cp2k/src/dm_ls_chebyshev.F
2024-05-30 09:53:28 +02:00

400 lines
19 KiB
Fortran

!--------------------------------------------------------------------------------------------------!
! CP2K: A general program to perform molecular dynamics simulations !
! Copyright 2000-2024 CP2K developers group <https://cp2k.org> !
! !
! SPDX-License-Identifier: GPL-2.0-or-later !
!--------------------------------------------------------------------------------------------------!
! **************************************************************************************************
!> \brief Routines using linear scaling chebyshev methods
!> \par History
!> 2012.10 created [Jinwoong Cha]
!> \author Jinwoong Cha
! **************************************************************************************************
MODULE dm_ls_chebyshev
USE arnoldi_api, ONLY: arnoldi_extremal
USE cp_dbcsr_api, ONLY: &
dbcsr_add, dbcsr_add_on_diag, dbcsr_copy, dbcsr_create, dbcsr_frobenius_norm, &
dbcsr_get_info, dbcsr_get_occupation, dbcsr_multiply, dbcsr_release, dbcsr_scale, &
dbcsr_set, dbcsr_trace, dbcsr_type, dbcsr_type_no_symmetry
USE cp_log_handling, ONLY: cp_get_default_logger,&
cp_logger_get_default_unit_nr,&
cp_logger_type
USE cp_output_handling, ONLY: cp_p_file,&
cp_print_key_finished_output,&
cp_print_key_should_output,&
cp_print_key_unit_nr
USE dm_ls_scf_qs, ONLY: write_matrix_to_cube
USE dm_ls_scf_types, ONLY: ls_scf_env_type
USE input_section_types, ONLY: section_get_ivals,&
section_vals_val_get
USE kinds, ONLY: default_string_length,&
dp
USE machine, ONLY: m_flush,&
m_walltime
USE mathconstants, ONLY: pi
USE qs_environment_types, ONLY: qs_environment_type
#include "./base/base_uses.f90"
IMPLICIT NONE
PRIVATE
CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'dm_ls_chebyshev'
PUBLIC :: compute_chebyshev
CONTAINS
! **************************************************************************************************
!> \brief compute chebyshev polynomials up to order n for a given value of x
!> \param value ...
!> \param x ...
!> \param n ...
!> \par History
!> 2012.11 created [Jinwoong Cha]
!> \author Jinwoong Cha
! **************************************************************************************************
SUBROUTINE chebyshev_poly(value, x, n)
REAL(KIND=dp), INTENT(OUT) :: value
REAL(KIND=dp), INTENT(IN) :: x
INTEGER, INTENT(IN) :: n
!polynomial values
!number of chev polynomials
value = COS((n - 1)*ACOS(x))
END SUBROUTINE chebyshev_poly
! **************************************************************************************************
!> \brief kernel for chebyshev polynomials expansion (Jackson kernel)
!> \param value ...
!> \param n ...
!> \param nc ...
!> \par History
!> 2012.11 created [Jinwoong Cha]
!> \author Jinwoong Cha
! **************************************************************************************************
SUBROUTINE kernel(value, n, nc)
REAL(KIND=dp), INTENT(OUT) :: value
INTEGER, INTENT(IN) :: n, nc
!kernel at n
!n-1 order of chebyshev polynomials
!number of total chebyshev polynomials
!Kernel define
value = 1.0_dp/(nc + 1.0_dp)*((nc - (n - 1) + 1.0_dp)* &
COS(pi*(n - 1)/(nc + 1.0_dp)) + SIN(pi*(n - 1)/(nc + 1.0_dp))*1.0_dp/TAN(pi/(nc + 1.0_dp)))
END SUBROUTINE kernel
! **************************************************************************************************
!> \brief compute properties based on chebyshev expansion
!> \param qs_env ...
!> \param ls_scf_env ...
