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colvartypes.cpp
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// -*- c++ -*-
#include <stdlib.h>
#include <string.h>
#include "colvarmodule.h"
#include "colvartypes.h"
#include "colvarparse.h"
bool
colvarmodule
::
rotation
::
monitor_crossings
=
false
;
cvm
::
real
colvarmodule
::
rotation
::
crossing_threshold
=
1.0E-02
;
std
::
string
cvm
::
rvector
::
to_simple_string
()
const
{
std
::
ostringstream
os
;
os
.
setf
(
std
::
ios
::
scientific
,
std
::
ios
::
floatfield
);
os
.
precision
(
cvm
::
cv_prec
);
os
<<
x
<<
" "
<<
y
<<
" "
<<
z
;
return
os
.
str
();
}
int
cvm
::
rvector
::
from_simple_string
(
std
::
string
const
&
s
)
{
std
::
stringstream
stream
(
s
);
if
(
!
(
stream
>>
x
)
||
!
(
stream
>>
y
)
||
!
(
stream
>>
z
)
)
{
return
COLVARS_ERROR
;
}
return
COLVARS_OK
;
}
std
::
ostream
&
operator
<<
(
std
::
ostream
&
os
,
colvarmodule
::
rvector
const
&
v
)
{
std
::
streamsize
const
w
=
os
.
width
();
std
::
streamsize
const
p
=
os
.
precision
();
os
.
width
(
2
);
os
<<
"( "
;
os
.
width
(
w
);
os
.
precision
(
p
);
os
<<
v
.
x
<<
" , "
;
os
.
width
(
w
);
os
.
precision
(
p
);
os
<<
v
.
y
<<
" , "
;
os
.
width
(
w
);
os
.
precision
(
p
);
os
<<
v
.
z
<<
" )"
;
return
os
;
}
std
::
istream
&
operator
>>
(
std
::
istream
&
is
,
colvarmodule
::
rvector
&
v
)
{
size_t
const
start_pos
=
is
.
tellg
();
char
sep
;
if
(
!
(
is
>>
sep
)
||
!
(
sep
==
'('
)
||
!
(
is
>>
v
.
x
)
||
!
(
is
>>
sep
)
||
!
(
sep
==
','
)
||
!
(
is
>>
v
.
y
)
||
!
(
is
>>
sep
)
||
!
(
sep
==
','
)
||
!
(
is
>>
v
.
z
)
||
!
(
is
>>
sep
)
||
!
(
sep
==
')'
)
)
{
is
.
clear
();
is
.
seekg
(
start_pos
,
std
::
ios
::
beg
);
is
.
setstate
(
std
::
ios
::
failbit
);
return
is
;
}
return
is
;
}
std
::
string
cvm
::
quaternion
::
to_simple_string
()
const
{
std
::
ostringstream
os
;
os
.
setf
(
std
::
ios
::
scientific
,
std
::
ios
::
floatfield
);
os
.
precision
(
cvm
::
cv_prec
);
os
<<
q0
<<
" "
<<
q1
<<
" "
<<
q2
<<
" "
<<
q3
;
return
os
.
str
();
}
int
cvm
::
quaternion
::
from_simple_string
(
std
::
string
const
&
s
)
{
std
::
stringstream
stream
(
s
);
if
(
!
(
stream
>>
q0
)
||
!
(
stream
>>
q1
)
||
!
(
stream
>>
q2
)
||
!
(
stream
>>
q3
)
)
{
return
COLVARS_ERROR
;
}
return
COLVARS_OK
;
}
std
::
ostream
&
operator
<<
(
std
::
ostream
&
os
,
colvarmodule
::
quaternion
const
&
q
)
{
std
::
streamsize
const
w
=
os
.
width
();
std
::
streamsize
const
p
=
os
.
precision
();
os
.
width
(
2
);
os
<<
"( "
;
os
.
width
(
w
);
os
.
precision
(
p
);
os
<<
q
.
q0
<<
" , "
;
os
.
width
(
w
);
os
.
precision
(
p
);
os
<<
q
.
q1
<<
" , "
;
os
.
width
(
w
);
os
.
precision
(
p
);
os
<<
q
.
q2
<<
" , "
;
os
.
width
(
w
);
os
.
precision
(
p
);
os
<<
q
.
q3
<<
" )"
;
return
os
;
}
std
::
istream
&
operator
>>
(
std
::
istream
&
is
,
colvarmodule
::
quaternion
&
q
)
{
size_t
const
start_pos
=
is
.
tellg
();
std
::
string
euler
(
""
);
if
(
(
is
>>
euler
)
&&
(
colvarparse
::
to_lower_cppstr
(
euler
)
==
std
::
string
(
"euler"
))
)
{
// parse the Euler angles
char
sep
;
cvm
::
real
phi
,
theta
,
psi
;
if
(
!
