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rLAMMPS lammps
angle_table.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: Chuanfu Luo (luochuanfu@gmail.com)
------------------------------------------------------------------------- */
#include "math.h"
#include "stdlib.h"
#include "string.h"
#include "angle_table.h"
#include "atom.h"
#include "neighbor.h"
#include "domain.h"
#include "comm.h"
#include "force.h"
#include "math_const.h"
#include "memory.h"
#include "error.h"
using
namespace
LAMMPS_NS
;
using
namespace
MathConst
;
enum
{
LINEAR
,
SPLINE
};
#define MAXLINE 1024
#define SMALL 0.001
#define TINY 1.E-10
/* ---------------------------------------------------------------------- */
AngleTable
::
AngleTable
(
LAMMPS
*
lmp
)
:
Angle
(
lmp
)
{
writedata
=
0
;
ntables
=
0
;
tables
=
NULL
;
}
/* ---------------------------------------------------------------------- */
AngleTable
::~
AngleTable
()
{
for
(
int
m
=
0
;
m
<
ntables
;
m
++
)
free_table
(
&
tables
[
m
]);
memory
->
sfree
(
tables
);
if
(
allocated
)
{
memory
->
destroy
(
setflag
);
memory
->
destroy
(
theta0
);
memory
->
destroy
(
tabindex
);
}
}
/* ---------------------------------------------------------------------- */
void
AngleTable
::
compute
(
int
eflag
,
int
vflag
)
{
int
i1
,
i2
,
i3
,
n
,
type
;
double
eangle
,
f1
[
3
],
f3
[
3
];
double
delx1
,
dely1
,
delz1
,
delx2
,
dely2
,
delz2
;
double
rsq1
,
rsq2
,
r1
,
r2
,
c
,
s
,
a
,
a11
,
a12
,
a22
;
double
theta
,
u
,
mdu
;
//mdu: minus du, -du/dx=f
eangle
=
0.0
;
if
(
eflag
||
vflag
)
ev_setup
(
eflag
,
vflag
);
else
evflag
=
0
;
double
**
x
=
atom
->
x
;
double
**
f
=
atom
->
f
;
int
**
anglelist
=
neighbor
->
anglelist
;
int
nanglelist
=
neighbor
->
nanglelist
;
int
nlocal
=
atom
->
nlocal
;
int
newton_bond
=
force
->
newton_bond
;
for
(
n
=
0
;
n
<
nanglelist
;
n
++
)
{
i1
=
anglelist
[
n
][
0
];
i2
=
anglelist
[
n
][
1
];
i3
=
anglelist
[
n
][
2
];
type
=
anglelist
[
n
][
3
];
// 1st bond
delx1
=
x
[
i1
][
0
]
-
x
[
i2
][
0
];
dely1
=
x
[
i1
][
1
]
-
x
[
i2
][
1
];
delz1
=
x
[
i1
][
2
]
-
x
[
i2
][
2
];
rsq1
=
delx1
*
delx1
+
dely1
*
dely1
+
delz1
*
delz1
;
r1
=
sqrt
(
rsq1
);
// 2nd bond
delx2
=
x
[
i3
][
0
]
-
x
[
i2
][
0
];
dely2
=
x
[
i3
][
1
]
-
x
[
i2
][
1
];
delz2
=
x
[
i3
][
2
]
-
x
[
i2
][
2
];
rsq2
=
delx2
*
delx2
+
dely2
*
dely2
+
delz2
*
delz2
;
r2
=
sqrt
(
rsq2
);
// angle (cos and sin)
c
=
delx1
*
delx2
+
dely1
*
dely2
+
delz1
*
delz2
;
c
/=
r1
*
r2
;
if
(
c
>
1.0
)
c
=
1.0
;
if
(
c
<
-
1.0
)
c
=
-
1.0
;
s
=
sqrt
(
1.0
-
c
*
c
);
if
(
s
<
SMALL
)
s
=
SMALL
;
s
=
1.0
/
s
;
// tabulated force & energy
