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mgpt_splinetab.cpp
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rLAMMPS lammps
mgpt_splinetab.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.
------------------------------------------------------------------------- */
/* ----------------------------------------------------------------------
This file is part of the MGPT implementation. See further comments
in pair_mgpt.cpp and pair_mgpt.h.
------------------------------------------------------------------------- */
#include "mgpt_splinetab.h"
static
void
trisolve
(
int
n
,
double
A
[][
3
],
double
y
[])
{
/* Backward elimination */
for
(
int
i
=
n
-
1
;
i
>
0
;
i
--
)
{
double
q
=
A
[
i
-
1
][
2
]
/
A
[
i
][
1
];
A
[
i
-
1
][
1
]
=
A
[
i
-
1
][
1
]
-
q
*
A
[
i
][
0
];
y
[
i
-
1
]
=
y
[
i
-
1
]
-
q
*
y
[
i
];
}
/* Forward substitution */
y
[
0
]
=
y
[
0
]
/
A
[
0
][
1
];
for
(
int
i
=
1
;
i
<
n
;
i
++
)
y
[
i
]
=
(
y
[
i
]
-
A
[
i
][
0
]
*
y
[
i
-
1
])
/
A
[
i
][
1
];
}
void
makespline
(
int
ntab
,
int
stride
,
double
tab
[],
double
C
[][
4
])
{
int
n
=
3
*
(
ntab
-
1
);
double
(
*
A
)[
3
]
=
new
double
[
n
][
3
];
double
*
y
=
new
double
[
n
];
double
h_left
,
h_right
,
d
;
int
i
,
j
;
/* Second order second derivative approximation
at end points. */
h_left
=
2.0
*
tab
[
stride
*
0
]
-
5.0
*
tab
[
stride
*
1
]
+
4.0
*
tab
[
stride
*
2
]
-
1.0
*
tab
[
stride
*
3
];
h_right
=
2.0
*
tab
[
stride
*
(
ntab
-
1
)]
-
5.0
*
tab
[
stride
*
(
ntab
-
2
)]
+
4.0
*
tab
[
stride
*
(
ntab
-
3
)]
-
1.0
*
tab
[
stride
*
(
ntab
-
4
)];
A
[
0
][
0
]
=
0.0
;
A
[
0
][
1
]
=
0.0
;
A
[
0
][
2
]
=
2.0
;
y
[
0
]
=
h_left
;
for
(
i
=
1
;
i
<
ntab
-
1
;
i
++
)
{
j
=
3
*
(
i
-
1
);
d
=
tab
[
stride
*
i
]
-
tab
[
stride
*
(
i
-
1
)];
A
[
j
+
1
][
0
]
=
1.0
;
A
[
j
+
1
][
1
]
=
1.0
;
A
[
j
+
1
][
2
]
=
1.0
;
y
[
j
+
1
]
=
d
;
A
[
j
+
2
][
0
]
=
1.0
;
A
[
j
+
2
][
1
]
=
2.0
;
A
[
j
+
2
][
2
]
=
-
1.0
;
y
[
j
+
2
]
=
-
d
;
A
[
j
+
3
][
0
]
=
2.0
;
A
[
j
+
3
][
1
]
=
2.0
;
A
[
j
+
3
][
2
]
=
-
2.0
;
y
[
j
+
3
]
=
2.0
*
d
;
}
j
=
3
*
(
ntab
-
2
);
d
=
tab
[
stride
*
(
ntab
-
1
)]
-
tab
[
stride
*
(
ntab
-
2
)];
A
[
j
+
1
][
0
]
=
1.0
;
A
[
j
+
1
][
1
]
=
1.0
;
A
[
j
+
1
][
2
]
=
1.0
;
y
[
j
+
1
]
=
d
;
A
[
j
+
2
][
0
]
=
2.0
;
A
[
j
+
2
][
1
]
=
6.0
;
A
[
j
+
2
][
2
]
=
0.0
;
y
[
j
+
2
]
=
h_right
;
trisolve
(
n
,
A
,
y
);
for
(
i
=
0
;
i
<
ntab
-
1
;
i
++
)
{
C
[
i
][
0
]
=
tab
[
stride
*
i
];
C
[
i
][
1
]
=
y
[
3
*
i
+
0
];
C
[
i
][
2
]
=
y
[
3
*
i
+
1
];
C
[
i
][
3
]
=
y
[
3
*
i
+
2
];
}
delete
[]
y
;
delete
[]
A
;
}
void
evalcubic
(
double
p
[
4
],
double
x
,
double
*
y
,
double
*
dy
,
double
*
d2y
)
{
double
t1
,
t2
,
t3
;
t1
=
p
[
2
]
+
x
*
p
[
3
];
t2
=
p
[
1
]
+
x
*
t1
;
t3
=
t1
+
x
*
p
[
3
];
*
y
=
p
[
0
]
+
x
*
t2
;
*
dy
=
(
t2
+
x
*
t3
);
*
d2y
=
2.0
*
(
t3
+
x
*
p
[
3
]);
}
void
evalspline
(
int
n
,
double
x0
,
double
x1
,
double
C
[][
4
],
double
x
,
double
*
y
,
double
*
dy
,
double
*
d2y
)
{
double
xhat
,
t1
,
t2
,
t3
;
double
*
p
;
int
idx
;
double
dxinv
=
n
/
(
x1
-
x0
);
xhat
=
(
x
-
x0
)
/
(
x1
-
x0
)
*
n
;
idx
=
(
int
)
xhat
;
if
(
idx
<
0
)
idx
=
0
;
if
(
idx
>
n
-
1
)
idx
=
n
-
1
;
xhat
=
xhat
-
idx
;
p
=
C
[
idx
];
if
(
0
)
{
*
y
=
p
[
0
]
+
xhat
*
(
p
[
1
]
+
xhat
*
(
p
[
2
]
+
xhat
*
p
[
3
]));
*
dy
=
p
[
1
]
+
xhat
*
(
2
*
p
[
2
]
+
xhat
*
3
*
p
[
3
]);
*
d2y
=
2
*
p
[
2
]
+
xhat
*
6
*
p
[
3
];
*
dy
*=
dxinv
;
*
d2y
*=
dxinv
*
dxinv
;
}
else
{
t1
=
p
[
2
]
+
xhat
*
p
[
3
];
t2
=
p
[
1
]
+
xhat
*
t1
;
t3
=
t1
+
xhat
*
p
[
3
];
*
y
=
p
[
0
]
+
xhat
*
t2
;
*
dy
=
(
t2
+
xhat
*
t3
)
*
dxinv
;
*
d2y
=
2.0
*
(
t3
+
xhat
*
p
[
3
])
*
(
dxinv
*
dxinv
);
}
}
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