(
is
>>
sep
)
||
!
(
sep
==
'('
)
||
!
(
is
>>
phi
)
||
!
(
is
>>
sep
)
||
!
(
sep
==
','
)
||
!
(
is
>>
theta
)
||
!
(
is
>>
sep
)
||
!
(
sep
==
','
)
||
!
(
is
>>
psi
)
||
!
(
is
>>
sep
)
||
!
(
sep
==
')'
)
)
{
is
.
clear
();
is
.
seekg
(
start_pos
,
std
::
ios
::
beg
);
is
.
setstate
(
std
::
ios
::
failbit
);
return
is
;
}
q
=
colvarmodule
::
quaternion
(
phi
,
theta
,
psi
);
}
else
{
// parse the quaternion components
is
.
seekg
(
start_pos
,
std
::
ios
::
beg
);
char
sep
;
if
(
!
(
is
>>
sep
)
||
!
(
sep
==
'('
)
||
!
(
is
>>
q
.
q0
)
||
!
(
is
>>
sep
)
||
!
(
sep
==
','
)
||
!
(
is
>>
q
.
q1
)
||
!
(
is
>>
sep
)
||
!
(
sep
==
','
)
||
!
(
is
>>
q
.
q2
)
||
!
(
is
>>
sep
)
||
!
(
sep
==
','
)
||
!
(
is
>>
q
.
q3
)
||
!
(
is
>>
sep
)
||
!
(
sep
==
')'
)
)
{
is
.
clear
();
is
.
seekg
(
start_pos
,
std
::
ios
::
beg
);
is
.
setstate
(
std
::
ios
::
failbit
);
return
is
;
}
}
return
is
;
}
cvm
::
quaternion
cvm
::
quaternion
::
position_derivative_inner
(
cvm
::
rvector
const
&
pos
,
cvm
::
rvector
const
&
vec
)
const
{
cvm
::
quaternion
result
(
0.0
,
0.0
,
0.0
,
0.0
);
result
.
q0
=
2.0
*
pos
.
x
*
q0
*
vec
.
x
+
2.0
*
pos
.
y
*
q0
*
vec
.
y
+
2.0
*
pos
.
z
*
q0
*
vec
.
z
-
2.0
*
pos
.
y
*
q3
*
vec
.
x
+
2.0
*
pos
.
z
*
q2
*
vec
.
x
+
2.0
*
pos
.
x
*
q3
*
vec
.
y
-
2.0
*
pos
.
z
*
q1
*
vec
.
y
-
2.0
*
pos
.
x
*
q2
*
vec
.
z
+
2.0
*
pos
.
y
*
q1
*
vec
.
z
;
result
.
q1
=
+
2.0
*
pos
.
x
*
q1
*
vec
.
x
-
2.0
*
pos
.
y
*
q1
*
vec
.
y
-
2.0
*
pos
.
z
*
q1
*
vec
.
z
+
2.0
*
pos
.
y
*
q2
*
vec
.
x
+
2.0
*
pos
.
z
*
q3
*
vec
.
x
+
2.0
*
pos
.
x
*
q2
*
vec
.
y
-
2.0
*
pos
.
z
*
q0
*
vec
.
y
+
2.0
*
pos
.
x
*
q3
*
vec
.
z
+
2.0
*
pos
.
y
*
q0
*
vec
.
z
;
result
.
q2
=
-
2.0
*
pos
.
x
*
q2
*
vec
.
x
+
2.0
*
pos
.
y
*
q2
*
vec
.
y
-
2.0
*
pos
.
z
*
q2
*
vec
.
z
+
2.0
*
pos
.
y
*
q1
*
vec
.
x
+
2.0
*
pos
.
