spectral_localizer_flatten Module Reference

Metric-covariant spectral flattening with existing distributed matrix iterations. More...

Functions/Subroutines
subroutine, public	localizer_flatten_checked (h, s, energy, scale, tolerance, metric_tolerance, gap_tolerance, para_env, flattened, gap, metric_ratio, residuals, status)
	Establish a positive AO metric and electronic gap before iterating the matrix sign.
subroutine, public	localizer_flatten_dbcsr (h, s, energy, scale, tolerance, para_env, flattened, residuals, status)
	Form scale*S*sign(S^-1*(H-energy*S)) without dense AO matrices or S^-1/2.

Detailed Description

Metric-covariant spectral flattening with existing distributed matrix iterations.

Author

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

Function/Subroutine Documentation

localizer_flatten_checked()

subroutine, public spectral_localizer_flatten::localizer_flatten_checked	(	type(localizer_matrix_type), intent(inout)	h,
		type(localizer_matrix_type), intent(inout)	s,
		real(dp), intent(in)	energy,
		real(dp), intent(in)	scale,
		real(dp), intent(in)	tolerance,
		real(dp), intent(in)	metric_tolerance,
		real(dp), intent(in)	gap_tolerance,
		type(mp_para_env_type), pointer	para_env,
		type(localizer_matrix_type), intent(out)	flattened,
		real(dp), dimension(2), intent(out)	gap,
		real(dp), intent(out)	metric_ratio,
		real(dp), dimension(4), intent(out)	residuals,
		integer, intent(out)	status )

Establish a positive AO metric and electronic gap before iterating the matrix sign.

Parameters

h	Covariant physical Hamiltonian, unchanged
s	Covariant physical metric, unchanged
energy	Reference energy
scale	Positive flattened-band energy
tolerance	Matrix-sign residual and Hermiticity tolerance
metric_tolerance	Minimum overlap eigenvalue ratio
gap_tolerance	Absolute minimum original electronic gap
para_env	Communicator
flattened	Newly initialized shifted Hamiltonian only on success
gap	Original electronic gap lower and upper bounds, not the flattened localizer gap
metric_ratio	Overlap eigenvalue ratio
residuals	Four matrix-sign residuals
status	0 success, 1 unresolved input gap, -1 input, -2 metric, -4 solver, -6 matrix-sign iteration or structure failure

Definition at line 58 of file spectral_localizer_flatten.F.

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localizer_flatten_dbcsr()

subroutine, public spectral_localizer_flatten::localizer_flatten_dbcsr	(	type(localizer_matrix_type), intent(inout)	h,
		type(localizer_matrix_type), intent(inout)	s,
		real(dp), intent(in)	energy,
		real(dp), intent(in)	scale,
		real(dp), intent(in)	tolerance,
		type(mp_para_env_type), pointer	para_env,
		type(localizer_matrix_type), intent(out)	flattened,
		real(dp), dimension(4), intent(out)	residuals,
		integer, intent(out)	status )

Form scale*S*sign(S^-1*(H-energy*S)) without dense AO matrices or S^-1/2.

Parameters

h	Covariant Hermitian Hamiltonian; unchanged
s	Positive definite AO metric; must be validated by the caller
energy	Reference energy, separated from the generalized spectrum at input accuracy
scale	Positive energy scale of the flattened bands
tolerance	Residual tolerance, not a certificate of the original Hamiltonian gap
para_env	DBCSR communicator
flattened	Newly initialized covariant operator only on success
residuals	Inverse, sign-square, complex-structure and Hermiticity residuals
status	0 success, -1 invalid input, 1 unconverged sign/inverse, 2 broken structure

Note

Caller must establish a positive metric and a resolved electronic gap independently. Matrix-sign convergence alone cannot certify the occupied subspace near a gap closing.

Definition at line 125 of file spectral_localizer_flatten.F.

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