SheafSystem  0.0.0.0
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

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

The type of degree of freedom in the section space.

Definition at line 78 of file fiber_bundle.h.

◆ 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

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]

◆ 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 
)

◆ deep_size() [13/19]

◆ deep_size() [14/19]

◆ deep_size() [15/19]

◆ deep_size() [16/19]

◆ deep_size() [17/19]

◆ deep_size() [18/19]

◆ 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()

◆ 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,
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()

◆ 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]

◆ 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]

◆ 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 
)

◆ 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 
)

◆ 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]

◆ operator<<() [28/67]

◆ operator<<() [29/67]

◆ operator<<() [30/67]

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

◆ operator<<() [31/67]

◆ operator<<() [32/67]

◆ 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 
)

◆ 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]

◆ 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_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 
)

◆ 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,
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 
)

◆ 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().