theta
=
acos
(
c
);
uf_lookup
(
type
,
theta
,
u
,
mdu
);
if
(
eflag
)
eangle
=
u
;
a
=
mdu
*
s
;
a11
=
a
*
c
/
rsq1
;
a12
=
-
a
/
(
r1
*
r2
);
a22
=
a
*
c
/
rsq2
;
f1
[
0
]
=
a11
*
delx1
+
a12
*
delx2
;
f1
[
1
]
=
a11
*
dely1
+
a12
*
dely2
;
f1
[
2
]
=
a11
*
delz1
+
a12
*
delz2
;
f3
[
0
]
=
a22
*
delx2
+
a12
*
delx1
;
f3
[
1
]
=
a22
*
dely2
+
a12
*
dely1
;
f3
[
2
]
=
a22
*
delz2
+
a12
*
delz1
;
// apply force to each of 3 atoms
if
(
newton_bond
||
i1
<
nlocal
)
{
f
[
i1
][
0
]
+=
f1
[
0
];
f
[
i1
][
1
]
+=
f1
[
1
];
f
[
i1
][
2
]
+=
f1
[
2
];
}
if
(
newton_bond
||
i2
<
nlocal
)
{
f
[
i2
][
0
]
-=
f1
[
0
]
+
f3
[
0
];
f
[
i2
][
1
]
-=
f1
[
1
]
+
f3
[
1
];
f
[
i2
][
2
]
-=
f1
[
2
]
+
f3
[
2
];
}
if
(
newton_bond
||
i3
<
nlocal
)
{
f
[
i3
][
0
]
+=
f3
[
0
];
f
[
i3
][
1
]
+=
f3
[
1
];
f
[
i3
][
2
]
+=
f3
[
2
];
}
if
(
evflag
)
ev_tally
(
i1
,
i2
,
i3
,
nlocal
,
newton_bond
,
eangle
,
f1
,
f3
,
delx1
,
dely1
,
delz1
,
delx2
,
dely2
,
delz2
);
}
}
/* ---------------------------------------------------------------------- */
void
AngleTable
::
allocate
()
{
allocated
=
1
;
int
n
=
atom
->
nangletypes
;
memory
->
create
(
theta0
,
n
+
1
,
"angle:theta0"
);
memory
->
create
(
tabindex
,
n
+
1
,
"angle:tabindex"
);
memory
->
create
(
setflag
,
n
+
1
,
"angle:setflag"
);
for
(
int
i
=
1
;
i
<=
n
;
i
++
)
setflag
[
i
]
=
0
;
}
/* ----------------------------------------------------------------------
global settings
------------------------------------------------------------------------- */
void
AngleTable
::
settings
(
int
narg
,
char
**
arg
)
{
if
(
narg
!=
2
)
error
->
all
(
FLERR
,
"Illegal angle_style command"
);
if
(
strcmp
(
arg
[
0
],
"linear"
)
==
0
)
tabstyle
=
LINEAR
;
else
if
(
strcmp
(
arg
[
0
],
"spline"
)
==
0
)
tabstyle
=
SPLINE
;
else
error
->
all
(
FLERR
,
"Unknown table style in angle style table"
);
tablength
=
force
->
inumeric
(
FLERR
,
arg
[
1
]);
if
(
tablength
<
2
)
error
->
all
(
FLERR
,
"Illegal number of angle table entries"
);
// delete old tables, since cannot just change settings
for
(
int
m
=
0
;
m
<
ntables
;
m
++
)
free_table
(
&
tables
[
m
]);
memory
->
sfree
(
tables
);
if
(
allocated
)
{
memory
->
destroy
(
setflag
);
memory
->
destroy
(
tabindex
);
}
allocated
=
0
;
ntables
=
0
;
tables
=
NULL
;
}
/* ----------------------------------------------------------------------
set coeffs for one or more type pairs
------------------------------------------------------------------------- */
void
AngleTable
::
coeff
(
int
narg
,
char
**
arg
)
{
if
(
narg
!=
3
)
error
->
all
(
FLERR
,
"Illegal angle_coeff command"
);
if
(
!
