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rLAMMPS lammps
lattice.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.
------------------------------------------------------------------------- */
#include "math.h"
#include "string.h"
#include "stdlib.h"
#include "lattice.h"
#include "update.h"
#include "force.h"
#include "comm.h"
#include "memory.h"
#include "error.h"
using
namespace
LAMMPS_NS
;
#define MIN(A,B) ((A) < (B)) ? (A) : (B)
#define MAX(A,B) ((A) > (B)) ? (A) : (B)
#define BIG 1.0e30
enum
{
NONE
,
SC
,
BCC
,
FCC
,
DIAMOND
,
SQ
,
SQ2
,
HEX
,
USER
};
/* ---------------------------------------------------------------------- */
Lattice
::
Lattice
(
LAMMPS
*
lmp
,
int
narg
,
char
**
arg
)
:
Pointers
(
lmp
)
{
// parse style arg
if
(
narg
<
1
)
error
->
all
(
"Illegal lattice command"
);
if
(
strcmp
(
arg
[
0
],
"none"
)
==
0
)
style
=
NONE
;
else
if
(
strcmp
(
arg
[
0
],
"sc"
)
==
0
)
style
=
SC
;
else
if
(
strcmp
(
arg
[
0
],
"bcc"
)
==
0
)
style
=
BCC
;
else
if
(
strcmp
(
arg
[
0
],
"fcc"
)
==
0
)
style
=
FCC
;
else
if
(
strcmp
(
arg
[
0
],
"diamond"
)
==
0
)
style
=
DIAMOND
;
else
if
(
strcmp
(
arg
[
0
],
"sq"
)
==
0
)
style
=
SQ
;
else
if
(
strcmp
(
arg
[
0
],
"sq2"
)
==
0
)
style
=
SQ2
;
else
if
(
strcmp
(
arg
[
0
],
"hex"
)
==
0
)
style
=
HEX
;
else
if
(
strcmp
(
arg
[
0
],
"user"
)
==
0
)
style
=
USER
;
else
error
->
all
(
"Illegal lattice command"
);
if
(
style
==
NONE
)
{
if
(
narg
>
1
)
error
->
all
(
"Illegal lattice command"
);
return
;
}
// check that lattice matches dimension
// style USER can be either 2d or 3d
int
dimension
=
force
->
dimension
;
if
(
dimension
==
2
)
{
if
(
style
==
SC
||
style
==
BCC
||
style
==
FCC
||
style
==
DIAMOND
)
error
->
all
(
"Lattice style incompatible with simulation dimension"
);
}
if
(
dimension
==
3
)
{
if
(
style
==
SQ
||
style
==
SQ2
||
style
==
HEX
)
error
->
all
(
"Lattice style incompatible with simulation dimension"
);
}
// scale = conversion factor between lattice and box units
if
(
narg
<
2
)
error
->
all
(
"Illegal lattice command"
);
scale
=
atof
(
arg
[
1
]);
if
(
scale
<=
0.0
)
error
->
all
(
"Illegal lattice command"
);
// set basis atoms for each style
// x,y,z = fractional coords within unit cell
// style USER will be defined by optional args
nbasis
=
0
;
basis
=
NULL
;
if
(
style
==
SC
)
{
add_basis
(
0.0
,
0.0
,
0.0
);
}
else
if
(
style
==
BCC
)
{
add_basis
(
0.0
,
0.0
,
0.0
);
add_basis
(
0.5
,
0.5
,
0.5
);
}
else
if
(
style
==
FCC
)
{
add_basis
(
0.0
,
0.0
,
0.0
);
add_basis
(
0.5
,
0.5
,
0.0
);
add_basis
(
0.5
,
0.0
,
0.5
);
add_basis
(
0.0
,
0.5
,
0.5
);
}
else
if
(
style
==
SQ
)
{
add_basis
(
0.0
,
0.0
,
0.0
);
}
else
if
(
style
==
SQ2
)
{
add_basis
(
0.0
,
0.0
,
0.0
);
add_basis
(
0.5
,
