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constraint_4x6.F
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!--------------------------------------------------------------------------------------------------!
! CP2K: A general program to perform molecular dynamics simulations !
! Copyright 2000-2021 CP2K developers group <https://cp2k.org> !
! !
! SPDX-License-Identifier: GPL-2.0-or-later !
!--------------------------------------------------------------------------------------------------!
! **************************************************************************************************
!> \par History
!> none
! **************************************************************************************************
MODULE constraint_4x6
USE atomic_kind_types, ONLY: atomic_kind_type,&
get_atomic_kind
USE constraint_fxd, ONLY: check_fixed_atom_cns_g4x6
USE kinds, ONLY: dp
USE linear_systems, ONLY: solve_system
USE mathlib, ONLY: dotprod_3d,&
matvec_3x3
USE molecule_kind_types, ONLY: fixd_constraint_type,&
g4x6_constraint_type,&
get_molecule_kind,&
molecule_kind_type
USE molecule_types, ONLY: get_molecule,&
global_constraint_type,&
local_g4x6_constraint_type,&
molecule_type
USE particle_types, ONLY: particle_type
#include "./base/base_uses.f90"
IMPLICIT NONE
PRIVATE
PUBLIC :: shake_4x6_int, &
rattle_4x6_int, &
shake_roll_4x6_int, &
rattle_roll_4x6_int, &
shake_4x6_ext, &
rattle_4x6_ext, &
shake_roll_4x6_ext, &
rattle_roll_4x6_ext
CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'constraint_4x6'
CONTAINS
! **************************************************************************************************
!> \brief Intramolecular shake_4x6
!> \param molecule ...
!> \param particle_set ...
!> \param pos ...
!> \param vel ...
!> \param dt ...
!> \param ishake ...
!> \param max_sigma ...
!> \par History
!> none
! **************************************************************************************************
SUBROUTINE shake_4x6_int(molecule, particle_set, pos, vel, dt, ishake, &
max_sigma)
TYPE(molecule_type), POINTER :: molecule
TYPE(particle_type), POINTER :: particle_set(:)
REAL(KIND=dp), INTENT(INOUT) :: pos(:, :), vel(:, :)
REAL(kind=dp), INTENT(in) :: dt
INTEGER, INTENT(IN) :: ishake
REAL(KIND=dp), INTENT(INOUT) :: max_sigma
INTEGER :: first_atom, ng4x6
TYPE(fixd_constraint_type), DIMENSION(:), POINTER :: fixd_list
TYPE(g4x6_constraint_type), POINTER :: g4x6_list(:)
TYPE(local_g4x6_constraint_type), POINTER :: lg4x6(:)
TYPE(molecule_kind_type), POINTER :: molecule_kind
NULLIFY (fixd_list)
molecule_kind => molecule%molecule_kind
CALL get_molecule_kind(molecule_kind, ng4x6=ng4x6, &
fixd_list=fixd_list, g4x6_list=g4x6_list)
CALL get_molecule(molecule, first_atom=first_atom, lg4x6=lg4x6)
! Real Shake
CALL shake_4x6_low(fixd_list, g4x6_list, lg4x6, ng4x6, first_atom, &
particle_set, pos, vel, dt, ishake, max_sigma)
END SUBROUTINE shake_4x6_int
! **************************************************************************************************
!> \brief Intramolecular shake_4x6_roll
!> \param molecule ...
!> \param particle_set ...
!> \param pos ...
!> \param vel ...
!> \param r_shake ...
!> \param dt ...
!> \param ishake ...
!> \param max_sigma ...
!> \par History
!> none
! **************************************************************************************************
SUBROUTINE shake_roll_4x6_int(molecule, particle_set, pos, vel, r_shake, &
dt, ishake, max_sigma)
TYPE(molecule_type), POINTER :: molecule
TYPE(particle_type), POINTER :: particle_set(:)
REAL(KIND=dp), INTENT(INOUT) :: pos(:, :), vel(:, :)
REAL(KIND=dp), DIMENSION(:, :), INTENT(IN) :: r_shake
REAL(kind=dp), INTENT(in) :: dt
INTEGER, INTENT(IN) :: ishake
REAL(KIND=dp), INTENT(INOUT) :: max_sigma
INTEGER :: first_atom, ng4x6
TYPE(fixd_constraint_type), DIMENSION(:), POINTER :: fixd_list
TYPE(g4x6_constraint_type), POINTER :: g4x6_list(:)
TYPE(local_g4x6_constraint_type), POINTER :: lg4x6(:)
TYPE(molecule_kind_type), POINTER :: molecule_kind
NULLIFY (fixd_list)
molecule_kind => molecule%molecule_kind
CALL get_molecule_kind(molecule_kind, ng4x6=ng4x6, &
fixd_list=fixd_list, g4x6_list=g4x6_list)
CALL get_molecule(molecule, first_atom=first_atom, lg4x6=lg4x6)
! Real Shake
CALL shake_roll_4x6_low(fixd_list, g4x6_list, lg4x6, ng4x6, first_atom, &
particle_set, pos, vel, r_shake, dt, ishake, max_sigma)
END SUBROUTINE shake_roll_4x6_int
! **************************************************************************************************
!> \brief Intramolecular rattle_4x6
!> \param molecule ...
!> \param particle_set ...
!> \param vel ...
!> \param dt ...
!> \par History
!> none
! **************************************************************************************************
SUBROUTINE rattle_4x6_int(molecule, particle_set, vel, dt)
TYPE(molecule_type), POINTER :: molecule
TYPE(particle_type), POINTER :: particle_set(:)
REAL(KIND=dp), INTENT(INOUT) :: vel(:, :)
REAL(kind=dp), INTENT(in) :: dt
INTEGER :: first_atom, ng4x6
TYPE(fixd_constraint_type), DIMENSION(:), POINTER :: fixd_list
TYPE(g4x6_constraint_type), POINTER :: g4x6_list(:)
TYPE(local_g4x6_constraint_type), POINTER :: lg4x6(:)
TYPE(molecule_kind_type), POINTER :: molecule_kind
NULLIFY (fixd_list)
molecule_kind => molecule%molecule_kind
CALL get_molecule_kind(molecule_kind, ng4x6=ng4x6, &
fixd_list=fixd_list, g4x6_list=g4x6_list)
CALL get_molecule(molecule, first_atom=first_atom, lg4x6=lg4x6)
! Real Rattle
CALL rattle_4x6_low(fixd_list, g4x6_list, lg4x6, first_atom, &
particle_set, vel, dt)
END SUBROUTINE rattle_4x6_int
! **************************************************************************************************
!> \brief Intramolecular rattle_4x6_roll
!> \param molecule ...
!> \param particle_set ...
!> \param vel ...
!> \param r_rattle ...
!> \param dt ...
!> \param veps ...
