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rLAMMPS lammps
pair_lcbop.cpp
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/* ----------------------------------------------------------------------
LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
http://lammps.sandia.gov, Sandia National Laboratories
Steve Plimpton, sjplimp@sandia.gov
Copyright (2003) Sandia Corporation. Under the terms of Contract
DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
certain rights in this software. This software is distributed under
the GNU General Public License.
See the README file in the top-level LAMMPS directory.
------------------------------------------------------------------------- */
/* ----------------------------------------------------------------------
Contributing author: Dominik Wójt (Wroclaw University of Technology)
based on pair_airebo by Ase Henry (MIT)
------------------------------------------------------------------------- */
#include "math.h"
#include "stdio.h"
#include "stdlib.h"
#include "string.h"
#include "mpi.h"
#include "pair_lcbop.h"
#include "atom.h"
#include "neighbor.h"
#include "neigh_request.h"
#include "force.h"
#include "comm.h"
#include "neighbor.h"
#include "neigh_list.h"
#include "neigh_request.h"
#include "my_page.h"
#include "math_const.h"
#include "memory.h"
#include "error.h"
using
namespace
LAMMPS_NS
;
using
namespace
MathConst
;
#define MAXLINE 1024
#define TOL 1.0e-9
#define PGDELTA 1
/* ---------------------------------------------------------------------- */
PairLCBOP
::
PairLCBOP
(
LAMMPS
*
lmp
)
:
Pair
(
lmp
)
{
single_enable
=
0
;
one_coeff
=
1
;
manybody_flag
=
1
;
ghostneigh
=
1
;
maxlocal
=
0
;
SR_numneigh
=
NULL
;
SR_firstneigh
=
NULL
;
ipage
=
NULL
;
pgsize
=
oneatom
=
0
;
N
=
NULL
;
M
=
NULL
;
}
/* ----------------------------------------------------------------------
check if allocated, since class can be destructed when incomplete
------------------------------------------------------------------------- */
PairLCBOP
::~
PairLCBOP
()
{
memory
->
destroy
(
SR_numneigh
);
memory
->
sfree
(
SR_firstneigh
);
delete
[]
ipage
;
memory
->
destroy
(
N
);
memory
->
destroy
(
M
);
if
(
allocated
)
{
memory
->
destroy
(
setflag
);
memory
->
destroy
(
cutsq
);
memory
->
destroy
(
cutghost
);
delete
[]
map
;
}
}
/* ---------------------------------------------------------------------- */
void
PairLCBOP
::
compute
(
int
eflag
,
int
vflag
)
{
if
(
eflag
||
vflag
)
ev_setup
(
eflag
,
vflag
);
else
evflag
=
vflag_fdotr
=
vflag_atom
=
0
;
SR_neigh
();
FSR
(
eflag
,
vflag
);
FLR
(
eflag
,
vflag
);
if
(
vflag_fdotr
)
virial_fdotr_compute
();
}
/* ----------------------------------------------------------------------
allocate all arrays
------------------------------------------------------------------------- */
void
PairLCBOP
::
allocate
()
{
allocated
=
1
;
int
n
=
atom
->
ntypes
;
memory
->
create
(
setflag
,
n
+
1
,
n
+
1
,
"pair:setflag"
);
for
(
int
i
=
1
;
i
<=
n
;
i
++
)
for
(
int
j
=
i
;
j
<=
n
;
j
++
)
setflag
[
i
][
j
]
=
0
;
memory
->
create
(
cutsq
,
n
+
1
,
n
+
1
,
"pair:cutsq"
);
memory
->
create
(
cutghost
,
n
+
1
,
n
+
1
,
"pair:cutghost"
);
map
=
new
int
[
n
+
1
];
}
/* ----------------------------------------------------------------------
global settings
------------------------------------------------------------------------- */
void
PairLCBOP
::
settings
(
int
narg
,
char
**
arg
)
{
if
(
narg
!=
0
)
error
->
all
(
FLERR
,
"Illegal pair_style command"
);
}
/* ----------------------------------------------------------------------
set coeffs for one or more type pairs
------------------------------------------------------------------------- */
void
PairLCBOP
::
coeff
(
int
narg
,
char
**
arg
)
{
if
(
!
allocated
)
allocate
();
if
(
narg
!=
3
+
atom
->
ntypes
)
error
->
all
(
FLERR
,
"Incorrect args for pair coefficients"
);
// insure I,J args are * *
if
(
strcmp
(
arg
[
0
],
"*"
)
!=
0
||
strcmp
(
arg
[
1
],
"*"
)
!=
0
)
error
->
all
(
FLERR
,
"Incorrect args for pair coefficients"
);
// read args that map atom types to C and NULL
// map[i] = which element (0 for C) the Ith atom type is, -1 if NULL
for
(
int
i
=
3
;
i
<
narg
;
i
++
)
{
if
(
strcmp
(
arg
[
i
],
"NULL"
)
==
0
)
{
map
[
i
-
2
]
=
-
1
;
}
else
if
(
strcmp
(
arg
[
i
],
"C"
)
==
0
)
{
map
[
i
-
2
]
=
0
;
}
else
error
->
all
(
FLERR
,
"Incorrect args for pair coefficients"
);
}
// read potential file and initialize fitting splines
read_file
(
arg
[
2
]);
spline_init
();
// clear setflag since coeff() called once with I,J = * *
int
n
=
atom
->
ntypes
;
for
(
int
i
=
1
;
i
<=
n
;
i
++
)
for
(
int
j
=
i
;
j
<=
n
;
j
++
)
setflag
[
i
][
j
]
=
0
;
// set setflag i,j for type pairs where both are mapped to elements
int
count
=
0
;
for
(
int
i
=
1
;
i
<=
n
;
i
++
)
for
(
int
j
=
i
;
j
<=
n
;
j
++
)
if
(
map
[
i
]
>=
0
&&
map
[
j
]
>=
0
)
{
setflag
[
i
][
j
]
=
1
;
count
++
;
}
if
(
count
==
0
)
error
->
all
(
FLERR
,
"Incorrect args for pair coefficients"
);
}
/* ----------------------------------------------------------------------
init specific to this pair style
------------------------------------------------------------------------- */
void
PairLCBOP
::
init_style
()
{
if
(
atom
->
tag_enable
==
0
)
error
->
all
(
FLERR
,
"Pair style LCBOP requires atom IDs"
);
if
(
force
->
newton_pair
==
0
)
error
->
all
(
FLERR
,
"Pair style LCBOP requires newton pair on"
);
// need a full neighbor list, including neighbors of ghosts
int
irequest
=
neighbor
->
request
(
this
);
neighbor
->
requests
[
irequest
]
->
half
=
0
;
neighbor
->
requests
[
irequest
]
->
full
=
1
;
neighbor
->
requests
[
irequest
]
->
ghost
=
1
;
// local SR neighbor list
// create pages if first time or if neighbor pgsize/oneatom has changed
int
create
=
0
;
if
(
ipage
==
NULL
)
create
=
1
;
if
(
pgsize
!=
neighbor
->
pgsize
)
create
=
1
;
if
(
oneatom
!=
neighbor
->
oneatom
)
create
=
1
;
if
(
create
)
{
delete
[]
ipage
;
pgsize
=
neighbor
->
pgsize
;
oneatom
=
neighbor
->
oneatom
;
int
nmypage
=
comm
->
nthreads
;
ipage
=
new
MyPage
<
int
>
[
nmypage
];
for
(
int
i
=
0
;
i
<
nmypage
;
i
++
)
ipage
[
i
].