0.5
,
0.0
);
}
else
if
(
style
==
HEX
)
{
add_basis
(
0.0
,
0.0
,
0.0
);
add_basis
(
0.5
,
0.5
,
0.0
);
}
else
if
(
style
==
DIAMOND
)
{
add_basis
(
0.0
,
0.0
,
0.0
);
add_basis
(
0.0
,
0.5
,
0.5
);
add_basis
(
0.5
,
0.0
,
0.5
);
add_basis
(
0.5
,
0.5
,
0.0
);
add_basis
(
0.25
,
0.25
,
0.25
);
add_basis
(
0.25
,
0.75
,
0.75
);
add_basis
(
0.75
,
0.25
,
0.75
);
add_basis
(
0.75
,
0.75
,
0.25
);
}
// set defaults for optional args
origin
[
0
]
=
origin
[
1
]
=
origin
[
2
]
=
0.0
;
orientx
[
0
]
=
1
;
orientx
[
1
]
=
0
;
orientx
[
2
]
=
0
;
orienty
[
0
]
=
0
;
orienty
[
1
]
=
1
;
orienty
[
2
]
=
0
;
orientz
[
0
]
=
0
;
orientz
[
1
]
=
0
;
orientz
[
2
]
=
1
;
a1
[
0
]
=
1.0
;
a1
[
1
]
=
0.0
;
a1
[
2
]
=
0.0
;
a2
[
0
]
=
0.0
;
a2
[
1
]
=
1.0
;
a2
[
2
]
=
0.0
;
a3
[
0
]
=
0.0
;
a3
[
1
]
=
0.0
;
a3
[
2
]
=
1.0
;
if
(
style
==
HEX
)
a2
[
1
]
=
sqrt
(
3.0
);
// process optional args
int
iarg
=
2
;
while
(
iarg
<
narg
)
{
if
(
strcmp
(
arg
[
iarg
],
"origin"
)
==
0
)
{
if
(
iarg
+
4
>
narg
)
error
->
all
(
"Illegal lattice command"
);
origin
[
0
]
=
atof
(
arg
[
iarg
+
1
]);
origin
[
1
]
=
atof
(
arg
[
iarg
+
2
]);
origin
[
2
]
=
atof
(
arg
[
iarg
+
3
]);
if
(
origin
[
0
]
<
0.0
||
origin
[
0
]
>=
1.0
||
origin
[
1
]
<
0.0
||
origin
[
1
]
>=
1.0
||
origin
[
2
]
<
0.0
||
origin
[
2
]
>=
1.0
)
error
->
all
(
"Illegal lattice command"
);
iarg
+=
4
;
}
else
if
(
strcmp
(
arg
[
iarg
],
"orient"
)
==
0
)
{
if
(
iarg
+
5
>
narg
)
error
->
all
(
"Illegal lattice command"
);
int
dim
;
if
(
strcmp
(
arg
[
iarg
+
1
],
"x"
)
==
0
)
dim
=
0
;
else
if
(
strcmp
(
arg
[
iarg
+
1
],
"y"
)
==
0
)
dim
=
1
;
else
if
(
strcmp
(
arg
[
iarg
+
1
],
"z"
)
==
0
)
dim
=
2
;
else
error
->
all
(
"Illegal lattice command"
);
int
*
orient
;
if
(
dim
==
0
)
orient
=
orientx
;
else
if
(
dim
==
1
)
orient
=
orienty
;
else
if
(
dim
==
2
)
orient
=
orientz
;
orient
[
0
]
=
atoi
(
arg
[
iarg
+
2
]);
orient
[
1
]
=
atoi
(
arg
[
iarg
+
3
]);
orient
[
2
]
=
atoi
(
arg
[
iarg
+
4
]);
iarg
+=
5
;
}
else
if
(
strcmp
(
arg
[
iarg
],
"a1"
)
==
0
)
{
if
(
iarg
+
4
>
narg
)
error
->
all
(
"Illegal lattice command"
);
if
(
style
!=
USER
)
error
->
all
(
"Invalid option in lattice command for non-user style"
);
a1
[
0
]
=
atof
(
arg
[
iarg
+
1
]);
a1
[
1
]
=
atof
(
arg
[
iarg
+
2
]);
a1
[
2
]
=
atof
(
arg
[
iarg
+
3
]);
iarg
+=
4
;
}
else
if
(
strcmp
(
arg
[
iarg
],
"a2"
)
==
0
)
{
if
(
iarg
+
4
>
narg
)
error
->
all
(
"Illegal lattice command"
);
if
(
style
!=
USER
)
error
->
all
(
"Invalid option in lattice command for non-user style"
);
a2
[
0
]
=
atof
(
arg
[
iarg
+
1
]);
a2
[
1
]
=
atof
(
arg
[
iarg
+
2
]);
a2
[
2
]
=
atof
(
arg
[
iarg
+
3
]);
iarg
+=
4
;
}
else
if
(
strcmp
(
arg
[
iarg
],
"a3"
)
==
0
)
{
if
(
iarg
+
4
>
narg
)
error
