fiber_bundle Namespace Reference

Namespace for the fiber_bundles component of the sheaf system. More...

Namespaces
	atp_algebra
	Namespace containing the antisymmetric tensor algrebra functions for the fiber_bundles component of the sheaf system.
	e2_algebra
	Namespace containing the 2D Euclidean vector algebra functions for the fiber_bundles component of the sheaf system.
	e3_algebra
	Namespace containing the 3D Euclidean vector algebra functions for the fiber_bundles component of the sheaf system.
	ed_algebra
	Namespace containing the Euclidean vector algebra functions for the fiber_bundles component of the sheaf system.
	jcb_algebra
	Namespace containing the Jacobian algrebra functions for the fiber_bundles component of the sheaf system.
	met_algebra
	Namespace containing the metric tensor algrebra functions for the fiber_bundles component of the sheaf system.
	sec_at0_algebra
	Namespace containing the algrebra functions for a section of a fiber bundle with a fiber type at0.
	sec_atp_algebra
	Namespace containing the algrebra functions for a a section of a fiber bundle with a fiber type atp.
	sec_e3_algebra
	Namespace containing the algrebra functions for a a section of a fiber bundle with a fiber type e3.
	sec_ed_algebra
	Namespace containing the algrebra functions for a a section of a fiber bundle with a fiber type ed.
	sec_jcb_algebra
	Namespace containing the algrebra functions for a a section of a fiber bundle with a fiber type jcb.
	sec_met_algebra
	Namespace containing the algrebra functions for a a section of a fiber bundle with a fiber type met.
	sec_st2_algebra
	Namespace containing the algrebra functions for a a section of a fiber bundle with a fiber type st2.
	sec_stp_algebra
	Namespace containing the algrebra functions for a a section of a fiber bundle with a fiber type stp.
	sec_tp_algebra
	Namespace containing the algrebra functions for a a section of a fiber bundle with a fiber type tp.
	sec_vd_algebra
	Namespace containing the algrebra functions for a a section of a fiber bundle with a d-dimensional vector space fiber.
	st2_algebra
	Namespace containing the 2d symmetric tensor algrebra functions for the fiber_bundles component of the sheaf system.
	stp_algebra
	Namespace containing the symmetric tensor algrebra functions for the fiber_bundles component of the sheaf system.
	tp_algebra
	Namespace containing the general tensor algrebra functions for the fiber_bundles component of the sheaf system.
	vd_algebra
	Namespace containing the vector algrebra functions for the fiber_bundles component of the sheaf system.

