proxsuite::linalg::dense::Ldlt< T > Struct Template Reference

#include <proxsuite/linalg/dense/ldlt.hpp>

Public Member Functions
	Ldlt ()=default
void	reserve_uninit (isize cap) noexcept
void	reserve (isize cap) noexcept
void	delete_at (isize const *indices, isize r, proxsuite::linalg::veg::dynstack::DynStackMut stack)
auto	choose_insertion_position (isize i, Eigen::Ref< Vec const > a) -> isize
void	insert_block_at (isize i, Eigen::Ref< ColMat const > a, proxsuite::linalg::veg::dynstack::DynStackMut stack)
void	diagonal_update_clobber_indices (isize *indices, isize r, Eigen::Ref< Vec const > alpha, proxsuite::linalg::veg::dynstack::DynStackMut stack)
void	rank_r_update (Eigen::Ref< ColMat const > w, Eigen::Ref< Vec const > alpha, proxsuite::linalg::veg::dynstack::DynStackMut stack)
auto	dim () const noexcept -> isize
auto	ld_col () const noexcept -> Eigen::Map< ColMat const, Eigen::Unaligned, Eigen::OuterStride< DYN > >
auto	ld_col_mut () noexcept -> Eigen::Map< ColMat, Eigen::Unaligned, Eigen::OuterStride< DYN > >
auto	ld_row () const noexcept -> Eigen::Map< RowMat const, Eigen::Unaligned, Eigen::OuterStride< DYN > >
auto	ld_row_mut () noexcept -> Eigen::Map< RowMat, Eigen::Unaligned, Eigen::OuterStride< DYN > >
auto	l () const noexcept -> LView
auto	l_mut () noexcept -> LViewMut
auto	lt () const noexcept -> LTView
auto	lt_mut () noexcept -> LTViewMut
auto	d () const noexcept -> DView
auto	d_mut () noexcept -> DViewMut
auto	p () const -> Perm
auto	pt () const -> Perm
void	factorize (Eigen::Ref< ColMat const > mat, proxsuite::linalg::veg::dynstack::DynStackMut stack)
void	solve_in_place (Eigen::Ref< Vec > rhs, proxsuite::linalg::veg::dynstack::DynStackMut stack) const
void	dual_solve_in_place (Eigen::Ref< Vec > rhs, isize n, proxsuite::linalg::veg::dynstack::DynStackMut stack) const
auto	dbg_reconstructed_matrix_internal () const -> ColMat
auto	dbg_reconstructed_matrix () const -> ColMat

Static Public Member Functions
static auto	rank_r_update_req (isize n, isize r) noexcept -> proxsuite::linalg::veg::dynstack::StackReq
static auto	delete_at_req (isize n, isize r) noexcept -> proxsuite::linalg::veg::dynstack::StackReq
static auto	insert_block_at_req (isize n, isize r) noexcept -> proxsuite::linalg::veg::dynstack::StackReq
static auto	diagonal_update_req (isize n, isize r) noexcept -> proxsuite::linalg::veg::dynstack::StackReq
static auto	factorize_req (isize n) -> proxsuite::linalg::veg::dynstack::StackReq
static auto	solve_in_place_req (isize n) -> proxsuite::linalg::veg::dynstack::StackReq

Detailed Description

template<typename T>
struct proxsuite::linalg::dense::Ldlt< T >

Wrapper class that handles an allocated LDLT decomposition, with an applied permutation. When provided with a matrix A, this internally stores a lower triangular matrix with unit diagonal L, a vector D, and a permutation P such that A = P.T L diag(D) L.T P.