->
all
(
"Illegal lattice command"
);
if
(
style
!=
USER
)
error
->
all
(
"Invalid option in lattice command for non-user style"
);
a3
[
0
]
=
atof
(
arg
[
iarg
+
1
]);
a3
[
1
]
=
atof
(
arg
[
iarg
+
2
]);
a3
[
2
]
=
atof
(
arg
[
iarg
+
3
]);
iarg
+=
4
;
}
else
if
(
strcmp
(
arg
[
iarg
],
"basis"
)
==
0
)
{
if
(
iarg
+
4
>
narg
)
error
->
all
(
"Illegal lattice command"
);
if
(
style
!=
USER
)
error
->
all
(
"Invalid option in lattice command for non-user style"
);
double
x
=
atof
(
arg
[
iarg
+
1
]);
double
y
=
atof
(
arg
[
iarg
+
2
]);
double
z
=
atof
(
arg
[
iarg
+
3
]);
if
(
x
<
0.0
||
x
>=
1.0
||
y
<
0.0
||
y
>=
1.0
||
z
<
0.0
||
z
>=
1.0
)
error
->
all
(
"Illegal lattice command"
);
add_basis
(
x
,
y
,
z
);
iarg
+=
4
;
}
else
error
->
all
(
"Illegal lattice command"
);
}
// check settings for errors
if
(
nbasis
==
0
)
error
->
all
(
"No basis atoms in lattice"
);
if
(
!
orthogonal
())
error
->
all
(
"Lattice orient vectors are not orthogonal"
);
if
(
!
right_handed
())
error
->
all
(
"Lattice orient vectors are not right-handed"
);
if
(
colinear
())
error
->
all
(
"Lattice primitive vectors are colinear"
);
if
(
dimension
==
2
)
{
if
(
origin
[
2
]
!=
0.0
)
error
->
all
(
"Lattice settings are not compatible with 2d simulation"
);
if
(
orientx
[
2
]
!=
0
||
orienty
[
2
]
!=
0
||
orientz
[
0
]
!=
0
||
orientz
[
1
]
!=
0
)
error
->
all
(
"Lattice settings are not compatible with 2d simulation"
);
if
(
a1
[
2
]
!=
0.0
||
a2
[
2
]
!=
0.0
||
a3
[
0
]
!=
0.0
||
a3
[
1
]
!=
0.0
)
error
->
all
(
"Lattice settings are not compatible with 2d simulation"
);
}
// reset scale for LJ units (input scale is rho*)
// scale = (Nbasis/(Vprimitive * rho*)) ^ (1/dim)
if
(
strcmp
(
update
->
unit_style
,
"lj"
)
==
0
)
{
double
vec
[
3
];
cross
(
a2
,
a3
,
vec
);
double
volume
=
dot
(
a1
,
vec
);
scale
=
pow
(
nbasis
/
volume
/
scale
,
1.0
/
dimension
);
}
// initialize lattice <-> box transformation matrices
setup_transform
();
// convert 8 corners of primitive unit cell from lattice coords to box coords
// min to max = bounding box around the pts in box space
// xlattice,ylattice,zlattice = extent of bbox in box space
// set xlattice,ylattice,zlattice to 0.0 initially
// since bbox uses them to shift origin (irrelevant for this computation)
double
xmin
,
ymin
,
zmin
,
xmax
,
ymax
,
zmax
;
xmin
=
ymin
=
zmin
=
BIG
;
xmax
=
ymax
=
zmax
=
-
BIG
;
xlattice
=
ylattice
=
zlattice
=
0.0
;
bbox
(
0
,
0.0
,
0.0
,
0.0
,
xmin
,
ymin
,
zmin
,
xmax
,
ymax
,
zmax
);
bbox
(
0
,
1.0
,
0.0
,
0.0
,
xmin
,
ymin
,
zmin
,
xmax
,
ymax
,
zmax
);
bbox
(
0
,
0.0
,
1.0
,
0.0
,
xmin
,
ymin
,
zmin
,
xmax
,
ymax
,
zmax
);
bbox
(
0
,
1.0
,
1.0
,
0.0
,
xmin
,
ymin
,
zmin
,
xmax
,
ymax
,
zmax
);
bbox
(
0
,
0.0
,
0.0
,
1.0
