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	detail

Classes
class	BlockCyclicMatrix

Functions
template<typename Array >
BlockCyclicMatrix< typename std::remove_cv_t< Array >::element_type >	array_to_block_cyclic (const Array &array, const blacspp::Grid &grid, size_t MB, size_t NB)
	Convert a dense DistArray to block-cyclic storage format. More...

template<typename Array >
std::remove_cv_t< Array >	block_cyclic_to_array (const BlockCyclicMatrix< typename std::remove_cv_t< Array >::element_type > &matrix, const TiledRange &trange)
	Convert a block-cyclic matrix to DistArray. More...

template<typename Array >
auto	cholesky (const Array &A, TiledRange l_trange=TiledRange(), size_t NB=default_block_size())
	Compute the Cholesky factorization of a HPD rank-2 tensor. More...

template<bool Both, typename Array >
auto	cholesky_linv (const Array &A, TiledRange l_trange=TiledRange(), size_t NB=default_block_size())
	Compute the inverse of the Cholesky factor of an HPD rank-2 tensor. Optionally return the Cholesky factor itself. More...

template<typename Array >
auto	cholesky_solve (const Array &A, const Array &B, TiledRange x_trange=TiledRange(), size_t NB=default_block_size())

template<typename Array >
auto	cholesky_lsolve (Op trans, const Array &A, const Array &B, TiledRange l_trange=TiledRange(), TiledRange x_trange=TiledRange(), size_t NB=default_block_size())

template<typename Array >
auto	heig (const Array &A, TiledRange evec_trange=TiledRange(), size_t NB=default_block_size())
	Solve the standard eigenvalue problem with ScaLAPACK. More...

template<typename ArrayA , typename ArrayB , typename EVecType = ArrayA>
auto	heig (const ArrayA &A, const ArrayB &B, TiledRange evec_trange=TiledRange(), size_t NB=default_block_size())
	Solve the generalized eigenvalue problem with ScaLAPACK. More...

template<typename ArrayA , typename ArrayB >
auto	lu_solve (const ArrayA &A, const ArrayB &B, TiledRange x_trange=TiledRange(), size_t NB=default_block_size(), size_t MB=default_block_size())
	Solve a linear system via LU factorization. More...

template<typename Array >
auto	lu_inv (const Array &A, TiledRange ainv_trange=TiledRange(), size_t NB=default_block_size(), size_t MB=default_block_size())
	Invert a matrix via LU. More...

template<SVD::Vectors Vectors, typename Array >
auto	svd (const Array &A, TiledRange u_trange, TiledRange vt_trange, size_t MB=default_block_size(), size_t NB=default_block_size())
	Compute the singular value decomposition (SVD) via ScaLAPACK. More...

scalapackpp::TransposeFlag	to_scalapackpp_transposeflag (Op t)

template<typename T >
void	zero_triangle (blacspp::Triangle tri, scalapack::BlockCyclicMatrix< T > &A, bool zero_diag=false)

std::size_t	default_block_size ()

void	set_default_block_size (std::size_t NB)

Function Documentation

◆ array_to_block_cyclic()

template<typename Array >

BlockCyclicMatrix<typename std::remove_cv_t<Array>::element_type> TiledArray::math::linalg::scalapack::array_to_block_cyclic	(	const Array &	array,
		const blacspp::Grid &	grid,
		size_t	MB,
		size_t	NB
	)

Convert a dense DistArray to block-cyclic storage format.

Template Parameters

T	Datatype of underlying tile

Parameters

[in]	array	DistArray to be converted to block-cyclic format
[in]	grid	BLACS grid context for block-cyclic matrix
[in]	MB	Row blocking factor of resulting block-cyclic matrix
[in]	NB	Column blocking factor of resulting block-cyclic matrix

Returns: Block-cyclic conversion of input DistArray

Definition at line 308 of file block_cyclic.h.

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◆ block_cyclic_to_array()

template<typename Array >

std::remove_cv_t<Array> TiledArray::math::linalg::scalapack::block_cyclic_to_array	(	const BlockCyclicMatrix< typename std::remove_cv_t< Array >::element_type > &	matrix,
		const TiledRange &	trange
	)

Convert a block-cyclic matrix to DistArray.