!> \par History
!> none
! **************************************************************************************************
SUBROUTINE rattle_roll_4x6_int(molecule, particle_set, vel, r_rattle, dt, veps)
TYPE(molecule_type), POINTER :: molecule
TYPE(particle_type), POINTER :: particle_set(:)
REAL(KIND=dp), INTENT(INOUT) :: vel(:, :)
REAL(KIND=dp), DIMENSION(:, :), INTENT(IN) :: r_rattle
REAL(kind=dp), INTENT(in) :: dt
REAL(KIND=dp), DIMENSION(:, :), INTENT(IN) :: veps
INTEGER :: first_atom, ng4x6
TYPE(fixd_constraint_type), DIMENSION(:), POINTER :: fixd_list
TYPE(g4x6_constraint_type), POINTER :: g4x6_list(:)
TYPE(local_g4x6_constraint_type), POINTER :: lg4x6(:)
TYPE(molecule_kind_type), POINTER :: molecule_kind
NULLIFY (fixd_list)
molecule_kind => molecule%molecule_kind
CALL get_molecule_kind(molecule_kind, ng4x6=ng4x6, &
fixd_list=fixd_list, g4x6_list=g4x6_list)
CALL get_molecule(molecule, first_atom=first_atom, lg4x6=lg4x6)
! Real Rattle
CALL rattle_roll_4x6_low(fixd_list, g4x6_list, lg4x6, first_atom, &
particle_set, vel, r_rattle, dt, veps)
END SUBROUTINE rattle_roll_4x6_int
! **************************************************************************************************
!> \brief Intramolecular shake_4x6
!> \param gci ...
!> \param particle_set ...
!> \param pos ...
!> \param vel ...
!> \param dt ...
!> \param ishake ...
!> \param max_sigma ...
!> \par History
!> none
! **************************************************************************************************
SUBROUTINE shake_4x6_ext(gci, particle_set, pos, vel, dt, ishake, &
max_sigma)
TYPE(global_constraint_type), POINTER :: gci
TYPE(particle_type), POINTER :: particle_set(:)
REAL(KIND=dp), INTENT(INOUT) :: pos(:, :), vel(:, :)
REAL(kind=dp), INTENT(in) :: dt
INTEGER, INTENT(IN) :: ishake
REAL(KIND=dp), INTENT(INOUT) :: max_sigma
INTEGER :: first_atom, ng4x6
TYPE(fixd_constraint_type), DIMENSION(:), POINTER :: fixd_list
TYPE(g4x6_constraint_type), POINTER :: g4x6_list(:)
TYPE(local_g4x6_constraint_type), POINTER :: lg4x6(:)
first_atom = 1
ng4x6 = gci%ng4x6
fixd_list => gci%fixd_list
g4x6_list => gci%g4x6_list
lg4x6 => gci%lg4x6
! Real Shake
CALL shake_4x6_low(fixd_list, g4x6_list, lg4x6, ng4x6, first_atom, &
particle_set, pos, vel, dt, ishake, max_sigma)
END SUBROUTINE shake_4x6_ext
! **************************************************************************************************
!> \brief Intramolecular shake_4x6_roll
!> \param gci ...
!> \param particle_set ...
!> \param pos ...
!> \param vel ...
!> \param r_shake ...
!> \param dt ...
!> \param ishake ...
!> \param max_sigma ...
!> \par History
!> none
! **************************************************************************************************
SUBROUTINE shake_roll_4x6_ext(gci, particle_set, pos, vel, r_shake, &
dt, ishake, max_sigma)
TYPE(global_constraint_type), POINTER :: gci
TYPE(particle_type), POINTER :: particle_set(:)
REAL(KIND=dp), INTENT(INOUT) :: pos(:, :), vel(:, :)
REAL(KIND=dp), DIMENSION(:, :), INTENT(IN) :: r_shake
REAL(kind=dp), INTENT(in) :: dt
INTEGER, INTENT(IN) :: ishake
REAL(KIND=dp), INTENT(INOUT) :: max_sigma
INTEGER :: first_atom, ng4x6
TYPE(fixd_constraint_type), DIMENSION(:), POINTER :: fixd_list
TYPE(g4x6_constraint_type), POINTER :: g4x6_list(:)
TYPE(local_g4x6_constraint_type), POINTER :: lg4x6(:)
first_atom = 1
ng4x6 = gci%ng4x6
fixd_list => gci%fixd_list
g4x6_list => gci%g4x6_list
lg4x6 => gci%lg4x6
! Real Shake
CALL shake_roll_4x6_low(fixd_list, g4x6_list, lg4x6, ng4x6, first_atom, &
particle_set, pos, vel, r_shake, dt, ishake, max_sigma)
END SUBROUTINE shake_roll_4x6_ext
! **************************************************************************************************
!> \brief Intramolecular rattle_4x6
!> \param gci ...
!> \param particle_set ...
!> \param vel ...
!> \param dt ...
!> \par History
!> none
! **************************************************************************************************
SUBROUTINE rattle_4x6_ext(gci, particle_set, vel, dt)
TYPE(global_constraint_type), POINTER :: gci
TYPE(particle_type), POINTER :: particle_set(:)
REAL(KIND=dp), INTENT(INOUT) :: vel(:, :)
REAL(kind=dp), INTENT(in) :: dt
INTEGER :: first_atom, ng4x6
TYPE(fixd_constraint_type), DIMENSION(:), POINTER :: fixd_list
TYPE(g4x6_constraint_type), POINTER :: g4x6_list(:)
TYPE(local_g4x6_constraint_type), POINTER :: lg4x6(:)
first_atom = 1
ng4x6 = gci%ng4x6
fixd_list => gci%fixd_list
g4x6_list => gci%g4x6_list
lg4x6 => gci%lg4x6
! Real Rattle
CALL rattle_4x6_low(fixd_list, g4x6_list, lg4x6, first_atom, &
particle_set, vel, dt)
END SUBROUTINE rattle_4x6_ext
! **************************************************************************************************
!> \brief Intramolecular rattle_4x6_roll
!> \param gci ...
!> \param particle_set ...
!> \param vel ...
!> \param r_rattle ...
!> \param dt ...
!> \param veps ...
!> \par History
!> none
! **************************************************************************************************
SUBROUTINE rattle_roll_4x6_ext(gci, particle_set, vel, r_rattle, dt, veps)
TYPE(global_constraint_type), POINTER :: gci
TYPE(particle_type), POINTER :: particle_set(:)
REAL(KIND=dp), INTENT(INOUT) :: vel(:, :)
REAL(KIND=dp), DIMENSION(:, :), INTENT(IN) :: r_rattle
REAL(kind=dp), INTENT(in) :: dt
REAL(KIND=dp), DIMENSION(:, :), INTENT(IN) :: veps
INTEGER :: first_atom, ng4x6
TYPE(fixd_constraint_type), DIMENSION(:), POINTER :: fixd_list
TYPE(g4x6_constraint_type), POINTER :: g4x6_list(:)
TYPE(local_g4x6_constraint_type), POINTER :: lg4x6(:)
first_atom = 1
ng4x6 = gci%ng4x6
fixd_list => gci%fixd_list
g4x6_list => gci%g4x6_list
lg4x6 => gci%lg4x6
! Real Rattle
CALL rattle_roll_4x6_low(fixd_list, g4x6_list, lg4x6, first_atom, &
particle_set, vel, r_rattle, dt, veps)
END SUBROUTINE rattle_roll_4x6_ext
! **************************************************************************************************
!> \brief ...
!> \param fixd_list ...