,
xmin
,
ymin
,
zmin
,
xmax
,
ymax
,
zmax
);
bbox
(
0
,
1.0
,
0.0
,
1.0
,
xmin
,
ymin
,
zmin
,
xmax
,
ymax
,
zmax
);
bbox
(
0
,
0.0
,
1.0
,
1.0
,
xmin
,
ymin
,
zmin
,
xmax
,
ymax
,
zmax
);
bbox
(
0
,
1.0
,
1.0
,
1.0
,
xmin
,
ymin
,
zmin
,
xmax
,
ymax
,
zmax
);
xlattice
=
xmax
-
xmin
;
ylattice
=
ymax
-
ymin
;
zlattice
=
zmax
-
zmin
;
// print lattice spacings
if
(
comm
->
me
==
0
)
{
if
(
screen
)
fprintf
(
screen
,
"Lattice spacing in x,y,z = %g %g %g
\n
"
,
xlattice
,
ylattice
,
zlattice
);
if
(
logfile
)
fprintf
(
logfile
,
"Lattice spacing in x,y,z = %g %g %g
\n
"
,
xlattice
,
ylattice
,
zlattice
);
}
}
/* ---------------------------------------------------------------------- */
Lattice
::~
Lattice
()
{
memory
->
destroy_2d_double_array
(
basis
);
}
/* ----------------------------------------------------------------------
check if 3 orientation vectors are mutually orthogonal
------------------------------------------------------------------------- */
int
Lattice
::
orthogonal
()
{
if
(
orientx
[
0
]
*
orienty
[
0
]
+
orientx
[
1
]
*
orienty
[
1
]
+
orientx
[
2
]
*
orienty
[
2
])
return
0
;
if
(
orienty
[
0
]
*
orientz
[
0
]
+
orienty
[
1
]
*
orientz
[
1
]
+
orienty
[
2
]
*
orientz
[
2
])
return
0
;
if
(
orientx
[
0
]
*
orientz
[
0
]
+
orientx
[
1
]
*
orientz
[
1
]
+
orientx
[
2
]
*
orientz
[
2
])
return
0
;
return
1
;
}
/* ----------------------------------------------------------------------
check righthandedness of orientation vectors
x cross y must be in same direction as z
------------------------------------------------------------------------- */
int
Lattice
::
right_handed
()
{
int
xy0
=
orientx
[
1
]
*
orienty
[
2
]
-
orientx
[
2
]
*
orienty
[
1
];
int
xy1
=
orientx
[
2
]
*
orienty
[
0
]
-
orientx
[
0
]
*
orienty
[
2
];
int
xy2
=
orientx
[
0
]
*
orienty
[
1
]
-
orientx
[
1
]
*
orienty
[
0
];
if
(
xy0
*
orientz
[
0
]
+
xy1
*
orientz
[
1
]
+
xy2
*
orientz
[
2
]
<=
0
)
return
0
;
return
1
;
}
/* ----------------------------------------------------------------------
check colinearity of each pair of primitive vectors
------------------------------------------------------------------------- */
int
Lattice
::
colinear
()
{
double
vec
[
3
];
cross
(
a1
,
a2
,
vec
);
if
(
dot
(
vec
,
vec
)
==
0.0
)
return
1
;
cross
(
a2
,
a3
,
vec
);
if
(
dot
(
vec
,
vec
)
==
0.0
)
return
1
;
cross
(
a1
,
a3
,
vec
);
if
(
dot
(
vec
,
vec
)
==
0.0
)
return
1
;
return
0
;
}
/* ----------------------------------------------------------------------
initialize lattice <-> box transformation matrices
------------------------------------------------------------------------- */
void
Lattice
::
setup_transform
()
{
double
length
;
// primitive = 3x3 matrix with primitive vectors as columns
primitive