init
(
oneatom
,
pgsize
,
PGDELTA
);
}
}
/* ----------------------------------------------------------------------
init for one type pair i,j and corresponding j,i
------------------------------------------------------------------------- */
double
PairLCBOP
::
init_one
(
int
i
,
int
j
)
{
if
(
setflag
[
i
][
j
]
==
0
)
error
->
all
(
FLERR
,
"All pair coeffs are not set"
);
// cut3rebo = 3 SR distances
cut3rebo
=
3.0
*
r_2
;
// cutmax = furthest distance from an owned atom
// at which another atom will feel force, i.e. the ghost cutoff
// for SR term in potential:
// interaction = M-K-I-J-L-N with I = owned and J = ghost
// I to N is max distance = 3 SR distances
// for V_LR term in potential:
// r_2_LR
// cutghost = SR cutoff used in SR_neigh() for neighbors of ghosts
double
cutmax
=
MAX
(
cut3rebo
,
r_2_LR
);
cutghost
[
i
][
j
]
=
r_2
;
cutLRsq
=
r_2_LR
*
r_2_LR
;
cutghost
[
j
][
i
]
=
cutghost
[
i
][
j
];
r_2_sq
=
r_2
*
r_2
;
return
cutmax
;
}
/* ----------------------------------------------------------------------
create SR neighbor list from main neighbor list
SR neighbor list stores neighbors of ghost atoms
------------------------------------------------------------------------- */
void
PairLCBOP
::
SR_neigh
()
{
int
i
,
j
,
ii
,
jj
,
n
,
allnum
,
jnum
;
double
xtmp
,
ytmp
,
ztmp
,
delx
,
dely
,
delz
,
rsq
,
dS
;
int
*
ilist
,
*
jlist
,
*
numneigh
,
**
firstneigh
;
int
*
neighptr
;
double
**
x
=
atom
->
x
;
int
nlocal
=
atom
->
nlocal
;
int
nall
=
nlocal
+
atom
->
nghost
;
if
(
atom
->
nmax
>
maxlocal
)
{
// ensure ther is enough space
maxlocal
=
atom
->
nmax
;
// for atoms and ghosts allocated
memory
->
destroy
(
SR_numneigh
);
memory
->
sfree
(
SR_firstneigh
);
memory
->
destroy
(
N
);
memory
->
destroy
(
M
);
memory
->
create
(
SR_numneigh
,
maxlocal
,
"LCBOP:numneigh"
);
SR_firstneigh
=
(
int
**
)
memory
->
smalloc
(
maxlocal
*
sizeof
(
int
*
),
"LCBOP:firstneigh"
);
memory
->
create
(
N
,
maxlocal
,
"LCBOP:N"
);
memory
->
create
(
M
,
maxlocal
,
"LCBOP:M"
);
}
allnum
=
list
->
inum
+
list
->
gnum
;
ilist
=
list
->
ilist
;
numneigh
=
list
->
numneigh
;
firstneigh
=
list
->
firstneigh
;
// store all SR neighs of owned and ghost atoms
// scan full neighbor list of I
ipage
->
reset
();
for
(
ii
=
0
;
ii
<
allnum
;
ii
++
)
{
i
=
ilist
[
ii
];
n
=
0
;
neighptr
=
ipage
->
vget
();
xtmp
=
x
[
i
][
0
];
ytmp
=
x
[
i
][
1
];
ztmp
=
x
[
i
][
2
];
N
[
i
]
=
0.0
;
jlist
=
firstneigh
[
i
];
jnum
=
numneigh
[
i
];
for
(
jj
=
0
;
jj
<
jnum
;
jj
++
)
{
j
=
jlist
[
jj
];
j
&=
NEIGHMASK
;
delx
=
xtmp
-
x
[
j
][
0
];
dely
=
ytmp
-
x
[
j
][
1
];
delz
=
ztmp
-
x
[
j
][
2
];
rsq
=
delx
*
delx
+
dely
*
dely
+
delz
*
delz
;
if
(
rsq
<
r_2_sq
)
{
neighptr
[
n
++
]
=
j
;
N
[
i
]
+=
f_c
(
sqrt
(
rsq
),
r_1
,
r_2
,
&
dS
);
}
}
SR_firstneigh
[
i
]
=
neighptr
;
SR_numneigh
[
i
]
=
n
;
ipage
->
vgot
(
n
);
if
(
ipage
->
status
())
error
->
one
(
FLERR
,
"Neighbor list overflow, boost neigh_modify one"
);
}
// calculate M_i
for
(
ii
=
0
;
ii
<
allnum
;
ii
++
)
{
i
=
ilist
[
ii
];
xtmp
=
x
[
i
][
0
];
ytmp
=
x
[
i
][
1
];
ztmp
=
x
[
i
][
2
];
M
[
i
]
=
0.0
;
jlist
=
SR_firstneigh
[
i
];
jnum
=
SR_numneigh
[
i
];
for
(
jj
=
0
;
jj
<
jnum
;
jj
++
)
{
j
=
jlist
[
jj
];
delx
=
xtmp
-
x
[
j
][
0
];
dely
=
ytmp
-
x
[
j
][
1
];
delz
=
ztmp
-
x
[
j
][
2
];
rsq
=
delx
*
delx
+
dely
*
dely
+
delz
*
delz
;
if
(
rsq
<
r_2_sq
)
{
double
f_c_ij
=
f_c
(
sqrt
(
rsq
),
r_1
,
r_2
,
&
dS
);
double
Nji
=
N
[
j
]
-
f_c_ij
;
// F(xij) = 1-f_c_LR(Nji, 2,3,&dummy)
M
[
i
]
+=
f_c_ij
*
(
1
-
f_c_LR
(
Nji
,
2
,
3
,
&
dS
)
);
}
}
}
}
/* ----------------------------------------------------------------------
Short range forces and energy
------------------------------------------------------------------------- */
void
PairLCBOP
::
FSR
(
int
eflag
,
int
vflag
)
{
int
i
,
j
,
jj
,
ii
,
inum
;
tagint
itag
,
jtag
;
double
delx
,
dely
,
delz
,
fpair
,
xtmp
,
ytmp
,
ztmp
;
double
r_sq
,
rijmag
,
f_c_ij
,
df_c_ij
;
double
VR
,
dVRdi
,
VA
,
Bij
,
dVAdi
,
dVA
;
double
d_f_c_ij
,
del
[
3
];
int
*
ilist
,
*
SR_neighs
;
double
**
x
=
atom
->
x
;
double
**
f
=
atom
->
f
;
tagint
*
tag
=
atom
->
tag
;
int
nlocal
=
atom
->
nlocal
;
int
newton_pair
=
force
->
newton_pair
;
inum
=
list
->
inum
;
ilist
=
list
->
ilist
;
// two-body interactions from SR neighbor list, skip half of them
for
(
ii
=
0
;
ii
<
inum
;
ii
++
)
{
i
=
ilist
[
ii
];
itag
=
tag
[
i
];
xtmp
=
x
[
i
][
0
];
ytmp
=
x
[
i
][
1
];
ztmp
=
x
[
i
][
2
];
SR_neighs
=
SR_firstneigh
[
i
];
for
(
jj
=
0
;
jj
<
SR_numneigh
[
i
];
jj
++
)
{
j
=
SR_neighs
[
jj
];
jtag
=
tag
[
j
];
if
(
itag
>
jtag
)
{
if
((
itag
+
jtag
)
%
2
==
0
)
continue
;
}
else
if
(
itag
<
jtag
)
{
if
((
itag
+
jtag
)
%
2
==
1
)
continue
;
}
else
{
if
(
x
[
j
][
2
]
<
ztmp
)
continue
;
if
(
x
[
j
][
2
]
==
ztmp
&&
x
[
j
][
1
]
<
ytmp
)
continue
;
if
(
x
[
j
][
2
]
==
ztmp
&&
x
[
j
][
1
]
==
ytmp
&&
x
[
j
][
0
]
<
xtmp
)
continue
;
}
delx
=
x
[
i
][
0
]
-
x
[
j
][
0
];
dely
=
x
[
i
][
1
]
-
x
[
j
][
1
];
delz
=
x
[
i
][
2
]
-
x
[
j
][
2
];
r_sq
=
delx
*
delx
+
dely
*
dely
+
delz
*
delz
;
rijmag
=
sqrt
(
r_sq
);
