Namespaces
namespace	_detail

namespace	concepts

namespace	tags

namespace	util

Classes
struct	DenseVecMut

struct	DenseVecRef

struct	MatMut

struct	MatRef

struct	SymbolicMatMut

struct	SymbolicMatRef

struct	VecRef

Enumerations
enum struct	Ordering : unsigned char { natural , user_provided , amd , ENUM_END }

Functions
	VEG_TAG (from_eigen, FromEigen)

template<typename I >
auto	transpose_req (proxsuite::linalg::veg::Tag< I >, isize nrows) noexcept -> proxsuite::linalg::veg::dynstack::StackReq

template<typename T , typename I >
void	transpose (MatMut< T, I > at, MatRef< T, I > a, DynStackMut stack) noexcept(VEG_CONCEPT(nothrow_copyable< T >))

template<typename I >
auto	transpose_symbolic_req (proxsuite::linalg::veg::Tag< I >, isize nrows) noexcept -> proxsuite::linalg::veg::dynstack::StackReq

template<typename I >
void	transpose_symbolic (SymbolicMatMut< I > at, SymbolicMatRef< I > a, DynStackMut stack) noexcept

template<typename T , typename I >
void	dense_lsolve (DenseVecMut< T > x, MatRef< T, I > l) noexcept(false)

template<typename T , typename I >
void	dense_ltsolve (DenseVecMut< T > x, MatRef< T, I > l) noexcept(false)

template<typename I >
auto	etree_req (proxsuite::linalg::veg::Tag< I >, isize n) noexcept -> proxsuite::linalg::veg::dynstack::StackReq

template<typename I >
VEG_INLINE void	etree (I *parent, SymbolicMatRef< I > a, DynStackMut stack) noexcept

template<typename I >
auto	postorder_req (proxsuite::linalg::veg::Tag< I >, isize n) noexcept -> proxsuite::linalg::veg::dynstack::StackReq

template<typename I >
void	postorder (I post, I const parent, isize n, DynStackMut stack) noexcept

template<typename I >
auto	column_counts_req (proxsuite::linalg::veg::Tag< I > tag, isize n, isize nnz) noexcept -> proxsuite::linalg::veg::dynstack::StackReq

template<typename I >
void	column_counts (I counts, SymbolicMatRef< I > a, I const parent, I const *post, DynStackMut stack) noexcept

template<typename I >
auto	amd_req (proxsuite::linalg::veg::Tag< I >, isize, isize nnz) noexcept -> proxsuite::linalg::veg::dynstack::StackReq

template<typename I >
void	amd (I *perm, SymbolicMatRef< I > mat, DynStackMut stack) noexcept

template<typename I >
auto	factorize_symbolic_req (proxsuite::linalg::veg::Tag< I > tag, isize n, isize nnz, Ordering o) noexcept -> proxsuite::linalg::veg::dynstack::StackReq

template<typename I >
void	factorize_symbolic_non_zeros (I nnz_per_col, I etree, I perm_inv, I const perm, SymbolicMatRef< I > a, DynStackMut stack) noexcept

template<typename I >
void	factorize_symbolic_col_counts (I col_ptrs, I etree, I perm_inv, I const perm, SymbolicMatRef< I > a, DynStackMut stack) noexcept

template<typename T , typename I >
auto	factorize_numeric_req (proxsuite::linalg::veg::Tag< T >, proxsuite::linalg::veg::Tag< I >, isize n, isize a_nnz, Ordering o) noexcept -> proxsuite::linalg::veg::dynstack::StackReq

template<typename T , typename I >
void	factorize_numeric (T values, I row_indices, proxsuite::linalg::veg::DoNotDeduce< T const * > diag_to_add, proxsuite::linalg::veg::DoNotDeduce< I const * > perm, I const col_ptrs, I const etree, I const *perm_inv, MatRef< T, I > a, DynStackMut stack) noexcept(false)

template<typename T , typename I >
auto	delete_row_req (proxsuite::linalg::veg::Tag< T >, proxsuite::linalg::veg::Tag< I >, isize n, isize max_nnz) noexcept -> proxsuite::linalg::veg::dynstack::StackReq

template<typename T , typename I >
auto	delete_row (MatMut< T, I > ld, I etree, I const perm_inv, isize pos, DynStackMut stack) noexcept(false) -> MatMut< T, I >

