#include <quala/broyden-good.hpp>

Detailed Description

Broyden's “Good” method for solving systems of nonlinear equations \( F(x) = 0 \).

\[ \begin{aligned} B_{k+1} &= B_k + \frac{\left(y_k - B_k s_k\right) s_k^\top} {s_k^\top s_k} \\ H_{k+1} &= H_k + \frac{\left(s_k - H_k y_k\right) \left(s_k^\top H_k\right)} {s_k^\top H_k y_k} \\ s_k &\triangleq x_{k+1} - x_k \\ y_k &\triangleq F(x_{k+1}) - F(x_k) \\ \end{aligned} \]

Where \( B_k \) approximates the Jacobian of \( F(x_k) \) and \( H_k \triangleq B_k^{-1} \).

Todo:: Damping.

Definition at line 83 of file broyden-good.hpp.

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Public Types
using	Params = BroydenGoodParams

Public Member Functions
	BroydenGood (Params params)

	BroydenGood (Params params, length_t n)

template<class VecS , class VecY >
bool	update_sy (const anymat< VecS > &s, const anymat< VecY > &y, bool forced=false)
	Update the inverse Jacobian approximation using the new vectors sₖ = xₖ₊₁ - xₖ and yₖ = pₖ₊₁ - pₖ. More...

bool	update (crvec xₖ, crvec xₙₑₓₜ, crvec pₖ, crvec pₙₑₓₜ, bool forced=false)
	Update the inverse Jacobian approximation using the new vectors xₖ₊₁ and pₖ₊₁. More...

bool	apply (rvec q, real_t γ)
	Apply the inverse Jacobian approximation to the given vector q, i.e. More...

void	reset ()
	Throw away the approximation and all previous vectors s and y. More...

void	resize (length_t n)
	Re-allocate storage for a problem with a different size. More...

const Params &	get_params () const
	Get the parameters. More...

length_t	n () const
	Get the size of the s and y vectors in the buffer. More...

length_t	history () const
	Get the number of previous vectors s and y stored in the buffer. More...

index_t	succ (index_t i) const
	Get the next index in the circular buffer of previous s and y vectors. More...

index_t	pred (index_t i) const
	Get the previous index in the circular buffer of s and y vectors. More...

length_t	current_history () const
	Get the number of previous s and y vectors currently stored in the buffer. More...

auto	s (index_t i)

auto	s (index_t i) const

auto	s̃ (index_t i)

auto	s̃ (index_t i) const

template<class F >
void	foreach_fwd (const F &fun) const
	Iterate over the indices in the history buffer, oldest first. More...

template<class F >
void	foreach_rev (const F &fun) const
	Iterate over the indices in the history buffer, newest first. More...

Private Attributes
BroydenStorage	sto

index_t	idx = 0

bool	full = false

Params	params

real_t	latest_γ = NaN

Member Typedef Documentation

◆ Params

using Params = BroydenGoodParams

Definition at line 85 of file broyden-good.hpp.

Constructor & Destructor Documentation

◆ BroydenGood() [1/2]

BroydenGood ( Params params )

inline

Definition at line 87 of file broyden-good.hpp.

◆ BroydenGood() [2/2]

BroydenGood	(	Params	params,
		length_t	n
	)

inline

Definition at line 88 of file broyden-good.hpp.

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Member Function Documentation

◆ update_sy()

bool update_sy	(	const anymat< VecS > &	s,
		const anymat< VecY > &	y,
		bool	forced = `false`
	)

Update the inverse Jacobian approximation using the new vectors sₖ = xₖ₊₁ - xₖ and yₖ = pₖ₊₁ - pₖ.

Definition at line 177 of file broyden-good.hpp.

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◆ update()

bool update	(	crvec	xₖ,
		crvec	xₙₑₓₜ,
		crvec	pₖ,
		crvec	pₙₑₓₜ,
		bool	forced = `false`
	)

inline

Update the inverse Jacobian approximation using the new vectors xₖ₊₁ and pₖ₊₁.

