#include <alpaqa/inner/detail/limited-memory-qr.hpp>

Detailed Description

Incremental QR factorization using modified Gram-Schmidt with reorthogonalization.

Computes A = QR while allowing efficient removal of the first column of A or adding new columns at the end of A.

Definition at line 14 of file limited-memory-qr.hpp.

Collaboration diagram for LimitedMemoryQR:

Public Types
template<class Derived >
using	solve_ret_t = std::conditional_t< Eigen::internal::traits< Derived >::ColsAtCompileTime==1, vec, mat >

Public Member Functions
	LimitedMemoryQR ()=default

	LimitedMemoryQR (size_t n, size_t m)

size_t	n () const

size_t	m () const

template<class VecV >
void	add_column (const VecV &v)
	Add the given column to the right. More...

void	remove_column ()
	Remove the leftmost column. More...

template<class VecB , class VecX >
void	solve_col (const VecB &b, VecX &x) const
	Solve the least squares problem Ax = b. More...

template<class MatB , class MatX >
void	solve (const MatB &B, MatX &X) const
	Solve the least squares problem AX = B. More...

template<class Derived >
solve_ret_t< Derived >	solve (const Eigen::DenseBase< Derived > &B)
	Solve the least squares problem AX = B. More...

const mat &	get_raw_Q () const
	Get the full, raw storage for the orthogonal matrix Q. More...

const mat &	get_raw_R () const
	Get the full, raw storage for the upper triangular matrix R. More...

mat	get_full_R () const
	Get the full storage for the upper triangular matrix R but with the columns in the correct order. More...

mat	get_R () const
	Get the matrix R such that Q times R is the original matrix. More...

mat	get_Q () const
	Get the matrix Q such that Q times R is the original matrix. More...

void	scale_R (real_t scal)
	Multiply the matrix R by a scalar. More...

size_t	get_reorth_count () const
	Get the number of MGS reorthogonalizations. More...

void	clear_reorth_count ()
	Reset the number of MGS reorthogonalizations. More...

void	reset ()
	Reset all indices, clearing the Q and R matrices. More...

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

size_t	num_columns () const
	Get the number of columns that are currently stored. More...

size_t	ring_head () const
	Get the head index of the circular buffer (points to the oldest element). More...

size_t	ring_tail () const
	Get the tail index of the circular buffer (points to one past the most recent element). More...

size_t	ring_next (size_t i) const
	Get the next index in the circular buffer. More...

size_t	ring_prev (size_t i) const
	Get the previous index in the circular buffer. More...

CircularRange< size_t >	ring_iter () const
	Get iterators in the circular buffer. More...

ReverseCircularRange< size_t >	ring_reverse_iter () const
	Get reverse iterators in the circular buffer. More...

Private Member Functions
size_t	r_succ (size_t i) const
	Get the next index in the circular storage for R. More...

size_t	r_pred (size_t i) const
	Get the previous index in the circular storage for R. More...

Private Attributes
mat	Q
	Storage for orthogonal factor Q. More...

mat	R
	Storage for upper triangular factor R. More...

size_t	q_idx = 0
	Number of columns of Q being stored. More...

size_t	r_idx_start = 0
	Index of the first column of R. More...

size_t	r_idx_end = 0
	Index of the one-past-last column of R. More...

size_t	reorth_count = 0
	Number of MGS reorthogonalizations. More...

Member Typedef Documentation

◆ solve_ret_t

using solve_ret_t = std::conditional_t< Eigen::internal::traits<Derived>::ColsAtCompileTime == 1, vec, mat>

Definition at line 154 of file limited-memory-qr.hpp.

Constructor & Destructor Documentation

◆ LimitedMemoryQR() [1/2]

LimitedMemoryQR ( )

default

◆ LimitedMemoryQR() [2/2]

LimitedMemoryQR	(	size_t	n,
		size_t	m
	)

inline

Parameters

n	The size of the vectors, the number of rows of A.
m	The maximum number of columns of A.

The maximum dimensions of Q are n×m and the maximum dimensions of R are m×m.

Definition at line 25 of file limited-memory-qr.hpp.

Member Function Documentation

◆ n()

size_t n ( ) const

inline

Definition at line 27 of file limited-memory-qr.hpp.

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◆ m()

size_t m ( ) const

inline

Definition at line 28 of file limited-memory-qr.hpp.

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◆ add_column()

void add_column ( const VecV & v )

inline

Add the given column to the right.

Definition at line 32 of file limited-memory-qr.hpp.

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◆ remove_column()

void remove_column ( )

inline

Remove the leftmost column.

Definition at line 75 of file limited-memory-qr.hpp.

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◆ solve_col()

void solve_col	(	const VecB &	b,
		VecX &	x
	)		const

inline

Solve the least squares problem Ax = b.

Definition at line 114 of file limited-memory-qr.hpp.

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◆ solve() [1/2]

void solve	(	const MatB &	B,
		MatX &	X
	)		const

inline

Solve the least squares problem AX = B.

Definition at line 141 of file limited-memory-qr.hpp.

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◆ solve() [2/2]

solve_ret_t< Derived > solve ( const Eigen::DenseBase< Derived > & B )

inline

Solve the least squares problem AX = B.

Definition at line 159 of file limited-memory-qr.hpp.

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◆ get_raw_Q()

const mat & get_raw_Q ( ) const

inline

Get the full, raw storage for the orthogonal matrix Q.

Definition at line 166 of file limited-memory-qr.hpp.

