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Matrix.cpp
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Thu, Sep 12, 18:13
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Sat, Sep 14, 18:13 (2 d)
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rLAMMPS lammps
Matrix.cpp
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#include "DenseMatrix.h"
#include "Solver.h"
//-----------------------------------------------------------------------------
//* performs a matrix-matrix multiply with optional transposes BLAS version
// C = b*C + a*A*B
//-----------------------------------------------------------------------------
void
MultAB
(
const
MATRIX
&
A
,
const
MATRIX
&
B
,
DENS_MAT
&
C
,
const
bool
At
,
const
bool
Bt
,
double
a
,
double
b
)
{
static
char
t
[
2
]
=
{
'N'
,
'T'
};
char
*
ta
=
t
+
At
,
*
tb
=
t
+
Bt
;
int
sA
[
2
]
=
{
A
.
nRows
(),
A
.
nCols
()};
// sizes of A
int
sB
[
2
]
=
{
B
.
nRows
(),
B
.
nCols
()};
// sizes of B
GCK
(
A
,
B
,
sA
[
!
At
]
!=
sB
[
Bt
],
"MultAB<double>: matrix-matrix multiply"
);
if
(
!
C
.
is_size
(
sA
[
At
],
sB
[
!
Bt
]))
{
C
.
resize
(
sA
[
At
],
sB
[
!
Bt
]);
if
(
b
!=
0.0
)
C
.
zero
();
}
// get pointers to the matrix sizes needed by BLAS
int
*
M
=
sA
+
At
;
// # of rows in op[A] (op[A] = A' if At='T' else A)
int
*
N
=
sB
+!
Bt
;
// # of cols in op[B]
int
*
K
=
sA
+!
At
;
// # of cols in op[A] or # of rows in op[B]
double
*
pa
=
A
.
get_ptr
(),
*
pb
=
B
.
get_ptr
(),
*
pc
=
C
.
get_ptr
();
#ifdef COL_STORAGE
dgemm_
(
ta
,
tb
,
M
,
N
,
K
,
&
a
,
pa
,
sA
,
pb
,
sB
,
&
b
,
pc
,
M
);
#else
dgemm_
(
tb
,
ta
,
N
,
M
,
K
,
&
a
,
pb
,
sB
+
1
,
pa
,
sA
+
1
,
&
b
,
pc
,
N
);
#endif
}
//-----------------------------------------------------------------------------
//* returns the inverse of a double precision matrix
//-----------------------------------------------------------------------------
DenseMatrix
<
double
>
inv
(
const
MATRIX
&
A
)
{
SQCK
(
A
,
"DenseMatrix::inv(), matrix not square"
);
// check matrix is square
DENS_MAT
invA
(
A
);
// Make copy of A to invert
// setup for call to BLAS
int
m
,
info
,
lwork
=-
1
;
m
=
invA
.
nRows
();
int
*
ipiv
=
new
int
[
m
<<
1
];
// need 2m storage
int
*
iwork
=
ipiv
+
m
;
dgetrf_
(
&
m
,
&
m
,
invA
.
get_ptr
(),
&
m
,
ipiv
,
&
info
);
// compute LU factorization
GCK
(
A
,
A
,
info
<
0
,
"DenseMatrix::inv() dgetrf error: Argument had bad value."
);
GCK
(
A
,
A
,
info
>
0
,
"DenseMatrix::inv() dgetrf error: Matrix not invertable."
);
// LU factorization succeeded
// Compute 1-norm of original matrix for use with dgecon
char
norm
=
'1'
;
// Use 1-norm
double
rcond
,
anorm
,
*
workc
=
new
double
[
4
*
m
];
anorm
=
dlange_
(
&
norm
,
&
m
,
&
m
,
A
.
get_ptr
(),
&
m
,
workc
);
// Condition number estimation (warn if bad)
dgecon_
(
&
norm
,
&
m
,
invA
.
get_ptr
(),
&
m
,
&
anorm
,
&
rcond
,
workc
,
iwork
,
&
info
);
GCK
(
A
,
A
,
info
<
0
,
"DenseMatrix::inv(): dgecon error: Argument had bad value."
);
GCK
(
A
,
A
,
rcond
<
1e-14
,
"DenseMatrix::inv(): Matrix nearly singular, RCOND<e-14"
);
// Now determine optimal work size for computation of matrix inverse
double
work_dummy
[
2
]
=
{
0.0
,
0.0
};
dgetri_
(
&
m
,
invA
.
get_ptr
(),
&
m
,
ipiv
,
work_dummy
,
&
lwork
,
&
info
);
GCK
(
A
,
A
,
info
<
0
,
"DenseMatrix::inv() dgetri error: Argument had bad value."