f_c_ij
=
f_c
(
rijmag
,
r_1
,
r_2
,
&
df_c_ij
);
if
(
f_c_ij
<=
TOL
)
continue
;
VR
=
A
*
exp
(
-
alpha
*
rijmag
);
dVRdi
=
-
alpha
*
VR
;
dVRdi
=
dVRdi
*
f_c_ij
+
df_c_ij
*
VR
;
// VR -> VR * f_c_ij
VR
*=
f_c_ij
;
VA
=
dVA
=
0.0
;
{
double
term
=
B_1
*
exp
(
-
beta_1
*
rijmag
);
VA
+=
term
;
dVA
+=
-
beta_1
*
term
;
term
=
B_2
*
exp
(
-
beta_2
*
rijmag
);
VA
+=
term
;
dVA
+=
-
beta_2
*
term
;
}
dVA
=
dVA
*
f_c_ij
+
df_c_ij
*
VA
;
// VA -> VA * f_c_ij
VA
*=
f_c_ij
;
del
[
0
]
=
delx
;
del
[
1
]
=
dely
;
del
[
2
]
=
delz
;
Bij
=
bondorder
(
i
,
j
,
del
,
rijmag
,
VA
,
f
,
vflag_atom
);
dVAdi
=
Bij
*
dVA
;
// F = (dVRdi+dVAdi)*(-grad rijmag)
// grad_i rijmag = \vec{rij} /rijmag
// grad_j rijmag = -\vec{rij} /rijmag
fpair
=
-
(
dVRdi
-
dVAdi
)
/
rijmag
;
f
[
i
][
0
]
+=
delx
*
fpair
;
f
[
i
][
1
]
+=
dely
*
fpair
;
f
[
i
][
2
]
+=
delz
*
fpair
;
f
[
j
][
0
]
-=
delx
*
fpair
;
f
[
j
][
1
]
-=
dely
*
fpair
;
f
[
j
][
2
]
-=
delz
*
fpair
;
double
evdwl
=
0.0
;
if
(
eflag
)
evdwl
=
VR
-
Bij
*
VA
;
if
(
evflag
)
ev_tally
(
i
,
j
,
nlocal
,
newton_pair
,
evdwl
,
0.0
,
fpair
,
delx
,
dely
,
delz
);
}
}
}
/* ----------------------------------------------------------------------
compute long range forces and energy
------------------------------------------------------------------------- */
void
PairLCBOP
::
FLR
(
int
eflag
,
int
vflag
)
{
int
i
,
j
,
jj
,
m
,
ii
;
tagint
itag
,
jtag
;
double
delx
,
dely
,
delz
,
fpair
,
xtmp
,
ytmp
,
ztmp
;
double
r_sq
,
rijmag
,
f_c_ij
,
df_c_ij
;
double
V
,
dVdi
;
double
**
x
=
atom
->
x
;
double
**
f
=
atom
->
f
;
tagint
*
tag
=
atom
->
tag
;
int
nlocal
=
atom
->
nlocal
;
int
newton_pair
=
force
->
newton_pair
;
int
inum
=
list
->
inum
;
int
*
ilist
=
list
->
ilist
;
int
*
numneigh
=
list
->
numneigh
;
int
**
firstneigh
=
list
->
firstneigh
;
// two-body interactions from full neighbor list, skip half of them
for
(
ii
=
0
;
ii
<
inum
;
ii
++
)
{
i
=
ilist
[
ii
];
itag
=
tag
[
i
];
xtmp
=
x
[
i
][
0
];
ytmp
=
x
[
i
][
1
];
ztmp
=
x
[
i
][
2
];
int
*
neighs
=
firstneigh
[
i
];
for
(
jj
=
0
;
jj
<
numneigh
[
i
];
jj
++
)
{
j
=
neighs
[
jj
];
j
&=
NEIGHMASK
;
jtag
=
tag
[
j
];
if
(
itag
>
jtag
)
{
if
((
itag
+
jtag
)
%
2
==
0
)
continue
;
}
else
if
(
itag
<
jtag
)
{
if
((
itag
+
jtag
)
%
2
==
1
)
continue
;
}
else
{
if
(
x
[
j
][
2
]
<
ztmp
)
continue
;
if
(
x
[
j
][
2
]
==
ztmp
&&
x
[
j
][
1
]
<
ytmp
)
continue
;
if
(
x
[
j
][
2
]
==
ztmp
&&
x
[
j
][
1
]
==
ytmp
&&
x
[
j
][
0
]
<
xtmp
)
continue
;
}
delx
=
x
[
i
][
0
]
-
x
[
j
][
0
];
dely
=
x
[
i
][
1
]
-
x
[
j
][
1
];
delz
=
x
[
i
][
2
]
-
x
[
j
][
2
];
r_sq
=
delx
*
delx
+
dely
*
dely
+
delz
*
delz
;
rijmag
=
sqrt
(
r_sq
);
f_c_ij
=
1
-
f_c
(
rijmag
,
r_1
,
r_2
,
&
df_c_ij
);
df_c_ij
=
-
df_c_ij
;
// derivative may be inherited from previous call, see f_c_LR definition
f_c_ij
*=
f_c_LR
(
rijmag
,
r_1_LR
,
r_2_LR
,
&
df_c_ij
);
if
(
f_c_ij
<=
TOL
)
continue
;
V
=
dVdi
=
0
;
if
(
rijmag
<
r_0
)
{
double
exp_part
=
exp
(
-
lambda_1
*
(
rijmag
-
r_0
)
);
V
=
eps_1
*
(
exp_part
*
exp_part
-
2
*
exp_part
)
+
v_1
;
dVdi
=
2
*
eps_1
*
lambda_1
*
exp_part
*
(
1
-
exp_part
);
}
else
{
double
exp_part
=
exp
(
-
lambda_2
*
(
rijmag
-
r_0
)
);
V
=
eps_2
*
(
exp_part
*
exp_part
-
2
*
exp_part
)
+
v_2
;
dVdi
=
2
*
eps_2
*
lambda_2
*
exp_part
*
(
1
-
exp_part
);
}
dVdi
=
dVdi
*
f_c_ij
+
df_c_ij
*
V
;
// V -> V * f_c_ij
V
*=
f_c_ij
;
// F = (dVdi)*(-grad rijmag)
// grad_i rijmag = \vec{rij} /rijmag
// grad_j rijmag = -\vec{rij} /rijmag
fpair
=
-
dVdi
/
rijmag
;
f
[
i
][
0
]
+=
delx
*
fpair
;
f
[
i
][
1
]
+=
dely
*
fpair
;
f
[
i
][
2
]
+=
delz
*
fpair
;
f
[
j
][
0
]
-=
delx
*
fpair
;
f
[
j
][
1
]
-=
dely
*
fpair
;
f
[
j
][
2
]
-=
delz
*
fpair
;
double
evdwl
=
0.0
;
if
(
eflag
)
evdwl
=
V
;
if
(
evflag
)
ev_tally
(
i
,
j
,
nlocal
,
newton_pair
,
evdwl
,
0.0
,
fpair
,
delx
,
dely
,
delz
);
}
}
}
/* ----------------------------------------------------------------------
forces for Nij and Mij
------------------------------------------------------------------------- */
void
PairLCBOP
::
FNij
(
int
i
,
int
j
,
double
factor
,
double
**
f
,
int
vflag_atom
)
{
int
atomi
=
i
;
int
atomj
=
j
;
int
*
SR_neighs
=
SR_firstneigh
[
i
];
double
**
x
=
atom
->
x
;
for
(
int
k
=
0
;
k
<
SR_numneigh
[
i
];
k
++
)
{
int
atomk
=
SR_neighs
[
k
];
if
(
atomk
!=
atomj
)
{
double
rik
[
3
];
rik
[
0
]
=
x
[
atomi
][
0
]
-
x
[
atomk
][
0
];
rik
[
1
]
=
x
[
atomi
][
1
]
-
x
[
atomk
][
1
];
rik
[
2
]
=
x
[
atomi
][
2
]
-
x
[
atomk
][
2
];
double
riksq
=
(
rik
[
0
]
*
rik
[
0
])
+
(
rik
[
1
]
*
rik
[
1
])
+
(
rik
[
2
]
*
rik
[
2
]);
if
(
riksq
>
r_1
*
r_1
)
{
// && riksq < r_2*r_2, if second condition not fulfilled neighbor would not be in the list
double
rikmag
=
sqrt
(
riksq
);
double
df_c_ik
;
double
f_c_ik
=
f_c
(
rikmag
,
r_1
,
r_2
,
&
df_c_ik
);
// F = factor*df_c_ik*(-grad rikmag)
// grad_i rikmag = \vec{rik} /rikmag
// grad_k rikmag = -\vec{rik} /rikmag
double
fpair
=
-
factor
*
df_c_ik
/
rikmag
;
f
[
atomi
][
0
]
+=
rik
[
0
]
*
fpair
;
f
[
atomi
][
1
]
+=
rik
[
1
]
*
fpair
;
f
[
atomi
][
2
]
+=
rik
[
2
]
*
fpair
;
f
[
atomk
][
0
]
-=
rik
