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constraint_3x3.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_3x3
USE atomic_kind_types, ONLY: atomic_kind_type,&
get_atomic_kind
USE constraint_fxd, ONLY: check_fixed_atom_cns_g3x3
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,&
g3x3_constraint_type,&
get_molecule_kind,&
molecule_kind_type
USE molecule_types, ONLY: get_molecule,&
global_constraint_type,&
local_g3x3_constraint_type,&
molecule_type
USE particle_types, ONLY: particle_type
#include "./base/base_uses.f90"
IMPLICIT NONE
PRIVATE
PUBLIC :: shake_3x3_int, &
rattle_3x3_int, &
shake_roll_3x3_int, &
rattle_roll_3x3_int, &
shake_3x3_ext, &
rattle_3x3_ext, &
shake_roll_3x3_ext, &
rattle_roll_3x3_ext
CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'constraint_3x3'
CONTAINS
! **************************************************************************************************
!> \brief ...
!> \param molecule ...
!> \param particle_set ...
!> \param pos ...
!> \param vel ...
!> \param dt ...
!> \param ishake ...
!> \param max_sigma ...
!> \par History
!> none
! **************************************************************************************************
SUBROUTINE shake_3x3_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, ng3x3
TYPE(fixd_constraint_type), DIMENSION(:), POINTER :: fixd_list
TYPE(g3x3_constraint_type), POINTER :: g3x3_list(:)
TYPE(local_g3x3_constraint_type), POINTER :: lg3x3(:)
TYPE(molecule_kind_type), POINTER :: molecule_kind
NULLIFY (fixd_list)
molecule_kind => molecule%molecule_kind
CALL get_molecule_kind(molecule_kind, ng3x3=ng3x3, &
g3x3_list=g3x3_list, fixd_list=fixd_list)
CALL get_molecule(molecule, first_atom=first_atom, lg3x3=lg3x3)
! Real Shake
CALL shake_3x3_low(fixd_list, g3x3_list, lg3x3, first_atom, ng3x3, &
particle_set, pos, vel, dt, ishake, max_sigma)
END SUBROUTINE shake_3x3_int
! **************************************************************************************************
!> \brief ...
!> \param molecule ...
!> \param particle_set ...
!> \param pos ...
!> \param vel ...
!> \param r_shake ...
!> \param v_shake ...
!> \param dt ...
!> \param ishake ...
!> \param max_sigma ...
!> \par History
!> none
! **************************************************************************************************
SUBROUTINE shake_roll_3x3_int(molecule, particle_set, pos, vel, r_shake, &
v_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, v_shake
REAL(kind=dp), INTENT(in) :: dt
INTEGER, INTENT(IN) :: ishake
REAL(KIND=dp), INTENT(INOUT) :: max_sigma
INTEGER :: first_atom, ng3x3
TYPE(fixd_constraint_type), DIMENSION(:), POINTER :: fixd_list
TYPE(g3x3_constraint_type), POINTER :: g3x3_list(:)
TYPE(local_g3x3_constraint_type), POINTER :: lg3x3(:)
TYPE(molecule_kind_type), POINTER :: molecule_kind
NULLIFY (fixd_list)
molecule_kind => molecule%molecule_kind
CALL get_molecule_kind(molecule_kind, ng3x3=ng3x3, &
g3x3_list=g3x3_list, fixd_list=fixd_list)
CALL get_molecule(molecule, first_atom=first_atom, lg3x3=lg3x3)
! Real Shake
CALL shake_roll_3x3_low(fixd_list, g3x3_list, lg3x3, first_atom, ng3x3, &
particle_set, pos, vel, r_shake, v_shake, dt, ishake, max_sigma)
END SUBROUTINE shake_roll_3x3_int
! **************************************************************************************************
!> \brief ...
!> \param molecule ...
!> \param particle_set ...
!> \param vel ...
!> \param r_rattle ...
!> \param dt ...
!> \param veps ...
!> \par History
!> none
! **************************************************************************************************
SUBROUTINE rattle_roll_3x3_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
TYPE(fixd_constraint_type), DIMENSION(:), POINTER :: fixd_list
TYPE(g3x3_constraint_type), POINTER :: g3x3_list(:)
TYPE(local_g3x3_constraint_type), POINTER :: lg3x3(:)
TYPE(molecule_kind_type), POINTER :: molecule_kind
NULLIFY (fixd_list)
molecule_kind => molecule%molecule_kind
CALL get_molecule_kind(molecule_kind, &
g3x3_list=g3x3_list, fixd_list=fixd_list)
CALL get_molecule(molecule, first_atom=first_atom, lg3x3=lg3x3)
! Real Rattle
CALL rattle_roll_3x3_low(fixd_list, g3x3_list, lg3x3, first_atom, &
particle_set, vel, r_rattle, dt, veps)
END SUBROUTINE rattle_roll_3x3_int
! **************************************************************************************************
!> \brief ...