allocated
)
allocate
();
int
ilo
,
ihi
;
force
->
bounds
(
arg
[
0
],
atom
->
nangletypes
,
ilo
,
ihi
);
int
me
;
MPI_Comm_rank
(
world
,
&
me
);
tables
=
(
Table
*
)
memory
->
srealloc
(
tables
,(
ntables
+
1
)
*
sizeof
(
Table
),
"angle:tables"
);
Table
*
tb
=
&
tables
[
ntables
];
null_table
(
tb
);
if
(
me
==
0
)
read_table
(
tb
,
arg
[
1
],
arg
[
2
]);
bcast_table
(
tb
);
// error check on table parameters
if
(
tb
->
ninput
<=
1
)
error
->
one
(
FLERR
,
"Invalid angle table length"
);
double
alo
,
ahi
;
alo
=
tb
->
afile
[
0
];
ahi
=
tb
->
afile
[
tb
->
ninput
-
1
];
if
(
fabs
(
alo
-
0.0
)
>
TINY
||
fabs
(
ahi
-
180.0
)
>
TINY
)
error
->
all
(
FLERR
,
"Angle table must range from 0 to 180 degrees"
);
// convert theta from degrees to radians
for
(
int
i
=
0
;
i
<
tb
->
ninput
;
i
++
){
tb
->
afile
[
i
]
*=
MY_PI
/
180.0
;
tb
->
ffile
[
i
]
*=
180.0
/
MY_PI
;
}
// spline read-in and compute a,e,f vectors within table
spline_table
(
tb
);
compute_table
(
tb
);
// store ptr to table in tabindex
int
count
=
0
;
for
(
int
i
=
ilo
;
i
<=
ihi
;
i
++
)
{
tabindex
[
i
]
=
ntables
;
setflag
[
i
]
=
1
;
theta0
[
i
]
=
tb
->
theta0
;
count
++
;
}
ntables
++
;
if
(
count
==
0
)
error
->
all
(
FLERR
,
"Illegal angle_coeff command"
);
}
/* ----------------------------------------------------------------------
return an equilbrium angle length
should not be used, since don't know minimum of tabulated function
------------------------------------------------------------------------- */
double
AngleTable
::
equilibrium_angle
(
int
i
)
{
return
theta0
[
i
];
}
/* ----------------------------------------------------------------------
proc 0 writes to restart file
------------------------------------------------------------------------- */
void
AngleTable
::
write_restart
(
FILE
*
fp
)
{
fwrite
(
&
tabstyle
,
sizeof
(
int
),
1
,
fp
);
fwrite
(
&
tablength
,
sizeof
(
int
),
1
,
fp
);
}
/* ----------------------------------------------------------------------
proc 0 reads from restart file, bcasts
------------------------------------------------------------------------- */
void
AngleTable
::
read_restart
(
FILE
*
fp
)
{
if
(
comm
->
me
==
0
)
{
fread
(
&
tabstyle
,
sizeof
(
int
),
1
,
fp
);
fread
(
&
tablength
,
sizeof
(
int
),
1
,
fp
);
}
MPI_Bcast
(
&
tabstyle
,
1
,
MPI_INT
,
0
,
world
);
MPI_Bcast
(
&
tablength
,
1
,
MPI_INT
,
0
,
world
);
allocate
();
}
/* ---------------------------------------------------------------------- */
