num::BandedMatrix Class Reference

Banded matrix with efficient storage for direct solvers. More...

#include <banded.hpp>

Public Member Functions
	BandedMatrix (idx n, idx kl, idx ku)
	Construct a banded matrix.
	BandedMatrix (idx n, idx kl, idx ku, real val)
	Construct with initial value.
	~BandedMatrix ()
	BandedMatrix (const BandedMatrix &)
	BandedMatrix (BandedMatrix &&) noexcept
BandedMatrix &	operator= (const BandedMatrix &)
BandedMatrix &	operator= (BandedMatrix &&) noexcept
idx	size () const
	Matrix dimension.
idx	rows () const
idx	cols () const
idx	kl () const
	Number of lower diagonals.
idx	ku () const
	Number of upper diagonals.
idx	bandwidth () const
	Total bandwidth (kl + ku + 1)
idx	ldab () const
	Leading dimension of band storage (2*kl + ku + 1)
real &	operator() (idx i, idx j)
	Access element at (row, col) in original matrix coordinates.
real	operator() (idx i, idx j) const
real &	band (idx band_row, idx col)
	Direct access to band storage.
real	band (idx band_row, idx col) const
real *	data ()
	Raw pointer to band storage (column-major)
const real *	data () const
bool	in_band (idx i, idx j) const
	Check if (i,j) is within the band.
void	to_gpu ()
void	to_cpu ()
real *	gpu_data ()
const real *	gpu_data () const
bool	on_gpu () const

Detailed Description

Banded matrix with efficient storage for direct solvers.

Uses LAPACK-style band storage format optimized for LU factorization. For a matrix with kl lower diagonals and ku upper diagonals, storage layout is:

• Rows 0 to kl-1: Extra space for fill-in during LU factorization
• Rows kl to kl+ku: Upper diagonals (ku at top, main diagonal at kl+ku)
• Rows kl+ku+1 to 2*kl+ku: Lower diagonals

Element A(i,j) is stored at band(kl + ku + i - j, j) for max(0,j-ku) <= i <= min(n-1,j+kl)

This format enables:

• Column-major access patterns for LU factorization
• SIMD-friendly memory layout
• Direct compatibility with LAPACK routines if needed

Definition at line 32 of file banded.hpp.

Constructor & Destructor Documentation

BandedMatrix() [1/4]

num::BandedMatrix::BandedMatrix	(	idx	n,
		idx	kl,
		idx	ku
	)

Construct a banded matrix.

Parameters

n	Matrix dimension (n x n)
kl	Number of lower diagonals
ku	Number of upper diagonals

Definition at line 20 of file banded.cpp.

BandedMatrix() [2/4]

num::BandedMatrix::BandedMatrix	(	idx	n,
		idx	kl,
		idx	ku,
		real	val
	)

Construct with initial value.

Definition at line 26 of file banded.cpp.

References num::ipow().

~BandedMatrix()

num::BandedMatrix::~BandedMatrix

(

)

Definition at line 31 of file banded.cpp.

References num::cuda::free().

BandedMatrix() [3/4]

num::BandedMatrix::BandedMatrix

(

const BandedMatrix &

other

)

Definition at line 37 of file banded.cpp.

References num::ipow().

BandedMatrix() [4/4]

num::BandedMatrix::BandedMatrix ( BandedMatrix &&  other )

noexcept

Definition at line 44 of file banded.cpp.

References num::ipow().

Member Function Documentation

band() [1/2]

real & num::BandedMatrix::band	(	idx	band_row,
		idx	col
	)

Direct access to band storage.

Parameters

band_row	Row in band storage (0 to ldab-1)
col	Column index (0 to n-1)

Definition at line 84 of file banded.cpp.

References num::ipow().

band() [2/2]

real num::BandedMatrix::band	(	idx	band_row,
		idx	col
	)		const

Definition at line 88 of file banded.cpp.

References num::ipow().

bandwidth()

idx num::BandedMatrix::bandwidth ( ) const

inline

Total bandwidth (kl + ku + 1)

Definition at line 63 of file banded.hpp.

cols()

idx num::BandedMatrix::cols ( ) const

inline

Definition at line 54 of file banded.hpp.

data() [1/2]

real * num::BandedMatrix::data ( )

inline

Raw pointer to band storage (column-major)

Definition at line 82 of file banded.hpp.

data() [2/2]

const real * num::BandedMatrix::data ( ) const

inline

Definition at line 83 of file banded.hpp.

gpu_data() [1/2]

real * num::BandedMatrix::gpu_data ( )

inline

Definition at line 91 of file banded.hpp.

gpu_data() [2/2]

const real * num::BandedMatrix::gpu_data ( ) const

inline

Definition at line 92 of file banded.hpp.

in_band()

bool num::BandedMatrix::in_band	(	idx	i,
		idx	j
	)		const

Check if (i,j) is within the band.

Definition at line 92 of file banded.cpp.

References num::ipow().

kl()

idx num::BandedMatrix::kl ( ) const

inline

Number of lower diagonals.

Definition at line 57 of file banded.hpp.

ku()

idx num::BandedMatrix::ku ( ) const

inline

Number of upper diagonals.

Definition at line 60 of file banded.hpp.

ldab()

idx num::BandedMatrix::ldab ( ) const

inline

Leading dimension of band storage (2*kl + ku + 1)

Definition at line 66 of file banded.hpp.

on_gpu()

bool num::BandedMatrix::on_gpu ( ) const

inline

Definition at line 93 of file banded.hpp.

operator()() [1/2]

real & num::BandedMatrix::operator()	(	idx	i,
		idx	j
	)

Access element at (row, col) in original matrix coordinates.

Parameters

i	Row index (0-based)
j	Column index (0-based)

Returns

Reference to element (undefined if outside band)

Definition at line 76 of file banded.cpp.

References num::ipow().

operator()() [2/2]

real num::BandedMatrix::operator()	(	idx	i,
		idx	j
	)		const

Definition at line 80 of file banded.cpp.

References num::ipow().

operator=() [1/2]

BandedMatrix & num::BandedMatrix::operator= ( BandedMatrix &&  other )

noexcept

Definition at line 63 of file banded.cpp.

References num::cuda::free(), and num::ipow().

operator=() [2/2]

BandedMatrix & num::BandedMatrix::operator=

(

const BandedMatrix &

other

)

Definition at line 51 of file banded.cpp.

References num::cuda::free(), and num::ipow().

rows()

idx num::BandedMatrix::rows ( ) const

inline

Definition at line 53 of file banded.hpp.

size()

idx num::BandedMatrix::size ( ) const

inline

Matrix dimension.

Definition at line 52 of file banded.hpp.

to_cpu()

void num::BandedMatrix::to_cpu

(

)

Definition at line 103 of file banded.cpp.

References num::cuda::to_host().

to_gpu()

void num::BandedMatrix::to_gpu

(

)

Definition at line 96 of file banded.cpp.

References num::cuda::alloc(), and num::cuda::to_device().

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

• /home/runner/work/numerics/numerics/include/linalg/banded/banded.hpp
• /home/runner/work/numerics/numerics/src/linalg/banded/banded.cpp