!> \param molecule ...
!> \param particle_set ...
!> \param vel ...
!> \param dt ...
!> \par History
!> none
! **************************************************************************************************
SUBROUTINE rattle_3x3_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
TYPE(fixd_constraint_type), DIMENSION(:), POINTER :: fixd_list
TYPE(g3x3_constraint_type), POINTER :: g3x3_list(:)
TYPE(local_g3x3_constraint_type), POINTER :: lg3x3(:)
TYPE(molecule_kind_type), POINTER :: molecule_kind
NULLIFY (fixd_list)
molecule_kind => molecule%molecule_kind
CALL get_molecule_kind(molecule_kind, &
g3x3_list=g3x3_list, fixd_list=fixd_list)
CALL get_molecule(molecule, first_atom=first_atom, lg3x3=lg3x3)
! Real Rattle
CALL rattle_3x3_low(fixd_list, g3x3_list, lg3x3, first_atom, &
particle_set, vel, dt)
END SUBROUTINE rattle_3x3_int
! **************************************************************************************************
!> \brief ...
!> \param gci ...
!> \param particle_set ...
!> \param pos ...
!> \param vel ...
!> \param dt ...
!> \param ishake ...
!> \param max_sigma ...
!> \par History
!> none
! **************************************************************************************************
SUBROUTINE shake_3x3_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, ng3x3
TYPE(fixd_constraint_type), DIMENSION(:), POINTER :: fixd_list
TYPE(g3x3_constraint_type), POINTER :: g3x3_list(:)
TYPE(local_g3x3_constraint_type), POINTER :: lg3x3(:)
first_atom = 1
ng3x3 = gci%ng3x3
g3x3_list => gci%g3x3_list
fixd_list => gci%fixd_list
lg3x3 => gci%lg3x3
! Real Shake
CALL shake_3x3_low(fixd_list, g3x3_list, lg3x3, first_atom, ng3x3, &
particle_set, pos, vel, dt, ishake, max_sigma)
END SUBROUTINE shake_3x3_ext
! **************************************************************************************************
!> \brief ...
!> \param gci ...
!> \param particle_set ...
!> \param pos ...
!> \param vel ...
!> \param r_shake ...
!> \param v_shake ...
!> \param dt ...
!> \param ishake ...
!> \param max_sigma ...
!> \par History
!> none
! **************************************************************************************************
SUBROUTINE shake_roll_3x3_ext(gci, particle_set, pos, vel, r_shake, &
v_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, v_shake
REAL(kind=dp), INTENT(in) :: dt
INTEGER, INTENT(IN) :: ishake
REAL(KIND=dp), INTENT(INOUT) :: max_sigma
INTEGER :: first_atom, ng3x3
TYPE(fixd_constraint_type), DIMENSION(:), POINTER :: fixd_list
TYPE(g3x3_constraint_type), POINTER :: g3x3_list(:)
TYPE(local_g3x3_constraint_type), POINTER :: lg3x3(:)
first_atom = 1
ng3x3 = gci%ng3x3
g3x3_list => gci%g3x3_list
fixd_list => gci%fixd_list
lg3x3 => gci%lg3x3
! Real Shake
CALL shake_roll_3x3_low(fixd_list, g3x3_list, lg3x3, first_atom, ng3x3, &
particle_set, pos, vel, r_shake, v_shake, dt, ishake, max_sigma)
END SUBROUTINE shake_roll_3x3_ext
! **************************************************************************************************
!> \brief ...
!> \param gci ...
!> \param particle_set ...
!> \param vel ...
!> \param r_rattle ...
!> \param dt ...
!> \param veps ...
!> \par History
!> none
! **************************************************************************************************
SUBROUTINE rattle_roll_3x3_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
TYPE(fixd_constraint_type), DIMENSION(:), POINTER :: fixd_list
TYPE(g3x3_constraint_type), POINTER :: g3x3_list(:)
TYPE(local_g3x3_constraint_type), POINTER :: lg3x3(:)
first_atom = 1
g3x3_list => gci%g3x3_list
fixd_list => gci%fixd_list
lg3x3 => gci%lg3x3
! Real Rattle
CALL rattle_roll_3x3_low(fixd_list, g3x3_list, lg3x3, first_atom, &
particle_set, vel, r_rattle, dt, veps)
END SUBROUTINE rattle_roll_3x3_ext
! **************************************************************************************************
!> \brief ...