Classes
class	antisymmetric_matrix_2x2
	Antisymmetric matrix with 2 rows and 2 columns. More...
class	antisymmetric_matrix_3x3
	Antisymmetric matrix with 3 rows and 3 columns. More...
class	any_lite
	Abstract base class with useful features for all volatile objects. More...
class	array_field_dof_map
	A contiguous tuple, contiguous fiber representation of the abstract map from section_space_schema_member ids to section dof values of homogeneous type double. More...
class	array_sec_vd_dof_map
	A contiguous tuple, contiguous fiber representation of the abstract map from section dof ids to section dof values of type sec_vd_dof_type. More...
class	array_section_dof_map
	A contiguous tuple, contiguous fiber representation of the abstract map from section dof ids to section dof values of heterogeneous type. More...
class	at0
	A scalar viewed as an antisymmetric tensor of degree 0. As the degree is 0 there is nothing to be symmetric or antisymmetric with respect to. Thus, this could have equivalently been the symmetric tensor with degree=0. The convention is to choose antisymmetric. More...
class	at0_lite
	Antisymetric tensor of degree 0 (volatile version). More...
class	at0_row_dofs_type
	Row dofs type for class at0. More...
class	at0_space
	A space of scalars viewed as an antisymmetric tensor space of degree 0. More...
class	at1
	A general antisymmetric tensor of degree 1 over an abstract vector space (persistent version). More...
class	at1_lite
	A general antisymmetric tensor of degree 1 over an abstract vector space (volatile version). More...
class	at1_space
	An abstract vector space viewed as an antisymmetric tensor space of degree 1. More...
class	at2
	A general antisymmetric tensor of degree 2 over an abstract vector space. More...
class	at2_e2
	An antisymmetric rank 2 tensor over a Euclidean vector space of dimension 2 (persistent version). More...
class	at2_e2_lite
	An antisymmetric rank 2 tensor over a Euclidean vector space of dimension 2 (volatile version). More...
class	at2_e2_row_dofs_type
	Row dofs type for class at2_e2. More...
class	at2_e3
	An antisymmetric rank 2 tensor over a Euclidean vector space of dimension 3. (persistent version). More...
class	at2_e3_lite
	An antisymmetric rank 2 tensor over a Euclidean vector space of dimension 3. (volatile version). More...
class	at2_e3_row_dofs_type
	Row dofs type for class at2_e3. More...
class	at2_lite
	A general antisymmetric tensor of degree 2 over an abstract vector space (volatile version). More...
class	at3
	An antisymmetric rank 3 tensor over an abstract vector space (volatile version). More...
class	at3_e3
	An antisymmetric rank 3 tensor over a 3D Euclidean vector space. More...
class	at3_e3_lite
	An antisymmetric rank 3 tensor over a Euclidean vector space of dimension 3. (volatile version). More...
class	at3_e3_row_dofs_type
	Row dofs type for class at3_e3. More...
class	at3_lite
	An antisymmetric rank 3 tensor over an abstract vector space (volatile version). More...
class	atp
	An antisymmetric tensor of degree p. More...
class	atp_lite
	An antisymmetric tensor of degree p over an abstract vector space (volatile version). More...
class	atp_space
	An abstract antisymmetric tensor space of degree p. More...
class	base_space_crg_interval
	Abstract emulator for a interval of implicit base space members. More...
class	base_space_factory
	A factory for making base space objects of type base_type. More...
class	base_space_member
	A client handle for a member of a base space poset. More...
class	base_space_member_row_dof_tuple_type
	The type of row dof tuple for base_space_member. More...
class	base_space_poset
	The lattice of closed cells of a cellular space; a lattice representation of a computational mesh. More...
class	base_space_poset_table_dof_tuple_type
	The type of table dof tuple for base_space_poset. More...
class	bilinear_2d
	A section evaluator using bilinear interpolation over a square 2D domain. More...
class	binary_index
	A pair of indices (i,j). More...
class	binary_index_space
	A bounded domain for binary_index objects. More...
class	binary_section_component_iterator
	Iterates in postorder over dofs of a schema member anchor. Attaches an a handle of type section_space_schema_member to the current member of the iteration. More...
class	binary_section_dof_iterator
	Iterates in postorder over dofs of a schema member anchor. Attaches an a handle of type section_space_schema_member to the current member of the iteration. More...
class	binary_section_space_schema_member
	A client handle for a poset member which has been prepared for use as a schema for a section space. See class binary_section_space_schema_poset for a description of the schema represented by this class. More...
class	binary_section_space_schema_poset
	A schema poset for a section space. A binary Cartesian product subspace of the binary tensor product of a base space lattice and a fiber schema lattice. The tensor product of two lattices B and F is the finite distributive lattice generated by the poset J(B) x J(F), where J(B) is the poset of jims of B and similarly for J(F). The jims of the tensor product are thus pairs (jB, jF) and the general member of the tensor product lattice is equivalent to a subset (in fact a down set) of J(B) x J(F). This class only represents those members of the tensor product which are equivalent to pairs (pB, pF), where pB and pF are arbitrary members of B and F, respectively. Members of this Cartesian product subspace of the tensor product can be represented more efficiently than the general members, since we do not to store the subset defines the member. More...
class	block_adjacency
	Node to zone adjacency relation for a block of zones of a given type. More...
class	block_connectivity
	Zone to node connectivity relation for a block of zones of a given type. More...
class	block_relation
	Abstract cell relation for a block of zones of a given type. More...
class	chart_point
	A point in chart space. More...
class	chart_point_1d
	A point in a 1D chart space. More...
class	chart_point_2d
	A point in a 2D chart space. More...
class	chart_point_3d
	A point in a 3D chart space. More...
class	constant_eval_family
	A family of section evaluators containing members for constant functions on primitive cells. More...
class	constant_fcn_space
	An section evaluator with a constant value over an abstract domain. More...
class	constant_hex
	A section evaluator using trilinear interpolation over a cubic 3D domain. More...
class	constant_point
	A section evaluator with a constant value over a 1D domain. More...
class	constant_quad
	A section evaluator with a constant value over a square 2D domain. More...
class	constant_segment
	A section evaluator with a constant value over a 1D domain. More...
class	constant_tet
	A section evaluator with a constant value over a tetrahedral 3D domain. More...
class	constant_triangle
	A section evaluator with a constant value over a triangular 2D domain. More...
class	differentiable_section_evaluator
	An abstract section evaluator that can be differentiated. More...
class	discretization_context
	A context for discretization members. Intended for implementing various iterators, especially concurrent iterations over multiple sections. More...
class	discretization_iterator
	Iterator over the discretization subposet associated with a section_space_schema_member anchor. More...
class	dlinear_eval_family
	A family of section evaluators containing uni-, bi-, and tri-linear evaluators. More...
class	e1
	Euclidean vector space of dimension 1 (persistent version). More...
class	e1_lite
	Euclidean vector space of dimension 1 (volatile version). More...
class	e1_row_dofs_type
	Row dofs type for class e1. More...
class	e2
	Euclidean vector space of dimension 2 (persistent version). More...
class	e2_lite
	Euclidean vector space of dimension 2 (volatile version). More...
class	e2_row_dofs_type
	Row dofs type for class e2. More...
class	e3
	Euclidean vector space of dimension 3 (persistent version). More...
class	e3_lite
	Euclidean vector space of dimension 3 (volatile version). More...
class	e3_row_dofs_type
	Row dofs type for class e3. More...
class	e4
	Euclidean vector space of dimension 4 (persistent version). More...
class	e4_lite
	Euclidean vector space of dimension 4 (volatile version). More...
class	e4_row_dofs_type
	Row dofs type for class e4. More...
class	ed
	Euclidean vector space of dimension d (peresistent version). More...
class	ed_lite
	Euclidean vector space of dimension d (volatile version). More...
class	eval_family
	A family of compatible section evaluators, one for each member of some family of cell types; a map from cell type to section evaluator. More...
class	eval_iterator
	An iterator over the members of the evaluation subposet contained in the downset of the base space of a section_space_schema_member. Extracts the connectivity (that is, the discretization members in the downset) of each evaluation member. More...
class	fiber_bundles_namespace
	The standard fiber bundles name space; extends the standard sheaves namespace by defining base space, fiber space and section space schema. More...
class	field_dof_map
	OBSOLETE: Use array_sec_vd_dof_map or sparse_section_dof_map. The abstract map from section_space_schema_member ids to section dof values of homogeneous type double. More...
class	general_matrix_1x2
	General matrix with 1 row and 2 columns. More...
class	general_matrix_1x3
	General matrix with 1 row and 3 columns. More...
class	general_matrix_2x1
	General matrix with 2 rows and 1 column. More...
class	general_matrix_2x2
	General matrix with 2 rows and 2 columns. More...
class	general_matrix_2x3
	General matrix with 2 rows and 3 columns. More...
class	general_matrix_3x1
	General matrix with 3 rows and 1 column. More...
class	general_matrix_3x2
	General matrix with 3 rows and 2 columns. More...
class	general_matrix_3x3
	General matrix with 3 rows and 3 columns. More...
class	gl2
	The mathematical group GL(2, R). The group of all invertible, linear transformations on the R2, the 2 dimension vector space over the reals. Equivalent to the set of all invertible 2x2 real matrices. More...
class	gl2_lite
	The mathematical group GL(2, R). The group of all invertible, linear transformations on the R2, the 2 dimension vector space over the reals. Equivalent to the set of all invertible 2x2 real matrices (volatile version). More...
class	gl2_row_dofs_type
	Row dofs type for class gl2. More...
class	gl3
	The mathematical group GL(3, R). The group of all invertible, linear transformations on the R3, the 3 dimension vector space over the reals. Equivalent to the set of all invertible 3x3 real matrices. More...
class	gl3_lite
	The mathematical group GL(3, R). The group of all invertible, linear transformations on the R3, the 3 dimension vector space over the reals. Equivalent to the set of all invertible 3x3 real matrices (volatile version). More...
class	gl3_row_dofs_type
	Row dofs type for class gl3. More...
class	gln
	The mathematical group GL(n, R). GL(n,R) is the group of general, invertible, linear transformations on a vector space of dimension n over the reals R. More...
class	gln_lite
	The mathematical group GL(n, R). GL(n,R) is the group of general, invertible, linear transformations on a vector space of dimension n over the reals R (volatile version). More...
class	gln_row_dofs_type
	Row dofs type for class gln. More...
class	gln_space
	A Cartesian product space. More...
class	gln_table_dofs_type
	Table dofs of gln. More...
class	group
	The general, abstract mathematical group (persistent version) More...
class	group_lite
	The general, abstract mathematical group (volatile version). More...
class	hex_connectivity
	Nodal connectivity for a block containing zones of type hex. More...
class	homogeneous_block
	A client handle for a base space member which represents a homgeneous collection of local cells, aka "zones" or "elements". More...
class	homogeneous_block_crg_interval
	Emulator for a interval of implicit base space members representing a homogeneous collection of cells. More...
class	i_adjacency_implicit_index_space_iterator
	An implementation of implicit_index_space_iterator for an implicit id space in an i_adjacency_index_space_interval. More...
class	i_adjacency_index_space_interval
	An implementation of index_space_interval for an interval of implicit id spaces for the adjacency of a 1-dimensional structured block. More...
class	i_connectivity_implicit_index_space_iterator
	An implementation of implicit_index_space_iterator for an implicit id space in an i_connectivity_index_space_interval. More...
class	i_connectivity_index_space_interval
	An implementation of index_space_interval for an interval of implicit id spaces for the connectivity of an 2-dimensional structured block. More...
class	ij_adjacency_implicit_index_space_iterator
	An implementation of implicit_index_space_iterator for an implicit id space in an ij_adjacency_index_space_interval. More...
class	ij_adjacency_index_space_interval
	An implementation of index_space_interval for an interval of implicit id spaces for the adjacency of a 2-dimensional structured block. More...
class	ij_connectivity_implicit_index_space_iterator
	An implementation of implicit_index_space_iterator for an implicit id space in an ij_connectivity_index_space_interval. More...
class	ij_connectivity_index_space_interval
	An implementation of index_space_interval for an interval of implicit id spaces for the connectivity of an 2-dimensional structured block. More...
class	ijk_adjacency_implicit_index_space_iterator
	An implementation of implicit_index_space_iterator for an implicit id space in an ijk_adjacency_index_space_interval. More...
class	ijk_adjacency_index_space_interval
	An implementation of index_space_interval for an interval of implicit id spaces for the adjacency of a 3-dimensional structured block. More...
class	ijk_connectivity_implicit_index_space_iterator
	An implementation of implicit_index_space_iterator for an implicit id space in an ijk_connectivity_index_space_interval. More...
class	ijk_connectivity_index_space_interval
	An implementation of index_space_interval for an interval of implicit id spaces for the connectivity of an 3-dimensional structured block. More...
class	integrable_section_evaluator
	An abstract section evaluator with a bounded domain that supports integration (volume calculation) as well as differntiation. More...
class	jcb
	Abstract jacobian class. More...
class	jcb_e13
	Jacobian of a map from a 1 dimensional domain (u) to a 3 dimensional Euclidean space (x, y, z). More...
class	jcb_e13_lite
	Jacobian of a map from a 1 dimensional domain (u) to a 3 dimensional Euclidean space (x, y, z) (volatile version). More...
class	jcb_e13_row_dofs_type
	Row dofs type for class jcb_e13. More...
class	jcb_e23
	Jacobian of a map from a 2 dimensional domain (u, v) to a 3 dimensional Euclidean space (x, y, z). More...
class	jcb_e23_lite
	Jacobian of a map from a 2 dimensional domain (u, v) to a 3 dimensional Euclidean space (x, y, z) (volatile version). More...
class	jcb_e23_row_dofs_type
	Row dofs type for class jcb_e23. More...
class	jcb_e33
	Jacobian of a map from a 3 dimensional domain (u, v, w) to a 3 dimensional Euclidean space (x, y, z). More...
class	jcb_e33_lite
	Jacobian of a map from a 3 dimensional domain (u, v, w) to a 3 dimensional Euclidean space (x, y, z) (volatile version). More...
class	jcb_e33_row_dofs_type
	Row dofs type for class jcb_e33. More...
class	jcb_ed
	Abstract jacobian for d dimensional Euclidean space (persistent version). More...
class	jcb_ed_lite
	Abstract jacobian for d dimensional Euclidean space (volatile version). More...
class	jcb_lite
	Abstract jacobian class (volatile version). More...
class	jcb_space
	An abstract space of Jacobians. More...
class	jcb_table_dofs_type
	Table dofs type for class jcb. More...
class	line_connectivity
	Nodal connectivity for a block containing zones of type segment. More...
class	linear_1d
	A section evaluator using linear interpolation over a 1D domain. More...
class	linear_2d
	A section evaluator using linear interpolation over a triangular 2D domain. More...
class	linear_3d
	A section evaluator using linear interpolation over a tetrahedral 3D domain. More...
class	linear_fcn_space
	An abstract integrable section evaluator which is a member of a linear function space. More...
class	local_base_space_member
	A client handle for a member of a base space poset. More...
class	mesh_partition
	A decomposition of a mesh into non-overlapping scopes. More...
class	met
	A metric tensor over an abstract vector space (persistent version). More...
class	met_e1
	A metric tensor over a 1 dimensional Euclidean vector space. More...
class	met_e1_lite
	A metric tensor over a 1 dimensional Euclidean vector space (volatile version). More...
class	met_e1_row_dofs_type
	Row dofs type for class met_e1. More...
class	met_e2
	A metric tensor over a 2 dimensional Euclidean vector space (persistent version). More...
class	met_e2_lite
	A metric tensor over a 2 dimensional Euclidean vector space (volatile version). More...
class	met_e2_row_dofs_type
	Row dofs type for class met_e2. More...
class	met_e3
	A metric tensor over a 3 dimensional Euclidean vector space (persistent version). More...
class	met_e3_lite
	A metric tensor over a 1 dimensional Euclidean vector space (volatile version). More...
class	met_e3_row_dofs_type
	Row dofs type for class met_e3. More...
class	met_ed
	A metric tensor over a d-dimensional Euclidean vector space (persistent version). More...
class	met_ed_lite
	A metric tensor over a d-dimensional Euclidean vector space (volatile version). More...
class	met_lite
	A metric tensor over an abstract vector space (volatile version). More...
class	point_block_1d
	A homogeneous collection of i_size() disconnected points; similar to a structured_block_1d, but without the segments. More...
class	point_block_2d
	A homogeneous collection of i_size() * j_size() disconnected points similar to a structured_block_2d, but without the quads. More...
class	point_block_3d
	A homogeneous collection of i_size()*j_size()*k_size() disconnected points similar to a structured_block_3d, but without the hexs. More...
class	point_block_crg_interval
	Emulator for a interval of implicit base space members representing a homogeneous collection of unconnected points. More...
class	point_connectivity
	Nodal connectivity for a block containing zones of type point. Since a point block is just a collection of disconnected points, the "connectivity" list for each point contains just the point itself. More...
class	product_section_dof_iterator
	Iterates in postorder over dofs of a schema member anchor. Attaches an a handle of type section_space_schema_member to the current member of the iteration. More...
class	product_section_space_schema_crg_range
	Emulator for a range of implicit section space schema members representing the Cartesian product the mesh poset and the attribute schema poset. More...
class	product_section_space_schema_member
	A client handle for a poset member which has been prepared for use as a schema for a section space. See class product_section_space_schema_poset for a description of the schema represented by this class. More...
class	product_section_space_schema_poset
	An schema poset for a section space represented by a Cartesian product subspace of the tensor product of a base space lattice, and a fiber schema lattice. More...
class	quad_connectivity
	Nodal connectivity for a block containing zones of type quad. More...
class	quadratic_1d
	A section evaluator using quadratic interpolation over a 1D domain. More...
class	quadratic_2d
	A section evaluator using quadratic interpolation over a triangular 2D domain. More...
class	quadratic_3d
	A section evaluator using quadratic interpolation over a tetrahedral 3D domain. More...
class	sec_at0
	Antisymetric tensor of degree 0. As the degree is 0 there is nothing to be symmetric or antisymmetric with respect to. Thus, this could have equivalently been the symmetric tensor with degree=0. The convention is to choose antisymmetric. More...
class	sec_at0_space
	A space of scalars viewed as an antisymmetric tensor section space of degree 0. More...
class	sec_at1
	A section of a bundle with fiber type at1. More...
class	sec_at1_space
	A space of scalars viewed as an antisymmetric tensor section space of degree 1. More...
class	sec_at2
	A section of a bundle with fiber type at2. More...
class	sec_at2_e2
	A section of a bundle with fiber type at2_e2. More...
class	sec_at2_e3
	A section of a bundle with fiber type at2_e3. More...
class	sec_at3
	A section of a bundle with fiber type at3. More...
class	sec_at3_e3
	A section of a bundle with fiber type at3_e3. More...
class	sec_atp
	A section of a bundle with fiber type atp. More...
class	sec_atp_space
	An abstract antisymmetric tensor section space of degree p. More...
class	sec_e1
	A section of a fiber bundle with a 1-dimensional Euclidean vector space fiber. More...
class	sec_e1_uniform
	A section of a fiber bundle with a 1-dimensional Euclidean vector space fiber. More...
class	sec_e2
	A section of a fiber bundle with a 2-dimensional Euclidean vector space fiber. More...
class	sec_e2_uniform
	A section of a fiber bundle with a 2-dimensional Euclidean vector space fiber. More...
class	sec_e3
	A section of a fiber bundle with a 3-dimensional Euclidean vector space fiber. More...
class	sec_e3_uniform
	A section of a fiber bundle with a 3-dimensional Euclidean vector space fiber. More...
class	sec_e4
	A section of a fiber bundle with a 4-dimensional Euclidean vector space fiber. More...
class	sec_ed
	A section of a fiber bundle with a d-dimensional Euclidean vector space fiber. More...
class	sec_jcb
	A section of a bundle with fiber type jcb. More...
class	sec_jcb_e13
	A section of a bundle with fiber type jcb_e13. More...
class	sec_jcb_e23
	A section of a bundle with fiber type jcb_e23. More...
class	sec_jcb_e33
	A section of a bundle with fiber type jcb_e33. More...
class	sec_jcb_ed
	A section of a bundle with fiber type jcb_ed. More...
class	sec_jcb_space
	An abstract section space of Jacobians. More...
class	sec_met
	A section of a bundle with fiber type met. More...
class	sec_met_e1
	A section of a bundle with fiber type met_e1. More...