[
0
]
*
fpair
;
f
[
atomk
][
1
]
-=
rik
[
1
]
*
fpair
;
f
[
atomk
][
2
]
-=
rik
[
2
]
*
fpair
;
if
(
vflag_atom
)
v_tally2
(
atomi
,
atomk
,
fpair
,
rik
);
}
}
}
}
/* ---------------------------------------------------------------------- */
void
PairLCBOP
::
FMij
(
int
i
,
int
j
,
double
factor
,
double
**
f
,
int
vflag_atom
)
{
int
atomi
=
i
;
int
atomj
=
j
;
int
*
SR_neighs
=
SR_firstneigh
[
i
];
double
**
x
=
atom
->
x
;
for
(
int
k
=
0
;
k
<
SR_numneigh
[
i
];
k
++
)
{
int
atomk
=
SR_neighs
[
k
];
if
(
atomk
!=
atomj
)
{
double
rik
[
3
];
rik
[
0
]
=
x
[
atomi
][
0
]
-
x
[
atomk
][
0
];
rik
[
1
]
=
x
[
atomi
][
1
]
-
x
[
atomk
][
1
];
rik
[
2
]
=
x
[
atomi
][
2
]
-
x
[
atomk
][
2
];
double
rikmag
=
sqrt
((
rik
[
0
]
*
rik
[
0
])
+
(
rik
[
1
]
*
rik
[
1
])
+
(
rik
[
2
]
*
rik
[
2
]));
double
df_c_ik
;
double
f_c_ik
=
f_c
(
rikmag
,
r_1
,
r_2
,
&
df_c_ik
);
double
Nki
=
N
[
k
]
-
(
f_c_ik
);
// double Mij = M[i] - f_c_ij*( 1-f_c(Nji, 2,3,&dummy) );
double
dF
=
0
;
double
Fx
=
1
-
f_c_LR
(
Nki
,
2
,
3
,
&
dF
);
dF
=
-
dF
;
if
(
df_c_ik
>
TOL
)
{
double
factor2
=
factor
*
df_c_ik
*
Fx
;
// F = factor2*(-grad rikmag)
// grad_i rikmag = \vec{rik} /rikmag
// grad_k rikmag = -\vec{rik} /rikmag
double
fpair
=
-
factor2
/
rikmag
;
f
[
atomi
][
0
]
+=
rik
[
0
]
*
fpair
;
f
[
atomi
][
1
]
+=
rik
[
1
]
*
fpair
;
f
[
atomi
][
2
]
+=
rik
[
2
]
*
fpair
;
f
[
atomk
][
0
]
-=
rik
[
0
]
*
fpair
;
f
[
atomk
][
1
]
-=
rik
[
1
]
*
fpair
;
f
[
atomk
][
2
]
-=
rik
[
2
]
*
fpair
;
if
(
vflag_atom
)
v_tally2
(
atomi
,
atomk
,
fpair
,
rik
);
}
if
(
dF
>
TOL
)
{
double
factor2
=
factor
*
f_c_ik
*
dF
;
FNij
(
atomk
,
atomi
,
factor2
,
f
,
vflag_atom
);
}
}
}
}
/* ----------------------------------------------------------------------
Bij function
------------------------------------------------------------------------- */
double
PairLCBOP
::
bondorder
(
int
i
,
int
j
,
double
rij
[
3
],
double
rijmag
,
double
VA
,
double
**
f
,
int
vflag_atom
)
{
double
bij
,
bji
;
/* bij & bji */
{
double
rji
[
3
];
rji
[
0
]
=
-
rij
[
0
];
rji
[
1
]
=
-
rij
[
1
];
rji
[
2
]
=
-
rij
[
2
];
bij
=
b
(
i
,
j
,
rij
,
rijmag
,
VA
,
f
,
vflag_atom
);
bji
=
b
(
j
,
i
,
rji
,
rijmag
,
VA
,
f
,
vflag_atom
);
}
double
Fij_conj
;
/* F_conj */
{
double
dummy
;
double
df_c_ij
;
double
f_c_ij
=
f_c
(
rijmag
,
r_1
,
r_2
,
&
df_c_ij
);
double
Nij
=
MIN
(
3
,
N
[
i
]
-
(
f_c_ij
)
);
double
Nji
=
MIN
(
3
,
N
[
j
]
-
(
f_c_ij
)
);
// F(xij) = 1-f_c(Nji, 2,3,&dummy)
double
Mij
=
M
[
i
]
-
f_c_ij
*
(
1
-
f_c
(
Nji
,
2
,
3
,
&
dummy
)
);
double
Mji
=
M
[
j
]
-
f_c_ij
*
(
1
-
f_c
(
Nij
,
2
,
3
,
&
dummy
)
);
Mij
=
MIN
(
Mij
,
3
);
Mji
=
MIN
(
Mji
,
3
);
double
Nij_el
,
dNij_el_dNij
,
dNij_el_dMij
;
double
Nji_el
,
dNji_el_dNji
,
dNji_el_dMji
;
{
double
num_Nij_el
=
4
-
Mij
;
double
num_Nji_el
=
4
-
Mji
;
double
den_Nij_el
=
Nij
+
1
-
Mij
;
double
den_Nji_el
=
Nji
+
1
-
Mji
;
Nij_el
=
num_Nij_el
/
den_Nij_el
;
Nji_el
=
num_Nji_el
/
den_Nji_el
;
dNij_el_dNij
=
-
Nij_el
/
den_Nij_el
;
dNji_el_dNji
=
-
Nji_el
/
den_Nji_el
;
dNij_el_dMij
=
(
-
1
+
Nij_el
)
/
den_Nij_el
;
dNji_el_dMji
=
(
-
1
+
Nji_el
)
/
den_Nji_el
;
}
double
Nconj
;
double
dNconj_dNij
;
double
dNconj_dNji
;
double
dNconj_dNel
;
{
double
num_Nconj
=
(
Nij
+
1
)
*
(
Nji
+
1
)
*
(
Nij_el
+
Nji_el
)
-
4
*
(
Nij
+
Nji
+
2
);
double
den_Nconj
=
Nij
*
(
3
-
Nij
)
*
(
Nji
+
1
)
+
Nji
*
(
3
-
Nji
)
*
(
Nij
+
1
)
+
eps
;
Nconj
=
num_Nconj
/
den_Nconj
;
if
(
Nconj
<=
0
)
{
Nconj
=
0
;
dNconj_dNij
=
0
;
dNconj_dNji
=
0
;
dNconj_dNel
=
0
;
}
else
if
(
Nconj
>=
1
)
{
Nconj
=
1
;
dNconj_dNij
=
0
;
dNconj_dNji
=
0
;
dNconj_dNel
=
0
;
}
else
{
dNconj_dNij
=
(
(
(
Nji
+
1
)
*
(
Nij_el
+
Nji_el
)
-
4
)
-
Nconj
*
(
(
Nji
+
1
)
*
(
3
-
2
*
Nij
)
+
Nji
*
(
3
-
Nji
)
)
)
/
den_Nconj
;
dNconj_dNji
=
(
(
(
Nij
+
1
)
*
(
Nji_el
+
Nij_el
)
-
4
)
-
Nconj
*
(
(
Nij
+
1
)
*
(
3
-
2
*
Nji
)
+
Nij
*
(
3
-
Nij
)
)
)
/
den_Nconj
;
dNconj_dNel
=
(
Nij
+
1
)
*
(
Nji
+
1
)
/
den_Nconj
;
}
}
double
dF_dNij
,
dF_dNji
,
dF_dNconj
;
Fij_conj
=
F_conj
(
Nij
,
Nji
,
Nconj
,
&
dF_dNij
,
&
dF_dNji
,
&
dF_dNconj
);
/*forces for Nij*/
if
(
3
-
Nij
>
TOL
)
{
double
factor
=
-
VA
*
0.5
*
(
dF_dNij
+
dF_dNconj
*
(
dNconj_dNij
+
dNconj_dNel
*
dNij_el_dNij
)
);
FNij
(
i
,
j
,
factor
,
f
,
vflag_atom
);
}
/*forces for Nji*/
if
(
3
-
Nji
>
TOL
)
{
double
factor
=
-
VA
*
0.5
*
(
dF_dNji
+
dF_dNconj
*
(
dNconj_dNji
+
dNconj_dNel
*
dNji_el_dNji
)
);
FNij
(
j
,
i
,
factor
,
f
,
vflag_atom
);
}
/*forces for Mij*/
if
(
3
-
Mij
>
TOL
)
{
double
factor
=
-
VA
*
0.5
*
(
dF_dNconj
*
dNconj_dNel
*
dNij_el_dMij
);
FMij
(
i
,
j
,
factor
,
f
,
vflag_atom
);
}
if
(
3
-
Mji
>
TOL
)
{
double
factor
=
-
VA
*
0.5
*
(
dF_dNconj
*
dNconj_dNel
*
dNji_el_dMji
);
FMij
(
j
,
i
,
factor
,
f
,
vflag_atom
);
}
}
double
Bij
=
0.5
*
(
bij
+
bji
+
Fij_conj
);
return
Bij
;
}
/* ----------------------------------------------------------------------
bij function
------------------------------------------------------------------------- */
double
PairLCBOP
::
b
(
int
i
,
int
j
,
double
rij
[
3
],
double
rijmag
,
double
VA
,
double
**
f
,
int
vflag_atom
)
{
int