!> \param g4x6_list ...
!> \param lg4x6 ...
!> \param ng4x6 ...
!> \param first_atom ...
!> \param particle_set ...
!> \param pos ...
!> \param vel ...
!> \param dt ...
!> \param ishake ...
!> \param max_sigma ...
!> \par History
!> none
! **************************************************************************************************
SUBROUTINE shake_4x6_low(fixd_list, g4x6_list, lg4x6, ng4x6, first_atom, &
particle_set, pos, vel, dt, ishake, max_sigma)
TYPE(fixd_constraint_type), DIMENSION(:), POINTER :: fixd_list
TYPE(g4x6_constraint_type), POINTER :: g4x6_list(:)
TYPE(local_g4x6_constraint_type), POINTER :: lg4x6(:)
INTEGER, INTENT(IN) :: ng4x6, first_atom
TYPE(particle_type), POINTER :: particle_set(:)
REAL(KIND=dp), INTENT(INOUT) :: pos(:, :), vel(:, :)
REAL(kind=dp), INTENT(in) :: dt
INTEGER, INTENT(IN) :: ishake
REAL(KIND=dp), INTENT(INOUT) :: max_sigma
INTEGER :: iconst, index_a, index_b, index_c, &
index_d
REAL(KIND=dp) :: dtby2, dtsqby2, idtsq, imass1, imass2, &
imass3, imass4, sigma
REAL(KIND=dp), DIMENSION(3) :: fc1, fc2, fc3, fc4, r0_12, r0_13, r0_14, &
r0_23, r0_24, r0_34, r1, r12, r13, &
r14, r2, r23, r24, r3, r34, r4, v1, &
v2, v3, v4, vec
REAL(KIND=dp), DIMENSION(6, 1) :: bvec
REAL(KIND=dp), DIMENSION(6, 6) :: amat, atemp
TYPE(atomic_kind_type), POINTER :: atomic_kind
dtsqby2 = dt*dt*.5_dp
idtsq = 1.0_dp/dt/dt
dtby2 = dt*.5_dp
DO iconst = 1, ng4x6
IF (g4x6_list(iconst)%restraint%active) CYCLE
index_a = g4x6_list(iconst)%a + first_atom - 1
index_b = g4x6_list(iconst)%b + first_atom - 1
index_c = g4x6_list(iconst)%c + first_atom - 1
index_d = g4x6_list(iconst)%d + first_atom - 1
IF (ishake == 1) THEN
r0_12(:) = pos(:, index_a) - pos(:, index_b)
r0_13(:) = pos(:, index_a) - pos(:, index_c)
r0_14(:) = pos(:, index_a) - pos(:, index_d)
r0_23(:) = pos(:, index_b) - pos(:, index_c)
r0_24(:) = pos(:, index_b) - pos(:, index_d)
r0_34(:) = pos(:, index_c) - pos(:, index_d)
atomic_kind => particle_set(index_a)%atomic_kind
imass1 = 1.0_dp/atomic_kind%mass
atomic_kind => particle_set(index_b)%atomic_kind
imass2 = 1.0_dp/atomic_kind%mass
atomic_kind => particle_set(index_c)%atomic_kind
imass3 = 1.0_dp/atomic_kind%mass
atomic_kind => particle_set(index_d)%atomic_kind
imass4 = 1.0_dp/atomic_kind%mass
lg4x6(iconst)%fa = -2.0_dp*(lg4x6(iconst)%ra_old - &
lg4x6(iconst)%rb_old)
lg4x6(iconst)%fb = -2.0_dp*(lg4x6(iconst)%ra_old - &
lg4x6(iconst)%rc_old)
lg4x6(iconst)%fc = -2.0_dp*(lg4x6(iconst)%ra_old - &
lg4x6(iconst)%rd_old)
lg4x6(iconst)%fd = -2.0_dp*(lg4x6(iconst)%rb_old - &
lg4x6(iconst)%rc_old)
lg4x6(iconst)%fe = -2.0_dp*(lg4x6(iconst)%rb_old - &
lg4x6(iconst)%rd_old)
lg4x6(iconst)%ff = -2.0_dp*(lg4x6(iconst)%rc_old - &
lg4x6(iconst)%rd_old)
! Check for fixed atom constraints
CALL check_fixed_atom_cns_g4x6(imass1, imass2, imass3, imass4, &
index_a, index_b, index_c, index_d, fixd_list, lg4x6(iconst))
! construct matrix
amat(1, 1) = (imass1 + imass2)*DOTPROD_3D(r0_12, lg4x6(iconst)%fa)
amat(1, 2) = imass1*DOTPROD_3D(r0_12, lg4x6(iconst)%fb)
amat(1, 3) = imass1*DOTPROD_3D(r0_12, lg4x6(iconst)%fc)
amat(1, 4) = -imass2*DOTPROD_3D(r0_12, lg4x6(iconst)%fd)
amat(1, 5) = -imass2*DOTPROD_3D(r0_12, lg4x6(iconst)%fe)
amat(1, 6) = 0.0_dp
amat(2, 1) = imass1*DOTPROD_3D(r0_13, lg4x6(iconst)%fa)
amat(2, 2) = (imass1 + imass3)*DOTPROD_3D(r0_13, lg4x6(iconst)%fb)
amat(2, 3) = imass1*DOTPROD_3D(r0_13, lg4x6(iconst)%fc)
amat(2, 4) = imass3*DOTPROD_3D(r0_13, lg4x6(iconst)%fd)
amat(2, 5) = 0.0_dp
amat(2, 6) = -imass3*DOTPROD_3D(r0_13, lg4x6(iconst)%ff)
amat(3, 1) = imass1*DOTPROD_3D(r0_14, lg4x6(iconst)%fa)
amat(3, 2) = imass1*DOTPROD_3D(r0_14, lg4x6(iconst)%fb)
amat(3, 3) = (imass1 + imass4)*DOTPROD_3D(r0_14, lg4x6(iconst)%fc)
amat(3, 4) = 0.0_dp
amat(3, 5) = imass4*DOTPROD_3D(r0_14, lg4x6(iconst)%fe)
amat(3, 6) = imass4*DOTPROD_3D(r0_14, lg4x6(iconst)%ff)
amat(4, 1) = -imass2*DOTPROD_3D(r0_23, lg4x6(iconst)%fa)
amat(4, 2) = imass3*DOTPROD_3D(r0_23, lg4x6(iconst)%fb)
amat(4, 3) = 0.0_dp
amat(4, 4) = (imass3 + imass2)*DOTPROD_3D(r0_23, lg4x6(iconst)%fd)
amat(4, 5) = imass2*DOTPROD_3D(r0_23, lg4x6(iconst)%fe)
amat(4, 6) = -imass3*DOTPROD_3D(r0_23, lg4x6(iconst)%ff)
amat(5, 1) = -imass2*DOTPROD_3D(r0_24, lg4x6(iconst)%fa)
amat(5, 2) = 0.0_dp
amat(5, 3) = imass4*DOTPROD_3D(r0_24, lg4x6(iconst)%fc)