class	sec_met_e2
	A section of a bundle with fiber type met_e2. More...
class	sec_met_e3
	A section of a bundle with fiber type met_e3. More...
class	sec_met_ed
	A section of a bundle with fiber type met_ed. More...
class	sec_rep_descriptor
	A description for a section representation scheme. More...
class	sec_rep_descriptor_poset
	The poset for sec_rep_descriptors. More...
class	sec_rep_descriptor_table_dofs_type
	Table dofs type for class sec_rep_descriptor_poset. More...
class	sec_rep_space
	A handle for a poset whose members are numerical representations of sections of a fiber bundle. More...
class	sec_rep_space_member
	A member of a sec_rep_space; a section. More...
class	sec_st2
	A section of a bundle with fiber type st2. More...
class	sec_st2_e2
	A section of a bundle with fiber type st2_e2. More...
class	sec_st2_e3
	A section of a bundle with fiber type st2_e3. More...
class	sec_st3
	A section of a bundle with fiber type st3. More...
class	sec_st3_e3
	A section of a bundle with fiber type st3_e3. More...
class	sec_st4
	A section of a bundle with fiber type st4. More...
class	sec_st4_e2
	A section of a bundle with fiber type st4_e2. More...
class	sec_st4_e3
	A section of a bundle with fiber type st4_e3. More...
class	sec_stp
	A section of a bundle with fiber type stp. More...
class	sec_stp_space
	An abstract symmetric tensor section space of degree p. More...
class	sec_t2
	A section of a bundle with fiber type tp. More...
class	sec_t2_e2
	A section of a bundle with fiber type t2_e2. More...
class	sec_t2_e3
	A section of a bundle with fiber type t2_e3. More...
class	sec_t3
	A section of a bundle with fiber type t3. More...
class	sec_t3_e3
	A section of a bundle with fiber type t3_e3. More...
class	sec_t4
	A section of a bundle with fiber type t4. More...
class	sec_t4_e2
	A section of a bundle with fiber type t4_e2. More...
class	sec_t4_e3
	A section of a bundle with fiber type t4_e3. More...
class	sec_tp
	A section of a bundle with fiber type tp. More...
class	sec_tp_space
	An abstract tensor section space of degree p. More...
class	sec_tuple
	A section of a bundle with fiber type tuple. More...
class	sec_tuple_space
	A Cartesian product section space. More...
class	sec_vd
	A section of a fiber bundle with a d-dimensional vector space fiber. More...
class	sec_vd_space
	An abstract vector section space of dimension d. More...
class	section_component_iterator
	Iterates in postorder over components of a section_space_schema_member anchor. The components of a section_space_schema_member m are those members m' <= m such that m'.base_space().is_same_state(m.base_space()) and m'.fiber_schema().is_component(). Attaches an a handle of type section_space_schema_member to the current member of the iteration. More...
class	section_dof_iterator
	Iterates in postorder over dofs of a schema member anchor. Attaches an a handle of type section_space_schema_member to the current member of the iteration. More...
class	section_dof_map
	The abstract map from section dof ids to section dof values of heterogeneous type. More...
class	section_eval_iterator
	Iterates over the evaluation members of a section space schema anchor; gathers the dof ids for each evaluation member. More...
class	section_evaluator
	An abstract local section evaluator; a map from {local coordinates x dofs} to section value. More...
class	section_iteration_state
	Descriptor for iteration state of individual section. Intended for implementing various iterators, especially concurrent iterations over multiple sections. More...
class	section_space_schema_crg_range
	Abstract emulator for a range of implicit section space schema members. More...
class	section_space_schema_jims_index_space_handle
	An implementation of class explicit_index_space_handle that has a section space schema jims id space state. More...
class	section_space_schema_jims_index_space_iterator
	An iterator over an id space in which the equivalence between the ids in the space and the hub id space is stored in an array. More...
class	section_space_schema_jims_index_space_state
	An implementation class explicit_index_space_state for the jims id space of the section space schema. More...
class	section_space_schema_member
	A client handle for a poset member which has been prepared for use as a schema for a section space. More...
class	section_space_schema_poset
	An abstract schema poset for a section space. A Cartesian product subspace of the tensor product of a base space lattice, a fiber schema lattice, and possibly a local schema lattice. More...
class	section_space_schema_table_dof_crg_range
	Abstract emulator for a range of implicit section space schema members. More...
class	section_space_schema_table_dofs_type
	Table dofs type for class section_space_schema_poset. More...
struct	section_traits
	Features describing a section type. Declaration only; there is no generic implementation for this template. It is implemented only via specializations. More...
struct	section_traits< sec_at0 >
	Features describing a sec_at0 as a section type. More...
struct	section_traits< sec_at1 >
	Features describing a sec_at1 as a section type. More...
struct	section_traits< sec_at2_e2 >
	Features describing a sec_at2_e2 as a section type. More...
struct	section_traits< sec_at2_e3 >
	Features describing a sec_at2_e3 as a section type. More...
struct	section_traits< sec_at3_e3 >
	Features describing a sec_at3_e3 as a section type. More...
struct	section_traits< sec_e1 >
	Features describing a sec_e1 as a section type. More...
struct	section_traits< sec_e1_uniform >
	Features describing a sec_e1_uniform as a section type. More...
struct	section_traits< sec_e2 >
	Features describing a sec_e2 as a section type. More...
struct	section_traits< sec_e2_uniform >
	Features describing a sec_e2_uniform as a section type. More...
struct	section_traits< sec_e3 >
	Features describing a sec_e3 as a section type. More...
struct	section_traits< sec_e3_uniform >
	Features describing a sec_e3_uniform as a section type. More...
struct	section_traits< sec_jcb_e13 >
	Features describing a sec_sec_jcb_e13 as a section type. More...
struct	section_traits< sec_jcb_e23 >
	Features describing a sec_jcb_e23 as a section type. More...
struct	section_traits< sec_jcb_e33 >
	Features describing a sec_jcb_e33 as a section type. More...
struct	section_traits< sec_met_e1 >
	Features describing a sec_met_e1 as a section type. More...
struct	section_traits< sec_met_e2 >
	Features describing a sec_met_e2 as a section type. More...
struct	section_traits< sec_met_e3 >
	Features describing a sec_met_e3 as a section type. More...
struct	section_traits< sec_st2_e2 >
	Features describing a sec_st2_e2 as a section type. More...
struct	section_traits< sec_st2_e3 >
	Features describing a sec_st2_e3 as a section type. More...
struct	section_traits< sec_st3_e3 >
	Features describing a sec_st3_e3 as a section type. More...
struct	section_traits< sec_st4_e2 >
	Features describing a sec_st4_e2 as a section type. More...
struct	section_traits< sec_st4_e3 >
	Features describing a sec_t3_e3 as a section type. More...
struct	section_traits< sec_t2_e2 >
	Features describing a sec_t2_e2 as a section type. More...
struct	section_traits< sec_t2_e3 >
	Features describing a sec_t2_e3 as a section type. More...
struct	section_traits< sec_t3_e3 >
	Features describing a sec_t3_e3 as a section type. More...
struct	section_traits< sec_t4_e2 >
	Features describing a sec_t4_e2 as a section type. More...
struct	section_traits< sec_t4_e3 >
	Features describing a sec_t3_e3 as a section type. More...
struct	section_traits< sec_vd >
	Features describing a sec_vd as a section type. More...
class	sparse_field_dof_map
	OBSOLETE: Use array_sec_vd_dof_map or sparse_section_dof_map. A representation of the abstract map from section_space_schema_member ids to section dof values of homogeneous type double optimized for the case in which most dofs have the same value. More...
class	sparse_section_dof_map
	A discontiguous tuple, discontiguous fiber representation of the abstract map from section dof ids to section dof values of type sec_vd_dof_type. This class assumes most of the dofs have some given value (0.0 by default) and only stores dofs with a non-default value. More...
class	st2
	A general symmetric tensor of degree 2 over an abstract vector space (persistent version). More...
class	st2_e2
	A symmetric tensor of degree 2 over a Euclidean vector space of dimension 2 (persistent version). More...
class	st2_e2_lite
	A symmetric tensor of degree 2 over a Euclidean vector space of dimension 2 (volatile version). More...
class	st2_e2_row_dofs_type
	Row dofs type for class st2_e2. More...
class	st2_e3
	A symmetric tensor of degree 2 over a Euclidean vector space of dimension 3 (persistent version). More...
class	st2_e3_lite
	A symmetric tensor of degree 2 over a Euclidean vector space of dimension 3 (volatile version). More...
class	st2_e3_row_dofs_type
	Row dofs type for class st2_e3. More...
class	st2_lite
	A general symmetric tensor of degree 2 over an abstract vector space (volatile version). More...
class	st3
	A symmetric rank 3 tensor over an abstract vector space (persistent version). More...
class	st3_e3
	A symmetric rank 3 tensor over a 3D Euclidean vector space (persistent version). More...
class	st3_e3_lite
	A symmetric rank 3 tensor over a Euclidean vector space of dimension 3. (volatile version). More...
class	st3_e3_row_dofs_type
	Row dofs type for class st3_e3. More...
class	st3_lite
	A symmetric rank 3 tensor over an abstract vector space. (volatile version). More...
class	st4
	A symmetric rank 4 tensor over an abstract vector space (persistent version). More...
class	st4_e2
	A symmetric rank 3 tensor over a 3D Euclidean vector space (persistent version). More...
class	st4_e2_lite
	A symmetric rank 4 tensor over a Euclidean vector space of dimension 3. (volatile version). More...
class	st4_e2_row_dofs_type
	Row dofs type for class st4_e2. More...
class	st4_e3
	A symmetric rank 3 tensor over a 3D Euclidean vector space (persistent version). More...
class	st4_e3_lite
	A symmetric rank 4 tensor over a Euclidean vector space of dimension 3. (volatile version). More...
class	st4_e3_row_dofs_type
	Row dofs type for class st4_e3. More...
class	st4_lite
	A symmetric rank 4 tensor over an abstract vector space. (volatile version). More...
class	stp
	A symmetric tensor of degree p over an abstract vector space. More...
class	stp_lite
	A symmetric tensor of degree p over an abstract vector space (volatile version). More...
class	stp_space
	An abstract symmetric tensor space of degree p. More...
class	structured_block
	A client handle for a base space member which represents a homgeneous collection of local cells. More...
class	structured_block_1d
	A homogeneous collection of connected segments arranged in an i_size() array. More...
class	structured_block_1d_crg_interval
	Emulator for a interval of implicit base space members representing a 1 dimensional structured block, that is, a homogeneous collection of connected quads arranged in an i_size() array. More...
class	structured_block_2d
	A homogeneous collection of connected quads arranged in an i_size() x j_size() array. More...
class	structured_block_2d_crg_interval
	Emulator for a interval of implicit base space members representing a 2 dimensional structured block, that is, a homogeneous collection of connected quads arranged in an i_size() x j_size() array. More...
class	structured_block_3d
	A homogeneous collection of connected hexahedra arranged in an i_size() x j_size() x k_size() array. More...
class	structured_block_3d_crg_interval
	Emulator for a interval of implicit base space members representing a 3 dimensional structured block, that is, a homogeneous collection of connected hexahedra arranged in an i_size() x j_size() x k_size() array. More...
class	symmetric_matrix_2x2
	Symmetric matrix with 2 rows and 2 columns. More...
class	symmetric_matrix_3x3
	Symmetric matrix with 3 rows and 3 columns. More...
class	t02_e2_row_dofs_type
class	t02_e3_row_dofs_type
class	t11_e2_row_dofs_type
class	t2
	A tensor of degree 2 over an abstract vector space (persistent version). More...
class	t2_e2
	A tensor of degree 2 over a Euclidean vector space of dimension 2 (persistent version). More...
class	t2_e2_lite
	A tensor of degree 2 over a Euclidean vector space of dimension 2 (volatile version). More...
class	t2_e2_row_dofs_type
	Row dofs type for class t2_e2. More...
class	t2_e3
	A tensor of degree 2 over a Euclidean vector space of dimension 3 (persistent version). More...
class	t2_e3_lite
	A tensor of degree 2 over a Euclidean vector space of dimension 3 (volatile version). More...
class	t2_e3_row_dofs_type
	Row dofs type for class t2_e3. More...
class	t2_lite
	A tensor of degree 2 over an abstract vector space (volatile version). More...
class	t3
	A tensor of degree 3 over an abstract vector space (persistent version). More...
class	t3_e3
	A tensor of degree 3 over a Euclidean vector space of dimension 3 (persistent version). More...
class	t3_e3_lite
	A tensor of degree 3 over a Euclidean vector space of dimension 3 (volatile version). More...
class	t3_e3_row_dofs_type
	Row dofs type for class t3_e3. More...
class	t3_lite
	A tensor of degree 3 over an abstract vector space (volatile version). More...
class	t4
	A tensor of degree 4 over an abstract vector space (persistent version). More...
class	t4_e2
	A tensor of degree 4 over a Euclidean vector space of dimension 2 (persistent version). More...
class	t4_e2_lite
	A tensor of degree 4 over a Euclidean vector space of dimension 2 (volatile version). More...
class	t4_e2_row_dofs_type
	Row dofs type for class t4_e2. More...
class	t4_e3
	A tensor of degree 4 over a Euclidean vector space of dimension 3 (persistent version). More...
class	t4_e3_lite
	A tensor of degree 4 over a Euclidean vector space of dimension 3 (volatile version). More...
class	t4_e3_row_dofs_type
	Row dofs type for class t4_e3. More...
class	t4_lite
	A tensor of degree 4 over an abstract vector space (volatile version). More...
class	tensor_section_traits
	Tensor types of degree P over VECTOR_TYPE. Must be specialized for every supported combination of VECTOR_TYPE and P. More...
class	tensor_section_traits< 0, sec_e2 >
	Specialization for degree 0 tensors over sec_e2. More...
class	tensor_section_traits< 0, sec_e3 >
	Specialization for degree 0 tensors over sec_e3. More...
class	tensor_section_traits< 0, sec_e4 >
	Specialization for degree 0 tensors over sec_e4. More...
class	tensor_section_traits< 0, sec_vd >
	Tensor types of degree 0 over sec_vd; full specialization. More...
class	tensor_section_traits< 1, sec_e2 >
	Specialization for degree 1 tensors over sec_e2. More...
class	tensor_section_traits< 1, sec_e3 >
	Specialization for degree 1 tensors over sec_e3. More...
class	tensor_section_traits< 1, sec_e4 >
	Specialization for degree 1 tensors over sec_e4. More...
class	tensor_section_traits< 1, sec_vd >
	Tensor types of degree 1 over sec_vd; full specialization. More...
class	tensor_section_traits< 2, sec_e2 >
	Specialization for degree 2 tensors over sec_e2. More...
class	tensor_section_traits< 2, sec_e3 >
	Specialization for degree 2 tensors over sec_e3. More...
class	tensor_section_traits< 2, sec_e4 >
	Specialization for degree 2 tensors over sec_e4. More...
class	tensor_section_traits< 2, sec_vd >
	Tensor types of degree 2 over sec_vd; full specialization. More...
class	tensor_section_traits< 3, sec_e3 >
	Specialization for degree 3 tensors over sec_e3. More...
class	tensor_section_traits< 3, sec_e4 >
	Specialization for degree 3 tensors over sec_e4. More...
class	tensor_section_traits< 3, sec_vd >
	Tensor types of degree 3 over sec_vd; full specialization. More...
class	tensor_section_traits< 4, sec_vd >
	Tensor types of degree 4 over sec_vd; full specialization. More...
class	tensor_section_traits< P, sec_vd >
	Tensor types of degree P over sec_vd; partial specialization. More...
class	tensor_traits
	Tensor types of degree P over VECTOR_TYPE. No generic implementation defined, must be specialized for every supported combination of VECTOR_TYPE and P. More...
class	tensor_traits< 0, e2 >
	Specialization for degree 0 tensors over e2. More...
class	tensor_traits< 0, e2_lite >
	Specialization for degree 0 tensors over e2_lite. More...
class	tensor_traits< 0, e3 >
	Specialization for degree 0 tensors over e3. More...
class	tensor_traits< 0, e3_lite >
	Specialization for degree 0 tensors over e3_lite. More...
class	tensor_traits< 0, e4 >
	Specialization for degree 0 tensors over e4. More...
class	tensor_traits< 0, e4_lite >
	Specialization for degree 0 tensors over e4_lite. More...
class	tensor_traits< 0, vd_lite >
	Tensor types of degree 0 over vd_lite; full specialization. More...
class	tensor_traits< 1, e2 >
	Specialization for degree 1 tensors over e2. More...
class	tensor_traits< 1, e2_lite >
	Specialization for degree 1 tensors over e2_lite. More...
class	tensor_traits< 1, e3 >
	Specialization for degree 1 tensors over e3. More...
class	tensor_traits< 1, e3_lite >
	Specialization for degree 1 tensors over e3_lite. More...
class	tensor_traits< 1, e4 >
	Specialization for degree 1 tensors over e4. More...
class	tensor_traits< 1, e4_lite >
	Specialization for degree 1 tensors over e4_lite. More...
class	tensor_traits< 1, vd_lite >
	Tensor types of degree 1 over vd_lite; full specialization. More...
class	tensor_traits< 2, e2 >
	Specialization for degree 2 tensors over e2. More...
class	tensor_traits< 2, e2_lite >
	Specialization for degree 2 tensors over e2_lite. More...
class	tensor_traits< 2, e3 >
	Specialization for degree 2 tensors over e3. More...
class	tensor_traits< 2, e3_lite >
	Specialization for degree 2 tensors over e3_lite. More...
class	tensor_traits< 2, e4 >
	Specialization for degree 2 tensors over e4. More...
class	tensor_traits< 2, e4_lite >
	Specialization for degree 2 tensors over e4_lite. More...
class	tensor_traits< 2, vd_lite >
	Tensor types of degree 2 over vd_lite; full specialization. More...
class	tensor_traits< 3, e2 >
	Specialization for degree 3 tensors over e2. More...
class	tensor_traits< 3, e2_lite >
	Specialization for degree 3 tensors over e2_lite. More...
class	tensor_traits< 3, e3 >
	Specialization for degree 3 tensors over e3. More...
class	tensor_traits< 3, e3_lite >
	Specialization for degree 3 tensors over e3_lite. More...
class	tensor_traits< 3, e4 >
	Specialization for degree 3 tensors over e4. More...
class	tensor_traits< 3, e4_lite >
	Specialization for degree 3 tensors over e4_lite. More...
class	tensor_traits< 3, vd_lite >
	Tensor types of degree 3 over vd_lite; full specialization. More...
class	tensor_traits< 4, e2 >
	Specialization for degree 4 tensors over e2. More...
class	tensor_traits< 4, e2_lite >
	Specialization for degree 4 tensors over e2_lite. More...
class	tensor_traits< 4, e3 >
	Specialization for degree 4 tensors over e3. More...
class	tensor_traits< 4, e3_lite >
	Specialization for degree 4 tensors over e3_lite. More...
class	tensor_traits< 4, e4 >
	Specialization for degree 4 tensors over e4. More...
class	tensor_traits< 4, e4_lite >
	Specialization for degree 4 tensors over e4_lite. More...
class	tensor_traits< 4, vd_lite >
	Tensor types of degree 4 over vd_lite; full specialization. More...
class	tensor_variance
	The "type" of a tensor; specifies the degree and the co- or contra-variance for each index of a tensor. More...
class	ternary_index
	A triple of indices (i,j, k). More...
class	ternary_index_space
	A bounded domain for ternary_index objects. More...
class	tetra_connectivity
	Nodal connectivity for a block containing zones of type tetra. More...
class	tp
	A general tensor of "degree" p and given "variance" over an abstract vector space. More...
class	tp_lite
	A general tensor of degree p over an abstract vector space (volatile version). Volatile version does not support tensor type ("variance"); see further comments in class tp. More...
class	tp_space
	An abstract tensor space of degree p. More...
class	tp_table_dofs_type
	Table dofs type for class tp. More...
class	triangle_connectivity
	Nodal connectivity for a block containing zones of type triangle. More...
class	trilinear_3d
	A section evaluator using trilinear interpolation over a cubic 3D domain. More...
class	tuple
	A member of a Cartesian product space; a tuple of attributes (persistent version). More...
class	tuple_lite
	A member of a Cartesian product space; a tuple of attributes (volatile version). More...
class	tuple_space
	A Cartesian product space. More...
class	tuple_table_dofs_type
	Table dofs type for class tuple_table_dofs_type. More...
class	unary_index_space
	A bounded domain for unary_index objects. More...
class	uniform_1d
	A section evaluator using linear interpolation over a 1D domain which is refined into a uniform mesh. More...
class	uniform_2d
	A section evaluator using bilinear interpolation over a square 2D domain. Intended for use with uniform meshes. More...
class	uniform_3d
	A section evaluator using trilinear interpolation over a cubic 3D domain. Intended for use with uniform meshes. More...
class	uniform_eval_family
	A family of evaluators for uniform meshes. More...
class	unstructured_block
	OBSOLETE: use zone_nodes_block or point_block_*d. A client handle for a base space member which represents a "unstructured" homogeneous collection of local cells. $$HACK: unstructured_block hack; must use unstructured_block::new_host. More...
class	unstructured_block_builder
	OBSOLETE: use zone_nodes_block or point_block_*d. A builder object for constructing unstructured blocks given a local cell template and atomic equivalences ("connectivity"). More...
class	vd
	Abstract vector space over dof_type. More...
class	vd_lite
	Abstract vector space over dof_type (volatile version). More...
class	vd_row_dofs_type
	Row dofs type for class vd. More...
class	vd_space
	An abstract vector space of dimension d. More...
class	vd_table_dofs_type
	Table dofs type for class vd_table_dofs_type. More...
class	zone_nodes_block
	A homogeneous collection of zones with nodal connectivity. More...
class	zone_nodes_block_crg_interval
	Emulator for a interval of implicit base space members representing an unstructured block, that is, a homogeneous collection of zones of a given type with nodal connectivity. More...