[
0
][
0
]
=
a1
[
0
];
primitive
[
1
][
0
]
=
a1
[
1
];
primitive
[
2
][
0
]
=
a1
[
2
];
primitive
[
0
][
1
]
=
a2
[
0
];
primitive
[
1
][
1
]
=
a2
[
1
];
primitive
[
2
][
1
]
=
a2
[
2
];
primitive
[
0
][
2
]
=
a3
[
0
];
primitive
[
1
][
2
]
=
a3
[
1
];
primitive
[
2
][
2
]
=
a3
[
2
];
// priminv = inverse of primitive
double
determinant
=
primitive
[
0
][
0
]
*
primitive
[
1
][
1
]
*
primitive
[
2
][
2
]
+
primitive
[
0
][
1
]
*
primitive
[
1
][
2
]
*
primitive
[
2
][
0
]
+
primitive
[
0
][
2
]
*
primitive
[
1
][
0
]
*
primitive
[
2
][
1
]
-
primitive
[
0
][
0
]
*
primitive
[
1
][
2
]
*
primitive
[
2
][
1
]
-
primitive
[
0
][
1
]
*
primitive
[
1
][
0
]
*
primitive
[
2
][
2
]
-
primitive
[
0
][
2
]
*
primitive
[
1
][
1
]
*
primitive
[
2
][
0
];
if
(
determinant
==
0.0
)
error
->
all
(
"Degenerate lattice primitive vectors"
);
priminv
[
0
][
0
]
=
(
primitive
[
1
][
1
]
*
primitive
[
2
][
2
]
-
primitive
[
1
][
2
]
*
primitive
[
2
][
1
])
/
determinant
;
priminv
[
1
][
0
]
=
(
primitive
[
1
][
2
]
*
primitive
[
2
][
0
]
-
primitive
[
1
][
0
]
*
primitive
[
2
][
2
])
/
determinant
;
priminv
[
2
][
0
]
=
(
primitive
[
1
][
0
]
*
primitive
[
2
][
1
]
-
primitive
[
1
][
1
]
*
primitive
[
2
][
0
])
/
determinant
;
priminv
[
0
][
1
]
=
(
primitive
[
0
][
2
]
*
primitive
[
2
][
1
]
-
primitive
[
0
][
1
]
*
primitive
[
2
][
2
])
/
determinant
;
priminv
[
1
][
1
]
=
(
primitive
[
0
][
0
]
*
primitive
[
2
][
2
]
-
primitive
[
0
][
2
]
*
primitive
[
2
][
0
])
/
determinant
;
priminv
[
2
][
1
]
=
(
primitive
[
0
][
1
]
*
primitive
[
2
][
0
]
-
primitive
[
0
][
0
]
*
primitive
[
2
][
1
])
/
determinant
;
priminv
[
0
][
2
]
=
(
primitive
[
0
][
1
]
*
primitive
[
1
][
2
]
-
primitive
[
0
][
2
]
*
primitive
[
1
][
1
])
/
determinant
;
priminv
[
1
][
2
]
=
(
primitive
[
0
][
2
]
*
primitive
[
1
][
0
]
-
primitive
[
0
][
0
]
*
primitive
[
1
][
2
])
/
determinant
;
priminv
[
2
][
2
]
=
(
primitive
[
0
][
0
]
*
primitive
[
1
][
1
]
-
primitive
[
0
][
1
]
*
primitive
[
1
][
0
])
/
determinant
;
// rotaterow = 3x3 matrix with normalized orient vectors as rows
length
=
sqrt
(
orientx
[
0
]
*
orientx
[
0
]
+
orientx
[
1
]
*
orientx
[
1
]
+
orientx
[
2
]
*
orientx
[
2
]);
if
(
length
==
0.0
)
error
->
all
(
"Zero-length lattice orient vector"
);
rotaterow
[
0
][
0
]
=
orientx
[
0
]
/
length
;
rotaterow
[
0
][
1
]
=
orientx
[
1
]
/
length
;
rotaterow
[
0
][
2
]
=
orientx
[
2
]
/
length
;
length
=
sqrt
(
orienty
[
0
]
*
orienty
[
0
]
+
orienty
[
1
]
*
orienty
[
1
]
+
orienty
[
2
]
*
orienty
[
2
]);
if
(
length
==
0.0
)
error
->
all
(
"Zero-length lattice orient vector"
);
rotaterow
[
1
][
0
]
=
orienty
[
0
]
/
length
;
rotaterow
[
1
][
1
]
=
orienty
[
1
]
/
length
;
rotaterow
[
1
][
2
]
=
orienty
[
2
]