amat(5, 4) = imass2*DOTPROD_3D(r0_24, lg4x6(iconst)%fd)
amat(5, 5) = (imass4 + imass2)*DOTPROD_3D(r0_24, lg4x6(iconst)%fe)
amat(5, 6) = imass4*DOTPROD_3D(r0_24, lg4x6(iconst)%ff)
amat(6, 1) = 0.0_dp
amat(6, 2) = -imass3*DOTPROD_3D(r0_34, lg4x6(iconst)%fb)
amat(6, 3) = imass4*DOTPROD_3D(r0_34, lg4x6(iconst)%fc)
amat(6, 4) = -imass3*DOTPROD_3D(r0_34, lg4x6(iconst)%fd)
amat(6, 5) = imass4*DOTPROD_3D(r0_34, lg4x6(iconst)%fe)
amat(6, 6) = (imass3 + imass4)*DOTPROD_3D(r0_34, lg4x6(iconst)%ff)
! Store values
lg4x6(iconst)%r0_12 = r0_12
lg4x6(iconst)%r0_13 = r0_13
lg4x6(iconst)%r0_14 = r0_14
lg4x6(iconst)%r0_23 = r0_23
lg4x6(iconst)%r0_24 = r0_24
lg4x6(iconst)%r0_34 = r0_34
lg4x6(iconst)%amat = amat
lg4x6(iconst)%imass1 = imass1
lg4x6(iconst)%imass2 = imass2
lg4x6(iconst)%imass3 = imass3
lg4x6(iconst)%imass4 = imass4
lg4x6(iconst)%lambda_old = 0.0_dp
lg4x6(iconst)%del_lambda = 0.0_dp
ELSE
! Retrieve values
r0_12 = lg4x6(iconst)%r0_12
r0_13 = lg4x6(iconst)%r0_13
r0_14 = lg4x6(iconst)%r0_14
r0_23 = lg4x6(iconst)%r0_23
r0_24 = lg4x6(iconst)%r0_24
r0_34 = lg4x6(iconst)%r0_34
amat = lg4x6(iconst)%amat
imass1 = lg4x6(iconst)%imass1
imass2 = lg4x6(iconst)%imass2
imass3 = lg4x6(iconst)%imass3
imass4 = lg4x6(iconst)%imass4
END IF
! Iterate until convergence:
vec = lg4x6(iconst)%lambda(1)*lg4x6(iconst)%fa*(imass1 + imass2) + &
lg4x6(iconst)%lambda(2)*imass1*lg4x6(iconst)%fb + &
lg4x6(iconst)%lambda(3)*imass1*lg4x6(iconst)%fc - &
lg4x6(iconst)%lambda(4)*imass2*lg4x6(iconst)%fd - &
lg4x6(iconst)%lambda(5)*imass2*lg4x6(iconst)%fe
bvec(1, 1) = g4x6_list(iconst)%dab*g4x6_list(iconst)%dab &
- dtsqby2*dtsqby2*DOTPROD_3D(vec, vec) - DOTPROD_3D(r0_12, r0_12)
vec = lg4x6(iconst)%lambda(2)*lg4x6(iconst)%fb*(imass1 + imass3) + &
lg4x6(iconst)%lambda(1)*imass1*lg4x6(iconst)%fa + &
lg4x6(iconst)%lambda(3)*imass1*lg4x6(iconst)%fc + &
lg4x6(iconst)%lambda(4)*imass3*lg4x6(iconst)%fd - &
lg4x6(iconst)%lambda(6)*imass3*lg4x6(iconst)%ff
bvec(2, 1) = g4x6_list(iconst)%dac*g4x6_list(iconst)%dac &
- dtsqby2*dtsqby2*DOTPROD_3D(vec, vec) - DOTPROD_3D(r0_13, r0_13)
vec = lg4x6(iconst)%lambda(3)*lg4x6(iconst)%fc*(imass1 + imass4) + &
lg4x6(iconst)%lambda(1)*imass1*lg4x6(iconst)%fa + &
lg4x6(iconst)%lambda(2)*imass1*lg4x6(iconst)%fb + &
lg4x6(iconst)%lambda(5)*imass4*lg4x6(iconst)%fe + &
lg4x6(iconst)%lambda(6)*imass4*lg4x6(iconst)%ff
bvec(3, 1) = g4x6_list(iconst)%dad*g4x6_list(iconst)%dad &
- dtsqby2*dtsqby2*DOTPROD_3D(vec, vec) - DOTPROD_3D(r0_14, r0_14)
vec = lg4x6(iconst)%lambda(4)*lg4x6(iconst)%fd*(imass2 + imass3) - &
lg4x6(iconst)%lambda(1)*imass2*lg4x6(iconst)%fa + &
lg4x6(iconst)%lambda(2)*imass3*lg4x6(iconst)%fb + &
lg4x6(iconst)%lambda(5)*imass2*lg4x6(iconst)%fe - &
lg4x6(iconst)%lambda(6)*imass3*lg4x6(iconst)%ff
bvec(4, 1) = g4x6_list(iconst)%dbc*g4x6_list(iconst)%dbc &
- dtsqby2*dtsqby2*DOTPROD_3D(vec, vec) - DOTPROD_3D(r0_23, r0_23)
vec = lg4x6(iconst)%lambda(5)*lg4x6(iconst)%fe*(imass2 + imass4) - &
lg4x6(iconst)%lambda(1)*imass2*lg4x6(iconst)%fa + &
lg4x6(iconst)%lambda(3)*imass4*lg4x6(iconst)%fc + &
lg4x6(iconst)%lambda(4)*imass2*lg4x6(iconst)%fd + &
lg4x6(iconst)%lambda(6)*imass4*lg4x6(iconst)%ff
bvec(5, 1) = g4x6_list(iconst)%dbd*g4x6_list(iconst)%dbd &
- dtsqby2*dtsqby2*DOTPROD_3D(vec, vec) - DOTPROD_3D(r0_24, r0_24)
vec = lg4x6(iconst)%lambda(6)*lg4x6(iconst)%ff*(imass3 + imass4) - &
lg4x6(iconst)%lambda(2)*imass3*lg4x6(iconst)%fb + &
lg4x6(iconst)%lambda(3)*imass4*lg4x6(iconst)%fc - &
lg4x6(iconst)%lambda(4)*imass3*lg4x6(iconst)%fd + &
lg4x6(iconst)%lambda(5)*imass4*lg4x6(iconst)%fe
bvec(6, 1) = g4x6_list(iconst)%dcd*g4x6_list(iconst)%dcd &
- dtsqby2*dtsqby2*DOTPROD_3D(vec, vec) - DOTPROD_3D(r0_34, r0_34)
bvec = bvec*idtsq
! get lambda
atemp = amat
CALL solve_system(atemp, 6, bvec)
lg4x6(iconst)%lambda(:) = bvec(:, 1)
lg4x6(iconst)%del_lambda(:) = lg4x6(iconst)%lambda(:) - &
lg4x6(iconst)%lambda_old(:)
lg4x6(iconst)%lambda_old(:) = lg4x6(iconst)%lambda(:)
fc1 = lg4x6(iconst)%del_lambda(1)*lg4x6(iconst)%fa + &
lg4x6(iconst)%del_lambda(2)*lg4x6(iconst)%fb + &
lg4x6(iconst)%del_lambda(3)*lg4x6(iconst)%fc
fc2 = -lg4x6(iconst)%del_lambda(1)*lg4x6(iconst)%fa + &
lg4x6(iconst)%del_lambda(4)*lg4x6(iconst)%fd + &
lg4x6(iconst)%del_lambda(5)*lg4x6(iconst)%fe
fc3 = -lg4x6(iconst)%del_lambda(2)*lg4x6(iconst)%fb - &
lg4x6(iconst)%del_lambda(4)*lg4x6(iconst)%fd + &