Typedefs
typedef double	chart_point_coord_type
	The type of local coordinate in the base space; the scalar type for the local coordinate vector space. More...
typedef double	vd_value_type
	The type of component in the fiber; the scalar type in the fiber vector space. More...
typedef double	vd_dof_type
	The type of degree of freedom in the fiber space. More...
typedef vd_value_type	sec_vd_value_type
	The type of component in the value of a section at a point. More...
typedef double	sec_vd_dof_type
	The type of degree of freedom in the section space. More...

Functions
SHEAF_DLL_SPEC size_t	deep_size (const base_space_crg_interval &m)
SHEAF_DLL_SPEC size_t	deep_size (const base_space_poset &xp, bool xinclude_shallow=true, size_t xresults[4]=0)
	The deep size of the referenced object of type poset_state_handle. if xinclude_shallow, add the sizeof xp to the result. if xresults is not null, the deep size of the poset_state parts returned; xresults[0] is the deep_size of poset_crg_state, xresults[1] is the deep_size of index_space_family, xresults[2] is the deep_size of poset_powerset_state, xresults[3] is the deep_size of poset_table_state. More...
SHEAF_DLL_SPEC std::ostream &	operator<< (std::ostream &os, const binary_index &xbi)
	Insert binary_index& xbi into ostream& os. More...
SHEAF_DLL_SPEC std::ostream &	operator<< (std::ostream &os, const binary_index_space &xbis)
	Insert binary_index_space& xbis into ostream& os. More...
SHEAF_DLL_SPEC std::ostream &	operator<< (std::ostream &xos, const block_adjacency &xconn)
	Print block_adjacency& xconn to stream xos. More...
SHEAF_DLL_SPEC std::ostream &	operator<< (std::ostream &xos, const block_connectivity &xconn)
	Print block_connectivity instance xconn to stream xos. More...
SHEAF_DLL_SPEC std::ostream &	operator<< (std::ostream &os, const chart_point &xpt)
	Insert chart_point_1d& xpt into ostream& os. More...
SHEAF_DLL_SPEC size_t	deep_size (const chart_point_1d &xp, bool xinclude_shallow=true)
	The deep size of the referenced object of type chart_point_1d. if xinclude_shallow, add the sizeof xp to the result. More...
SHEAF_DLL_SPEC size_t	deep_size (const chart_point_2d &xp, bool xinclude_shallow=true)
	The deep size of the referenced object of type chart_point_2d. if xinclude_shallow, add the sizeof xp to the result. More...
SHEAF_DLL_SPEC size_t	deep_size (const chart_point_3d &xp, bool xinclude_shallow=true)
	The deep size of the referenced object of type chart_point_3d. if xinclude_shallow, add the sizeof xp to the result. More...
SHEAF_DLL_SPEC size_t	deep_size (const structured_block &x0, bool xinclude_shallow=true)
	The deep size of the referenced object of type structured_block. if xinclude_shallow, add the sizeof x0 to the result. More...
SHEAF_DLL_SPEC std::ostream &	operator<< (std::ostream &os, const ternary_index &xbi)
	Insert ternary_index& xbi into ostream& os. More...
SHEAF_DLL_SPEC std::ostream &	operator<< (std::ostream &os, const ternary_index_space &xbis)
	Insert ternary_index_space& xbis into ostream& os. More...
SHEAF_DLL_SPEC std::ostream &	operator<< (std::ostream &os, const unary_index_space &xbis)
	Insert unary_index_space& xbis into ostream& os. More...
size_t SHEAF_DLL_SPEC	deep_size (const differentiable_section_evaluator &xe, bool xinclude_shallow=true)
	The deep size of the referenced object of type differentiable_section_evaluator. if xinclude_shallow, add the sizeof xpath to the result. More...
size_t SHEAF_DLL_SPEC	deep_size (const integrable_section_evaluator &xe, bool xinclude_shallow=true)
	The deep size of the referenced object of type integrable_section_evaluator. if xinclude_shallow, add the sizeof xpath to the result. More...
size_t SHEAF_DLL_SPEC	deep_size (const section_evaluator &xe, bool xinclude_shallow=true)
	The deep size of the referenced object of type section_evaluator. if xinclude_shallow, add the sizeof xpath to the result. More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const at0_row_dofs_type< T > &xrdt)
	Insert at0_row_dofs_type<T>& xrdt into ostream& xos. More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const at2_e2_row_dofs_type< T > &xrdt)
	Insert at2_e2_row_dofs_type<T>& xrdt into ostream& xos. More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const at2_e3_row_dofs_type< T > &xrdt)
	Insert at2_e3_row_dofs_type<T>& xrdt into ostream& xos. More...
template<typename T >
SHEAF_DLL_SPEC std::ostream &	operator<< (std::ostream &xos, const at3_e3_row_dofs_type< T > &xrdt)
	Insert at3_e3_row_dofs_type<T>& xrdt into ostream& xos. More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const at3_e3_row_dofs_type< T > &xrdt)
	Insert at3_e3_row_dofs_type<T>& xrdt into ostream& xos. More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const e1_row_dofs_type< T > &xrdt)
	Insert e1_row_dofs_type<T>& xrdt into ostream& xos. More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const e2_row_dofs_type< T > &xrdt)
	Insert e2_row_dofs_type<T>& xrdt into ostream& xos. More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const e3_row_dofs_type< T > &xrdt)
	Insert e3_row_dofs_type<T>& xrdt into ostream& xos. More...
size_t SHEAF_DLL_SPEC	deep_size (const e3_lite &x0, bool xinclude_shallow=true)
	The deep size of the referenced object of type e3_lite. if xinclude_shallow, add the sizeof x0 to the result. More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const e4_row_dofs_type< T > &xrdt)
	Insert e4_row_dofs_type<T>& xrdt into ostream& xos. More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const gl2_row_dofs_type< T > &xrdt)
	Insert gl2_row_dofs_type<T>& xrdt into ostream& xos. More...
SHEAF_DLL_SPEC std::ostream &	operator<< (std::ostream &xos, const gl2_lite &xlite)
	Insert gl2_lite& xlite into ostream& xos. More...
SHEAF_DLL_SPEC std::ostream &	operator<< (std::ostream &xos, const gl2 &xpersistent)
	Insert gl2& xpersistent into ostream& xos. More...
SHEAF_DLL_SPEC void	inverse (const gl2_lite &xlite, gl2_lite &xresult)
	Inverse (pre-allocated version for volatile type). More...
SHEAF_DLL_SPEC void	inverse (const gl2 &xgl, gl2 &xresult)
	Inverse (pre-allocated version for persistent type). More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const gl3_row_dofs_type< T > &xrdt)
	Insert gl3_row_dofs_type<T>& xrdt into ostream& xos. More...
SHEAF_DLL_SPEC std::ostream &	operator<< (std::ostream &xos, const gl3_lite &xlite)
	Insert gl3_lite& xlite into ostream& xos. More...
SHEAF_DLL_SPEC std::ostream &	operator<< (std::ostream &xos, const gl3 &xpersistent)
	Insert gl3& xpersistent into ostream& xos. More...
SHEAF_DLL_SPEC void	inverse (const gl3_lite &xlite, gl3_lite &xresult)
	Inverse (pre-allocated version for volatile type). More...
SHEAF_DLL_SPEC void	inverse (const gl3 &xgl, gl3 &xresult)
	Inverse (pre-allocated version for persistent type). More...
SHEAF_DLL_SPEC double	rad (double degrees)
	Converts degress to radians. Convenience function for use with rotation routines. More...
SHEAF_DLL_SPEC std::ostream &	operator<< (std::ostream &xos, gln_lite &xv)
	Insert gln_lite& xv into ostream& xos. More...
SHEAF_DLL_SPEC std::ostream &	operator<< (std::ostream &xos, gln_lite::table_dofs_type &xt)
	Insert gln_lite::table_dofs_type& xt into ostream& xos. More...
SHEAF_DLL_SPEC std::ostream &	operator<< (std::ostream &xos, jcb_lite::table_dofs_type &xt)
	Insert jcb_lite::table_dofs_type& xt into ostream& xos. More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const jcb_e13_row_dofs_type< T > &xrdt)
	Insert jcb_e13_row_dofs_type<T>& xrdt into ostream& xos. More...
template<typename T >
SHEAF_DLL_SPEC std::ostream &	operator<< (std::ostream &xos, const jcb_e23_row_dofs_type< T > &xrdt)
	Insert jcb_e23_row_dofs_type<T>& xrdt into ostream& xos. More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const jcb_e23_row_dofs_type< T > &xrdt)
	Insert jcb_e23_row_dofs_type<T>& xrdt into ostream& xos. More...
template<typename T >
SHEAF_DLL_SPEC std::ostream &	operator<< (std::ostream &xos, const jcb_e33_row_dofs_type< T > &xrdt)
	Insert jcb_e33_row_dofs_type<T>& xrdt into ostream& xos. More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const jcb_e33_row_dofs_type< T > &xrdt)
	Insert jcb_e33_row_dofs_type<T>& xrdt into ostream& xos. More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const met_e1_row_dofs_type< T > &xrdt)
	Insert met_e1_row_dofs_type<T>& xrdt into ostream& xos. More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const met_e2_row_dofs_type< T > &xrdt)
	Insert met_e2_row_dofs_type<T>& xrdt into ostream& xos. More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const met_e3_row_dofs_type< T > &xrdt)
	Insert met_e3_row_dofs_type<T>& xrdt into ostream& xos. More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const st2_e2_row_dofs_type< T > &xrdt)
	Insert st2_e2_row_dofs_type<T>& xrdt into ostream& xos. More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const st2_e3_row_dofs_type< T > &xrdt)
	Insert st2_e3_row_dofs_type<T>& xrdt into ostream& xos. More...
template<typename T >
SHEAF_DLL_SPEC std::ostream &	operator<< (std::ostream &xos, const st3_e3_row_dofs_type< T > &xrdt)
	Insert st3_e3_row_dofs_type<T>& xrdt into ostream& xos. More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const st3_e3_row_dofs_type< T > &xrdt)
	Insert st3_e3_row_dofs_type<T>& xrdt into ostream& xos. More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const st4_e2_row_dofs_type< T > &xrdt)
	Insert st4_e2_row_dofs_type<T>& xrdt into ostream& xos. More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const st4_e3_row_dofs_type< T > &xrdt)
	Insert st4_e3_row_dofs_type<T>& xrdt into ostream& xos. More...
template<typename T >
SHEAF_DLL_SPEC std::ostream &	operator<< (std::ostream &xos, const t2_e2_row_dofs_type< T > &xrdt)
	Insert t2_e2_row_dofs_type<T>& xrdt into ostream& xos. More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const t2_e2_row_dofs_type< T > &xrdt)
	Insert t2_e2_row_dofs_type<T>& xrdt into ostream& xos. More...
template<typename T >
SHEAF_DLL_SPEC std::ostream &	operator<< (std::ostream &xos, const t2_e3_row_dofs_type< T > &xrdt)
	Insert t2_e3_row_dofs_type<T>& xrdt into ostream& xos. More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const t2_e3_row_dofs_type< T > &xrdt)
	Insert t2_e3_row_dofs_type<T>& xrdt into ostream& xos. More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const t3_e3_row_dofs_type< T > &xrdt)
	Insert t3_e3_row_dofs_type<T>& xrdt into ostream& xos. More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const t4_e2_row_dofs_type< T > &xrdt)
	Insert t4_e2_row_dofs_type<T>& xrdt into ostream& xos. More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const t4_e3_row_dofs_type< T > &xrdt)
	Insert t4_e3_row_dofs_type<T>& xrdt into ostream& xos. More...
SHEAF_DLL_SPEC tensor_variance	contract (const tensor_variance &x0, int xp, int xq)
	The variance of the contration of a tensor with variance x0 on indices xp and xq. More...
SHEAF_DLL_SPEC tensor_variance	tensor_product (const tensor_variance &x0, const tensor_variance &x1)
	The variance of the tensor product of tensors with variance x0 and x1. More...
SHEAF_DLL_SPEC tensor_variance	hook (const tensor_variance &x0)
	The variance of the hook of a tensor with variance x0. More...
SHEAF_DLL_SPEC tensor_variance	star (const tensor_variance &x0, int xdd)
	The variance of the Hodge star of a tensor with variance x0 over a vector space of dimension xdd. More...
SHEAF_DLL_SPEC tensor_variance	wedge (const tensor_variance &x0, const tensor_variance &x1)
	The variance of the wedge of a tensor with variance x0 with a tnesor with variance x1. More...
SHEAF_DLL_SPEC tensor_variance	raise (const tensor_variance &x0, int xi)
	The variance of the raise of a tensor with variance x0 on index xi. More...
SHEAF_DLL_SPEC tensor_variance	lower (const tensor_variance &x0, int xi)
	The variance of the lower of a tensor with variance x0 on index xi. More...
SHEAF_DLL_SPEC std::ostream &	operator<< (std::ostream &xos, tp_lite::table_dofs_type &xt)
	Insert tp_lite::table_dofs_type& xt into ostream& xos. More...
SHEAF_DLL_SPEC std::ostream &	operator<< (std::ostream &xos, const vd_lite &x0)
	Insert vd_lite& x0 into ostream& xos. More...
SHEAF_DLL_SPEC std::ostream &	operator<< (std::ostream &xos, const vd &x0)
	Insert vd& x0 into ostream& xos. More...
SHEAF_DLL_SPEC void	print_prereq_paths (std::ostream &xos, const vd_space &xspace, const std::string &xheading, const std::string &xindent, bool xauto_access=true)
	Print the paths for xspace and its prerequisites: schema, scalar space, etc. More...
poset_path SHEAF_DLL_SPEC	standard_section_space_path (const poset_path &xfiber_path, const poset_path &xbase_path)
	The standard path for the section space with fiber space path xfiber_path and base space path xbase_path. More...
poset_path SHEAF_DLL_SPEC	standard_section_space_schema_path (const poset_path &xsection_space_path)
	The standard path for the section space schema. More...
poset_path SHEAF_DLL_SPEC	standard_fiber_path ()
	The standard path for the fiber. More...
poset_path SHEAF_DLL_SPEC	standard_vector_space_path ()
	The standard path for the vector space. More...
SHEAF_DLL_SPEC size_t	deep_size (const i_adjacency_index_space_interval &xn, bool xinclude_shallow=true)
	The deep size of i_adjacency_index_space_interval& xn. More...
SHEAF_DLL_SPEC size_t	deep_size (const i_connectivity_index_space_interval &xn, bool xinclude_shallow=true)
	The deep size of i_connectivity_index_space_interval& xn. More...
SHEAF_DLL_SPEC size_t	deep_size (const ij_adjacency_index_space_interval &xn, bool xinclude_shallow=true)
	The deep size of ij_adjacency_index_space_interval& xn. More...
SHEAF_DLL_SPEC size_t	deep_size (const ij_connectivity_index_space_interval &xn, bool xinclude_shallow=true)
	The deep size of ij_connectivity_index_space_interval& xn. More...
SHEAF_DLL_SPEC size_t	deep_size (const ijk_adjacency_index_space_interval &xn, bool xinclude_shallow=true)
	The deep size of ijk_adjacency_index_space_interval& xn. More...
SHEAF_DLL_SPEC size_t	deep_size (const ijk_connectivity_index_space_interval &xn, bool xinclude_shallow=true)
	The deep size of ijk_connectivity_index_space_interval& xn. More...
SHEAF_DLL_SPEC size_t	deep_size (const section_space_schema_jims_index_space_state &xn, bool xinclude_shallow=true)
	The deep size of section_space_schema_jims_index_space_state& xn. More...
SHEAF_DLL_SPEC std::ostream &	operator<< (std::ostream &xos, const discretization_context &xc)
	Insert discretization_context xc into ostream& xos. More...
size_t SHEAF_DLL_SPEC	deep_size (const discretization_context &xc, bool xinclude_shallow=true)
	The deep size of the referenced object of type discretization_context. if xinclude_shallow, add the sizeof xpath to the result. More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const antisymmetric_matrix_2x2< T > &xm)
	Insert antisymmetric_matrix_2x2<T> xm into output stream xos. More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const antisymmetric_matrix_3x3< T > &xm)
	Insert antisymmetric_matrix_3x3<T> xm into output stream xos. More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const general_matrix_1x2< T > &xm)
	Insert general_matrix_1x2<T> xm into output stream xos. More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const general_matrix_1x3< T > &xm)
	Insert general_matrix_1x3<T> xm into output stream xos. More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const general_matrix_2x1< T > &xm)
	Insert general_matrix_2x1<T> xm into output stream xos. More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const general_matrix_2x2< T > &xm)
	Insert general_matrix_2x2<T> xm into output stream xos. More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const general_matrix_2x3< T > &xm)
	Insert general_matrix_2x3<T> xm into output stream xos. More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const general_matrix_3x1< T > &xm)
	Insert general_matrix_3x1<T> xm into output stream xos. More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const general_matrix_3x2< T > &xm)
	Insert general_matrix_3x2<T> xm into output stream xos. More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const general_matrix_3x3< T > &xm)
	Insert general_matrix_3x3<T> xm into output stream xos. More...
SHEAF_DLL_SPEC bool	svd_decompose (double *xa, double *xs, double *xv, int xnrows, int xncols)
	Perform single value decomposition. More...
SHEAF_DLL_SPEC bool	svd_reduce (double *xa, double *xw, double *xv, int nrows, int ncols, double *ltemp, double &lnorm)
	Householder reduction to bidiagonal form. Convenience function. More...
SHEAF_DLL_SPEC bool	svd_diagonalize (double *xa, double *xw, double *xv, int nrows, int ncols, double *xtemp, double lnorm)
	Diagonalization of the bidiagonal form. Convenience function. More...
SHEAF_DLL_SPEC double	same_sign (double xa, double xb)
	Convert xa to have the same sign as xb. More...
SHEAF_DLL_SPEC double	svd_pythag (double xa, double xb)
	Pthagorean theorem calculation. More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const symmetric_matrix_2x2< T > &xm)
	Insert symmetric_matrix_2x2<T> xm into output stream xos. More...
template<typename T >
std::ostream &	operator<< (std::ostream &xos, const symmetric_matrix_3x3< T > &xm)
	Insert symmetric_matrix_3x3<T> xm into output stream xos. More...
template<typename T >
void	jacobi_transformation (const symmetric_matrix_3x3< T > &xm, general_matrix_3x3< T > &xeigenvectors, T xeigenvalues[3])
	Determine the eigenvectors and eigenvalues of a real symmetric matrix xm. More...
template<typename T >
void	jacobi_transformation (const symmetric_matrix_3x3< T > &xm, general_matrix_3x3< T > &xeigenvectors, symmetric_matrix_3x3< T > &xdiagonal)
	Determine the eigenvectors and eigenvalues of a real symmetric matrix xm. More...
template<typename T >
void	sort_eigenvalues (general_matrix_3x3< T > &xeigenvectors, T xeigenvalues[3])
	Utility function to sort the eigenvalues into ascending order. Called from jacobi_transformation. More...
SHEAF_DLL_SPEC std::ostream &	operator<< (std::ostream &xos, const sec_at0 &xv)
	Insert sec_at0& xv into ostream& xos. More...
template<typename S0 , typename S1 , typename SR >
void	hook (const S0 &x0, const S1 &x1, SR &xresult, bool xauto_access)
template<typename S0 , typename SR >
void	star (const S0 &x0, SR &xresult, bool xauto_access)
template<typename S0 , typename S1 , typename SR >
void	wedge (const S0 &x0, const S1 &x1, SR &xresult, bool xauto_access)
SHEAF_DLL_SPEC std::ostream &	operator<< (std::ostream &xos, const sec_e3 &xv)
	Insert sec_e3& xv into ostream& xos. More...
std::ostream &	operator<< (std::ostream &xos, sec_e4 &xv)
	Insert sec_e4& xv into ostream& xos. More...
template<typename S , typename SR >
void	dot (const S &x0, const S &x1, SR &xresult, bool xauto_access)
template<typename S , typename SR >
void	length (const S &x0, SR &xresult, bool xauto_access)
template<typename S >
void	put_length (S &x0, const vd_value_type &xlength, bool xauto_access)
template<typename S , typename SR >
void	normalize (const S &x0, SR &xresult, bool xauto_access)
template<typename T >
void	normalize (T &x0, bool xauto_access)
template<typename SJCB , typename SCOVECTOR , typename SR >
void	pull (const SJCB &xjcb, const SCOVECTOR &xcovector, SR &xresult, bool xauto_access)
template<typename SJCB , typename SVECTOR , typename SR >
void	push (const SJCB &xjcb, const SVECTOR &xvector, SR &xresult, bool xauto_access)
template<typename SMET , typename SVECTOR , typename SR >
void	lower (const SMET &xmetric, const SVECTOR &xvector, SR &xresult, bool xauto_access)
template<typename SMET , typename SCOVECTOR , typename SR >
void	raise (const SMET &xmetric, const SCOVECTOR &xcovector, SR &xresult, bool xauto_access)
template<typename S0 , typename SR >
void	trace (const S0 &x0, SR &xresult, bool xauto_access)
template<typename S0 , typename SR >
void	determinant (const S0 &x0, SR &xresult, bool xauto_access)
template<typename S0 , typename S1 , typename SR >
void	symmetric_product (const S0 &x0, const S1 &x1, SR &xresult, bool xauto_access)
template<typename GT , typename AT >
void	alt (const GT &x0, AT &xresult, bool xauto_access)
template<typename GT , typename ST >
void	sym (const GT &x0, ST &xresult, bool xauto_access)
template<typename S0 , typename S1 , typename SR >
void	tensor (const S0 &x0, const S1 &x1, SR &xresult, bool xauto_access)
template<typename S0 , typename SR >
void	contract (const S0 &x0, int xp, int xq, SR &xresult, bool xauto_access)
template<>
void	contract (const sec_t2_e2 &x0, int xp, int xq, sec_at0 &xresult, bool xauto_access)
template<>
void	contract (const sec_t2_e3 &x0, int xp, int xq, sec_at0 &xresult, bool xauto_access)
SHEAF_DLL_SPEC size_t	deep_size (const sec_tuple &x0, bool xinclude_shallow=true)
	The deep size of the referenced object of type sec_tuple. if xinclude_shallow, add the sizeof x0 to the result. More...
SHEAF_DLL_SPEC size_t	deep_size (const sec_vd &x0, bool xinclude_shallow=true)
	The deep size of the referenced object of type sec_vd. if xinclude_shallow, add the sizeof x0 to the result. More...
SHEAF_DLL_SPEC void	print_prereq_paths (std::ostream &xos, const sec_vd_space &xspace, const std::string &xheading, const std::string &xindex, bool xauto_access)
	Print the paths for xspace and its prerequisites: schema, rep, base, fiber, scalar space, etc. More...
SHEAF_DLL_SPEC std::ostream &	operator<< (std::ostream &os, section_space_schema_member &p)
	Insert section_space_schema_member& p into ostream& os. More...

Variables
class SHEAF_DLL_SPEC	sec_ed
class SHEAF_DLL_SPEC	sec_at0
class SHEAF_DLL_SPEC	at0
class SHEAF_DLL_SPEC	at0_lite
class SHEAF_DLL_SPEC	sec_at1
class SHEAF_DLL_SPEC	at1
class SHEAF_DLL_SPEC	at1_lite
class SHEAF_DLL_SPEC	sec_at2
class SHEAF_DLL_SPEC	at2
class SHEAF_DLL_SPEC	at2_lite
class SHEAF_DLL_SPEC	sec_at2_e2
class SHEAF_DLL_SPEC	at2_e2
class SHEAF_DLL_SPEC	at2_e2_lite
class SHEAF_DLL_SPEC	sec_at2_e3
class SHEAF_DLL_SPEC	at2_e3
class SHEAF_DLL_SPEC	at2_e3_lite
class SHEAF_DLL_SPEC	sec_at3
class SHEAF_DLL_SPEC	at3
class SHEAF_DLL_SPEC	at3_lite
class SHEAF_DLL_SPEC	sec_at3_e3
class SHEAF_DLL_SPEC	at3_e3
class SHEAF_DLL_SPEC	at3_e3_lite
class SHEAF_DLL_SPEC	sec_atp
class SHEAF_DLL_SPEC	atp
class SHEAF_DLL_SPEC	atp_lite
class SHEAF_DLL_SPEC	sec_e1
class SHEAF_DLL_SPEC	e1
class SHEAF_DLL_SPEC	e1_lite
class SHEAF_DLL_SPEC	sec_e1_uniform
class SHEAF_DLL_SPEC	sec_e2
class SHEAF_DLL_SPEC	e2
class SHEAF_DLL_SPEC	e2_lite
class SHEAF_DLL_SPEC	sec_e2_uniform
class SHEAF_DLL_SPEC	sec_e3
class SHEAF_DLL_SPEC	e3
class SHEAF_DLL_SPEC	e3_lite
class SHEAF_DLL_SPEC	sec_e3_uniform
class SHEAF_DLL_SPEC	sec_e4
class SHEAF_DLL_SPEC	e4
class SHEAF_DLL_SPEC	e4_lite
class SHEAF_DLL_SPEC	ed
class SHEAF_DLL_SPEC	ed_lite
class SHEAF_DLL_SPEC	sec_jcb
class SHEAF_DLL_SPEC	jcb
class SHEAF_DLL_SPEC	jcb_lite
class SHEAF_DLL_SPEC	sec_jcb_e13
class SHEAF_DLL_SPEC	jcb_e13
class SHEAF_DLL_SPEC	jcb_e13_lite
class SHEAF_DLL_SPEC	sec_jcb_e23
class SHEAF_DLL_SPEC	jcb_e23
class SHEAF_DLL_SPEC	jcb_e23_lite
class SHEAF_DLL_SPEC	sec_jcb_e33
class SHEAF_DLL_SPEC	jcb_e33
class SHEAF_DLL_SPEC	jcb_e33_lite
class SHEAF_DLL_SPEC	sec_jcb_ed
class SHEAF_DLL_SPEC	jcb_ed
class SHEAF_DLL_SPEC	jcb_ed_lite
class SHEAF_DLL_SPEC	sec_met
class SHEAF_DLL_SPEC	met
class SHEAF_DLL_SPEC	met_lite
class SHEAF_DLL_SPEC	sec_met_e1
class SHEAF_DLL_SPEC	met_e1
class SHEAF_DLL_SPEC	met_e1_lite
class SHEAF_DLL_SPEC	sec_met_e2
class SHEAF_DLL_SPEC	met_e2
class SHEAF_DLL_SPEC	met_e2_lite
class SHEAF_DLL_SPEC	sec_met_e3
class SHEAF_DLL_SPEC	met_e3
class SHEAF_DLL_SPEC	met_e3_lite
class SHEAF_DLL_SPEC	sec_met_ed
class SHEAF_DLL_SPEC	met_ed
class SHEAF_DLL_SPEC	met_ed_lite
class SHEAF_DLL_SPEC	sec_st2
class SHEAF_DLL_SPEC	st2
class SHEAF_DLL_SPEC	st2_lite
class SHEAF_DLL_SPEC	sec_st2_e2
class SHEAF_DLL_SPEC	st2_e2
class SHEAF_DLL_SPEC	st2_e2_lite
class SHEAF_DLL_SPEC	sec_st2_e3
class SHEAF_DLL_SPEC	st2_e3
class SHEAF_DLL_SPEC	st2_e3_lite
class SHEAF_DLL_SPEC	sec_st3
class SHEAF_DLL_SPEC	st3
class SHEAF_DLL_SPEC	st3_lite
class SHEAF_DLL_SPEC	sec_st3_e3
class SHEAF_DLL_SPEC	st3_e3
class SHEAF_DLL_SPEC	st3_e3_lite
class SHEAF_DLL_SPEC	sec_st4
class SHEAF_DLL_SPEC	st4
class SHEAF_DLL_SPEC	st4_lite
class SHEAF_DLL_SPEC	sec_st4_e2
class SHEAF_DLL_SPEC	st4_e2
class SHEAF_DLL_SPEC	st4_e2_lite
class SHEAF_DLL_SPEC	sec_st4_e3
class SHEAF_DLL_SPEC	st4_e3
class SHEAF_DLL_SPEC	st4_e3_lite
class SHEAF_DLL_SPEC	sec_stp
class SHEAF_DLL_SPEC	stp
class SHEAF_DLL_SPEC	stp_lite
class SHEAF_DLL_SPEC	sec_t2
class SHEAF_DLL_SPEC	t2
class SHEAF_DLL_SPEC	t2_lite
class SHEAF_DLL_SPEC	sec_t2_e2
class SHEAF_DLL_SPEC	t2_e2
class SHEAF_DLL_SPEC	t2_e2_lite
class SHEAF_DLL_SPEC	sec_t2_e3
class SHEAF_DLL_SPEC	t2_e3
class SHEAF_DLL_SPEC	t2_e3_lite
class SHEAF_DLL_SPEC	sec_t3
class SHEAF_DLL_SPEC	t3
class SHEAF_DLL_SPEC	t3_lite
class SHEAF_DLL_SPEC	sec_t3_e3
class SHEAF_DLL_SPEC	t3_e3
class SHEAF_DLL_SPEC	t3_e3_lite
class SHEAF_DLL_SPEC	sec_t4
class SHEAF_DLL_SPEC	t4
class SHEAF_DLL_SPEC	t4_lite
class SHEAF_DLL_SPEC	sec_t4_e2
class SHEAF_DLL_SPEC	t4_e2
class SHEAF_DLL_SPEC	t4_e2_lite
class SHEAF_DLL_SPEC	sec_t4_e3
class SHEAF_DLL_SPEC	t4_e3
class SHEAF_DLL_SPEC	t4_e3_lite
class SHEAF_DLL_SPEC	sec_tp
class SHEAF_DLL_SPEC	tp
class SHEAF_DLL_SPEC	tp_lite