z
*
q0
*
vec
.
x
+
2.0
*
pos
.
x
*
q1
*
vec
.
y
+
2.0
*
pos
.
z
*
q3
*
vec
.
y
-
2.0
*
pos
.
x
*
q0
*
vec
.
z
+
2.0
*
pos
.
y
*
q3
*
vec
.
z
;
result
.
q3
=
-
2.0
*
pos
.
x
*
q3
*
vec
.
x
-
2.0
*
pos
.
y
*
q3
*
vec
.
y
+
2.0
*
pos
.
z
*
q3
*
vec
.
z
-
2.0
*
pos
.
y
*
q0
*
vec
.
x
+
2.0
*
pos
.
z
*
q1
*
vec
.
x
+
2.0
*
pos
.
x
*
q0
*
vec
.
y
+
2.0
*
pos
.
z
*
q2
*
vec
.
y
+
2.0
*
pos
.
x
*
q1
*
vec
.
z
+
2.0
*
pos
.
y
*
q2
*
vec
.
z
;
return
result
;
}
// Calculate the optimal rotation between two groups, and implement it
// as a quaternion. Uses the method documented in: Coutsias EA,
// Seok C, Dill KA. Using quaternions to calculate RMSD. J Comput
// Chem. 25(15):1849-57 (2004) DOI: 10.1002/jcc.20110 PubMed: 15376254
void
colvarmodule
::
rotation
::
build_matrix
(
std
::
vector
<
cvm
::
atom_pos
>
const
&
pos1
,
std
::
vector
<
cvm
::
atom_pos
>
const
&
pos2
,
cvm
::
matrix2d
<
cvm
::
real
>
&
S
)
{
// build the correlation matrix
C
.
resize
(
3
,
3
);
C
.
reset
();
size_t
i
;
for
(
i
=
0
;
i
<
pos1
.
size
();
i
++
)
{
C
.
xx
()
+=
pos1
[
i
].
x
*
pos2
[
i
].
x
;
C
.
xy
()
+=
pos1
[
i
].
x
*
pos2
[
i
].
y
;
C
.
xz
()
+=
pos1
[
i
].
x
*
pos2
[
i
].
z
;
C
.
yx
()
+=
pos1
[
i
].
y
*
pos2
[
i
].
x
;
C
.
yy
()
+=
pos1
[
i
].
y
*
pos2
[
i
].
y
;
C
.
yz
()
+=
pos1
[
i
].
y
*
pos2
[
i
].
z
;
C
.
zx
()
+=
pos1
[
i
].
z
*
pos2
[
i
].
x
;
C
.
zy
()
+=
pos1
[
i
].
z
*
pos2
[
i
].
y
;
C
.
zz
()
+=
pos1
[
i
].
z
*
pos2
[
i
].
z
;
}
// build the "overlap" matrix, whose eigenvectors are stationary
// points of the RMSD in the space of rotations
S
[
0
][
0
]
=
C
.
xx
()
+
C
.
yy
()
+
C
.
zz
();
S
[
1
][
0
]
=
C
.
yz
()
-
C
.
zy
();
S
[
0
][
1
]
=
S
[
1
][
0
];
S
[
2
][
0
]
=
-
C
.
xz
()
+
C
.
zx
()
;
S
[
0
][
2
]
=
S
[
2
][
0
];
S
[
3
][
0
]
=
C
.
xy
()
-
C
.
yx
();
S
[
0
][
3
]
=
S
[
3
][
0
];
S
[
1
][
1
]
=
C
.
xx
()
-
C
.
yy
()
-
C
.
zz
();
S
[
2
][
1
]
=
C
.
xy
()
+
C
.
yx
();
S
[
1
][
2
]
=
S
[
2
][
1
];
S
[
3
][
1
]
=
C
.
xz
()
+
C
.
zx
();
S
[
1
][
3
]
=
S
[
3
][
1
];
S
[
2
][
2
]
=
-
C
.
xx
()
+
C
.
yy
()
-
C
.
zz
();
S
[
3
][
2
]
=
C
.
yz
()
+
C
.
zy
();
S
[
2
][
3
]
=
S
[
3
][
2
];
S
[
3
][
3
]
=
-
C
.
xx
()
-
C
.