*
SR_neighs
=
SR_firstneigh
[
i
];
double
**
x
=
atom
->
x
;
int
atomi
=
i
;
int
atomj
=
j
;
//calculate bij magnitude
double
bij
=
1.0
;
for
(
int
k
=
0
;
k
<
SR_numneigh
[
i
];
k
++
)
{
int
atomk
=
SR_neighs
[
k
];
if
(
atomk
!=
atomj
)
{
double
rik
[
3
];
rik
[
0
]
=
x
[
atomi
][
0
]
-
x
[
atomk
][
0
];
rik
[
1
]
=
x
[
atomi
][
1
]
-
x
[
atomk
][
1
];
rik
[
2
]
=
x
[
atomi
][
2
]
-
x
[
atomk
][
2
];
double
rikmag
=
sqrt
((
rik
[
0
]
*
rik
[
0
])
+
(
rik
[
1
]
*
rik
[
1
])
+
(
rik
[
2
]
*
rik
[
2
]));
double
delta_ijk
=
rijmag
-
rikmag
;
double
dummy
;
double
f_c_ik
=
f_c
(
rikmag
,
r_1
,
r_2
,
&
dummy
);
double
cos_ijk
=
((
rij
[
0
]
*
rik
[
0
])
+
(
rij
[
1
]
*
rik
[
1
])
+
(
rij
[
2
]
*
rik
[
2
]))
/
(
rijmag
*
rikmag
);
cos_ijk
=
MIN
(
cos_ijk
,
1.0
);
cos_ijk
=
MAX
(
cos_ijk
,
-
1.0
);
double
G
=
gSpline
(
cos_ijk
,
&
dummy
);
double
H
=
hSpline
(
delta_ijk
,
&
dummy
);
bij
+=
(
f_c_ik
*
G
*
H
);
}
}
bij
=
pow
(
bij
,
-
delta
);
// bij forces
for
(
int
k
=
0
;
k
<
SR_numneigh
[
i
];
k
++
)
{
int
atomk
=
SR_neighs
[
k
];
if
(
atomk
!=
atomj
)
{
double
rik
[
3
];
rik
[
0
]
=
x
[
atomi
][
0
]
-
x
[
atomk
][
0
];
rik
[
1
]
=
x
[
atomi
][
1
]
-
x
[
atomk
][
1
];
rik
[
2
]
=
x
[
atomi
][
2
]
-
x
[
atomk
][
2
];
double
rikmag
=
sqrt
((
rik
[
0
]
*
rik
[
0
])
+
(
rik
[
1
]
*
rik
[
1
])
+
(
rik
[
2
]
*
rik
[
2
]));
double
delta_ijk
=
rijmag
-
rikmag
;
double
df_c_ik
;
double
f_c_ik
=
f_c
(
rikmag
,
r_1
,
r_2
,
&
df_c_ik
);
double
cos_ijk
=
((
rij
[
0
]
*
rik
[
0
])
+
(
rij
[
1
]
*
rik
[
1
])
+
(
rij
[
2
]
*
rik
[
2
]))
/
(
rijmag
*
rikmag
);
cos_ijk
=
MIN
(
cos_ijk
,
1.0
);
cos_ijk
=
MAX
(
cos_ijk
,
-
1.0
);
double
dcos_ijk_dri
[
3
],
dcos_ijk_drj
[
3
],
dcos_ijk_drk
[
3
];
dcos_ijk_drj
[
0
]
=
-
rik
[
0
]
/
(
rijmag
*
rikmag
)
+
cos_ijk
*
rij
[
0
]
/
(
rijmag
*
rijmag
);
dcos_ijk_drj
[
1
]
=
-
rik
[
1
]
/
(
rijmag
*
rikmag
)
+
cos_ijk
*
rij
[
1
]
/
(
rijmag
*
rijmag
);
dcos_ijk_drj
[
2
]
=
-
rik
[
2
]
/
(
rijmag
*
rikmag
)
+
cos_ijk
*
rij
[
2
]
/
(
rijmag
*
rijmag
);
dcos_ijk_drk
[
0
]
=
-
rij
[
0
]
/
(
rijmag
*
rikmag
)
+
cos_ijk
*
rik
[
0
]
/
(
rikmag
*
rikmag
);
dcos_ijk_drk
[
1
]
=
-
rij
[
1
]
/
(
rijmag
*
rikmag
)
+
cos_ijk
*
rik
[
1
]
/
(
rikmag
*
rikmag
);
dcos_ijk_drk
[
2
]
=
-
rij
[
2
]
/
(
rijmag
*
rikmag
)
+
cos_ijk
*
rik
[
2
]
/
(
rikmag
*
rikmag
);
dcos_ijk_dri
[
0
]
=
-
dcos_ijk_drk
[
0
]
-
dcos_ijk_drj
[
0
];
dcos_ijk_dri
[
1
]
=
-
dcos_ijk_drk
[
1
]
-
dcos_ijk_drj
[
1
];
dcos_ijk_dri
[
2
]
=
-
dcos_ijk_drk
[
2
]
-
dcos_ijk_drj
[
2
];
double
dG
,
dH
;
double
G
=
gSpline
(
cos_ijk
,
&
dG
);
double
H
=
hSpline
(
delta_ijk
,
&
dH
);
double
tmp
=
-
VA
*
0.5
*
(
-
0.5
*
bij
*
bij
*
bij
);
double
fi
[
3
],
fj
[
3
],
fk
[
3
];
double
tmp2
=
-
tmp
*
df_c_ik
*
G
*
H
/
rikmag
;
// F = tmp*df_c_ik*G*H*(-grad rikmag)
// grad_i rikmag = \vec{rik} /rikmag
// grad_k rikmag = -\vec{rik} /rikmag
fi
[
0
]
=
tmp2
*
rik
[
0
];
fi
[
1
]
=
tmp2
*
rik
[
1
];
fi
[
2
]
=
tmp2
*
rik
[
2
];
fk
[
0
]
=
-
tmp2
*
rik
[
0
];
fk
[
1
]
=
-
tmp2
*
rik
[
1
];
fk
[
2
]
=
-
tmp2
*
rik
[
2
];
tmp2
=
-
tmp
*
f_c_ik
*
dG
*
H
;
// F = tmp*f_c_ik*dG*H*(-grad cos_ijk)
// grad_i cos_ijk = dcos_ijk_dri
// grad_j cos_ijk = dcos_ijk_drj
// grad_k cos_ijk = dcos_ijk_drk
fi
[
0
]
+=
tmp2
*
dcos_ijk_dri
[
0
];
fi
[
1
]
+=
tmp2
*
dcos_ijk_dri
[
1
];
fi
[
2
]
+=
tmp2
*
dcos_ijk_dri
[
2
];
fj
[
0
]
=
tmp2
*
dcos_ijk_drj
[
0
];
fj
[
1
]
=
tmp2
*
dcos_ijk_drj
[
1
];
fj
[
2
]
=
tmp2
*
dcos_ijk_drj
[
2
];
fk
[
0
]
+=
tmp2
*
dcos_ijk_drk
[
0
];
fk
[
1
]
+=
tmp2
*
dcos_ijk_drk
[
1
];
fk
[
2
]
+=
tmp2
*
dcos_ijk_drk
[
2
];
tmp2
=
-
tmp
*
f_c_ik
*
G
*
dH
;
// F = tmp*f_c_ik*G*dH*(-grad delta_ijk)
// grad_i delta_ijk = \vec{rij} /rijmag - \vec{rik} /rijmag
// grad_j delta_ijk = -\vec{rij} /rijmag
// grad_k delta_ijk = \vec{rik} /rikmag
fi
[
0
]
+=
tmp2
*
(
rij
[
0
]
/
rijmag
-
rik
[
0
]
/
rikmag
);
fi
[
1
]
+=
tmp2
*
(
rij
[
1
]
/
rijmag
-
rik
[
1
]
/
rikmag
);
fi
[
2
]
+=
tmp2
*
(
rij
[
2
]
/
rijmag
-
rik
[
2
]
/
rikmag
);
fj
[
0
]
+=
tmp2
*
(
-
rij
[
0
]
/
rijmag
);
fj
[
1
]
+=
tmp2
*
(
-
rij
[
1
]
/
rijmag
);
fj
[
2
]
+=
tmp2
*
(
-
rij
[
2
]
/
rijmag
);
fk
[
0
]
+=
tmp2
*
(
rik
[
0
]
/
rikmag
);
fk
[
1
]
+=
tmp2
*
(
rik
[
1
]
/
rikmag
);
fk
[
2
]
+=
tmp2
*
(
rik
[
2
]
/
rikmag
);
f
[
atomi
][
0
]
+=
fi
[
0
];
f
[
atomi
][
1
]
+=
fi
[
1
];
f
[
atomi
][
2
]
+=
fi
[
2
];
f
[
atomj
][
0
]
+=
fj
[
0
];
f
[
atomj
][
1
]
+=
fj
[
1
];
f
[
atomj
][
2
]
+=
fj
[
2
];
f
[
atomk
][
0
]
+=
fk
[
0
];
f
[
atomk
][
1
]
+=
fk
[
1
];
f
[
atomk
][
2
]
+=
fk
[
2
];
if
(
vflag_atom
)
{
double
rji
[
3
],
rki
[
3
];
rji
[
0
]
=
-
rij
[
0
];
rji
[
1
]
=
-
rij
[
1
];
rji
[
2
]
=
-
rij
[
2
];
rki
[
0
]
=
-
rik
[
0
];
rki
[
1
]
=
-
rik
[
1
];
rki
[
2
]
=
-
rik
[
2
];
v_tally3
(
atomi
,
atomj
,
atomk
,
fj
,
fk
,
rji
,
rki
);
}
}
}
return
bij
;
}
/* ----------------------------------------------------------------------
spline interpolation for G
------------------------------------------------------------------------- */
void
PairLCBOP
::
g_decompose_x
(
double
x
,
size_t
*
field_idx
,
double
*
offset
)
{
size_t
i
=
0
;
while
(
i
<
(
6
-
1
)
&&
!