Detailed Description

Namespace for the fiber_bundles component of the sheaf system.

Typedef Documentation

chart_point_coord_type

typedef double fiber_bundle::chart_point_coord_type

The type of local coordinate in the base space; the scalar type for the local coordinate vector space.

Definition at line 57 of file fiber_bundle.h.

sec_vd_dof_type

typedef double fiber_bundle::sec_vd_dof_type

The type of degree of freedom in the section space.

Definition at line 78 of file fiber_bundle.h.

sec_vd_value_type

typedef vd_value_type fiber_bundle::sec_vd_value_type

The type of component in the value of a section at a point.

Definition at line 73 of file fiber_bundle.h.

vd_dof_type

typedef double fiber_bundle::vd_dof_type

The type of degree of freedom in the fiber space.

Definition at line 68 of file fiber_bundle.h.

vd_value_type

typedef double fiber_bundle::vd_value_type

The type of component in the fiber; the scalar type in the fiber vector space.

Definition at line 63 of file fiber_bundle.h.

Function Documentation

alt()

template<typename GT , typename AT >

void fiber_bundle::alt	(	const GT &	x0,
		AT &	xresult,
		bool	xauto_access
	)

Precondition

• x0.state_is_auto_read_accessible(xauto_access)

• xresult.state_is_auto_read_accessible(xauto_access)

• x0.dd(xauto_access) == xresult.dd(xauto_access)

• !x0.variance(xauto_access).is_mixed()

Postcondition

• xresult.variance(xauto_access) == x0.variance(xauto_access)

• -unexecutable( "xresult is equal to the antisymmetric part of x0" )

Definition at line 140 of file sec_tp.impl.h.

References fiber_bundle::sec_vd_algebra::unary_op().

contract() [1/4]

fiber_bundle::tensor_variance fiber_bundle::contract	(	const tensor_variance &	x0,
		int	xp,
		int	xq
	)

The variance of the contration of a tensor with variance x0 on indices xp and xq.

Precondition

• (0 <= xp) && (xp < x0.p())

• (0 <= xq) && (xq < x0.p())

Postcondition

• result.p() == x0.p() - 2

Definition at line 380 of file tensor_variance.cc.

References fiber_bundle::tensor_variance::p(), fiber_bundle::tensor_variance::put_variance(), tensor_product(), and fiber_bundle::tensor_variance::variance().

Referenced by contract(), and fiber_bundle::tensor_variance::purify().

contract() [2/4]

template<typename S0 , typename SR >

void fiber_bundle::contract	(	const S0 &	x0,
		int	xp,
		int	xq,
		SR &	xresult,
		bool	xauto_access
	)

Precondition

• x0.state_is_auto_read_accessible(xauto_access)

• xresult.state_is_auto_read_accessible(xauto_access)

• xp != xq

• xp >= 0 && xp < x0.p(xauto_access)

• xq >= 0 && xq < x0.p(xauto_access)

• xresult.p(xauto_access) == x0.p(xauto_access) - 2

• x0.is_contravariant(xp, xauto_access) != \ x0.is_contravariant(xq, xauto_access)

Postcondition

• xresult.variance(xauto_access) == \ contract(x0.variance(xauto_access), xp, xq)

• -unexecutable( "xresult is the contraction of x0 on indices xp and xq" )

Definition at line 279 of file sec_tp.impl.h.

References contract(), and fiber_bundle::sec_vd_algebra::unary_op().

contract() [3/4]

template<>

void fiber_bundle::contract	(	const sec_t2_e2 &	x0,
		int	xp,
		int	xq,
		sec_at0 &	xresult,
		bool	xauto_access
	)

Precondition

• x0.state_is_auto_read_accessible(xauto_access)

• xresult.state_is_auto_read_accessible(xauto_access)

• xp != xq

• xp >= 0 && xp < x0.p(xauto_access)

• xq >= 0 && xq < x0.p(xauto_access)

• x0.is_contravariant(xp, xauto_access) != \ x0.is_contravariant(xq, xauto_access)

Postcondition

• -unexecutable( "xresult is the contraction of x0 on indices xp and xq" )

Definition at line 327 of file sec_tp.impl.h.

References sheaf::poset_component::get_read_access(), sheaf::poset_component::get_read_write_access(), fiber_bundle::sec_tp::is_contravariant(), fiber_bundle::sec_tp::p(), sheaf::poset_component::release_access(), sheaf::read_write_monitor_handle::state_is_auto_read_accessible(), and fiber_bundle::sec_vd_algebra::unary_op().

contract() [4/4]

template<>

void fiber_bundle::contract	(	const sec_t2_e3 &	x0,
		int	xp,
		int	xq,
		sec_at0 &	xresult,
		bool	xauto_access
	)

Precondition

• x0.state_is_auto_read_accessible(xauto_access)

• xresult.state_is_auto_read_accessible(xauto_access)

• xp != xq

• xp >= 0 && xp < x0.p(xauto_access)

• xq >= 0 && xq < x0.p(xauto_access)

• x0.is_contravariant(xp, xauto_access) != \ x0.is_contravariant(xq, xauto_access)

Postcondition

• -unexecutable( "xresult is the contraction of x0 on indices xp and xq" )

Definition at line 371 of file sec_tp.impl.h.

References sheaf::poset_component::get_read_access(), sheaf::poset_component::get_read_write_access(), fiber_bundle::sec_tp::is_contravariant(), fiber_bundle::sec_tp::p(), sheaf::poset_component::release_access(), sheaf::read_write_monitor_handle::state_is_auto_read_accessible(), and fiber_bundle::sec_vd_algebra::unary_op().

deep_size() [1/19]

size_t fiber_bundle::deep_size	(	const base_space_poset &	xp,
		bool	xinclude_shallow = true,
		size_t	xresults[4] = 0
	)

The deep size of the referenced object of type poset_state_handle. if xinclude_shallow, add the sizeof xp to the result. if xresults is not null, the deep size of the poset_state parts returned; xresults[0] is the deep_size of poset_crg_state, xresults[1] is the deep_size of index_space_family, xresults[2] is the deep_size of poset_powerset_state, xresults[3] is the deep_size of poset_table_state.

Precondition

• xp.state_is_read_accessible()

Hack:

Should have an deep size policy for computing the size of the block without calling deep size on the pointers.

Postcondition

• result >= 0

Definition at line 3024 of file base_space_poset.cc.

References deep_size(), and sheaf::read_write_monitor_handle::state_is_read_accessible().

deep_size() [2/19]

size_t fiber_bundle::deep_size	(	const discretization_context &	xc,
		bool	xinclude_shallow = true
	)

The deep size of the referenced object of type discretization_context. if xinclude_shallow, add the sizeof xpath to the result.

Issue:

This function is incorrectly implemented.

Todo:

Implement correctly.

Postcondition

• result == 0

Definition at line 58 of file discretization_context.cc.

deep_size() [3/19]

size_t fiber_bundle::deep_size	(	const differentiable_section_evaluator &	xe,
		bool	xinclude_shallow = true
	)

The deep size of the referenced object of type differentiable_section_evaluator. if xinclude_shallow, add the sizeof xpath to the result.

Issue:

This function is incorrectly implemented.

Todo:

Implement correctly.

Postcondition

• result == 0

Definition at line 320 of file differentiable_section_evaluator.cc.

deep_size() [4/19]

size_t fiber_bundle::deep_size	(	const integrable_section_evaluator &	xe,
		bool	xinclude_shallow = true
	)

The deep size of the referenced object of type integrable_section_evaluator. if xinclude_shallow, add the sizeof xpath to the result.

Issue:

This function is incorrectly implemented.

Todo:

Implement correctly.

Postcondition

• result == 0

Definition at line 315 of file integrable_section_evaluator.cc.

deep_size() [5/19]

size_t fiber_bundle::deep_size	(	const chart_point_1d &	xp,
		bool	xinclude_shallow = true
	)

The deep size of the referenced object of type chart_point_1d. if xinclude_shallow, add the sizeof xp to the result.

Issue:

This function is incorrectly implemented.

Todo:

Implement correctly.

Postcondition

• result == 0

Definition at line 508 of file chart_point_1d.cc.

deep_size() [6/19]

size_t fiber_bundle::deep_size	(	const chart_point_2d &	xp,
		bool	xinclude_shallow = true
	)

The deep size of the referenced object of type chart_point_2d. if xinclude_shallow, add the sizeof xp to the result.

Issue:

This function is incorrectly implemented.

Todo:

Implement correctly.

Postcondition

• result == 0

Definition at line 522 of file chart_point_2d.cc.

deep_size() [7/19]

size_t fiber_bundle::deep_size	(	const chart_point_3d &	xp,
		bool	xinclude_shallow = true
	)

The deep size of the referenced object of type chart_point_3d. if xinclude_shallow, add the sizeof xp to the result.

Issue:

This function is incorrectly implemented.

Todo:

Implement correctly.

Postcondition

• result == 0

Definition at line 553 of file chart_point_3d.cc.

deep_size() [8/19]

size_t fiber_bundle::deep_size	(	const section_evaluator &	xe,
		bool	xinclude_shallow = true
	)

The deep size of the referenced object of type section_evaluator. if xinclude_shallow, add the sizeof xpath to the result.

Issue:

This function is incorrectly implemented.

Todo:

Implement correctly.

Postcondition

• result == 0

Definition at line 825 of file section_evaluator.cc.

deep_size() [9/19]

size_t fiber_bundle::deep_size	(	const sec_tuple &	x0,
		bool	xinclude_shallow = true
	)

The deep size of the referenced object of type sec_tuple. if xinclude_shallow, add the sizeof x0 to the result.

Issue:

This function is incorrectly implemented.

Todo:

Implement correctly.

Postcondition

• result == 0

Definition at line 805 of file sec_tuple.cc.

deep_size() [10/19]

size_t fiber_bundle::deep_size	(	const i_connectivity_index_space_interval &	xn,
		bool	xinclude_shallow = true
	)

The deep size of i_connectivity_index_space_interval& xn.

Postcondition

• result >= 0

Definition at line 929 of file i_connectivity_index_space_interval.cc.

References fiber_bundle::i_connectivity_index_space_interval::_handles, fiber_bundle::i_connectivity_index_space_interval::_iterators, and fiber_bundle::i_connectivity_index_space_interval::deep_size.

Referenced by fiber_bundle::i_connectivity_index_space_interval::i_connectivity_index_space_interval().

deep_size() [11/19]

size_t fiber_bundle::deep_size	(	const structured_block &	x0,
		bool	xinclude_shallow = true
	)

The deep size of the referenced object of type structured_block. if xinclude_shallow, add the sizeof x0 to the result.

Issue:

This function is incorrectly implemented.

Todo:

Implement correctly.

Postcondition

• result == 0

Definition at line 659 of file structured_block.cc.

deep_size() [12/19]

size_t fiber_bundle::deep_size	(	const i_adjacency_index_space_interval &	xn,
		bool	xinclude_shallow = true
	)

The deep size of i_adjacency_index_space_interval& xn.

Postcondition

• result >= 0

Definition at line 1026 of file i_adjacency_index_space_interval.cc.

References fiber_bundle::i_adjacency_index_space_interval::_handles, fiber_bundle::i_adjacency_index_space_interval::_iterators, and fiber_bundle::i_adjacency_index_space_interval::deep_size.

deep_size() [13/19]

size_t fiber_bundle::deep_size	(	const ij_connectivity_index_space_interval &	xn,
		bool	xinclude_shallow = true
	)

The deep size of ij_connectivity_index_space_interval& xn.

Postcondition

• result >= 0

Definition at line 1071 of file ij_connectivity_index_space_interval.cc.

References fiber_bundle::ij_connectivity_index_space_interval::_handles, fiber_bundle::ij_connectivity_index_space_interval::_iterators, and fiber_bundle::ij_connectivity_index_space_interval::deep_size.

deep_size() [14/19]

size_t fiber_bundle::deep_size	(	const section_space_schema_jims_index_space_state &	xn,
		bool	xinclude_shallow = true
	)

The deep size of section_space_schema_jims_index_space_state& xn.

Postcondition

• result >= 0

Definition at line 1096 of file section_space_schema_jims_index_space_state.cc.

References fiber_bundle::section_space_schema_jims_index_space_state::deep_size(), and fiber_bundle::section_space_schema_jims_index_space_state::section_space_schema_product_structure().

deep_size() [15/19]

size_t fiber_bundle::deep_size	(	const ij_adjacency_index_space_interval &	xn,
		bool	xinclude_shallow = true
	)

The deep size of ij_adjacency_index_space_interval& xn.

Postcondition

• result >= 0

Definition at line 1167 of file ij_adjacency_index_space_interval.cc.

References fiber_bundle::ij_adjacency_index_space_interval::_handles, fiber_bundle::ij_adjacency_index_space_interval::_iterators, and fiber_bundle::ij_adjacency_index_space_interval::deep_size.

deep_size() [16/19]

size_t fiber_bundle::deep_size	(	const ijk_connectivity_index_space_interval &	xn,
		bool	xinclude_shallow = true
	)

The deep size of ijk_connectivity_index_space_interval& xn.

Postcondition

• result >= 0

Definition at line 1246 of file ijk_connectivity_index_space_interval.cc.

References fiber_bundle::ijk_connectivity_index_space_interval::_handles, fiber_bundle::ijk_connectivity_index_space_interval::_iterators, and fiber_bundle::ijk_connectivity_index_space_interval::deep_size.

deep_size() [17/19]

size_t fiber_bundle::deep_size	(	const ijk_adjacency_index_space_interval &	xn,
		bool	xinclude_shallow = true
	)

The deep size of ijk_adjacency_index_space_interval& xn.

Postcondition

• result >= 0

Definition at line 1247 of file ijk_adjacency_index_space_interval.cc.

References fiber_bundle::ijk_adjacency_index_space_interval::_handles, fiber_bundle::ijk_adjacency_index_space_interval::_iterators, and fiber_bundle::ijk_adjacency_index_space_interval::deep_size.

deep_size() [18/19]

size_t fiber_bundle::deep_size	(	const sec_vd &	x0,
		bool	xinclude_shallow = true
	)

The deep size of the referenced object of type sec_vd. if xinclude_shallow, add the sizeof x0 to the result.

Issue:

This function is incorrectly implemented.

Todo:

Implement correctly.

Postcondition

• result == 0

Definition at line 1448 of file sec_vd.cc.