template<typename T , typename I >
auto	add_row_req (proxsuite::linalg::veg::Tag< T >, proxsuite::linalg::veg::Tag< I >, isize n, bool id_perm, isize nnz, isize max_nnz) noexcept -> proxsuite::linalg::veg::dynstack::StackReq

template<typename T , typename I >
auto	add_row (MatMut< T, I > ld, I etree, I const perm_inv, isize pos, VecRef< T, I > new_col, proxsuite::linalg::veg::DoNotDeduce< T > diag_element, DynStackMut stack) noexcept(false) -> MatMut< T, I >

template<typename I >
auto	merge_second_col_into_first_req (proxsuite::linalg::veg::Tag< I >, isize second_size) noexcept -> proxsuite::linalg::veg::dynstack::StackReq

template<typename T , typename I >
auto	merge_second_col_into_first (I difference, T first_values, I *first_ptr, PROXSUITE_MAYBE_UNUSED isize first_full_len, isize first_initial_len, Slice< I > second, proxsuite::linalg::veg::DoNotDeduce< I > ignore_threshold_inclusive, bool move_values, DynStackMut stack) noexcept(false) -> proxsuite::linalg::veg::Tuple< SliceMut< T >, SliceMut< I >, SliceMut< I > >

template<typename T , typename I >
auto	rank1_update_req (proxsuite::linalg::veg::Tag< T >, proxsuite::linalg::veg::Tag< I >, isize n, bool id_perm, isize col_nnz) noexcept -> proxsuite::linalg::veg::dynstack::StackReq

template<typename T , typename I >
auto	rank1_update (MatMut< T, I > ld, I etree, I const perm_inv, VecRef< T, I > w, proxsuite::linalg::veg::DoNotDeduce< T > alpha, DynStackMut stack) noexcept(false) -> MatMut< T, I >

Enumeration Type Documentation

◆ Ordering

enum struct proxsuite::linalg::sparse::Ordering : unsigned char

strong

Enumerator
natural
user_provided
amd
ENUM_END

Definition at line 915 of file factorize.hpp.

Function Documentation

◆ transpose_req()

template<typename I >

auto proxsuite::linalg::sparse::transpose_req	(	proxsuite::linalg::veg::Tag< I >	,
		isize	nrows ) -> proxsuite::linalg::veg::dynstack::StackReq

noexcept

Definition at line 17 of file factorize.hpp.

◆ transpose()

template<typename T , typename I >

void proxsuite::linalg::sparse::transpose	(	MatMut< T, I >	at,
		MatRef< T, I >	a,
		DynStackMut	stack )

noexcept

Definition at line 26 of file factorize.hpp.

◆ transpose_symbolic_req()

template<typename I >

auto proxsuite::linalg::sparse::transpose_symbolic_req	(	proxsuite::linalg::veg::Tag< I >	,
		isize	nrows ) -> proxsuite::linalg::veg::dynstack::StackReq

noexcept

Definition at line 86 of file factorize.hpp.

◆ transpose_symbolic()

template<typename I >

void proxsuite::linalg::sparse::transpose_symbolic	(	SymbolicMatMut< I >	at,
		SymbolicMatRef< I >	a,
		DynStackMut	stack )

noexcept

Definition at line 95 of file factorize.hpp.

◆ dense_lsolve()

template<typename T , typename I >

void proxsuite::linalg::sparse::dense_lsolve	(	DenseVecMut< T >	x,
		MatRef< T, I >	l )

l is unit lower triangular whose diagonal elements are ignored. Solves l×y = x and store the solution in x.

Parameters

x	RHS of the system, solution storage.
l	matrix to be inverted.

Definition at line 149 of file factorize.hpp.

◆ dense_ltsolve()

template<typename T , typename I >

void proxsuite::linalg::sparse::dense_ltsolve	(	DenseVecMut< T >	x,
		MatRef< T, I >	l )

l is unit lower triangular whose diagonal elements are ignored. Solves l.T×y = x and store the solution in x.

Parameters

x	RHS of the system, solution storage.
l	matrix to be inverted.

Definition at line 188 of file factorize.hpp.

◆ etree_req()

template<typename I >

auto proxsuite::linalg::sparse::etree_req	(	proxsuite::linalg::veg::Tag< I >	,
		isize	n ) -> proxsuite::linalg::veg::dynstack::StackReq

noexcept

Computes the stack memory requirements of etree computation.

Parameters

n	dimension of the matrix.