Example usage:

#include <proxsuite/linalg/dense/ldlt.hpp>
#include <proxsuite/linalg/veg/util/dynstack_alloc.hpp>

auto main() -> int {
constexpr auto DYN = Eigen::Dynamic;
using Matrix = Eigen::Matrix<double, DYN, DYN>;
using Vector = Eigen::Matrix<double, DYN, 1>;
using Ldlt = proxsuite::linalg::dense::Ldlt<double>;
using proxsuite::linalg::veg::dynstack::StackReq;

// allocate a matrix `a`
auto a0 = Matrix{
2,
2,
};

// workspace memory requirements
auto req =
Ldlt::factorize_req(2) | // initial
factorization of dim 2 Ldlt::insert_block_at_req(2, 1) | // or 1 insertion to
matrix of dim 2 Ldlt::delete_at_req(3, 2) | // or 2 deletions from matrix
of dim 3 Ldlt::solve_in_place_req(1); // or solve in place with dim 1

VEG_MAKE_STACK(stack, req);

Ldlt ldl;

// fill up the lower triangular part
// matrix is
// 1.0 2.0
// 2.0 3.0
a0(0, 0) = 1.0;
a0(1, 0) = 2.0;
a0(1, 1) = 3.0;

ldl.factorize(a0, stack);

// add one column at the index 1
// matrix is
// 1.0 4.0 2.0
// 4.0 5.0 6.0
// 2.0 6.0 3.0
auto c = Matrix{3, 1};
c(0, 0) = 4.0;
c(1, 0) = 5.0;
c(2, 0) = 6.0;
ldl.insert_block_at(1, c, stack);

// then delete two rows and columns at indices 0 and 2
// matrix is
// 5.0
proxsuite::linalg::veg::isize const indices[] = {0, 2};
ldl.delete_at(indices, 2, stack);

auto rhs = Vector{1};
rhs[0] = 5.0;

ldl.solve_in_place(rhs, stack);
VEG_ASSERT(rhs[0] == 1.0);
}

Definition at line 165 of file ldlt.hpp.

Constructor & Destructor Documentation

Ldlt()

template<typename T>

proxsuite::linalg::dense::Ldlt< T >::Ldlt ( )

default

Default constructor, initialized with a 0×0 empty matrix.

Member Function Documentation

reserve_uninit()

template<typename T>

void proxsuite::linalg::dense::Ldlt< T >::reserve_uninit ( isize cap )

inlinenoexcept

Reserves enough internal storage for a matrix A of size at least cap×cap. This operation invalidates the existing decomposition.

Parameters

cap	new capacity

Definition at line 241 of file ldlt.hpp.

reserve()

template<typename T>

void proxsuite::linalg::dense::Ldlt< T >::reserve ( isize cap )

inlinenoexcept

Reserves enough internal storage for a matrix A of size at least cap×cap. This operation preserves the existing decomposition.

Parameters

cap	new capacity

Definition at line 266 of file ldlt.hpp.

rank_r_update_req()

template<typename T>

auto proxsuite::linalg::dense::Ldlt< T >::rank_r_update_req ( isize n, isize r ) -> proxsuite::linalg::veg::dynstack::StackReq

inlinestaticnoexcept

Returns the memory storage requirements for performing a rank k update on a matrix with size at most n×n, with k ≤ r.

Parameters

n	maximum dimension of the matrix
r	maximum number of simultaneous rank updates

Definition at line 299 of file ldlt.hpp.

delete_at_req()

template<typename T>

auto proxsuite::linalg::dense::Ldlt< T >::delete_at_req ( isize n, isize r ) -> proxsuite::linalg::veg::dynstack::StackReq

inlinestaticnoexcept

Returns the memory storage requirements for deleting at most r rows and columns from a matrix with size at most n×n.

Parameters

n	maximum dimension of the matrix
r	maximum number of rows to be deleted

Definition at line 320 of file ldlt.hpp.

delete_at()

template<typename T>

void proxsuite::linalg::dense::Ldlt< T >::delete_at ( isize const * indices, isize r, proxsuite::linalg::veg::dynstack::DynStackMut stack )

inline

Given an LDLT decomposition for a matrix A, this computes the decomposition for the matrix A with r columns and rows removed, as indicated by the indices indices[0], ..., indices[r-1].

Parameters

indices	pointer to the array of indices to be deleted
r	number of the indices to be deleted
stack	workspace memory stack

Definition at line 340 of file ldlt.hpp.

choose_insertion_position()

template<typename T>

auto proxsuite::linalg::dense::Ldlt< T >::choose_insertion_position ( isize i, Eigen::Ref< Vec const > a ) -> isize

inline

Definition at line 389 of file ldlt.hpp.

insert_block_at_req()

template<typename T>

auto proxsuite::linalg::dense::Ldlt< T >::insert_block_at_req ( isize n, isize r ) -> proxsuite::linalg::veg::dynstack::StackReq

inlinestaticnoexcept

Returns the memory storage requirements for inserting at most r rows and columns from a matrix with size at most n×n.