!> \param gci ...
!> \param particle_set ...
!> \param vel ...
!> \param dt ...
!> \par History
!> none
! **************************************************************************************************
SUBROUTINE rattle_3x3_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
TYPE(fixd_constraint_type), DIMENSION(:), POINTER :: fixd_list
TYPE(g3x3_constraint_type), POINTER :: g3x3_list(:)
TYPE(local_g3x3_constraint_type), POINTER :: lg3x3(:)
first_atom = 1
g3x3_list => gci%g3x3_list
fixd_list => gci%fixd_list
lg3x3 => gci%lg3x3
! Real Rattle
CALL rattle_3x3_low(fixd_list, g3x3_list, lg3x3, first_atom, &
particle_set, vel, dt)
END SUBROUTINE rattle_3x3_ext
! **************************************************************************************************
!> \brief ...
!> \param fixd_list ...
!> \param g3x3_list ...
!> \param lg3x3 ...
!> \param first_atom ...
!> \param ng3x3 ...
!> \param particle_set ...
!> \param pos ...
!> \param vel ...
!> \param dt ...
!> \param ishake ...
!> \param max_sigma ...
!> \par History
!> none
! **************************************************************************************************
SUBROUTINE shake_3x3_low(fixd_list, g3x3_list, lg3x3, first_atom, ng3x3, &
particle_set, pos, vel, dt, ishake, max_sigma)
TYPE(fixd_constraint_type), DIMENSION(:), POINTER :: fixd_list
TYPE(g3x3_constraint_type), POINTER :: g3x3_list(:)
TYPE(local_g3x3_constraint_type), POINTER :: lg3x3(:)
INTEGER, INTENT(IN) :: first_atom, ng3x3
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
REAL(KIND=dp) :: dtby2, dtsqby2, idtsq, imass1, imass2, &
imass3, sigma
REAL(KIND=dp), DIMENSION(3) :: fc1, fc2, fc3, r0_12, r0_13, r0_23, r1, &
r12, r13, r2, r23, r3, v1, v2, v3, vec
REAL(KIND=dp), DIMENSION(3, 1) :: bvec
REAL(KIND=dp), DIMENSION(3, 3) :: 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, ng3x3
IF (g3x3_list(iconst)%restraint%active) CYCLE
index_a = g3x3_list(iconst)%a + first_atom - 1
index_b = g3x3_list(iconst)%b + first_atom - 1
index_c = g3x3_list(iconst)%c + 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)
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
lg3x3(iconst)%fa = -2.0_dp*(lg3x3(iconst)%ra_old - &
lg3x3(iconst)%rb_old)
lg3x3(iconst)%fb = -2.0_dp*(lg3x3(iconst)%ra_old - &
lg3x3(iconst)%rc_old)
lg3x3(iconst)%fc = -2.0_dp*(lg3x3(iconst)%rb_old - &
lg3x3(iconst)%rc_old)
! Check for fixed atom constraints
CALL check_fixed_atom_cns_g3x3(imass1, imass2, imass3, &
index_a, index_b, index_c, fixd_list, lg3x3(iconst))
! construct matrix
amat(1, 1) = (imass1 + imass2)*DOTPROD_3D(r0_12, lg3x3(iconst)%fa)
amat(1, 2) = imass1*DOTPROD_3D(r0_12, lg3x3(iconst)%fb)
amat(1, 3) = -imass2*DOTPROD_3D(r0_12, lg3x3(iconst)%fc)
amat(2, 1) = imass1*DOTPROD_3D(r0_13, lg3x3(iconst)%fa)
amat(2, 2) = (imass1 + imass3)*DOTPROD_3D(r0_13, lg3x3(iconst)%fb)
amat(2, 3) = imass3*DOTPROD_3D(r0_13, lg3x3(iconst)%fc)
amat(3, 1) = -imass2*DOTPROD_3D(r0_23, lg3x3(iconst)%fa)
amat(3, 2) = imass3*DOTPROD_3D(r0_23, lg3x3(iconst)%fb)
