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cg.c
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Created
Mon, May 6, 09:56
Size
4 KB
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text/x-c
Expires
Wed, May 8, 09:56 (2 d)
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blob
Format
Raw Data
Handle
17506183
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rCGPHPC CG-PHPC
cg.c
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#include "cg.h"
const
double
TOLERANCE
=
1.0e-10
;
const
double
NEARZERO
=
1.0e-14
;
/*
cgsolver solves the linear equation A*x = b where A is
of size m x n
Code based on MATLAB code (from wikipedia ;-) ):
function x = conjgrad(A, b, x)
r = b - A * x;
p = r;
rsold = r' * r;
for i = 1:length(b)
Ap = A * p;
alpha = rsold / (p' * Ap);
x = x + alpha * p;
r = r - alpha * Ap;
rsnew = r' * r;
if sqrt(rsnew) < 1e-10
break;
end
p = r + (rsnew / rsold) * p;
rsold = rsnew;
end
end
*/
void
cgsolver
(
double
*
A
,
double
*
b
,
double
*
x
,
int
m
,
int
n
){
double
*
r
;
double
*
p
;
double
rsold
;
double
rsnew
;
double
*
Ap
;
double
*
tmp
;
double
alpha
;
int
lda
=
m
;
double
al
=
1.
;
double
be
=
0.
;
int
k
=
0
;
r
=
(
double
*
)
malloc
(
n
*
sizeof
(
double
));
p
=
(
double
*
)
malloc
(
n
*
sizeof
(
double
));
Ap
=
(
double
*
)
malloc
(
n
*
sizeof
(
double
));
tmp
=
(
double
*
)
malloc
(
n
*
sizeof
(
double
));
// r = b - A * x;
memset
(
Ap
,
0.
,
n
*
sizeof
(
double
));
cblas_dgemv
(
CblasColMajor
,
CblasNoTrans
,
m
,
n
,
1.
,
A
,
n
,
x
,
1
,
0.
,
Ap
,
1
);
cblas_dcopy
(
n
,
b
,
1
,
tmp
,
1
);
cblas_daxpy
(
n
,
-
1.
,
Ap
,
1
,
tmp
,
1
);
cblas_dcopy
(
n
,
tmp
,
1
,
r
,
1
);
// p = r;
cblas_dcopy
(
n
,
r
,
1
,
p
,
1
);
// rsold = r' * r;
rsold
=
cblas_ddot
(
n
,
r
,
1
,
r
,
1
);
// for i = 1:length(b)
while
(
k
<
n
){
// Ap = A * p;
memset
(
Ap
,
0.
,
n
*
sizeof
(
double
));
cblas_dgemv
(
CblasColMajor
,
CblasNoTrans
,
m
,
n
,
al
,
A
,
lda
,
p
,
1
,
be
,
Ap
,
1
);
// alpha = rsold / (p' * Ap);
alpha
=
rsold
/
fmax
(
cblas_ddot
(
n
,
p
,
1
,
Ap
,
1
),
rsold
*
NEARZERO
);
// x = x + alpha * p;
cblas_daxpy
(
n
,
alpha
,
p
,
1
,
x
,
1
);
// r = r - alpha * Ap;
cblas_daxpy
(
n
,
-
alpha
,
Ap
,
1
,
r
,
1
);
// rsnew = r' * r;
rsnew
=
cblas_ddot
(
n
,
r
,
1
,
r
,
1
);
// if sqrt(rsnew) < 1e-10
// break;
if
(
sqrt
(
rsnew
)
<
TOLERANCE
)
break
;
// Convergence test
// p = r + (rsnew / rsold) * p;
cblas_dcopy
(
n
,
r
,
1
,
tmp
,
1
);
cblas_daxpy
(
n
,
(
double
)(
rsnew
/
rsold
),
p
,
1
,
tmp
,
1
);
cblas_dcopy
(
n
,
tmp
,
1
,
p
,
1
);
// rsold = rsnew;
rsold
=
rsnew
;
printf
(
"
\t
[STEP %d] residual = %E
\r
"
,
k
,
sqrt
(
rsold
));
fflush
(
stdout
);
k
++
;
}
memset
(
r
,
0.
,
n
*
sizeof
(
double
));
cblas_dgemv
(
CblasColMajor
,
CblasNoTrans
,
m
,
n
,
al
,
A
,
lda
,
x
,
1
,
be
,
r
,
1
);
cblas_daxpy
(
n
,
-
1.
