Workspace queries for routines that require a temporary workspace to perform their computations. More...

Functions
template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_SVECTOR vector_t, enable_if_t< is_complex< type_t< vector_t > >, int > >
WorkInfo	tlapack::aggressive_early_deflation_worksize (bool want_t, bool want_z, size_type< matrix_t > ilo, size_type< matrix_t > ihi, size_type< matrix_t > nw, const matrix_t &A, const vector_t &s, const matrix_t &Z, const size_type< matrix_t > &ns, const size_type< matrix_t > &nd, const FrancisOpts &opts)
	Worspace query of aggressive_early_deflation().

template<class T , TLAPACK_SMATRIX matrix_t>
constexpr WorkInfo	tlapack::internal::aggressive_early_deflation_worksize_gehrd (size_type< matrix_t > ilo, size_type< matrix_t > ihi, size_type< matrix_t > nw, const matrix_t &A)
	Workspace query for gehrd() in aggressive_early_deflation().

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_SVECTOR vector_t>
constexpr WorkInfo	tlapack::bidiag_worksize (const matrix_t &A, const vector_t &tauv, const vector_t &tauw, const BidiagOpts &opts={})
	Worspace query of bidiag()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_VECTOR vector_t>
constexpr WorkInfo	tlapack::gebd2_worksize (const matrix_t &A, const vector_t &tauv, const vector_t &tauw)
	Worspace query of gebd2().

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_SVECTOR vector_t>
constexpr WorkInfo	tlapack::gebrd_worksize (const matrix_t &A, const vector_t &tauq, const vector_t &taup, const GebrdOpts &opts={})
	Worspace query of gebrd()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_VECTOR vector_t>
constexpr WorkInfo	tlapack::gehd2_worksize (size_type< matrix_t > ilo, size_type< matrix_t > ihi, const matrix_t &A, const vector_t &tau)
	Worspace query of gehd2()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_SVECTOR vector_t>
constexpr WorkInfo	tlapack::gehrd_worksize (size_type< matrix_t > ilo, size_type< matrix_t > ihi, const matrix_t &A, const vector_t &tau, const GehrdOpts &opts={})
	Worspace query of gehrd()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_VECTOR vector_t>
constexpr WorkInfo	tlapack::gelq2_worksize (const matrix_t &A, const vector_t &tauw)
	Worspace query of gelq2()

template<class T , TLAPACK_SMATRIX A_t, TLAPACK_SVECTOR tau_t>
constexpr WorkInfo	tlapack::gelqf_worksize (const A_t &A, const tau_t &tau, const GelqfOpts &opts={})
	Worspace query of gelqf()

template<class T , TLAPACK_SMATRIX matrix_t>
constexpr WorkInfo	tlapack::gelqt_worksize (const matrix_t &A, const matrix_t &TT)
	Worspace query of gelqt()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_VECTOR vector_t, TLAPACK_DIRECTION direction_t, TLAPACK_STOREV storage_t>
constexpr WorkInfo	tlapack::gen_householder_q_worksize (direction_t direction, storage_t storeMode, const matrix_t &A, const vector_t &tau, const GenHouseholderQOpts &opts={})
	Worspace query of gen_householder_q()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_VECTOR vector_t>
constexpr WorkInfo	tlapack::geql2_worksize (const matrix_t &A, const vector_t &tau)
	Worspace query of geql2()

template<class T , TLAPACK_SMATRIX A_t, TLAPACK_SVECTOR tau_t>
constexpr WorkInfo	tlapack::geqlf_worksize (const A_t &A, const tau_t &tau, const GeqlfOpts &opts={})
	Worspace query of geqlf()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_VECTOR vector_t>
constexpr WorkInfo	tlapack::geqr2_worksize (const matrix_t &A, const vector_t &tau)
	Worspace query of geqr2()

template<class T , TLAPACK_SMATRIX A_t, TLAPACK_SVECTOR tau_t>
constexpr WorkInfo	tlapack::geqrf_worksize (const A_t &A, const tau_t &tau, const GeqrfOpts &opts={})
	Worspace query of geqrf()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_VECTOR vector_t>
constexpr WorkInfo	tlapack::gerq2_worksize (const matrix_t &A, const vector_t &tau)
	Worspace query of gerq2()

template<class T , TLAPACK_SMATRIX A_t, TLAPACK_SVECTOR tau_t>
constexpr WorkInfo	tlapack::gerqf_worksize (const A_t &A, const tau_t &tau, const GerqfOpts &opts={})
	Worspace query of gerqf()

template<class T , TLAPACK_SMATRIX matrix_t>
constexpr WorkInfo	tlapack::getri_uxli_worksize (const matrix_t &A)
	Worspace query of getri()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_VECTOR piv_t>
constexpr WorkInfo	tlapack::getri_worksize (const matrix_t &A, const piv_t &piv, const GetriOpts &opts={})
	Worspace query of getri()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_SVECTOR vector_t>
constexpr WorkInfo	tlapack::hessenberg_worksize (size_type< matrix_t > ilo, size_type< matrix_t > ihi, const matrix_t &A, const vector_t &tau, const HessenbergOpts &opts={})
	Workspace query of hessenberg()

template<class T , TLAPACK_MATRIX matrix_t, TLAPACK_VECTOR vector_t>
constexpr WorkInfo	tlapack::householder_lq_worksize (const matrix_t &A, const vector_t &tau, const HouseholderLQOpts &opts={})
	Worspace query of householder_lq()

template<class T , TLAPACK_SMATRIX matrixV_t, TLAPACK_SMATRIX matrixC_t, TLAPACK_SVECTOR vector_t, TLAPACK_SIDE side_t, TLAPACK_OP trans_t, TLAPACK_DIRECTION direction_t, TLAPACK_STOREV storage_t>
constexpr WorkInfo	tlapack::householder_q_mul_worksize (side_t side, trans_t trans, direction_t direction, storage_t storeMode, const matrixV_t &V, const vector_t &tau, const matrixC_t &C, const HouseholderQMulOpts &opts={})
	Workspace query of householder_q_mul()

template<class T , TLAPACK_MATRIX matrix_t, TLAPACK_VECTOR vector_t>
constexpr WorkInfo	tlapack::householder_ql_worksize (const matrix_t &A, const vector_t &tau, const HouseholderQLOpts &opts={})
	Worspace query of householder_ql()

template<class T , TLAPACK_MATRIX matrix_t, TLAPACK_VECTOR vector_t>
constexpr WorkInfo	tlapack::householder_qr_worksize (const matrix_t &A, const vector_t &tau, const HouseholderQROpts &opts={})
	Worspace query of householder_qr()

template<class T , TLAPACK_MATRIX matrix_t, TLAPACK_VECTOR vector_t>
constexpr WorkInfo	tlapack::householder_rq_worksize (const matrix_t &A, const vector_t &tau, const HouseholderRQOpts &opts={})
	Worspace query of householder_rq()

template<class T , TLAPACK_MATRIX matrix_t>
constexpr WorkInfo	tlapack::infnorm_colmajor_worksize (const matrix_t &A)
	Worspace query of infnorm_colmajor()

template<class T , TLAPACK_UPLO uplo_t, TLAPACK_MATRIX matrix_t>
constexpr WorkInfo	tlapack::infnorm_hermitian_colmajor_worksize (uplo_t uplo, const matrix_t &A)
	Worspace query of infnorm_hermitian_colmajor()

template<class T , TLAPACK_UPLO uplo_t, TLAPACK_MATRIX matrix_t>
constexpr WorkInfo	tlapack::infnorm_symmetric_colmajor_worksize (uplo_t uplo, const matrix_t &A)
	Worspace query of infnorm_symmetric_colmajor()

template<class T , TLAPACK_UPLO uplo_t, TLAPACK_DIAG diag_t, TLAPACK_MATRIX matrix_t>
constexpr WorkInfo	tlapack::infnorm_triangular_colmajor_worksize (uplo_t uplo, diag_t diag, const matrix_t &A)
	Worspace query of infnorm_triangular_colmajor()

template<class T , TLAPACK_SIDE side_t, TLAPACK_DIRECTION direction_t, TLAPACK_STOREV storage_t, TLAPACK_SVECTOR vector_t, TLAPACK_SCALAR tau_t, TLAPACK_SMATRIX matrix_t, enable_if_t< std::is_convertible_v< direction_t, Direction >, int > = 0>
constexpr WorkInfo	tlapack::larf_worksize (side_t side, direction_t direction, storage_t storeMode, vector_t const &v, const tau_t &tau, const matrix_t &C)
	Worspace query of larf().

