The SP2 Fermi module. More...

Functions/Subroutines
subroutine, public	prg_sp2_fermi_init (h_bml, nsteps, nocc, tscale, threshold, occErrLimit, traceLimit, x_bml, mu, beta, h1, hN, sgnlist)
	Truncated SP2 prg_initialization. More...

subroutine, public	prg_sp2_fermi_init_norecs (h_bml, nsteps, nocc, tscale, threshold, occErrLimit, traceLimit, x_bml, mu, beta, h1, hN, sgnlist, verbose)
	Truncated SP2 prg_initialization. This routine also gives back the Number of SP2 recursive steps that gets a Pseudo-Fermi distribution with a temperature close to the target temperature which is entered using parameter beta = (1/KbT). More...

subroutine, public	prg_sp2_fermi (h_bml, osteps, nsteps, nocc, mu, beta, h1, hN, sgnlist, threshold, eps, traceLimit, x_bml)
	Calculate Truncated SP2. More...

subroutine, public	prg_sp2_entropy_function (mu, h1, hN, nsteps, sgnlist, GG, ee)
	Calculate SP2 entropy function using gaussian quadrature. Note that GG and ee are allocated and returned from this routine. More...

real(dp) function, public	sp2_entropy_ts (D0_bml, GG, ee)
	Test SP2 entropy. Get the entropy contribution TS to the total free energy. More...

real(dp) function, public	sp2_inverse (f, mu, h1, hN, nsteps, sgnlist)
	Calculate the SP2 inverse. More...

real(dp) function	absmaxderivative (func, de)
	Gets the absolute maximum of the derivative of a function. More...

Variables
integer, parameter	dp = kind(1.0d0)

Detailed Description

The SP2 Fermi module.

This subroutine implements Niklasson's truncated SP2 density matrix purification algorithm.

Function/Subroutine Documentation

◆ absmaxderivative()

real(dp) function prg_sp2_fermi_mod::absmaxderivative	(	real(dp), dimension(:), intent(in)	func,
		real(dp), intent(in)	de
	)

private

Gets the absolute maximum of the derivative of a function.

Parameters

func.
de	Energy step.

Definition at line 617 of file prg_sp2_fermi_mod.F90.

◆ prg_sp2_entropy_function()

subroutine, public prg_sp2_fermi_mod::prg_sp2_entropy_function	(	real(dp), intent(in)	mu,
		real(dp), intent(in)	h1,
		real(dp), intent(in)	hN,
		integer, intent(in)	nsteps,
		integer, dimension(:), intent(in)	sgnlist,
		real(dp), dimension(:), intent(inout), allocatable	GG,
		real(dp), dimension(:), intent(inout), allocatable	ee
	)

Calculate SP2 entropy function using gaussian quadrature. Note that GG and ee are allocated and returned from this routine.

Parameters

mu	Shifted chemical potential
h1	Minimum scaled Gershgorin bound
hN	Maximum scaled Gershgorin bound
nsteps	Number of SP2 steps
sgnlist	SP2 sequence
GG	Entropy function
ee	1D mesh

Definition at line 482 of file prg_sp2_fermi_mod.F90.

◆ prg_sp2_fermi()

subroutine, public prg_sp2_fermi_mod::prg_sp2_fermi	(	type(bml_matrix_t), intent(in)	h_bml,
		integer, intent(in)	osteps,
		integer, intent(in)	nsteps,
		real(dp), intent(in)	nocc,
		real(dp), intent(inout)	mu,
		real(dp), intent(inout)	beta,
		real(dp), intent(inout)	h1,
		real(dp), intent(inout)	hN,
		integer, dimension(:), intent(in)	sgnlist,
		real(dp), intent(in)	threshold,
		real(dp), intent(in)	eps,
		real(dp), intent(in)	traceLimit,
		type(bml_matrix_t), intent(inout)	x_bml
	)

Calculate Truncated SP2.

Parameters

h_bml	Hamiltonian matrix
osteps	Outer loop steps
nsteps	Number of sequence branches
nocc	Number of occupation states
mu	Shifted chemical potential
beta	Inverse temperature
h1	Minimum scaled Gershgorin bound.
hN	Maximum scaled Gershgorin bound.
sgnlist	SP2 sequence
threshold	Threshold for multiplies
eps	Occupation error limit
traceLimit	Trace limit
x_bml	Output density matrix

Definition at line 388 of file prg_sp2_fermi_mod.F90.