!> \par History
!> 2012.10 created [Jinwoong Cha]
!> \author Jinwoong Cha
! **************************************************************************************************
SUBROUTINE compute_chebyshev(qs_env, ls_scf_env)
TYPE(qs_environment_type), POINTER :: qs_env
TYPE(ls_scf_env_type) :: ls_scf_env
CHARACTER(len=*), PARAMETER :: routineN = 'compute_chebyshev'
REAL(KIND=dp), PARAMETER :: scale_evals = 1.01_dp
CHARACTER(LEN=30) :: middle_name
CHARACTER(LEN=default_string_length) :: title
INTEGER :: handle, icheb, igrid, iinte, ispin, &
iwindow, n_gridpoint_dos, ncheb, &
ninte, Nrows, nwindow, unit_cube, &
unit_dos, unit_nr
LOGICAL :: converged, write_cubes
REAL(KIND=dp) :: chev_T, chev_T_dos, dummy1, final, frob_matrix, initial, interval_a, &
interval_b, max_ev, min_ev, occ, orbital_occ, summa, t1, t2
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:) :: chev_E, chev_Es_dos, dos, dummy2, ev1, &
ev2, kernel_g, mu, sev1, sev2, trace_dm
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :) :: aitchev_T, E_inte, gdensity, sqrt_vec
REAL(KIND=dp), DIMENSION(:), POINTER :: tmp_r
TYPE(cp_logger_type), POINTER :: logger
TYPE(dbcsr_type) :: matrix_dummy1, matrix_F, matrix_tmp1, &
matrix_tmp2, matrix_tmp3
TYPE(dbcsr_type), DIMENSION(:), POINTER :: matrix_dummy2
IF (.NOT. ls_scf_env%chebyshev%compute_chebyshev) RETURN
CALL timeset(routineN, handle)
! get a useful output_unit
logger => cp_get_default_logger()
IF (logger%para_env%is_source()) THEN
unit_nr = cp_logger_get_default_unit_nr(logger, local=.TRUE.)
ELSE
unit_nr = -1
END IF
ncheb = ls_scf_env%chebyshev%n_chebyshev
ninte = 2*ncheb
n_gridpoint_dos = ls_scf_env%chebyshev%n_gridpoint_dos
write_cubes = BTEST(cp_print_key_should_output(logger%iter_info, ls_scf_env%chebyshev%print_key_cube), cp_p_file)
IF (write_cubes) THEN
IF (ASSOCIATED(ls_scf_env%chebyshev%min_energy)) DEALLOCATE (ls_scf_env%chebyshev%min_energy)
CALL section_vals_val_get(ls_scf_env%chebyshev%print_key_cube, "MIN_ENERGY", r_vals=tmp_r)
ALLOCATE (ls_scf_env%chebyshev%min_energy(SIZE(tmp_r)))
ls_scf_env%chebyshev%min_energy = tmp_r
IF (ASSOCIATED(ls_scf_env%chebyshev%max_energy)) DEALLOCATE (ls_scf_env%chebyshev%max_energy)
CALL section_vals_val_get(ls_scf_env%chebyshev%print_key_cube, "MAX_ENERGY", r_vals=tmp_r)
ALLOCATE (ls_scf_env%chebyshev%max_energy(SIZE(tmp_r)))
ls_scf_env%chebyshev%max_energy = tmp_r
nwindow = SIZE(ls_scf_env%chebyshev%min_energy)
ELSE
nwindow = 0
END IF
ALLOCATE (ev1(1:nwindow))
ALLOCATE (ev2(1:nwindow))
ALLOCATE (sev1(1:nwindow))
ALLOCATE (sev2(1:nwindow))
ALLOCATE (trace_dm(1:nwindow))
ALLOCATE (matrix_dummy2(1:nwindow))
DO iwindow = 1, nwindow
ev1(iwindow) = ls_scf_env%chebyshev%min_energy(iwindow)
ev2(iwindow) = ls_scf_env%chebyshev%max_energy(iwindow)
END DO
IF (unit_nr > 0) THEN
WRITE (unit_nr, '()')
WRITE (unit_nr, '(T2,A)') "STARTING CHEBYSHEV CALCULATION"
END IF
! create 3 temporary matrices
CALL dbcsr_create(matrix_tmp1, template=ls_scf_env%matrix_s, matrix_type=dbcsr_type_no_symmetry)
CALL dbcsr_create(matrix_tmp2, template=ls_scf_env%matrix_s, matrix_type=dbcsr_type_no_symmetry)
CALL dbcsr_create(matrix_tmp3, template=ls_scf_env%matrix_s, matrix_type=dbcsr_type_no_symmetry)