template<class T , TLAPACK_SIDE side_t, TLAPACK_STOREV storage_t, TLAPACK_VECTOR vector_t, TLAPACK_SCALAR tau_t, TLAPACK_VECTOR vectorC0_t, TLAPACK_MATRIX matrixC1_t, enable_if_t< std::is_convertible_v< storage_t, StoreV >, int > = 0>
constexpr WorkInfo	tlapack::larf_worksize (side_t side, storage_t storeMode, vector_t const &x, const tau_t &tau, const vectorC0_t &C0, const matrixC1_t &C1)
	Worspace query of larf().

template<class T , TLAPACK_SMATRIX matrixV_t, TLAPACK_MATRIX matrixT_t, TLAPACK_SMATRIX matrixC_t, TLAPACK_SIDE side_t, TLAPACK_OP trans_t, TLAPACK_DIRECTION direction_t, TLAPACK_STOREV storage_t>
constexpr WorkInfo	tlapack::larfb_worksize (side_t side, trans_t trans, direction_t direction, storage_t storeMode, const matrixV_t &V, const matrixT_t &Tmatrix, const matrixC_t &C)
	Worspace query of larfb()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_VECTOR vector_t, enable_if_t< is_complex< type_t< vector_t > >, bool > = true>
constexpr WorkInfo	tlapack::multishift_QR_sweep_worksize (bool want_t, bool want_z, size_type< matrix_t > ilo, size_type< matrix_t > ihi, const matrix_t &A, const vector_t &s, const matrix_t &Z)
	Worspace query of multishift_QR_sweep()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_SVECTOR vector_t, enable_if_t< is_complex< type_t< vector_t > >, int > = 0>
WorkInfo	tlapack::multishift_qr_worksize (bool want_t, bool want_z, size_type< matrix_t > ilo, size_type< matrix_t > ihi, const matrix_t &A, const vector_t &w, const matrix_t &Z, const FrancisOpts &opts)
	Worspace query of multishift_qr()

template<class T , TLAPACK_MATRIX matrix_t, TLAPACK_VECTOR vector_t, enable_if_t< is_complex< type_t< vector_t > >, int > = 0>
constexpr WorkInfo	tlapack::qr_iteration_worksize (bool want_t, bool want_z, size_type< matrix_t > ilo, size_type< matrix_t > ihi, const matrix_t &A, const vector_t &w, const matrix_t &Z, const QRIterationOpts &opts={})
	Worspace query of qr_iteration()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_VECTOR vector_t>
constexpr WorkInfo	tlapack::ung2l_worksize (const matrix_t &A, const vector_t &tau)
	Worspace query of ung2l()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_VECTOR vector_t>
constexpr WorkInfo	tlapack::ung2r_worksize (const matrix_t &A, const vector_t &tau)
	Worspace query of ung2r()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_SVECTOR vector_t>
constexpr WorkInfo	tlapack::ungbr_p_worksize (const size_type< matrix_t > k, matrix_t &A, const vector_t &tau, const UngbrOpts &opts={})
	Worspace query of ungbr_p()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_SVECTOR vector_t>
constexpr WorkInfo	tlapack::ungbr_q_worksize (const size_type< matrix_t > k, matrix_t &A, const vector_t &tau, const UngbrOpts &opts={})
	Worspace query of ungbr_q()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_SVECTOR vector_t>
constexpr WorkInfo	tlapack::unghr_worksize (size_type< matrix_t > ilo, size_type< matrix_t > ihi, const matrix_t &A, const vector_t &tau)
	Worspace query of unghr()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_VECTOR vector_t>
constexpr WorkInfo	tlapack::ungl2_worksize (const matrix_t &Q, const vector_t &tauw)
	Worspace query of ungl2()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_SVECTOR vector_t, TLAPACK_DIRECTION direction_t, TLAPACK_STOREV storage_t>
constexpr WorkInfo	tlapack::ungq_level2_worksize (direction_t direction, storage_t storeMode, const matrix_t &A, const vector_t &tau)
	Worspace query of ungq_level2()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_SVECTOR vector_t, TLAPACK_DIRECTION direction_t, TLAPACK_STOREV storage_t>
constexpr WorkInfo	tlapack::ungq_worksize (direction_t direction, storage_t storeMode, const matrix_t &A, const vector_t &tau, const UngqOpts &opts={})
	Worspace query of ungq()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_VECTOR vector_t>
constexpr WorkInfo	tlapack::ungr2_worksize (const matrix_t &A, const vector_t &tau)
	Worspace query of ungr2()

template<class T , TLAPACK_SMATRIX matrixA_t, TLAPACK_SMATRIX matrixC_t, TLAPACK_VECTOR tau_t, TLAPACK_SIDE side_t, TLAPACK_OP trans_t>
constexpr WorkInfo	tlapack::unm2l_worksize (side_t side, trans_t trans, const matrixA_t &A, const tau_t &tau, const matrixC_t &C)
	Worspace query of unm2l()

template<class T , TLAPACK_SMATRIX matrixA_t, TLAPACK_SMATRIX matrixC_t, TLAPACK_VECTOR tau_t, TLAPACK_SIDE side_t, TLAPACK_OP trans_t>
constexpr WorkInfo	tlapack::unm2r_worksize (side_t side, trans_t trans, const matrixA_t &A, const tau_t &tau, const matrixC_t &C)
	Worspace query of unm2r()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_SVECTOR vector_t>
constexpr WorkInfo	tlapack::unmhr_worksize (Side side, Op trans, size_type< matrix_t > ilo, size_type< matrix_t > ihi, const matrix_t &A, const vector_t &tau, const matrix_t &C)
	Worspace query of unmhr()

template<class T , TLAPACK_SMATRIX matrixA_t, TLAPACK_SMATRIX matrixC_t, TLAPACK_VECTOR tau_t, TLAPACK_SIDE side_t, TLAPACK_OP trans_t>
constexpr WorkInfo	tlapack::unml2_worksize (side_t side, trans_t trans, const matrixA_t &A, const tau_t &tau, const matrixC_t &C)
	Worspace query of unml2()

template<class T , TLAPACK_SMATRIX matrixA_t, TLAPACK_SMATRIX matrixC_t, TLAPACK_SVECTOR tau_t, TLAPACK_SIDE side_t, TLAPACK_OP trans_t>
constexpr WorkInfo	tlapack::unmlq_worksize (side_t side, trans_t trans, const matrixA_t &A, const tau_t &tau, const matrixC_t &C, const UnmlqOpts &opts={})
	Worspace query of unmlq()

template<class T , TLAPACK_SMATRIX matrixV_t, TLAPACK_SMATRIX matrixC_t, TLAPACK_VECTOR vector_t, TLAPACK_SIDE side_t, TLAPACK_OP trans_t, TLAPACK_DIRECTION direction_t, TLAPACK_STOREV storage_t>
constexpr WorkInfo	tlapack::unmq_level2_worksize (side_t side, trans_t trans, direction_t direction, storage_t storeMode, const matrixV_t &V, const vector_t &tau, const matrixC_t &C)
	Worspace query of unmq_level2()

template<class T , TLAPACK_SMATRIX matrixV_t, TLAPACK_SMATRIX matrixC_t, TLAPACK_SVECTOR vector_t, TLAPACK_SIDE side_t, TLAPACK_OP trans_t, TLAPACK_DIRECTION direction_t, TLAPACK_STOREV storage_t>
constexpr WorkInfo	tlapack::unmq_worksize (side_t side, trans_t trans, direction_t direction, storage_t storeMode, const matrixV_t &V, const vector_t &tau, const matrixC_t &C, const UnmqOpts &opts={})
	Worspace query of unmq()

template<class T , TLAPACK_SMATRIX matrixA_t, TLAPACK_SMATRIX matrixC_t, TLAPACK_SVECTOR tau_t, TLAPACK_SIDE side_t, TLAPACK_OP trans_t>
constexpr WorkInfo	tlapack::unmql_worksize (side_t side, trans_t trans, const matrixA_t &A, const tau_t &tau, const matrixC_t &C, const UnmqlOpts &opts={})
	Applies unitary matrix Q from an QL factorization to a matrix C.

template<class T , TLAPACK_SMATRIX matrixA_t, TLAPACK_SMATRIX matrixC_t, TLAPACK_SVECTOR tau_t, TLAPACK_SIDE side_t, TLAPACK_OP trans_t>
constexpr WorkInfo	tlapack::unmqr_worksize (side_t side, trans_t trans, const matrixA_t &A, const tau_t &tau, const matrixC_t &C, const UnmqrOpts &opts={})
	Worspace query of unmqr()

template<class T , TLAPACK_SMATRIX matrixA_t, TLAPACK_SMATRIX matrixC_t, TLAPACK_VECTOR tau_t, TLAPACK_SIDE side_t, TLAPACK_OP trans_t>
constexpr WorkInfo	tlapack::unmr2_worksize (side_t side, trans_t trans, const matrixA_t &A, const tau_t &tau, const matrixC_t &C)
	Worspace query of unmr2()

template<class T , TLAPACK_SMATRIX matrixA_t, TLAPACK_SMATRIX matrixC_t, TLAPACK_SVECTOR tau_t, TLAPACK_SIDE side_t, TLAPACK_OP trans_t>
constexpr WorkInfo	tlapack::unmrq_worksize (side_t side, trans_t trans, const matrixA_t &A, const tau_t &tau, const matrixC_t &C, const UnmrqOpts &opts={})
	Worspace query of unmrq()

Detailed Description

Workspace queries for routines that require a temporary workspace to perform their computations.