(
x
<
gX
[
i
+
1
]
)
)
i
++
;
*
field_idx
=
i
;
*
offset
=
(
x
-
gX
[
i
]
);
}
/* ---------------------------------------------------------------------- */
double
PairLCBOP
::
gSpline
(
double
x
,
double
*
dgdc
)
{
size_t
i
;
double
x_n
;
g_decompose_x
(
x
,
&
i
,
&
x_n
);
double
sum
=
0
;
*
dgdc
=
0
;
double
pow_x_n
=
1.0
;
for
(
size_t
j
=
0
;
j
<
5
;
j
++
)
{
sum
+=
gC
[
j
][
i
]
*
pow_x_n
;
*
dgdc
+=
gC
[
j
+
1
][
i
]
*
(
j
+
1
)
*
pow_x_n
;
pow_x_n
*=
x_n
;
}
sum
+=
gC
[
5
][
i
]
*
pow_x_n
;
return
sum
;
}
/* ---------------------------------------------------------------------- */
double
PairLCBOP
::
hSpline
(
double
x
,
double
*
dhdx
)
{
if
(
x
<
-
d
)
{
double
z
=
kappa
*
(
x
+
d
);
double
y
=
pow
(
z
,
10.0
);
double
w
=
pow
(
1
+
y
,
-
0.1
);
*
dhdx
=
kappa
*
L
*
w
/
(
1
+
y
);
return
L
*
(
1
+
z
*
w
);
}
if
(
x
>
d
)
{
*
dhdx
=
R_1
;
return
R_0
+
R_1
*
(
x
-
d
);
}
double
result
=
1
+
C_1
*
x
;
*
dhdx
=
C_1
*
result
;
double
pow_x
=
x
*
x
;
result
+=
0.5
*
C_1
*
C_1
*
pow_x
;
pow_x
*=
x
;
// == x^3
*
dhdx
+=
4
*
C_4
*
pow_x
;
pow_x
*=
x
;
// == x^4
result
+=
C_4
*
pow_x
;
pow_x
*=
x
;
// == x^5
*
dhdx
+=
6
*
C_6
*
pow_x
;
pow_x
*=
x
;
// == x^5
result
+=
C_6
*
pow_x
;
return
result
;
}
/* ---------------------------------------------------------------------- */
double
PairLCBOP
::
F_conj
(
double
N_ij
,
double
N_ji
,
double
N_conj_ij
,
double
*
dFN_ij
,
double
*
dFN_ji
,
double
*
dFN_ij_conj
)
{
size_t
N_ij_int
=
MIN
(
static_cast
<
size_t
>
(
floor
(
N_ij
)
),
2
);
// 2 is the highest number of field
size_t
N_ji_int
=
MIN
(
static_cast
<
size_t
>
(
floor
(
N_ji
)
),
2
);
// cast to suppress warning
double
x
=
N_ij
-
N_ij_int
;
double
y
=
N_ji
-
N_ji_int
;
const
TF_conj_field
&
f0
=
F_conj_field
[
N_ij_int
][
N_ji_int
][
0
];
const
TF_conj_field
&
f1
=
F_conj_field
[
N_ij_int
][
N_ji_int
][
1
];
double
F_0
=
0
;
double
F_1
=
0
;
double
dF_0_dx
=
0
,
dF_0_dy
=
0
;
double
dF_1_dx
=
0
,
dF_1_dy
=
0
;
double
l
,
r
;
if
(
N_conj_ij
<
1
)
{
l
=
(
1
-
y
)
*
(
1
-
x
);
r
=
(
f0
.
f_00
+
x
*
x
*
f0
.
f_x_10
+
y
*
y
*
f0
.
f_y_01
);
F_0
+=
l
*
r
;
dF_0_dx
+=
-
(
1
-
y
)
*
r
+
l
*
2
*
x
*
f0
.
f_x_10
;
dF_0_dy
+=
-
(
1
-
x
)
*
r
+
l
*
2
*
y
*
f0
.
f_y_01
;
l
=
(
1
-
y
)
*
x
;
r
=
(
f0
.
f_10
+
(
1
-
x
)
*
(
1
-
x
)
*
f0
.
f_x_00
+
y
*
y
*
f0
.
f_y_11
);
F_0
+=
l
*
r
;
dF_0_dx
+=
(
1
-
y
)
*
r
-
l
*
2
*
(
1
-
x
)
*
f0
.
f_x_00
;
dF_0_dy
+=
-
x
*
r
+
l
*
2
*
y
*
f0
.
f_y_11
;
l
=
y
*
(
1
-
x
);
r
=
(
f0
.
f_01
+
x
*
x
*
f0
.
f_x_11
+
(
1
-
y
)
*
(
1
-
y
)
*
f0
.
f_y_00
);
F_0
+=
l
*
r
;
dF_0_dx
+=
-
y
*
r
+
l
*
2
*
x
*
f0
.
f_x_11
;
dF_0_dy
+=
(
1
-
x
)
*
r
-
l
*
2
*
(
1
-
y
)
*
f0
.
f_y_00
;
l
=
y
*
x
;
r
=
(
f0
.
f_11
+
(
1
-
x
)
*
(
1
-
x
)
*
f0
.
f_x_01
+
(
1
-
y
)
*
(
1
-
y
)
*
f0
.
f_y_10
);
F_0
+=
l
*
r
;
dF_0_dx
+=
y
*
r
-
l
*
2
*
(
1
-
x
)
*
f0
.
f_x_01
;
dF_0_dy
+=
x
*
r
-
l
*
2
*
(
1
-
y
)
*
f0
.
f_y_10
;
}
if
(
N_conj_ij
>
0
)
{
l
=
(
1
-
y
)
*
(
1
-
x
);
r
=
(
f0
.
f_00
+
x
*
x
*
f1
.
f_x_10
+
y
*
y
*
f1
.
f_y_01
);
F_1
+=
l
*
r
;
dF_1_dx
+=
-
(
1
-
y
)
*
r
+
l
*
2
*
x
*
f1
.
f_x_10
;
dF_1_dy
+=
-
(
1
-
x
)
*
r
+
l
*
2
*
y
*
f1
.
f_y_01
;
l
=
(
1
-
y
)
*
x
;
r
=
(
f1
.
f_10
+
(
1
-
x
)
*
(
1
-
x
)
*
f1
.
f_x_00
+
y
*
y
*
f1
.
f_y_11
);
F_1
+=
l
*
r
;
dF_1_dx
+=
(
1
-
y
)
*
r
-
l
*
2
*
(
1
-
x
)
*
f1
.
f_x_00
;
dF_1_dy
+=
-
x
*
r
+
l
*
2
*
y
*
f1
.
f_y_11
;
l
=
y
*
(
1
-
x
);
r
=
(
f1
.
f_01
+
x
*
x
*
f1
.
f_x_11
+
(
1
-
y
)
*
(
1
-
y
)
*
f1
.
f_y_00
);
F_1
+=
l
*
r
;
dF_1_dx
+=
-
y
*
r
+
l
*
2
*
x
*
f1
.
f_x_11
;
dF_1_dy
+=
(
1
-
x
)
*
r
-
l
*
2
*
(
1
-
y
)
*
f1
.
f_y_00
;
l
=
y
*
x
;
r
=
(
f1
.
f_11
+
(
1
-
x
)
*
(
1
-
x
)
*
f1
.
f_x_01
+
(
1
-
y
)
*
(
1
-
y
)
*
f1
.
f_y_10
);
F_1
+=
l
*
r
;
dF_1_dx
+=
y
*
r
-
l
*
2
*
(
1
-
x
)
*
f1
.
f_x_01
;
dF_1_dy
+=
x
*
r
-
l
*
2
*
(
1
-
y
)
*
f1
.