◆ get_raw_R()

const mat & get_raw_R ( ) const

inline

Get the full, raw storage for the upper triangular matrix R.

The columns of this matrix are permuted because it's stored as a circular buffer for efficiently appending columns to the end and popping columns from the front.

Definition at line 171 of file limited-memory-qr.hpp.

◆ get_full_R()

mat get_full_R ( ) const

inline

Get the full storage for the upper triangular matrix R but with the columns in the correct order.

Note: Meant for tests only, creates a permuted copy.

Definition at line 176 of file limited-memory-qr.hpp.

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◆ get_R()

mat get_R ( ) const

inline

Get the matrix R such that Q times R is the original matrix.

Note: Meant for tests only, creates a permuted copy.

Definition at line 190 of file limited-memory-qr.hpp.

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◆ get_Q()

mat get_Q ( ) const

inline

Get the matrix Q such that Q times R is the original matrix.

Note: Meant for tests only, creates a copy.

Definition at line 197 of file limited-memory-qr.hpp.

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◆ scale_R()

void scale_R ( real_t scal )

inline

Multiply the matrix R by a scalar.

Definition at line 200 of file limited-memory-qr.hpp.

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◆ get_reorth_count()

size_t get_reorth_count ( ) const

inline

Get the number of MGS reorthogonalizations.

Definition at line 206 of file limited-memory-qr.hpp.

◆ clear_reorth_count()

void clear_reorth_count ( )

inline

Reset the number of MGS reorthogonalizations.

Definition at line 208 of file limited-memory-qr.hpp.

◆ reset()

void reset ( )

inline

Reset all indices, clearing the Q and R matrices.

Definition at line 211 of file limited-memory-qr.hpp.

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◆ resize()

void resize	(	size_t	n,
		size_t	m
	)

inline

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

Causes a reset.

Definition at line 220 of file limited-memory-qr.hpp.

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◆ num_columns()

size_t num_columns ( ) const

inline

Get the number of columns that are currently stored.

Definition at line 227 of file limited-memory-qr.hpp.

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◆ ring_head()

size_t ring_head ( ) const

inline

Get the head index of the circular buffer (points to the oldest element).

Definition at line 230 of file limited-memory-qr.hpp.

◆ ring_tail()

size_t ring_tail ( ) const

inline

Get the tail index of the circular buffer (points to one past the most recent element).

Definition at line 233 of file limited-memory-qr.hpp.

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◆ ring_next()

size_t ring_next ( size_t i ) const

inline

Get the next index in the circular buffer.

Definition at line 235 of file limited-memory-qr.hpp.

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◆ ring_prev()

size_t ring_prev ( size_t i ) const

inline

Get the previous index in the circular buffer.

Definition at line 237 of file limited-memory-qr.hpp.

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◆ ring_iter()

CircularRange< size_t > ring_iter ( ) const

inline

Get iterators in the circular buffer.

Definition at line 240 of file limited-memory-qr.hpp.

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◆ ring_reverse_iter()

ReverseCircularRange< size_t > ring_reverse_iter ( ) const

inline

Get reverse iterators in the circular buffer.

Definition at line 244 of file limited-memory-qr.hpp.

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◆ r_succ()

size_t r_succ ( size_t i ) const

inlineprivate

Get the next index in the circular storage for R.

Definition at line 259 of file limited-memory-qr.hpp.

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◆ r_pred()

size_t r_pred ( size_t i ) const

inlineprivate

Get the previous index in the circular storage for R.

Definition at line 261 of file limited-memory-qr.hpp.

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Member Data Documentation

◆ Q

mat Q

private

Storage for orthogonal factor Q.

Definition at line 249 of file limited-memory-qr.hpp.

◆ R

mat R

private

Storage for upper triangular factor R.

Definition at line 250 of file limited-memory-qr.hpp.

◆ q_idx

size_t q_idx = 0

private

Number of columns of Q being stored.

Definition at line 252 of file limited-memory-qr.hpp.

◆ r_idx_start

size_t r_idx_start = 0

private

Index of the first column of R.

Definition at line 253 of file limited-memory-qr.hpp.

◆ r_idx_end

size_t r_idx_end = 0

private

Index of the one-past-last column of R.

Definition at line 254 of file limited-memory-qr.hpp.

◆ reorth_count

size_t reorth_count = 0

private

Number of MGS reorthogonalizations.

Definition at line 256 of file limited-memory-qr.hpp.

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

limited-memory-qr.hpp

Detailed Description

Public Types

Public Member Functions

Private Member Functions

Private Attributes

Member Typedef Documentation

◆ solve_ret_t

Constructor & Destructor Documentation

◆ LimitedMemoryQR() [1/2]

◆ LimitedMemoryQR() [2/2]

Member Function Documentation

◆ n()

◆ m()

◆ add_column()

◆ remove_column()

◆ solve_col()

◆ solve() [1/2]

◆ solve() [2/2]

◆ get_raw_Q()

◆ get_raw_R()

◆ get_full_R()

◆ get_R()

◆ get_Q()

◆ scale_R()

◆ get_reorth_count()

◆ clear_reorth_count()

◆ reset()

◆ resize()

◆ num_columns()

◆ ring_head()

◆ ring_tail()

◆ ring_next()

◆ ring_prev()

◆ ring_iter()

◆ ring_reverse_iter()

◆ r_succ()

◆ r_pred()

Member Data Documentation

◆ Q

◆ R

◆ q_idx

◆ r_idx_start

◆ r_idx_end

◆ reorth_count