Mind that workspaces are optional. If not provided, the routine will allocate temporary memory internally.

Function Documentation

◆ aggressive_early_deflation_worksize()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_SVECTOR vector_t, enable_if_t< is_complex< type_t< vector_t > >, int > >

WorkInfo tlapack::aggressive_early_deflation_worksize	(	bool	want_t,
		bool	want_z,
		size_type< matrix_t >	ilo,
		size_type< matrix_t >	ihi,
		size_type< matrix_t >	nw,
		const matrix_t &	A,
		const vector_t &	s,
		const matrix_t &	Z,
		const size_type< matrix_t > &	ns,
		const size_type< matrix_t > &	nd,
		const FrancisOpts &	opts
	)

Worspace query of aggressive_early_deflation().

Parameters

[in]	want_t	bool. If true, the full Schur factor T will be computed.
[in]	want_z	bool. If true, the Schur vectors Z will be computed.
[in]	ilo	integer. Either ilo=0 or A(ilo,ilo-1) = 0.
[in]	ihi	integer. ilo and ihi determine an isolated block in A.
[in]	nw	integer. Desired window size to perform aggressive early deflation on. If the matrix is not large enough to provide the scratch space or if the isolated block is small, a smaller value may be used.
[in]	A	n by n matrix. Hessenberg matrix on which AED will be performed
	s	Not referenced.
[in]	Z	n by n matrix. On entry, the previously calculated Schur factors.
	ns	Not referenced.
	nd	Not referenced.
[in]	opts	Options.

Returns: WorkInfo The amount workspace required.

◆ aggressive_early_deflation_worksize_gehrd()

template<class T , TLAPACK_SMATRIX matrix_t>

constexpr WorkInfo tlapack::internal::aggressive_early_deflation_worksize_gehrd	(	size_type< matrix_t >	ilo,
		size_type< matrix_t >	ihi,
		size_type< matrix_t >	nw,
		const matrix_t &	A
	)

constexpr

Workspace query for gehrd() in aggressive_early_deflation().

Parameters

[in]	ilo	integer. Either ilo=0 or A(ilo,ilo-1) = 0.
[in]	ihi	integer. ilo and ihi determine an isolated block in A.
[in]	nw	integer. Desired window size to perform aggressive early deflation on. If the matrix is not large enough to provide the scratch space or if the isolated block is small, a smaller value may be used.
[in]	A	n by n matrix. Hessenberg matrix on which AED will be performed

Returns: WorkInfo The amount workspace required.

◆ bidiag_worksize()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_SVECTOR vector_t>

constexpr WorkInfo tlapack::bidiag_worksize	(	const matrix_t &	A,
		const vector_t &	tauv,
		const vector_t &	tauw,
		const BidiagOpts &	opts = `{}`
	)

constexpr

Worspace query of bidiag()

Parameters

[in]	A	m-by-n matrix.
[in]	tauv	vector of length min(m,n).
[in]	tauw	vector of length min(m,n).
[in]	opts	Options. `opts.variant:` Variant of the algorithm to use.

Returns: WorkInfo The amount workspace required.

◆ gebd2_worksize()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_VECTOR vector_t>

constexpr WorkInfo tlapack::gebd2_worksize	(	const matrix_t &	A,
		const vector_t &	tauv,
		const vector_t &	tauw
	)

constexpr

Worspace query of gebd2().

Parameters

[in]	A	m-by-n matrix. On entry, the m by n general matrix to be reduced.
	tauv	Not referenced.
	tauw	Not referenced.

Returns: WorkInfo The amount workspace required.

◆ gebrd_worksize()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_SVECTOR vector_t>

constexpr WorkInfo tlapack::gebrd_worksize	(	const matrix_t &	A,
		const vector_t &	tauq,
		const vector_t &	taup,
		const GebrdOpts &	opts = `{}`
	)

constexpr

Worspace query of gebrd()

Parameters

[in,out]	A	m-by-n matrix.
[out]	tauq	vector of length min(m,n). The scalar factors of the elementary reflectors which represent the unitary matrix Q.
[out]	taup	vector of length min(m,n). The scalar factors of the elementary reflectors which represent the unitary matrix P.

Returns: WorkInfo The amount workspace required.

Parameters

[in] opts Options.

◆ gehd2_worksize()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_VECTOR vector_t>

constexpr WorkInfo tlapack::gehd2_worksize	(	size_type< matrix_t >	ilo,
		size_type< matrix_t >	ihi,
		const matrix_t &	A,
		const vector_t &	tau
	)

constexpr

Worspace query of gehd2()

Parameters

[in]	ilo	integer
[in]	ihi	integer It is assumed that A is already upper Hessenberg in columns 0:ilo and rows ihi:n and is already upper triangular in columns ihi+1:n and rows 0:ilo. 0 <= ilo <= ihi <= max(1,n).
[in]	A	n-by-n matrix. On entry, the n by n general matrix to be reduced.
	tau	Not referenced.

Returns: WorkInfo The amount workspace required.

◆ gehrd_worksize()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_SVECTOR vector_t>

constexpr WorkInfo tlapack::gehrd_worksize	(	size_type< matrix_t >	ilo,
		size_type< matrix_t >	ihi,
		const matrix_t &	A,
		const vector_t &	tau,
		const GehrdOpts &	opts = `{}`
	)

constexpr

Worspace query of gehrd()

Parameters

[in]	ilo	integer
[in]	ihi	integer It is assumed that A is already upper Hessenberg in columns 0:ilo and rows ihi:n and is already upper triangular in columns ihi+1:n and rows 0:ilo. 0 <= ilo <= ihi <= max(1,n).
[in]	A	n-by-n matrix. On entry, the n by n general matrix to be reduced.
	tau	Vector of length n-1.
[in]	opts	Options.

Returns: WorkInfo The amount workspace required.

◆ gelq2_worksize()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_VECTOR vector_t>

constexpr WorkInfo tlapack::gelq2_worksize	(	const matrix_t &	A,
		const vector_t &	tauw
	)

constexpr

Worspace query of gelq2()

Parameters

[in]	A	m-by-n matrix.
	tauw	Not referenced.

Returns: WorkInfo The amount workspace required.

◆ gelqf_worksize()

template<class T , TLAPACK_SMATRIX A_t, TLAPACK_SVECTOR tau_t>

constexpr WorkInfo tlapack::gelqf_worksize	(	const A_t &	A,
		const tau_t &	tau,
		const GelqfOpts &	opts = `{}`
	)

constexpr

Worspace query of gelqf()

Parameters

[in]	A	m-by-n matrix.
	tau	min(n,m) vector.
[in]	opts	Options.

Returns: WorkInfo The amount workspace required.

◆ gelqt_worksize()

template<class T , TLAPACK_SMATRIX matrix_t>

constexpr WorkInfo tlapack::gelqt_worksize	(	const matrix_t &	A,
		const matrix_t &	TT
	)

constexpr

Worspace query of gelqt()

Parameters

[in]	A	m-by-n matrix.
	TT	m-by-nb matrix.

Returns: WorkInfo The amount workspace required.

◆ gen_householder_q_worksize()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_VECTOR vector_t, TLAPACK_DIRECTION direction_t, TLAPACK_STOREV storage_t>

constexpr WorkInfo tlapack::gen_householder_q_worksize	(	direction_t	direction,
		storage_t	storeMode,
		const matrix_t &	A,
		const vector_t &	tau,
		const GenHouseholderQOpts &	opts = `{}`
	)

constexpr

Worspace query of gen_householder_q()

Parameters

[in]	direction	Direction of the Householder reflectors.
[in]	storeMode	Storage mode of the Householder reflectors.
[in]	A	m-by-n matrix.
[in]	tau	vector of length k.
[in]	opts	Options. `opts.variant:` Variant of the algorithm to use.

