Functions/Subroutines
subroutine, public	prg_implicit_fermi_save_inverse (Inv_bml, h_bml, p_bml, nsteps, nocc, mu, beta, occErrLimit, threshold, tol, SCF_IT, occiter, totns)
	Recursive Implicit Fermi Dirac for finite temperature. More...

subroutine, public	prg_implicit_fermi (h_bml, p_bml, nsteps, k, nocc, mu, beta, method, osteps, occErrLimit, threshold, tol)
	Recursive Implicit Fermi Dirac for finite temperature. More...

subroutine, public	prg_implicit_fermi_zero (h_bml, p_bml, nsteps, mu, method, threshold, tol)
	Recursive Implicit Fermi Dirac for zero temperature. More...

subroutine, public	prg_implicit_fermi_first_order_response (H0_bml, H1_bml, P0_bml, P1_bml, Inv_bml, nsteps, mu0, beta, nocc, threshold)
	Calculate first order density matrix response to perturbations using Implicit Fermi Dirac. More...

subroutine, public	prg_implicit_fermi_response (H0_bml, H1_bml, H2_bml, H3_bml, P0_bml, P1_bml, P2_bml, P3_bml, nsteps, mu0, mu, beta, nocc, occ_tol, lin_tol, order, threshold)
	Calculate density matrix response to perturbations using Implicit Fermi Dirac. More...

subroutine, public	prg_finite_diff (H0_bml, H_list, mu0, mu_list, beta, order, lambda, h, threshold)
	Calculate density matrix response from perturbations in the Hamiltonian. More...

subroutine	prg_setup_linsys (p_bml, A_bml, b_bml, p2_bml, y_bml, aux_bml, aux1_bml, k, threshold)
	Set up linear system for Implicit Fermi Dirac. More...

subroutine	prg_newtonschulz (a_bml, ai_bml, r_bml, tmp_bml, d_bml, I_bml, tol, threshold, num_iter)
	Find the inverse of the matrix A with Newton-Schulz iteration. More...

subroutine	prg_pcg (A_bml, p_bml, p2_bml, d_bml, wtmp_bml, cg_tol, threshold)
	Solve the system AX = B with conjugate gradient. More...

subroutine	prg_conjgrad (A_bml, p_bml, p2_bml, tmp_bml, d_bml, w_bml, cg_tol, threshold)
	Solve the system AX = B with conjugate gradient. More...

subroutine	prg_get_density_matrix (ham_bml, p_bml, beta, mu, threshold)
	Calculate the density matrix with diagonalization. More...

subroutine, public	prg_test_density_matrix (ham_bml, p_bml, beta, mu, nocc, osteps, occErrLimit, threshold)
	Calculate the density matrix with diagonalization and converge chemical. More...

real(dp) function	fermi (e, mu, beta)
	Gives the Fermi distribution value for energy e. More...

Variables
integer, parameter	dp = kind(1.0d0)

Function/Subroutine Documentation

◆ fermi()

real(dp) function prg_implicit_fermi_mod::fermi	(	real(dp), intent(in)	e,
		real(dp), intent(in)	mu,
		real(dp), intent(in)	beta
	)

private

Gives the Fermi distribution value for energy e.

Parameters

e	Energy.
mu	Fermi energy.
beta	Inverse temperature

Definition at line 1192 of file prg_implicit_fermi_mod.F90.

◆ prg_conjgrad()

subroutine prg_implicit_fermi_mod::prg_conjgrad	(	type(bml_matrix_t), intent(in)	A_bml,
		type(bml_matrix_t), intent(inout)	p_bml,
		type(bml_matrix_t), intent(in)	p2_bml,
		type(bml_matrix_t), intent(inout)	tmp_bml,
		type(bml_matrix_t), intent(inout)	d_bml,
		type(bml_matrix_t), intent(inout)	w_bml,
		real(dp), intent(in)	cg_tol,
		real(dp), intent(in)	threshold
	)

private

Solve the system AX = B with conjugate gradient.

Parameters

A_bml	Coefficient matrix A
p_bml	Output solution X
p2_bml	Right side matrix B
d_bml	Auxillary matrix
w_bml	Auxillary matrix
cg_tol	Convergence condition (OBS squared Frobenius norm of residual matrix)
threshold	Threshold for matrix algebra

Definition at line 1006 of file prg_implicit_fermi_mod.F90.