yy
()
+
C
.
zz
();
}
void
colvarmodule
::
rotation
::
diagonalize_matrix
(
cvm
::
matrix2d
<
cvm
::
real
>
&
S
,
cvm
::
vector1d
<
cvm
::
real
>
&
S_eigval
,
cvm
::
matrix2d
<
cvm
::
real
>
&
S_eigvec
)
{
S_eigval
.
resize
(
4
);
S_eigval
.
reset
();
S_eigvec
.
resize
(
4
,
4
);
S_eigvec
.
reset
();
// diagonalize
int
jac_nrot
=
0
;
jacobi
(
S
.
c_array
(),
S_eigval
.
c_array
(),
S_eigvec
.
c_array
(),
&
jac_nrot
);
eigsrt
(
S_eigval
.
c_array
(),
S_eigvec
.
c_array
());
// jacobi saves eigenvectors by columns
transpose
(
S_eigvec
.
c_array
());
// normalize eigenvectors
for
(
size_t
ie
=
0
;
ie
<
4
;
ie
++
)
{
cvm
::
real
norm2
=
0.0
;
size_t
i
;
for
(
i
=
0
;
i
<
4
;
i
++
)
{
norm2
+=
std
::
pow
(
S_eigvec
[
ie
][
i
],
int
(
2
));
}
cvm
::
real
const
norm
=
std
::
sqrt
(
norm2
);
for
(
i
=
0
;
i
<
4
;
i
++
)
{
S_eigvec
[
ie
][
i
]
/=
norm
;
}
}
}
// Calculate the rotation, plus its derivatives
void
colvarmodule
::
rotation
::
calc_optimal_rotation
(
std
::
vector
<
cvm
::
atom_pos
>
const
&
pos1
,
std
::
vector
<
cvm
::
atom_pos
>
const
&
pos2
)
{
S
.
resize
(
4
,
4
);
S
.
reset
();
build_matrix
(
pos1
,
pos2
,
S
);
S_backup
.
resize
(
4
,
4
);
S_backup
=
S
;
if
(
b_debug_gradients
)
{
cvm
::
log
(
"S = "
+
cvm
::
to_str
(
cvm
::
to_str
(
S_backup
),
cvm
::
cv_width
,
cvm
::
cv_prec
)
+
"
\n
"
);
}
diagonalize_matrix
(
S
,
S_eigval
,
S_eigvec
);
// eigenvalues and eigenvectors
cvm
::
real
const
L0
=
S_eigval
[
0
];
cvm
::
real
const
L1
=
S_eigval
[
1
];
cvm
::
real
const
L2
=
S_eigval
[
2
];
cvm
::
real
const
L3
=
S_eigval
[
3
];
cvm
::
quaternion
const
Q0
(
S_eigvec
[
0
]);
cvm
::
quaternion
const
Q1
(
S_eigvec
[
1
]);
cvm
::
quaternion
const
Q2
(
S_eigvec
[
2
]);
cvm
::
quaternion
const
Q3
(
S_eigvec
[
3
]);
lambda
=
L0
;
q
=
Q0
;
if
(
cvm
::
rotation
::
monitor_crossings
)
{
if
(
q_old
.
norm2
()
>
0.0
)
{
q
.
match
(
q_old
);
if
(
q_old
.
inner
(
q
)
<
(
1.0
-
crossing_threshold
))
{
cvm
::
log
(
"Warning: one molecular orientation has changed by more than "
+
cvm
::
to_str
(
crossing_threshold
)
+
": discontinuous rotation ?
\n
"
);
}
}
q_old
=
q
;
}
if
(
b_debug_gradients
)
{
cvm
::
log
(
"L0 = "
+
cvm
::
to_str
(
L0
,
cvm
::
cv_width
,
cvm
::
cv_prec
)
+
", Q0 = "
+
cvm
::
to_str
(
Q0
,
cvm
::
cv_width
,
cvm
::
cv_prec
)
+
", Q0*Q0 = "
+
cvm
::
to_str
(
Q0
.