lg4x6(iconst)%del_lambda(6)*lg4x6(iconst)%ff
fc4 = -lg4x6(iconst)%del_lambda(3)*lg4x6(iconst)%fc - &
lg4x6(iconst)%del_lambda(5)*lg4x6(iconst)%fe - &
lg4x6(iconst)%del_lambda(6)*lg4x6(iconst)%ff
r1(:) = pos(:, index_a) + imass1*dtsqby2*fc1(:)
r2(:) = pos(:, index_b) + imass2*dtsqby2*fc2(:)
r3(:) = pos(:, index_c) + imass3*dtsqby2*fc3(:)
r4(:) = pos(:, index_d) + imass4*dtsqby2*fc4(:)
v1(:) = vel(:, index_a) + imass1*dtby2*fc1(:)
v2(:) = vel(:, index_b) + imass2*dtby2*fc2(:)
v3(:) = vel(:, index_c) + imass3*dtby2*fc3(:)
v4(:) = vel(:, index_d) + imass4*dtby2*fc4(:)
r12 = r1 - r2
r13 = r1 - r3
r14 = r1 - r4
r23 = r2 - r3
r24 = r2 - r4
r34 = r3 - r4
! compute the tolerance:
sigma = DOT_PRODUCT(r12, r12) - g4x6_list(iconst)%dab* &
g4x6_list(iconst)%dab
max_sigma = MAX(max_sigma, ABS(sigma))
sigma = DOT_PRODUCT(r13, r13) - g4x6_list(iconst)%dac* &
g4x6_list(iconst)%dac
max_sigma = MAX(max_sigma, ABS(sigma))
sigma = DOT_PRODUCT(r14, r14) - g4x6_list(iconst)%dad* &
g4x6_list(iconst)%dad
max_sigma = MAX(max_sigma, ABS(sigma))
sigma = DOT_PRODUCT(r23, r23) - g4x6_list(iconst)%dbc* &
g4x6_list(iconst)%dbc
max_sigma = MAX(max_sigma, ABS(sigma))
sigma = DOT_PRODUCT(r24, r24) - g4x6_list(iconst)%dbd* &
g4x6_list(iconst)%dbd
max_sigma = MAX(max_sigma, ABS(sigma))
sigma = DOT_PRODUCT(r34, r34) - g4x6_list(iconst)%dcd* &
g4x6_list(iconst)%dcd
max_sigma = MAX(max_sigma, ABS(sigma))
! update positions with full multiplier
pos(:, index_a) = r1(:)
pos(:, index_b) = r2(:)
pos(:, index_c) = r3(:)
pos(:, index_d) = r4(:)
! update velocites with full multiplier
vel(:, index_a) = v1(:)
vel(:, index_b) = v2(:)
vel(:, index_c) = v3(:)
vel(:, index_d) = v4(:)
END DO
END SUBROUTINE shake_4x6_low
! **************************************************************************************************
!> \brief ...
!> \param fixd_list ...
!> \param g4x6_list ...
!> \param lg4x6 ...
!> \param ng4x6 ...
!> \param first_atom ...
!> \param particle_set ...
!> \param pos ...
!> \param vel ...
!> \param r_shake ...
!> \param dt ...
!> \param ishake ...
!> \param max_sigma ...
!> \par History
!> none
! **************************************************************************************************
SUBROUTINE shake_roll_4x6_low(fixd_list, g4x6_list, lg4x6, ng4x6, first_atom, &
particle_set, pos, vel, r_shake, dt, ishake, max_sigma)
TYPE(fixd_constraint_type), DIMENSION(:), POINTER :: fixd_list
TYPE(g4x6_constraint_type), POINTER :: g4x6_list(:)
TYPE(local_g4x6_constraint_type), POINTER :: lg4x6(:)
INTEGER, INTENT(IN) :: ng4x6, first_atom
TYPE(particle_type), POINTER :: particle_set(:)
REAL(KIND=dp), INTENT(INOUT) :: pos(:, :), vel(:, :)
REAL(KIND=dp), DIMENSION(:, :), INTENT(IN) :: r_shake
REAL(kind=dp), INTENT(in) :: dt
INTEGER, INTENT(IN) :: ishake
REAL(KIND=dp), INTENT(INOUT) :: max_sigma
INTEGER :: iconst, index_a, index_b, index_c, &
index_d
REAL(KIND=dp) :: dtby2, dtsqby2, idtsq, imass1, imass2, &
imass3, imass4, sigma
REAL(KIND=dp), DIMENSION(3) :: f_roll1, f_roll2, f_roll3, f_roll4, f_roll5, f_roll6, fc1, &
fc2, fc3, fc4, r0_12, r0_13, r0_14, r0_23, r0_24, r0_34, r1, r12, r13, r14, r2, r23, r24, &
r3, r34, r4, v1, v2, v3, v4, vec
REAL(KIND=dp), DIMENSION(6, 1) :: bvec
REAL(KIND=dp), DIMENSION(6, 6) :: amat, atemp
TYPE(atomic_kind_type), POINTER :: atomic_kind
dtsqby2 = dt*dt*.5_dp
idtsq = 1.0_dp/dt/dt
dtby2 = dt*.5_dp
DO iconst = 1, ng4x6
IF (g4x6_list(iconst)%restraint%active) CYCLE
index_a = g4x6_list(iconst)%a + first_atom - 1
index_b = g4x6_list(iconst)%b + first_atom - 1
index_c = g4x6_list(iconst)%c + first_atom - 1
index_d = g4x6_list(iconst)%d + first_atom - 1
IF (ishake == 1) THEN
r0_12(:) = pos(:, index_a) - pos(:, index_b)
r0_13(:) = pos(:, index_a) - pos(:, index_c)
r0_23(:) = pos(:, index_b) - pos(:, index_c)
r0_14(:) = pos(:, index_a) - pos(:, index_d)
r0_24(:) = pos(:, index_b) - pos(:, index_d)
r0_34(:) = pos(:, index_c) - pos(:, index_d)
atomic_kind => particle_set(index_a)%atomic_kind
imass1 = 1.0_dp/atomic_kind%mass
atomic_kind => particle_set(index_b)%atomic_kind
imass2 = 1.0_dp/atomic_kind%mass
atomic_kind => particle_set(index_c)%atomic_kind
imass3 = 1.0_dp/atomic_kind%mass
atomic_kind => particle_set(index_d)%atomic_kind
imass4 = 1.0_dp/atomic_kind%mass