CALL dbcsr_create(matrix_F, template=ls_scf_env%matrix_s, matrix_type=dbcsr_type_no_symmetry)
CALL dbcsr_create(matrix_dummy1, template=ls_scf_env%matrix_s, matrix_type=dbcsr_type_no_symmetry)
DO iwindow = 1, nwindow
CALL dbcsr_create(matrix_dummy2(iwindow), template=ls_scf_env%matrix_s, &
matrix_type=dbcsr_type_no_symmetry)
END DO
DO ispin = 1, SIZE(ls_scf_env%matrix_ks)
! create matrix_F=inv(sqrt(S))*H*inv(sqrt(S))
CALL dbcsr_multiply("N", "N", 1.0_dp, ls_scf_env%matrix_s_sqrt_inv, ls_scf_env%matrix_ks(ispin), &
0.0_dp, matrix_tmp1, filter_eps=ls_scf_env%eps_filter)
CALL dbcsr_multiply("N", "N", 1.0_dp, matrix_tmp1, ls_scf_env%matrix_s_sqrt_inv, &
0.0_dp, matrix_F, filter_eps=ls_scf_env%eps_filter)
! find largest and smallest eigenvalues
CALL arnoldi_extremal(matrix_F, max_ev, min_ev, converged=converged, max_iter=ls_scf_env%max_iter_lanczos, &
threshold=ls_scf_env%eps_lanczos) !Lanczos algorithm to calculate eigenvalue
IF (unit_nr > 0) WRITE (unit_nr, '(T2,A,2F16.8,A,L2)') &
"smallest largest eigenvalue", min_ev, max_ev, " converged ", converged
IF (nwindow > 0) THEN
IF (unit_nr > 0) WRITE (unit_nr, '(T2,A,1000F16.8)') "requested interval-min_energy", ev1(:)
IF (unit_nr > 0) WRITE (unit_nr, '(T2,A,1000F16.8)') "requested interval-max_energy", ev2(:)
END IF
interval_a = (max_ev - min_ev)*scale_evals/2
interval_b = (max_ev + min_ev)/2
sev1(:) = (ev1(:) - interval_b)/interval_a !scaled ev1 vector
sev2(:) = (ev2(:) - interval_b)/interval_a !scaled ev2 vector
!chebyshev domain,pi*sqrt(1-x^2) vector construction and chebyshev polynomials for integration (for g(E))
ALLOCATE (E_inte(1:ninte + 1, 1:nwindow))
ALLOCATE (sqrt_vec(1:ninte + 1, 1:nwindow))
DO iwindow = 1, nwindow
DO iinte = 1, ninte + 1
E_inte(iinte, iwindow) = sev1(iwindow) + ((sev2(iwindow) - sev1(iwindow))/ninte)*(iinte - 1)
sqrt_vec(iinte, iwindow) = pi*SQRT(1.0_dp - E_inte(iinte, iwindow)*E_inte(iinte, iwindow))
END DO
END DO
!integral.. (identical to the coefficient for g(E))
ALLOCATE (aitchev_T(1:ncheb, 1:nwindow)) !after intergral. =>ainte
DO iwindow = 1, nwindow
DO icheb = 1, ncheb
CALL chebyshev_poly(initial, E_inte(1, iwindow), icheb)
CALL chebyshev_poly(final, E_inte(1, iwindow), icheb)
summa = (sev2(iwindow) - sev1(iwindow))/(2.0_dp*ninte)*(initial/sqrt_vec(1, iwindow) + final/sqrt_vec(ninte + 1, iwindow))
DO iinte = 2, ninte
CALL chebyshev_poly(chev_T, E_inte(iinte, iwindow), icheb)
summa = summa + ((sev2(iwindow) - sev1(iwindow))/ninte)*(chev_T/sqrt_vec(iinte, iwindow))
END DO
aitchev_T(icheb, iwindow) = summa
summa = 0
END DO
END DO
! scale the matrix to get evals in the interval -1,1
CALL dbcsr_add_on_diag(matrix_F, -interval_b)
CALL dbcsr_scale(matrix_F, 1/interval_a)
! compute chebyshev matrix recursion
CALL dbcsr_get_info(matrix=matrix_F, nfullrows_total=Nrows) !get information about a matrix
CALL dbcsr_set(matrix_dummy1, 0.0_dp) !empty matrix creation(for density matrix)
DO iwindow = 1, nwindow
CALL dbcsr_set(matrix_dummy2(iwindow), 0.0_dp) !empty matrix creation(for density matrix)
END DO
ALLOCATE (mu(1:ncheb))
ALLOCATE (kernel_g(1:ncheb))
CALL kernel(kernel_g(1), 1, ncheb)
CALL kernel(kernel_g(2), 2, ncheb)
CALL dbcsr_set(matrix_tmp1, 0.0_dp) !matrix creation