inner
(
Q0
),
cvm
::
cv_width
,
cvm
::
cv_prec
)
+
"
\n
"
);
cvm
::
log
(
"L1 = "
+
cvm
::
to_str
(
L1
,
cvm
::
cv_width
,
cvm
::
cv_prec
)
+
", Q1 = "
+
cvm
::
to_str
(
Q1
,
cvm
::
cv_width
,
cvm
::
cv_prec
)
+
", Q0*Q1 = "
+
cvm
::
to_str
(
Q0
.
inner
(
Q1
),
cvm
::
cv_width
,
cvm
::
cv_prec
)
+
"
\n
"
);
cvm
::
log
(
"L2 = "
+
cvm
::
to_str
(
L2
,
cvm
::
cv_width
,
cvm
::
cv_prec
)
+
", Q2 = "
+
cvm
::
to_str
(
Q2
,
cvm
::
cv_width
,
cvm
::
cv_prec
)
+
", Q0*Q2 = "
+
cvm
::
to_str
(
Q0
.
inner
(
Q2
),
cvm
::
cv_width
,
cvm
::
cv_prec
)
+
"
\n
"
);
cvm
::
log
(
"L3 = "
+
cvm
::
to_str
(
L3
,
cvm
::
cv_width
,
cvm
::
cv_prec
)
+
", Q3 = "
+
cvm
::
to_str
(
Q3
,
cvm
::
cv_width
,
cvm
::
cv_prec
)
+
", Q0*Q3 = "
+
cvm
::
to_str
(
Q0
.
inner
(
Q3
),
cvm
::
cv_width
,
cvm
::
cv_prec
)
+
"
\n
"
);
}
// calculate derivatives of L0 and Q0 with respect to each atom in
// either group; note: if dS_1 is a null vector, nothing will be
// calculated
size_t
ia
;
for
(
ia
=
0
;
ia
<
dS_1
.
size
();
ia
++
)
{
cvm
::
real
const
&
a2x
=
pos2
[
ia
].
x
;
cvm
::
real
const
&
a2y
=
pos2
[
ia
].
y
;
cvm
::
real
const
&
a2z
=
pos2
[
ia
].
z
;
cvm
::
matrix2d
<
cvm
::
rvector
>
&
ds_1
=
dS_1
[
ia
];
// derivative of the S matrix
ds_1
.
reset
();
ds_1
[
0
][
0
].
set
(
a2x
,
a2y
,
a2z
);
ds_1
[
1
][
0
].
set
(
0.0
,
a2z
,
-
a2y
);
ds_1
[
0
][
1
]
=
ds_1
[
1
][
0
];
ds_1
[
2
][
0
].
set
(
-
a2z
,
0.0
,
a2x
);
ds_1
[
0
][
2
]
=
ds_1
[
2
][
0
];
ds_1
[
3
][
0
].
set
(
a2y
,
-
a2x
,
0.0
);
ds_1
[
0
][
3
]
=
ds_1
[
3
][
0
];
ds_1
[
1
][
1
].
set
(
a2x
,
-
a2y
,
-
a2z
);
ds_1
[
2
][
1
].
set
(
a2y
,
a2x
,
0.0
);
ds_1
[
1
][
2
]
=
ds_1
[
2
][
1
];
ds_1
[
3
][
1
].
set
(
a2z
,
0.0
,
a2x
);
ds_1
[
1
][
3
]
=
ds_1
[
3
][
1
];
ds_1
[
2
][
2
].
set
(
-
a2x
,
a2y
,
-
a2z
);
ds_1
[
3
][
2
].
set
(
0.0
,
a2z
,
a2y
);
ds_1
[
2
][
3
]
=
ds_1
[
3
][
2
];
ds_1
[
3
][
3
].
set
(
-
a2x
,
-
a2y
,
a2z
);
cvm
::
rvector
&
dl0_1
=
dL0_1
[
ia
];
cvm
::
vector1d
<
cvm
::
rvector
>
&
dq0_1
=
dQ0_1
[
ia
];
// matrix multiplications; derivatives of L_0 and Q_0 are
// calculated using Hellmann-Feynman theorem (i.e. exploiting the
// fact that the eigenvectors Q_i form an orthonormal basis)
dl0_1
.
reset
();
for
(
size_t
i
=
0
;
i
<
4
;
i
++
)
{
for
(
size_t
j
=
0
;
j
<
4
;
j
++
)
{
dl0_1
+=
Q0
[
i
]
*
ds_1
[
i
][
j
]
*
Q0
[
j
];
}
}
dq0_1
.