lg4x6(iconst)%fa = -2.0_dp*(lg4x6(iconst)%ra_old - &
lg4x6(iconst)%rb_old)
lg4x6(iconst)%fb = -2.0_dp*(lg4x6(iconst)%ra_old - &
lg4x6(iconst)%rc_old)
lg4x6(iconst)%fc = -2.0_dp*(lg4x6(iconst)%ra_old - &
lg4x6(iconst)%rd_old)
lg4x6(iconst)%fd = -2.0_dp*(lg4x6(iconst)%rb_old - &
lg4x6(iconst)%rc_old)
lg4x6(iconst)%fe = -2.0_dp*(lg4x6(iconst)%rb_old - &
lg4x6(iconst)%rd_old)
lg4x6(iconst)%ff = -2.0_dp*(lg4x6(iconst)%rc_old - &
lg4x6(iconst)%rd_old)
! Check for fixed atom constraints
CALL check_fixed_atom_cns_g4x6(imass1, imass2, imass3, imass4, &
index_a, index_b, index_c, index_d, fixd_list, lg4x6(iconst))
! rotate fconst:
CALL matvec_3x3(f_roll1, r_shake, lg4x6(iconst)%fa)
CALL matvec_3x3(f_roll2, r_shake, lg4x6(iconst)%fb)
CALL matvec_3x3(f_roll3, r_shake, lg4x6(iconst)%fc)
CALL matvec_3x3(f_roll4, r_shake, lg4x6(iconst)%fd)
CALL matvec_3x3(f_roll5, r_shake, lg4x6(iconst)%fe)
CALL matvec_3x3(f_roll6, r_shake, lg4x6(iconst)%ff)
! construct matrix
amat(1, 1) = (imass1 + imass2)*DOTPROD_3D(r0_12, f_roll1)
amat(1, 2) = imass1*DOTPROD_3D(r0_12, f_roll2)
amat(1, 3) = imass1*DOTPROD_3D(r0_12, f_roll3)
amat(1, 4) = -imass2*DOTPROD_3D(r0_12, f_roll4)
amat(1, 5) = -imass2*DOTPROD_3D(r0_12, f_roll5)
amat(1, 6) = 0.0_dp
amat(2, 1) = imass1*DOTPROD_3D(r0_13, f_roll1)
amat(2, 2) = (imass1 + imass3)*DOTPROD_3D(r0_13, f_roll2)
amat(2, 3) = imass1*DOTPROD_3D(r0_13, f_roll3)
amat(2, 4) = imass3*DOTPROD_3D(r0_13, f_roll4)
amat(2, 5) = 0.0_dp
amat(2, 6) = -imass3*DOTPROD_3D(r0_13, f_roll6)
amat(3, 1) = imass1*DOTPROD_3D(r0_14, f_roll1)
amat(3, 2) = imass1*DOTPROD_3D(r0_14, f_roll2)
amat(3, 3) = (imass1 + imass4)*DOTPROD_3D(r0_14, f_roll3)
amat(3, 4) = 0.0_dp
amat(3, 5) = imass4*DOTPROD_3D(r0_14, f_roll5)
amat(3, 6) = imass4*DOTPROD_3D(r0_14, f_roll6)
amat(4, 1) = -imass2*DOTPROD_3D(r0_23, f_roll1)
amat(4, 2) = imass3*DOTPROD_3D(r0_23, f_roll2)
amat(4, 3) = 0.0_dp
amat(4, 4) = (imass3 + imass2)*DOTPROD_3D(r0_23, f_roll4)
amat(4, 5) = imass2*DOTPROD_3D(r0_23, f_roll5)
amat(4, 6) = -imass3*DOTPROD_3D(r0_23, f_roll6)
amat(5, 1) = -imass2*DOTPROD_3D(r0_24, f_roll1)
amat(5, 2) = 0.0_dp
amat(5, 3) = imass4*DOTPROD_3D(r0_24, f_roll3)
amat(5, 4) = imass2*DOTPROD_3D(r0_24, f_roll4)
amat(5, 5) = (imass4 + imass2)*DOTPROD_3D(r0_24, f_roll5)
amat(5, 6) = imass4*DOTPROD_3D(r0_24, f_roll6)
amat(6, 1) = 0.0_dp
amat(6, 2) = -imass3*DOTPROD_3D(r0_34, f_roll2)
amat(6, 3) = imass4*DOTPROD_3D(r0_34, f_roll3)
amat(6, 4) = -imass3*DOTPROD_3D(r0_34, f_roll4)
amat(6, 5) = imass4*DOTPROD_3D(r0_34, f_roll5)
amat(6, 6) = (imass3 + imass4)*DOTPROD_3D(r0_34, f_roll6)
! Store values
lg4x6(iconst)%r0_12 = r0_12
lg4x6(iconst)%r0_13 = r0_13
lg4x6(iconst)%r0_14 = r0_14
lg4x6(iconst)%r0_23 = r0_23
lg4x6(iconst)%r0_24 = r0_24
lg4x6(iconst)%r0_34 = r0_34
lg4x6(iconst)%f_roll1 = f_roll1
lg4x6(iconst)%f_roll2 = f_roll2
lg4x6(iconst)%f_roll3 = f_roll3
lg4x6(iconst)%f_roll4 = f_roll4
lg4x6(iconst)%f_roll5 = f_roll5
lg4x6(iconst)%f_roll6 = f_roll6
lg4x6(iconst)%amat = amat
lg4x6(iconst)%imass1 = imass1
lg4x6(iconst)%imass2 = imass2
lg4x6(iconst)%imass3 = imass3
lg4x6(iconst)%imass4 = imass4
lg4x6(iconst)%lambda_old = 0.0_dp
lg4x6(iconst)%del_lambda = 0.0_dp
ELSE
! Retrieve values
r0_12 = lg4x6(iconst)%r0_12
r0_13 = lg4x6(iconst)%r0_13
r0_14 = lg4x6(iconst)%r0_14
r0_23 = lg4x6(iconst)%r0_23
r0_24 = lg4x6(iconst)%r0_24
r0_34 = lg4x6(iconst)%r0_34
f_roll1 = lg4x6(iconst)%f_roll1
f_roll2 = lg4x6(iconst)%f_roll2
f_roll3 = lg4x6(iconst)%f_roll3
f_roll4 = lg4x6(iconst)%f_roll4
f_roll5 = lg4x6(iconst)%f_roll5
f_roll6 = lg4x6(iconst)%f_roll6
amat = lg4x6(iconst)%amat
imass1 = lg4x6(iconst)%imass1
imass2 = lg4x6(iconst)%imass2
imass3 = lg4x6(iconst)%imass3
imass4 = lg4x6(iconst)%imass4
END IF
! Iterate until convergence:
vec = lg4x6(iconst)%lambda(1)*f_roll1*(imass1 + imass2) + &
lg4x6(iconst)%lambda(2)*imass1*f_roll2 + &
lg4x6(iconst)%lambda(3)*imass1*f_roll3 - &
lg4x6(iconst)%lambda(4)*imass2*f_roll4 - &
lg4x6(iconst)%lambda(5)*imass2*f_roll5
bvec(1, 1) = g4x6_list(iconst)%dab*g4x6_list(iconst)%dab &
- dtsqby2*dtsqby2*DOTPROD_3D(vec, vec) - DOTPROD_3D(r0_12, r0_12)
vec = lg4x6(iconst)%lambda(2)*f_roll2*(imass1 + imass3) + &
lg4x6(iconst)%lambda(1)*imass1*f_roll1 + &
lg4x6(iconst)%lambda(3)*imass1*f_roll3 + &
lg4x6(iconst)%lambda(4)*imass3*f_roll4 - &
lg4x6(iconst)%lambda(6)*imass3*f_roll6