Definition at line 252 of file factorize.hpp.

◆ etree()

template<typename I >

VEG_INLINE void proxsuite::linalg::sparse::etree	(	I *	parent,
		SymbolicMatRef< I >	a,
		DynStackMut	stack )

noexcept

Computes the elimination tree of the cholesky factor of a of size n. a is considered symmetric but should only contain terms from the upper triangular part.

Parameters

parent	pointer to the elimination tree storage, of size `n`.
a	symbolic structure of the matrix to be factorized.
stack	temporary allocation stack

Definition at line 269 of file factorize.hpp.

◆ postorder_req()

template<typename I >

auto proxsuite::linalg::sparse::postorder_req	(	proxsuite::linalg::veg::Tag< I >	,
		isize	n ) -> proxsuite::linalg::veg::dynstack::StackReq

noexcept

Computes the memory requirements of the postordering of the cholesky factorization.

Parameters

n	dimension of the matrix to be factorized.

Definition at line 459 of file factorize.hpp.

◆ postorder()

template<typename I >

void proxsuite::linalg::sparse::postorder	(	I *	post,
		I const *	parent,
		isize	n,
		DynStackMut	stack )

noexcept

Computes the postordering of the cholesky factorization of dimension n.

Parameters

post	storage for the postordering, of size `n`
parent	pointer to the elimination tree
n	dimension of the matrix to be factorized
stack	temporary allocation stack

Definition at line 475 of file factorize.hpp.

◆ column_counts_req()

template<typename I >

auto proxsuite::linalg::sparse::column_counts_req	(	proxsuite::linalg::veg::Tag< I >	tag,
		isize	n,
		isize	nnz ) -> proxsuite::linalg::veg::dynstack::StackReq

noexcept

Definition at line 582 of file factorize.hpp.

◆ column_counts()

template<typename I >

void proxsuite::linalg::sparse::column_counts	(	I *	counts,
		SymbolicMatRef< I >	a,
		I const *	parent,
		I const *	post,
		DynStackMut	stack )

noexcept

Definition at line 596 of file factorize.hpp.

◆ amd_req()

template<typename I >

auto proxsuite::linalg::sparse::amd_req	(	proxsuite::linalg::veg::Tag< I >	,
		isize	,
		isize	nnz ) -> proxsuite::linalg::veg::dynstack::StackReq

noexcept

Definition at line 719 of file factorize.hpp.

◆ amd()

template<typename I >

void proxsuite::linalg::sparse::amd	(	I *	perm,
		SymbolicMatRef< I >	mat,
		DynStackMut	stack )

noexcept

Definition at line 728 of file factorize.hpp.

◆ factorize_symbolic_req()

template<typename I >

auto proxsuite::linalg::sparse::factorize_symbolic_req	(	proxsuite::linalg::veg::Tag< I >	tag,
		isize	n,
		isize	nnz,
		Ordering	o ) -> proxsuite::linalg::veg::dynstack::StackReq

noexcept

Computes the stack memory requirements of symbolic factorization.

Parameters

n	dimension of the matrix to be factorized.
nnz	number of non zeros of the matrix to be factorized.
o	the kind of permutation that is applied to the matrix before factorization.

Definition at line 933 of file factorize.hpp.

◆ factorize_symbolic_non_zeros()

template<typename I >

void proxsuite::linalg::sparse::factorize_symbolic_non_zeros	(	I *	nnz_per_col,
		I *	etree,
		I *	perm_inv,
		I const *	perm,
		SymbolicMatRef< I >	a,
		DynStackMut	stack )

noexcept

Performs symbolic factorization and computed the number of non-zeros in each column of the cholesky factor of dimension n.

Parameters

nnz_per_col	storage for non-zeros per column, of size `n`
etree	storage for elimination tree, of size `n`
perm_inv	storage for inverse permutation, of size `n`
perm	optionally user-provided permutation, either null or of size `n`
a	matrix to be symbolically factorized
stack	temporary allocation stack

Definition at line 987 of file factorize.hpp.

◆ factorize_symbolic_col_counts()

template<typename I >

void proxsuite::linalg::sparse::factorize_symbolic_col_counts	(	I *	col_ptrs,
		I *	etree,
		I *	perm_inv,
		I const *	perm,
		SymbolicMatRef< I >	a,
		DynStackMut	stack )

noexcept

Performs symbolic factorization and computed the column pointers for each column of the cholesky factor of dimension n.