,
b
,
1
,
r
,
1
);
double
res
=
cblas_ddot
(
n
,
r
,
1
,
r
,
1
);
printf
(
"
\t
[STEP %d] residual = %E, ||Ax -b|| = %E
\n
"
,
k
,
sqrt
(
rsold
),
sqrt
(
res
));
free
(
r
);
free
(
p
);
free
(
Ap
);
free
(
tmp
);
}
/*
Sparse version of the cg solver
*/
void
cgsolver_sparse
(
double
*
Aval
,
int
*
row
,
int
*
col
,
double
*
b
,
double
*
x
,
int
n
){
double
*
r
;
double
*
p
;
double
rsold
;
double
rsnew
;
double
*
Ap
;
double
*
tmp
;
double
alpha
;
int
incx
=
1
;
int
incy
=
1
;
int
k
=
0
;
r
=
(
double
*
)
malloc
(
n
*
sizeof
(
double
));
p
=
(
double
*
)
malloc
(
n
*
sizeof
(
double
));
Ap
=
(
double
*
)
malloc
(
n
*
sizeof
(
double
));
tmp
=
(
double
*
)
malloc
(
n
*
sizeof
(
double
));
// r = b - A * x;
smvm
(
n
,
Aval
,
col
,
row
,
x
,
Ap
);
cblas_dcopy
(
n
,
b
,
1
,
r
,
1
);
cblas_daxpy
(
n
,
-
1.
,
Ap
,
1
,
r
,
1
);
// p = r;
cblas_dcopy
(
n
,
r
,
incx
,
p
,
incy
);
// rsold = r' * r;
rsold
=
cblas_ddot
(
n
,
r
,
1
,
r
,
1
);
// for i = 1:length(b)
while
(
k
<
n
){
// Ap = A * p;
smvm
(
n
,
Aval
,
col
,
row
,
p
,
Ap
);
// alpha = rsold / (p' * Ap);
alpha
=
rsold
/
fmax
(
cblas_ddot
(
n
,
p
,
1
,
Ap
,
1
),
rsold
*
NEARZERO
);
// x = x + alpha * p;
cblas_daxpy
(
n
,
alpha
,
p
,
1
,
x
,
1
);
// r = r - alpha * Ap;
cblas_daxpy
(
n
,
-
alpha
,
Ap
,
1
,
r
,
1
);
// rsnew = r' * r;
rsnew
=
cblas_ddot
(
n
,
r
,
1
,
r
,
1
);
// if sqrt(rsnew) < 1e-10
// break;
if
(
sqrt
(
rsnew
)
<
TOLERANCE
)
break
;
// Convergence test
// p = r + (rsnew / rsold) * p;
cblas_dcopy
(
n
,
r
,
1
,
tmp
,
1
);
cblas_daxpy
(
n
,
rsnew
/
rsold
,
p
,
1
,
tmp
,
1
);
cblas_dcopy
(
n
,
tmp
,
1
,
p
,
1
);
//cblas_dcopy(n,p,1,pt,1);
// rsold = rsnew;
rsold
=
rsnew
;
printf
(
"
\t
[STEP %d] residual = %E
\r
"
,
k
,
sqrt
(
rsold
));
k
++
;
}
smvm
(
n
,
Aval
,
col
,
row
,
x
,
r
);
cblas_daxpy
(
n
,
-
1.
,
b
,
1
,
r
,
1
);
double
res
=
cblas_ddot
(
n
,
r
,
1
,
r
,
1
);
printf
(
"
\t
[STEP %d] residual = %E, ||Ax -b|| = %E
\n
"
,
k
,
sqrt
(
rsold
),
sqrt
(
res
));
free
(
r
);
free
(
p
);
free
(
Ap
);
free
(
tmp
);
}
/*
Sparse matrix vector multiplication
*/
void
smvm
(
int
m
,
const
double
*
val
,
const
int
*
col
,
const
int
*
row
,
const
double
*
x
,
double
*
y
)
{
for
(
int
i
=
0
;
i
<
m
;
++
i
)
{
y
[
i
]
=
0.0
;
for
(
int
j
=
row
[
i
];
j
<
row
[
i
+
1
];
++
j
){
y
[
i
]
+=
val
[
j
-
1
]
*
x
[
col
[
j
-
1
]
-
1
];
}
}
}
/*
Initialization of the source term b
*/
double
*
init_source_term
(
int
n
,
double
h
){
double
*
f
;
int
i
;
f
=
(
double
*
)
malloc
(
n
*
sizeof
(
double
*
));
for
(
i
=
0
;
i
<
n
;
i
++
)
{
f
[
i
]
=
(
double
)
i
*
-
2.
*
M_PI
*
M_PI
*
sin
(
10.
*
M_PI
*
i
*
h
)
*
sin
(
10.
*
M_PI
*
i
*
h
);
}
return
f
;
}
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