f_y_10
;
}
double
result
=
(
1
-
N_conj_ij
)
*
F_0
+
N_conj_ij
*
F_1
;
*
dFN_ij
=
(
1
-
N_conj_ij
)
*
dF_0_dx
+
N_conj_ij
*
dF_1_dx
;
*
dFN_ji
=
(
1
-
N_conj_ij
)
*
dF_0_dy
+
N_conj_ij
*
dF_1_dy
;
*
dFN_ij_conj
=
-
F_0
+
F_1
;
return
result
;
}
/* ----------------------------------------------------------------------
read LCBOP potential file
------------------------------------------------------------------------- */
void
PairLCBOP
::
read_file
(
char
*
filename
)
{
int
i
,
j
,
k
,
l
,
limit
;
char
s
[
MAXLINE
];
MPI_Comm_rank
(
world
,
&
me
);
// read file on proc 0
if
(
me
==
0
)
{
FILE
*
fp
=
open_potential
(
filename
);
if
(
fp
==
NULL
)
{
char
str
[
128
];
sprintf
(
str
,
"Cannot open LCBOP potential file %s"
,
filename
);
error
->
one
(
FLERR
,
str
);
}
// skip initial comment lines
while
(
1
)
{
fgets
(
s
,
MAXLINE
,
fp
);
if
(
s
[
0
]
!=
'#'
)
break
;
}
// read parameters
fgets
(
s
,
MAXLINE
,
fp
);
sscanf
(
s
,
"%lg"
,
&
r_1
);
fgets
(
s
,
MAXLINE
,
fp
);
sscanf
(
s
,
"%lg"
,
&
r_2
);
fgets
(
s
,
MAXLINE
,
fp
);
sscanf
(
s
,
"%lg"
,
&
gamma_1
);
fgets
(
s
,
MAXLINE
,
fp
);
sscanf
(
s
,
"%lg"
,
&
A
);
fgets
(
s
,
MAXLINE
,
fp
);
sscanf
(
s
,
"%lg"
,
&
B_1
);
fgets
(
s
,
MAXLINE
,
fp
);
sscanf
(
s
,
"%lg"
,
&
B_2
);
fgets
(
s
,
MAXLINE
,
fp
);
sscanf
(
s
,
"%lg"
,
&
alpha
);
fgets
(
s
,
MAXLINE
,
fp
);
sscanf
(
s
,
"%lg"
,
&
beta_1
);
fgets
(
s
,
MAXLINE
,
fp
);
sscanf
(
s
,
"%lg"
,
&
beta_2
);
fgets
(
s
,
MAXLINE
,
fp
);
sscanf
(
s
,
"%lg"
,
&
d
);
fgets
(
s
,
MAXLINE
,
fp
);
sscanf
(
s
,
"%lg"
,
&
C_1
);
fgets
(
s
,
MAXLINE
,
fp
);
sscanf
(
s
,
"%lg"
,
&
C_4
);
fgets
(
s
,
MAXLINE
,
fp
);
sscanf
(
s
,
"%lg"
,
&
C_6
);
fgets
(
s
,
MAXLINE
,
fp
);
sscanf
(
s
,
"%lg"
,
&
L
);
fgets
(
s
,
MAXLINE
,
fp
);
sscanf
(
s
,
"%lg"
,
&
kappa
);
fgets
(
s
,
MAXLINE
,
fp
);
sscanf
(
s
,
"%lg"
,
&
R_0
);
fgets
(
s
,
MAXLINE
,
fp
);
sscanf
(
s
,
"%lg"
,
&
R_1
);
fgets
(
s
,
MAXLINE
,
fp
);
sscanf
(
s
,
"%lg"
,
&
r_0
);
fgets
(
s
,
MAXLINE
,
fp
);
sscanf
(
s
,
"%lg"
,
&
r_1_LR
);
fgets
(
s
,
MAXLINE
,
fp
);
sscanf
(
s
,
"%lg"
,
&
r_2_LR
);
fgets
(
s
,
MAXLINE
,
fp
);
sscanf
(
s
,
"%lg"
,
&
v_1
);
fgets
(
s
,
MAXLINE
,
fp
);
sscanf
(
s
,
"%lg"
,
&
v_2
);
fgets
(
s
,
MAXLINE
,
fp
);
sscanf
(
s
,
"%lg"
,
&
eps_1
);
fgets
(
s
,
MAXLINE
,
fp
);
sscanf
(
s
,
"%lg"
,
&
eps_2
);
fgets
(
s
,
MAXLINE
,
fp
);
sscanf
(
s
,
"%lg"
,
&
lambda_1
);
fgets
(
s
,
MAXLINE
,
fp
);
sscanf
(
s
,
"%lg"
,
&
lambda_2
);
fgets
(
s
,
MAXLINE
,
fp
);
sscanf
(
s
,
"%lg"
,
&
eps
);
fgets
(
s
,
MAXLINE
,
fp
);
sscanf
(
s
,
"%lg"
,
&
delta
);
while
(
1
)
{
fgets
(
s
,
MAXLINE
,
fp
);
if
(
s
[
0
]
!=
'#'
)
break
;
}
// F_conj spline
for
(
k
=
0
;
k
<
2
;
k
++
)
{
// 2 values of N_ij_conj
for
(
l
=
0
;
l
<
3
;
l
++
)
{
// 3 types of data: f, dfdx, dfdy
for
(
i
=
0
;
i
<
4
;
i
++
)
{
// 4x4 matrix
fgets
(
s
,
MAXLINE
,
fp
);
sscanf
(
s
,
"%lg %lg %lg %lg"
,
&
F_conj_data
[
i
][
0
][
k
][
l
],
&
F_conj_data
[
i
][
1
][
k
][
l
],
&
F_conj_data
[
i
][
2
][
k
][
l
],
&
F_conj_data
[
i
][
3
][
k
][
l
]);
}
while
(
1
)
{
fgets
(
s
,
MAXLINE
,
fp
);
if
(
s
[
0
]
!=
'#'
)
break
;
}
}
}
// G spline
// x coordinates of mesh points
fgets
(
s
,
MAXLINE
,
fp
);
sscanf
(
s
,
"%lg %lg %lg %lg %lg %lg"
,
&
gX
[
0
],
&
gX
[
1
],
&
gX
[
2
],
&
gX
[
3
],
&
gX
[
4
],
&
gX
[
5
]
);
for
(
i
=
0
;
i
<
6
;
i
++
)
{
// for each power in polynomial
fgets
(
s
,
MAXLINE
,
fp
);
sscanf
(
s
,
"%lg %lg %lg %lg %lg"
,
&
gC
[
i
][
0
],
&
gC
[
i
][
1
],
&
gC
[
i
][
2
],
&
gC
[
i
][
3
],
&
gC
[
i
][
4
]
);
}
fclose
(
fp
);
}
// broadcast read-in and setup values
MPI_Bcast
(
&
r_1
,
1
,
MPI_DOUBLE
,
0
,
world
);
MPI_Bcast
(
&
r_2
,
1
,
MPI_DOUBLE
,
0
,
world
);
MPI_Bcast
(
&
gamma_1
,
1
,
MPI_DOUBLE
,
0
,
world
);
MPI_Bcast
(
&
A
,
1
,
MPI_DOUBLE
,
0
,
world
);
MPI_Bcast
(
&
B_1
,
1
,
MPI_DOUBLE
,
0
,
world
);
MPI_Bcast
(
&
B_2
,
1
,
MPI_DOUBLE
,
0
,
world
);
MPI_Bcast
(
&
alpha
,
1
,
MPI_DOUBLE
,
0
,
world
);
MPI_Bcast
(
&
beta_1
,
1
,
MPI_DOUBLE
,
0
,
world
);
MPI_Bcast
(
&
beta_2
,
1
,
MPI_DOUBLE
,
0
,
world
);
MPI_Bcast
(
&
d
,
1
,
MPI_DOUBLE
,
0
,
world
);
MPI_Bcast
(
&
C_1
,
1
,
MPI_DOUBLE
,
0
,
world
);
MPI_Bcast
(
&
C_4
,
1
,
MPI_DOUBLE
,
0
,
world
);
MPI_Bcast
(
&
C_6
,
1
,
MPI_DOUBLE
,
0
,
world
);
MPI_Bcast
(
&
L
,
1
,
MPI_DOUBLE
,
0
,
world
);
MPI_Bcast
(
&
kappa
,
1
,
MPI_DOUBLE
,
0
,
world
);
MPI_Bcast
(
&
R_0
,
1
,
MPI_DOUBLE
,
0
,
world
);
MPI_Bcast
(
&
R_1
,
1
,
MPI_DOUBLE
,
0
,
world
);
MPI_Bcast
(
&
r_0
,
1
,
MPI_DOUBLE
,
0
,
world
);
MPI_Bcast
(
&
r_1_LR
,
1
,
MPI_DOUBLE
,
0
,
world
);
MPI_Bcast
(
&
r_2_LR
,
1
,
MPI_DOUBLE
,
0
,
world
);
MPI_Bcast
(
&
v_1
,
1
,
MPI_DOUBLE
,
0
,
world
);
MPI_Bcast
(
&
v_2
,
1
,
MPI_DOUBLE
,
0
,
world
);
MPI_Bcast
(
&
eps_1
,
1
,
MPI_DOUBLE
,
0
,
world
);
MPI_Bcast
(
&
eps_2
,
1
,
MPI_DOUBLE
,
0
,
world
);
MPI_Bcast
(
&
lambda_1
,
1
,
MPI_DOUBLE
,
0
,
world
);
MPI_Bcast
(
&
lambda_2
,
1
,
MPI_DOUBLE
,
0
,
world
);
MPI_Bcast
(
&
eps
,
1
,
MPI_DOUBLE
,
0
,
world
);
MPI_Bcast
(
&
delta
,
1
,
MPI_DOUBLE
,
0
,
world
);
MPI_Bcast
(
&
gX
[
0
]
,
6
,
MPI_DOUBLE
,
0
,
world
);
MPI_Bcast
(
&
gC
[
0
][
0
]
,(
6
-
1
)
*
(
5
+
1
),
MPI_DOUBLE
,
0
,
world
);
MPI_Bcast
(
&
F_conj_data
[
0
],
6
*
4
*
4
,
MPI_DOUBLE
,
0
,
world
);
}
/* ----------------------------------------------------------------------
init coefficients for TF_conj
------------------------------------------------------------------------- */
#include <iostream>
#include <fstream>
#include <functional>
template
<
class
function
>
void
print_function
(
double
x_0
,
double
x_1
,
size_t
n
,
function
f
,
std
::
ostream
&
stream
)
{
double
dx
=
(
x_1
-
x_0
)
/
n
;
for
(
double
x
=
x_0
;
x
<=
x_1
+
0.0001
;
x
+=
dx
)
{
double
f_val
,
df
;
f_val
=
f
(
x
,
&
df
);
stream
<<
x
<<
" "
<<
f_val
<<
" "
<<
df
<<
std
::
endl
;
}
stream
<<
std
::
endl
;
}
void
PairLCBOP
::
spline_init
()
{
for
(
size_t
N_conj_ij
=
0
;
N_conj_ij
<
2
;
N_conj_ij
++
)
// N_conj_ij
for
(
size_t
N_ij
=
0
;
N_ij
<
4
-
1
;
N_ij
++
)
for
(
size_t
N_ji
=
0
;
N_ji
<
4
-
1
;
N_ji
++
)
{
TF_conj_field
&
field
=
F_conj_field
[
N_ij
][
N_ji
][
N_conj_ij
];
field
.