Parameters

col_ptrs	storage for column pointers, of size `n + 1`
etree	storage for elimination tree, of size `n`
perm_inv	storage for inverse permutation, of size `n`
perm	optionally user-provided permutation, either null or of size `n`
a	matrix to be symbolically factorized
stack	temporary allocation stack

Definition at line 1076 of file factorize.hpp.

◆ factorize_numeric_req()

template<typename T , typename I >

auto proxsuite::linalg::sparse::factorize_numeric_req	(	proxsuite::linalg::veg::Tag< T >	,
		proxsuite::linalg::veg::Tag< I >	,
		isize	n,
		isize	a_nnz,
		Ordering	o ) -> proxsuite::linalg::veg::dynstack::StackReq

noexcept

Computes the stack memory requirements of numerical factorization.

Parameters

n	dimension of the matrix to be factorized.
a_nnz	number of non zeros of the matrix to be factorized.
o	the kind of permutation that is applied to the matrix before factorization.

Definition at line 1111 of file factorize.hpp.

◆ factorize_numeric()

template<typename T , typename I >

void proxsuite::linalg::sparse::factorize_numeric	(	T *	values,
		I *	row_indices,
		proxsuite::linalg::veg::DoNotDeduce< T const * >	diag_to_add,
		proxsuite::linalg::veg::DoNotDeduce< I const * >	perm,
		I const *	col_ptrs,
		I const *	etree,
		I const *	perm_inv,
		MatRef< T, I >	a,
		DynStackMut	stack )

Performs numerical LDLT factorization, assuming the symbolic factorization and column counts have already been computed. L and D are stored in the same matrix, with the elements of D replacing the implicit diagonal 1 element of each column of L.

Parameters

values	pointer to the values of the factorization
row_indices	pointer to the row indices of the factorization
diag_to_add	pointer to a vector that is added to the diagonal of the matrix during factorization, if `diag_to_add` and `perm` are both non null
perm	pointer to the pre-computed permutation that is applied to `diag`.
col_ptrs	pointer to the already computed column pointers
etree	pointer to the already computed elimination tree
perm_inv	pointer to the already computed inverse permutation. Must be the inverse of `perm`
a	matrix to be factorized
stack	temporary allocation stack

Definition at line 1159 of file factorize.hpp.

◆ delete_row_req()

template<typename T , typename I >

auto proxsuite::linalg::sparse::delete_row_req	(	proxsuite::linalg::veg::Tag< T >	,
		proxsuite::linalg::veg::Tag< I >	,
		isize	n,
		isize	max_nnz ) -> proxsuite::linalg::veg::dynstack::StackReq

noexcept

Computes the memory requirements for deleting a row and column for the ldlt factors

Parameters

n	: dimension of the matrix
max_nnz	: upper bound of non zero counts over the columns of the matrix. n is always a valid value.

Definition at line 25 of file rowmod.hpp.

◆ delete_row()

template<typename T , typename I >

auto proxsuite::linalg::sparse::delete_row	(	MatMut< T, I >	ld,
		I *	etree,
		I const *	perm_inv,
		isize	pos,
		DynStackMut	stack ) -> MatMut<T, I>

Given the ldlt factors of matrix a, computes the ldlt factors of the matrix a with row and column at position pos replaced by those of the identity matrix It returns a view of the updated factors.

Parameters

ld	: the ldlt factors
etree	pointer to the elimination tree
perm_inv	pointer to inverse permutation (for ex AMD). If this is null, the permutation is assumed to be the identity.
pos	position of the row and column to be deleted
stack	is the memory stack

Definition at line 52 of file rowmod.hpp.

◆ add_row_req()

template<typename T , typename I >

auto proxsuite::linalg::sparse::add_row_req	(	proxsuite::linalg::veg::Tag< T >	,
		proxsuite::linalg::veg::Tag< I >	,
		isize	n,
		bool	id_perm,
		isize	nnz,
		isize	max_nnz ) -> proxsuite::linalg::veg::dynstack::StackReq

noexcept

Computes the memory requirements for adding a row and column for the ldlt factors

Parameters

n	: dimension of the matrix
id_perm	: whether the permutation corresponds to the identity
nnz	: number of non zero elements in the added vector
max_nnz	: upper bound of non zero counts over the columns of the matrix. n is always a valid value.

Definition at line 143 of file rowmod.hpp.