References fiber_bundle::sec_vd_algebra::add(), fiber_bundle::vd_algebra::add(), fiber_bundle::tp_algebra::contract(), fiber_bundle::vd_algebra::divide(), fiber_bundle::vd_algebra::multiply(), and fiber_bundle::vd_algebra::subtract().

Referenced by deep_size(), fiber_bundle::i_connectivity_index_space_interval::deep_size(), fiber_bundle::i_adjacency_index_space_interval::deep_size(), fiber_bundle::ij_connectivity_index_space_interval::deep_size(), fiber_bundle::section_space_schema_jims_index_space_state::deep_size(), fiber_bundle::ij_adjacency_index_space_interval::deep_size(), fiber_bundle::ijk_connectivity_index_space_interval::deep_size(), and fiber_bundle::ijk_adjacency_index_space_interval::deep_size().

deep_size() [19/19]

size_t fiber_bundle::deep_size	(	const e3_lite &	x0,
		bool	xinclude_shallow = true
	)

The deep size of the referenced object of type e3_lite. if xinclude_shallow, add the sizeof x0 to the result.

Issue:

This function is incorrectly implemented.

Todo:

Implement correctly.

Postcondition

• result == 0

Definition at line 2080 of file e3.cc.

determinant()

template<typename S0 , typename SR >

void fiber_bundle::determinant	(	const S0 &	x0,
		SR &	xresult,
		bool	xauto_access
	)

Precondition

• x0.state_is_auto_read_accessible(xauto_access)

Definition at line 131 of file sec_st2.impl.h.

References fiber_bundle::sec_vd_algebra::unary_op().

Referenced by fiber_bundle::antisymmetric_matrix_2x2< T >::determinant(), fiber_bundle::antisymmetric_matrix_3x3< T >::determinant(), fiber_bundle::symmetric_matrix_2x2< T >::determinant(), fiber_bundle::symmetric_matrix_3x3< T >::determinant(), fiber_bundle::general_matrix_3x3< T >::determinant(), fiber_bundle::general_matrix_2x2< T >::determinant(), fiber_bundle::symmetric_matrix_3x3< T >::diagonalization(), fiber_bundle::general_matrix_3x3< T >::diagonalization(), fiber_bundle::symmetric_matrix_3x3< T >::inverse(), fiber_bundle::symmetric_matrix_2x2< T >::inverse(), fiber_bundle::general_matrix_3x3< T >::inverse(), fiber_bundle::general_matrix_2x2< T >::inverse(), and fiber_bundle::symmetric_matrix_2x2< T >::is_positive_definite().

dot()

template<typename S , typename SR >

void fiber_bundle::dot	(	const S &	x0,
		const S &	x1,
		SR &	xresult,
		bool	xauto_access
	)

Precondition

• x0.state_is_auto_read_accessible(xauto_access)

• x1.state_is_auto_read_accessible(xauto_access)

• x0.is_same_type(&x1)

• x0.is_p_form(xauto_access) == x1.is_p_form(xauto_access)

Definition at line 144 of file sec_ed.impl.h.

References fiber_bundle::sec_vd_algebra::binary_op().

hook() [1/2]

template<typename S0 , typename S1 , typename SR >

void fiber_bundle::hook	(	const S0 &	x0,
		const S1 &	x1,
		SR &	xresult,
		bool	xauto_access
	)

Precondition

• x0.state_is_auto_read_accessible(xauto_access)

• x1.state_is_auto_read_accessible(xauto_access)

• xresult.state_is_auto_read_accessible(xauto_access)

• x1.dd(xauto_access) == x0.dd(xauto_access)

• x0.is_p_form(xauto_access) == x1.is_p_form(xauto_access)

• xresult.p(xauto_access) == x0.p(xauto_access) - 1

Postcondition

• xresult.variance(xauto_access) == hook(x0.variance(xauto_access))

Definition at line 116 of file sec_atp.impl.h.

References fiber_bundle::sec_vd_algebra::binary_op(), and hook().

hook() [2/2]

fiber_bundle::tensor_variance fiber_bundle::hook

(

const tensor_variance &

x0

)

The variance of the hook of a tensor with variance x0.

Precondition

• x0.is_covariant() || x0.is_contravariant()

• x0.p() >= 1

Postcondition

• result.p() == x0.p() - 1

• x0.is_covariant() ? result.is_covariant() : true

• x0.is_contravariant() ? result.is_contravariant() : true

Definition at line 450 of file tensor_variance.cc.

References fiber_bundle::tensor_variance::is_contravariant(), fiber_bundle::tensor_variance::is_covariant(), fiber_bundle::tensor_variance::p(), fiber_bundle::tensor_variance::put_variance(), and star().

Referenced by hook(), and tensor_product().

inverse() [1/4]

void fiber_bundle::inverse	(	const gl2_lite &	xlite,
		gl2_lite &	xresult
	)

Inverse (pre-allocated version for volatile type).

Issue:

What do we want to do here? If the component matrix is already the inverse of the basis matrix we just need to swap the basis and component matrices here.

Todo:

Implement a way to deal with the above issue.

Postcondition

• -unexecutable( "xresult is the inverse of xgl" )

Definition at line 1484 of file gl2.cc.

References fiber_bundle::gl2_lite::basis_matrix(), and fiber_bundle::gl2_lite::component_matrix().

Referenced by fiber_bundle::antisymmetric_matrix_2x2< T >::inverse(), fiber_bundle::antisymmetric_matrix_3x3< T >::inverse(), fiber_bundle::symmetric_matrix_3x3< T >::inverse(), fiber_bundle::symmetric_matrix_2x2< T >::inverse(), fiber_bundle::general_matrix_3x3< T >::inverse(), fiber_bundle::general_matrix_2x2< T >::inverse(), inverse(), and operator<<().

inverse() [2/4]

void fiber_bundle::inverse	(	const gl2 &	xgl,
		gl2 &	xresult
	)

Inverse (pre-allocated version for persistent type).

Todo:

Add auto_access argument or eliminate this function.

Precondition

• xgl.state_is_read_accessible()

• xresult.state_is_read_accessible()

Issue:

What do we want to do here? If the component matrix is already the inverse of the basis matrix we just need to swap the basis and component matrices here.

Todo:

Implement a way to deal with the above issue.

Postcondition

• -unexecutable( "xresult is the inverse of xgl" )

Definition at line 1512 of file gl2.cc.

References sheaf::read_write_monitor_handle::state_is_read_accessible().

inverse() [3/4]

void fiber_bundle::inverse	(	const gl3_lite &	xlite,
		gl3_lite &	xresult
	)

Inverse (pre-allocated version for volatile type).

Issue:

What do we want to do here? If the component matrix is already the inverse of the basis matrix we just need to swap the basis and component matrices here.

Todo:

Implement a way to deal with the above issue.

Postcondition

• -unexecutable( "xresult is the inverse of xgl" )

Definition at line 1625 of file gl3.cc.

References fiber_bundle::gl3_lite::basis_matrix(), fiber_bundle::gl3_lite::component_matrix(), and inverse().

inverse() [4/4]

void fiber_bundle::inverse	(	const gl3 &	xgl,
		gl3 &	xresult
	)

Inverse (pre-allocated version for persistent type).

Todo:

Add auto_access argument or eliminate this function.

Precondition

• xgl.state_is_read_accessible()

• xresult.state_is_read_accessible()

Issue:

What do we want to do here? If the component matrix is already the inverse of the basis matrix we just need to swap the basis and component matrices here.

Todo:

Implement a way to deal with the above issue.

Postcondition

• -unexecutable( "xresult is the inverse of xgl" )

Definition at line 1654 of file gl3.cc.

References sheaf::read_write_monitor_handle::state_is_read_accessible().

jacobi_transformation() [1/2]

template<typename T >

void fiber_bundle::jacobi_transformation	(	const symmetric_matrix_3x3< T > &	xm,
		general_matrix_3x3< T > &	xeigenvectors,
		T	xeigenvalues[3]
	)

Determine the eigenvectors and eigenvalues of a real symmetric matrix xm.

The eigenvalues are returned in xeigenvalues and the corresponding eigenvectors in the columns of xeigenvectors.

Definition at line 1402 of file symmetric_matrix_3x3.impl.h.

References fiber_bundle::sec_at0_algebra::cos(), fiber_bundle::sec_at0_algebra::fabs(), fiber_bundle::general_matrix_3x3< T >::identity(), fiber_bundle::sec_at0_algebra::sin(), sort_eigenvalues(), and fiber_bundle::sec_at0_algebra::sqrt().

Referenced by fiber_bundle::st2_algebra::determinant(), and jacobi_transformation().

jacobi_transformation() [2/2]

template<typename T >

void fiber_bundle::jacobi_transformation	(	const symmetric_matrix_3x3< T > &	xm,
		general_matrix_3x3< T > &	xeigenvectors,
		symmetric_matrix_3x3< T > &	xdiagonal
	)

Determine the eigenvectors and eigenvalues of a real symmetric matrix xm.

The eigenvalues are returned in the diagonal of xdiagonal and the corresponding eigenvectors in the columns of xeigenvectors.

Definition at line 1372 of file symmetric_matrix_3x3.impl.h.

References jacobi_transformation().

length()

template<typename S , typename SR >

void fiber_bundle::length	(	const S &	x0,
		SR &	xresult,
		bool	xauto_access
	)

Precondition

• x0.state_is_auto_read_accessible(xauto_access)

Definition at line 181 of file sec_ed.impl.h.

References fiber_bundle::sec_vd_algebra::unary_op().

Referenced by fiber_bundle::product_section_space_schema_member::dof_descriptors(), fiber_bundle::binary_section_space_schema_member::dof_descriptors(), fiber_bundle::sparse_field_dof_map::get_component_dofs(), fiber_bundle::array_field_dof_map::get_component_dofs(), fiber_bundle::sparse_field_dof_map::get_discretization_dofs(), fiber_bundle::array_field_dof_map::get_discretization_dofs(), fiber_bundle::array_field_dof_map::get_dof(), fiber_bundle::sparse_field_dof_map::get_dofs(), fiber_bundle::array_field_dof_map::get_dofs(), fiber_bundle::sparse_field_dof_map::put_component_dofs(), fiber_bundle::array_field_dof_map::put_component_dofs(), fiber_bundle::sparse_field_dof_map::put_discretization_dofs(), fiber_bundle::array_field_dof_map::put_discretization_dofs(), fiber_bundle::array_field_dof_map::put_dof(), fiber_bundle::sparse_field_dof_map::put_dofs(), and fiber_bundle::array_field_dof_map::put_dofs().

lower() [1/2]

template<typename SMET , typename SVECTOR , typename SR >

void fiber_bundle::lower	(	const SMET &	xmetric,
		const SVECTOR &	xvector,
		SR &	xresult,
		bool	xauto_access
	)

Precondition

• xmetric.state_is_auto_read_accessible(xauto_access)

• xvector.state_is_auto_read_accessible(xauto_access)

• xresult.state_is_auto_read_write_accessible(xauto_access)

• xmetric.is_covariant(0, xauto_access)

• xvector.is_contravariant(0, xauto_access)

Postcondition

• xresult.is_covariant(0, xauto_access)

Definition at line 95 of file sec_met.impl.h.

References fiber_bundle::sec_vd_algebra::binary_op().

lower() [2/2]

fiber_bundle::tensor_variance fiber_bundle::lower	(	const tensor_variance &	x0,
		int	xi
	)

The variance of the lower of a tensor with variance x0 on index xi.

Precondition

• (0 <= xi) && (xi < x0.p())

Postcondition

• result.p() == x0.p()

• result.is_covariant(xi)

Definition at line 565 of file tensor_variance.cc.

References fiber_bundle::tensor_variance::is_covariant(), fiber_bundle::tensor_variance::p(), and fiber_bundle::tensor_variance::put_variance().

Referenced by raise().

normalize() [1/2]

template<typename S , typename SR >

void fiber_bundle::normalize	(	const S &	x0,
		SR &	xresult,
		bool	xauto_access
	)

Precondition

• x0.state_is_auto_read_accessible(xauto_access)

• xresult.state_is_auto_read_write_accessible(xauto_access)

• x0.is_same_type(&xresult)

• x0.is_p_form(xauto_access) == xresult.is_p_form(xauto_access)

Postcondition

• xresult.is_p_form(xauto_access) == x0.is_p_form(xauto_access)

• -unexecutable( "length(xresult, xauto_access) == 1.0" )

Definition at line 246 of file sec_ed.impl.h.

References fiber_bundle::sec_vd_algebra::unary_op().

Referenced by normalize().

normalize() [2/2]

template<typename T >

void fiber_bundle::normalize	(	T &	x0,
		bool	xauto_access
	)

Precondition

• precondition_of(normalize(x0, x0, xauto_access))

Postcondition

• postcondition_of(normalize(x0, x0, xauto_access))

Definition at line 284 of file sec_ed.impl.h.

References normalize().

operator<<() [1/67]

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const discretization_context &	xc
	)

Insert discretization_context xc into ostream& xos.

Definition at line 33 of file discretization_context.cc.

References fiber_bundle::discretization_context::disc_id, fiber_bundle::discretization_context::eval_id, fiber_bundle::discretization_context::local_id, and fiber_bundle::discretization_context::values.

operator<<() [2/67]

template<typename T >

std::ostream& fiber_bundle::operator<<	(	std::ostream &	xos,
		const at3_e3_row_dofs_type< T > &	xrdt
	)

Insert at3_e3_row_dofs_type<T>& xrdt into ostream& xos.

Definition at line 145 of file at3_e3.impl.h.

References fiber_bundle::at3_e3_row_dofs_type< T >::d().

operator<<() [3/67]

template<typename T >

std::ostream& fiber_bundle::operator<<	(	std::ostream &	xos,
		const st3_e3_row_dofs_type< T > &	xrdt
	)

Insert st3_e3_row_dofs_type<T>& xrdt into ostream& xos.

Definition at line 145 of file st3_e3.impl.h.

References fiber_bundle::st3_e3_row_dofs_type< T >::d().

operator<<() [4/67]

template<typename T >

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const general_matrix_2x1< T > &	xm
	)

Insert general_matrix_2x1<T> xm into output stream xos.

Definition at line 478 of file general_matrix_2x1.impl.h.

References fiber_bundle::general_matrix_1x2< T >::number_of_rows().

operator<<() [5/67]

std::ostream & fiber_bundle::operator<<	(	std::ostream &	os,
		const binary_index &	xbi
	)

Insert binary_index& xbi into ostream& os.

Definition at line 35 of file binary_index.cc.

References fiber_bundle::binary_index::i, and fiber_bundle::binary_index::j.

Referenced by fiber_bundle::section_space_schema_member::attach_to_state(), fiber_bundle::sec_e4::clone(), fiber_bundle::block_adjacency::invariant(), fiber_bundle::sec_e3::invariant(), fiber_bundle::jcb::invariant(), fiber_bundle::tp::invariant(), fiber_bundle::vd::invariant(), fiber_bundle::block_connectivity::is_ancestor_of(), fiber_bundle::gl3::is_ancestor_of(), fiber_bundle::unary_index_space::neighbor_list(), fiber_bundle::binary_index_space::neighbor_list(), fiber_bundle::ternary_index_space::neighbor_list(), operator<<(), rad(), and fiber_bundle::chart_point::to_string().

operator<<() [6/67]

template<typename T >

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const general_matrix_3x1< T > &	xm
	)

Insert general_matrix_3x1<T> xm into output stream xos.

Definition at line 501 of file general_matrix_3x1.impl.h.

References fiber_bundle::general_matrix_1x3< T >::number_of_rows().

operator<<() [7/67]

template<typename T >

std::ostream& fiber_bundle::operator<<	(	std::ostream &	xos,
		const jcb_e23_row_dofs_type< T > &	xrdt
	)

Insert jcb_e23_row_dofs_type<T>& xrdt into ostream& xos.

Definition at line 179 of file jcb_e23.impl.h.

References fiber_bundle::jcb_e23_row_dofs_type< T >::d().

operator<<() [8/67]

template<typename T >

std::ostream& fiber_bundle::operator<<	(	std::ostream &	xos,
		const jcb_e33_row_dofs_type< T > &	xrdt
	)

Insert jcb_e33_row_dofs_type<T>& xrdt into ostream& xos.

Definition at line 179 of file jcb_e33.impl.h.

References fiber_bundle::jcb_e33_row_dofs_type< T >::d().

operator<<() [9/67]

template<typename T >

std::ostream& fiber_bundle::operator<<	(	std::ostream &	xos,
		const t2_e3_row_dofs_type< T > &	xrdt
	)

Insert t2_e3_row_dofs_type<T>& xrdt into ostream& xos.

Definition at line 179 of file t2_e3.impl.h.

References fiber_bundle::t2_e3_row_dofs_type< T >::d().

operator<<() [10/67]

template<typename T >

std::ostream& fiber_bundle::operator<<	(	std::ostream &	xos,
		const t2_e2_row_dofs_type< T > &	xrdt
	)

Insert t2_e2_row_dofs_type<T>& xrdt into ostream& xos.

Definition at line 180 of file t2_e2.impl.h.

References fiber_bundle::t2_e2_row_dofs_type< T >::d().

operator<<() [11/67]

template<typename T >

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const general_matrix_1x2< T > &	xm
	)

Insert general_matrix_1x2<T> xm into output stream xos.

Definition at line 527 of file general_matrix_1x2.impl.h.

References fiber_bundle::general_matrix_2x1< T >::number_of_rows().

operator<<() [12/67]

template<typename T >

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const general_matrix_1x3< T > &	xm
	)

Insert general_matrix_1x3<T> xm into output stream xos.

Definition at line 528 of file general_matrix_1x3.impl.h.

References fiber_bundle::general_matrix_3x1< T >::number_of_rows().

operator<<() [13/67]

std::ostream & fiber_bundle::operator<<	(	std::ostream &	os,
		const ternary_index &	xbi
	)

Insert ternary_index& xbi into ostream& os.

Definition at line 33 of file ternary_index.cc.