bvec(2, 1) = g4x6_list(iconst)%dac*g4x6_list(iconst)%dac &
- dtsqby2*dtsqby2*DOTPROD_3D(vec, vec) - DOTPROD_3D(r0_13, r0_13)
vec = lg4x6(iconst)%lambda(3)*f_roll3*(imass1 + imass4) + &
lg4x6(iconst)%lambda(1)*imass1*f_roll1 + &
lg4x6(iconst)%lambda(2)*imass1*f_roll2 + &
lg4x6(iconst)%lambda(5)*imass4*f_roll5 + &
lg4x6(iconst)%lambda(6)*imass4*f_roll6
bvec(3, 1) = g4x6_list(iconst)%dad*g4x6_list(iconst)%dad &
- dtsqby2*dtsqby2*DOTPROD_3D(vec, vec) - DOTPROD_3D(r0_14, r0_14)
vec = lg4x6(iconst)%lambda(4)*f_roll4*(imass2 + imass3) - &
lg4x6(iconst)%lambda(1)*imass2*f_roll1 + &
lg4x6(iconst)%lambda(2)*imass3*f_roll2 + &
lg4x6(iconst)%lambda(5)*imass2*f_roll5 - &
lg4x6(iconst)%lambda(6)*imass3*f_roll6
bvec(4, 1) = g4x6_list(iconst)%dbc*g4x6_list(iconst)%dbc &
- dtsqby2*dtsqby2*DOTPROD_3D(vec, vec) - DOTPROD_3D(r0_23, r0_23)
vec = lg4x6(iconst)%lambda(5)*f_roll5*(imass2 + imass4) - &
lg4x6(iconst)%lambda(1)*imass2*f_roll1 + &
lg4x6(iconst)%lambda(3)*imass4*f_roll3 + &
lg4x6(iconst)%lambda(4)*imass2*f_roll4 + &
lg4x6(iconst)%lambda(6)*imass4*f_roll6
bvec(5, 1) = g4x6_list(iconst)%dbd*g4x6_list(iconst)%dbd &
- dtsqby2*dtsqby2*DOTPROD_3D(vec, vec) - DOTPROD_3D(r0_24, r0_24)
vec = lg4x6(iconst)%lambda(6)*f_roll6*(imass3 + imass4) - &
lg4x6(iconst)%lambda(2)*imass3*f_roll2 + &
lg4x6(iconst)%lambda(3)*imass4*f_roll3 - &
lg4x6(iconst)%lambda(4)*imass3*f_roll4 + &
lg4x6(iconst)%lambda(5)*imass4*f_roll5
bvec(6, 1) = g4x6_list(iconst)%dcd*g4x6_list(iconst)%dcd &
- dtsqby2*dtsqby2*DOTPROD_3D(vec, vec) - DOTPROD_3D(r0_34, r0_34)
bvec = bvec*idtsq
! get lambda
atemp = amat
CALL solve_system(atemp, 6, bvec)
lg4x6(iconst)%lambda(:) = bvec(:, 1)
lg4x6(iconst)%del_lambda(:) = lg4x6(iconst)%lambda(:) - &
lg4x6(iconst)%lambda_old(:)
lg4x6(iconst)%lambda_old(:) = lg4x6(iconst)%lambda(:)
fc1 = lg4x6(iconst)%del_lambda(1)*lg4x6(iconst)%fa + &
lg4x6(iconst)%del_lambda(2)*lg4x6(iconst)%fb + &
lg4x6(iconst)%del_lambda(3)*lg4x6(iconst)%fc
fc2 = -lg4x6(iconst)%del_lambda(1)*lg4x6(iconst)%fa + &
lg4x6(iconst)%del_lambda(4)*lg4x6(iconst)%fd + &
lg4x6(iconst)%del_lambda(5)*lg4x6(iconst)%fe
fc3 = -lg4x6(iconst)%del_lambda(2)*lg4x6(iconst)%fb - &
lg4x6(iconst)%del_lambda(4)*lg4x6(iconst)%fd + &
lg4x6(iconst)%del_lambda(6)*lg4x6(iconst)%ff
fc4 = -lg4x6(iconst)%del_lambda(3)*lg4x6(iconst)%fc - &
lg4x6(iconst)%del_lambda(5)*lg4x6(iconst)%fe - &
lg4x6(iconst)%del_lambda(6)*lg4x6(iconst)%ff
CALL MATVEC_3x3(vec, r_shake, fc1)
r1(:) = pos(:, index_a) + imass1*dtsqby2*vec
CALL MATVEC_3x3(vec, r_shake, fc2)
r2(:) = pos(:, index_b) + imass2*dtsqby2*vec
CALL MATVEC_3x3(vec, r_shake, fc3)
r3(:) = pos(:, index_c) + imass3*dtsqby2*vec
CALL MATVEC_3x3(vec, r_shake, fc4)
r4(:) = pos(:, index_d) + imass4*dtsqby2*vec
CALL MATVEC_3x3(vec, r_shake, fc1)
v1(:) = vel(:, index_a) + imass1*dtby2*vec
CALL MATVEC_3x3(vec, r_shake, fc2)
v2(:) = vel(:, index_b) + imass2*dtby2*vec
CALL MATVEC_3x3(vec, r_shake, fc3)
v3(:) = vel(:, index_c) + imass3*dtby2*vec
CALL MATVEC_3x3(vec, r_shake, fc4)
v4(:) = vel(:, index_d) + imass4*dtby2*vec
r12 = r1 - r2
r13 = r1 - r3
r23 = r2 - r3
r14 = r1 - r4
r24 = r2 - r4
r34 = r3 - r4
! compute the tolerance:
sigma = DOT_PRODUCT(r12, r12) - g4x6_list(iconst)%dab* &
g4x6_list(iconst)%dab
max_sigma = MAX(max_sigma, ABS(sigma))
sigma = DOT_PRODUCT(r13, r13) - g4x6_list(iconst)%dac* &
g4x6_list(iconst)%dac
max_sigma = MAX(max_sigma, ABS(sigma))
sigma = DOT_PRODUCT(r14, r14) - g4x6_list(iconst)%dad* &
g4x6_list(iconst)%dad
max_sigma = MAX(max_sigma, ABS(sigma))
sigma = DOT_PRODUCT(r23, r23) - g4x6_list(iconst)%dbc* &
g4x6_list(iconst)%dbc
max_sigma = MAX(max_sigma, ABS(sigma))
sigma = DOT_PRODUCT(r24, r24) - g4x6_list(iconst)%dbd* &
g4x6_list(iconst)%dbd
max_sigma = MAX(max_sigma, ABS(sigma))
sigma = DOT_PRODUCT(r34, r34) - g4x6_list(iconst)%dcd* &
g4x6_list(iconst)%dcd
max_sigma = MAX(max_sigma, ABS(sigma))
! update positions with full multiplier
pos(:, index_a) = r1(:)
pos(:, index_b) = r2(:)
pos(:, index_c) = r3(:)
pos(:, index_d) = r4(:)
! update velocites with full multiplier
vel(:, index_a) = v1(:)
vel(:, index_b) = v2(:)
vel(:, index_c) = v3(:)
vel(:, index_d) = v4(:)
END DO
END SUBROUTINE shake_roll_4x6_low
! **************************************************************************************************
!> \brief ...