/
length
;
length
=
sqrt
(
orientz
[
0
]
*
orientz
[
0
]
+
orientz
[
1
]
*
orientz
[
1
]
+
orientz
[
2
]
*
orientz
[
2
]);
if
(
length
==
0.0
)
error
->
all
(
"Zero-length lattice orient vector"
);
rotaterow
[
2
][
0
]
=
orientz
[
0
]
/
length
;
rotaterow
[
2
][
1
]
=
orientz
[
1
]
/
length
;
rotaterow
[
2
][
2
]
=
orientz
[
2
]
/
length
;
// rotatecol = 3x3 matrix with normalized orient vectors as columns
rotatecol
[
0
][
0
]
=
rotaterow
[
0
][
0
];
rotatecol
[
1
][
0
]
=
rotaterow
[
0
][
1
];
rotatecol
[
2
][
0
]
=
rotaterow
[
0
][
2
];
rotatecol
[
0
][
1
]
=
rotaterow
[
1
][
0
];
rotatecol
[
1
][
1
]
=
rotaterow
[
1
][
1
];
rotatecol
[
2
][
1
]
=
rotaterow
[
1
][
2
];
rotatecol
[
0
][
2
]
=
rotaterow
[
2
][
0
];
rotatecol
[
1
][
2
]
=
rotaterow
[
2
][
1
];
rotatecol
[
2
][
2
]
=
rotaterow
[
2
][
2
];
}
/* ----------------------------------------------------------------------
convert lattice coords to box coords
input x,y,z = point in lattice coords
output x,y,z = point in box coords
transformation: xyz_box = Rotate_row * scale * P * xyz_lattice + offset
xyz_box = 3-vector of output box coords
Rotate_row = 3x3 matrix = normalized orient vectors as rows
scale = scale factor
P = 3x3 matrix = primitive vectors as columns
xyz_lattice = 3-vector of input lattice coords
offset = 3-vector = (xlatt*origin[0], ylatt*origin[1], zlatt*origin[2])
------------------------------------------------------------------------- */
void
Lattice
::
lattice2box
(
double
&
x
,
double
&
y
,
double
&
z
)
{
double
x1
=
primitive
[
0
][
0
]
*
x
+
primitive
[
0
][
1
]
*
y
+
primitive
[
0
][
2
]
*
z
;
double
y1
=
primitive
[
1
][
0
]
*
x
+
primitive
[
1
][
1
]
*
y
+
primitive
[
1
][
2
]
*
z
;
double
z1
=
primitive
[
2
][
0
]
*
x
+
primitive
[
2
][
1
]
*
y
+
primitive
[
2
][
2
]
*
z
;
x1
*=
scale
;
y1
*=
scale
;
z1
*=
scale
;
double
xnew
=
rotaterow
[
0
][
0
]
*
x1
+
rotaterow
[
0
][
1
]
*
y1
+
rotaterow
[
0
][
2
]
*
z1
;
double
ynew
=
rotaterow
[
1
][
0
]
*
x1
+
rotaterow
[
1
][
1
]
*
y1
+
rotaterow
[
1
][
2
]
*
z1
;
double
znew
=
rotaterow
[
2
][
0
]
*
x1
+
rotaterow
[
2
][
1
]
*
y1
+
rotaterow
[
2
][
2
]
*
z1
;
x
=
xnew
+
xlattice
*
origin
[
0
];
y
=
ynew
+
ylattice
*
origin
[
1
];
z
=
znew
+
zlattice
*
origin
[
2
];
}
/* ----------------------------------------------------------------------
convert box coords to lattice coords
input x,y,z = point in box coords
output x,y,z = point in lattice coords
transformation: xyz_latt = P_inv * 1/scale * Rotate_col * (xyz_box - offset)
xyz_lattice = 3-vector of output lattice coords
P_inv = 3x3 matrix = inverse of primitive vectors as columns
scale = scale factor
Rotate_col = 3x3 matrix = normalized orient vectors as columns
xyz_box = 3-vector of input box coords