References fiber_bundle::ternary_index::i, fiber_bundle::ternary_index::j, and fiber_bundle::ternary_index::k.

operator<<() [14/67]

template<typename T >

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const general_matrix_3x2< T > &	xm
	)

Insert general_matrix_3x2<T> xm into output stream xos.

Definition at line 630 of file general_matrix_3x2.impl.h.

References fiber_bundle::general_matrix_2x3< T >::number_of_rows().

operator<<() [15/67]

template<typename T >

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const general_matrix_2x3< T > &	xm
	)

Insert general_matrix_2x3<T> xm into output stream xos.

Definition at line 607 of file general_matrix_2x3.impl.h.

References fiber_bundle::general_matrix_3x2< T >::number_of_rows().

operator<<() [16/67]

std::ostream & fiber_bundle::operator<<	(	std::ostream &	os,
		const unary_index_space &	xbis
	)

Insert unary_index_space& xbis into ostream& os.

Definition at line 83 of file unary_index_space.cc.

References fiber_bundle::unary_index_space::i_size, and fiber_bundle::unary_index_space::size.

operator<<() [17/67]

std::ostream & fiber_bundle::operator<<	(	std::ostream &	os,
		const chart_point &	xpt
	)

Insert chart_point_1d& xpt into ostream& os.

Definition at line 549 of file chart_point.cc.

References fiber_bundle::chart_point::chart_id(), fiber_bundle::chart_point::db(), and fiber_bundle::chart_point::local_coord().

operator<<() [18/67]

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const block_connectivity &	xconn
	)

Print block_connectivity instance xconn to stream xos.

Definition at line 405 of file block_connectivity.cc.

References fiber_bundle::block_connectivity::to_stream().

operator<<() [19/67]

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const block_adjacency &	xconn
	)

Print block_adjacency& xconn to stream xos.

Definition at line 420 of file block_adjacency.cc.

References fiber_bundle::block_adjacency::begin(), and fiber_bundle::block_adjacency::end().

operator<<() [20/67]

template<typename T >

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const antisymmetric_matrix_2x2< T > &	xm
	)

Insert antisymmetric_matrix_2x2<T> xm into output stream xos.

Definition at line 956 of file antisymmetric_matrix_2x2.impl.h.

operator<<() [21/67]

template<typename T >

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const antisymmetric_matrix_3x3< T > &	xm
	)

Insert antisymmetric_matrix_3x3<T> xm into output stream xos.

Definition at line 1041 of file antisymmetric_matrix_3x3.impl.h.

References fiber_bundle::antisymmetric_matrix_3x3< T >::number_of_rows().

operator<<() [22/67]

template<typename T >

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const symmetric_matrix_2x2< T > &	xm
	)

Insert symmetric_matrix_2x2<T> xm into output stream xos.

Definition at line 1131 of file symmetric_matrix_2x2.impl.h.

operator<<() [23/67]

template<typename T >

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const symmetric_matrix_3x3< T > &	xm
	)

Insert symmetric_matrix_3x3<T> xm into output stream xos.

Definition at line 1333 of file symmetric_matrix_3x3.impl.h.

References fiber_bundle::symmetric_matrix_3x3< T >::number_of_rows().

operator<<() [24/67]

template<typename T >

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const general_matrix_3x3< T > &	xm
	)

Insert general_matrix_3x3<T> xm into output stream xos.

Definition at line 1345 of file general_matrix_3x3.impl.h.

References fiber_bundle::symmetric_matrix_3x3< T >::number_of_rows().

operator<<() [25/67]

std::ostream & fiber_bundle::operator<<	(	std::ostream &	os,
		const binary_index_space &	xbis
	)

Insert binary_index_space& xbis into ostream& os.

Definition at line 91 of file binary_index_space.cc.

References fiber_bundle::binary_index_space::i_size, fiber_bundle::binary_index_space::j_size, and fiber_bundle::binary_index_space::size.

operator<<() [26/67]

template<typename T >

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const general_matrix_2x2< T > &	xm
	)

Insert general_matrix_2x2<T> xm into output stream xos.

Definition at line 1181 of file general_matrix_2x2.impl.h.

operator<<() [27/67]

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		sec_e4 &	xv
	)

Insert sec_e4& xv into ostream& xos.

Definition at line 736 of file sec_e4.cc.

References sheaf::poset_dof_map::dof(), fiber_bundle::sec_rep_space_member::dof_map(), sheaf::index_space_handle::get_iterator(), sheaf::index_space_iterator::index(), sheaf::index_space_iterator::is_done(), sheaf::index_space_iterator::next(), sheaf::index_space_handle::release_iterator(), sheaf::schema_poset_member::row_dof_id_space(), and fiber_bundle::sec_rep_space_member::schema().

operator<<() [28/67]

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const sec_e3 &	xv
	)

Insert sec_e3& xv into ostream& xos.

Definition at line 746 of file sec_e3.cc.

References fiber_bundle::sec_e3_algebra::cross(), fiber_bundle::e3_algebra::cross(), sheaf::poset_dof_map::dof(), fiber_bundle::sec_rep_space_member::dof_map(), sheaf::index_space_handle::get_iterator(), sheaf::index_space_iterator::index(), sheaf::index_space_iterator::is_done(), sheaf::index_space_iterator::next(), sheaf::index_space_handle::release_iterator(), sheaf::schema_poset_member::row_dof_id_space(), and fiber_bundle::sec_rep_space_member::schema().

operator<<() [29/67]

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const sec_at0 &	xv
	)

Insert sec_at0& xv into ostream& xos.

Definition at line 904 of file sec_at0.cc.

References fiber_bundle::sec_at0_algebra::acos(), fiber_bundle::sec_at0_algebra::asin(), fiber_bundle::sec_at0_algebra::atan(), fiber_bundle::sec_at0_algebra::atan2(), fiber_bundle::sec_at0_algebra::ceil(), fiber_bundle::sec_at0_algebra::cos(), fiber_bundle::sec_at0_algebra::cosh(), sheaf::poset_dof_map::dof(), fiber_bundle::sec_rep_space_member::dof_map(), fiber_bundle::sec_at0_algebra::exp(), fiber_bundle::sec_at0_algebra::fabs(), fiber_bundle::sec_at0_algebra::floor(), fiber_bundle::sec_at0_algebra::fmod(), fiber_bundle::sec_at0_algebra::frexp(), sheaf::index_space_handle::get_iterator(), sheaf::index_space_iterator::index(), sheaf::index_space_iterator::is_done(), fiber_bundle::sec_at0_algebra::ldexp(), fiber_bundle::sec_at0_algebra::log(), fiber_bundle::sec_at0_algebra::log10(), fiber_bundle::sec_at0_algebra::modf(), sheaf::index_space_iterator::next(), fiber_bundle::sec_at0_algebra::pow(), sheaf::index_space_handle::release_iterator(), sheaf::schema_poset_member::row_dof_id_space(), fiber_bundle::sec_rep_space_member::schema(), fiber_bundle::sec_at0_algebra::sin(), fiber_bundle::sec_at0_algebra::sinh(), fiber_bundle::sec_at0_algebra::sqrt(), fiber_bundle::sec_at0_algebra::tan(), and fiber_bundle::sec_at0_algebra::tanh().

operator<<() [30/67]

std::ostream & fiber_bundle::operator<<	(	std::ostream &	os,
		const ternary_index_space &	xbis
	)

Insert ternary_index_space& xbis into ostream& os.

Definition at line 96 of file ternary_index_space.cc.

References fiber_bundle::ternary_index_space::i_size, fiber_bundle::ternary_index_space::j_size, fiber_bundle::ternary_index_space::k_size, and fiber_bundle::ternary_index_space::size.

operator<<() [31/67]

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		jcb_lite::table_dofs_type &	xt
	)

Insert jcb_lite::table_dofs_type& xt into ostream& xos.

Definition at line 1346 of file jcb.cc.

References fiber_bundle::jcb_table_dofs_type::d, fiber_bundle::jcb_table_dofs_type::dd, fiber_bundle::jcb_table_dofs_type::domain_path, fiber_bundle::jcb_table_dofs_type::dr, fiber_bundle::jcb_table_dofs_type::factor_ct, fiber_bundle::jcb_algebra::push(), and fiber_bundle::jcb_table_dofs_type::range_path.

operator<<() [32/67]

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		tp_lite::table_dofs_type &	xt
	)

Insert tp_lite::table_dofs_type& xt into ostream& xos.

Definition at line 1436 of file tp.cc.

References fiber_bundle::tp_algebra::contract(), fiber_bundle::tp_table_dofs_type::d, fiber_bundle::tp_table_dofs_type::dd, fiber_bundle::tp_table_dofs_type::factor_ct, fiber_bundle::tp_table_dofs_type::p, fiber_bundle::tp_table_dofs_type::scalar_space_path, and fiber_bundle::tp_table_dofs_type::vector_space_path.

operator<<() [33/67]

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		gln_lite &	xv
	)

Insert gln_lite& xv into ostream& xos.

Definition at line 1513 of file gln.cc.

References fiber_bundle::gln_lite::d().

operator<<() [34/67]

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		gln_lite::table_dofs_type &	xt
	)

Insert gln_lite::table_dofs_type& xt into ostream& xos.

Definition at line 1502 of file gln.cc.

References fiber_bundle::gln_table_dofs_type::n, operator<<(), fiber_bundle::gln_table_dofs_type::scalar_space_path, and fiber_bundle::gln_table_dofs_type::vector_space_path.

operator<<() [35/67]

template<typename T >

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const t4_e2_row_dofs_type< T > &	xrdt
	)

Insert t4_e2_row_dofs_type<T>& xrdt into ostream& xos.

Definition at line 144 of file t4_e2.impl.h.

References fiber_bundle::t4_e2_row_dofs_type< T >::d().

operator<<() [36/67]

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const vd_lite &	x0
	)

Insert vd_lite& x0 into ostream& xos.

Definition at line 1611 of file vd.cc.

References fiber_bundle::vd_lite::component(), fiber_bundle::vd_lite::d(), and operator<<().

operator<<() [37/67]

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const vd &	x0
	)

Insert vd& x0 into ostream& xos.

Definition at line 1628 of file vd.cc.

References fiber_bundle::vd_algebra::add(), fiber_bundle::vd::component(), and fiber_bundle::vd::d().

operator<<() [38/67]

template<typename T >

SHEAF_DLL_SPEC std::ostream& fiber_bundle::operator<<	(	std::ostream &	xos,
		const st3_e3_row_dofs_type< T > &	xrdt
	)

Insert st3_e3_row_dofs_type<T>& xrdt into ostream& xos.

Definition at line 145 of file st3_e3.impl.h.

References fiber_bundle::st3_e3_row_dofs_type< T >::d().

operator<<() [39/67]

template<typename T >

SHEAF_DLL_SPEC std::ostream& fiber_bundle::operator<<	(	std::ostream &	xos,
		const at3_e3_row_dofs_type< T > &	xrdt
	)

Insert at3_e3_row_dofs_type<T>& xrdt into ostream& xos.

Definition at line 145 of file at3_e3.impl.h.

References fiber_bundle::at3_e3_row_dofs_type< T >::d().

operator<<() [40/67]

template<typename T >

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const st4_e2_row_dofs_type< T > &	xrdt
	)

Insert st4_e2_row_dofs_type<T>& xrdt into ostream& xos.

Definition at line 145 of file st4_e2.impl.h.

References fiber_bundle::st4_e2_row_dofs_type< T >::d().

operator<<() [41/67]

template<typename T >

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const st4_e3_row_dofs_type< T > &	xrdt
	)

Insert st4_e3_row_dofs_type<T>& xrdt into ostream& xos.

Definition at line 145 of file st4_e3.impl.h.

References fiber_bundle::st4_e3_row_dofs_type< T >::d().

operator<<() [42/67]

template<typename T >

SHEAF_DLL_SPEC std::ostream& fiber_bundle::operator<<	(	std::ostream &	xos,
		const jcb_e23_row_dofs_type< T > &	xrdt
	)

Insert jcb_e23_row_dofs_type<T>& xrdt into ostream& xos.

Definition at line 179 of file jcb_e23.impl.h.

References fiber_bundle::jcb_e23_row_dofs_type< T >::d().

operator<<() [43/67]

template<typename T >

SHEAF_DLL_SPEC std::ostream& fiber_bundle::operator<<	(	std::ostream &	xos,
		const jcb_e33_row_dofs_type< T > &	xrdt
	)

Insert jcb_e33_row_dofs_type<T>& xrdt into ostream& xos.

Definition at line 179 of file jcb_e33.impl.h.

References fiber_bundle::jcb_e33_row_dofs_type< T >::d().

operator<<() [44/67]

template<typename T >

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const t3_e3_row_dofs_type< T > &	xrdt
	)

Insert t3_e3_row_dofs_type<T>& xrdt into ostream& xos.

Definition at line 144 of file t3_e3.impl.h.

References fiber_bundle::t3_e3_row_dofs_type< T >::d().

operator<<() [45/67]

template<typename T >

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const gl2_row_dofs_type< T > &	xrdt
	)

Insert gl2_row_dofs_type<T>& xrdt into ostream& xos.

Definition at line 258 of file gl2.impl.h.

References fiber_bundle::gl2_row_dofs_type< T >::d().

operator<<() [46/67]

template<typename T >

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const met_e1_row_dofs_type< T > &	xrdt
	)

Insert met_e1_row_dofs_type<T>& xrdt into ostream& xos.

Definition at line 145 of file met_e1.impl.h.

References fiber_bundle::met_e1_row_dofs_type< T >::d().

operator<<() [47/67]

template<typename T >

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const at2_e2_row_dofs_type< T > &	xrdt
	)

Insert at2_e2_row_dofs_type<T>& xrdt into ostream& xos.

Definition at line 177 of file at2_e2.impl.h.

References fiber_bundle::at2_e2_row_dofs_type< T >::d().

operator<<() [48/67]

template<typename T >

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const t4_e3_row_dofs_type< T > &	xrdt
	)

Insert t4_e3_row_dofs_type<T>& xrdt into ostream& xos.

Definition at line 144 of file t4_e3.impl.h.

References fiber_bundle::t4_e3_row_dofs_type< T >::d().

operator<<() [49/67]

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const gl2_lite &	xlite
	)

Insert gl2_lite& xlite into ostream& xos.

Definition at line 1451 of file gl2.cc.

operator<<() [50/67]

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const gl2 &	xpersistent
	)

Insert gl2& xpersistent into ostream& xos.

Definition at line 1466 of file gl2.cc.

operator<<() [51/67]

template<typename T >

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const jcb_e13_row_dofs_type< T > &	xrdt
	)

Insert jcb_e13_row_dofs_type<T>& xrdt into ostream& xos.

Definition at line 179 of file jcb_e13.impl.h.

References fiber_bundle::jcb_e13_row_dofs_type< T >::d().

operator<<() [52/67]

template<typename T >

SHEAF_DLL_SPEC std::ostream& fiber_bundle::operator<<	(	std::ostream &	xos,
		const t2_e2_row_dofs_type< T > &	xrdt
	)

Insert t2_e2_row_dofs_type<T>& xrdt into ostream& xos.

Definition at line 180 of file t2_e2.impl.h.

References fiber_bundle::t2_e2_row_dofs_type< T >::d().

operator<<() [53/67]

template<typename T >

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const at0_row_dofs_type< T > &	xrdt
	)

Insert at0_row_dofs_type<T>& xrdt into ostream& xos.

Definition at line 200 of file at0.impl.h.

References fiber_bundle::at0_row_dofs_type< T >::d().

operator<<() [54/67]

template<typename T >

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const st2_e2_row_dofs_type< T > &	xrdt
	)

Insert st2_e2_row_dofs_type<T>& xrdt into ostream& xos.

Definition at line 183 of file st2_e2.impl.h.

References fiber_bundle::st2_e2_row_dofs_type< T >::d().

operator<<() [55/67]

template<typename T >

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const at2_e3_row_dofs_type< T > &	xrdt
	)

Insert at2_e3_row_dofs_type<T>& xrdt into ostream& xos.

Definition at line 178 of file at2_e3.impl.h.

References fiber_bundle::at2_e3_row_dofs_type< T >::d().

operator<<() [56/67]

template<typename T >

SHEAF_DLL_SPEC std::ostream& fiber_bundle::operator<<	(	std::ostream &	xos,
		const t2_e3_row_dofs_type< T > &	xrdt
	)

Insert t2_e3_row_dofs_type<T>& xrdt into ostream& xos.

Definition at line 179 of file t2_e3.impl.h.

References fiber_bundle::t2_e3_row_dofs_type< T >::d().

operator<<() [57/67]

template<typename T >

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const e1_row_dofs_type< T > &	xrdt
	)

Insert e1_row_dofs_type<T>& xrdt into ostream& xos.

Definition at line 149 of file e1.impl.h.

References fiber_bundle::e1_row_dofs_type< T >::d().

operator<<() [58/67]

template<typename T >

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const st2_e3_row_dofs_type< T > &	xrdt
	)

Insert st2_e3_row_dofs_type<T>& xrdt into ostream& xos.

Definition at line 180 of file st2_e3.impl.h.

References fiber_bundle::st2_e3_row_dofs_type< T >::d().

operator<<() [59/67]

template<typename T >

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const e2_row_dofs_type< T > &	xrdt
	)

Insert e2_row_dofs_type<T>& xrdt into ostream& xos.

Definition at line 148 of file e2.impl.h.

References fiber_bundle::e2_row_dofs_type< T >::d().

operator<<() [60/67]

template<typename T >

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const e4_row_dofs_type< T > &	xrdt
	)

Insert e4_row_dofs_type<T>& xrdt into ostream& xos.

Definition at line 148 of file e4.impl.h.

References fiber_bundle::e4_row_dofs_type< T >::d().

operator<<() [61/67]

template<typename T >

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const gl3_row_dofs_type< T > &	xrdt
	)

Insert gl3_row_dofs_type<T>& xrdt into ostream& xos.

