table_dofs_type.
file	tuple.cc [code]
	Implementation for class tuple.
file	tuple.h [code]
	Interface for class tuple.
file	tuple.impl.h [code]
	Implementation for tuple facet function templates.
file	tuple_table_dofs_type.h [code]
	Interface for class tuple_table_dofs_type.
file	vd.cc [code]
	Implementation for class vd.
file	vd.h [code]
	Interface for class vd.
file	vd.impl.h [code]
	Implementation for vd facet function templates.
file	vd_table_dofs_type.h [code]
	Interface for class vd_table_dofs_type.

Detailed Description

Fiber Algebra

The classes in the fiber_spaces cluster provide the various algebraic types used in theoretical physics to describe the properties of particles and systems. Each of these algebraic types has an associated set of operations, an algebra. In this overview we summarize the operations associated with each type. See the class documentation for a complete descriptiuon of the operations and the numerous signatures supported for each operation.

Abstract vectors (vector algebra)

Class vd and its descendants support the operations of vector algebra (linear algebra). The main(int xargc, char* xargv[]) operations are:

add	Add two vectors.
subtract	Subtract one vector from another.
multiply	Multiply a vector by a scalar.
divide	Divide a vector by a scalar.
min	Find the minimum component of a vector.
max	Find the maximum component of a vector.
contract	Contract a vector with a covector.

Euclidean vectors (Euclidean vector algebra)

dot	The Euclidean scalar product of two vectors.
length	The length of a vector.
put_length	Sets the length of a vector.
normalize	Sets the length of a vector to 1.
cross	The vector ("cross") product of an e3 vector with another.

General tensors

Class tp and its descendants support general tensor algebra. The main(int xargc, char* xargv[]) operations are:

tensor	The tensor product of one tensor with another.
alt	The antisymmetric ("alternating") part of a tensor.
sym	The symmetric part of a tensor.
contract	Contract a tensor on one contravariant and one covariant index.

Antisymmetric tensors (exterior algebra)

Class atp and its descendants support exterior algebra. the main(int xargc, char* xargv[]) operations are:

wedge	The exterior ("wedge") product of two antisymmetric tensors.
hook	The interior ("hook") product of an antisymmetric tensor and a vector.
star	The Hodge star ("dual") of an antisymmetric tensor.

Symmetric tensors (symmetric algebra)

symmetric_product	The symmetric product of one symmetric tensor with another.
trace	The trace of a degree 2 symmetric tensor.
determinant	The determinant of a degree 2 symmetric tensor.
to_principal_axes	Diagonalizes a degree 2 symmetric tensor.

Metric tensors

raise	Make a given index of a tensor contravariant.
lower	Make a given index of a tensor covariant.

Jacobians

push	Push a vector from the domain(int xargc, char* xargv[]) to the range of a Jacobian.
pull	Pull a covector from the range to the domain(int xargc, char* xargv[]) of a Jacobian.

Transformation groups

inverse	The inverse of a linear transformation
transform_basis_by	Transform the basis and components of a tensor

Multiple signatures

Each of the above operations is represented by a family of functions implementing multiple signatures for the operation. Typically each operation is provided for both regular fiber types and the associated lite fiber types. In addition, auto-allocated, pre-allocated and self-allocated variants are provided. Finally, whenver it makes sense, operator variants are provided. As an example, the full set of functions for the add operation is as follows:

///
/// x0 add x1 (auto-allocated version for lite types).
///
template <typename T> T* add(const T& x0, const T&amp x1);

///
/// x0 add x1 (pre-allocated version for regular types).
///
void add(const vd& x0, const vd& x1, vd& xresult, bool xauto_access);

///
/// x0 add x1 (pre-allocated version for lite types).
///
void add(const vd_lite& x0, const vd_lite& x1, vd_lite& xresult);

///
/// x0 add_equal x1 (self-allocated version for regular types);
/// synonym for add(xresult, xother, xresult, xauto_access).
///
void add_equal(vd& xresult, const vd& xother, bool xauto_access);

///
/// x0 add_equal x1 (self-allocated version for lite types).
///
template <typename T> void add_equal(T& xresult, const T& xother);

///
/// x0 + x1 (auto-allocated for lite types);
/// synonym for add(x0, x1).
///
template <typename T> T* operator+(const T& x0, const T& x1);

///
/// x0 += x1 (self-allocated for lite types);
/// synonym for add_equal(x0, x1).
///
template <typename T> T& operator+=(T& xresult, const T& xother);

The full fiber algebra consists of all the various signatures for all the various operations and thus contains approximately 100 functions.