Template Parameters

Datatype of underlying tile

Parameters

[in]	matrix	Block-cyclic matrix to convert to DistArray
[in]	trange	Tiled ranges for the resulting DistArray

Returns: DistArray conversion of input block-cyclic matrix

Definition at line 325 of file block_cyclic.h.

◆ cholesky()

template<typename Array >

auto TiledArray::math::linalg::scalapack::cholesky	(	const Array &	A,
		TiledRange	l_trange = `TiledRange()`,
		size_t	NB = `default_block_size()`
	)

Compute the Cholesky factorization of a HPD rank-2 tensor.

A(i,j) = L(i,k) * conj(L(j,k))

Example Usage:

auto L = cholesky(A, ...)

Template Parameters

Array Input array type, must be convertible to BlockCyclicMatrix

Parameters

[in]	A	Input array to be diagonalized. Must be rank-2
[in]	l_trange	TiledRange for resulting Cholesky factor. If left empty, will default to array.trange()
[in]	NB	ScaLAPACK block size. Defaults to 128

Returns: The lower triangular Cholesky factor L in TA format

Definition at line 60 of file cholesky.h.

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◆ cholesky_linv()

template<bool Both, typename Array >

auto TiledArray::math::linalg::scalapack::cholesky_linv	(	const Array &	A,
		TiledRange	l_trange = `TiledRange()`,
		size_t	NB = `default_block_size()`
	)

Compute the inverse of the Cholesky factor of an HPD rank-2 tensor. Optionally return the Cholesky factor itself.

A(i,j) = L(i,k) * conj(L(j,k)) -> compute Linv

Example Usage:

auto Linv = cholesky_Linv(A, ...) auto [L,Linv] = cholesky_Linv<decltype(A),true>(A, ...)

Template Parameters

Array	Input array type, must be convertible to BlockCyclicMatrix
Both	Whether or not to return the cholesky factor

Parameters

[in]	A	Input array to be diagonalized. Must be rank-2
[in]	l_trange	TiledRange for resulting inverse Cholesky factor. If left empty, will default to array.trange()
[in]	NB	ScaLAPACK block size. Defaults to 128

Returns: The inverse lower triangular Cholesky factor in TA format

Definition at line 114 of file cholesky.h.

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◆ cholesky_lsolve()

template<typename Array >

auto TiledArray::math::linalg::scalapack::cholesky_lsolve	(	Op	trans,
		const Array &	A,
		const Array &	B,
		TiledRange	l_trange = `TiledRange()`,
		TiledRange	x_trange = `TiledRange()`,
		size_t	NB = `default_block_size()`
	)

Definition at line 218 of file cholesky.h.

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◆ cholesky_solve()

template<typename Array >

auto TiledArray::math::linalg::scalapack::cholesky_solve	(	const Array &	A,
		const Array &	B,
		TiledRange	x_trange = `TiledRange()`,
		size_t	NB = `default_block_size()`
	)

Definition at line 169 of file cholesky.h.

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◆ default_block_size()

std::size_t TiledArray::math::linalg::scalapack::default_block_size ( )

inline

Definition at line 88 of file util.h.

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◆ heig() [1/2]

template<typename Array >

auto TiledArray::math::linalg::scalapack::heig	(	const Array &	A,
		TiledRange	evec_trange = `TiledRange()`,
		size_t	NB = `default_block_size()`
	)

Solve the standard eigenvalue problem with ScaLAPACK.

A(i,k) X(k,j) = X(i,j) E(j)

Example Usage:

auto [E, X] = heig(A, ...)

Template Parameters

Array Input array type, must be convertible to BlockCyclicMatrix

Parameters

[in]	A	Input array to be diagonalized. Must be rank-2
[in]	evec_trange	TiledRange for resulting eigenvectors. If left empty, will default to array.trange()
[in]	NB	ScaLAPACK block size. Defaults to 128

Returns: A tuple containing the eigenvalues and eigenvectors of input array as std::vector and in TA format, respectively.

Definition at line 59 of file heig.h.

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◆ heig() [2/2]

template<typename ArrayA , typename ArrayB , typename EVecType = ArrayA>

auto TiledArray::math::linalg::scalapack::heig	(	const ArrayA &	A,
		const ArrayB &	B,
		TiledRange	evec_trange = `TiledRange()`,
		size_t	NB = `default_block_size()`
	)

Solve the generalized eigenvalue problem with ScaLAPACK.