Parameters

n	maximum dimension of the matrix
r	maximum number of rows to be inserted

Definition at line 410 of file ldlt.hpp.

insert_block_at()

template<typename T>

void proxsuite::linalg::dense::Ldlt< T >::insert_block_at ( isize i, Eigen::Ref< ColMat const > a, proxsuite::linalg::veg::dynstack::DynStackMut stack )

inline

Given an LDLT decomposition for a matrix A, this computes the decomposition for the matrix A with extra r columns and rows from a added at the index i.

Parameters

i	index where the block should be inserted
a	matrix of the new columns that are inserted
stack	workspace memory stack

Definition at line 431 of file ldlt.hpp.

diagonal_update_req()

template<typename T>

auto proxsuite::linalg::dense::Ldlt< T >::diagonal_update_req ( isize n, isize r ) -> proxsuite::linalg::veg::dynstack::StackReq

inlinestaticnoexcept

Returns the memory storage requirements for a diagonal subsection update with size at most r, in a matrix with size at most n×n.

Parameters

n	maximum dimension of the matrix
r	maximum size of diagonal subsection that gets updated

Definition at line 484 of file ldlt.hpp.

diagonal_update_clobber_indices()

template<typename T>

void proxsuite::linalg::dense::Ldlt< T >::diagonal_update_clobber_indices ( isize * indices, isize r, Eigen::Ref< Vec const > alpha, proxsuite::linalg::veg::dynstack::DynStackMut stack )

inline

Given an LDLT decomposition for a matrix A, this computes the decomposition for the matrix A with the vector alpha added to a diagonal subset, as specified by the provided indices.

The values pointed at by indices are unspecified after a call to this function.

Parameters

indices	pointer to the array of indices of diagonal elements that are updated
r	number of the indices to be updated
stack	workspace memory stack

Definition at line 516 of file ldlt.hpp.

rank_r_update()

template<typename T>

void proxsuite::linalg::dense::Ldlt< T >::rank_r_update ( Eigen::Ref< ColMat const > w, Eigen::Ref< Vec const > alpha, proxsuite::linalg::veg::dynstack::DynStackMut stack )

inline

Given an LDLT decomposition for a matrix A, this computes the decomposition for the rank-updated matrix A + w×diag(alpha)×w.T

Parameters

w	rank update matrix
alpha	rank update diagonal vector
stack	workspace memory stack

Definition at line 580 of file ldlt.hpp.

dim()

template<typename T>

auto proxsuite::linalg::dense::Ldlt< T >::dim ( ) const -> isize

inlinenoexcept

Returns the dimension of the stored decomposition.

Definition at line 614 of file ldlt.hpp.

ld_col()

template<typename T>

auto proxsuite::linalg::dense::Ldlt< T >::ld_col ( ) const -> Eigen::Map< ColMat const, Eigen::Unaligned, Eigen::OuterStride<DYN>>

inlinenoexcept

Definition at line 616 of file ldlt.hpp.

ld_col_mut()

template<typename T>

auto proxsuite::linalg::dense::Ldlt< T >::ld_col_mut ( ) -> Eigen::Map< ColMat, Eigen::Unaligned, Eigen::OuterStride<DYN>>

inlinenoexcept

Definition at line 623 of file ldlt.hpp.

ld_row()

template<typename T>

auto proxsuite::linalg::dense::Ldlt< T >::ld_row ( ) const -> Eigen::Map< RowMat const, Eigen::Unaligned, Eigen::OuterStride<DYN>>

inlinenoexcept

Definition at line 630 of file ldlt.hpp.

ld_row_mut()

template<typename T>

auto proxsuite::linalg::dense::Ldlt< T >::ld_row_mut ( ) -> Eigen::Map< RowMat, Eigen::Unaligned, Eigen::OuterStride<DYN>>

inlinenoexcept

Definition at line 642 of file ldlt.hpp.

