docs(docs): built docs

Note for now much of the docs is LLM written. This was done to save time and focus on code development. The docs have been LOOSLEY reviewed. However, the code itself has been either fully written by hand or fully reviewed. Therefore, the docs should at the moment be seen as a loose resource rather than authoratiative (and this is on top of the general ability for docs to drift)

docs/man/man3/ordering.hpp.3

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+.TH "src/include/serif/backend/mfem/solver/preconditioner/computations/ordering.hpp" 3 "Version v0.0.1a" "SERiF" \" -*- nroff -*-
+.ad l
+.nh
+.SH NAME
+src/include/serif/backend/mfem/solver/preconditioner/computations/ordering.hpp
+.SH SYNOPSIS
+.br
+.PP
+\fR#include <limits>\fP
+.br
+\fR#include <vector>\fP
+.br
+\fR#include 'serif/backend/mfem/operators/linearized_block\&.hpp'\fP
+.br
+\fR#include 'serif/operators/linearized_system_view\&.hpp'\fP
+.br
+\fR#include 'serif/discretization/blocks/system_layout\&.hpp'\fP
+.br
+\fR#include 'serif/discretization/blocks/keys\&.hpp'\fP
+.br
+\fR#include 'serif/backend/mfem/solver/preconditioner/border\&.hpp'\fP
+.br
+\fR#include 'serif/utils/dependencies/computation\&.hpp'\fP
+.br
+
+.SS "Classes"
+
+.in +1c
+.ti -1c
+.RI "struct \fBserif::solver::preconditioner::keys::Preconditioner\fP"
+.br
+.ti -1c
+.RI "struct \fBserif::solver::preconditioner::computations::detail::PhysicalSources< utils::dependencies::KeyList< Keys\&.\&.\&. > >\fP"
+.br
+.in -1c
+.SS "Namespaces"
+
+.in +1c
+.ti -1c
+.RI "namespace \fBserif\fP"
+.br
+.ti -1c
+.RI "namespace \fBserif::solver\fP"
+.br
+.ti -1c
+.RI "namespace \fBserif::solver::preconditioner\fP"
+.br
+.ti -1c
+.RI "namespace \fBserif::solver::preconditioner::keys\fP"
+.br
+.ti -1c
+.RI "namespace \fBserif::solver::preconditioner::computations\fP"
+.br
+.ti -1c
+.RI "namespace \fBserif::solver::preconditioner::computations::detail\fP"
+.br
+.in -1c
+.SS "Typedefs"
+
+.in +1c
+.ti -1c
+.RI "using \fBserif::solver::preconditioner::keys::Layout\fP = \fBdiscretization::blocks::keys::Layout\fP"
+.br
+.RI "Preconditioning consumes the same coordinate layout as every other numerical service\&. "
+.in -1c
+.SS "Functions"
+
+.in +1c
+.ti -1c
+.RI "template<\fBdiscretization::blocks::RepresentedValueKind\fP Kind, typename Layout, typename\&.\&.\&. Coordinates> std::size_t \fBserif::solver::preconditioner::computations::selected_size\fP (const Layout &layout, \fButils::dependencies::KeyList\fP< Coordinates\&.\&.\&. >)"
+.br
+.RI "Count the declared coordinates of a selected physical block\&. "
+.ti -1c
+.RI "template<typename Key, typename Layout> std::expected< void, \fBFailure\fP > \fBserif::solver::preconditioner::computations::validate_physical_layout\fP (const Layout &layout, const \fBoperators::backend::mfem::LinearizedBlock\fP &block)"
+.br
+.RI "Detect incorrect per-field sizes even when the total packed dimensions happen to agree\&. "
+.ti -1c
+.RI "template<\fBdiscretization::blocks::RepresentedValueKind\fP Kind, typename Layout, typename\&.\&.\&. Coordinates> std::expected< std::vector< int >, \fBFailure\fP > \fBserif::solver::preconditioner::computations::ordered_indices\fP (const Layout &layout, \fButils::dependencies::KeyList\fP< Coordinates\&.\&.\&. >)"
+.br
+.RI "Map each root coefficient to the recipe's explicit subsystem ordering\&. "
+.ti -1c
+.RI "template<typename Recipe, typename Layout, typename\&.\&.\&. PhysicalKeys> auto \fBserif::solver::preconditioner::computations::ordering\fP (\fButils::dependencies::KeyList\fP< PhysicalKeys\&.\&.\&. >)"
+.br
+.RI "Bind one inverse to independently ordered state and residual vectors through the common layout\&. "
+.in -1c
+.SS "Variables"
+
+.in +1c
+.ti -1c
+.RI "template<typename Key> constexpr bool \fBserif::solver::preconditioner::computations::detail::is_physical_block\fP = false"
+.br
+.ti -1c
+.RI "template<typename Rows, typename Values> constexpr bool \fBserif::solver::preconditioner::computations::detail::is_physical_block< operators::PhysicalBlock< Rows, Values > >\fP = true"
+.br
+.in -1c
+.SH "Author"
+.PP 
+Generated automatically by Doxygen for SERiF from the source code\&.