f_00
=
F_conj_data
[
N_ij
][
N_ji
][
N_conj_ij
][
0
];
field
.
f_01
=
F_conj_data
[
N_ij
][
N_ji
+
1
][
N_conj_ij
][
0
];
field
.
f_10
=
F_conj_data
[
N_ij
+
1
][
N_ji
][
N_conj_ij
][
0
];
field
.
f_11
=
F_conj_data
[
N_ij
+
1
][
N_ji
+
1
][
N_conj_ij
][
0
];
field
.
f_x_00
=
F_conj_data
[
N_ij
][
N_ji
][
N_conj_ij
][
1
]
-
field
.
f_10
+
field
.
f_00
;
field
.
f_x_01
=
F_conj_data
[
N_ij
][
N_ji
+
1
][
N_conj_ij
][
1
]
-
field
.
f_11
+
field
.
f_01
;
field
.
f_x_10
=
-
(
F_conj_data
[
N_ij
+
1
][
N_ji
][
N_conj_ij
][
1
]
-
field
.
f_10
+
field
.
f_00
);
field
.
f_x_11
=
-
(
F_conj_data
[
N_ij
+
1
][
N_ji
+
1
][
N_conj_ij
][
1
]
-
field
.
f_11
+
field
.
f_01
);
field
.
f_y_00
=
F_conj_data
[
N_ij
][
N_ji
][
N_conj_ij
][
2
]
-
field
.
f_01
+
field
.
f_00
;
field
.
f_y_01
=
-
(
F_conj_data
[
N_ij
][
N_ji
+
1
][
N_conj_ij
][
2
]
-
field
.
f_01
+
field
.
f_00
);
field
.
f_y_10
=
F_conj_data
[
N_ij
+
1
][
N_ji
][
N_conj_ij
][
2
]
-
field
.
f_11
+
field
.
f_10
;
field
.
f_y_11
=
-
(
F_conj_data
[
N_ij
+
1
][
N_ji
+
1
][
N_conj_ij
][
2
]
-
field
.
f_11
+
field
.
f_10
);
}
//some testing:
// std::ofstream file( "test.txt" );
// file << "gX:\n";
// file << gX[0] << " "
// << gX[1] << " "
// << gX[2] << " "
// << gX[3] << " "
// << gX[4] << " "
// << gX[5] << std::endl;
// file << "gC:\n";
// for( int i=0; i<6; i++ )
// file << gC[i][0] << " "
// << gC[i][1] << " "
// << gC[i][2] << " "
// << gC[i][3] << " "
// << gC[i][4] << std::endl;
// file << std::endl;
//
// file << "gamma_1 = " << gamma_1 << std::endl;
// file << "r_1 = " << r_1 << std::endl;
// file << "r_2 = " << r_2 << std::endl;
// file << "A = " << A << std::endl;
// file << "B_1 = " << B_1 << std::endl;
// file << "B_2 = " << B_2 << std::endl;
// file << "alpha = " << alpha << std::endl;
// file << "beta_1 = " << beta_1 << std::endl;
// file << "beta_2 = " << beta_2 << std::endl;
// file << "d = " << d << std::endl;
// file << "C_1 = " << C_1 << std::endl;
// file << "C_4 = " << C_4 << std::endl;
// file << "C_6 = " << C_6 << std::endl;
// file << "L = " << L << std::endl;
// file << "kappa = " << kappa << std::endl;
// file << "R_0 = " << R_0 << std::endl;
// file << "R_1 = " << R_1 << std::endl;
// file << "r_0 = " << r_0 << std::endl;
// file << "r_1_LR = " << r_1_LR << std::endl;
// file << "r_2_LR = " << r_2_LR << std::endl;
// file << "v_1 = " << v_1 << std::endl;
// file << "v_2 = " << v_2 << std::endl;
// file << "eps_1 = " << eps_1 << std::endl;
// file << "eps_2 = " << eps_2 << std::endl;
// file << "lambda_1 = " << lambda_1 << std::endl;
// file << "lambda_2 = " << lambda_2 << std::endl;
// file << "eps = " << eps << std::endl;
// file << "delta = " << delta << std::endl;
// file << "r_2_sq = " << r_2_sq << std::endl;
// file << std::endl;
//
//
// file << "gSpline:" << std::endl;
// double x_1 = 1, x_0 = -1;
// int n=1000;
// double dx = (x_1-x_0)/n;
// for( double x=x_0; x<=x_1+0.0001; x+=dx ) {
// double g, dg;
// g = gSpline(x, &dg);
// file << x << " " << g << " " << dg << std::endl;
// }
// file << std::endl;
//
// file << "hSpline:" << std::endl;
// double x_1 = 1, x_0 = -1;
// int n=1000;
// double dx = (x_1-x_0)/n;
// for( double x=x_0; x<=x_1+0.0001; x+=dx ) {
// double h, dh;
// h = hSpline(x, &dh);
// file << x << " " << h << " " << dh << std::endl;
// }
// file << std::endl;
//
//
// file << "f_c:" << std::endl;
// double x_1 = 4, x_0 = 0;
// int n=1000;
// double dx = (x_1-x_0)/n;
// for( double x=x_0; x<=x_1+0.0001; x+=dx ) {
// double f, df;
// f = f_c(x, r_1, r_2, &df);
// file << x << " " << f << " " << df << std::endl;
// }
// file << std::endl;
// file << "F_conj_data\n";
// for (int k = 0; k < 2; k++) { // 2 values of N_ij_conj
// for (int l = 0; l < 3; l++) { // 3 types of data: f, dfdx, dfdy
// for (int i = 0; i < 4; i++) { // 4x4 matrix
// file
// << F_conj_data[i][0][k][l] << " "
// << F_conj_data[i][1][k][l] << " "
// << F_conj_data[i][2][k][l] << " "
// << F_conj_data[i][3][k][l] << std::endl;
// }
// file << std::endl;
// }
// }
//
//
// file << "F_conj_0 ";
// double dummy;
// for( double y=0; y<=3.0+0.0001; y+=0.1 )
// file << y << " ";
// file << std::endl;
// for( double x=0; x<=3.0+0.0001; x+=0.1 ){
// file << x << " ";
// for( double y=0; y<=3.0+0.0001; y+=0.1 )
// file << F_conj( x, y, 0, &dummy, &dummy, &dummy ) << " ";
// file << std::endl;
// }
//
// file << "dF0_dx ";
// for( double y=0; y<=3.0+0.0001; y+=0.1 )
// file << y << " ";
// file << std::endl;
// for( double x=0; x<=3.0+0.0001; x+=0.1 ){
// file << x << " ";
// for( double y=0; y<=3.0+0.0001; y+=0.1 ) {
// double dF_dx;
// F_conj( x, y, 0, &dF_dx, &dummy, &dummy );
// file << dF_dx << " ";
// }
// file << std::endl;
// }
//
//
//
// file << "F_conj_1 ";
// for( double y=0; y<=3.0+0.0001; y+=0.1 )
// file << y << " ";
// file << std::endl;
// for( double x=0; x<=3.0+0.0001; x+=0.1 ){
// file << x << " ";
// for( double y=0; y<=3.0+0.0001; y+=0.1 )
// file << F_conj( x, y, 0, &dummy, &dummy, &dummy ) << " ";
// file << std::endl;
// }
}
/* ----------------------------------------------------------------------
memory usage of local atom-based arrays
------------------------------------------------------------------------- */
double
PairLCBOP
::
memory_usage
()
{
double
bytes
=
0.0
;
bytes
+=
maxlocal
*
sizeof
(
int
);
bytes
+=
maxlocal
*
sizeof
(
int
*
);
for
(
int
i
=
0
;
i
<
comm
->
nthreads
;
i
++
)
bytes
+=
ipage
[
i
].
size
();
bytes
+=
3
*
maxlocal
*
sizeof
(
double
);
return
bytes
;
}
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