Functions
template<typename Tile , typename Policy >
auto	rank_local_cholesky (const DistArray< Tile, Policy > &A)

template<typename Array , typename = std::enable_if_t<TiledArray::detail::is_array_v<Array>>>
auto	cholesky (const Array &A, TiledRange l_trange=TiledRange())
	Compute the Cholesky factorization of a HPD rank-2 tensor. More...

template<typename ContiguousTensor , typename = std::enable_if_t< TiledArray::detail::is_contiguous_tensor_v<ContiguousTensor>>>
auto	cholesky (const ContiguousTensor &A)
	Compute the Cholesky factorization of a HPD rank-2 tensor. More...

template<bool Both, typename Array , typename = std::enable_if_t<TiledArray::detail::is_array_v<Array>>>
auto	cholesky_linv (const Array &A, TiledRange l_trange=TiledRange())
	Compute the inverse of the Cholesky factor of an HPD rank-2 tensor. Optionally return the Cholesky factor itself. More...

template<typename Array , typename = std::enable_if_t<TiledArray::detail::is_array_v<Array>>>
auto	cholesky_solve (const Array &A, const Array &B, TiledRange x_trange=TiledRange())

template<typename Array , typename = std::enable_if_t<TiledArray::detail::is_array_v<Array>>>
auto	cholesky_lsolve (Op transpose, const Array &A, const Array &B, TiledRange l_trange=TiledRange(), TiledRange x_trange=TiledRange())

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

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

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

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

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

Function Documentation

◆ cholesky() [1/2]

template<typename Array , typename = std::enable_if_t<TiledArray::detail::is_array_v<Array>>>

auto TiledArray::math::linalg::non_distributed::cholesky	(	const Array &	A,
		TiledRange	l_trange = `TiledRange()`
	)

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 a DistArray type (i.e., is_array_v<Array> is true)

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()

Returns: The lower triangular Cholesky factor L in TA format

Note: this is a collective operation with respect to the world of A

Definition at line 72 of file cholesky.h.

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◆ cholesky() [2/2]

template<typename ContiguousTensor , typename = std::enable_if_t< TiledArray::detail::is_contiguous_tensor_v<ContiguousTensor>>>

auto TiledArray::math::linalg::non_distributed::cholesky ( const ContiguousTensor & A )

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

ContiguousTensor a contiguous tensor type (i.e., is_contiguous_tensor_v<ContiguousTensor> is true)

Parameters

[in] A Input array to be diagonalized. Must be rank-2

Returns: The lower triangular Cholesky factor L as a ContiguousTensor

Note: this is a non-collective operation, only computes on the rank on which invoked

Definition at line 99 of file cholesky.h.

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◆ cholesky_linv()

template<bool Both, typename Array , typename = std::enable_if_t<TiledArray::detail::is_array_v<Array>>>

auto TiledArray::math::linalg::non_distributed::cholesky_linv	(	const Array &	A,
		TiledRange	l_trange = `TiledRange()`
	)

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	a DistArray type (i.e., `is_array_v<Array>` is true)
RetL	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()

Returns: The inverse lower triangular Cholesky factor in TA format

Note: this is a collective operation with respect to the world of A

Definition at line 129 of file cholesky.h.

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◆ cholesky_lsolve()

template<typename Array , typename = std::enable_if_t<TiledArray::detail::is_array_v<Array>>>

auto TiledArray::math::linalg::non_distributed::cholesky_lsolve	(	Op	transpose,
		const Array &	A,
		const Array &	B,
		TiledRange	l_trange = `TiledRange()`,
		TiledRange	x_trange = `TiledRange()`
	)

Definition at line 176 of file cholesky.h.

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◆ cholesky_solve()

template<typename Array , typename = std::enable_if_t<TiledArray::detail::is_array_v<Array>>>

auto TiledArray::math::linalg::non_distributed::cholesky_solve	(	const Array &	A,
		const Array &	B,
		TiledRange	x_trange = `TiledRange()`
	)

Definition at line 156 of file cholesky.h.

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◆ heig() [1/2]

template<typename Array >

auto TiledArray::math::linalg::non_distributed::heig	(	const Array &	A,
		TiledRange	evec_trange = `TiledRange()`
	)

Solve the standard eigenvalue problem with LAPACK.

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

Example Usage:

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

Template Parameters

Array Input array type

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()

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

Definition at line 54 of file heig.h.

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◆ heig() [2/2]

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

auto TiledArray::math::linalg::non_distributed::heig	(	const ArrayA &	A,
		const ArrayB &	B,
		TiledRange	evec_trange = `TiledRange()`
	)

Solve the generalized eigenvalue problem with LAPACK.

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

Parameters

[in]	A	Input array to be diagonalized. Must be rank-2
[in]	B	Positive-definite matrix
[in]	evec_trange	TiledRange for resulting eigenvectors. If left empty, will default to array.trange()

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

Definition at line 95 of file heig.h.

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◆ lu_inv()

template<typename Array >

auto TiledArray::math::linalg::non_distributed::lu_inv	(	const Array &	A,
		TiledRange	ainv_trange = `TiledRange()`
	)

Invert a matrix via LU.

Definition at line 58 of file lu.h.

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◆ lu_solve()

template<typename ArrayA , typename ArrayB >

auto TiledArray::math::linalg::non_distributed::lu_solve	(	const ArrayA &	A,
		const ArrayB &	B,
		TiledRange	x_trange = `TiledRange()`
	)

Solve a linear system via LU factorization.

Definition at line 40 of file lu.h.

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◆ rank_local_cholesky()

template<typename Tile , typename Policy >

auto TiledArray::math::linalg::non_distributed::rank_local_cholesky ( const DistArray< Tile, Policy > & A )

Definition at line 36 of file cholesky.h.

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◆ svd()

template<SVD::Vectors Vectors, typename Array >

auto TiledArray::math::linalg::non_distributed::svd	(	const Array &	A,
		TiledRange	u_trange = `TiledRange()`,
		TiledRange	vt_trange = `TiledRange()`
	)

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<SVDLeftstd::vectors> (A, ...) auto [S, VT] = svd<SVDRightstd::vectors>(A, ...) auto [S, U, VT] = svd<SVDAllstd::vectors> (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).

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 svd.h.

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Functions

Function Documentation

◆ cholesky() [1/2]

◆ cholesky() [2/2]

◆ cholesky_linv()

◆ cholesky_lsolve()

◆ cholesky_solve()

◆ heig() [1/2]

◆ heig() [2/2]

◆ lu_inv()

◆ lu_solve()

◆ rank_local_cholesky()

◆ svd()