Definition at line 263 of file gl3.impl.h.

References fiber_bundle::gl3_row_dofs_type< T >::d().

operator<<() [62/67]

template<typename T >

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const met_e2_row_dofs_type< T > &	xrdt
	)

Insert met_e2_row_dofs_type<T>& xrdt into ostream& xos.

Definition at line 179 of file met_e2.impl.h.

References fiber_bundle::met_e2_row_dofs_type< T >::d().

operator<<() [63/67]

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const gl3_lite &	xlite
	)

Insert gl3_lite& xlite into ostream& xos.

Definition at line 1585 of file gl3.cc.

References operator<<().

operator<<() [64/67]

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const gl3 &	xpersistent
	)

Insert gl3& xpersistent into ostream& xos.

Definition at line 1604 of file gl3.cc.

References inverse().

operator<<() [65/67]

template<typename T >

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const met_e3_row_dofs_type< T > &	xrdt
	)

Insert met_e3_row_dofs_type<T>& xrdt into ostream& xos.

Definition at line 180 of file met_e3.impl.h.

References fiber_bundle::met_e3_row_dofs_type< T >::d().

operator<<() [66/67]

template<typename T >

std::ostream & fiber_bundle::operator<<	(	std::ostream &	xos,
		const e3_row_dofs_type< T > &	xrdt
	)

Insert e3_row_dofs_type<T>& xrdt into ostream& xos.

Definition at line 147 of file e3.impl.h.

References fiber_bundle::e3_row_dofs_type< T >::d().

operator<<() [67/67]

SHEAF_DLL_SPEC std::ostream & fiber_bundle::operator<<	(	std::ostream &	os,
		section_space_schema_member &	p
	)

Insert section_space_schema_member& p into ostream& os.

Definition at line 2975 of file section_space_schema_member.cc.

References fiber_bundle::section_space_schema_member::base_space(), sheaf::any::disable_invariant_check(), sheaf::any::enable_invariant_check(), fiber_bundle::section_space_schema_member::fiber_space(), sheaf::poset_component::get_read_access(), sheaf::poset_component::host(), fiber_bundle::section_space_schema_member::host(), sheaf::scoped_index::hub_pod(), sheaf::poset_component::index(), sheaf::poset_component::is_attached(), sheaf::poset_state_handle::name(), sheaf::schema_poset_member::name(), sheaf::abstract_poset_member::name(), sheaf::scoped_index::pod(), sheaf::poset_component::release_access(), and sheaf::poset_component::version().

print_prereq_paths() [1/2]

void fiber_bundle::print_prereq_paths	(	std::ostream &	xos,
		const vd_space &	xspace,
		const std::string &	xheading,
		const std::string &	xindent,
		bool	xauto_access = true
	)

Print the paths for xspace and its prerequisites: schema, scalar space, etc.

Precondition

• xspace.state_is_auto_read_accessible(xauto_access)

• xspace.name_space()->state_is_auto_read_accessible(xauto_access)

Definition at line 962 of file vd_space.cc.

References sheaf::poset_state_handle::get_read_access(), sheaf::namespace_poset::member_poset(), sheaf::poset_state_handle::name_space(), sheaf::poset_component::path(), sheaf::poset_state_handle::path(), sheaf::poset_state_handle::release_access(), fiber_bundle::vd_space::scalar_space_path(), sheaf::poset_state_handle::schema(), and sheaf::read_write_monitor_handle::state_is_auto_read_accessible().

Referenced by fiber_bundle::sec_vd_space::invariant(), and print_prereq_paths().

print_prereq_paths() [2/2]

void fiber_bundle::print_prereq_paths	(	std::ostream &	xos,
		const sec_vd_space &	xspace,
		const std::string &	xheading,
		const std::string &	xindex,
		bool	xauto_access
	)

Print the paths for xspace and its prerequisites: schema, rep, base, fiber, scalar space, etc.

Precondition

• xspace.state_is_auto_read_accessible(xauto_access)

• xspace.name_space()->state_is_auto_read_accessible(xauto_access)

Definition at line 1013 of file sec_vd_space.cc.

References fiber_bundle::section_space_schema_member::base_space(), fiber_bundle::section_space_schema_member::fiber_space(), sheaf::poset_state_handle::get_read_access(), sheaf::namespace_poset::member_poset(), sheaf::poset_state_handle::name_space(), sheaf::poset_component::path(), sheaf::poset_state_handle::path(), print_prereq_paths(), sheaf::poset_state_handle::release_access(), fiber_bundle::section_space_schema_member::rep(), fiber_bundle::sec_vd_space::scalar_space_path(), fiber_bundle::sec_rep_space::schema(), and sheaf::read_write_monitor_handle::state_is_auto_read_accessible().

pull()

template<typename SJCB , typename SCOVECTOR , typename SR >

void fiber_bundle::pull	(	const SJCB &	xjcb,
		const SCOVECTOR &	xcovector,
		SR &	xresult,
		bool	xauto_access
	)

Precondition

• xjcb.state_is_auto_read_accessible(xauto_access)

• xcovector.state_is_auto_read_accessible(xauto_access)

• xresult.state_is_auto_read_write_accessible(xauto_access)

• xcovector.is_p_form(xauto_access)

Postcondition

• xresult.is_p_form(xauto_access)

Definition at line 95 of file sec_jcb.impl.h.

References fiber_bundle::sec_vd_algebra::binary_op().

push()

template<typename SJCB , typename SVECTOR , typename SR >

void fiber_bundle::push	(	const SJCB &	xjcb,
		const SVECTOR &	xvector,
		SR &	xresult,
		bool	xauto_access
	)

Precondition

• xjcb.state_is_auto_read_accessible(xauto_access)

• xvector.state_is_auto_read_accessible(xauto_access)

• xresult.state_is_auto_read_write_accessible(xauto_access)

• xvector.is_p_vector(xauto_access)

Postcondition

• xresult.is_p_vector(xauto_access)

Definition at line 143 of file sec_jcb.impl.h.

References fiber_bundle::sec_vd_algebra::binary_op().

put_length()

template<typename S >

void fiber_bundle::put_length	(	S &	x0,
		const vd_value_type &	xlength,
		bool	xauto_access
	)

Precondition

• x0.state_is_auto_read_write_accessible(xauto_access)

Postcondition

• xlength >= 0.0

• -unexecutable( "length(x0, xauto_access) == xlength" )

Definition at line 213 of file sec_ed.impl.h.

References fiber_bundle::sec_vd_algebra::unary_op().

rad()

double fiber_bundle::rad

(

double

degrees

)

Converts degress to radians. Convenience function for use with rotation routines.

Definition at line 1494 of file gln.cc.

References operator<<().

Referenced by fiber_bundle::gln::is_ancestor_of().

raise() [1/2]

template<typename SMET , typename SCOVECTOR , typename SR >

void fiber_bundle::raise	(	const SMET &	xmetric,
		const SCOVECTOR &	xcovector,
		SR &	xresult,
		bool	xauto_access
	)

Precondition

• xmetric.state_is_auto_read_accessible(xauto_access)

• xcovector.state_is_auto_read_accessible(xauto_access)

• xresult.state_is_auto_read_write_accessible(xauto_access)

• xmetric.is_contravariant(0, xauto_access)

• xcovector.is_covariant(0, xauto_access)

Postcondition

• xresult.is_contravariant(0, xauto_access)

Definition at line 145 of file sec_met.impl.h.

References fiber_bundle::sec_vd_algebra::binary_op().

raise() [2/2]

fiber_bundle::tensor_variance fiber_bundle::raise	(	const tensor_variance &	x0,
		int	xi
	)

The variance of the raise of a tensor with variance x0 on index xi.

Precondition

• (0 <= xi) && (xi < x0.p())

Postcondition

• result.p() == x0.p()

• result.is_contravariant(xi)

Definition at line 540 of file tensor_variance.cc.

References fiber_bundle::tensor_variance::is_contravariant(), lower(), fiber_bundle::tensor_variance::p(), and fiber_bundle::tensor_variance::put_variance().

Referenced by wedge().

same_sign()

double fiber_bundle::same_sign	(	double	xa,
		double	xb
	)

Convert xa to have the same sign as xb.

Definition at line 521 of file svd.cc.

References svd_pythag().

Referenced by geometry::line_surface_intersecter::intersect(), svd_diagonalize(), and svd_reduce().

sort_eigenvalues()

template<typename T >

void fiber_bundle::sort_eigenvalues	(	general_matrix_3x3< T > &	xeigenvectors,
		T	xeigenvalues[3]
	)

Utility function to sort the eigenvalues into ascending order. Called from jacobi_transformation.

Definition at line 1580 of file symmetric_matrix_3x3.impl.h.

Referenced by jacobi_transformation().

standard_fiber_path()

poset_path SHEAF_DLL_SPEC fiber_bundle::standard_fiber_path

(

)

The standard path for the fiber.

standard_section_space_path()

sheaf::poset_path fiber_bundle::standard_section_space_path	(	const poset_path &	xfiber_path,
		const poset_path &	xbase_path
	)

The standard path for the section space with fiber space path xfiber_path and base space path xbase_path.

Postcondition

• !result.empty()

• !result.full()

Definition at line 30 of file fiber_bundle.cc.

References sheaf::poset_path::empty(), sheaf::poset_path::full(), sheaf::poset_path::poset_name(), sheaf::poset_path::put_poset_name(), and standard_section_space_schema_path().

standard_section_space_schema_path()

sheaf::poset_path fiber_bundle::standard_section_space_schema_path

(

const poset_path &

xsection_space_path

)

The standard path for the section space schema.

Postcondition

• !result.empty()

• result.full()

Definition at line 55 of file fiber_bundle.cc.

References sheaf::poset_path::empty(), sheaf::poset_path::full(), sheaf::poset_path::member_name(), sheaf::poset_path::poset_name(), sheaf::poset_path::put_member_name(), and sheaf::poset_path::put_poset_name().

Referenced by standard_section_space_path().

standard_vector_space_path()

poset_path SHEAF_DLL_SPEC fiber_bundle::standard_vector_space_path

(

)

The standard path for the vector space.

star() [1/2]

template<typename S0 , typename SR >

void fiber_bundle::star	(	const S0 &	x0,
		SR &	xresult,
		bool	xauto_access
	)

Precondition

• x0.state_is_auto_read_accessible(xauto_access)

• xresult.state_is_auto_read_write_accessible(xauto_access)

Postcondition

• (x0.p(xauto_access)>0) \ ? (xresult.is_p_form(xauto_access) == x0.is_p_form(xauto_access)) : true

• (x0.p(xauto_access)==0) \ ? (xresult.is_p_form(xauto_access) == old_xresult_is_p_form): true

Definition at line 169 of file sec_atp.impl.h.

References star(), and fiber_bundle::sec_vd_algebra::unary_op().

star() [2/2]

fiber_bundle::tensor_variance fiber_bundle::star	(	const tensor_variance &	x0,
		int	xdd
	)

The variance of the Hodge star of a tensor with variance x0 over a vector space of dimension xdd.

Precondition

• x0.is_covariant() || x0.is_contravariant()

• x0.p() > 0

• x0.p() <= xdd

Postcondition

• result.p() == xdd - x0.p()

• x0.is_covariant() ? result.is_covariant() : true

• x0.is_contravariant() ? result.is_contravariant() : true

Definition at line 479 of file tensor_variance.cc.

References fiber_bundle::tensor_variance::is_contravariant(), fiber_bundle::tensor_variance::is_covariant(), fiber_bundle::tensor_variance::p(), fiber_bundle::tensor_variance::put_variance(), and wedge().

Referenced by hook(), and star().

svd_decompose()

bool fiber_bundle::svd_decompose	(	double *	xa,
		double *	xs,
		double *	xv,
		int	xnrows,
		int	xncols
	)

Perform single value decomposition.

Definition at line 38 of file svd.cc.

References svd_diagonalize(), and svd_reduce().

svd_diagonalize()

bool fiber_bundle::svd_diagonalize	(	double *	xa,
		double *	xw,
		double *	xv,
		int	nrows,
		int	ncols,
		double *	xtemp,
		double	lnorm
	)

Diagonalization of the bidiagonal form. Convenience function.

Definition at line 321 of file svd.cc.

References same_sign(), and svd_pythag().

Referenced by svd_decompose(), and svd_reduce().

svd_pythag()

double fiber_bundle::svd_pythag	(	double	xa,
		double	xb
	)

Pthagorean theorem calculation.

Definition at line 548 of file svd.cc.

References fiber_bundle::sec_at0_algebra::sqrt().

Referenced by same_sign(), and svd_diagonalize().

svd_reduce()

bool fiber_bundle::svd_reduce	(	double *	xa,
		double *	xw,
		double *	xv,
		int	nrows,
		int	ncols,
		double *	ltemp,
		double &	lnorm
	)

Householder reduction to bidiagonal form. Convenience function.

Definition at line 98 of file svd.cc.

References fiber_bundle::vd_algebra::max(), fiber_bundle::vd_algebra::min(), same_sign(), fiber_bundle::sec_at0_algebra::sqrt(), and svd_diagonalize().

Referenced by svd_decompose().

sym()

template<typename GT , typename ST >

void fiber_bundle::sym	(	const GT &	x0,
		ST &	xresult,
		bool	xauto_access
	)

Precondition

• x0.state_is_auto_read_accessible(xauto_access)

• xresult.state_is_auto_read_accessible(xauto_access)

• x0.dd(xauto_access) == xresult.dd(xauto_access)

• !x0.variance(xauto_access).is_mixed()

Postcondition

• xresult.variance(xauto_access) == x0.variance(xauto_access)

• -unexecutable( "xresult is equal to the symmetric part of x0" )

Definition at line 184 of file sec_tp.impl.h.

References fiber_bundle::sec_vd_algebra::unary_op().

tensor()

template<typename S0 , typename S1 , typename SR >

void fiber_bundle::tensor	(	const S0 &	x0,
		const S1 &	x1,
		SR &	xresult,
		bool	xauto_access
	)

Precondition

• x0.state_is_auto_read_accessible(xauto_access)

• x1.state_is_auto_read_accessible(xauto_access)

• xresult.state_is_auto_read_accessible(xauto_access)

• x1.dd(xauto_access) == x0.dd(xauto_access)

• xresult.dd(xauto_access) == x0.dd(xauto_access)

Postcondition

• xresult.variance(xauto_access) == \ tensor_product(x0.variance(xauto_access), x1.variance(xauto_access))

Definition at line 228 of file sec_tp.impl.h.

References fiber_bundle::sec_vd_algebra::binary_op(), and tensor_product().

tensor_product()

fiber_bundle::tensor_variance fiber_bundle::tensor_product	(	const tensor_variance &	x0,
		const tensor_variance &	x1
	)

The variance of the tensor product of tensors with variance x0 and x1.

Postcondition

• result.p() == x0.p() + x1.p()

• result.is_covariant() == x0.is_covariant()

Definition at line 414 of file tensor_variance.cc.

References hook(), fiber_bundle::tensor_variance::is_covariant(), fiber_bundle::tensor_variance::p(), fiber_bundle::tensor_variance::put_variance(), and fiber_bundle::tensor_variance::variance().

Referenced by contract(), tensor(), fiber_bundle::sec_tp_algebra::tensor(), and fiber_bundle::tp_algebra::tensor().

trace()

template<typename S0 , typename SR >

void fiber_bundle::trace	(	const S0 &	x0,
		SR &	xresult,
		bool	xauto_access
	)

Precondition

• x0.state_is_auto_read_accessible(xauto_access)

Definition at line 99 of file sec_st2.impl.h.

References fiber_bundle::sec_vd_algebra::unary_op().

Referenced by fiber_bundle::antisymmetric_matrix_2x2< T >::trace(), fiber_bundle::antisymmetric_matrix_3x3< T >::trace(), fiber_bundle::general_matrix_3x3< T >::trace(), fiber_bundle::general_matrix_2x2< T >::trace(), fiber_bundle::symmetric_matrix_3x3< T >::trace(), and fiber_bundle::symmetric_matrix_2x2< T >::trace().

wedge() [1/2]

fiber_bundle::tensor_variance fiber_bundle::wedge	(	const tensor_variance &	x0,
		const tensor_variance &	x1
	)

The variance of the wedge of a tensor with variance x0 with a tnesor with variance x1.

Precondition

• x0.is_covariant() || x0.is_contravariant()

• x1.is_covariant() || x1.is_contravariant()

• x0.is_covariant() == x1.is_covariant()

Postcondition

• result.p() == x0.p() + x1.p()

• result.is_covariant() == x0.is_covariant()

Definition at line 509 of file tensor_variance.cc.

References fiber_bundle::tensor_variance::is_contravariant(), fiber_bundle::tensor_variance::is_covariant(), fiber_bundle::tensor_variance::p(), fiber_bundle::tensor_variance::put_variance(), and raise().

Referenced by star(), and wedge().

wedge() [2/2]

template<typename S0 , typename S1 , typename SR >

void fiber_bundle::wedge	(	const S0 &	x0,
		const S1 &	x1,
		SR &	xresult,
		bool	xauto_access
	)

Precondition

• x0.state_is_auto_read_accessible(xauto_access)

• x1.state_is_auto_read_accessible(xauto_access)

• xresult.state_is_auto_read_write_accessible(xauto_access)

• x0.dd(xauto_access) >= xresult.dd(xauto_access)

• x1.dd(xauto_access) >= xresult.dd(xauto_access)

• xresult.p(xauto_access) == x0.p(xauto_access) + x1.p(xauto_access)

• x0.is_p_form(xauto_access) == x1.is_p_form(xauto_access)

Postcondition

• xresult.variance(xauto_access) == \ wedge(x0.variance(xauto_access), x1.variance(xauto_access))

Definition at line 222 of file sec_atp.impl.h.

References fiber_bundle::sec_vd_algebra::binary_op(), and wedge().