CALL dbcsr_add_on_diag(matrix_tmp1, 1.0_dp) !add a only number to diagonal elements
CALL dbcsr_trace(matrix_tmp1, trace=mu(1))
CALL dbcsr_copy(matrix_tmp2, matrix_F) !make matrix_tmp2 = matrix_F
CALL dbcsr_trace(matrix_tmp2, trace=mu(2))
DO iwindow = 1, nwindow
CALL dbcsr_copy(matrix_dummy1, matrix_tmp1)
CALL dbcsr_copy(matrix_dummy2(iwindow), matrix_tmp2) !matrix_dummy2=
CALL dbcsr_scale(matrix_dummy1, kernel_g(1)*aitchev_T(1, iwindow)) !first term of chebyshev poly(matrix)
CALL dbcsr_scale(matrix_dummy2(iwindow), 2.0_dp*kernel_g(2)*aitchev_T(2, iwindow)) !second term of chebyshev poly(matrix)
CALL dbcsr_add(matrix_dummy2(iwindow), matrix_dummy1, 1.0_dp, 1.0_dp)
END DO
DO icheb = 2, ncheb - 1
t1 = m_walltime()
CALL dbcsr_multiply("N", "N", 2.0_dp, matrix_F, matrix_tmp2, &
-1.0_dp, matrix_tmp1, filter_eps=ls_scf_env%eps_filter) !matrix multiplication(Recursion)
CALL dbcsr_copy(matrix_tmp3, matrix_tmp1)
CALL dbcsr_copy(matrix_tmp1, matrix_tmp2)
CALL dbcsr_copy(matrix_tmp2, matrix_tmp3)
CALL dbcsr_trace(matrix_tmp2, trace=mu(icheb + 1)) !icheb+1 th coefficient
CALL kernel(kernel_g(icheb + 1), icheb + 1, ncheb)
DO iwindow = 1, nwindow
CALL dbcsr_copy(matrix_dummy1, matrix_tmp2)
CALL dbcsr_scale(matrix_dummy1, 2.0_dp*kernel_g(icheb + 1)*aitchev_T(icheb + 1, iwindow)) !second term of chebyshev poly(matrix)
CALL dbcsr_add(matrix_dummy2(iwindow), matrix_dummy1, 1.0_dp, 1.0_dp)
CALL dbcsr_trace(matrix_dummy2(iwindow), trace=trace_dm(iwindow)) !icheb+1 th coefficient
END DO
occ = dbcsr_get_occupation(matrix_tmp1)
t2 = m_walltime()
IF (unit_nr > 0 .AND. MOD(icheb, 20) == 0) THEN
CALL m_flush(unit_nr)
IF (nwindow > 0) THEN
WRITE (unit_nr, '(T2,A,I5,1X,A,1X,F8.3,1X,A,1X,F8.6,1X,A,1X,1000F16.8)') &
"Iter.", icheb, "time=", t2 - t1, "occ=", occ, "traces=", trace_dm(:)
ELSE
WRITE (unit_nr, '(T2,A,I5,1X,A,1X,F8.3,1X,A,1X,F8.6)') &
"Iter.", icheb, "time=", t2 - t1, "occ=", occ
END IF
END IF
END DO
DO iwindow = 1, nwindow
IF (SIZE(ls_scf_env%matrix_ks) == 1) THEN
orbital_occ = 2.0_dp
ELSE
orbital_occ = 1.0_dp
END IF
CALL dbcsr_multiply("N", "N", 1.0_dp, ls_scf_env%matrix_s_sqrt_inv, matrix_dummy2(iwindow), &
0.0_dp, matrix_tmp1, filter_eps=ls_scf_env%eps_filter)
CALL dbcsr_multiply("N", "N", orbital_occ, matrix_tmp1, ls_scf_env%matrix_s_sqrt_inv, &
0.0_dp, matrix_tmp2, filter_eps=ls_scf_env%eps_filter)
CALL dbcsr_copy(matrix_dummy2(iwindow), matrix_tmp2)
! look at the difference with the density matrix from the ls routines
IF (.FALSE.) THEN
CALL dbcsr_copy(matrix_tmp1, matrix_tmp2)
CALL dbcsr_add(matrix_tmp1, ls_scf_env%matrix_p(ispin), 1.0_dp, -1.0_dp) !comparison
frob_matrix = dbcsr_frobenius_norm(matrix_tmp1)
IF (unit_nr > 0) WRITE (unit_nr, *) "Difference between Chebyshev DM and LS DM", frob_matrix
END IF
END DO
write_cubes = BTEST(cp_print_key_should_output(logger%iter_info, &
ls_scf_env%chebyshev%print_key_cube), cp_p_file)
IF (write_cubes) THEN
DO iwindow = 1, nwindow
WRITE (middle_name, "(A,I0)") "E_DENSITY_WINDOW_", iwindow
WRITE (title, "(A,1X,F16.8,1X,A,1X,F16.8)") "Energy range : ", ev1(iwindow), "to", ev2(iwindow)
unit_cube = cp_print_key_unit_nr(logger, ls_scf_env%chebyshev%print_key_cube, &
"", extension=".cube", & !added 01/22/2012
middle_name=TRIM(middle_name), log_filename=.FALSE.)