amat(3, 3) = (imass3 + imass2)*DOTPROD_3D(r0_23, lg3x3(iconst)%fc)
! Store values
lg3x3(iconst)%r0_12 = r0_12
lg3x3(iconst)%r0_13 = r0_13
lg3x3(iconst)%r0_23 = r0_23
lg3x3(iconst)%amat = amat
lg3x3(iconst)%lambda_old = 0.0_dp
lg3x3(iconst)%del_lambda = 0.0_dp
ELSE
! Retrieve values
r0_12 = lg3x3(iconst)%r0_12
r0_13 = lg3x3(iconst)%r0_13
r0_23 = lg3x3(iconst)%r0_23
amat = lg3x3(iconst)%amat
imass1 = lg3x3(iconst)%imass1
imass2 = lg3x3(iconst)%imass2
imass3 = lg3x3(iconst)%imass3
END IF
! Iterate until convergence
vec = lg3x3(iconst)%lambda(1)*lg3x3(iconst)%fa*(imass1 + imass2) + &
lg3x3(iconst)%lambda(2)*imass1*lg3x3(iconst)%fb - &
lg3x3(iconst)%lambda(3)*imass2*lg3x3(iconst)%fc
bvec(1, 1) = g3x3_list(iconst)%dab*g3x3_list(iconst)%dab &
- dtsqby2*dtsqby2*DOTPROD_3D(vec, vec) - DOTPROD_3D(r0_12, r0_12)
vec = lg3x3(iconst)%lambda(1)*lg3x3(iconst)%fa*imass1 + &
lg3x3(iconst)%lambda(2)*(imass1 + imass3)*lg3x3(iconst)%fb + &
lg3x3(iconst)%lambda(3)*imass3*lg3x3(iconst)%fc
bvec(2, 1) = g3x3_list(iconst)%dac*g3x3_list(iconst)%dac &
- dtsqby2*dtsqby2*DOTPROD_3D(vec, vec) - DOTPROD_3D(r0_13, r0_13)
vec = -lg3x3(iconst)%lambda(1)*lg3x3(iconst)%fa*imass2 + &
lg3x3(iconst)%lambda(2)*imass3*lg3x3(iconst)%fb + &
lg3x3(iconst)%lambda(3)*(imass2 + imass3)*lg3x3(iconst)%fc
bvec(3, 1) = g3x3_list(iconst)%dbc*g3x3_list(iconst)%dbc &
- dtsqby2*dtsqby2*DOTPROD_3D(vec, vec) - DOTPROD_3D(r0_23, r0_23)
bvec = bvec*idtsq
! get lambda
atemp = amat
CALL solve_system(atemp, 3, bvec)
lg3x3(iconst)%lambda(:) = bvec(:, 1)
lg3x3(iconst)%del_lambda(:) = lg3x3(iconst)%lambda(:) - &
lg3x3(iconst)%lambda_old(:)
lg3x3(iconst)%lambda_old(:) = lg3x3(iconst)%lambda(:)
fc1 = lg3x3(iconst)%del_lambda(1)*lg3x3(iconst)%fa + &
lg3x3(iconst)%del_lambda(2)*lg3x3(iconst)%fb
fc2 = -lg3x3(iconst)%del_lambda(1)*lg3x3(iconst)%fa + &
lg3x3(iconst)%del_lambda(3)*lg3x3(iconst)%fc
fc3 = -lg3x3(iconst)%del_lambda(2)*lg3x3(iconst)%fb - &
lg3x3(iconst)%del_lambda(3)*lg3x3(iconst)%fc
r1(:) = pos(:, index_a) + imass1*dtsqby2*fc1(:)
r2(:) = pos(:, index_b) + imass2*dtsqby2*fc2(:)
r3(:) = pos(:, index_c) + imass3*dtsqby2*fc3(:)
v1(:) = vel(:, index_a) + imass1*dtby2*fc1(:)
v2(:) = vel(:, index_b) + imass2*dtby2*fc2(:)
v3(:) = vel(:, index_c) + imass3*dtby2*fc3(:)
r12 = r1 - r2
r13 = r1 - r3
r23 = r2 - r3
! compute the tolerance:
sigma = DOT_PRODUCT(r12, r12) - g3x3_list(iconst)%dab* &
g3x3_list(iconst)%dab
max_sigma = MAX(max_sigma, ABS(sigma))
sigma = DOT_PRODUCT(r13, r13) - g3x3_list(iconst)%dac* &
g3x3_list(iconst)%dac
max_sigma = MAX(max_sigma, ABS(sigma))
sigma = DOT_PRODUCT(r23, r23) - g3x3_list(iconst)%dbc* &
g3x3_list(iconst)%dbc
max_sigma = MAX(max_sigma, ABS(sigma))
! update positions with full multiplier
pos(:, index_a) = r1(:)
pos(:, index_b) = r2(:)
pos(:, index_c) = r3(:)
! update velocites with full multiplier
vel(:, index_a) = v1(:)
vel(:, index_b) = v2(:)
vel(:, index_c) = v3(:)
END DO
END SUBROUTINE shake_3x3_low
! **************************************************************************************************
!> \brief ...