double
AngleTable
::
single
(
int
type
,
int
i1
,
int
i2
,
int
i3
)
{
double
**
x
=
atom
->
x
;
double
delx1
=
x
[
i1
][
0
]
-
x
[
i2
][
0
];
double
dely1
=
x
[
i1
][
1
]
-
x
[
i2
][
1
];
double
delz1
=
x
[
i1
][
2
]
-
x
[
i2
][
2
];
domain
->
minimum_image
(
delx1
,
dely1
,
delz1
);
double
r1
=
sqrt
(
delx1
*
delx1
+
dely1
*
dely1
+
delz1
*
delz1
);
double
delx2
=
x
[
i3
][
0
]
-
x
[
i2
][
0
];
double
dely2
=
x
[
i3
][
1
]
-
x
[
i2
][
1
];
double
delz2
=
x
[
i3
][
2
]
-
x
[
i2
][
2
];
domain
->
minimum_image
(
delx2
,
dely2
,
delz2
);
double
r2
=
sqrt
(
delx2
*
delx2
+
dely2
*
dely2
+
delz2
*
delz2
);
double
c
=
delx1
*
delx2
+
dely1
*
dely2
+
delz1
*
delz2
;
c
/=
r1
*
r2
;
if
(
c
>
1.0
)
c
=
1.0
;
if
(
c
<
-
1.0
)
c
=
-
1.0
;
double
theta
=
acos
(
c
);
double
u
=
0.0
;
u_lookup
(
type
,
theta
,
u
);
return
u
;
}
/* ---------------------------------------------------------------------- */
void
AngleTable
::
null_table
(
Table
*
tb
)
{
tb
->
afile
=
tb
->
efile
=
tb
->
ffile
=
NULL
;
tb
->
e2file
=
tb
->
f2file
=
NULL
;
tb
->
ang
=
tb
->
e
=
tb
->
de
=
NULL
;
tb
->
f
=
tb
->
df
=
tb
->
e2
=
tb
->
f2
=
NULL
;
}
/* ---------------------------------------------------------------------- */
void
AngleTable
::
free_table
(
Table
*
tb
)
{
memory
->
destroy
(
tb
->
afile
);
memory
->
destroy
(
tb
->
efile
);
memory
->
destroy
(
tb
->
ffile
);
memory
->
destroy
(
tb
->
e2file
);
memory
->
destroy
(
tb
->
f2file
);
memory
->
destroy
(
tb
->
ang
);
memory
->
destroy
(
tb
->
e
);
memory
->
destroy
(
tb
->
de
);
memory
->
destroy
(
tb
->
f
);
memory
->
destroy
(
tb
->
df
);
memory
->
destroy
(
tb
->
e2
);
memory
->
destroy
(
tb
->
f2
);
}
/* ----------------------------------------------------------------------
read table file, only called by proc 0
------------------------------------------------------------------------- */
void
AngleTable
::
read_table
(
Table
*
tb
,
char
*
file
,
char
*
keyword
)
{
char
line
[
MAXLINE
];
// open file
FILE
*
fp
=
force
->
open_potential
(
file
);
if
(
fp
==
NULL
)
{
char
str
[
128
];
sprintf
(
str
,
"Cannot open file %s"
,
file
);
error
->
one
(
FLERR
,
str
);
}
// loop until section found with matching keyword
while
(
1
)
{
if
(
fgets
(
line
,
MAXLINE
,
fp
)
==
NULL
)
error
->
one
(
FLERR
,
"Did not find keyword in table file"
);
if
(
strspn
(
line
,
"
\t\n
"
)
==
strlen
(
line
))
continue
;
// blank line
if
(
line
[
0
]
==
'#'
)
continue
;
// comment
char
*
word
=
strtok
(
line
,
"
\t\n\r