Returns: WorkInfo The amount workspace required.

◆ geql2_worksize()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_VECTOR vector_t>

constexpr WorkInfo tlapack::geql2_worksize	(	const matrix_t &	A,
		const vector_t &	tau
	)

constexpr

Worspace query of geql2()

Parameters

[in]	A	m-by-n matrix.
	tau	Not referenced.

Returns: WorkInfo The amount workspace required.

◆ geqlf_worksize()

template<class T , TLAPACK_SMATRIX A_t, TLAPACK_SVECTOR tau_t>

constexpr WorkInfo tlapack::geqlf_worksize	(	const A_t &	A,
		const tau_t &	tau,
		const GeqlfOpts &	opts = `{}`
	)

constexpr

Worspace query of geqlf()

Parameters

[in]	A	m-by-n matrix.
	tau	min(n,m) vector.
[in]	opts	Options.

Returns: WorkInfo The amount workspace required.

◆ geqr2_worksize()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_VECTOR vector_t>

constexpr WorkInfo tlapack::geqr2_worksize	(	const matrix_t &	A,
		const vector_t &	tau
	)

constexpr

Worspace query of geqr2()

Parameters

[in]	A	m-by-n matrix.
	tau	Not referenced.

Returns: WorkInfo The amount workspace required.

◆ geqrf_worksize()

template<class T , TLAPACK_SMATRIX A_t, TLAPACK_SVECTOR tau_t>

constexpr WorkInfo tlapack::geqrf_worksize	(	const A_t &	A,
		const tau_t &	tau,
		const GeqrfOpts &	opts = `{}`
	)

constexpr

Worspace query of geqrf()

Parameters

[in]	A	m-by-n matrix.
	tau	min(n,m) vector.
[in]	opts	Options.

Returns: WorkInfo The amount workspace required.

◆ gerq2_worksize()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_VECTOR vector_t>

constexpr WorkInfo tlapack::gerq2_worksize	(	const matrix_t &	A,
		const vector_t &	tau
	)

constexpr

Worspace query of gerq2()

Parameters

[in]	A	m-by-n matrix.
	tau	Not referenced.

Returns: WorkInfo The amount workspace required.

◆ gerqf_worksize()

template<class T , TLAPACK_SMATRIX A_t, TLAPACK_SVECTOR tau_t>

constexpr WorkInfo tlapack::gerqf_worksize	(	const A_t &	A,
		const tau_t &	tau,
		const GerqfOpts &	opts = `{}`
	)

constexpr

Worspace query of gerqf()

Parameters

[in]	A	m-by-n matrix.
	tau	min(n,m) vector.
[in]	opts	Options.

Returns: WorkInfo The amount workspace required.

◆ getri_uxli_worksize()

template<class T , TLAPACK_SMATRIX matrix_t>

constexpr WorkInfo tlapack::getri_uxli_worksize ( const matrix_t & A )

constexpr

Worspace query of getri()

Parameters

[in] A n-by-n matrix.

Returns: WorkInfo The amount workspace required.

◆ getri_worksize()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_VECTOR piv_t>

constexpr WorkInfo tlapack::getri_worksize	(	const matrix_t &	A,
		const piv_t &	piv,
		const GetriOpts &	opts = `{}`
	)

constexpr

Worspace query of getri()

Parameters

[in]	A	n-by-n matrix.
[in]	piv	pivot vector of size at least n.
[in]	opts	Options. `opts.variant:` UILI = 'D', ///< Method D from doi:10.1137/1.9780898718027 UXLI = 'C' ///< Method C from doi:10.1137/1.9780898718027

Returns: WorkInfo The amount workspace required.

◆ hessenberg_worksize()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_SVECTOR vector_t>

constexpr WorkInfo tlapack::hessenberg_worksize	(	size_type< matrix_t >	ilo,
		size_type< matrix_t >	ihi,
		const matrix_t &	A,
		const vector_t &	tau,
		const HessenbergOpts &	opts = `{}`
	)

constexpr

Workspace query of hessenberg()

Parameters

[in]	ilo	integer
[in]	ihi	integer
[in]	A	n-by-n matrix.
[in]	tau	Vector of length n-1.
[in]	opts	Options. `opts.variant:` Variant of the algorithm to use.

Returns: WorkInfo The amount workspace required.

◆ householder_lq_worksize()

template<class T , TLAPACK_MATRIX matrix_t, TLAPACK_VECTOR vector_t>

constexpr WorkInfo tlapack::householder_lq_worksize	(	const matrix_t &	A,
		const vector_t &	tau,
		const HouseholderLQOpts &	opts = `{}`
	)

constexpr

Worspace query of householder_lq()

Parameters

[in]	A	m-by-n matrix.
[in]	tau	min(n,m) vector.
[in]	opts	Options. `opts.variant:` Variant of the algorithm to use.

Returns: WorkInfo The amount workspace required.

◆ householder_q_mul_worksize()

template<class T , TLAPACK_SMATRIX matrixV_t, TLAPACK_SMATRIX matrixC_t, TLAPACK_SVECTOR vector_t, TLAPACK_SIDE side_t, TLAPACK_OP trans_t, TLAPACK_DIRECTION direction_t, TLAPACK_STOREV storage_t>

constexpr WorkInfo tlapack::householder_q_mul_worksize	(	side_t	side,
		trans_t	trans,
		direction_t	direction,
		storage_t	storeMode,
		const matrixV_t &	V,
		const vector_t &	tau,
		const matrixC_t &	C,
		const HouseholderQMulOpts &	opts = `{}`
	)

constexpr

Workspace query of householder_q_mul()

Parameters

[in]	side	Specifies which side op(Q) is to be applied. Side::Left: C := op(Q) C; Side::Right: C := C op(Q).
[in]	trans	The operation \(op(Q)\) to be used: Op::NoTrans: \(op(Q) = Q\); Op::ConjTrans: \(op(Q) = Q^H\). Op::Trans is a valid value if the data type of A is real. In this case, the algorithm treats Op::Trans as Op::ConjTrans.
[in]	direction	Indicates how Q is formed from a product of elementary reflectors. Direction::Forward: \(Q = H_1 H_2 ... H_k\). Direction::Backward: \(Q = H_k ... H_2 H_1\).
[in]	storeMode	Indicates how the vectors which define the elementary reflectors are stored: StoreV::Columnwise. StoreV::Rowwise.
[in]	V	If storeMode = StoreV::Columnwise: if side = Side::Left, the m-by-k matrix V; if side = Side::Right, the n-by-k matrix V. If storeMode = StoreV::Rowwise: if side = Side::Left, the k-by-m matrix V; if side = Side::Right, the k-by-n matrix V.
[in]	tau	Vector of length k. Scalar factors of the elementary reflectors.
[in]	C	m-by-n matrix.
[in]	opts	Options. `opts.variant:` Variant of the algorithm to use.

Returns: WorkInfo The amount workspace required.

◆ householder_ql_worksize()

template<class T , TLAPACK_MATRIX matrix_t, TLAPACK_VECTOR vector_t>

constexpr WorkInfo tlapack::householder_ql_worksize	(	const matrix_t &	A,
		const vector_t &	tau,
		const HouseholderQLOpts &	opts = `{}`
	)

constexpr

Worspace query of householder_ql()

Parameters

[in]	A	m-by-n matrix.
[in]	tau	min(n,m) vector.
[in]	opts	Options. `opts.variant:` Variant of the algorithm to use.

Returns: WorkInfo The amount workspace required.

◆ householder_qr_worksize()

template<class T , TLAPACK_MATRIX matrix_t, TLAPACK_VECTOR vector_t>

constexpr WorkInfo tlapack::householder_qr_worksize	(	const matrix_t &	A,
		const vector_t &	tau,
		const HouseholderQROpts &	opts = `{}`
	)

constexpr

Worspace query of householder_qr()

Parameters

[in]	A	m-by-n matrix.
[in]	tau	min(n,m) vector.
[in]	opts	Options. `opts.variant:` Variant of the algorithm to use.

Returns: WorkInfo The amount workspace required.

◆ householder_rq_worksize()

template<class T , TLAPACK_MATRIX matrix_t, TLAPACK_VECTOR vector_t>

constexpr WorkInfo tlapack::householder_rq_worksize	(	const matrix_t &	A,
		const vector_t &	tau,
		const HouseholderRQOpts &	opts = `{}`
	)

constexpr

Worspace query of householder_rq()

Parameters

[in]	A	m-by-n matrix.
[in]	tau	min(n,m) vector.
[in]	opts	Options. `opts.variant:` Variant of the algorithm to use.