◆ prg_finite_diff()

subroutine, public prg_implicit_fermi_mod::prg_finite_diff	(	type(bml_matrix_t), intent(in)	H0_bml,
		type(bml_matrix_t), dimension(:), intent(in), allocatable	H_list,
		real(dp), intent(in)	mu0,
		real(dp), dimension(:), intent(in), allocatable	mu_list,
		real(dp), intent(in)	beta,
		integer, intent(in)	order,
		real(dp), intent(in)	lambda,
		real(dp), intent(in)	h,
		real(dp), intent(in)	threshold
	)

Calculate density matrix response from perturbations in the Hamiltonian.

Definition at line 726 of file prg_implicit_fermi_mod.F90.

◆ prg_get_density_matrix()

subroutine prg_implicit_fermi_mod::prg_get_density_matrix	(	type(bml_matrix_t), intent(in)	ham_bml,
		type(bml_matrix_t), intent(inout)	p_bml,
		real(dp), intent(in)	beta,
		real(dp), intent(in)	mu,
		real(dp), intent(in)	threshold
	)

private

Calculate the density matrix with diagonalization.

Parameters

ham_bml	Input hamiltonian
p_bml	Output density matrix
beta	Inverse temperature
mu	Chemical potential
threshold	Threshold for matrix algebra

Definition at line 1056 of file prg_implicit_fermi_mod.F90.

◆ prg_implicit_fermi()

subroutine, public prg_implicit_fermi_mod::prg_implicit_fermi	(	type(bml_matrix_t), intent(in)	h_bml,
		type(bml_matrix_t), intent(inout)	p_bml,
		integer, intent(in)	nsteps,
		integer, intent(in)	k,
		real(dp), intent(in)	nocc,
		real(dp), intent(inout)	mu,
		real(dp), intent(in)	beta,
		integer, intent(in)	method,
		integer, intent(in)	osteps,
		real(dp), intent(in)	occErrLimit,
		real(dp), intent(in)	threshold,
		real(dp), intent(in)	tol
	)

Recursive Implicit Fermi Dirac for finite temperature.

Parameters

h_bml	Input Hamiltonian matrix.
p_bml	Output density matrix.
nsteps	Number of recursion steps.
k	Expansion order
nocc	Number of occupied states.
mu	Shifted chemical potential
beta	Input inverse temperature.
method	0 - conjugate gradient, 1 - newton-schultz
osteps	Outer loop steps to converge chemical potential
occErrLimit	Occupation error limit.
threshold	Threshold for multiplication.
tol	Tolerance for linear system solver See

Definition at line 209 of file prg_implicit_fermi_mod.F90.

◆ prg_implicit_fermi_first_order_response()

subroutine, public prg_implicit_fermi_mod::prg_implicit_fermi_first_order_response	(	type(bml_matrix_t), intent(in)	H0_bml,
		type(bml_matrix_t), intent(in)	H1_bml,
		type(bml_matrix_t), intent(inout)	P0_bml,
		type(bml_matrix_t), intent(inout)	P1_bml,
		type(bml_matrix_t), dimension(nsteps), intent(in)	Inv_bml,
		integer, intent(in)	nsteps,
		real(dp), intent(in)	mu0,
		real(dp), intent(in)	beta,
		real(dp), intent(in)	nocc,
		real(dp), intent(in)	threshold
	)

Calculate first order density matrix response to perturbations using Implicit Fermi Dirac.

Parameters

H0_bml	Input Hamiltonian matrix.
H1_bml	Input First order perturbation of H0.
P0_bml	Output density matrix.
P1_bml	Output First order density matrix response.
nsteps	Number of recursion steps.
mu0	Shifted chemical potential.
beta	Input inverse temperature.
nocc	Number of occupied states.
threshold	Threshold for matrix algebra. See

Definition at line 439 of file prg_implicit_fermi_mod.F90.