reset
();
for
(
size_t
p
=
0
;
p
<
4
;
p
++
)
{
for
(
size_t
i
=
0
;
i
<
4
;
i
++
)
{
for
(
size_t
j
=
0
;
j
<
4
;
j
++
)
{
dq0_1
[
p
]
+=
(
Q1
[
i
]
*
ds_1
[
i
][
j
]
*
Q0
[
j
])
/
(
L0
-
L1
)
*
Q1
[
p
]
+
(
Q2
[
i
]
*
ds_1
[
i
][
j
]
*
Q0
[
j
])
/
(
L0
-
L2
)
*
Q2
[
p
]
+
(
Q3
[
i
]
*
ds_1
[
i
][
j
]
*
Q0
[
j
])
/
(
L0
-
L3
)
*
Q3
[
p
];
}
}
}
}
// do the same for the second group
for
(
ia
=
0
;
ia
<
dS_2
.
size
();
ia
++
)
{
cvm
::
real
const
&
a1x
=
pos1
[
ia
].
x
;
cvm
::
real
const
&
a1y
=
pos1
[
ia
].
y
;
cvm
::
real
const
&
a1z
=
pos1
[
ia
].
z
;
cvm
::
matrix2d
<
cvm
::
rvector
>
&
ds_2
=
dS_2
[
ia
];
ds_2
.
reset
();
ds_2
[
0
][
0
].
set
(
a1x
,
a1y
,
a1z
);
ds_2
[
1
][
0
].
set
(
0.0
,
-
a1z
,
a1y
);
ds_2
[
0
][
1
]
=
ds_2
[
1
][
0
];
ds_2
[
2
][
0
].
set
(
a1z
,
0.0
,
-
a1x
);
ds_2
[
0
][
2
]
=
ds_2
[
2
][
0
];
ds_2
[
3
][
0
].
set
(
-
a1y
,
a1x
,
0.0
);
ds_2
[
0
][
3
]
=
ds_2
[
3
][
0
];
ds_2
[
1
][
1
].
set
(
a1x
,
-
a1y
,
-
a1z
);
ds_2
[
2
][
1
].
set
(
a1y
,
a1x
,
0.0
);
ds_2
[
1
][
2
]
=
ds_2
[
2
][
1
];
ds_2
[
3
][
1
].
set
(
a1z
,
0.0
,
a1x
);
ds_2
[
1
][
3
]
=
ds_2
[
3
][
1
];
ds_2
[
2
][
2
].
set
(
-
a1x
,
a1y
,
-
a1z
);
ds_2
[
3
][
2
].
set
(
0.0
,
a1z
,
a1y
);
ds_2
[
2
][
3
]
=
ds_2
[
3
][
2
];
ds_2
[
3
][
3
].
set
(
-
a1x
,
-
a1y
,
a1z
);
cvm
::
rvector
&
dl0_2
=
dL0_2
[
ia
];
cvm
::
vector1d
<
cvm
::
rvector
>
&
dq0_2
=
dQ0_2
[
ia
];
dl0_2
.
reset
();
for
(
size_t
i
=
0
;
i
<
4
;
i
++
)
{
for
(
size_t
j
=
0
;
j
<
4
;
j
++
)
{
dl0_2
+=
Q0
[
i
]
*
ds_2
[
i
][
j
]
*
Q0
[
j
];
}
}
dq0_2
.