Returns: WorkInfo The amount workspace required.

◆ infnorm_colmajor_worksize()

template<class T , TLAPACK_MATRIX matrix_t>

constexpr WorkInfo tlapack::infnorm_colmajor_worksize ( const matrix_t & A )

constexpr

Worspace query of infnorm_colmajor()

Parameters

[in] A m-by-n matrix.

Returns: WorkInfo The amount workspace required.

◆ infnorm_hermitian_colmajor_worksize()

template<class T , TLAPACK_UPLO uplo_t, TLAPACK_MATRIX matrix_t>

constexpr WorkInfo tlapack::infnorm_hermitian_colmajor_worksize	(	uplo_t	uplo,
		const matrix_t &	A
	)

constexpr

Worspace query of infnorm_hermitian_colmajor()

Parameters

[in]	uplo	Uplo::Upper: Upper triangle of A is referenced; Uplo::Lower: Lower triangle of A is referenced.
[in]	A	n-by-n matrix.

Returns: WorkInfo The amount workspace required.

◆ infnorm_symmetric_colmajor_worksize()

template<class T , TLAPACK_UPLO uplo_t, TLAPACK_MATRIX matrix_t>

constexpr WorkInfo tlapack::infnorm_symmetric_colmajor_worksize	(	uplo_t	uplo,
		const matrix_t &	A
	)

constexpr

Worspace query of infnorm_symmetric_colmajor()

Parameters

[in]	uplo	Uplo::Upper: Upper triangle of A is referenced; Uplo::Lower: Lower triangle of A is referenced.
[in]	A	n-by-n matrix.

Returns: WorkInfo The amount workspace required.

◆ infnorm_triangular_colmajor_worksize()

template<class T , TLAPACK_UPLO uplo_t, TLAPACK_DIAG diag_t, TLAPACK_MATRIX matrix_t>

constexpr WorkInfo tlapack::infnorm_triangular_colmajor_worksize	(	uplo_t	uplo,
		diag_t	diag,
		const matrix_t &	A
	)

constexpr

Worspace query of infnorm_triangular_colmajor()

Parameters

[in]	uplo	Uplo::Upper: Upper triangle of A is referenced; Uplo::Lower: Lower triangle of A is referenced.
[in]	diag	Whether A has a unit or non-unit diagonal: Diag::Unit: A is assumed to be unit triangular. Diag::NonUnit: A is not assumed to be unit triangular.
[in]	A	m-by-n matrix.

Returns: WorkInfo The amount workspace required.

◆ larf_worksize() [1/2]

template<class T , TLAPACK_SIDE side_t, TLAPACK_DIRECTION direction_t, TLAPACK_STOREV storage_t, TLAPACK_SVECTOR vector_t, TLAPACK_SCALAR tau_t, TLAPACK_SMATRIX matrix_t, enable_if_t< std::is_convertible_v< direction_t, Direction >, int > = 0>

constexpr WorkInfo tlapack::larf_worksize	(	side_t	side,
		direction_t	direction,
		storage_t	storeMode,
		vector_t const &	v,
		const tau_t &	tau,
		const matrix_t &	C
	)

constexpr

Worspace query of larf().

Parameters

[in]	side	Side::Left: apply \(H\) from the Left. Side::Right: apply \(H\) from the Right.
[in]	direction	v = [ 1 x ] if direction == Direction::Forward and v = [ x 1 ] if direction == Direction::Backward.
[in]	storeMode	Indicates how the vectors which define the elementary reflectors are stored: StoreV::Columnwise. StoreV::Rowwise.
[in]	v	Vector of size m if side = Side::Left, or n if side = Side::Right.
[in]	tau	Value of tau in the representation of H.
[in]	C	On entry, the m-by-n matrix C.

Returns: WorkInfo The amount workspace required.

◆ larf_worksize() [2/2]

template<class T , TLAPACK_SIDE side_t, TLAPACK_STOREV storage_t, TLAPACK_VECTOR vector_t, TLAPACK_SCALAR tau_t, TLAPACK_VECTOR vectorC0_t, TLAPACK_MATRIX matrixC1_t, enable_if_t< std::is_convertible_v< storage_t, StoreV >, int > = 0>

constexpr WorkInfo tlapack::larf_worksize	(	side_t	side,
		storage_t	storeMode,
		vector_t const &	x,
		const tau_t &	tau,
		const vectorC0_t &	C0,
		const matrixC1_t &	C1
	)

constexpr

Worspace query of larf().

Parameters

[in]	side	Side::Left: apply \(H\) from the Left. Side::Right: apply \(H\) from the Right.
[in]	storeMode	Indicates how the vectors which define the elementary reflectors are stored: StoreV::Columnwise. StoreV::Rowwise.
[in]	x	Vector of size m-1 if side = Side::Left, or n-1 if side = Side::Right.
[in]	tau	Value of tau in the representation of H.
[in]	C0	On entry, the m-by-n matrix C.
[in]	C1	On entry, the m-by-n matrix C.

Returns: WorkInfo The amount workspace required.

◆ larfb_worksize()

template<class T , TLAPACK_SMATRIX matrixV_t, TLAPACK_MATRIX matrixT_t, TLAPACK_SMATRIX matrixC_t, TLAPACK_SIDE side_t, TLAPACK_OP trans_t, TLAPACK_DIRECTION direction_t, TLAPACK_STOREV storage_t>

constexpr WorkInfo tlapack::larfb_worksize	(	side_t	side,
		trans_t	trans,
		direction_t	direction,
		storage_t	storeMode,
		const matrixV_t &	V,
		const matrixT_t &	Tmatrix,
		const matrixC_t &	C
	)

constexpr

Worspace query of larfb()

Parameters

[in]	side	Side::Left: apply \(H\) or \(H^H\) from the Left. Side::Right: apply \(H\) or \(H^H\) from the Right.
[in]	trans	Op::NoTrans: apply \(H \) (No transpose). Op::Trans: apply \(H^T\) (Transpose, only allowed if the type of H is Real). Op::ConjTrans: apply \(H^H\) (Conjugate transpose).
[in]	direction	Indicates how H is formed from a product of elementary reflectors. Direction::Forward: \(H = H(1) H(2) ... H(k)\). Direction::Backward: \(H = H(k) ... H(2) H(1)\).
[in]	storeMode	Indicates how the vectors which define the elementary reflectors are stored: StoreV::Columnwise. StoreV::Rowwise.
[in]	V	If storeMode = StoreV::Columnwise: if side = Side::Left, the m-by-k matrix V; if side = Side::Right, the n-by-k matrix V. If storeMode = StoreV::Rowwise: if side = Side::Left, the k-by-m matrix V; if side = Side::Right, the k-by-n matrix V.
[in]	Tmatrix	The k-by-k matrix T. The triangular k-by-k matrix T in the representation of the block reflector.
[in]	C	On entry, the m-by-n matrix C.

Returns: WorkInfo The amount workspace required.

◆ multishift_QR_sweep_worksize()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_VECTOR vector_t, enable_if_t< is_complex< type_t< vector_t > >, bool > = true>

constexpr WorkInfo tlapack::multishift_QR_sweep_worksize	(	bool	want_t,
		bool	want_z,
		size_type< matrix_t >	ilo,
		size_type< matrix_t >	ihi,
		const matrix_t &	A,
		const vector_t &	s,
		const matrix_t &	Z
	)

constexpr

Worspace query of multishift_QR_sweep()

Parameters

[in]	want_t	bool. If true, the full Schur factor T will be computed.
[in]	want_z	bool. If true, the Schur vectors Z will be computed.
[in]	ilo	integer. Either ilo=0 or A(ilo,ilo-1) = 0.
[in]	ihi	integer. ilo and ihi determine an isolated block in A.
[in]	A	n by n matrix. Hessenberg matrix on which AED will be performed
[in]	s	complex vector. Vector containing the shifts to be used during the sweep
[in]	Z	n by n matrix. On entry, the previously calculated Schur factors.

Returns: WorkInfo The amount workspace required.

◆ multishift_qr_worksize()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_SVECTOR vector_t, enable_if_t< is_complex< type_t< vector_t > >, int > = 0>

WorkInfo tlapack::multishift_qr_worksize	(	bool	want_t,
		bool	want_z,
		size_type< matrix_t >	ilo,
		size_type< matrix_t >	ihi,
		const matrix_t &	A,
		const vector_t &	w,
		const matrix_t &	Z,
		const FrancisOpts &	opts
	)

Worspace query of multishift_qr()

Parameters

[in]	want_t	bool. If true, the full Schur factor T will be computed.
[in]	want_z	bool. If true, the Schur vectors Z will be computed.
[in]	ilo	integer. Either ilo=0 or A(ilo,ilo-1) = 0.
[in]	ihi	integer. The matrix A is assumed to be already quasi-triangular in rows and columns ihi:n.
[in]	A	n by n matrix.
	w	Not referenced.
[in]	Z	n by n matrix.
[in,out]	opts	Options.