!> \param fixd_list ...
!> \param g3x3_list ...
!> \param lg3x3 ...
!> \param first_atom ...
!> \param ng3x3 ...
!> \param particle_set ...
!> \param pos ...
!> \param vel ...
!> \param r_shake ...
!> \param v_shake ...
!> \param dt ...
!> \param ishake ...
!> \param max_sigma ...
!> \par History
!> none
! **************************************************************************************************
SUBROUTINE shake_roll_3x3_low(fixd_list, g3x3_list, lg3x3, first_atom, ng3x3, &
particle_set, pos, vel, r_shake, v_shake, dt, ishake, max_sigma)
TYPE(fixd_constraint_type), DIMENSION(:), POINTER :: fixd_list
TYPE(g3x3_constraint_type), POINTER :: g3x3_list(:)
TYPE(local_g3x3_constraint_type), POINTER :: lg3x3(:)
INTEGER, INTENT(IN) :: first_atom, ng3x3
TYPE(particle_type), POINTER :: particle_set(:)
REAL(KIND=dp), INTENT(INOUT) :: pos(:, :), vel(:, :)
REAL(KIND=dp), DIMENSION(:, :), INTENT(IN) :: r_shake, v_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
REAL(KIND=dp) :: dtby2, dtsqby2, idtsq, imass1, imass2, &
imass3, sigma
REAL(KIND=dp), DIMENSION(3) :: f_roll1, f_roll2, f_roll3, fc1, fc2, &
fc3, r0_12, r0_13, r0_23, r1, r12, &
r13, r2, r23, r3, v1, v2, v3, vec
REAL(KIND=dp), DIMENSION(3, 1) :: bvec
REAL(KIND=dp), DIMENSION(3, 3) :: 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, ng3x3
IF (g3x3_list(iconst)%restraint%active) CYCLE
index_a = g3x3_list(iconst)%a + first_atom - 1
index_b = g3x3_list(iconst)%b + first_atom - 1
index_c = g3x3_list(iconst)%c + 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)
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
lg3x3(iconst)%fa = -2.0_dp*(lg3x3(iconst)%ra_old - &
lg3x3(iconst)%rb_old)
lg3x3(iconst)%fb = -2.0_dp*(lg3x3(iconst)%ra_old - &
lg3x3(iconst)%rc_old)
lg3x3(iconst)%fc = -2.0_dp*(lg3x3(iconst)%rb_old - &
lg3x3(iconst)%rc_old)
! Check for fixed atom constraints
CALL check_fixed_atom_cns_g3x3(imass1, imass2, imass3, &
index_a, index_b, index_c, fixd_list, lg3x3(iconst))
! rotate fconst:
CALL matvec_3x3(f_roll1, r_shake, lg3x3(iconst)%fa)
CALL matvec_3x3(f_roll2, r_shake, lg3x3(iconst)%fb)
CALL matvec_3x3(f_roll3, r_shake, lg3x3(iconst)%fc)
! 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) = -imass2*DOTPROD_3D(r0_12, f_roll3)
amat(2, 1) = imass1*DOTPROD_3D(r0_13, f_roll1)
amat(2, 2) = (imass1 + imass3)*DOTPROD_3D(r0_13, f_roll2)
amat(2, 3) = imass3*DOTPROD_3D(r0_13, f_roll3)
amat(3, 1) = -imass2*DOTPROD_3D(r0_23, f_roll1)
amat(3, 2) = imass3*DOTPROD_3D(r0_23, f_roll2)
amat(3, 3) = (imass3 + imass2)*DOTPROD_3D(r0_23, f_roll3)
! Store values
lg3x3(iconst)%r0_12 = r0_12
lg3x3(iconst)%r0_13 = r0_13
lg3x3(iconst)%r0_23 = r0_23
lg3x3(iconst)%f_roll1 = f_roll1
lg3x3(iconst)%f_roll2 = f_roll2
lg3x3(iconst)%f_roll3 = f_roll3
lg3x3(iconst)%amat = amat
lg3x3(iconst)%lambda_old = 0.0_dp
lg3x3(iconst)%del_lambda = 0.0_dp
ELSE
! Retrieve values
r0_12 = lg3x3(iconst)%r0_12
r0_13 = lg3x3(iconst)%r0_13