reset
();
for
(
size_t
p
=
0
;
p
<
4
;
p
++
)
{
for
(
size_t
i
=
0
;
i
<
4
;
i
++
)
{
for
(
size_t
j
=
0
;
j
<
4
;
j
++
)
{
dq0_2
[
p
]
+=
(
Q1
[
i
]
*
ds_2
[
i
][
j
]
*
Q0
[
j
])
/
(
L0
-
L1
)
*
Q1
[
p
]
+
(
Q2
[
i
]
*
ds_2
[
i
][
j
]
*
Q0
[
j
])
/
(
L0
-
L2
)
*
Q2
[
p
]
+
(
Q3
[
i
]
*
ds_2
[
i
][
j
]
*
Q0
[
j
])
/
(
L0
-
L3
)
*
Q3
[
p
];
}
}
}
if
(
b_debug_gradients
)
{
cvm
::
matrix2d
<
cvm
::
real
>
S_new
(
4
,
4
);
cvm
::
vector1d
<
cvm
::
real
>
S_new_eigval
(
4
);
cvm
::
matrix2d
<
cvm
::
real
>
S_new_eigvec
(
4
,
4
);
// make an infitesimal move along each cartesian coordinate of
// this atom, and solve again the eigenvector problem
for
(
size_t
comp
=
0
;
comp
<
3
;
comp
++
)
{
S_new
=
S_backup
;
// diagonalize the new overlap matrix
for
(
size_t
i
=
0
;
i
<
4
;
i
++
)
{
for
(
size_t
j
=
0
;
j
<
4
;
j
++
)
{
S_new
[
i
][
j
]
+=
colvarmodule
::
debug_gradients_step_size
*
ds_2
[
i
][
j
][
comp
];
}
}
// cvm::log("S_new = "+cvm::to_str(cvm::to_str (S_new), cvm::cv_width, cvm::cv_prec)+"\n");
diagonalize_matrix
(
S_new
,
S_new_eigval
,
S_new_eigvec
);
cvm
::
real
const
&
L0_new
=
S_new_eigval
[
0
];
cvm
::
quaternion
const
Q0_new
(
S_new_eigvec
[
0
]);
cvm
::
real
const
DL0
=
(
dl0_2
[
comp
])
*
colvarmodule
::
debug_gradients_step_size
;
cvm
::
quaternion
const
DQ0
(
dq0_2
[
0
][
comp
]
*
colvarmodule
::
debug_gradients_step_size
,
dq0_2
[
1
][
comp
]
*
colvarmodule
::
debug_gradients_step_size
,
dq0_2
[
2
][
comp
]
*
colvarmodule
::
debug_gradients_step_size
,
dq0_2
[
3
][
comp
]
*
colvarmodule
::
debug_gradients_step_size
);
cvm
::
log
(
"|(l_0+dl_0) - l_0^new|/l_0 = "
+
cvm
::
to_str
(
std
::
fabs
(
L0
+
DL0
-
L0_new
)
/
L0
,
cvm
::
cv_width
,
cvm
::
cv_prec
)
+
", |(q_0+dq_0) - q_0^new| = "
+
cvm
::
to_str
((
Q0
+
DQ0
-
Q0_new
).
norm
(),
cvm
::
cv_width
,
cvm
::
cv_prec
)
+
"
\n
"
);
}
}
}
}
// Numerical Recipes routine for diagonalization
#define ROTATE(a,i,j,k,l) g=a[i][j]; \
h=a[k][l]; \
a[i][j]=g-s*(h+g*tau); \
a[k][l]=h+s*(g-h*tau);
#define n 4
void
jacobi
(
cvm
::
real
**
a
,
cvm
::
real
*
d
,
cvm
::
real
**
v
,
int
*
nrot
)
{
int
j
,
iq
,
ip
,
i
;
cvm
::
real
tresh
,
theta
,
tau
,
t
,
sm
,
s
,
h
,
g
,
c
;
cvm
::
vector1d
<
cvm
::
real
>
b
(
n
);
cvm
::
vector1d
<
cvm
::
real
>
z
(
n
);
for
(
ip
=
0
;
ip
<
n
;
ip
++
)
{
for
(
iq
=
0
;
iq
<
n
;
iq
++
)
{
v
[
ip
][
iq
]
=
0.0
;
}