Definition at line 243 of file broyden-good.hpp.

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◆ apply()

bool apply	(	rvec	q,
		real_t	γ
	)

inline

Apply the inverse Jacobian approximation to the given vector q, i.e.

\( q \leftarrow H_k q \). Initial inverse Hessian approximation is set to \( H_0 = \gamma I \). The result is scaled by a factor γ. If γ is negative, the result is scaled by \( \frac{s^\top y}{y^\top y} \).

Definition at line 224 of file broyden-good.hpp.

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◆ reset()

void reset ( )

inline

Throw away the approximation and all previous vectors s and y.

Definition at line 164 of file broyden-good.hpp.

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◆ resize()

void resize ( length_t n )

inline

Re-allocate storage for a problem with a different size.

Causes a reset.

Definition at line 169 of file broyden-good.hpp.

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◆ get_params()

const Params & get_params ( ) const

inline

Get the parameters.

Definition at line 115 of file broyden-good.hpp.

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◆ n()

length_t n ( ) const

inline

Get the size of the s and y vectors in the buffer.

Definition at line 118 of file broyden-good.hpp.

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◆ history()

length_t history ( ) const

inline

Get the number of previous vectors s and y stored in the buffer.

Definition at line 120 of file broyden-good.hpp.

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◆ succ()

index_t succ ( index_t i ) const

inline

Get the next index in the circular buffer of previous s and y vectors.

Definition at line 122 of file broyden-good.hpp.

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◆ pred()

index_t pred ( index_t i ) const

inline

Get the previous index in the circular buffer of s and y vectors.

Definition at line 124 of file broyden-good.hpp.

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◆ current_history()

length_t current_history ( ) const

inline

Get the number of previous s and y vectors currently stored in the buffer.

Definition at line 127 of file broyden-good.hpp.

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◆ s() [1/2]

auto s ( index_t i )

inline

Definition at line 129 of file broyden-good.hpp.

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◆ s() [2/2]

auto s ( index_t i ) const

inline

Definition at line 130 of file broyden-good.hpp.

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◆ s̃() [1/2]

auto s̃ ( index_t i )

inline

Definition at line 131 of file broyden-good.hpp.

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◆ s̃() [2/2]

auto s̃ ( index_t i ) const

inline

Definition at line 132 of file broyden-good.hpp.

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◆ foreach_fwd()

void foreach_fwd ( const F & fun ) const

inline

Iterate over the indices in the history buffer, oldest first.

Definition at line 136 of file broyden-good.hpp.

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◆ foreach_rev()

void foreach_rev ( const F & fun ) const

inline

Iterate over the indices in the history buffer, newest first.

Definition at line 147 of file broyden-good.hpp.

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Member Data Documentation

◆ sto

BroydenStorage sto

private

Definition at line 157 of file broyden-good.hpp.

◆ idx

index_t idx = 0

private

Definition at line 158 of file broyden-good.hpp.

◆ full

bool full = false

private

Definition at line 159 of file broyden-good.hpp.

◆ params

Params params

private

Definition at line 160 of file broyden-good.hpp.

◆ latest_γ

real_t latest_γ = NaN

private

Definition at line 161 of file broyden-good.hpp.

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

broyden-good.hpp

Detailed Description

Public Types

Public Member Functions

Private Attributes

Member Typedef Documentation

◆ Params

Constructor & Destructor Documentation

◆ BroydenGood() [1/2]

◆ BroydenGood() [2/2]

Member Function Documentation

◆ update_sy()

◆ update()

◆ apply()

◆ reset()

◆ resize()

◆ get_params()

◆ n()

◆ history()

◆ succ()

◆ pred()

◆ current_history()

◆ s() [1/2]

◆ s() [2/2]

◆ s̃() [1/2]

◆ s̃() [2/2]

◆ foreach_fwd()

◆ foreach_rev()

Member Data Documentation

◆ sto

◆ idx

◆ full

◆ params

◆ latest_γ