l()

template<typename T>

auto proxsuite::linalg::dense::Ldlt< T >::l ( ) const -> LView

inlinenoexcept

Definition at line 655 of file ldlt.hpp.

l_mut()

template<typename T>

auto proxsuite::linalg::dense::Ldlt< T >::l_mut ( ) -> LViewMut

inlinenoexcept

Definition at line 659 of file ldlt.hpp.

lt()

template<typename T>

auto proxsuite::linalg::dense::Ldlt< T >::lt ( ) const -> LTView

inlinenoexcept

Definition at line 663 of file ldlt.hpp.

lt_mut()

template<typename T>

auto proxsuite::linalg::dense::Ldlt< T >::lt_mut ( ) -> LTViewMut

inlinenoexcept

Definition at line 667 of file ldlt.hpp.

d()

template<typename T>

auto proxsuite::linalg::dense::Ldlt< T >::d ( ) const -> DView

inlinenoexcept

Definition at line 672 of file ldlt.hpp.

d_mut()

template<typename T>

auto proxsuite::linalg::dense::Ldlt< T >::d_mut ( ) -> DViewMut

inlinenoexcept

Definition at line 681 of file ldlt.hpp.

p()

template<typename T>

auto proxsuite::linalg::dense::Ldlt< T >::p ( ) const -> Perm

inline

Definition at line 690 of file ldlt.hpp.

pt()

template<typename T>

auto proxsuite::linalg::dense::Ldlt< T >::pt ( ) const -> Perm

inline

Definition at line 691 of file ldlt.hpp.

factorize_req()

template<typename T>

auto proxsuite::linalg::dense::Ldlt< T >::factorize_req ( isize n ) -> proxsuite::linalg::veg::dynstack::StackReq

inlinestatic

Returns the memory storage requirements for a factorization of a matrix of size at most n×n

Parameters

n	maximum dimension of the matrix

Definition at line 699 of file ldlt.hpp.

factorize()

template<typename T>

void proxsuite::linalg::dense::Ldlt< T >::factorize ( Eigen::Ref< ColMat const > mat, proxsuite::linalg::veg::dynstack::DynStackMut stack )

inline

Computes the decomposition of a given matrix A. The matrix is interpreted as a symmetric matrix and only the lower triangular part of A is accessed.

Parameters

mat	matrix whose decomposition should be computed
stack	workspace memory stack

Definition at line 718 of file ldlt.hpp.

solve_in_place_req()

template<typename T>

auto proxsuite::linalg::dense::Ldlt< T >::solve_in_place_req ( isize n ) -> proxsuite::linalg::veg::dynstack::StackReq

inlinestatic

Returns the memory storage requirements for solving a linear system with a decomposition of dimension at most n

Parameters

n	maximum dimension of the matrix

Definition at line 752 of file ldlt.hpp.

solve_in_place()

template<typename T>

void proxsuite::linalg::dense::Ldlt< T >::solve_in_place ( Eigen::Ref< Vec > rhs, proxsuite::linalg::veg::dynstack::DynStackMut stack ) const

inline

Solves the system A×x = rhs, and stores the result in rhs.

Parameters

rhs	right hand side of the linear system
stack	workspace memory stack

Definition at line 767 of file ldlt.hpp.

dual_solve_in_place()

template<typename T>

void proxsuite::linalg::dense::Ldlt< T >::dual_solve_in_place ( Eigen::Ref< Vec > rhs, isize n, proxsuite::linalg::veg::dynstack::DynStackMut stack ) const

inline

Definition at line 784 of file ldlt.hpp.

dbg_reconstructed_matrix_internal()

template<typename T>

auto proxsuite::linalg::dense::Ldlt< T >::dbg_reconstructed_matrix_internal ( ) const -> ColMat

inline

Definition at line 802 of file ldlt.hpp.

dbg_reconstructed_matrix()

template<typename T>

auto proxsuite::linalg::dense::Ldlt< T >::dbg_reconstructed_matrix ( ) const -> ColMat

inline

Definition at line 812 of file ldlt.hpp.

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The documentation for this struct was generated from the following file:

• include/proxsuite/linalg/dense/ldlt.hpp