"
);
if
(
strcmp
(
word
,
keyword
)
==
0
)
break
;
// matching keyword
fgets
(
line
,
MAXLINE
,
fp
);
// no match, skip section
param_extract
(
tb
,
line
);
fgets
(
line
,
MAXLINE
,
fp
);
for
(
int
i
=
0
;
i
<
tb
->
ninput
;
i
++
)
fgets
(
line
,
MAXLINE
,
fp
);
}
// read args on 2nd line of section
// allocate table arrays for file values
fgets
(
line
,
MAXLINE
,
fp
);
param_extract
(
tb
,
line
);
memory
->
create
(
tb
->
afile
,
tb
->
ninput
,
"angle:afile"
);
memory
->
create
(
tb
->
efile
,
tb
->
ninput
,
"angle:efile"
);
memory
->
create
(
tb
->
ffile
,
tb
->
ninput
,
"angle:ffile"
);
// read a,e,f table values from file
int
itmp
;
fgets
(
line
,
MAXLINE
,
fp
);
for
(
int
i
=
0
;
i
<
tb
->
ninput
;
i
++
)
{
fgets
(
line
,
MAXLINE
,
fp
);
sscanf
(
line
,
"%d %lg %lg %lg"
,
&
itmp
,
&
tb
->
afile
[
i
],
&
tb
->
efile
[
i
],
&
tb
->
ffile
[
i
]);
}
fclose
(
fp
);
}
/* ----------------------------------------------------------------------
build spline representation of e,f over entire range of read-in table
this function sets these values in e2file,f2file
------------------------------------------------------------------------- */
void
AngleTable
::
spline_table
(
Table
*
tb
)
{
memory
->
create
(
tb
->
e2file
,
tb
->
ninput
,
"angle:e2file"
);
memory
->
create
(
tb
->
f2file
,
tb
->
ninput
,
"angle:f2file"
);
double
ep0
=
-
tb
->
ffile
[
0
];
double
epn
=
-
tb
->
ffile
[
tb
->
ninput
-
1
];
spline
(
tb
->
afile
,
tb
->
efile
,
tb
->
ninput
,
ep0
,
epn
,
tb
->
e2file
);
if
(
tb
->
fpflag
==
0
)
{
tb
->
fplo
=
(
tb
->
ffile
[
1
]
-
tb
->
ffile
[
0
])
/
(
tb
->
afile
[
1
]
-
tb
->
afile
[
0
]);
tb
->
fphi
=
(
tb
->
ffile
[
tb
->
ninput
-
1
]
-
tb
->
ffile
[
tb
->
ninput
-
2
])
/
(
tb
->
afile
[
tb
->
ninput
-
1
]
-
tb
->
afile
[
tb
->
ninput
-
2
]);
}
double
fp0
=
tb
->
fplo
;
double
fpn
=
tb
->
fphi
;
spline
(
tb
->
afile
,
tb
->
ffile
,
tb
->
ninput
,
fp0
,
fpn
,
tb
->
f2file
);
}
/* ----------------------------------------------------------------------
compute a,e,f vectors from splined values
------------------------------------------------------------------------- */
void
AngleTable
::
compute_table
(
Table
*
tb
)
{
// delta = table spacing in angle for N-1 bins
int
tlm1
=
tablength
-
1
;
tb
->
delta
=
MY_PI
/
tlm1
;
tb
->
invdelta
=
1.0
/
tb
->
delta
;
tb
->
deltasq6
=
tb
->
delta
*
tb
->
delta
/
6.0
;
// N-1 evenly spaced bins in angle from 0 to PI
// ang,e,f = value at lower edge of bin
// de,df values = delta values of e,f