offset = 3-vector = (xlatt*origin[0], ylatt*origin[1], zlatt*origin[2])
------------------------------------------------------------------------- */
void
Lattice
::
box2lattice
(
double
&
x
,
double
&
y
,
double
&
z
)
{
x
-=
xlattice
*
origin
[
0
];
y
-=
ylattice
*
origin
[
1
];
z
-=
zlattice
*
origin
[
2
];
double
x1
=
rotatecol
[
0
][
0
]
*
x
+
rotatecol
[
0
][
1
]
*
y
+
rotatecol
[
0
][
2
]
*
z
;
double
y1
=
rotatecol
[
1
][
0
]
*
x
+
rotatecol
[
1
][
1
]
*
y
+
rotatecol
[
1
][
2
]
*
z
;
double
z1
=
rotatecol
[
2
][
0
]
*
x
+
rotatecol
[
2
][
1
]
*
y
+
rotatecol
[
2
][
2
]
*
z
;
x1
/=
scale
;
y1
/=
scale
;
z1
/=
scale
;
x
=
priminv
[
0
][
0
]
*
x1
+
priminv
[
0
][
1
]
*
y1
+
priminv
[
0
][
2
]
*
z1
;
y
=
priminv
[
1
][
0
]
*
x1
+
priminv
[
1
][
1
]
*
y1
+
priminv
[
1
][
2
]
*
z1
;
z
=
priminv
[
2
][
0
]
*
x1
+
priminv
[
2
][
1
]
*
y1
+
priminv
[
2
][
2
]
*
z1
;
}
/* ----------------------------------------------------------------------
add a basis atom to list
x,y,z = fractional coords within unit cell
------------------------------------------------------------------------- */
void
Lattice
::
add_basis
(
double
x
,
double
y
,
double
z
)
{
basis
=
memory
->
grow_2d_double_array
(
basis
,
nbasis
+
1
,
3
,
"lattice:basis"
);
basis
[
nbasis
][
0
]
=
x
;
basis
[
nbasis
][
1
]
=
y
;
basis
[
nbasis
][
2
]
=
z
;
nbasis
++
;
}
/* ----------------------------------------------------------------------
return x dot y
------------------------------------------------------------------------- */
double
Lattice
::
dot
(
double
*
x
,
double
*
y
)
{
return
x
[
0
]
*
y
[
0
]
+
x
[
1
]
*
y
[
1
]
+
x
[
2
]
*
y
[
2
];
}
/* ----------------------------------------------------------------------
z = x cross y
------------------------------------------------------------------------- */
void
Lattice
::
cross
(
double
*
x
,
double
*
y
,
double
*
z
)
{
z
[
0
]
=
x
[
1
]
*
y
[
2
]
-
x
[
2
]
*
y
[
1
];
z
[
1
]
=
x
[
2
]
*
y
[
0
]
-
x
[
0
]
*
y
[
2
];
z
[
2
]
=
x
[
0
]
*
y
[
1
]
-
x
[
1
]
*
y
[
0
];
}
/* ----------------------------------------------------------------------
convert x,y,z from lattice coords to box coords (flag = 0) or vice versa
use new point to expand bounding box (min to max)
------------------------------------------------------------------------- */
void
Lattice
::
bbox
(
int
flag
,
double
x
,
double
y
,
double
z
,
double
&
xmin
,
double
&
ymin
,
double
&
zmin
,
double
&
xmax
,
double
&
ymax
,
double
&
zmax
)
{
if
(
flag
==
0
)
lattice2box
(
x
,
y
,
z
);
else
box2lattice
(
x
,
y
,
z
);
xmin
=
MIN
(
x
,
xmin
);
ymin
=
MIN
(
y
,
ymin
);
zmin
=
MIN
(
z
,
zmin
);
xmax
=
MAX
(
x
,
xmax
);
ymax
=
MAX
(
y
,
ymax
);
zmax
=
MAX
(
z
,
zmax
);
}
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