Newer
Older
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
//*****************************************************************
// Iterative template routine -- CG
//
// CG solves the symmetric positive definite linear
// system Ax=b using the Conjugate Gradient method.
//
// CG follows the algorithm described on p. 15 in the
// SIAM Templates book.
//
// The return value indicates convergence within max_iter (input)
// iterations (0), or no convergence within max_iter iterations (1).
//
// Upon successful return, output arguments have the following values:
//
// x -- approximate solution to Ax = b
// max_iter -- the number of iterations performed before the
// tolerance was reached
// tol -- the residual after the final iteration
//
//*****************************************************************
//
// Slightly modified version of IML++ template. See ReadMe file.
//
// Jesper Andersson
//
#ifndef cg_h
#define cg_h
namespace MISCMATHS {
template < class Matrix, class Vector, class Preconditioner, class Real >
int
CG(const Matrix &A, Vector &x, const Vector &b,
const Preconditioner &M, int &max_iter, Real &tol)
{
Real resid;
Vector p, z, q;
Vector alpha(1), beta(1), rho(1), rho_1(1);
Real normb = b.NormFrobenius();
Vector r = b - A*x;
if (normb == 0.0)
normb = 1;
if ((resid = r.NormFrobenius() / normb) <= tol) {
tol = resid;
max_iter = 0;
return 0;
}
for (int i = 1; i <= max_iter; i++) {
z = M.solve(r);
rho(1) = DotProduct(r, z);
if (i == 1)
p = z;
else {
beta(1) = rho(1) / rho_1(1);
p = z + beta(1) * p;
}
q = A*p;
alpha(1) = rho(1) / DotProduct(p, q);
x += alpha(1) * p;
r -= alpha(1) * q;
if ((resid = r.NormFrobenius() / normb) <= tol) {
tol = resid;
max_iter = i;
return 0;
}
rho_1(1) = rho(1);
}
tol = resid;
return 1;
}
} // End namespace MISCMATHS
#endif // End #ifndef cg_h