spectral_localizer_dbcsr Module Reference

Distributed block-sparse finite localizers, retaining the covariant AO metric. More...

Data Types
type	localizer_matrix_type

Functions/Subroutines
subroutine, public	localizer_dbcsr_3d_build (h, s, positions, point, energy, kappa, block, metric, soc, shifted_hamiltonian, periodic_cosines)
	Build the 3D AII chiral block in DBCSR; not a Hermitian 2D localizer.
subroutine, public	localizer_dbcsr_realify (matrix, realified)
	Distributed real matrix R(A)=[Re(A),-Im(A);Im(A),Re(A)].
subroutine, public	localizer_dbcsr_from_real (realified, template, matrix)
	Extract the two left quadrants of R(A); does not average away structure errors.
subroutine, public	localizer_ao_operators (h, s, positions, operators, metric, soc)
	Shared AO Hamiltonian, Hermitian scalar observables and optional GTH physical-spin SOC.
subroutine, public	localizer_dbcsr_gap_pencil (h, s, energy, pencil, metric)
	Pair H-E*S with its negative to reuse the metric-aware localizer gap solvers.
subroutine, public	localizer_dbcsr_build (h, s, x, y, point, energy, kappa, localizer, metric, soc, periodic_cosines, shifted_hamiltonian)
	Assemble L and B=diag(S,S), including optional physical spin and SOC, without dense AOs.
subroutine, public	localizer_dbcsr_dense (matrix, para_env, dense)
	Collect the size-limited dense oracle; sparse solvers must not call this routine.
subroutine, public	localizer_dbcsr_check (matrix, para_env, tolerance, valid, relative_error)
	Check both components before a sparse solver discards the upper triangle.
subroutine, public	localizer_dbcsr_release (matrix)
	Release both real components of a complex sparse operator.

Detailed Description

Distributed block-sparse finite localizers, retaining the covariant AO metric.

Author

Thomas D. Kuehne, tkueh.nosp@m.ne@c.nosp@m.p2k.o.nosp@m.rg

Function/Subroutine Documentation

localizer_dbcsr_3d_build()

subroutine, public spectral_localizer_dbcsr::localizer_dbcsr_3d_build	(	type(dbcsr_type), intent(in)	h,
		type(dbcsr_type), intent(in)	s,
		type(dbcsr_p_type), dimension(:), intent(in)	positions,
		real(dp), dimension(3), intent(in)	point,
		real(dp), intent(in)	energy,
		real(dp), intent(in)	kappa,
		type(localizer_matrix_type), intent(out)	block,
		type(localizer_matrix_type), intent(out)	metric,
		type(dbcsr_p_type), dimension(:, :), intent(in)	soc,
		type(localizer_matrix_type), intent(in), optional	shifted_hamiltonian,
		type(dbcsr_p_type), dimension(:), intent(in), optional	periodic_cosines )

Build the 3D AII chiral block in DBCSR; not a Hermitian 2D localizer.

Parameters

h	Scalar AO Hamiltonian
s	Scalar AO overlap
positions	Three Cartesian AO first moments
point	Cartesian position query
energy	Absolute energy query
kappa	Positive energy/length scale
block	Chiral block, with auxiliary index outside physical up/down spin
metric	Block metric I_aux tensor I_spin tensor S
soc	Three real antisymmetric SOC components
shifted_hamiltonian	Optional already energy-shifted physical-spin Hamiltonian
periodic_cosines	Three cos(G.r) matrices. Then positions are sin(G.r), point is in radians, and kappa is the periodic energy scale eta.

Definition at line 55 of file spectral_localizer_dbcsr.F.

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localizer_dbcsr_realify()

subroutine, public spectral_localizer_dbcsr::localizer_dbcsr_realify	(	type(localizer_matrix_type), intent(in)	matrix,
		type(dbcsr_type), intent(out)	realified )

Distributed real matrix R(A)=[Re(A),-Im(A);Im(A),Re(A)].

Parameters

matrix	Complex operator with full-storage components
realified	Newly initialized real DBCSR operator

Definition at line 126 of file spectral_localizer_dbcsr.F.

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localizer_dbcsr_from_real()

subroutine, public spectral_localizer_dbcsr::localizer_dbcsr_from_real	(	type(dbcsr_type), intent(inout)	realified,
		type(localizer_matrix_type), intent(in)	template,
		type(localizer_matrix_type), intent(out)	matrix )

Extract the two left quadrants of R(A); does not average away structure errors.

Parameters

realified	Fully stored real operator with two repeated component distributions
template	Original complex operator defining the physical AO block distribution
matrix	Newly initialized complex operator; caller must check realification residual

Definition at line 149 of file spectral_localizer_dbcsr.F.