CALL write_matrix_to_cube(qs_env, ls_scf_env, matrix_dummy2(iwindow), unit_cube, title, &
section_get_ivals(ls_scf_env%chebyshev%print_key_cube, "STRIDE"))
CALL cp_print_key_finished_output(unit_cube, logger, ls_scf_env%chebyshev%print_key_cube, "")
END DO
END IF
END DO
! Chebyshev expansion with calculated coefficient
! grid construction and rescaling (by J)
unit_dos = cp_print_key_unit_nr(logger, ls_scf_env%chebyshev%print_key_dos, "", extension=".xy", &
middle_name="DOS", log_filename=.FALSE.)
IF (unit_dos > 0) THEN
ALLOCATE (dos(1:n_gridpoint_dos))
ALLOCATE (gdensity(1:n_gridpoint_dos, 1:nwindow))
ALLOCATE (chev_E(1:n_gridpoint_dos))
ALLOCATE (chev_Es_dos(1:n_gridpoint_dos))
ALLOCATE (dummy2(1:nwindow))
DO igrid = 1, n_gridpoint_dos
chev_E(igrid) = min_ev + (igrid - 1)*(max_ev - min_ev)/(n_gridpoint_dos - 1)
chev_Es_dos(igrid) = (chev_E(igrid) - interval_b)/interval_a
END DO
DO igrid = 1, n_gridpoint_dos
dummy1 = 0.0_dp !summation of polynomials
dummy2(:) = 0.0_dp !summation of polynomials
DO icheb = 2, ncheb
CALL chebyshev_poly(chev_T_dos, chev_Es_dos(igrid), icheb)
dummy1 = dummy1 + kernel_g(icheb)*mu(icheb)*chev_T_dos
DO iwindow = 1, nwindow
dummy2(iwindow) = dummy2(iwindow) + kernel_g(icheb)*aitchev_T(icheb, iwindow)*chev_T_dos
END DO
END DO
dos(igrid) = 1.0_dp/(interval_a*Nrows* &
(pi*SQRT(1.0_dp - chev_Es_dos(igrid)*chev_Es_dos(igrid))))*(kernel_g(1)*mu(1) + 2.0_dp*dummy1)
DO iwindow = 1, nwindow
gdensity(igrid, iwindow) = kernel_g(1)*aitchev_T(1, iwindow) + 2.0_dp*dummy2(iwindow)
END DO
WRITE (unit_dos, '(1000F16.8)') chev_E(igrid), dos(igrid), gdensity(igrid, :)
END DO
DEALLOCATE (chev_Es_dos, chev_E, dos, gdensity)
END IF
CALL cp_print_key_finished_output(unit_dos, logger, ls_scf_env%chebyshev%print_key_dos, "")
! free the matrices
CALL dbcsr_release(matrix_tmp1)
CALL dbcsr_release(matrix_tmp2)
CALL dbcsr_release(matrix_tmp3)
CALL dbcsr_release(matrix_F)
CALL dbcsr_release(matrix_dummy1)
DO iwindow = 1, nwindow
CALL dbcsr_release(matrix_dummy2(iwindow))
END DO
DEALLOCATE (ev1, ev2, sev1, sev2, matrix_dummy2)
!Need deallocation
DEALLOCATE (mu, kernel_g, aitchev_T, E_inte, sqrt_vec)
IF (unit_nr > 0) WRITE (unit_nr, '(T2,A)') "ENDING CHEBYSHEV CALCULATION"
CALL timestop(handle)
END SUBROUTINE compute_chebyshev
END MODULE dm_ls_chebyshev