C++ API Reference

hyhound

template<class T = real_t>
using hyhound::MatrixView = guanaqo::MatrixView<T, index_t>

Non-owning view of a dense matrix (column-major storage order with unit inner stride).

Template Parameters:

T – The matrix element type.

template<class T, Config<T> Conf = {}, class UpDown>
void hyhound::update_cholesky(MatrixView<T> L, MatrixView<T> A, UpDown signs, MatrixView<T> Ws = {{}})

Update the Cholesky factorization \( LL^\top = H \) such that the updated factorization satisfies \( \tilde L \tilde L^\top = H + A S A^\top \).

\( S \) is a diagonal matrix with the diagonal elements determined by the signs parameter:

• If signs is of type Update, then \( S = \mathrm{I} \);

• If signs is of type Downdate, then \( S = -\mathrm{I} \);

• If signs is of type UpDowndate, then \( S = \mathrm{diag}(s) \), where \( s = \mathrm{copysign}(1, \texttt{signs.signs}) \), and where signs.signs contains only the values +0.0 and -0.0;

• If signs is of type DownUpdate, then \( S = -\mathrm{diag}(s) \), where \( s = \mathrm{copysign}(1, \texttt{signs.signs}) \), and where signs.signs contains only the values +0.0 and -0.0;

• If signs is of type DiagonalUpDowndate, then \( S = \mathrm{diag}(\texttt{signs.diag}) \).

If \( L \) is a tall matrix, the function also returns a matrix \( \tilde A \) such that \( \tilde L \tilde L^\top + \begin{pmatrix} 0 \\ \tilde A \end{pmatrix} S \begin{pmatrix} 0 & \tilde A^\top \end{pmatrix} = L L^\top + A S A^\top \).

Parameters:

• L – [inout] (k × n, lower trapezoidal) On input, the lower-triangular Cholesky factor \( L \) of \( H \). On output, the lower-triangular Cholesky factor \( \tilde L \) of \( H + A S A^\top \).

• A – [inout] (k × m) On input, the matrix \( A \). On output, the top n rows are overwritten, and the bottom k-n rows contain the matrix \( \tilde A \).

• signs – [in] The update/downdate specification. See above for details.

• Ws – [out] (r × n) If specified, this matrix will contain part of the block Householder representation that was applied to perform the update/downdate, and the top n rows of A will contain the corresponding Householder reflectors. The number of rows r depends on the block size specified by Config::block_size_r.

template<class T, Config<T> Conf = {}, class UpDown>
void hyhound::apply_householder(MatrixView<T> L, MatrixView<T> A, UpDown signs, std::type_identity_t<MatrixView<const T>> B, std::type_identity_t<MatrixView<const T>> Ws)

Apply a block Householder transformation \( \breve Q \), returning \( \begin{pmatrix} \tilde L & \tilde A \end{pmatrix} = \begin{pmatrix} L & A \end{pmatrix} \breve Q \).

Parameters:

• L – [inout] (l × n) On input, the matrix \( L \). On output, the matrix \( \tilde L \).

• A – [inout] (l × m) On input, the matrix \( A \). On output, the matrix \( \tilde A \).

• signs – [in] The update/downdate specification. See update_cholesky for details.

• B – [in] (n × m) The Householder reflectors generated by update_cholesky.

• Ws – [in] (r × n) The upper triangular block Householder representation generated by update_cholesky.

template<class T>
struct Config

Blocking and packing parameters for the update_cholesky and apply_householder functions.

Public Members

index_t block_size_r = detail::DefaultMicroKernelSizes<T>::DefaultSizeR

Block size of the block column of L to process in the micro-kernels.

index_t block_size_s = detail::DefaultMicroKernelSizes<T>::DefaultSizeS

Block size of the block row of L to process in the micro-kernels.

index_t num_blocks_r = 1

Number of block columns per cache block.

index_t prefetch_dist_col_a = 4

Column prefetch distance for the matrix A.

bool enable_packing = true

Enable cache blocking by copying the current block row of A to a temporary buffer.

struct Update

Perform a factorization update, i.e. given the factorization of \( H \), compute the factorization of \( H + A A^\top \).

struct Downdate

Perform a factorization downdate, i.e. given the factorization of \( H \), compute the factorization of \( H - A A^\top \).

template<class T>
struct UpDowndate

Perform a factorization update or downdate, depending on the given signs, i.e. given the factorization of \( H \), compute the factorization of \( H + A S A^\top \), where \( S \) is a diagonal matrix with \( S_{jj} = 1 \) if signs[j] is +0.0, and \( S_{jj} = -1 \) if signs[j] is -0.0. Other values for signs are not allowed.

Public Functions

inline index_t size() const

Public Members

std::span<const T> signs

template<class T>
struct DownUpdate

Perform a factorization downdate or update, depending on the given signs, i.e. given the factorization of \( H \), compute the factorization of \( H - A S A^\top \), where \( S \) is a diagonal matrix with \( S_{jj} = 1 \) if signs[j] is +0.0, and \( S_{jj} = -1 \) if signs[j] is -0.0. Other values for signs are not allowed.

Public Functions

inline index_t size() const

Public Members

std::span<const T> signs

template<class T>
struct DiagonalUpDowndate

Perform a factorization update or downdate with a general diagonal matrix, i.e. given the factorization of \( H \), compute the factorization of \( H + A D A^\top \).

Public Functions

inline index_t size() const

Public Members

std::span<const T> diag

OCP

namespace ocp

Typedefs

using mat = Eigen::MatrixX<real_t>

using vec = Eigen::VectorX<real_t>

Functions

template<class T>
auto vw(T &&t)

void factor(RiccatiFactor &factor, Eigen::Ref<const mat> Sigma)

void update(RiccatiFactor &factor, Eigen::Ref<const mat> DeltaSigma)

void solve(RiccatiFactor &factor)

void factor(SchurFactor &factor, Eigen::Ref<const mat> Sigma)

void update(SchurFactor &factor, Eigen::Ref<const mat> DeltaSigma)

void solve(SchurFactor &factor)

static auto with_signature_matrix(auto &&S)

static void update_schur_rank_one(SchurFactor &factor, index_t j, index_t i, real_t Sigma_ji)

struct OCPDataRiccati

#include <riccati.hpp>

struct RiccatiFactor

#include <riccati.hpp>

struct OCPDataSchur

#include <schur.hpp>

struct SchurFactor

#include <schur.hpp>