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localizer_ao_operators()

subroutine, public spectral_localizer_dbcsr::localizer_ao_operators	(	type(dbcsr_type), intent(in)	h,
		type(dbcsr_type), intent(in)	s,
		type(dbcsr_p_type), dimension(:), intent(in)	positions,
		type(localizer_matrix_type), dimension(:), intent(out)	operators,
		type(localizer_matrix_type), intent(out)	metric,
		type(dbcsr_p_type), dimension(:, :), intent(in), optional	soc )

Shared AO Hamiltonian, Hermitian scalar observables and optional GTH physical-spin SOC.

Parameters

h	Scalar Hamiltonian
s	AO metric
positions	Covariant scalar observables, such as first moments or trigonometric coordinates
operators	Newly initialized Hamiltonian followed by the supplied observables
metric	Newly initialized physical-spin metric
soc	Optional antisymmetric real GTH SOC components

Definition at line 221 of file spectral_localizer_dbcsr.F.

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localizer_dbcsr_gap_pencil()

subroutine, public spectral_localizer_dbcsr::localizer_dbcsr_gap_pencil	(	type(localizer_matrix_type), intent(in)	h,
		type(localizer_matrix_type), intent(in)	s,
		real(dp), intent(in)	energy,
		type(localizer_matrix_type), intent(out)	pencil,
		type(localizer_matrix_type), intent(out)	metric )

Pair H-E*S with its negative to reuse the metric-aware localizer gap solvers.

Parameters

h	Complex physical Hamiltonian, including spin if present
s	Complex physical metric with the same AO block layout
energy	Reference energy
pencil	Newly allocated diag(H-E*S,-H+E*S)
metric	Newly allocated diag(S,S)

Definition at line 270 of file spectral_localizer_dbcsr.F.

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localizer_dbcsr_build()

subroutine, public spectral_localizer_dbcsr::localizer_dbcsr_build	(	type(dbcsr_type), intent(in)	h,
		type(dbcsr_type), intent(in)	s,
		type(dbcsr_type), intent(in)	x,
		type(dbcsr_type), intent(in)	y,
		real(kind=dp), dimension(2), intent(in)	point,
		real(kind=dp), intent(in)	energy,
		real(kind=dp), intent(in)	kappa,
		type(localizer_matrix_type), intent(out)	localizer,
		type(localizer_matrix_type), intent(out)	metric,
		type(dbcsr_p_type), dimension(:, :), intent(in), optional	soc,
		type(dbcsr_p_type), dimension(:), intent(in), optional	periodic_cosines,
		type(localizer_matrix_type), intent(in), optional	shifted_hamiltonian )

Assemble L and B=diag(S,S), including optional physical spin and SOC, without dense AOs.

Parameters

h	Real scalar Hamiltonian
s	Real AO overlap
x	First oriented real AO position
y	Second oriented real AO position
point	Two Cartesian coordinates
energy	Reference energy
kappa	Energy/length scale
localizer	Newly created complex DBCSR localizer
metric	Newly created complex DBCSR metric
soc	Real antisymmetric SOC components from V_SOC_xyz_from_pseudopotential
periodic_cosines	Optional two cos(G.r) matrices. Then x,y are sin(G.r), point is G.r0, and kappa is the energy scale eta (not the finite energy/length scale).
shifted_hamiltonian	Optional replacement for the physical H-E*S including SOC. Requires energy=0; the scalar h and SOC contributions are then not added again.

Note

Component-major ordering: auxiliary index, physical spin, then atomic AO blocks.

Definition at line 309 of file spectral_localizer_dbcsr.F.

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localizer_dbcsr_dense()

subroutine, public spectral_localizer_dbcsr::localizer_dbcsr_dense	(	type(localizer_matrix_type), intent(inout)	matrix,
		type(mp_para_env_type), pointer	para_env,
		complex(kind=dp), dimension(:, :), intent(out), allocatable	dense )

Collect the size-limited dense oracle; sparse solvers must not call this routine.

Parameters

matrix	Fully stored complex block-sparse matrix
para_env	Matrix communicator
dense	Replicated matrix

Definition at line 464 of file spectral_localizer_dbcsr.F.

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localizer_dbcsr_check()

subroutine, public spectral_localizer_dbcsr::localizer_dbcsr_check	(	type(localizer_matrix_type), intent(inout)	matrix,
		type(mp_para_env_type), pointer	para_env,
		real(kind=dp), intent(in)	tolerance,
		logical, intent(out)	valid,
		real(kind=dp), intent(out), optional	relative_error )

Check both components before a sparse solver discards the upper triangle.

Parameters

matrix	Fully stored complex matrix
para_env	Matrix communicator
tolerance	Relative Hermiticity tolerance
valid	Whether all entries are finite and the matrix is Hermitian
relative_error	Largest component transpose residual divided by the largest component entry; HUGE for nonfinite entries or residuals

Definition at line 506 of file spectral_localizer_dbcsr.F.

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localizer_dbcsr_release()

subroutine, public spectral_localizer_dbcsr::localizer_dbcsr_release

(

type(localizer_matrix_type), intent(inout)

matrix

)

Release both real components of a complex sparse operator.

Parameters

matrix

Sparse operator

Definition at line 593 of file spectral_localizer_dbcsr.F.

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