// ang,e,f are N in length so de,df arrays can compute difference
memory
->
create
(
tb
->
ang
,
tablength
,
"angle:ang"
);
memory
->
create
(
tb
->
e
,
tablength
,
"angle:e"
);
memory
->
create
(
tb
->
de
,
tlm1
,
"angle:de"
);
memory
->
create
(
tb
->
f
,
tablength
,
"angle:f"
);
memory
->
create
(
tb
->
df
,
tlm1
,
"angle:df"
);
memory
->
create
(
tb
->
e2
,
tablength
,
"angle:e2"
);
memory
->
create
(
tb
->
f2
,
tablength
,
"angle:f2"
);
double
a
;
for
(
int
i
=
0
;
i
<
tablength
;
i
++
)
{
a
=
i
*
tb
->
delta
;
tb
->
ang
[
i
]
=
a
;
tb
->
e
[
i
]
=
splint
(
tb
->
afile
,
tb
->
efile
,
tb
->
e2file
,
tb
->
ninput
,
a
);
tb
->
f
[
i
]
=
splint
(
tb
->
afile
,
tb
->
ffile
,
tb
->
f2file
,
tb
->
ninput
,
a
);
}
for
(
int
i
=
0
;
i
<
tlm1
;
i
++
)
{
tb
->
de
[
i
]
=
tb
->
e
[
i
+
1
]
-
tb
->
e
[
i
];
tb
->
df
[
i
]
=
tb
->
f
[
i
+
1
]
-
tb
->
f
[
i
];
}
double
ep0
=
-
tb
->
f
[
0
];
double
epn
=
-
tb
->
f
[
tlm1
];
spline
(
tb
->
ang
,
tb
->
e
,
tablength
,
ep0
,
epn
,
tb
->
e2
);
spline
(
tb
->
ang
,
tb
->
f
,
tablength
,
tb
->
fplo
,
tb
->
fphi
,
tb
->
f2
);
}
/* ----------------------------------------------------------------------
extract attributes from parameter line in table section
format of line: N value FP fplo fphi EQ theta0
N is required, other params are optional
------------------------------------------------------------------------- */
void
AngleTable
::
param_extract
(
Table
*
tb
,
char
*
line
)
{
tb
->
ninput
=
0
;
tb
->
fpflag
=
0
;
tb
->
theta0
=
180.0
;
char
*
word
=
strtok
(
line
,
"
\t\n\r\f
"
);
while
(
word
)
{
if
(
strcmp
(
word
,
"N"
)
==
0
)
{
word
=
strtok
(
NULL
,
"
\t\n\r\f
"
);
tb
->
ninput
=
atoi
(
word
);
}
else
if
(
strcmp
(
word
,
"FP"
)
==
0
)
{
tb
->
fpflag
=
1
;
word
=
strtok
(
NULL
,
"
\t\n\r\f
"
);
tb
->
fplo
=
atof
(
word
);
word
=
strtok
(
NULL
,
"
\t\n\r\f
"
);
tb
->
fphi
=
atof
(
word
);
tb
->
fplo
*=
(
180.0
/
MY_PI
)
*
(
180.0
/
MY_PI
);
tb
->
fphi
*=
(
180.0
/
MY_PI
)
*
(
180.0
/
MY_PI
);
}
else
if
(
strcmp
(
word
,
"EQ"
)
==
0
)
{
word
=
strtok
(
NULL
,
"
\t\n\r\f
"
);
tb
->
theta0
=
atof
(
word
);
}
else
{
error
->
one
(
FLERR
,
"Invalid keyword in angle table parameters"
);
}
word
=
strtok
(
NULL
,
"
\t\n\r\f
"
);
}
if
(
tb
->
ninput
==
0
)
error
->
one
(
FLERR
,
"Angle table parameters did not set N"
);
}
/* ----------------------------------------------------------------------
broadcast read-in table info from proc 0 to other procs