v
[
ip
][
ip
]
=
1.0
;
}
for
(
ip
=
0
;
ip
<
n
;
ip
++
)
{
b
[
ip
]
=
d
[
ip
]
=
a
[
ip
][
ip
];
z
[
ip
]
=
0.0
;
}
*
nrot
=
0
;
for
(
i
=
0
;
i
<=
50
;
i
++
)
{
sm
=
0.0
;
for
(
ip
=
0
;
ip
<
n
-
1
;
ip
++
)
{
for
(
iq
=
ip
+
1
;
iq
<
n
;
iq
++
)
sm
+=
std
::
fabs
(
a
[
ip
][
iq
]);
}
if
(
sm
==
0.0
)
{
return
;
}
if
(
i
<
4
)
tresh
=
0.2
*
sm
/
(
n
*
n
);
else
tresh
=
0.0
;
for
(
ip
=
0
;
ip
<
n
-
1
;
ip
++
)
{
for
(
iq
=
ip
+
1
;
iq
<
n
;
iq
++
)
{
g
=
100.0
*
std
::
fabs
(
a
[
ip
][
iq
]);
if
(
i
>
4
&&
(
cvm
::
real
)(
std
::
fabs
(
d
[
ip
])
+
g
)
==
(
cvm
::
real
)
std
::
fabs
(
d
[
ip
])
&&
(
cvm
::
real
)(
std
::
fabs
(
d
[
iq
])
+
g
)
==
(
cvm
::
real
)
std
::
fabs
(
d
[
iq
]))
a
[
ip
][
iq
]
=
0.0
;
else
if
(
std
::
fabs
(
a
[
ip
][
iq
])
>
tresh
)
{
h
=
d
[
iq
]
-
d
[
ip
];
if
((
cvm
::
real
)(
std
::
fabs
(
h
)
+
g
)
==
(
cvm
::
real
)
std
::
fabs
(
h
))
t
=
(
a
[
ip
][
iq
])
/
h
;
else
{
theta
=
0.5
*
h
/
(
a
[
ip
][
iq
]);
t
=
1.0
/
(
std
::
fabs
(
theta
)
+
std
::
sqrt
(
1.0
+
theta
*
theta
));
if
(
theta
<
0.0
)
t
=
-
t
;
}
c
=
1.0
/
std
::
sqrt
(
1
+
t
*
t
);
s
=
t
*
c
;
tau
=
s
/
(
1.0
+
c
);
h
=
t
*
a
[
ip
][
iq
];
z
[
ip
]
-=
h
;
z
[
iq
]
+=
h
;
d
[
ip
]
-=
h
;
d
[
iq
]
+=
h
;
a
[
ip
][
iq
]
=
0.0
;
for
(
j
=
0
;
j
<=
ip
-
1
;
j
++
)
{
ROTATE
(
a
,
j
,
ip
,
j
,
iq
)
}
for
(
j
=
ip
+
1
;
j
<=
iq
-
1
;
j
++
)
{
ROTATE
(
a
,
ip
,
j
,
j
,
iq
)
}
for
(
j
=
iq
+
1
;
j
<
n
;
j
++
)
{
ROTATE
(
a
,
ip
,
j
,
iq
,
j
)
}
for
(
j
=
0
;
j
<
n
;
j
++
)
{
ROTATE
(
v
,
j
,
ip
,
j
,
iq
)
}
++
(
*
nrot
);
}
}
}
for
(
ip
=
0
;
ip
<
n
;
ip
++
)
{
b
[
ip
]
+=
z
[
ip
];
d
[
ip
]
=
b
[
ip
];
z
[
ip
]
=
0.0
;
}
}
cvm
::
error
(
"Too many iterations in routine jacobi.
\n
"
);
}
void
eigsrt
(
cvm
::
real
*
d
,
cvm
::
real
**
v
)
{
int
k
,
j
,
i
;
cvm
::
real
p
;
for
(
i
=
0
;
i
<
n
;
i
++
)
{
p
=
d
[
k
=
i
];
for
(
j
=
i
+
1
;
j
<
n
;
j
++
)
if
(
d
[
j
]
>=
p
)
p
=
d
[
k
=
j
];
if
(
k
!=
i
)
{
d
[
k
]
=
d
[
i
];
d
[
i
]
=
p
;
for
(
j
=
0
;
j
<
n
;
j
++
)
{
p
=
v
[
j
][
i
];
v
[
j
][
i
]
=
v
[
j
][
k
];
v
[
j
][
k
]
=
p
;
}
}
}
}
void
transpose
(
cvm
::
real
**
v
)
{
cvm
::
real
p
;
int
i
,
j
;
for
(
i
=
0
;
i
<
n
;
i
++
)
{
for
(
j
=
i
+
1
;
j
<
n
;
j
++
)
{
p
=
v
[
i
][
j
];
v
[
i
][
j
]
=
v
[
j
][
i
];
v
[
j
][
i
]
=
p
;
}
}
}
#undef n
#undef ROTATE
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