◆ add_row()

template<typename T , typename I >

auto proxsuite::linalg::sparse::add_row	(	MatMut< T, I >	ld,
		I *	etree,
		I const *	perm_inv,
		isize	pos,
		VecRef< T, I >	new_col,
		proxsuite::linalg::veg::DoNotDeduce< T >	diag_element,
		DynStackMut	stack ) -> MatMut<T, I>

Given the ldlt factors of matrix a, computes the ldlt factors of the matrix a with added row and column at position pos. It is assumed that the row and column are empty except the diagonal element. It returns a view of the updated factors.

Parameters

ld	: the ldlt factors
etree	pointer to the elimination tree
perm_inv	pointer to inverse permutation (for ex AMD). If this is null, the permutation is assumed to be the identity.
pos	position of the row and column to be added
new_col	: new column to be added without the diagonal element (of size nnz-1)
diag_element	: diagonal element of the added row and column
stack	is the memory stack

Definition at line 190 of file rowmod.hpp.

◆ merge_second_col_into_first_req()

template<typename I >

auto proxsuite::linalg::sparse::merge_second_col_into_first_req	(	proxsuite::linalg::veg::Tag< I >	,
		isize	second_size ) -> proxsuite::linalg::veg::dynstack::StackReq

noexcept

Definition at line 21 of file update.hpp.

◆ merge_second_col_into_first()

template<typename T , typename I >

auto proxsuite::linalg::sparse::merge_second_col_into_first	(	I *	difference,
		T *	first_values,
		I *	first_ptr,
		PROXSUITE_MAYBE_UNUSED isize	first_full_len,
		isize	first_initial_len,
		Slice< I >	second,
		proxsuite::linalg::veg::DoNotDeduce< I >	ignore_threshold_inclusive,
		bool	move_values,
		DynStackMut	stack ) -> proxsuite::linalg::veg::Tuple<SliceMut<T>, SliceMut<I>, SliceMut<I>>

Definition at line 33 of file update.hpp.

◆ rank1_update_req()

template<typename T , typename I >

auto proxsuite::linalg::sparse::rank1_update_req	(	proxsuite::linalg::veg::Tag< T >	,
		proxsuite::linalg::veg::Tag< I >	,
		isize	n,
		bool	id_perm,
		isize	col_nnz ) -> proxsuite::linalg::veg::dynstack::StackReq

noexcept

Computes the memory requirements for rank one update.

Parameters

n	dimension of matrix
id_perm	whether the permutation is implicitly the identity or not
col_nnz	number of nnz elts in the update vector

Definition at line 170 of file update.hpp.

◆ rank1_update()

template<typename T , typename I >

auto proxsuite::linalg::sparse::rank1_update	(	MatMut< T, I >	ld,
		I *	etree,
		I const *	perm_inv,
		VecRef< T, I >	w,
		proxsuite::linalg::veg::DoNotDeduce< T >	alpha,
		DynStackMut	stack ) -> MatMut<T, I>

Performs a rank one update in place. Given ldlt factor l, and d, of a matrix a, this computes the ldlt factors of a + alpha w w.T It returns a view on the updated factors.

Parameters

ld	: ldlt factors of a (lower triangular with d on the diagonal)
etree	pointer to the elimination tree
perm_inv	pointer to inverse permutation (for ex AMD). If this is null, the permutation is assumed to be the identity.
w	is the update vector
alpha	is the update coefficient
stack	is the memory stack

Definition at line 207 of file update.hpp.

Namespaces

Classes

Enumerations

Functions

Enumeration Type Documentation

◆ Ordering

Function Documentation

◆ transpose_req()

◆ transpose()

◆ transpose_symbolic_req()

◆ transpose_symbolic()

◆ dense_lsolve()

◆ dense_ltsolve()

◆ etree_req()

◆ etree()

◆ postorder_req()

◆ postorder()

◆ column_counts_req()

◆ column_counts()

◆ amd_req()

◆ amd()

◆ factorize_symbolic_req()

◆ factorize_symbolic_non_zeros()

◆ factorize_symbolic_col_counts()

◆ factorize_numeric_req()

◆ factorize_numeric()

◆ delete_row_req()

◆ delete_row()

◆ add_row_req()

◆ add_row()

◆ merge_second_col_into_first_req()

◆ merge_second_col_into_first()

◆ rank1_update_req()

◆ rank1_update()