);
GCK
(
A
,
A
,
info
>
0
,
"DenseMatrix::inv() dgetri error: Matrix not invertable."
);
// Work size query succeded
lwork
=
(
int
)
work_dummy
[
0
];
double
*
work
=
new
double
[
lwork
];
// Allocate vector of appropriate size
// Compute and store matrix inverse
dgetri_
(
&
m
,
invA
.
get_ptr
(),
&
m
,
ipiv
,
work
,
&
lwork
,
&
info
);
GCK
(
A
,
A
,
info
<
0
,
"DenseMatrix::inv() dgetri error: Argument had bad value."
);
GCK
(
A
,
A
,
info
>
0
,
"DenseMatrix::inv() dgetri error: Matrix not invertable."
);
// Clean-up
delete
[]
ipiv
;
delete
[]
workc
;
delete
[]
work
;
return
invA
;
}
//-----------------------------------------------------------------------------
//* computes the determinant of a square matrix by LU decomposition (if n>3)
//-----------------------------------------------------------------------------
double
det
(
const
MATRIX
&
A
)
{
static
const
double
sign
[
2
]
=
{
1.0
,
-
1.0
};
SQCK
(
A
,
"Matrix::det(), matrix not square"
);
// check matrix is square
int
m
=
A
.
nRows
();
switch
(
m
)
// explicit determinant for small matrix sizes
{
case
1
:
return
A
(
0
,
0
);
case
2
:
return
A
(
0
,
0
)
*
A
(
1
,
1
)
-
A
(
0
,
1
)
*
A
(
1
,
0
);
case
3
:
return
A
(
0
,
0
)
*
(
A
(
1
,
1
)
*
A
(
2
,
2
)
-
A
(
1
,
2
)
*
A
(
2
,
1
))
+
A
(
0
,
1
)
*
(
A
(
1
,
2
)
*
A
(
2
,
0
)
-
A
(
1
,
0
)
*
A
(
2
,
2
))
+
A
(
0
,
2
)
*
(
A
(
1
,
0
)
*
A
(
2
,
1
)
-
A
(
1
,
1
)
*
A
(
2
,
0
));
default
:
break
;
}
// First compute LU factorization
int
info
,
*
ipiv
=
new
int
[
m
];
double
det
=
1.0
;
DENS_MAT
PLUA
(
A
);
dgetrf_
(
&
m
,
&
m
,
PLUA
.
get_ptr
(),
&
m
,
ipiv
,
&
info
);
GCK
(
A
,
A
,
info
>
0
,
"Matrix::det() dgetrf error: Bad argument value."
);
if
(
!
info
)
// matrix is non-singular
{
// Compute det(A) = det(P)*det(L)*det(U) = +/-1 * det(U)
int
i
,
OddNumPivots
;
det
=
PLUA
(
0
,
0
);
OddNumPivots
=
ipiv
[
0
]
!=
(
1
);
for
(
i
=
1
;
i
<
m
;
i
++
)
{
det
*=
PLUA
(
i
,
i
);
OddNumPivots
+=
(
ipiv
[
i
]
!=
(
i
+
1
));
// # pivots even/odd
}
det
*=
sign
[
OddNumPivots
&
1
];
}
delete
[]
ipiv
;
// Clean-up
return
det
;
}
//-----------------------------------------------------------------------------
//* Returns the maximum eigenvalue of a matrix.
//-----------------------------------------------------------------------------
double
max_eigenvalue
(
const
Matrix
<
double
>&
A
)
{
GCK
(
A
,
A
,
!
is_size
(
3
,
3
),
"max_eigenvalue only implimented for 3x3"
);
const
double
c0
=
det
(
A
);
const
double
c1
=
A
(
1
,
0
)
*
A
(
0
,
1
)
+
A
(
2
,
0
)
*
A
(
0
,
2
)
+
A
(
1
,
2
)
*
A
(
2
,
1
)
-
A
(
0
,
0
)
*
A
(
1
,
1
)
-
A
(
0
,
0
)
*
A
(
2
,
2
)
-
A
(
1
,
1
)
*
A
(
2
,
2
);
const
double
c2
=
trace
(
A
);
double
c
[
4
]
=
{
c0
,
c1
,
c2
,
-
1.0
},
x
[
3
];
int
num_roots
=
ATC
::
solve_cubic
(
c
,
x
);
double
max_root
=
0.0
;
for
(
int
i
=
0
;
i
<
num_roots
;
i
++
)
max_root
=
std
::
max
(
x
[
i
],
max_root
);
return
max_root
;
}
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