this function communicates these values in Table:
ninput,afile,efile,ffile,fpflag,fplo,fphi,theta0
------------------------------------------------------------------------- */
void
AngleTable
::
bcast_table
(
Table
*
tb
)
{
MPI_Bcast
(
&
tb
->
ninput
,
1
,
MPI_INT
,
0
,
world
);
int
me
;
MPI_Comm_rank
(
world
,
&
me
);
if
(
me
>
0
)
{
memory
->
create
(
tb
->
afile
,
tb
->
ninput
,
"angle:afile"
);
memory
->
create
(
tb
->
efile
,
tb
->
ninput
,
"angle:efile"
);
memory
->
create
(
tb
->
ffile
,
tb
->
ninput
,
"angle:ffile"
);
}
MPI_Bcast
(
tb
->
afile
,
tb
->
ninput
,
MPI_DOUBLE
,
0
,
world
);
MPI_Bcast
(
tb
->
efile
,
tb
->
ninput
,
MPI_DOUBLE
,
0
,
world
);
MPI_Bcast
(
tb
->
ffile
,
tb
->
ninput
,
MPI_DOUBLE
,
0
,
world
);
MPI_Bcast
(
&
tb
->
fpflag
,
1
,
MPI_INT
,
0
,
world
);
if
(
tb
->
fpflag
)
{
MPI_Bcast
(
&
tb
->
fplo
,
1
,
MPI_DOUBLE
,
0
,
world
);
MPI_Bcast
(
&
tb
->
fphi
,
1
,
MPI_DOUBLE
,
0
,
world
);
}
MPI_Bcast
(
&
tb
->
theta0
,
1
,
MPI_DOUBLE
,
0
,
world
);
}
/* ----------------------------------------------------------------------
spline and splint routines modified from Numerical Recipes
------------------------------------------------------------------------- */
void
AngleTable
::
spline
(
double
*
x
,
double
*
y
,
int
n
,
double
yp1
,
double
ypn
,
double
*
y2
)
{
int
i
,
k
;
double
p
,
qn
,
sig
,
un
;
double
*
u
=
new
double
[
n
];
if
(
yp1
>
0.99e30
)
y2
[
0
]
=
u
[
0
]
=
0.0
;
else
{
y2
[
0
]
=
-
0.5
;
u
[
0
]
=
(
3.0
/
(
x
[
1
]
-
x
[
0
]))
*
((
y
[
1
]
-
y
[
0
])
/
(
x
[
1
]
-
x
[
0
])
-
yp1
);
}
for
(
i
=
1
;
i
<
n
-
1
;
i
++
)
{
sig
=
(
x
[
i
]
-
x
[
i
-
1
])
/
(
x
[
i
+
1
]
-
x
[
i
-
1
]);
p
=
sig
*
y2
[
i
-
1
]
+
2.0
;
y2
[
i
]
=
(
sig
-
1.0
)
/
p
;
u
[
i
]
=
(
y
[
i
+
1
]
-
y
[
i
])
/
(
x
[
i
+
1
]
-
x
[
i
])
-
(
y
[
i
]
-
y
[
i
-
1
])
/
(
x
[
i
]
-
x
[
i
-
1
]);
u
[
i
]
=
(
6.0
*
u
[
i
]
/
(
x
[
i
+
1
]
-
x
[
i
-
1
])
-
sig
*
u
[
i
-
1
])
/
p
;
}
if
(
ypn
>
0.99e30
)
qn
=
un
=
0.0
;
else
{
qn
=
0.5
;
un
=
(
3.0
/
(
x
[
n
-
1
]
-
x
[
n
-
2
]))
*
(
ypn
-
(
y
[
n
-
1
]
-
y
[
n
-
2
])
/
(
x
[
n
-
1
]
-
x
[
n
-
2
]));
}
y2
[
n
-
1
]
=
(
un
-
qn
*
u
[
n
-
2
])
/
(
qn
*
y2
[
n
-
2
]
+
1.0
);
for
(
k
=
n
-
2
;
k
>=
0
;
k
--
)
y2
[
k
]
=
y2
[
k
]
*
y2
[
k
+
1
]
+
u
[
k
];
delete
[]
u
;
}
/* ---------------------------------------------------------------------- */
double
AngleTable
::
splint
(
double
*
xa
,
double
*
ya
,
double
*
y2a
,
int
n
,
double
x
)
{
int
klo
,
khi
,
k
;
double
h
,
b
,
a
,
y
;
klo
=
0
;
