alpaqa::sets Namespace Reference

Classes
struct	Box

Functions
template<Config Conf>
Conf::real_t	alpaqa_tag_invoke (tag_t< alpaqa::prox >, Box< Conf > &self, typename Conf::crmat in, typename Conf::rmat out, typename Conf::real_t γ)
template<Config Conf>
Conf::real_t	alpaqa_tag_invoke (tag_t< alpaqa::prox_step >, Box< Conf > &self, typename Conf::crmat in, typename Conf::crmat fwd_step, typename Conf::rmat out, typename Conf::rmat fb_step, typename Conf::real_t γ, typename Conf::real_t γ_fwd)
template<Config Conf>
auto	project (const auto &v, const Box< Conf > &box)
	Project a vector onto a box.
template<Config Conf>
auto	projecting_difference (const auto &v, const Box< Conf > &box)
	Get the difference between the given vector and its projection.
template<Config Conf>
auto	dist_squared (const auto &v, const Box< Conf > &box)
	Get the distance squared between the given vector and its projection.
template<Config Conf>
auto	dist_squared (const auto &v, const Box< Conf > &box, const auto &Σ) -> real_t< Conf >
	Get the distance squared between the given vector and its projection in the Σ norm.

Function Documentation

alpaqa_tag_invoke() [1/2]

template<Config Conf>

Conf::real_t alpaqa_tag_invoke	(	tag_t< alpaqa::prox >	,
		Box< Conf > &	self,
		typename Conf::crmat	in,
		typename Conf::rmat	out,
		typename Conf::real_t	γ
	)

Definition at line 12 of file indicator-box.hpp.

alpaqa_tag_invoke() [2/2]

template<Config Conf>

Conf::real_t alpaqa_tag_invoke	(	tag_t< alpaqa::prox_step >	,
		Box< Conf > &	self,
		typename Conf::crmat	in,
		typename Conf::crmat	fwd_step,
		typename Conf::rmat	out,
		typename Conf::rmat	fb_step,
		typename Conf::real_t	γ,
		typename Conf::real_t	γ_fwd
	)

Definition at line 29 of file indicator-box.hpp.

project()

template<Config Conf>

auto project ( const auto &  v, const Box< Conf > &  box  )

inline

Project a vector onto a box.

$${\mathrm{\Pi }}_C(v)$$

Parameters

[in]	v	The vector to project
[in]	box	The box to project onto

Definition at line 37 of file box.hpp.

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projecting_difference()

template<Config Conf>

auto projecting_difference ( const auto &  v, const Box< Conf > &  box  )

inline

Get the difference between the given vector and its projection.

$$v-{\mathrm{\Pi }}_C(v)$$

Warning

Beware catastrophic cancellation!

Parameters

[in]	v	The vector to project
[in]	box	The box to project onto

Definition at line 48 of file box.hpp.

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dist_squared() [1/2]

template<Config Conf>

auto dist_squared ( const auto &  v, const Box< Conf > &  box  )

inline

Get the distance squared between the given vector and its projection.

$${\Vert v-{\mathrm{\Pi }}_C(v)\Vert }_2^2$$

Warning

Beware catastrophic cancellation!

Parameters

[in]	v	The vector to project
[in]	box	The box to project onto

Definition at line 59 of file box.hpp.

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dist_squared() [2/2]

template<Config Conf>

auto dist_squared ( const auto &  v, const Box< Conf > &  box, const auto &  Σ  ) -> real_t<Conf>

inline

Get the distance squared between the given vector and its projection in the Σ norm.

$${\Vert v-{\mathrm{\Pi }}_C(v)\Vert }_{\mathrm{\Sigma }}^2={(v-{\mathrm{\Pi }}_C(v))}^{\mathrm{\top }}\mathrm{\Sigma }(v-{\mathrm{\Pi }}_C(v))$$

Warning

Beware catastrophic cancellation!

Parameters

[in]	v	The vector to project
[in]	box	The box to project onto
[in]	Σ	Diagonal matrix defining norm

Definition at line 71 of file box.hpp.

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