Returns: WorkInfo The amount workspace required.

◆ qr_iteration_worksize()

template<class T , TLAPACK_MATRIX matrix_t, TLAPACK_VECTOR vector_t, enable_if_t< is_complex< type_t< vector_t > >, int > = 0>

constexpr WorkInfo tlapack::qr_iteration_worksize	(	bool	want_t,
		bool	want_z,
		size_type< matrix_t >	ilo,
		size_type< matrix_t >	ihi,
		const matrix_t &	A,
		const vector_t &	w,
		const matrix_t &	Z,
		const QRIterationOpts &	opts = `{}`
	)

constexpr

Worspace query of qr_iteration()

Parameters

[in]	want_t	bool. If true, the full Schur factor T will be computed.
[in]	want_z	bool. If true, the Schur vectors Z will be computed.
[in]	ilo	integer. Either ilo=0 or A(ilo,ilo-1) = 0.
[in]	ihi	integer. The matrix A is assumed to be already quasi-triangular in rows and columns ihi:n.
[in]	A	n by n matrix.
[in]	w	n vector.
[in]	Z	n by n matrix.
[in]	opts	Options. `opts.variant:` Variant of the algorithm to use.

Returns: WorkInfo The amount workspace required.

◆ ung2l_worksize()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_VECTOR vector_t>

constexpr WorkInfo tlapack::ung2l_worksize	(	const matrix_t &	A,
		const vector_t &	tau
	)

constexpr

Worspace query of ung2l()

Parameters

[in]	A	m-by-n matrix.
[in]	tau	Real vector of length min(m,n). The scalar factors of the elementary reflectors.

Returns: WorkInfo The amount workspace required.

◆ ung2r_worksize()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_VECTOR vector_t>

constexpr WorkInfo tlapack::ung2r_worksize	(	const matrix_t &	A,
		const vector_t &	tau
	)

constexpr

Worspace query of ung2r()

Parameters

[in]	A	m-by-n matrix.
[in]	tau	Real vector of length min(m,n). The scalar factors of the elementary reflectors.

Returns: WorkInfo The amount workspace required.

◆ ungbr_p_worksize()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_SVECTOR vector_t>

constexpr WorkInfo tlapack::ungbr_p_worksize	(	const size_type< matrix_t >	k,
		matrix_t &	A,
		const vector_t &	tau,
		const UngbrOpts &	opts = `{}`
	)

constexpr

Worspace query of ungbr_p()

Parameters

[in]	k	integer. k is the number of rows in the original k-by-n matrix reduced by gebrd.
[in,out]	A	m-by-n matrix.
[in]	tau	vector. tau is a vector of length min(k,n) tau(i) must contain the scalar factor of the elementary reflector G(i), which determines P**H, as returned by gebrd in its array argument taup.

Returns: WorkInfo The amount workspace required.

Parameters

[in] opts Options.

◆ ungbr_q_worksize()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_SVECTOR vector_t>

constexpr WorkInfo tlapack::ungbr_q_worksize	(	const size_type< matrix_t >	k,
		matrix_t &	A,
		const vector_t &	tau,
		const UngbrOpts &	opts = `{}`
	)

constexpr

Worspace query of ungbr_q()

Parameters

[in]	k	integer. k is the number of columns in the original m-by-k matrix reduced by gebrd.
[in,out]	A	m-by-n matrix.
[in]	tau	vector. tau is a vector of length min(m,k) tau(i) must contain the scalar factor of the elementary reflector H(i), which determines Q, as returned by gebrd in its array argument tauq.

Returns: WorkInfo The amount workspace required.

Parameters

[in] opts Options.

◆ unghr_worksize()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_SVECTOR vector_t>

constexpr WorkInfo tlapack::unghr_worksize	(	size_type< matrix_t >	ilo,
		size_type< matrix_t >	ihi,
		const matrix_t &	A,
		const vector_t &	tau
	)

constexpr

Worspace query of unghr()

Parameters

[in]	ilo	integer
[in]	ihi	integer ilo and ihi must have the same values as in the previous call to gehrd. Q is equal to the unit matrix except in the submatrix Q(ilo+1:ihi,ilo+1:ihi). 0 <= ilo <= ihi <= max(1,n).
[in]	A	m-by-n matrix.
[in]	tau	Real vector of length n-1. The scalar factors of the elementary reflectors.

Returns: WorkInfo The amount workspace required.

◆ ungl2_worksize()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_VECTOR vector_t>

constexpr WorkInfo tlapack::ungl2_worksize	(	const matrix_t &	Q,
		const vector_t &	tauw
	)

constexpr

Worspace query of ungl2()

Parameters

[in]	Q	k-by-n matrix.
[in]	tauw	Complex vector of length min(m,n). tauw(j) must contain the scalar factor of the elementary reflector H(j), as returned by gelq2.

Returns: WorkInfo The amount workspace required.

◆ ungq_level2_worksize()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_SVECTOR vector_t, TLAPACK_DIRECTION direction_t, TLAPACK_STOREV storage_t>

constexpr WorkInfo tlapack::ungq_level2_worksize	(	direction_t	direction,
		storage_t	storeMode,
		const matrix_t &	A,
		const vector_t &	tau
	)

constexpr

Worspace query of ungq_level2()

Parameters

[in]	direction	Indicates how Q is formed from a product of elementary reflectors. Direction::Forward: \(Q = H_1 H_2 ... H_k\). Direction::Backward: \(Q = H_k ... H_2 H_1\).
[in]	storeMode	Indicates how the vectors which define the elementary reflectors are stored: StoreV::Columnwise. StoreV::Rowwise.
[in]	A	m-by-n matrix.
[in]	tau	Vector of length k. Scalar factors of the elementary reflectors.

Returns: WorkInfo The amount workspace required.

◆ ungq_worksize()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_SVECTOR vector_t, TLAPACK_DIRECTION direction_t, TLAPACK_STOREV storage_t>

constexpr WorkInfo tlapack::ungq_worksize	(	direction_t	direction,
		storage_t	storeMode,
		const matrix_t &	A,
		const vector_t &	tau,
		const UngqOpts &	opts = `{}`
	)

constexpr

Worspace query of ungq()

Parameters

[in]	direction	Indicates how Q is formed from a product of elementary reflectors. Direction::Forward: \(Q = H_1 H_2 ... H_k\). Direction::Backward: \(Q = H_k ... H_2 H_1\).
[in]	storeMode	Indicates how the vectors which define the elementary reflectors are stored: StoreV::Columnwise. StoreV::Rowwise.
[in]	A	m-by-n matrix.
[in]	tau	Vector of length k. Scalar factors of the elementary reflectors.
[in]	opts	Options.

Returns: WorkInfo The amount workspace required.

◆ ungr2_worksize()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_VECTOR vector_t>

constexpr WorkInfo tlapack::ungr2_worksize	(	const matrix_t &	A,
		const vector_t &	tau
	)

constexpr

Worspace query of ungr2()

Parameters

[in]	A	m-by-n matrix.
[in]	tau	Real vector of length min(m,n). The scalar factors of the elementary reflectors.

Returns: WorkInfo The amount workspace required.

◆ unm2l_worksize()

template<class T , TLAPACK_SMATRIX matrixA_t, TLAPACK_SMATRIX matrixC_t, TLAPACK_VECTOR tau_t, TLAPACK_SIDE side_t, TLAPACK_OP trans_t>

constexpr WorkInfo tlapack::unm2l_worksize	(	side_t	side,
		trans_t	trans,
		const matrixA_t &	A,
		const tau_t &	tau,
		const matrixC_t &	C
	)

constexpr

Worspace query of unm2l()

Parameters

[in]	side	Specifies which side op(Q) is to be applied. Side::Left: C := op(Q) C; Side::Right: C := C op(Q).
[in]	trans	The operation \(op(Q)\) to be used: Op::NoTrans: \(op(Q) = Q\); Op::ConjTrans: \(op(Q) = Q^H\). Op::Trans is a valid value if the data type of A is real. In this case, the algorithm treats Op::Trans as Op::ConjTrans.
[in]	A	side = Side::Left: m-by-k matrix; side = Side::Right: n-by-k matrix.
[in]	tau	Vector of length k Contains the scalar factors of the elementary reflectors.
[in]	C	m-by-n matrix.