khi
=
n
-
1
;
while
(
khi
-
klo
>
1
)
{
k
=
(
khi
+
klo
)
>>
1
;
if
(
xa
[
k
]
>
x
)
khi
=
k
;
else
klo
=
k
;
}
h
=
xa
[
khi
]
-
xa
[
klo
];
a
=
(
xa
[
khi
]
-
x
)
/
h
;
b
=
(
x
-
xa
[
klo
])
/
h
;
y
=
a
*
ya
[
klo
]
+
b
*
ya
[
khi
]
+
((
a
*
a
*
a
-
a
)
*
y2a
[
klo
]
+
(
b
*
b
*
b
-
b
)
*
y2a
[
khi
])
*
(
h
*
h
)
/
6.0
;
return
y
;
}
/* ----------------------------------------------------------------------
calculate potential u and force f at angle x
------------------------------------------------------------------------- */
void
AngleTable
::
uf_lookup
(
int
type
,
double
x
,
double
&
u
,
double
&
f
)
{
int
itable
;
double
fraction
,
a
,
b
;
Table
*
tb
=
&
tables
[
tabindex
[
type
]];
if
(
tabstyle
==
LINEAR
)
{
itable
=
static_cast
<
int
>
(
x
*
tb
->
invdelta
);
fraction
=
(
x
-
tb
->
ang
[
itable
])
*
tb
->
invdelta
;
u
=
tb
->
e
[
itable
]
+
fraction
*
tb
->
de
[
itable
];
f
=
tb
->
f
[
itable
]
+
fraction
*
tb
->
df
[
itable
];
}
else
if
(
tabstyle
==
SPLINE
)
{
itable
=
static_cast
<
int
>
(
x
*
tb
->
invdelta
);
fraction
=
(
x
-
tb
->
ang
[
itable
])
*
tb
->
invdelta
;
b
=
(
x
-
tb
->
ang
[
itable
])
*
tb
->
invdelta
;
a
=
1.0
-
b
;
u
=
a
*
tb
->
e
[
itable
]
+
b
*
tb
->
e
[
itable
+
1
]
+
((
a
*
a
*
a
-
a
)
*
tb
->
e2
[
itable
]
+
(
b
*
b
*
b
-
b
)
*
tb
->
e2
[
itable
+
1
])
*
tb
->
deltasq6
;
f
=
a
*
tb
->
f
[
itable
]
+
b
*
tb
->
f
[
itable
+
1
]
+
((
a
*
a
*
a
-
a
)
*
tb
->
f2
[
itable
]
+
(
b
*
b
*
b
-
b
)
*
tb
->
f2
[
itable
+
1
])
*
tb
->
deltasq6
;
}
}
/* ----------------------------------------------------------------------
calculate potential u at angle x
------------------------------------------------------------------------- */
void
AngleTable
::
u_lookup
(
int
type
,
double
x
,
double
&
u
)
{
int
itable
;
double
fraction
,
a
,
b
;
Table
*
tb
=
&
tables
[
tabindex
[
type
]];
if
(
tabstyle
==
LINEAR
)
{
itable
=
static_cast
<
int
>
(
x
*
tb
->
invdelta
);
fraction
=
(
x
-
tb
->
ang
[
itable
])
*
tb
->
invdelta
;
u
=
tb
->
e
[
itable
]
+
fraction
*
tb
->
de
[
itable
];
}
else
if
(
tabstyle
==
SPLINE
)
{
itable
=
static_cast
<
int
>
(
x
*
tb
->
invdelta
);
fraction
=
(
x
-
tb
->
ang
[
itable
])
*
tb
->
invdelta
;
b
=
(
x
-
tb
->
ang
[
itable
])
*
tb
->
invdelta
;
a
=
1.0
-
b
;
u
=
a
*
tb
->
e
[
itable
]
+
b
*
tb
->
e
[
itable
+
1
]
+
((
a
*
a
*
a
-
a
)
*
tb
->
e2
[
itable
]
+
(
b
*
b
*
b
-
b
)
*
tb
->
e2
[
itable
+
1
])
*
tb
->
deltasq6
;
}
}
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