r0_23 = lg3x3(iconst)%r0_23
f_roll1 = lg3x3(iconst)%f_roll1
f_roll2 = lg3x3(iconst)%f_roll2
f_roll3 = lg3x3(iconst)%f_roll3
amat = lg3x3(iconst)%amat
imass1 = lg3x3(iconst)%imass1
imass2 = lg3x3(iconst)%imass2
imass3 = lg3x3(iconst)%imass3
END IF
! Iterate until convergence
vec = lg3x3(iconst)%lambda(1)*f_roll1*(imass1 + imass2) + &
lg3x3(iconst)%lambda(2)*imass1*f_roll2 - &
lg3x3(iconst)%lambda(3)*imass2*f_roll3
bvec(1, 1) = g3x3_list(iconst)%dab*g3x3_list(iconst)%dab &
- dtsqby2*dtsqby2*DOTPROD_3D(vec, vec) - DOTPROD_3D(r0_12, r0_12)
vec = lg3x3(iconst)%lambda(1)*f_roll1*imass1 + &
lg3x3(iconst)%lambda(2)*(imass1 + imass3)*f_roll2 + &
lg3x3(iconst)%lambda(3)*imass3*f_roll3
bvec(2, 1) = g3x3_list(iconst)%dac*g3x3_list(iconst)%dac &
- dtsqby2*dtsqby2*DOTPROD_3D(vec, vec) - DOTPROD_3D(r0_13, r0_13)
vec = -lg3x3(iconst)%lambda(1)*f_roll1*imass2 + &
lg3x3(iconst)%lambda(2)*imass3*f_roll2 + &
lg3x3(iconst)%lambda(3)*(imass2 + imass3)*f_roll3
bvec(3, 1) = g3x3_list(iconst)%dbc*g3x3_list(iconst)%dbc &
- dtsqby2*dtsqby2*DOTPROD_3D(vec, vec) - DOTPROD_3D(r0_23, r0_23)
bvec = bvec*idtsq
! get lambda
atemp = amat
CALL solve_system(atemp, 3, bvec)
lg3x3(iconst)%lambda(:) = bvec(:, 1)
lg3x3(iconst)%del_lambda(:) = lg3x3(iconst)%lambda(:) - &
lg3x3(iconst)%lambda_old(:)
lg3x3(iconst)%lambda_old(:) = lg3x3(iconst)%lambda(:)
fc1 = lg3x3(iconst)%del_lambda(1)*lg3x3(iconst)%fa + &
lg3x3(iconst)%del_lambda(2)*lg3x3(iconst)%fb
fc2 = -lg3x3(iconst)%del_lambda(1)*lg3x3(iconst)%fa + &
lg3x3(iconst)%del_lambda(3)*lg3x3(iconst)%fc
fc3 = -lg3x3(iconst)%del_lambda(2)*lg3x3(iconst)%fb - &
lg3x3(iconst)%del_lambda(3)*lg3x3(iconst)%fc
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, v_shake, fc1)
v1(:) = vel(:, index_a) + imass1*dtby2*vec
CALL MATVEC_3x3(vec, v_shake, fc2)
v2(:) = vel(:, index_b) + imass2*dtby2*vec
CALL MATVEC_3x3(vec, v_shake, fc3)
v3(:) = vel(:, index_c) + imass3*dtby2*vec
r12 = r1 - r2
r13 = r1 - r3
r23 = r2 - r3
! compute the tolerance:
sigma = DOT_PRODUCT(r12, r12) - g3x3_list(iconst)%dab* &
g3x3_list(iconst)%dab
max_sigma = MAX(max_sigma, ABS(sigma))
sigma = DOT_PRODUCT(r13, r13) - g3x3_list(iconst)%dac* &
g3x3_list(iconst)%dac
max_sigma = MAX(max_sigma, ABS(sigma))
sigma = DOT_PRODUCT(r23, r23) - g3x3_list(iconst)%dbc* &
g3x3_list(iconst)%dbc
max_sigma = MAX(max_sigma, ABS(sigma))
! update positions with full multiplier
pos(:, index_a) = r1(:)
pos(:, index_b) = r2(:)
pos(:, index_c) = r3(:)
! update velocites with full multiplier
vel(:, index_a) = v1(:)
vel(:, index_b) = v2(:)
vel(:, index_c) = v3(:)
END DO
END SUBROUTINE shake_roll_3x3_low
! **************************************************************************************************
!> \brief ...
!> \param fixd_list ...
!> \param g3x3_list ...
!> \param lg3x3 ...
!> \param first_atom ...
!> \param particle_set ...
!> \param vel ...
!> \param r_rattle ...
!> \param dt ...
!> \param veps ...