!> \param fixd_list ...
!> \param g4x6_list ...
!> \param lg4x6 ...
!> \param first_atom ...
!> \param particle_set ...
!> \param vel ...
!> \param dt ...
!> \par History
!> none
! **************************************************************************************************
SUBROUTINE rattle_4x6_low(fixd_list, g4x6_list, lg4x6, first_atom, &
particle_set, vel, dt)
TYPE(fixd_constraint_type), DIMENSION(:), POINTER :: fixd_list
TYPE(g4x6_constraint_type), POINTER :: g4x6_list(:)
TYPE(local_g4x6_constraint_type), POINTER :: lg4x6(:)
INTEGER, INTENT(IN) :: first_atom
TYPE(particle_type), POINTER :: particle_set(:)
REAL(KIND=dp), INTENT(INOUT) :: vel(:, :)
REAL(kind=dp), INTENT(in) :: dt
INTEGER :: iconst, index_a, index_b, index_c, &
index_d
REAL(KIND=dp) :: dtby2, idt, imass1, imass2, imass3, &
imass4, mass
REAL(KIND=dp), DIMENSION(3) :: fc1, fc2, fc3, fc4, r12, r13, r14, r23, &
r24, r34, v12, v13, v14, v23, v24, v34
REAL(KIND=dp), DIMENSION(6, 1) :: bvec
REAL(KIND=dp), DIMENSION(6, 6) :: amat
TYPE(atomic_kind_type), POINTER :: atomic_kind
idt = 1.0_dp/dt
dtby2 = dt*.5_dp
DO iconst = 1, SIZE(g4x6_list)
IF (g4x6_list(iconst)%restraint%active) CYCLE
index_a = g4x6_list(iconst)%a + first_atom - 1
index_b = g4x6_list(iconst)%b + first_atom - 1
index_c = g4x6_list(iconst)%c + first_atom - 1
index_d = g4x6_list(iconst)%d + first_atom - 1
v12(:) = vel(:, index_a) - vel(:, index_b)
v13(:) = vel(:, index_a) - vel(:, index_c)
v14(:) = vel(:, index_a) - vel(:, index_d)
v23(:) = vel(:, index_b) - vel(:, index_c)
v24(:) = vel(:, index_b) - vel(:, index_d)
v34(:) = vel(:, index_c) - vel(:, index_d)
r12(:) = particle_set(index_a)%r(:) - particle_set(index_b)%r(:)
r13(:) = particle_set(index_a)%r(:) - particle_set(index_c)%r(:)
r14(:) = particle_set(index_a)%r(:) - particle_set(index_d)%r(:)
r23(:) = particle_set(index_b)%r(:) - particle_set(index_c)%r(:)
r24(:) = particle_set(index_b)%r(:) - particle_set(index_d)%r(:)
r34(:) = particle_set(index_c)%r(:) - particle_set(index_d)%r(:)
atomic_kind => particle_set(index_a)%atomic_kind
CALL get_atomic_kind(atomic_kind=atomic_kind, mass=mass)
imass1 = 1.0_dp/mass
atomic_kind => particle_set(index_b)%atomic_kind
CALL get_atomic_kind(atomic_kind=atomic_kind, mass=mass)
imass2 = 1.0_dp/mass
atomic_kind => particle_set(index_c)%atomic_kind
CALL get_atomic_kind(atomic_kind=atomic_kind, mass=mass)
imass3 = 1.0_dp/mass
atomic_kind => particle_set(index_d)%atomic_kind
CALL get_atomic_kind(atomic_kind=atomic_kind, mass=mass)
imass4 = 1.0_dp/mass
lg4x6(iconst)%fa = -2.0_dp*r12
lg4x6(iconst)%fb = -2.0_dp*r13
lg4x6(iconst)%fc = -2.0_dp*r14
lg4x6(iconst)%fd = -2.0_dp*r23
lg4x6(iconst)%fe = -2.0_dp*r24
lg4x6(iconst)%ff = -2.0_dp*r34
! Check for fixed atom constraints
CALL check_fixed_atom_cns_g4x6(imass1, imass2, imass3, imass4, &
index_a, index_b, index_c, index_d, fixd_list, lg4x6(iconst))
! construct matrix
amat(1, 1) = (imass1 + imass2)*DOTPROD_3D(r12, lg4x6(iconst)%fa)
amat(1, 2) = imass1*DOTPROD_3D(r12, lg4x6(iconst)%fb)
amat(1, 3) = imass1*DOTPROD_3D(r12, lg4x6(iconst)%fc)
amat(1, 4) = -imass2*DOTPROD_3D(r12, lg4x6(iconst)%fd)
amat(1, 5) = -imass2*DOTPROD_3D(r12, lg4x6(iconst)%fe)
amat(1, 6) = 0.0_dp
amat(2, 1) = imass1*DOTPROD_3D(r13, lg4x6(iconst)%fa)
amat(2, 2) = (imass1 + imass3)*DOTPROD_3D(r13, lg4x6(iconst)%fb)
amat(2, 3) = imass1*DOTPROD_3D(r13, lg4x6(iconst)%fc)
amat(2, 4) = imass3*DOTPROD_3D(r13, lg4x6(iconst)%fd)
amat(2, 5) = 0.0_dp
amat(2, 6) = -imass3*DOTPROD_3D(r13, lg4x6(iconst)%ff)
amat(3, 1) = imass1*DOTPROD_3D(r14, lg4x6(iconst)%fa)
amat(3, 2) = imass1*DOTPROD_3D(r14, lg4x6(iconst)%fb)
amat(3, 3) = (imass1 + imass4)*DOTPROD_3D(r14, lg4x6(iconst)%fc)
amat(3, 4) = 0.0_dp
amat(3, 5) = imass4*DOTPROD_3D(r14, lg4x6(iconst)%fe)
amat(3, 6) = imass4*DOTPROD_3D(r14, lg4x6(iconst)%ff)
amat(4, 1) = -imass2*DOTPROD_3D(r23, lg4x6(iconst)%fa)
amat(4, 2) = imass3*DOTPROD_3D(r23, lg4x6(iconst)%fb)
amat(4, 3) = 0.0_dp
amat(4, 4) = (imass3 + imass2)*DOTPROD_3D(r23, lg4x6(iconst)%fd)
amat(4, 5) = imass2*DOTPROD_3D(r23, lg4x6(iconst)%fe)
amat(4, 6) = -imass3*DOTPROD_3D(r23, lg4x6(iconst)%ff)
amat(5, 1) = -imass2*DOTPROD_3D(r24, lg4x6(iconst)%fa)