Returns: WorkInfo The amount workspace required.

◆ unm2r_worksize()

template<class T , TLAPACK_SMATRIX matrixA_t, TLAPACK_SMATRIX matrixC_t, TLAPACK_VECTOR tau_t, TLAPACK_SIDE side_t, TLAPACK_OP trans_t>

constexpr WorkInfo tlapack::unm2r_worksize	(	side_t	side,
		trans_t	trans,
		const matrixA_t &	A,
		const tau_t &	tau,
		const matrixC_t &	C
	)

constexpr

Worspace query of unm2r()

Parameters

[in]	side	Specifies which side op(Q) is to be applied. Side::Left: C := op(Q) C; Side::Right: C := C op(Q).
[in]	trans	The operation \(op(Q)\) to be used: Op::NoTrans: \(op(Q) = Q\); Op::ConjTrans: \(op(Q) = Q^H\). Op::Trans is a valid value if the data type of A is real. In this case, the algorithm treats Op::Trans as Op::ConjTrans.
[in]	A	side = Side::Left: m-by-k matrix; side = Side::Right: n-by-k matrix.
[in]	tau	Vector of length k Contains the scalar factors of the elementary reflectors.
[in]	C	m-by-n matrix.

Returns: WorkInfo The amount workspace required.

◆ unmhr_worksize()

template<class T , TLAPACK_SMATRIX matrix_t, TLAPACK_SVECTOR vector_t>

constexpr WorkInfo tlapack::unmhr_worksize	(	Side	side,
		Op	trans,
		size_type< matrix_t >	ilo,
		size_type< matrix_t >	ihi,
		const matrix_t &	A,
		const vector_t &	tau,
		const matrix_t &	C
	)

constexpr

Worspace query of unmhr()

Parameters

[in]	side	Specifies which side op(Q) is to be applied. Side::Left: C := op(Q) C; Side::Right: C := C op(Q).
[in]	trans	The operation \(op(Q)\) to be used: Op::NoTrans: \(op(Q) = Q\); Op::ConjTrans: \(op(Q) = Q^H\). Op::Trans is a valid value if the data type of A is real. In this case, the algorithm treats Op::Trans as Op::ConjTrans.
[in]	ilo	integer
[in]	ihi	integer ilo and ihi must have the same values as in the previous call to gehrd. Q is equal to the unit matrix except in the submatrix Q(ilo+1:ihi,ilo+1:ihi). 0 <= ilo <= ihi <= max(1,n).
[in]	A	n-by-n matrix Matrix containing orthogonal vectors, as returned by gehrd
[in]	tau	Vector of length n-1 Contains the scalar factors of the elementary reflectors.
[in]	C	m-by-n matrix.

Returns: WorkInfo The amount workspace required.

◆ unml2_worksize()

template<class T , TLAPACK_SMATRIX matrixA_t, TLAPACK_SMATRIX matrixC_t, TLAPACK_VECTOR tau_t, TLAPACK_SIDE side_t, TLAPACK_OP trans_t>

constexpr WorkInfo tlapack::unml2_worksize	(	side_t	side,
		trans_t	trans,
		const matrixA_t &	A,
		const tau_t &	tau,
		const matrixC_t &	C
	)

constexpr

Worspace query of unml2()

Parameters

[in]	side	Specifies which side op(Q) is to be applied. Side::Left: C := op(Q) C; Side::Right: C := C op(Q).
[in]	trans	The operation \(op(Q)\) to be used: Op::NoTrans: \(op(Q) = Q\); Op::ConjTrans: \(op(Q) = Q^H\). Op::Trans is a valid value if the data type of A is real. In this case, the algorithm treats Op::Trans as Op::ConjTrans.
[in]	A	side = Side::Left: k-by-m matrix; side = Side::Right: k-by-n matrix.
[in]	tau	Vector of length k Contains the scalar factors of the elementary reflectors.
[in]	C	m-by-n matrix.

Returns: WorkInfo The amount workspace required.

◆ unmlq_worksize()

template<class T , TLAPACK_SMATRIX matrixA_t, TLAPACK_SMATRIX matrixC_t, TLAPACK_SVECTOR tau_t, TLAPACK_SIDE side_t, TLAPACK_OP trans_t>

constexpr WorkInfo tlapack::unmlq_worksize	(	side_t	side,
		trans_t	trans,
		const matrixA_t &	A,
		const tau_t &	tau,
		const matrixC_t &	C,
		const UnmlqOpts &	opts = `{}`
	)

constexpr

Worspace query of unmlq()

Parameters

[in]	side	Specifies which side op(Q) is to be applied. Side::Left: C := op(Q) C; Side::Right: C := C op(Q).
[in]	trans	The operation \(op(Q)\) to be used: Op::NoTrans: \(op(Q) = Q\); Op::ConjTrans: \(op(Q) = Q^H\). Op::Trans is a valid value if the data type of A is real. In this case, the algorithm treats Op::Trans as Op::ConjTrans.
[in]	A	side = Side::Left: k-by-m matrix; side = Side::Right: k-by-n matrix. Contains the vectors that define the reflectors
[in]	tau	Vector of length k Contains the scalar factors of the elementary reflectors.
[in]	C	m-by-n matrix.
[in]	opts	Options.

Returns: WorkInfo The amount workspace required.

See also: unmlq

◆ unmq_level2_worksize()

template<class T , TLAPACK_SMATRIX matrixV_t, TLAPACK_SMATRIX matrixC_t, TLAPACK_VECTOR vector_t, TLAPACK_SIDE side_t, TLAPACK_OP trans_t, TLAPACK_DIRECTION direction_t, TLAPACK_STOREV storage_t>

constexpr WorkInfo tlapack::unmq_level2_worksize	(	side_t	side,
		trans_t	trans,
		direction_t	direction,
		storage_t	storeMode,
		const matrixV_t &	V,
		const vector_t &	tau,
		const matrixC_t &	C
	)

constexpr

Worspace query of unmq_level2()

Parameters

[in]	side	Specifies which side op(Q) is to be applied. Side::Left: C := op(Q) C; Side::Right: C := C op(Q).
[in]	trans	The operation \(op(Q)\) to be used: Op::NoTrans: \(op(Q) = Q\); Op::ConjTrans: \(op(Q) = Q^H\). Op::Trans is a valid value if the data type of A is real. In this case, the algorithm treats Op::Trans as Op::ConjTrans.
[in]	direction	Indicates how Q is formed from a product of elementary reflectors. Direction::Forward: \(Q = H_1 H_2 ... H_k\). Direction::Backward: \(Q = H_k ... H_2 H_1\).
[in]	storeMode	Indicates how the vectors which define the elementary reflectors are stored: StoreV::Columnwise. StoreV::Rowwise.
[in]	V	If storeMode = StoreV::Columnwise: if side = Side::Left, the m-by-k matrix V; if side = Side::Right, the n-by-k matrix V. If storeMode = StoreV::Rowwise: if side = Side::Left, the k-by-m matrix V; if side = Side::Right, the k-by-n matrix V.
[in]	tau	Vector of length k. Scalar factors of the elementary reflectors.
[in]	C	m-by-n matrix.

Returns: WorkInfo The amount workspace required.

◆ unmq_worksize()

template<class T , TLAPACK_SMATRIX matrixV_t, TLAPACK_SMATRIX matrixC_t, TLAPACK_SVECTOR vector_t, TLAPACK_SIDE side_t, TLAPACK_OP trans_t, TLAPACK_DIRECTION direction_t, TLAPACK_STOREV storage_t>

constexpr WorkInfo tlapack::unmq_worksize	(	side_t	side,
		trans_t	trans,
		direction_t	direction,
		storage_t	storeMode,
		const matrixV_t &	V,
		const vector_t &	tau,
		const matrixC_t &	C,
		const UnmqOpts &	opts = `{}`
	)

constexpr

Worspace query of unmq()

Parameters

[in]	side	Specifies which side op(Q) is to be applied. Side::Left: C := op(Q) C; Side::Right: C := C op(Q).
[in]	trans	The operation \(op(Q)\) to be used: Op::NoTrans: \(op(Q) = Q\); Op::ConjTrans: \(op(Q) = Q^H\). Op::Trans is a valid value if the data type of A is real. In this case, the algorithm treats Op::Trans as Op::ConjTrans.
[in]	direction	Indicates how Q is formed from a product of elementary reflectors. Direction::Forward: \(Q = H_1 H_2 ... H_k\). Direction::Backward: \(Q = H_k ... H_2 H_1\).
[in]	storeMode	Indicates how the vectors which define the elementary reflectors are stored: StoreV::Columnwise. StoreV::Rowwise.
[in]	V	If storeMode = StoreV::Columnwise: if side = Side::Left, the m-by-k matrix V; if side = Side::Right, the n-by-k matrix V. If storeMode = StoreV::Rowwise: if side = Side::Left, the k-by-m matrix V; if side = Side::Right, the k-by-n matrix V.
[in]	tau	Vector of length k. Scalar factors of the elementary reflectors.
[in]	C	m-by-n matrix.
[in]	opts	Options.