!> \par History
!> none
! **************************************************************************************************
SUBROUTINE rattle_roll_3x3_low(fixd_list, g3x3_list, lg3x3, first_atom, &
particle_set, vel, r_rattle, dt, veps)
TYPE(fixd_constraint_type), DIMENSION(:), POINTER :: fixd_list
TYPE(g3x3_constraint_type), POINTER :: g3x3_list(:)
TYPE(local_g3x3_constraint_type), POINTER :: lg3x3(:)
INTEGER, INTENT(IN) :: first_atom
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 :: iconst, index_a, index_b, index_c
REAL(KIND=dp) :: dtby2, idt, imass1, imass2, imass3, mass
REAL(KIND=dp), DIMENSION(3) :: f_roll1, f_roll2, f_roll3, fc1, fc2, &
fc3, lambda, r12, r13, r23, v12, v13, &
v23, vec
REAL(KIND=dp), DIMENSION(3, 1) :: bvec
REAL(KIND=dp), DIMENSION(3, 3) :: amat
TYPE(atomic_kind_type), POINTER :: atomic_kind
idt = 1.0_dp/dt
dtby2 = dt*.5_dp
DO iconst = 1, SIZE(g3x3_list)
IF (g3x3_list(iconst)%restraint%active) CYCLE
index_a = g3x3_list(iconst)%a + first_atom - 1
index_b = g3x3_list(iconst)%b + first_atom - 1
index_c = g3x3_list(iconst)%c + first_atom - 1
v12(:) = vel(:, index_a) - vel(:, index_b)
v13(:) = vel(:, index_a) - vel(:, index_c)
v23(:) = vel(:, index_b) - vel(:, index_c)
r12(:) = particle_set(index_a)%r(:) - particle_set(index_b)%r(:)
r13(:) = particle_set(index_a)%r(:) - particle_set(index_c)%r(:)
r23(:) = particle_set(index_b)%r(:) - particle_set(index_c)%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
lg3x3(iconst)%fa = -2.0_dp*r12
lg3x3(iconst)%fb = -2.0_dp*r13
lg3x3(iconst)%fc = -2.0_dp*r23
! Check for fixed atom constraints
CALL check_fixed_atom_cns_g3x3(imass1, imass2, imass3, &
index_a, index_b, index_c, fixd_list, lg3x3(iconst))
! roll the fc
CALL MATVEC_3x3(f_roll1, r_rattle, lg3x3(iconst)%fa)
CALL MATVEC_3x3(f_roll2, r_rattle, lg3x3(iconst)%fb)
CALL MATVEC_3x3(f_roll3, r_rattle, lg3x3(iconst)%fc)
! construct matrix
amat(1, 1) = (imass1 + imass2)*DOTPROD_3D(r12, f_roll1)
amat(1, 2) = imass1*DOTPROD_3D(r12, f_roll2)
amat(1, 3) = -imass2*DOTPROD_3D(r12, f_roll3)
amat(2, 1) = imass1*DOTPROD_3D(r13, f_roll1)
amat(2, 2) = (imass1 + imass3)*DOTPROD_3D(r13, f_roll2)
amat(2, 3) = imass3*DOTPROD_3D(r13, f_roll3)
amat(3, 1) = -imass2*DOTPROD_3D(r23, f_roll1)
amat(3, 2) = imass3*DOTPROD_3D(r23, f_roll2)
amat(3, 3) = (imass2 + imass3)*DOTPROD_3D(r23, f_roll3)
! construct solution vector
CALL matvec_3x3(vec, veps, r12)
bvec(1, 1) = DOTPROD_3D(r12, v12 + vec)
CALL matvec_3x3(vec, veps, r13)
bvec(2, 1) = DOTPROD_3D(r13, v13 + vec)
CALL matvec_3x3(vec, veps, r23)
bvec(3, 1) = DOTPROD_3D(r23, v23 + vec)
bvec = -bvec*2.0_dp*idt
! get lambda
CALL solve_system(amat, 3, bvec)
lambda(:) = bvec(:, 1)
lg3x3(iconst)%lambda(:) = lambda
fc1 = lambda(1)*f_roll1 + &
lambda(2)*f_roll2
fc2 = -lambda(1)*f_roll1 + &
lambda(3)*f_roll3
fc3 = -lambda(2)*f_roll2 - &
lambda(3)*f_roll3
vel(:, index_a) = vel(:, index_a) + imass1*dtby2*fc1(:)
vel(:, index_b) = vel(:, index_b) + imass2*dtby2*fc2(:)
vel(:, index_c) = vel(:, index_c) + imass3*dtby2*fc3(:)
END DO
END SUBROUTINE rattle_roll_3x3_low
! **************************************************************************************************
!> \brief ...
!> \param fixd_list ...