◆ prg_implicit_fermi_response()

subroutine, public prg_implicit_fermi_mod::prg_implicit_fermi_response	(	type(bml_matrix_t), intent(in)	H0_bml,
		type(bml_matrix_t), intent(in)	H1_bml,
		type(bml_matrix_t), intent(in)	H2_bml,
		type(bml_matrix_t), intent(in)	H3_bml,
		type(bml_matrix_t), intent(inout)	P0_bml,
		type(bml_matrix_t), intent(inout)	P1_bml,
		type(bml_matrix_t), intent(inout)	P2_bml,
		type(bml_matrix_t), intent(inout)	P3_bml,
		integer, intent(in)	nsteps,
		real(dp), intent(inout)	mu0,
		real(dp), dimension(:), intent(inout), allocatable	mu,
		real(dp), intent(in)	beta,
		real(dp), intent(in)	nocc,
		real(dp), intent(in)	occ_tol,
		real(dp), intent(in)	lin_tol,
		integer	order,
		real(dp)	threshold
	)

Calculate density matrix response to perturbations using Implicit Fermi Dirac.

Parameters

H0_bml	Input Hamiltonian matrix.
H1_bml,H2_bml,H3_bml	Input First to third order perturbations of H0.
P0_bml	Output density matrix.
P1_bml,P2_bml,P3_bml	Output First to third order density matrix response.
nsteps	Number of recursion steps.
mu0	Shifted chemical potential.
mu	Pre-allocated array of length order.
beta	Input inverse temperature.
nocc	Number of occupied states.
occ_tol	Occupation error tolerance.
lin_tol	Linear solver tolerance.
order	Calculate response up to this order.
threshold	Threshold for matrix algebra. See

Definition at line 547 of file prg_implicit_fermi_mod.F90.

◆ prg_implicit_fermi_save_inverse()

subroutine, public prg_implicit_fermi_mod::prg_implicit_fermi_save_inverse	(	type(bml_matrix_t), dimension(nsteps), intent(inout)	Inv_bml,
		type(bml_matrix_t), intent(in)	h_bml,
		type(bml_matrix_t), intent(inout)	p_bml,
		integer, intent(in)	nsteps,
		real(dp), intent(in)	nocc,
		real(dp), intent(inout)	mu,
		real(dp), intent(in)	beta,
		real(dp), intent(in)	occErrLimit,
		real(dp), intent(in)	threshold,
		real(dp), intent(in)	tol,
		integer, intent(in)	SCF_IT,
		integer, intent(inout)	occiter,
		integer, intent(inout)	totns
	)

Recursive Implicit Fermi Dirac for finite temperature.

Parameters

Inv_bml	Inverses generated by algorithm.
h_bml	Input Hamiltonian matrix.
p_bml	Output density matrix.
nsteps	Number of recursion steps.
nocc	Number of occupied states.
mu	Shifted chemical potential
beta	Input inverse temperature.
occErrLimit	Occupation error limit.
threshold	Threshold for multiplication.
tol	Tolerance for linear system solver.
SCF_IT	The current SCF iteration.
occiter	Counts the total nr of DM calculations during MD. See

Definition at line 46 of file prg_implicit_fermi_mod.F90.

◆ prg_implicit_fermi_zero()

subroutine, public prg_implicit_fermi_mod::prg_implicit_fermi_zero	(	type(bml_matrix_t), intent(in)	h_bml,
		type(bml_matrix_t), intent(inout)	p_bml,
		integer, intent(in)	nsteps,
		real(dp), intent(in)	mu,
		integer, intent(in)	method,
		real(dp), intent(in)	threshold,
		real(dp), intent(inout), optional	tol
	)

Recursive Implicit Fermi Dirac for zero temperature.

Parameters

h_bml	Input Hamiltonian matrix.
p_bml	Output density matrix.
nsteps	Number of recursion steps.
mu	Shifted chemical potential
beta	Input inverse temperature.
method	0 - conjugate gradient, 1 - newton-schultz
threshold	Threshold for multiplication.
tol	Tolerance for linear system solver

Definition at line 347 of file prg_implicit_fermi_mod.F90.