Returns: WorkInfo The amount workspace required.

◆ unmql_worksize()

template<class T , TLAPACK_SMATRIX matrixA_t, TLAPACK_SMATRIX matrixC_t, TLAPACK_SVECTOR tau_t, TLAPACK_SIDE side_t, TLAPACK_OP trans_t>

constexpr WorkInfo tlapack::unmql_worksize	(	side_t	side,
		trans_t	trans,
		const matrixA_t &	A,
		const tau_t &	tau,
		const matrixC_t &	C,
		const UnmqlOpts &	opts = `{}`
	)

constexpr

Applies unitary matrix Q from an QL factorization to a matrix C.

side = Side::Left & trans = Op::NoTrans: \(C := Q C\);
side = Side::Right & trans = Op::NoTrans: \(C := C Q\);
side = Side::Left & trans = Op::ConjTrans: \(C := C Q^H\);
side = Side::Right & trans = Op::ConjTrans: \(C := Q^H C\).

The matrix Q is represented as a product of elementary reflectors as returned by geqlf

Template Parameters

side_t	Either Side or any class that implements `operator Side()`.
trans_t	Either Op or any class that implements `operator Op()`.

Parameters

[in]	side	Specifies which side op(Q) is to be applied. Side::Left: C := op(Q) C; Side::Right: C := C op(Q).
[in]	trans	The operation \(op(Q)\) to be used: Op::NoTrans: \(op(Q) = Q\); Op::ConjTrans: \(op(Q) = Q^H\). Op::Trans is a valid value if the data type of A is real. In this case, the algorithm treats Op::Trans as Op::ConjTrans.
[in]	A	side = Side::Left: m-by-k matrix; side = Side::Right: n-by-k matrix.
[in]	tau	Vector of length k Contains the scalar factors of the elementary reflectors.
[in,out]	C	m-by-n matrix. On exit, C is replaced by one of the following: side = Side::Left & trans = Op::NoTrans: \(C := Q C\); side = Side::Right & trans = Op::NoTrans: \(C := C Q\); side = Side::Left & trans = Op::ConjTrans: \(C := C Q^H\); side = Side::Right & trans = Op::ConjTrans: \(C := Q^H C\).

Returns: WorkInfo The amount workspace required.

Parameters

[in] opts Options.

◆ unmqr_worksize()

template<class T , TLAPACK_SMATRIX matrixA_t, TLAPACK_SMATRIX matrixC_t, TLAPACK_SVECTOR tau_t, TLAPACK_SIDE side_t, TLAPACK_OP trans_t>

constexpr WorkInfo tlapack::unmqr_worksize	(	side_t	side,
		trans_t	trans,
		const matrixA_t &	A,
		const tau_t &	tau,
		const matrixC_t &	C,
		const UnmqrOpts &	opts = `{}`
	)

constexpr

Worspace query of unmqr()

Parameters

[in]	side	Specifies which side op(Q) is to be applied. Side::Left: C := op(Q) C; Side::Right: C := C op(Q).
[in]	trans	The operation \(op(Q)\) to be used: Op::NoTrans: \(op(Q) = Q\); Op::ConjTrans: \(op(Q) = Q^H\). Op::Trans is a valid value if the data type of A is real. In this case, the algorithm treats Op::Trans as Op::ConjTrans.
[in]	A	side = Side::Left: m-by-k matrix; side = Side::Right: n-by-k matrix. Contains the vectors that define the reflectors
[in]	tau	Vector of length k Contains the scalar factors of the elementary reflectors.
[in]	C	m-by-n matrix.
[in]	opts	Options.

Returns: WorkInfo The amount workspace required.

See also: unmqr

◆ unmr2_worksize()

template<class T , TLAPACK_SMATRIX matrixA_t, TLAPACK_SMATRIX matrixC_t, TLAPACK_VECTOR tau_t, TLAPACK_SIDE side_t, TLAPACK_OP trans_t>

constexpr WorkInfo tlapack::unmr2_worksize	(	side_t	side,
		trans_t	trans,
		const matrixA_t &	A,
		const tau_t &	tau,
		const matrixC_t &	C
	)

constexpr

Worspace query of unmr2()

Parameters

[in]	side	Specifies which side op(Q) is to be applied. Side::Left: C := op(Q) C; Side::Right: C := C op(Q).
[in]	trans	The operation \(op(Q)\) to be used: Op::NoTrans: \(op(Q) = Q\); Op::ConjTrans: \(op(Q) = Q^H\). Op::Trans is a valid value if the data type of A is real. In this case, the algorithm treats Op::Trans as Op::ConjTrans.
[in]	A	side = Side::Left: k-by-m matrix; side = Side::Right: k-by-n matrix.
[in]	tau	Vector of length k Contains the scalar factors of the elementary reflectors.
[in]	C	m-by-n matrix.

Returns: WorkInfo The amount workspace required.

◆ unmrq_worksize()

template<class T , TLAPACK_SMATRIX matrixA_t, TLAPACK_SMATRIX matrixC_t, TLAPACK_SVECTOR tau_t, TLAPACK_SIDE side_t, TLAPACK_OP trans_t>

constexpr WorkInfo tlapack::unmrq_worksize	(	side_t	side,
		trans_t	trans,
		const matrixA_t &	A,
		const tau_t &	tau,
		const matrixC_t &	C,
		const UnmrqOpts &	opts = `{}`
	)

constexpr

Worspace query of unmrq()

Parameters

[in]	side	Specifies which side op(Q) is to be applied. Side::Left: C := op(Q) C; Side::Right: C := C op(Q).
[in]	trans	The operation \(op(Q)\) to be used: Op::NoTrans: \(op(Q) = Q\); Op::ConjTrans: \(op(Q) = Q^H\). Op::Trans is a valid value if the data type of A is real. In this case, the algorithm treats Op::Trans as Op::ConjTrans.
[in]	A	side = Side::Left: k-by-m matrix; side = Side::Right: k-by-n matrix. Contains the vectors that define the reflectors
[in]	tau	Vector of length k Contains the scalar factors of the elementary reflectors.
[in]	C	m-by-n matrix.
[in]	opts	Options.

Returns: WorkInfo The amount workspace required.

See also: unmrq

Functions

Detailed Description

Function Documentation

◆ aggressive_early_deflation_worksize()

◆ aggressive_early_deflation_worksize_gehrd()

◆ bidiag_worksize()

◆ gebd2_worksize()

◆ gebrd_worksize()

◆ gehd2_worksize()

◆ gehrd_worksize()

◆ gelq2_worksize()

◆ gelqf_worksize()

◆ gelqt_worksize()

◆ gen_householder_q_worksize()

◆ geql2_worksize()

◆ geqlf_worksize()

◆ geqr2_worksize()

◆ geqrf_worksize()

◆ gerq2_worksize()

◆ gerqf_worksize()

◆ getri_uxli_worksize()

◆ getri_worksize()

◆ hessenberg_worksize()

◆ householder_lq_worksize()

◆ householder_q_mul_worksize()

◆ householder_ql_worksize()

◆ householder_qr_worksize()

◆ householder_rq_worksize()

◆ infnorm_colmajor_worksize()

◆ infnorm_hermitian_colmajor_worksize()

◆ infnorm_symmetric_colmajor_worksize()

◆ infnorm_triangular_colmajor_worksize()

◆ larf_worksize() [1/2]

◆ larf_worksize() [2/2]

◆ larfb_worksize()

◆ multishift_QR_sweep_worksize()

◆ multishift_qr_worksize()

◆ qr_iteration_worksize()

◆ ung2l_worksize()

◆ ung2r_worksize()

◆ ungbr_p_worksize()

◆ ungbr_q_worksize()

◆ unghr_worksize()

◆ ungl2_worksize()

◆ ungq_level2_worksize()

◆ ungq_worksize()

◆ ungr2_worksize()

◆ unm2l_worksize()

◆ unm2r_worksize()

◆ unmhr_worksize()

◆ unml2_worksize()

◆ unmlq_worksize()

◆ unmq_level2_worksize()

◆ unmq_worksize()

◆ unmql_worksize()

◆ unmqr_worksize()

◆ unmr2_worksize()

◆ unmrq_worksize()