A(i,k) X(k,j) = B(i,k) X(k,j) E(j)

with

X(k,i) B(k,l) X(l,j) = I(i,j)

Example Usage:

auto [E, X] = heig(A, B, ...)

Template Parameters

Array Input array type, must be convertible to BlockCyclicMatrix

Parameters

[in]	A	Input array to be diagonalized. Must be rank-2
[in]	B	Metric
[in]	evec_trange	TiledRange for resulting eigenvectors. If left empty, will default to array.trange()
[in]	NB	ScaLAPACK block size. Defaults to 128

Returns: A tuple containing the eigenvalues and eigenvectors of input array as std::vector and in TA format, respectively.

Definition at line 122 of file heig.h.

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◆ lu_inv()

template<typename Array >

auto TiledArray::math::linalg::scalapack::lu_inv	(	const Array &	A,
		TiledRange	ainv_trange = `TiledRange()`,
		size_t	NB = `default_block_size()`,
		size_t	MB = `default_block_size()`
	)

Invert a matrix via LU.

Definition at line 90 of file lu.h.

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◆ lu_solve()

template<typename ArrayA , typename ArrayB >

auto TiledArray::math::linalg::scalapack::lu_solve	(	const ArrayA &	A,
		const ArrayB &	B,
		TiledRange	x_trange = `TiledRange()`,
		size_t	NB = `default_block_size()`,
		size_t	MB = `default_block_size()`
	)

Solve a linear system via LU factorization.

Definition at line 43 of file lu.h.

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◆ set_default_block_size()

void TiledArray::math::linalg::scalapack::set_default_block_size ( std::size_t NB )

inline

Definition at line 92 of file util.h.

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◆ svd()

template<SVD::Vectors Vectors, typename Array >

auto TiledArray::math::linalg::scalapack::svd	(	const Array &	A,
		TiledRange	u_trange,
		TiledRange	vt_trange,
		size_t	MB = `default_block_size()`,
		size_t	NB = `default_block_size()`
	)

Compute the singular value decomposition (SVD) via ScaLAPACK.

A(i,j) = S(k) U(i,k) conj(V(j,k))

Example Usage:

auto S = svd<SVDValuesOnly> (A, ...) auto [S, U] = svd<SVDLeftVectors> (A, ...) auto [S, VT] = svd<SVDRightVectors>(A, ...) auto [S, U, VT] = svd<SVDAllVectors> (A, ...)

Template Parameters

Array Input array type, must be convertible to BlockCyclicMatrix

Parameters

[in]	A	Input array to be decomposed. Must be rank-2
[in]	u_trange	TiledRange for resulting left singular vectors.
[in]	vt_trange	TiledRange for resulting right singular vectors (transposed).
[in]	MB	ScaLAPACK row block size. Defaults to 128
[in]	NB	ScaLAPACK column block size. Defaults to 128

Returns: A tuple containing the eigenvalues and eigenvectors of input array as std::vector and in TA format, respectively.

Definition at line 63 of file svd.h.

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◆ to_scalapackpp_transposeflag()

scalapackpp::TransposeFlag TiledArray::math::linalg::scalapack::to_scalapackpp_transposeflag ( Op t )

inline

Definition at line 36 of file util.h.

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◆ zero_triangle()

template<typename T >

void TiledArray::math::linalg::scalapack::zero_triangle	(	blacspp::Triangle	tri,
		scalapack::BlockCyclicMatrix< T > &	A,
		bool	zero_diag = `false`
	)

Definition at line 50 of file util.h.

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Namespaces

Classes

Functions

Function Documentation

◆ array_to_block_cyclic()

◆ block_cyclic_to_array()

◆ cholesky()

◆ cholesky_linv()

◆ cholesky_lsolve()

◆ cholesky_solve()

◆ default_block_size()

◆ heig() [1/2]

◆ heig() [2/2]

◆ lu_inv()

◆ lu_solve()

◆ set_default_block_size()

◆ svd()

◆ to_scalapackpp_transposeflag()

◆ zero_triangle()