!> \param g3x3_list ...
!> \param lg3x3 ...
!> \param first_atom ...
!> \param particle_set ...
!> \param vel ...
!> \param dt ...
!> \par History
!> none
! **************************************************************************************************
SUBROUTINE rattle_3x3_low(fixd_list, g3x3_list, lg3x3, first_atom, &
particle_set, vel, dt)
TYPE(fixd_constraint_type), DIMENSION(:), POINTER :: fixd_list
TYPE(g3x3_constraint_type), POINTER :: g3x3_list(:)
TYPE(local_g3x3_constraint_type), POINTER :: lg3x3(:)
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
REAL(KIND=dp) :: dtby2, idt, imass1, imass2, imass3, mass
REAL(KIND=dp), DIMENSION(3) :: fc1, fc2, fc3, r12, r13, r23, v12, v13, &
v23
REAL(KIND=dp), DIMENSION(3, 1) :: bvec
REAL(KIND=dp), DIMENSION(3, 3) :: amat
TYPE(atomic_kind_type), POINTER :: atomic_kind
idt = 1.0_dp/dt
dtby2 = dt*.5_dp
DO iconst = 1, SIZE(g3x3_list)
IF (g3x3_list(iconst)%restraint%active) CYCLE
index_a = g3x3_list(iconst)%a + first_atom - 1
index_b = g3x3_list(iconst)%b + first_atom - 1
index_c = g3x3_list(iconst)%c + first_atom - 1
v12(:) = vel(:, index_a) - vel(:, index_b)
v13(:) = vel(:, index_a) - vel(:, index_c)
v23(:) = vel(:, index_b) - vel(:, index_c)
r12(:) = particle_set(index_a)%r(:) - particle_set(index_b)%r(:)
r13(:) = particle_set(index_a)%r(:) - particle_set(index_c)%r(:)
r23(:) = particle_set(index_b)%r(:) - particle_set(index_c)%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
lg3x3(iconst)%fa = -2.0_dp*r12
lg3x3(iconst)%fb = -2.0_dp*r13
lg3x3(iconst)%fc = -2.0_dp*r23
! Check for fixed atom constraints
CALL check_fixed_atom_cns_g3x3(imass1, imass2, imass3, &
index_a, index_b, index_c, fixd_list, lg3x3(iconst))
! construct matrix
amat(1, 1) = (imass1 + imass2)*DOTPROD_3D(r12, lg3x3(iconst)%fa)
amat(1, 2) = imass1*DOTPROD_3D(r12, lg3x3(iconst)%fb)
amat(1, 3) = -imass2*DOTPROD_3D(r12, lg3x3(iconst)%fc)
amat(2, 1) = imass1*DOTPROD_3D(r13, lg3x3(iconst)%fa)
amat(2, 2) = (imass1 + imass3)*DOTPROD_3D(r13, lg3x3(iconst)%fb)
amat(2, 3) = imass3*DOTPROD_3D(r13, lg3x3(iconst)%fc)
amat(3, 1) = -imass2*DOTPROD_3D(r23, lg3x3(iconst)%fa)
amat(3, 2) = imass3*DOTPROD_3D(r23, lg3x3(iconst)%fb)
amat(3, 3) = (imass2 + imass3)*DOTPROD_3D(r23, lg3x3(iconst)%fc)
! construct solution vector
bvec(1, 1) = DOTPROD_3D(r12, v12)
bvec(2, 1) = DOTPROD_3D(r13, v13)
bvec(3, 1) = DOTPROD_3D(r23, v23)
bvec = -bvec*2.0_dp*idt
! get lambda
CALL solve_system(amat, 3, bvec)
lg3x3(iconst)%lambda(:) = bvec(:, 1)
fc1 = lg3x3(iconst)%lambda(1)*lg3x3(iconst)%fa + &
lg3x3(iconst)%lambda(2)*lg3x3(iconst)%fb
fc2 = -lg3x3(iconst)%lambda(1)*lg3x3(iconst)%fa + &
lg3x3(iconst)%lambda(3)*lg3x3(iconst)%fc
fc3 = -lg3x3(iconst)%lambda(2)*lg3x3(iconst)%fb - &
lg3x3(iconst)%lambda(3)*lg3x3(iconst)%fc
vel(:, index_a) = vel(:, index_a) + imass1*dtby2*fc1(:)
vel(:, index_b) = vel(:, index_b) + imass2*dtby2*fc2(:)
vel(:, index_c) = vel(:, index_c) + imass3*dtby2*fc3(:)
END DO
END SUBROUTINE rattle_3x3_low
END MODULE constraint_3x3