◆ prg_sp2_fermi_init()

subroutine, public prg_sp2_fermi_mod::prg_sp2_fermi_init	(	type(bml_matrix_t), intent(in)	h_bml,
		integer, intent(in)	nsteps,
		real(dp), intent(in)	nocc,
		real(dp), intent(in)	tscale,
		real(dp), intent(in)	threshold,
		real(dp), intent(in)	occErrLimit,
		real(dp), intent(in)	traceLimit,
		type(bml_matrix_t), intent(inout)	x_bml,
		real(dp), intent(inout)	mu,
		real(dp), intent(inout)	beta,
		real(dp), intent(inout)	h1,
		real(dp), intent(inout)	hN,
		integer, dimension(:), intent(inout)	sgnlist
	)

Truncated SP2 prg_initialization.

Parameters

h_bml	Input Hamiltonian matrix.
nsteps	Number of sp2 iterations.
nocc	Number of occupied states.
tscale	Temperature rescaling factor.
threshold	Threshold for multiplication.
occErrLimit	Occupation error limit.
traceLimit	Trace limit.
x_bml	Output prg_initial matrix.
mu	Shifted chemical potential
beta	Output inverse temperature.
h1	Output temperature-scaled minimum gershgorin bound.
hN	Output temperature-scaled maximum gershgorin bound.
sgnlist	SP2 sequence

Calculate Gershgorin bounds and rescale

Determine sequence branching first time through

Definition at line 43 of file prg_sp2_fermi_mod.F90.

◆ prg_sp2_fermi_init_norecs()

subroutine, public prg_sp2_fermi_mod::prg_sp2_fermi_init_norecs	(	type(bml_matrix_t), intent(in)	h_bml,
		integer, intent(inout)	nsteps,
		real(dp), intent(in)	nocc,
		real(dp), intent(in)	tscale,
		real(dp), intent(in)	threshold,
		real(dp), intent(in)	occErrLimit,
		real(dp), intent(in)	traceLimit,
		type(bml_matrix_t), intent(inout)	x_bml,
		real(dp), intent(inout)	mu,
		real(dp), intent(inout)	beta,
		real(dp), intent(inout)	h1,
		real(dp), intent(inout)	hN,
		integer, dimension(:), intent(inout)	sgnlist,
		integer, optional	verbose
	)

Truncated SP2 prg_initialization. This routine also gives back the Number of SP2 recursive steps that gets a Pseudo-Fermi distribution with a temperature close to the target temperature which is entered using parameter beta = (1/KbT).

Parameters

h_bml	Input Hamiltonian matrix.
nsteps	Output number of sp2 iterations.
nocc	Number of occupied states.
tscale	Temperature rescaling factor.
threshold	Threshold for multiplication.
occErrLimit	Occupation error limit.
traceLimit	Trace limit.
x_bml	Output prg_initial matrix.
mu	Shifted chemical potential
beta	Input guess and output inverse temperature.
h1	Output temperature-scaled minimum gershgorin bound.
hN	Output temperature-scaled maximum gershgorin bound.
sgnlist	SP2 sequence
verbose	Optional parameter for verbosity.

Calculate Gershgorin bounds and rescale

Determine sequence branching first time through

Definition at line 198 of file prg_sp2_fermi_mod.F90.

◆ sp2_entropy_ts()

real(dp) function, public prg_sp2_fermi_mod::sp2_entropy_ts	(	type(bml_matrix_t), intent(in)	D0_bml,
		real(dp), dimension(*), intent(in)	GG,
		real(dp), dimension(*), intent(in)	ee
	)

Test SP2 entropy. Get the entropy contribution TS to the total free energy.

Parameters

D0_bml	BML matrix
GG	Entropy function
ee	1D mesh
TS	Energy contribution

Definition at line 540 of file prg_sp2_fermi_mod.F90.

◆ sp2_inverse()

real(dp) function, public prg_sp2_fermi_mod::sp2_inverse	(	real(dp), intent(in)	f,
		real(dp), intent(in)	mu,
		real(dp), intent(in)	h1,
		real(dp), intent(in)	hN,
		integer, intent(in)	nsteps,
		integer, dimension(:), intent(in)	sgnlist
	)

Calculate the SP2 inverse.

Parameters

f	Occupation factor
mu	Shifted chemical potential
h1	Minimum scaled Gershgorin bound
hN	Maximum scaled Gershgorin bound
nsteps	Numbers of SP2 iterations
sgnlist	SP2 sequence
ee	Energy value

Definition at line 592 of file prg_sp2_fermi_mod.F90.

Variable Documentation

◆ dp

integer, parameter prg_sp2_fermi_mod::dp = kind(1.0d0)

private

Definition at line 18 of file prg_sp2_fermi_mod.F90.

Functions/Subroutines

Variables

Detailed Description

Function/Subroutine Documentation

◆ absmaxderivative()

◆ prg_sp2_entropy_function()

◆ prg_sp2_fermi()

◆ prg_sp2_fermi_init()

◆ prg_sp2_fermi_init_norecs()

◆ sp2_entropy_ts()

◆ sp2_inverse()

Variable Documentation

◆ dp