◆ prg_newtonschulz()

subroutine prg_implicit_fermi_mod::prg_newtonschulz	(	type(bml_matrix_t), intent(in)	a_bml,
		type(bml_matrix_t), intent(inout)	ai_bml,
		type(bml_matrix_t), intent(inout)	r_bml,
		type(bml_matrix_t), intent(inout)	tmp_bml,
		type(bml_matrix_t), intent(inout)	d_bml,
		type(bml_matrix_t), intent(in)	I_bml,
		real(dp), intent(in)	tol,
		real(dp), intent(in)	threshold,
		integer, intent(out)	num_iter
	)

private

Find the inverse of the matrix A with Newton-Schulz iteration.

Parameters

a_bml	Input matrix A
ai_bml	Input starting guess and output inverse
r_bml	Auxillary matrix
tmp_bml	Auxillary matrix
tol	Convergence criterion (Frobenius norm of residual matrix)
threshold	Threshold for matrix algebra

Definition at line 888 of file prg_implicit_fermi_mod.F90.

◆ prg_pcg()

subroutine prg_implicit_fermi_mod::prg_pcg	(	type(bml_matrix_t), intent(in)	A_bml,
		type(bml_matrix_t), intent(inout)	p_bml,
		type(bml_matrix_t), intent(inout)	p2_bml,
		type(bml_matrix_t), intent(inout)	d_bml,
		type(bml_matrix_t), intent(inout)	wtmp_bml,
		real(dp), intent(in)	cg_tol,
		real(dp), intent(in)	threshold
	)

private

Solve the system AX = B with conjugate gradient.

Parameters

A_bml	Coefficient matrix A
p_bml	Output solution X
p2_bml	Right side matrix B
d_bml	Auxillary matrix
w_bml	Auxillary matrix
cg_tol	Convergence condition (OBS squared Frobenius norm of residual matrix)
threshold	Threshold for matrix algebra

Definition at line 934 of file prg_implicit_fermi_mod.F90.

◆ prg_setup_linsys()

subroutine prg_implicit_fermi_mod::prg_setup_linsys	(	type(bml_matrix_t), intent(in)	p_bml,
		type(bml_matrix_t), intent(inout)	A_bml,
		type(bml_matrix_t), intent(inout)	b_bml,
		type(bml_matrix_t), intent(inout)	p2_bml,
		type(bml_matrix_t), intent(inout)	y_bml,
		type(bml_matrix_t), intent(inout)	aux_bml,
		type(bml_matrix_t), intent(inout)	aux1_bml,
		integer, intent(in)	k,
		real(dp), intent(in)	threshold
	)

private

Set up linear system for Implicit Fermi Dirac.

Parameters

p_bml	Input X_i matrix.
p2_bml	Output X_i^k matrix.
A_bml	Output [X_i^k + (I - X_i)^k] matrix.
y_bml	Auxillary matrix.
aux_bml	Auxillary matrix
aux1_bml	Auxillary matrix.
k	Expansion order (an even number)
threshold	Threshold for multiplication. OBS this routine can be numerically unstable for k > 4

Definition at line 843 of file prg_implicit_fermi_mod.F90.

◆ prg_test_density_matrix()

subroutine, public prg_implicit_fermi_mod::prg_test_density_matrix	(	type(bml_matrix_t), intent(in)	ham_bml,
		type(bml_matrix_t), intent(inout)	p_bml,
		real(dp), intent(in)	beta,
		real(dp), intent(inout)	mu,
		real(dp), intent(in)	nocc,
		integer, intent(in)	osteps,
		real(dp), intent(in)	occErrLimit,
		real(dp), intent(in)	threshold
	)

Calculate the density matrix with diagonalization and converge chemical.

Definition at line 1112 of file prg_implicit_fermi_mod.F90.

Variable Documentation

◆ dp

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

private

Definition at line 20 of file prg_implicit_fermi_mod.F90.

Functions/Subroutines

Variables

Function/Subroutine Documentation

◆ fermi()

◆ prg_conjgrad()

◆ prg_finite_diff()

◆ prg_get_density_matrix()

◆ prg_implicit_fermi()

◆ prg_implicit_fermi_first_order_response()

◆ prg_implicit_fermi_response()

◆ prg_implicit_fermi_save_inverse()

◆ prg_implicit_fermi_zero()

◆ prg_newtonschulz()

◆ prg_pcg()

◆ prg_setup_linsys()

◆ prg_test_density_matrix()

Variable Documentation

◆ dp